essays on asset allocation strategies for defined...

Essays on Asset Allocation Strategies for Defined Contribution Plans

Anup Kumar Basu MBA QUT, BSc (Hons) Cal

Submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy The School of Economics and Finance Queensland University of Technology

Brisbane, Australia

January 2008

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Keywords and Abbreviations

• Asset Allocation

• Bootstrap Resampling

• Defined Contribution (DC) Plan

• Downside Risk

• Dynamic Lifecycle Strategy

• Expected Tail Loss (ETL)

• Lifecycle Fund

• Lower Partial Moment (LPM)

• Monte Carlo Simulation (MCS)

• Stochastic Dominance (SD)

• Tail Risk

• Terminal Wealth

• Value at Risk (VaR)

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Abstract

Asset allocation is the most influential factor driving investment performance.

While researchers have made substantial progress in the field of asset allocation

since the introduction of mean-variance framework by Markowitz, there is little

agreement about appropriate portfolio choice for multi-period long horizon

investors. Nowhere this is more evident than trustees of retirement plans

choosing different asset allocation strategies as default investment options for

their members. This doctoral dissertation consists of four essays each of which

explores either a novel or an unresolved issue in the area of asset allocation for

individual retirement plan participants. The goal of the thesis is to provide

greater insight into the subject of portfolio choice in retirement plans and

advance scholarship in this field.

The first study evaluates different constant mix or fixed weight asset allocation

strategies and comments on their relative appeal as default investment options.

In contrast to past research which deals mostly with theoretical or hypothetical

models of asset allocation, we investigate asset allocation strategies that are

actually used as default investment options by superannuation funds in

Australia. We find that strategies with moderate allocation to stocks are

consistently outperformed in terms of upside potential of exceeding the

participant’s wealth accumulation target as well as downside risk of falling

below that target by very aggressive strategies whose allocation to stocks

approach 100%. The risk of extremely adverse wealth outcomes for plan

participants does not appear to be very sensitive to asset allocation.

Drawing on the evidence of the previous study, the second essay explores

possible solutions to the well known problem of gender inequality in retirement

investment outcomes. Using non-parametric stochastic simulation, we simulate

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and compare the retirement wealth outcomes for a hypothetical female and male

worker under different assumptions about breaks in employment,

superannuation contribution rates, and asset allocation strategies. We argue that

modest changes in contribution and asset allocation strategy for the female plan

participant are necessary to ensure an equitable wealth outcome in retirement.

The findings provide strong evidence against gender-neutral default contribution

and asset allocation policy currently institutionalized in Australia and other

countries.

In the third study we examine the efficacy of lifecycle asset allocation models

which allocate aggressively to risky asset classes when the employee

participants are young and gradually switch to more conservative asset classes

as they approach retirement. We show that the conventional lifecycle strategies

make a costly mistake by ignoring the change in portfolio size over time as a

critical input in the asset allocation decision. Due to this portfolio size effect,

which has hitherto remained unexplored in literature, the terminal value of

accumulation in retirement account is critically dependent on the asset allocation

strategy adopted by the participant in later years relative to early years.

The final essay extends the findings of the previous chapter by proposing an

alternative approach to lifecycle asset allocation which incorporates

performance feedback. We demonstrate that strategies that dynamically alter

allocation between growth and conservative asset classes at different points on

the investment horizon based on cumulative portfolio performance relative to a

set target generally result in superior wealth outcomes compared to those of

conventional lifecycle strategies. The dynamic allocation strategy exhibits clear

second-degree stochastic dominance over conventional strategies which switch

assets in a deterministic manner as well as balanced diversified strategies.

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Contents

1. INTRODUCTION................................................................................................. 1

1.1 Background ...................................................................................................................... 1

1.2 Motivation ........................................................................................................................ 3

1.3 Research Objectives ......................................................................................................... 6

1.4 Thesis Structure and Research Description................................................................... 10

2. LITERATURE REVIEW ............................... ..................................................... 14

2.1 Behavioural Biases Influencing Portfolio Choice........................................................... 15

2.2 Default Investment Options in Retirement Plans .......................................................... 18

2.3 Modern Portfolio Theory and Asset Allocation............................................................. 25

2.4 Lifecycle Asset Allocation Strategies.............................................................................. 32

2.5 Optimal Asset Allocation Strategy for DC plans ........................................................... 45

2.6 Strategic Asset Allocation: Role of Equity Premium.....................................................52

2.7 Measures of Risk ............................................................................................................ 56

2.8 Measures of Investment Performance............................................................................ 62

3. METHODOLOGY AND DATA ............................ .............................................. 68

3.1 Model Description .......................................................................................................... 68 3.1.1 General Structure................................................................................................... 68 3.1.2 Control Variables.................................................................................................... 70 3.1.3 Other Variables....................................................................................................... 71

3.2 Asset Class Return Generating Process ......................................................................... 72 3.2.1 Monte Carlo Simulation......................................................................................... 74 3.2.2 Bootstrap Resampling............................................................................................. 77

3.3 Data ................................................................................................................................ 80 3.3.1 Asset Class Returns................................................................................................. 80 3.3.2Asset Allocation of Default Strategies...................................................................... 83 3.3.3 Earnings Data......................................................................................................... 83

4. EVALUATION OF FIXED WEIGHT STRATEGIES AS DEFAULT OPTIONS... 84

4.1 Introduction.................................................................................................................... 84

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4.1.1 Background............................................................................................................. 84 4.1.2 Research Description.............................................................................................. 86 4.1.3 Summary of Findings.............................................................................................. 89

4.2 Metrics for Evaluating Retirement Wealth Outcomes .................................................. 90

4.3 Methodology ................................................................................................................... 96

4.4 Data ................................................................................................................................ 98

4.4 Results and Discussion ..................................................................................................104 4.4.1 RWR Distribution..................................................................................................105 4.4.2 Downside Risk and Risk-Adjusted Performance Estimates..................................111 4.4.3 Tail-Related Risk Estimates...................................................................................117

4.5 Conclusion .....................................................................................................................124

5. GENDER-SENSITIVE CONTRIBUTION AND ASSET ALLOCATI ON STRATEGIES IN SUPERANNUATION PLANS ................. .................................142

5.1 Introduction...................................................................................................................142 5.1.1 Background............................................................................................................142 5.1.2 Research Description.............................................................................................143 5.1.3 Summary of Findings.............................................................................................144

5.2 Methodology ..................................................................................................................144

5.3 Data ...............................................................................................................................148 5.3.1 Earnings Data........................................................................................................148 5.3.2 Asset Class Returns................................................................................................153

5.4 Results and Discussion ..................................................................................................153 5.4.1 Contribution Rate..................................................................................................153 5.4.2 Asset Allocation......................................................................................................157 5.4.3 Combination...........................................................................................................163

5.5 Conclusion .....................................................................................................................167

6. PORTFOLIO SIZE EFFECT AND LIFECYCLE ASSET ALLOCA TION ..........169


6.2 Methodology ..................................................................................................................174 6.2.1 Lifecycle and Contrarian Strategy Pairs...............................................................175 6.2.2 Bootstrap Resampling............................................................................................180 6.2.3 Data........................................................................................................................181

6.3 Results and Discussion ..................................................................................................182 6.3.1 Terminal Wealth Estimates...................................................................................182

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6.3.2 Accumulation Paths over Horizon.........................................................................185 6.3.3 Adverse Outcomes and Tail Risk...........................................................................190

6.4 Conclusion .....................................................................................................................193

7. A DYNAMIC ASSET ALLOCATION FRAMEWORK FOR LIFECYC LE INVESTING IN RETIREMENT PLANS ...................... ......................................... 200


7.2 Methodology ..................................................................................................................205 7.2.1 Conventional Versus Dynamic Lifecycle Strategy.................................................205 7.2.2 Bootstrap Resampling............................................................................................208 7.2.3 Stochastic Dominance............................................................................................210 7.2.4 Shortfall Measures for Dynamic Strategy.............................................................211

7.3 Results and Discussion ..................................................................................................212 7.3.1 Terminal Wealth Estimates...................................................................................212 7.3.2 CDF and Stochastic Dominance Test.....................................................................214 7.3.3 Shortfall Estimates for Dynamic Strategy.............................................................218 7.3.4 Extreme Adverse Outcomes...................................................................................221

7.4 Conclusion .....................................................................................................................223

8. CONCLUSION................................................................................................ 226

8.1 Scholarly Contributions ................................................................................................226

8.2 Relevance.......................................................................................................................229

8.3 Limitations & Avenues for Future Research................................................................230

REFERENCES.................................................................................................... 233

APPENDIX A: REAL RETURN DATA FOR AUSTRALIAN AND US ASSET CLASSES............................................ ............................................................... 253

APPENDIX B: NOMINAL RETURNS DATA FOR AUSTRALIAN ASS ET CLASSES (1900-2004)................................ ....................................................... 256

APPENDIX C: NOMINAL RETURNS DATA FOR US ASSET CLASS ES (1900-2004) ........................................................................................................ 257

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List of Tables

TABLE 4.1: ASSET ALLOCATION OF DEFAULT INVESTMENT OPTIONS..................102

TABLE 4.2: DISTRIBUTION PARAMETERS OF RETIREMENT WEALTH RATIO (RWR)

....................................................................................................................................105

TABLE 4.3: ESTIMATES FOR DOWNSIDE RISK AND PERFORMANCE MEASURES..113

TABLE 4. 4: TAIL RISK ESTIMATES FOR RWR DISTRIBUTION...................................119

TABLE 4B.1 DISTRIBUTION PARAMETERS FOR RWR .................................................129

TABLE 4B.2 ESTIMATES FOR DOWNSIDE RISK & PERFORMANCE MEASURES......130

TABLE 4B.3 TAIL RISK ESTIMATES................................................................................131

TABLE 4C.1 ASSET ALLOCATION FOR DEFAULT INVESTMENT OPTIONS..............132

TABLE 4C.2 DISTRIBUTION PARAMETERS OF RETIREMENT WEALTH RATIO (RWR)

....................................................................................................................................133

TABLE 4C.3 ESTIMATES FOR DOWNSIDE RISK AND PERFORMANCE MEASURES 136

TABLE 4C.4 TAIL RISK ESTIMATES FOR RWR DISTRIBUTION ..................................139

TABLE 5.1: WEEKLY INDIVIDUAL INCOME OF AUSTRALIAN MEN AND WOMEN BY

AGE............................................................................................................................149

TABLE 5.2 ACCUMULATION OUTCOMES FOR DIFFERENT FEMALE CONTRIBUTION

RATES........................................................................................................................155

TABLE 5.3: ACCUMULATION OUTCOMES FOR DIFFERENT FEMALE ASSET

ALLOCATION STRATEGIES....................................................................................159

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TABLE 5.4: EXTREME ADVERSE OUTCOMES FOR DIFFERENT FEMALE ASSET

ALLOCATION STRATEGIES....................................................................................162

TABLE 5.5: ACCUMULATION OUTCOMES FOR DIFFERENT FEMALE

CONTRIBUTION RATES AND ASSET ALLOCATION STRATEGIES....................165

TABLE 6.1: TERMINAL VALUE OF RETIREMENT PORTFOLIO IN NOMINAL

DOLLARS ..................................................................................................................183

TABLE 6.2: VAR ESTIMATES FOR LIFECYCLE & CONTRARIAN STRATEGIES ........191

TABLE 7.1: TERMINAL VALUE OF RETIREMENT PORTFOLIO IN NOMINAL

DOLLARS ..................................................................................................................213

TABLE 7.2: SHORTFALL MEASURES OF DYNAMIC STRATEGIES RELATIVE TO

OTHER ASSET ALLOCATION STRATEGIES..........................................................219

TABLE 7.3: VAR ESTIMATES FOR DIFFERENT ASSET ALLOCATION STRATEGIES222

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List of Figures FIGURE 4.1 RWR DISTRIBUTION PARAMETERS OF ASSET ALLOCATION

STRATEGIES.............................................................................................................109 FIGURE 4.2 DOWNSIDE RISK ESTIMATES OF ASSET ALLOCATION STRATEGIES..112 FIGURE 4.3 TAIL RISK ESTIMATES OF ASSET ALLOCATION STRATEGIES .............122

FIGURE 4A.1: SIMULATED RWR DISTRIBUTION..........................................................127

FIGURE 5.1: INCOME DISTRIBUTION OF AUSTRALIAN POPULATION......................151 FIGURE 5.2: EARNINGS PROFILE OF AUSTRALIAN POPULATION BY AGE .............152

FIGURE 6.1: ASSET ALLOCATION OVER INVESTMENT HORIZON (PAIR A) ............176

FIGURE 6.2: ASSET ALLOCATION OVER INVESTMENT HORIZON (PAIR B).............177

FIGURE 6.3: ASSET ALLOCATION OVER INVESTMENT HORIZON (PAIR C).............178

FIGURE 6.4: ASSET ALLOCATION OVER INVESTMENT HORIZON (PAIR D) ............179

FIGURE 6.5: SIMULATED ACCUMULATION PATHS OVER INVESTMENT HORIZON

(PAIR A) .....................................................................................................................186


(PAIR B) .....................................................................................................................187


(PAIR C) .....................................................................................................................188


(PAIR D) .....................................................................................................................189

FIGURE 6A.1: TWO-DIMENSIONAL VIEW OF ACCUMULATION PATHS OVER

HORIZON (PAIR A) ...................................................................................................196 FIGURE 6A.2: TWO-DIMENSIONAL VIEW OF ACCUMULATION PATHS OVER

HORIZON (PAIR B) ...................................................................................................197

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FIGURE 6A.3: TWO-DIMENSIONAL VIEW OF ACCUMULATION PATHS OVER HORIZON (PAIR C) ...................................................................................................198

FIGURE 6A.4 TWO-DIMENSIONAL VIEW OF ACCUMULATION PATHS OVER

HORIZON (PAIR D) ...................................................................................................199

FIGURE 7.1: CUMULATIVE DISTRIBUTION PLOTS FOR FIRST PAIR OF LIFECYCLE

AND DYNAMIC STRATEGIES ( 20,20LC AND )20,20DLC ....................................215

FIGURE 7. 2: CUMULATIVE DISTRIBUTION PLOTS FOR SECOND PAIR OF

LIFECYCLE AND DYNAMIC STRATEGIES ( 10,30LC AND )10,30DLC ...............217

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Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution. To

the best of my knowledge and belief, the thesis contains no material previously

published or written by another person except where due reference is made.

Signature: Date:

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Acknowledgements

This thesis is the outcome of an amazing voyage during which I have been supported by many people. I wish to acknowledge the efforts of these remarkable individuals who have enriched my journey in several ways. Professor Michael Drew, the principal supervisor of my thesis, was instrumental in my relocating to Australia and joining the doctoral research program three years back. Whatever progress has been achieved since then, academic and otherwise, is largely because of Mike’s constant support and guidance for which I would remain ever indebted. I would also like to express great appreciation for the efforts of Peter Whelan who, as my associate supervisor, has provided valuable feedback on many aspects of the research. Apart from the supervisory team, several other members within the school have extended helpful support throughout the program. Special thanks go to Professor Stan Hurn and Associate Professor Adam Clements for being extremely generous with their time whenever approached. Such collegial relationships are essential for nurturing early career researchers and I consider myself very fortunate to have colleagues like Stan and Adam around. I would like to thank Dr. Robert Bianchi, Evan Reedman, and John Polichronis for their friendship which lightened up many afternoons that were often quite ordinary in terms of research output. Being a recent recipient of the doctorate degree, Rob has also been helpful in passing on some of the ‘tricks of the trade’. The research has benefited from ongoing discussions with several prominent scholars from different academic institutions around the world. Those who deserve special mentioning include Martin Gruber and Stephen Brown from New York University, Christopher James from University of Florida, and Alistair Byrne from University of Edinburgh. Finally, I express deepest gratitude to my family members. To my parents, Piyush and Sipra, who have always reposed their trust on my abilities and provided unwavering support to all my endeavours. To my sister, Mousumi, her prayers and good wishes have been with me all the time. To my uncle, Debesh, for taking keen interest in my career at all times. To my wife, Swati, for her constant love, care, encouragement, not to forget outstanding proofreading skills, which have all contributed to smooth completion of the thesis. Her patience in bearing with my absence over numerous weekends, withstanding the relentless clatter of the keyboard into the wee hours of many a morning, and compensating for my general lack of attention to household affairs has left me with no excuse for not completing the task on time. Our newborn son, Siddharth, has also been very cooperative (perhaps knowingly) by sleeping quietly through most evenings while finishing touches were being applied to this document.

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1. Introduction

1.1 Background

In most developed countries, the rapidly aging population, with a rising

proportion of retirees, have started placing considerable pressure on current

social security programs. This demographic trend is likely to continue rendering

benefits from social security uncertain for future retirees, unless there is a sharp

increase in productivity. In light of this situation, many governments are

attempting to limit their social security related commitments by moving out of a

pay-as-you-go social security framework towards a funded system where

individuals build up their retirement savings during their working life through

investment of mandatory or voluntary contributions into retirement plans

(generally set up by their employers or other private providers). These

retirement savings, they feel, would promote better income security and standard

of living for retirees while rationalizing the burden of running costly social

security programs.

Currently retirement plans mainly belong to two broad categories – defined

benefit (DB) and defined contribution (DC) – which differ in terms of

distribution of risk between the plan sponsor and the participants. In the former,

the sponsor undertakes to pay the employee participants (members) on their

retirement a fixed benefit proportionate to their final or average salary, with the

proportion generally determined by the length of their tenure in the plan. In

doing so, the sponsor assumes the investment risk because the benefits have to

be paid even if the plan assets decline in value. In contrast to this, investment

risk in a DC plan is borne by the participants because retirement benefits are

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entirely dependent on their contributions to the plan and accumulated investment

returns.

DC plans are fast becoming the principal foundation of private sector retirement

system around the world.1 These plans are typically self-directed or self-

managed in nature where the participant makes investment decision of their plan

contributions by selecting from a range of investment options provided by the

plan provider. This is in line with the worldwide trend of giving the individual

participants more control over the decision of how their retirement plan assets

are invested. However, whether such choice is actually exercised also remains a

matter of choice i.e. in most plans the participants are free to decide whether or

not to exercise control over the investment of their plan contributions.

The idea of providing employees more autonomy and choice over investments

in DC plans is underpinned by an implicit assumption – the employee-

participants are well-informed economic agents who are capable of maximizing

their self interests by making rational investment decisions and implementing

them. The investment decision for the participants in a DC plan, typically,

involves selecting an asset allocation strategy for investing the plan

contributions i.e. how to allocate capital between available asset classes like

stocks, bonds, cash, and other alternative assets. But there is now sufficient

global evidence to suggest that majority of plan participants refrain from

selecting the investment strategies for their own retirement accounts (for

example, Choi, Laibson, Madrian & Metrick, 2002; Cronqvist & Thaler, 2004).

For all participants who do not choose an investment strategy for their plan

assets, most retirement plans provide a default investment strategy to direct their

plan contributions. The asset allocation decision, irrespective of whether it is

made by the plan sponsors or the participants themselves, has a significant

1 For instance, in Australia, which has a more well-established private retirement system than most countries, the majority of retirement plans belong to the DC category.

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impact on the final wealth outcome and, therefore, on their financial well being

of the participants in retirement. The asset allocation strategies that are currently

offered by DC plan providers and those suggested in literature constitute the

focal point of our investigation in this doctoral dissertation.

1.2 Motivation

The value of the retirement portfolio at the end of an employee’s working life

determines the amount of annuity that he or she is able to purchase at retirement

and how much of the pre-retirement income he or she is able to replace after

retirement.2 Ignoring transaction costs and taxes, the value of retirement

portfolio of an individual during the accumulation phase (normally the

employment tenure of the individual) depends on two factors: (i) contribution

rate and (ii) investment returns on the accumulated contributions. If

contributions are only those made by the employers at the mandatory rate

prescribed by the government, investment returns solely determine the variation

in retirement wealth accumulated by an individual at the end of his or her

working life.3 Following the seminal work of Brinson, Hood, and Beebower

(1986), most academics and practitioners accept that asset allocation is the

dominant driver of a portfolio’s investment returns over long horizons. Since

retirement plan assets of individuals in DC plans are invested over a span of

several decades, it is reasonable to identify asset allocation as the key

determinant of their final retirement wealth.

2For example, Vittas (1992) show that with 40 years of contribution at the rate of 10%, real wage growth of 2%, and life expectancy of 20 years after retirement, real return of 3% would obtain an indexed pension of 33% of final salary while a real return of 5% would obtain an indexed pension to replace 60% of final salary. 3 This applies to much of the working population in Australia.

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Given such important role of asset allocation in influencing the wealth outcome

at retirement, one would expect that the investment choices within DC plans and

their asset allocation structures are designed with utmost care by the plan

sponsors or the trustees. The nomination of the default option among available

investment choices in a plan is even more important considering that there is

enough evidence (for instance, Beshears, Choi, Laibson & Madrian, 2006) to

suggest that many individuals perceive the default choices offered to them as

recommendation or endorsement of a particular course of action by the provider.

Not only do most participants adopt the default choice, but they are also likely to

persist with it for much of their working life. Given the very long horizon of

retirement plan investments, a sub-optimal default asset allocation strategy runs

enormous risk for the participants. A mistake committed at the outset is unlikely

to be reversed at a later date and the compounding effect over the long horizon

can lead to very adverse outcomes, even potentially ruinous in some cases.

Whether the failure of participants to exercise choice is due to perceived lack of

relevant investment knowledge and skills, inadequacy of the available options,

or common biases in human behaviour is a topic that has been widely debated

and researched in recent times. Much less attention has been devoted towards

the appropriateness of the default and other investment options made available

to the participants. This is surprising considering that there is wide disparity in

asset allocation of the default fund which indicates a complete lack of consensus

among retirement plan providers on the subject. The range of asset allocation

strategies and lifecycle profiles used as default choices by different plans is so

wide that it leads Blake, Byrne, Cairns, and Dowd (2006) to comment that the

concerned members face a virtual lottery in terms of retirement outcomes. In

Australia, the problem of members across different superannuation funds facing

significantly different end benefits due to difference in their default choices is

highlighted by Gallery, Gallery, and Brown (2004). The difference is even more

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acute when one compares retirement plans across different countries.4 Although

there is general agreement about the objective of these investment vehicles -

generating adequate retirement wealth for the participants - it seems plan

sponsors in different countries have very different ideas about the ‘right’ asset

allocation strategy needed to achieve this goal.

While the reasons for retirement plan participants’ apparent reluctance to take

charge of their own financial destiny is a topic worthy of debate in its own right,

we feel the question of appropriateness of the asset allocation strategy is more

important from a practical standpoint and deserves serious attention from the

academic community. Retirement plans with their long investment horizons

provide fertile testing ground for examining the desirability of alternative asset

allocation strategies for long term investors. The researcher has good

opportunity to study their outcomes over many periods and comment on their

appropriateness.

The issue of default choice is particularly important from policy perspective.

Although public policy is neutral regarding setting the default investment option

(or even the menu of investment choices) offered to participants in DC plans i.e.

individual plan sponsors are free to choose the asset allocation structure for

default options as they deem fit, as Beshears et al. (2006) point out the defaults

themselves are not neutral since they either facilitate or hinder the desired

retirement outcome. One of the foremost goals of public policy associated with

retirement savings is to promote institutions that provide sufficient income to

retired individuals in order to reduce the government’s burden in running costly

social welfare programs. As asset allocation choices can significantly affect the

retirement outcome for participants in DC plans, it is important to find out

whether policy intervention is necessary to encourage any particular type of

4 Although no study to our knowledge has documented the issue of inter-country differences in selection of default options in retirement plans, we present evidence for four countries in 2.2.

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asset allocation approach as default investment strategy for investment of

retirement assets. This is the key motivation behind this doctoral dissertation.

1.3 Research Objectives

Empirical research on asset allocation for DC plan investors is still in the

developing stage. Therefore researchers are presented with opportunities to

examine a number of interesting issues and add to the existing body of

knowledge. Although studies like Gallery et al. (2003) and Blake et al. (2006)

have highlighted the vast range of asset allocation strategies used by trustees as

default investment strategies in retirement plans, little progress has been made

by researchers in evaluating these strategies and commenting on their

appropriateness as default arrangements. This investigation is necessary to

adjudge the best course of action given our experience with return

characteristics from different asset classes over past several decades. Also,

gender inequality in the labour market outcomes is a serious problem and

several authors have expressed concern that this overflows to the retirement

system and tends to create major disparity in wealth accumulation between the

typical male and female employee. Yet most studies of default options in DC

plans have universally considered the case of a male worker with uninterrupted

career profile. No suggestion has been made in the literature to put up an

alternative investment strategy for the female worker which would alleviate this

problem.

Although academic research on asset allocation strategies in DC plans is a

relatively new area of interest, asset allocation per se is not a new topic in

investment; the basic concept is known to be prevalent from the days of the

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Talmud almost 2000 years ago.5 But as with practitioners, there is a glaring lack

of agreement among scholars in this field on the issue of appropriateness of

asset allocation decisions over long horizons. Siegel (2003) recommends

investors to allocate heavily to equities over long horizons. Kim and Wong

(1997) also find 100% equity strategy dominant over all other strategies for long

horizon investors. This is supported by Vigna and Haberman (2002) but only in

case of a risk neutral investor. Other studies like Booth and Yakoubov (2002)

and Blake, Cairns, and Dowd (2001) do not support such strong conclusions.

They suggest that DC plan participants should pursue a well diversified strategy

till retirement.

There is also considerable debate about adoption of lifecycle strategies, which

has gained substantial popularity among retirement planners in recent years.6

Lifecycle funds in USA and UK have enjoyed phenomenal growth in recent

years so much so that they are the most commonly used default investment

options in the latter. Yet, most Australian superannuation funds do not offer

lifecycle investment options to their members. Typically lifecycle models

recommend investing heavily in the stock market when the plan participants are

young and have a long investment horizon but systematically switch towards

less volatile assets like bonds and cash in the last few years before retirement.

The belief that stocks are less risky over long horizons than over short horizons

has been theoretically challenged by Samuelson (1963, 1989). Bodie (1995)

lends support to this using option pricing theory. Among empirical research,

Hibbert and Mowbray (2002) as well as Blake, Byrne, Cairns, and Dowd (2006)

5 ‘Let every man divide his money into three parts, and invest a third in land, a third in business, and a third let him keep in reserve’ says the Talmud, Circa 1200 B.C.- 500 A.D (Gibson, 2000) 6 Sometimes the term ‘lifestyle’ is used interchangeably with ‘lifecycle’ by some authors in the popular press. But these two are distinct investment strategies. The former allocates a constant proportion of assets to risky investments according to investor’s risk tolerance whereas the latter gradually changes allocation to risky assets according to the investor’s age or length of the investment horizon. Viciera (2007) provides a good exposition on the subject.

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find that lifecycle strategies can be effective in reducing investment risk, but at

the cost of lowering the expected terminal wealth for the plan participant.

However, recent research like Poterba, Roth, Venti, and Wise (2006) indicate

that the retirement wealth distribution in case of lifecycle strategies do not differ

from those of other strategies in many cases. Shiller (2005a) does not find

evidence to support of the lifecycle asset allocation model.

The lifecycle model of asset allocation has remained a controversial area for

academic researchers. While the model has been popular among practitioners in

many countries, its claim of superiority especially over constant mix strategies

has received mixed support from scholars in this field. Even among the

proponents of lifecycle strategy, there is little agreement about the precise point

of time when the asset switching should commence as well as the switching

mechanism itself.7 Moreover, the current literature in DC plan investments has

largely ignored the fact that the size of contributions of DC plan investors are

likely to grow over the years (Shiller, 2005b), which along with compounding of

investment returns, would contribute to a growing portfolio size as one

approaches retirement. The significance of the interplay between this increasing

portfolio size and asset allocation strategy in determining the final wealth

outcome of the retirement plan investor has never been examined. This has

resulted in lack of proper understanding about what precisely leads to success or

failure of lifecycle strategies (relative to other strategies) in generating desired

wealth outcomes for participants in DC plans. A number of studies in recent

years do not find any evidence to justify the popularity of lifecycle strategies

among plan sponsors and investors. But since this body of work barely

investigates the reason behind this apparently inferior performance of the

lifecycle strategy, there is noticeable reluctance among scholars to propose an

7 For example, linear versus non-linear.

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alternative model of lifecycle asset allocation that would yield superior

outcomes.8

In terms of methodology and research design, a review of the current literature

on DC plans reveals three shortcomings. Firstly, most of these studies seem to

examine only a small number of asset allocation strategies compared to the vast

number of possible alternatives. Also, very few of these directly investigate the

actual strategies offered by DC plan providers. Secondly, researchers have

focussed on conventional measures of risk and rewards in ranking alternative

approaches to asset allocation. A few studies are exclusively based on risk

measures like value-at risk (VaR), whose validity has been questioned in recent

times. Important downside risk measures like lower partial moments (Bawa,

1975; Fishburn, 1977), which can be extremely useful in evaluating investment

outcomes, have remained largely ignored. Finally, almost all research on DC

plans has used asset class return data from either the United States (US) or the

United Kingdom (UK). There is a growing body of evidence (Dimson, Marsh &

Staunton, 2002)) that the experiences of these markets over the last century have

not been necessarily similar to that of every other nation. Since evaluation of

asset allocation strategies is largely dependent on the data used by the

researchers, the relevance of their findings for DC plan participants in other

markets remains questionable to some extent.

This doctoral research seeks to address some of the above inadequacies and

advance academic research on asset allocation decisions of DC plans. We test

asset allocation strategies with the specific aim to evaluate their appeal as

default investment options in DC plans. The study then further examines the

case for instituting a gender-specific default investment option to reduce the

disparity in wealth outcomes between male and female participants. In our study

8 Blake et al. (2001) is one of the exceptions in testing novel allocation strategies for DC plan participants. However, it does not pose these models as alternatives to lifecycle model and therefore, does not attempt to address the latter’s shortcomings.

10

of lifecycle and other asset allocation strategies, we not only consider the final

investment outcomes in terms of their risk-return characteristics but also explore

the accumulation process over the entire investment horizon. This leads to a

better understanding of the interplay of asset allocation with the portfolio size at

different points on the horizon and how this influences the final outcome.

In contrast to most researchers who have tested theoretical or hypothetical

models of asset allocation, a part of this doctoral dissertation examines many

asset allocation strategies that are actually used as default options within DC

plans. In addition, we investigate asset allocation models that are suggested in

literature but which are not currently used by practitioners. We adopt a

fundamentally different approach than many of the past studies in using

alternative measures of risk based on wealth accumulation target. The robust

measures of downside risk and related performance metrics exploited in this

research have been suggested earlier in economics literature but rarely employed

in evaluation of competing asset allocation models. A part of the novelty of this

research lies in the fact that it employs long run return data (over one hundred

years) for Australian asset classes for the first time to evaluate asset allocation

decisions in DC plans.

1.4 Thesis Structure and Research Description

The essays in this dissertation share the common theme of asset allocation in DC

plan investments. Each of these examines a distinct, well defined research

problem related to the main topic and occupies a separate chapter. In addition,

the thesis contains chapters on literature review, and methodology and data,

which apply commonly to all the research problems within this doctoral study.

Brief outline of each chapter is provided below.

11

The following chapter reviews the literature relevant to all the essays in this

dissertation. It initially covers the behavioural foundations of investment choice

and default options in DC plan. Next, we review the pioneering work of

researchers in the field of modern portfolio theory and how it relates to asset

allocation decision over long horizon. Further, the theoretical and empirical

research conducted so far in the area of asset allocation within DC plans is

discussed. The role of equity premium in asset allocation and related research is

also covered in this context. Finally, we look into the existing literature for

proposed measures of downside risk and investment performance as these play a

significant role in evaluation of asset allocation strategies in this thesis.

In Chapter 3, we put forward the stochastic simulation model used to generate

terminal wealth outcomes for DC plan participants. This general model is used

in all the four essays with minor variations that are discussed within each

chapter. We also explain two methods that have been employed to generate

returns every period for individual asset classes. The bootstrap resampling

method is used in all the chapters in generating portfolio returns over the

investment horizon while the Monte Carlo method is additionally employed in

the research taken up in chapter 4. Finally, we discuss the data used in this

dissertation. This mainly comprises of historical returns on different asset

classes in the Australian (used in chapters 4 and 5) and the US (used in chapters

6 and 7) market. In addition, chapter 4 uses data on default asset allocation for

several Australian superannuation funds and chapter 5 makes use of earnings

data for different age categories of Australian male and female workers.

Chapter 4 investigates the first research problem that focuses on fixed weight or

constant mix asset allocation strategies as most plan superannuation funds in

Australia currently offer this type of pre-mixed options to the employee

participants. Trustees of different funds choose different asset allocation mixes

as their default option ranging from ‘capital stable’ strategies whose allocation

12

to stocks is well below 50% to extremely aggressive strategies that invest the

entire portfolio in equities. We examine which of the ‘constant mix’ asset

allocation strategies result in best outcome for participants and therefore is the

most suitable candidate for selection as default strategy. We investigate whether

lifecycle investment strategies offered by a few Australian superannuation funds

are more likely to result in superior outcomes for plan participants as compared

to fixed weight asset allocation strategies.

The second research study, taken up in chapter 5, examines the well known

problem of inequity of wealth outcomes between male and female participants

in DC plans. Typically female participants accumulate far less in their retirement

accounts than their male counterparts mainly due to lower career wage profile

and broken patterns in employment. We investigate whether gender-specific

default investment options to mitigate this problem. We consider different

combination rates and asset allocation strategies and find out to what extent they

can reduce the gender gap in wealth accumulation under different assumptions

regarding employment pattern for the female worker.

In Chapter 6 we investigate the ‘lifecycle’ investment approach which is widely

used in DC plans in USA and UK (but rarely used in Australia). Here the funds

gradually reduce their allocation to equities in the participants’ accounts and

increase that to bonds (and cash) as they approach retirement. However

empirical research has not always been supportive of this concept. Shiller

(2005b) specifically questions the rationale of switching from growth to

conservative assets later in the lifecycle when the participants’ contribution

amounts grow larger. This essay examines different switching strategies from

equities to bonds (and cash) at different points of time on the investment horizon

in testing Shiller’s contention that the growing size of contributions would

warrant a reversal of the direction of switching as proposed by conventional

lifecycle strategy. In this context, we study the interplay between growing

13

portfolio size and asset allocation strategies resulting in different wealth

outcomes and their associated riskiness.

In chapter 7, we examine an alternative to conventional lifecycle strategy in

light of the latter’s apparent shortcomings. The fixed weight and lifecycle asset

allocation strategies discussed in previous chapters are static in nature since the

allocation rule for the entire horizon is set right at the beginning i.e. when the

participant joins the plan. Based on suggestions made by a few earlier studies,

we model and test a dynamic asset allocation strategy which uses past

performance feedback in order to determine the direction and extent of asset

switching. The wealth outcomes for the plan participant under the dynamic

allocation rule are then compared to those under lifecycle and fixed weight

allocation strategies.

Chapter 8 concludes the thesis. In addition to enumerating several scholarly

contributions made by this study, we discuss the relevance of the research

findings for pension plan sponsors, trustees, investors, and policymakers.

Finally, we point out the limitations of the current dissertation and suggest a few

areas that deserve the attention from future research in this field.

14

2. Literature Review

This chapter consists of eight sections. In section 2.1, we review research on

behavioural anomalies which influence investment choices of individuals since

this underlines the importance of default investment choices offered to DC plan

participants. Next, we present evidence on default investment choices offered by

plan sponsors in four countries – Australia, Sweden, UK, and USA – and

highlight the differences in asset allocation structures of these default funds in

section 2.2. The tenets of modern portfolio theory and their implications on asset

allocation are discussed in section 2.3. The desirability of ‘lifecycle’ strategies

over ‘constant mix’ asset allocation strategies is a key research topic in this

dissertation. Section 2.4 reviews the theoretical issues concerning lifecycle

models of investment as well as the empirical evidence in this area. Past

research on optimal asset allocation strategies for DC plans is presented in

section 2.5 as the current dissertation draws on this body of work to make

further advancement. Since the role of equity premium is considered to be

critical in determining asset allocation strategies for long term investors like DC

plan participants, section 2.6 analyses the research evidence in this area. The

concept of risk and its various measures are discussed in section 2.7 as asset

allocation strategies are heavily influenced by how individuals view risk and its

trade-off with investment return objective. Finally, section 2.8 reviews

investment performance measures used in academic and practitioner literature as

some of these would be employed in this dissertation to evaluate the outcomes

of alternative asset allocation strategies.

15

2.1 Behavioural Biases Influencing Portfolio Choice

The assumption of classical microeconomic theories regarding rational human

behaviour in making optimal decisions was questioned by Keynes (1936) who

argued that human decisions are a result of ‘animal spirits - a spontaneous urge

to action rather than inaction’ and not of ‘a weighted average of quantitative

benefits multiplied by quantitative probabilities’. Later, Simon (1955), among

others, highlighted the ‘bounded rationality’ problem where decisions made by

human beings are limited by knowledge and cognitive ability and therefore, can

be sub-optimal in maximising expected utility. This perspective has gained

considerable clout in recent times primarily due to influential work of

researchers working at the confluence of psychology, economics, finance, and

even sociology. The growing discipline of behavioural economics and finance

not only questions the validity of standard assumptions like rational behaviour

but importantly, cites evidence on several common biases in human decision-

making process caused by cognitive limitations, emotional constraints, and the

presence of certain external factors.

Contrary to the view held by market economists, researchers in psychology have

often argued that an expansion in choice does not always make the consumer

better off. According to them, too much choice can be confusing for most

consumers, a problem they term as choice overload. This often leads to inaction

on their part as they are overwhelmed and less confident about the soundness of

their decisions. The problem with excessive choice has been demonstrated in a

well-known experiment documented by Iyengar and Lepper (2000). In their

experiment, these researchers set up two booths outside an upscale grocery store

offering to sell jams to shoppers who passed by. While one booth offered 6

varieties of jams, the other had 24 varieties for shoppers to select from. They

found that although more shoppers were attracted to the booth offering wider

selection of jams, only 3 percent of them made any purchase. On the other hand,

16

30 percent of visitors to the booth offering a limited choice of 6 varieties bought

a jar of jam. It seems to indicate that having more choice actually inhibited their

motivation to make a purchase decision.

According to psychologists, the problem people face in making decisions when

faced with alternatives may be caused by their desire to avoid regret and self-

recrimination. While human beings dislike bad outcomes, they feel even worse

when such outcomes are perceived as fallout of their own decisions i.e. different

decisions could have resulted in better consequences (Sugden, 1985). While the

actual regret is caused only after the consequence of a decision becomes known,

people can experience anxiety at the time of making a decision fearing the

possibility of future regret in case of an unfavourable outcome. According to

decision researchers, the anxiety is particularly heightened in two situations: (i)

when decision makers feel that they lack proficiency in the concerned field

(Heath & Tversky, 1991) and (ii) when decisions involve difficult tradeoffs e.g.

when choosing between a high risk, high expected return investment option and

a low risk, low return one (Loewenstein, 2000).

Whether individuals have necessary willpower and self control to exercise

investment choice, as normally assumed by advocates of more investment

choice, is highly debatable. According to some researchers, inertia and

procrastination bias seem to play a major role in investment decisions. Madrian

and Shea (2001) finds evidence of high level of inertia among retirement plan

participants in their retaining both the default contribution rate and asset

allocation. In their study of 2.3 million participants at the Vanguard Group,

Mitchell and Utkus (2004) find that less than 10 percent of plan participants

actually change their contribution allocations each year. They also find that new

participants are sensitive to market conditions in allocating contributions during

enrolment but later display inertia by not reallocating their retirement plan

assets to reflect changes in market conditions. The initial portfolio choice,

17

therefore serves as an anchor which influences subsequent portfolio changes,

and therefore serves as evidence of anchoring effect under which final outcome

is strongly influenced by the starting allocations. In Australia, Fry, Heaney, and

Mckewon (2007) find evidence of inertia among superannuation fund members

with respect to exercising choice of funds.

Even where investors make their own investment decisions, it does not

necessarily follow that such decisions are optimal. In recent times, researchers in

the field of behavioural finance have questioned how good investors actually

understand and act on the predictions of rational models like mean-variance

optimisation.9 If investors are rational, as assumed in standard finance theories,

there should be substantial evidence of individual investors demonstrating

reasonable competence in constructing portfolios that are indeed mean-variance

efficient. However, several studies on human behaviour show that individuals

often make decisions based on heuristics or rules-of thumb when confronted

with complicated problems or when the outcomes are uncertain. Simonson

(1990) and Read and Loewenstein (1995) documents a diversification heuristic

where human beings tend to choose ‘a bit of everything’ when uncertain.

Benartzi and Thaler (2001) finds evidence of diversification heuristic or its

extreme form, the 1/n heuristic (where investors divide their investments equally

among the n options offered to them) , among participants in DC plans in United

States. If investors are rational in a mean-variance sense, one can also expect

them to have well-defined risk attitudes and demonstrate firm preferences in

constructing their portfolios. However, results of an experiment carried out by

Benartzi and Thaler (2002) among employees of University of California and

Swedish American Health Systems indicated that retirement plan participants

ranked the median portfolio higher than the portfolios they chose for themselves

and therefore demonstrated relatively weak preference for their own portfolios.

9 This is the cornerstone of modern portfolio theory and is described in section 2.3.

18

The above behavioural research findings have very important implications for

this research. They not only motivate the research by highlighting the problem

with choices (and therefore the need for appropriate default options) but also

suggest that the use of conventional utility based measures used by economists

in modelling investor preferences may have inherent deficiencies. The latter in

turn warrants the use of robust performance measures that are independent of

specific utility functions and therefore can be used to develop an appropriate

default investment strategy for any plan participant who do not make a choice.

2.2 Default Investment Options in Retirement Plans

A substantial body of recent empirical work demonstrates that although

members of retirement plans have the option to exercise choice, most accept the

default arrangements in the plans. Choi et al. (2002) find that in USA,

employees tend to accept default arrangements in their plans even for critical

features like contribution rate and investment choice. In their study, between

42% and 71% of employees accept the default contribution rate and between

48% and 81% plan assets are invested in the default fund. In another study

conducted by Beshears et al. (2006), 86% of existing employees who were

subject to automatic enrolment in the company retirement plan had some of their

assets invested in default fund, with 61% having all their assets in the default

fund. They conclude that automatic enrolment tends to anchor employees

towards default asset allocation just as it anchors them towards default

contribution rate. According to consulting firm Hewitt Bacon and Woodrow,

about 80% of group personal pension scheme members in UK accept the default

option (Bridgeland, 2002). Also consistent with the US evidence, Byrne (2004)

finds that many members in UK retirement plans lack the knowledge and

interest to exercise active choice and therefore opt for default options. Cronqvist

19

and Thaler (2004) find that in Sweden, about two-thirds of the participants

actively chose their retirement funds in 2000, when mandatory individual

accounts were introduced by the government and fund choice was offered to the

participants. However, fund choice dramatically dropped off in the subsequent

years and between 2003 and 2005, only 10% of the new participants who were

eligible to choose their funds actually made any choice.

The situation is not much different in Australia. In December 2002, the

Association of Superannuation Funds of Australia (ASFA), the apex body of

superannuation industry, conducted a survey of industry superannuation funds to

find that between 1% and 25% of members exercised active choice in selecting

from various investment options offered to them (Duffield & Burke, 2003). Also

as per ASFA, only 10% of the Australian superannuation fund members who are

offered investment choices actually make a choice (Bowman, 2003). According

to statistics of Australian Prudential Regulatory Authority (APRA), as of June

2004, about 60% of all assets held by all superannuation entities with more than

four members are in default investment strategies (APRA Annual

Superannuation Bulletin, 2005).

While the issue of whether people are better off with more choice is vigorously

debated among academics and policymakers, there is strong evidence to suggest

that majority of members in retirement plans do not make active decisions in

selecting their investment choice. Contributions for these members end up in the

default investment options offered by their respective plans. Therefore, the role

of the default investment option, the asset allocation structure of which is

normally decided by the fund trustees, becomes critical in determining the value

of superannuation accumulated by a vast majority of members at the end of their

working lives. There is also a growing body of evidence that suggests trustees of

retirement plans make better asset allocation choices than the participants

(Benartzi & Thaler 2001, Cronqvist & Thaler, 2004). This makes selecting the

20

default investment option a significant responsibility for trustees which deserves

serious consideration and analysis.

So what determines selection of asset allocation structure for default options?

For retirement plans, it is generally the plan sponsors or trustees who assume

fiduciary responsibility for investment of assets when a participant does not

make an active investment choice. In discharging such responsibility, sponsors

are expected to diligently formulate investment strategies that benefit the

members enrolled to the default option. Bateman (2003) observes that in

countries with established principles of trust law there is little investment

regulation and asset allocation is only subject to the prudent person standard.

For example, the Employee Retirement Income Security Act (ERISA) of 1974

in USA specifies ‘prudent investor’ principle as a standard for plan fiduciary

decisions. Thus, the plan sponsors are expected to possess a level of investment

knowledge and expertise at par with prudent investors and superior to prudent

layperson (Utkus, 2005).

The ERISA does not prescribe any list of approved investments and put no

obligation on plan sponsors to allocate assets exclusively to conservative form

of investments like money market funds. To ensure better compliance with the

requirements of Pensions Act 2004, the Pension Regulator (2004) in UK

specifies that the trustees have a duty to exercise reasonable care and act

prudently, particularly in dealing with investments ‘as it is a way of coping with

risk’. The guideline also asks trustees to decide on investment strategies by

aiming to get the best financial returns achievable at the desired level of risk.

Although stakeholder schemes are required to offer a default fund, the

regulations do not prescribe the nature of any default fund and various

providers, as we discuss below, choose very different investment strategies. In

Australia, the guidelines for trustees provided by the regulatory authority

emphasises the benefits of diversification as, according to them, it would ‘result

21

in a lower overall level of risk to achieve desired return’ (APRA, 1999). The

regulator also makes it necessary for trustees to identify a default strategy where

investment choice is offered to standard employer-sponsored members.10

In USA, a cash or stable value option is typically used as default choice for all

members. Choi et al. (2003) note that 66% of plans in their study have

nominated a stable value fund as the default investment option. The authors

question whether this automatic enrolment to such conservative investment

choice actually makes the participants better off. In December 2004, out of a

sample of nearly 1,889 DC plans administered by Vanguard, one of largest

investment mangers in USA, 81% were found to have chosen a money market or

an investment contract fund as their default options while only 16% used

balanced funds and 3% selected equity funds as their default investment choices

(Utkus, 2005). However, Feinberg (2004) indicates that there is a growing trend

among American retirement plans in selecting balanced or lifecycle funds as

default investment options in recent years.

Blake et al. (2004) examine stakeholder pension schemes in UK, which were

introduced in UK in April 2001 to improve pensions for low to middle income

earners. These schemes share features that are common to most DC pension

arrangements as well as some extra features like no penalties for ceasing,

reducing or transferring contributions and charges capped to 1% per annum. In

addition, these schemes have to compulsorily offer a default fund so that no

member is compelled to make an explicit investment choice. Among the 35 non-

trivially distinct schemes studied by them, 19 offered a ‘balanced’ fund as

default investment option (typically invested 70-80% in equities, 10-20% in

bonds, and up to 5% in cash) while a further 13 schemes had a 100% equity

fund as default choice. The remaining 3 funds had an average asset allocation of

60% equities and 40% fixed interest.

10 Exception can be made where active choice is a pre-condition for membership.

22

Sweden uses a government-operated universal default fund known as the

Premium Savings Fund for those employees who do not choose a fund for their

individual investment account or prefer the government to manage their

investment. The objective of the fund is stated as ‘People who do not have a

fund manager, for whatever reason, should receive the same pension as others-

that is our goal’ (Weaver, 2004). The default fund follows a static asset

allocation strategy with investment in equities between 80% and 90% with a cap

of 75% on international stock holdings (Palme, Sunden & Soderlind, 2005). The

remaining portion (10-20%) is invested in bonds. Of late the target asset

allocation is slightly modified to include 4% investment in private equity and

another 4% in hedge funds (Weaver, 2004).

In Australia, most superannuation funds offer a balanced diversified investment

strategy as the default choice (Duffield & Burke, 2005). An examination of

current top 50 default investment options (in terms of investment performance

as of 31 October 2005) offered by Australian superannuation funds reveals that

majority are called ‘balanced’ investment option while a few are categorised as

‘growth’ options. None of the default options in the list belongs to the ‘cash’ or

the ‘capital stable’ category. At the end of June 2004, the majority of default

strategy assets were held in equities: 33 % in Australian shares and 21 % in

international shares. A further 15 % was in Australian fixed interest, 6 % in

international fixed interest, 7 % in cash, 6 % in property, and 12 % was in other

assets (APRA, 2005).

From the above evidence it seems clear that although a majority of plan

participants passively direct their contributions to the default fund chosen by the

providers, the default options themselves differ substantially in their strategic

asset allocation with strategies ranging from very conservative capital stable

options with investments mostly in money market instruments to extremely

23

aggressive high growth options allocating 100% (or nearly 100%) of their assets

to equities. Since behavioural researchers have shown that the majority of the

members passively accept the default investment option in their plan, such

variation in asset allocation profiles is bound to result in significant differences

in retirement wealth for employees belonging to the same cohort. This virtually

renders the pension plan, as Blake et al. (2004) points out, a lottery for the

participants in terms of subsequent retirement income. Drew and Stanford

(2003) observe the existence of agency problems among Australian

superannuation funds which often leads to sub-optimal investment decisions to

the detriment of the members.

Even among retirement plans in UK and Australia, where balanced diversified

funds are more commonly selected as default investment options for members

who do not exercise choice, a fair degree of heterogeneity exists between the

balanced funds in terms of their benchmark asset allocation. Blake et al. (2004)

finds evidence of wide dispersion in characteristics across default options

offered by occupational pension schemes in UK. According to their study, the

allocation to equity within balanced funds range between 70% and 80%. This is

remarkably different from balanced funds offered as default choice by plan

providers in Australia where the average allocation of default options to equities

is about 56% (APRA, 2005). However, Australian superannuation plans tend to

make significant investments in property and alternative asset classes like

private equities and hedge funds. If one includes average allocations to these

asset classes, the total allocation to risky assets excluding bonds rises to 74%.

Apparently the above data on asset allocation of balanced diversified funds

chosen as default options in Australia and UK indicates that there is very little

difference in risk-return profile between these funds. Yet there is a marked

difference in their asset allocation strategies when one considers the entire

investment horizon of the plan member. In UK, a majority of the default funds

24

(including the balanced funds) are lifecycle funds which gradually decrease their

allocation to equities in favour of less risky asset classes like bonds and bills as

the member approaches retirement. In other words, the equity exposure of the

plan portfolio declines with the age of the member. Out of 35 stakeholder

schemes examined by Blake et al. (2005), 24 offered some form of switching of

assets with lifecycle either as default or as a choice the members could opt for.

Expectedly, this was more common where the initial asset allocation to equity

was high. For example, they found that 6 of the 7 funds with 100% equity

allocation used a lifecycle strategy as a default arrangement. In contrast, most

Australian plans have employed static asset allocation strategy which allows for

diversification among various asset categories but does not change with the age

of the member. This is despite the regulator’s explicit guideline that default

strategies may vary with the age of the members. However, lifecycle funds with

target retirement dates have recently been introduced in Australia but offered by

only a handful of providers (Drury, 2005).

Use of lifecycle funds as default options in 401(k) plans have also been growing

in popularity in United States (Feinberg, 2004). Mottola and Utkus (2005)

observe that participant adoption of static asset allocation funds is on the decline

in recent years while there is an upward trend for funds with target maturity

dates which are gradually rebalanced to achieve a more conservative asset

allocation as the members approach retirement. The life-cycle portfolio is also

the centrepiece of the US President’s proposed plan to reform the social security

system (Shiller, 2005a). According to this, investing in life-cycle fund would be

optional for younger workers but all personal accounts would be invested in a

life-cycle portfolio by default once an employee reaches the age of 47, unless he

or she specifically desires to opt out of it. In Sweden, only 4% of the available

retirement funds belong to the life-cycle category (Sundén, 2004). The universal

default fund is also not a life-cycle fund.

25

The above review of the literature on default funds clearly reveals the lack of

agreement among pension plan providers in different countries about the

appropriateness of asset allocation strategies used as default investment options.

Academic researchers, so far, have barely addressed the issue, let alone propose

any resolution to the conundrum. The current thesis aims to investigate the

suitability of different asset allocation strategies as default options and, thereby,

provide valuable insight on the subject.

2.3 Modern Portfolio Theory and Asset Allocation

Modern portfolio theory provides the theoretical foundation to the asset

allocation decisions in finance. Markowitz (1952) formally describes mean-

variance optimisation framework where expected return (mean) and volatility

(variance) are the only portfolio characteristics which influence investors’

utility. 11 With knowledge about expected returns, standard deviation of returns,

and the correlation between different asset classes, an optimal set of portfolios

can be constructed which lie on the mean-variance efficient frontier. One of the

key prescriptions of portfolio theory is that investors should hold well-

diversified portfolios. Although the mean-variance framework has been widely

accepted as a standard model in finance literature, questions have been raised on

whether investors and financial advisors actually follow its recommendations as

well as on its assumptions and implementation.

In mean variance optimisation model, investor behaviour is assumed to be

consistent with a utility which increases with mean (return) and decreases with

return variance (risk) and is given by

11 If the return distributions are normal i.e. can be defined by the two parameters of mean and variance only, the optimisation rule would obviously hold irrespective of whether investors’ utility function is quadratic or not.

26

1( ) * ( )

2U E r A V r= − (1)

where A is a risk-aversion parameter. The return r is a combination of returns

on investment at risk-free rate fr and that on risky asset with returnRr . If α is

the proportion of funds invested in risk asset, then

(1 ) f Rr r rα α= − + (2)

Maximization of the utility function U in (1) using (2) results in mean-variance

optimal allocation as given by

( )

* ( )R f

R

E r r

A V rα

−= (3)

While the mean-variance optimization model of Markowitz was originally

intended to construct efficient stock portfolios, it has been mostly employed in

deciding how investors should allocate their funds among major asset classes

such as stocks, bonds, property, and cash (Haugen, 2001).12 Radcliffe (1997)

defines this as strategic asset allocation (SAA) which represents the optimal

combination of various asset classes where investors believe that the aggregate

asset classes are efficiently priced.13 As opposed to this, if the investors believe

certain asset classes are mispriced, they would employ tactical asset allocation

(TAA). Haugen (2001) differentiates the two types of asset allocation from the

investment horizon perspective. According to him, SAA decisions relate to

relative amounts invested in different asset classes over long horizons i.e.

horizon periods for estimates of volatilities, correlations, and expected returns

are typically decades long while those for TAA are much shorter – a year or

less.

12 According to some authors like Jahnke(1997) and Nawrocki (1997) the Wells Fargo Bank was the first to apply portfolio theory to asset allocation decisions in the late 1970s. 13 The term ‘strategic asset allocation’ was coined by Brennan, Schwartz, and Lagnado (1997).

27

To employ modern portfolio theory to formulate strategic asset allocation

requires obtaining estimates of expected returns on asset classes under

consideration, the volatility of these returns, and the correlation among them.

These estimates, then, can be used to approach asset allocation formally through

mean-variance optimization which solves for asset class weights that maximizes

returns at each level of risk or minimizes risk at each level of return.

Traditionally, researchers have used historical record of asset class returns to

derive the estimates of expected return, volatility, and correlations which are

used as inputs to the mean-variance optimisation model. However, many authors

like Michaud (1998) have advised users to exercise extreme caution about the

reliability of these estimates, since small changes in the inputs can result in

dramatic changes in suggested asset class weights.

For mean-variance efficiency to be consistent with expected utility

maximization, which most financial economists consider as the basis for rational

decision making, either of the two conditions – normally distributed asset

returns or quadratic utility function - must hold (Michaud, 1998). Although the

limitations of these assumptions are well known to most investment analysts,

mean-variance efficiency is a reasonable approximation of expected utility

maximization in many situations and therefore, provides a practical framework

for portfolio optimization (Levy & Markowitz, 1979; Kroll, Levy & Markowitz,

1984).

However, as a framework for portfolio choice for long horizon investors, the

mean-variance paradigm has been severely criticised because of its myopic

nature being essentially a single period model.14 For the DC plan participant,

this single period can be as large as 40 years. Therefore, to employ mean

variance optimisation to the portfolio choice in this case one has to accurately

14 However, some scholars show this model to be applicable in a multi-period setting under certain restrictive assumptions. Elton and Gruber (1974) offers an excellent synthesis of the arguments.

28

estimate expected returns for available asset classes over this period as well as

their standard deviations and correlation coefficients. Campbell and Viceira

(2002) show that such myopic portfolio selection can be optimal for long term

investors only under extremely restrictive conditions which are likely to be

violated in practice. They argue that in reality long horizon investors are free to

periodically rebalance their portfolios, a possibility that the single period model

fails to recognise.

The two sets of conditions under which such myopic portfolio choice prescribed

by mean-variance paradigm would be valid for long horizon investor is given by

Samuelson (1969) and Merton (1969, 1971). First, investors live in world of

constant risk and return and second, investors treat financial wealth independent

of income. Although these assumptions were considered good approximations of

reality by scholars and practitioners for past several decades, recent research has

argued that they fail to hold in several ways. Campbell and Viciera (2002) show

time varying investment opportunities to be an important consideration for

portfolio choice over long horizons. Similarly, they argue that most investors

use their income stream along with their financial wealth to support their

lifestyle thus violating the second condition.

The conundrum of asset allocation gets deeper when we consider the issue of

investors advised to hold a different proportion of stocks and bonds in their

portfolio according to their level of risk tolerance. Tobin (1958) and several

other analyses of financial markets have shown that the portfolio allocation

decision can be reduced to a two stage decision process: first decision involving

the relative allocation of wealth across the risky assets, and second decision on

how to divide total wealth between the risky assets and the safe asset. In

particular, the mutual fund separation theorem (Cass & Stiglitz, 1970), which is

based on portfolio theory, shows that investors should hold a portfolio of

riskless and risky assets in a proportion determined by their risk preferences

29

(higher the degree of risk aversion, higher the proportion of riskless asset in

portfolio and vice versa). The composition of risky assets, however, is

independent of the investors’ risk attitudes. However, Canner, Mankiw, and

Weil (1997) observe systematic violation of this basic finance theory by

professional investment advisors leading to what they describe as ‘asset

allocation puzzle’. Among the portfolios recommended by the financial

advisors, those with a higher proportion of stocks have a smaller ratio of bonds

to stocks and vice versa. This is in contradiction to the prediction of the textbook

mutual fund separation theorem.15 According to the authors this puzzle can only

be solved under the assumption that human capital has similar risk-return

characteristics to stock. However they are sceptical of the validity of such

restrictive assumption. Also, if human capital indeed shared a similar risk-return

profile to stock, it would lead to investors holding a smaller fraction of stock in

their portfolio when they are young (and hold more human capital) than when

they are old. This is exactly opposite of what is observed in practice and also

goes against the conventional asset allocation advice imparted by financial

advisors.

There have been other attempts made by researchers to reconcile academic

theory with practitioners’ view on portfolio choice. Notable among them is the

work of Campbell and Viceira (2002) who argue that the asset allocation advice

of financial advisors can be consistent with theory if one considers the

limitations of the single period mean-variance analysis which treats cash as

riskless asset and bonds as another risky asset like stock. According to them,

long horizon analysis lends a different view as cash (money market instruments)

is no longer riskless due to inherent reinvestment risk. For long horizon

investors, an inflation-indexed long term bond may be less risky than cash and

conservative investors would actually shift from equities to these inflation-

15 The rationality of asset allocation decisions has also been examined by Elton and Gruber (2000) but with different conclusions.

30

indexed bonds if available. In case the inflation risk is low, even nominal bonds

can be favoured by these investors. Their conclusion indicates that asset

allocation over long term is not just dependent on conditional means and

variances that drive myopic portfolio choice but also on relevant state variables

like inflation and real interest rates.

Due to the seminal work of Brinson, Hood, and Beebower (1986), [hereafter

BHB], it is now well accepted that a portfolio’s SAA is by far the major

determinant of its investment performance. Analysing data from 91 large US

pension plans over the period 1974-83, they observe that asset allocation policy,

which select asset classes for investments and their relative weights in the

portfolio, explains on average 93.6% of the variation in total returns. Two other

factors, security selection and market timing (akin to TAA), are found to

contribute much less to returns. An update of this study by the same authors

(Brinson, Hood, & Beebower, 1991) reached similar conclusions. Blake,

Lehmann, and Timbermann (1999) also find that asset allocation is responsible

for most of the variation in pension fund returns in UK.

But the conclusions of BHB study have come under attack from some authors.

Hensel, Ezra, and Ilkiw (1991) observe that BHB’s findings are largely

dependent on the choice of the benchmark portfolio. They show that while asset

allocation policy largely explains variations in returns when comparing an

average portfolio to a T-bill portfolio, it plays a less dominant role in

determining returns when a diversified portfolio, even a naively diversified one,

is used as a benchmark. Jahnke (1997) uses holding period returns (rather than

return variability used in BHB study) to show that less than 15% of the holding

period returns in BHB sample accounts can be attributed to asset allocation. In

spite of these criticisms, the importance of strategic asset allocation on portfolio

performance has been well accepted by the academic community although there

is some disagreement on the extent of its dominance as indicated by BHB.

31

Asset allocation strategies can not only differ from one another in terms of their

distribution of funds to different asset categories. Several other factors like

frequency of rebalancing and horizon dependence (or independence) can cause

considerable variation between strategies. Perold and Sharpe (1988), among

others, point out that the fluctuations in the market value of assets held within a

portfolio may result in its drifting from its strategic asset allocation over time

and discuss methods to deal with the problem, two of which are most commonly

used by investors. The first of these is a static buy-and-hold strategy where

assets are purchased after deciding on an initial mix and then held during the

entire investment horizon without doing anything. The effect of fluctuations in

market value of assets on their allocations is, therefore, ignored. In contrast,

constant mix strategy aims to maintain the initial allocation among asset classes

through periodic rebalancing – whenever actual asset allocations move away

from the target range. Hence, unlike buy-and-hold, it is considered to be a

dynamic strategy. Baker, Logue, and Rader (2005) argue that the relative

performance of the two strategies depends on the nature of the relative

performance of the asset classes. For example, in a two asset class scenario, if

the relative performance of stocks to bills makes a sustained move (either up or

down), the buy-and-hold strategy would outperform the rebalancing approach.

However, if asset class returns are mean reverting i.e. relative performance of

stocks to bills is not sustained, the constant mix strategy is likely to produce a

superior outcome.

Given the importance accorded to strategic asset allocation and the amount of

resource spent in developing strategic target weights, Buetow, Sellers, Trotter,

Hunt, and Whipple Jr. (2002) argue that plan sponsors would deliberately not

allow any portfolio’s asset mix deviate significantly from its established targets.

Yet they find current practice among sponsors range from disciplined to random

rebalancing. Using actual return data from 1968 to 1991 to investigate various

32

rebalancing strategies for two asset class portfolios, Arnott and Lovell (1993)

find that more frequent rebalancing produces better results than less frequent

rebalancing. They also find the periodic rebalancing is superior to non-periodic

rebalancing based on drift intervals from target allocation. Their findings receive

support from Plaxco and Arnott (2002) whose study encompasses a global

portfolio as well as from Buetow et al. (2002) who use simulation approach to

evaluate different rebalancing strategies for a four asset class portfolio.

2.4 Lifecycle Asset Allocation Strategies

As we have discussed in 2.2, most superannuation funds in Australia currently

use constant mix or fixed weight asset allocation strategies as default investment

option i.e. the relative weights of different asset classes in the default strategy

remain constant irrespective of the plan participant’s age or time to retirement.

However in addition to such strategies, this dissertation investigates the

suitability of lifecycle strategies as default investment options for DC plan

participants in comparison with fixed weight asset allocation strategies. Like

fixed weight strategies, lifecycle strategies automatically rebalance the

investments to keep the overall portfolio mix of the fund in line with a pre-

specified target asset allocation. Unlike fixed weight strategies, however,

lifecycle funds do not keep the asset weightings constant over time; instead, they

change their target asset mix according to a predefined schedule until they reach

target maturity date of the fund. Typically, the target asset allocation for

lifecycle funds becomes increasingly conservative over time i.e. investments are

switched away from risky assets like equities towards less volatile assets like

bonds and cash.

An important investment principle anchoring most participant education

programs in USA is the belief that younger individuals can assume greater risk

33

than older individuals and therefore invest more in risky assets like equities

(Utkus, 2005). This, therefore, could qualify as a rationale for choice of default

options by plan sponsors. Malkiel (1996) asserts that risk tolerance is a function

of both risk attitude of the investor as well as his or her risk capacity. While risk

attitude is subjective, according to Malkiel, risk capacity depends on his position

in the lifecycle. This implies the portfolio of an older investor would be different

from that of a younger investor i.e. optimal portfolio structure depends on the

age of the investor. This is the centrepiece of all lifecycle models of investment.

As explained in the previous paragraph, lifecycle strategies would follow

aggressive allocation to risky asset classes earlier and gradually move towards a

more conservative asset allocation later. In the context of retirement plan

investments, the lifecycle portfolio would be one that is heavily concentrated in

stocks at the beginning of worklife when the investor is young, and then

gradually shifting towards bonds and cash as retirement nears. Malkiel’s

reference portfolios move from an allocation of 70% to stocks for investors in

their mid-twenties to 30% when they are in their mid-fifties. The allocation to

bonds increases from 25% to 60% during the same period while that to cash

increases from 5% to 10%. Although lifecycle models differ from one another in

respect to how and when the switching from equities to bonds/bills occurs, there

is almost total consensus about the direction of the switch with most

commentators favouring higher allocation to equities (70%-90%) during early

years of employment with gradual shift to conservative asset classes

encompassing bonds and cash as the investor approaches retirement (Baker et

al., 2005).

One theoretical justification for adopting the lifecycle asset allocation strategy

rests on the concept of time diversification, according to which risk of investing

decreases with time or length of horizons and therefore, investors should be

more inclined to hold risky assets with higher expected returns over long

34

horizons than over shorter periods of time.16 It is usual advice given by financial

planners to their clients, especially to those who save for retirement. This advice

is underpinned by the argument put forward by academics like Siegel (2003) and

practitioners (for example, Greer, 2003). The risk of a portfolio containing risky

assets like stocks decreases with the increase in investment horizon. Direct

fallout of this logic is investors with long horizon should allocate higher

proportions of their portfolios to equities and reduce the proportions as they age.

The belief that time reduces risk has been forcefully challenged by academics

like Samuelson (1963, 1969) and Bodie (1995). Samuelson (1963) points out

that the reasoning behind time diversification is a fallacious interpretation of law

of large numbers. Using repeated lotteries, Samuelson demonstrates that if an

agent rejects a lottery at all wealth levels, he will also reject any sequence of that

lottery with same distribution. Therefore, if at each income or wealth level

within a range, the expected utility of a certain investment or bet is worse than

abstention, then no sequence of such independent ventures can have a

favourable expected utility. The result implies that although the probability of

loss on an investment reduces with the length of investment horizon, it is offset

by an increase in the magnitude of potential loss.

Bodie (1995) uses option-pricing theory to demonstrate the fallacy with the

notion of time diversification. According to him, if stocks are actually less risky

in the long run, the cost of insurance against any shortfall in stock return over

risk-free rate would decrease. However, using the Black-Scholes option pricing

model in computing cost of such insurance (which is essentially a European put

option), he shows that the value of the put option actually increases with time

approaching 100% of the investment at infinite horizon. However, Bodie’s using

a constant annualised standard deviation of 20% in stock returns as a key input

in the option pricing model to get his results has been challenged by Taylor and

16 See Kritzman (2000) among others.

35

Brown (1996) since variation in standard deviation of risky assets like stocks is

most critical to the argument for time diversification.

A careful analysis of the arguments reveals the following key assumptions made

by financial theorists like Samuelson while refuting time diversification.

1. Stock returns are serially uncorrelated i.e. follow a random walk

2. Investors have a constant relative risk aversion (CRRA)

3. Investors’ future wealth depends only on their investment portfolio

Although the mathematical correctness behind the ‘irrelevance of time’

argument is well accepted, the abovementioned assumptions under which the

proof of irrelevance is derived are open to challenge.17 While the second and

the third assumption have been discussed in the literature, it is the validity of the

first assumption that has drawn the most attention from researchers. If asset

prices truly follow a random walk, tp is the logarithm of assetj ’s price in time

t, tj ,ε is a white noise with mean 0 and variance 2jσ then:

ttjtj pp εα ++= −1,, (4)

or in the return form:

ttjr εα +=, (5)

If tjR , is the mean return over τ periods, then:

17 A few researchers have tried to explore time diversification or its irrelevance from the perspective of traditional mean-variance framework. In the previous section, it was shown that

mean-variance optimal allocation is given by ( )

* ( )R f

R

E r r

A V rα

−= , where ( )RE r and ( )RV r denotes

expected return and variance respectively. Thorley (1995) shows mathematically that with increase in time horizon ( )RV r increases at a faster rate than ( )RE r under any distribution

assumption, including lognormality. This results in decrease in mean-variance optimal risky asset allocation,α , with increase in investment horizon. Therefore, unlike Samuelson (1963) mean variance optimisation model does not predict investment horizon indifference but rather takes the other extreme and counterintuitive position to imply that longer horizon investors should be less inclined to invest in risky assets.

36

∑−

=−=

1

0,,

1 τ

τ iitjtj rR (6)

This gives the following expected returns and variance for tR .

α=)( ,tjRE (7)

τσ 2

, )( jtjRVar = (8)

The above equations imply that if asset returns follow a random walk, the

expected return over long horizon (tjR , ) is the same as that of the short horizon

( tr ). However the variance decreases with the length of the investment

horizonτ . The volatility, given by standard deviation oftjR , , decays by a factor

of τ over long horizon. But if returns from stocks, bonds, and bills all follow

random walk, then standard deviations of all these asset classes would shrink by

the same factor i.e. the risk of stocks would not decline faster relative to the risk

of bonds and bills. In such a case, there is no reason why risk averse investors

would prefer to hold higher proportion of stocks over long horizon than what

they are willing to hold over short horizon. Therefore, investment horizon

should not have any impact on asset allocation.

However the assumption of random walk of asset class returns is not well

supported by empirical evidence. It is possible for asset class return generation

to be a stationary autoregressive process with either negative or positive serial

autocorrelation observed in the return series. If we assume asset returns to

follow a simple stationary autoregressive process, then:

tjtjtj rr ,1,, εβα ++= − (9)

The mean and the variance in this case would be given by18

18 For derivation, see Guo and Darnell (2005).

37

βα−

=1

)( ,tjRE (10)

( )

−+−

= ∑−

=

1

12

2

,

21

)1()(

τ

βττβτ

σk

ktj kRVar (11)

If 0<β , the process is commonly known as mean-reversion. In that case, the

standard deviation of tjR , would decay by a factor greater thanτ . On the other

hand, when 0>β , the process is standard positively autocorrelated. The

volatility in this case also decreases with the length of the investment horizon

but at a slower rate, the rate of decay being less than τ . Therefore, if returns

from an asset class follow mean reversion while returns from another asset class

is positively correlated over time or follow a random walk, the riskiness of

investing the former (relative to the latter) would decline with increase in

investment horizon.

Historical data of asset class returns in the US market has not been supportive of

the random walk hypothesis. Using real returns data from 1802 to 2001, Siegel

(2003) reports that the risk of investing in stocks diminishes over long holding

periods at a rate that is faster than what is predicted under the random walk

assumption. However the risk of investing in bonds and bills seem to decline at

a slower rate than the prediction of random walk model over long horizons. This

evidence suggests that stock returns show mean reversion while returns from

fixed income securities show mean aversion. Earlier work like Poterba and

Summers (1988), and Fama and French (1988) had also observed mean-

reversion in stock prices. Dimson, Marsh, and Staunton (2002) provide

corroborating evidence from other countries.

38

The above findings have provided support for the argument that investing in

stocks is indeed less risky over a long horizon. Thus the conventional wisdom of

lifecycle model which recommends holding a higher proportion of stocks in

one’s portfolio when the horizon is longer seems to be justified. However such a

claim is strongly refuted by researchers like McEnally (1985) who contends that

the appropriate measure for investment risk is the variability of the terminal

wealth outcomes that arise by holding an asset for the intended investment

horizon and not the variability of periodic returns of the asset around its average

return. The underlying argument here is that although the standard deviation of

asset returns becomes smaller as the holding period increases, the dispersion in

terminal wealth for all asset classes actually increases. This implies that if

investors emphasize on total returns over the investment horizon, risk uniformly

increases with horizon length (Samuelson, 1969).

In measuring the risk associated with the cumulative wealth, we can again

examine the expected mean and variance under random walk or stationary

models. If investors only aim to maximize cumulative wealth ( τttj RW += 1, ),

we have under the random walk assumption:

τα jtjWE += 1)( , (12)

τσ 2, )( jtjWVar = (13)

The expected wealth as well as its variance rise at the rate given by the length of

the investment horizonτ . The standard deviation, therefore, increases at the rate

of τ . However this is again true for all asset classes (stocks, bonds, bills) and

therefore, stocks would not appear to be less risky relative to bonds and bills

over long horizons. Thus, as with the case for returns, the wealth maximisation

39

objective under the random walk model does not prescribe changing asset

allocation over different horizons.

Under the stationarity assumption, however, asset allocation does not remain

time invariant. The expected cumulative wealth and its variance in this case is

given by

τα jtjWE += 1)( , (14)

ij

ijjtj iWVar βτστσ

τ

)(2)(1

1

22, ∑

−

=−+= (15)

Although the expected wealth is still increasing at a rate τ the variance of tjW , is

dependent on the magnitude of jβ and its sign. If jβ is negative for stocks and

positive for bonds and bills as indicated by empirical evidence, the variance of

wealth for stocks rises at a slower rate than τ while the variance for bills and

bonds rises at a rate faster than τ . The asset allocation should thus be more

tilted towards stocks over longer holding periods.

Although mean reversion in stock market returns can cause relative riskiness of

stocks to decline over longer holding periods relative to bonds and bills, the

literature is divided over whether that makes stocks a safe bet over long

horizons. McEnally (1985) reports that investment in stocks results in highest

dispersion in terminal wealth outcomes while investment in T-Bills shows the

lowest. According to him, this indicates that stocks are riskier than other asset

classes over longer investment horizons. But several other researchers argue that

the uncertainty is not about whether stocks would outperform T-bills over long

holding periods but about to what degree the former would outperform the latter.

Their contention is that the greater risk of investing in stocks over safe assets for

40

long holding periods as shown by McEnally is more about upside uncertainty

than any risk of underperformance, which the investors seem to be more

concerned about. For example, Butler and Domian (1991) estimate that the

chance of equities underperforming bonds over 20 year holding periods is about

5%, assuming that future returns would be drawn randomly from past history of

returns (US. data for 1926-1988 period in their study). If one believes in mean

reversion of stock prices over the long run, the risk of underperformance would

be even lower (Thaler and Williamson, 1994). Siegel (1992) finds that between

1871 and 1990, over horizons of 20 years and longer, stocks in US

underperformed short-term bonds on only one occasion and outperformed long-

term bonds 95% of the time. For 5 year holding periods, stocks outperformed

long-term and short term bonds, but only by about a three-to-one margin i.e.

about 75% of the times.

Empirical evidence overwhelmingly suggests that probability of stocks

underperforming less risky assets like bills and bonds (shortfall) over longer

holding periods is very low. Yet many researchers are unwilling to accept this as

a proof that the risk of investments in stocks reduces with time. According to

them, although the probability of shortfall declines with the length of the

investment horizon, it is an imperfect measure of risk since it does not say

anything about how large the potential shortfall can be. To do so one has to

focus on the magnitude of potential negative returns. Bodie (1995) makes this

point by showing that the worst possible outcomes from investing in stocks

actually increase with the investment horizon.

Now we take up the Samuelson’s second assumption of CRRA in describing

investors’ utility function. If we accept Samuelson’s argument that the ratio of

risky assets to total wealth remains unchanged, we automatically assume CRRA.

This issue is most important in resolving the time diversification debate since

decreasing, increasing, or constant RRA will have positive, negative, or nil

41

impact respectively on time diversification strategies. One popular functional

form of utility used by economists (for example, Arrow, 1971) in describing

investor’s relative risk aversion (RRA) is given by

1( ) 1( ) ,

1

WU W

γηγ

−− −=−

(16)

where η and γ are investor-specific risk aversion parameters.

Pratt (1964) and Arrow (1971) show that RRA is mathematically given by

( )R W WU U′′ ′= − (17)

This when applied to the above form of utility function gives

( )1 ( )

R WW

γη

=−

(18)

If η =0, ( )R W =γ i.e. a constant at all levels of wealth. But when η >0, then

relative risk aversion ( )R W decreases with increase in wealth level (W ).

Several techniques have been used to estimate RRA of investors. The

measurement seems to be sensitive to what measure of wealth is used by the

particular researcher. There has been conflicting evidence with findings of

increasing (Siegel and Hoban, 1982), constant (Szpiro, 1986) and decreasing

(Levy, 1994) risk aversion, which implies that the debate on time diversification

remains wide open.

The detractors of time diversification, nevertheless, admit that there can be a

different rationale for investors to reduce exposure to risky assets as they age.

The total wealth of an individual is a summation of investment and human

capital and with age both of these undergo changes. It is quite plausible that

young investors with long investment horizons may be induced to invest more in

risky assets because if the investments perform poorly they can compensate by

42

postponing consumption or working harder to generate more labour income

(Bodie & Samuelson, 1989). On the other hand, as investors get older, their

stock of human capital declines and so does their ability to alter labour income.

Although this violates the third assumption in the mathematical derivation of

time diversification irrelevance, Samuelson (1989) points out that this does not

validate the notion that time diversifies risk but only provides a rational basis for

investors being more risk tolerant when young than when old. Samuelson (1994)

argues that with age human capital gets converted into liquid capital resulting in

a fractional holding of stocks appearing to decrease when compared to liquid

capital, whereas the fraction actually remains unchanged when compared to total

wealth. Viceira (2001) shows that even with a random future income, time

diversification is optimal as long as there is low correlation between labour

income and stock returns.19 Cocco, Gomes, and Maenhout (2005) also find that

a lifecycle investment strategy that reduces equity exposure with age may be

optimal depending on the shape of labour income profile.

The Markowitz mean-variance optimisation model assumes that investors are

‘myopic’ in a sense that they make decisions in a static, single-period

framework. Among contemporary theoretical works in finance which aims to

address this problem, the most widely accepted framework is Merton’s (1992)

continuous-time model of optimal consumption and portfolio choice. In its most

developed version (Bodie, Merton & Samuelson, 1992), this model includes

human capital as a choice variable. In this model, individuals decide on their

consumption, proportion of financial wealth to invest in risky assets and fraction

of their labour income to be spent on leisure to maximise their expected lifetime

utility at any point of time. This implies that the fraction of an individual’s

wealth invested in equities would normally decline with age due to several

reasons like difference in riskiness between equity and human capital, decline of

19 More sophisticated models are reviewed in Campbell and Viciera (2002). The conclusions, however, are the same.

43

human capital as a proportion of wealth as a person ages, and varying degree of

flexibility to alter labour income at different stages of life.

The Bodie-Merton-Samuelson model has received some empirical support in

United States and elsewhere. Other life-cycle theories like Jagannathan and

Kocherlachota (1996) suggest that as individuals age, their stream of future

income shortens, which diminishes the value of their human capital. According

to them, individuals should offset this decline in the value of their human capital

by reducing the risk of their financial portfolio. While many studies conducted

among retirement plan participants confirm the inverse relationship between

stocks and age (Bodie & Crane, 1997; Agnew, Balduzzi & Sunden, 2003),

Ameriks and Zeldes (2001) find that the relationship follows a hump-shaped

pattern with the proportion of stocks first increasing with age and then declining.

They observe that the relationship is very much sensitive to the choice of sample

period and do not rule out the possibility of a cohort effect influencing the

results. According to them, earlier-born cohorts are less likely to hold stocks in

their portfolio compared to later-born cohorts and they also find evidence of

individuals making few changes in their portfolios as they age. Other empirical

studies on actual age-specific investment patterns of households find weak

evidence of decline in equity exposure with age (Poterba & Samwick, 2001;

Gomes & Michaelides, 2005).

It is important to note that age (or length of the investor’s time horizon) is not

the only determinant of riskiness of a portfolio in the life-cycle model of Bodie,

Merton, and Samuelson (1992). Their model emphasises the value of human

capital and degree of labour flexibility which may be influenced by factors other

than age like occupational categories (opportunities for working extra hours,

taking extra jobs, delaying retirement) or family status (number of workers or

potential workers in a family). Poterba and Wise (1996) find evidence of age-

related and income-related patterns of asset allocation where younger

44

participants in retirement plans and high income households tend to hold

significantly higher proportion stocks in their portfolios while Agnew, Balduzzi,

and Sundén (2003) find that equity allocations are higher for males, married

investors, and for those with higher earnings and more seniority on the job.

Exley, Mehta, Smith, and Van Bezooyen (1998) reviews some other arguments

supporting lifecycle switching of portfolios for retirement plan participants. One

important reason is the possibility of younger investors being more inclined to

invest in stocks if this asset class has low correlation to the value of their future

labour income (residual human capital). The preference for stocks, however,

would decline with age as the overall proportion of human wealth to total wealth

declines. Second, since it is difficult or impossible to use retirement account

balances for consumption prior to retirement, the participants may place

significant discounts on the value of assets in pension accounts and therefore,

may select high-risk investment strategies. This effect would be more

pronounced the farther they are away from retirement and decline as they

approach it. Finally, there is the concept of people becoming more risk averse

when they are nearing retirement because they get used to certain level of

consumption and are unwilling to adjust that level downwards.20 Samuelson

(1989) finds merit in the argument that if investors care about accumulating a

target wealth outcome to ensure subsistence in old age, there would be a

tendency to switch from equities to fixed income assets before retirement.

However, according to optimal consumption and investment rules derived by

Dybvig (1995) under the extreme condition of intolerance for any decline in

standard of living, the equity allocation should be increased when the market

returns increase and vice versa. As a strategy, this is quite the opposite of what

is suggested by the proponents of mean reversion in equity markets and

therefore it does not sit comfortably with the time diversification rationale for

adopting lifecycle strategies.

20 In economics literature, this is known as habit formation in consumption.

45

Whilst all lifecycle funds start with high initial concentration in stocks and

gradually move towards bonds and cash, this practice does not enjoy universal

approval from all theorists. Many authors, who make assumptions about the

correlation of stock returns with labour income different from Viceira (2001),

actually find that younger investors should invest less in stocks and increase the

allocation as they age. Benzoni, Collin-Dufresne, and Goldstein (2004) argue

that if one considers the correlation between stock returns and labour income

through time, younger investors should be well advised not only to invest less in

stocks but to actually short the stock market. Lynch and Tan (2004) argue that

young people should hold a lower proportion of stocks than older people, given

that when stock returns are low (as in periods of recession), there is also lower

mean income growth and higher volatility.

Lifecycle investment strategies offered by retirement plans constitute a critical

component of this thesis. The above review of the literature suggests that design

of lifecycle strategies is a complex and contentious affair. It is evident that such

strategies differ considerably from one another not only in their initial and final

allocation but also in terms of key switching characteristics like the timing,

mode, and direction of the switch. Also, deterministic switching according to

some pre-set rule may not be optimal considering the dynamic nature of

portfolio risk and returns. We examine these issues in chapter 6 and 7. However,

our investigation chooses to focus only on financial assets in the retirement plan

and ignore any possible impact that human capital may have on asset allocation

decisions of participants in investing their plan contributions.

2.5 Optimal Asset Allocation Strategy for DC plans

In nominating a default among available investment choices, a prudent approach

for DC plan providers is to examine the risk-return trade-off for individual

46

strategies. The strategy with the optimal risk-return combination can then be

selected as the default option. While some researchers have attempted to

optimise risk and return through theoretical approaches by applying dynamic

programming techniques, most research on asset allocation strategies in the

literature for DC plans have been based on this empirical approach of evaluating

currently used strategies and some of the alternatives. This doctoral dissertation

also adopts the empirical route to explore the research problems.

Research investigating the optimality of strategic asset allocation strategies for

DC plans is mostly very recent. Among these works, Butler and Domian (1991)

simulate outcomes for strategies that invested in stocks, bonds, and lifecycle

accounts and derive probability distributions for terminal wealth. Their results

suggest that common stocks are the best vehicle for long-term retirement

savings. The lifecycle portfolio in their study outperforms a portfolio comprising

of 100% stocks in only about 8 percent of cases. Ho, Milevsky, and Robinson

(1994) also emphasize the importance of stocks, arguing that investments with

high return-risk trade-off may be necessary to minimize the chances of outliving

one’s assets after retirement.

Very few studies on DC plans examine the entire distribution of terminal wealth.

Kim and Wong (1997) employ simulation and stochastic dominance tests to

evaluate merits of different allocation strategies using US asset return data since

1926. Their results indicate that the optimal allocation strategy should generally

be one heavily tilted towards equities till the individual is close to retirement. In

fact, under more restrictive assumptions of second order stochastic dominance,

they find a 100% equity strategy dominant over all other strategies for horizons

of 25 years or longer. However, they do not find any benefit for retirement

investors in adding international stocks to their portfolio.

47

Asset allocation strategies following the lifecycle principle of investing may

differ in terms of switching rules. Hickman, Hunter, Byrd, Beck, and Terpening

(2001) conduct a simulation study of two lifecycle switching rules: (i) Malkiel’s

(1996) rule, and (ii) the “100-minus age” rule, and also compare the results with

a strategy that invests 100% in the Standard & Poors’ (S&P) 500 index fund.21

Using a 30-year holding period, the two lifecycle approaches yield very similar

outcomes and produce median wealth at retirement that is almost half of that

associated with the index fund. Only in about 15 percent of the simulations the

life-cycle approaches are able to outperform the S&P 500, which suggests that

occasionally the switch to bonds and money market securities at later ages may

prove to be a correct strategy. However, the authors question whether this small

benefit of protection against such relatively rare adverse outcomes warrant

accepting large reduction in expected terminal wealth.

Among other research scrutinising lifecycle strategies, Booth and Yakoubov

(2000) investigate both accumulated amount at retirement and annuity value for

DC plan participants for five different lifecycle strategies. Using both empirical

data and stochastic modelling, they find no evidence to support the superiority

of lifecycle strategies that advocate gradually moving from predominantly

equity based portfolio to investments like bonds and cash as the investor

approaches retirement. Although their finding suggests that automatic switching

to less volatile assets before retirement may not be appropriate for DC plan

participants, the authors are not able to draw a strong conclusion that continuing

with the equity based strategy is necessarily better. They recommend the

member participant maintain a well diversified strategy until retirement.

A handful of scholarly work so far has examined the impact of asset allocation

on the potential of confronting extremely adverse outcomes at retirement.

Ludvik (1994) finds that if predictability of ‘floor’ level (only 5% of outcomes

21 Malkiel’s switching rule is explained in 2.4.

48

are below this level) matter most to the DC investor, 100% bonds or 100% cash

strategies produce superior outcomes to 100% equity or a lifecycle switching

strategy. However, the floor level of the 100% equity strategy is higher than

those for 100% bonds or 100% cash strategies. The lifecycle strategy, according

to his results, has improved ‘floor’ level relative to 100% bonds and 100% cash

strategies and reduced volatility of the floor level relative to 100% equity

strategy. Blake, Cairns, and Dowd (2001) evaluate a range of static and dynamic

asset allocation strategies for DC plans by estimating the value at risk (VaR)

measure for target pension outcomes.22 They find that the VaR estimates are

extremely sensitive to their choice of asset allocation strategy. Their results

indicate that a static diversified asset allocation strategy with high equity content

delivers superior results to dynamic strategies including the lifecycle approach

over a long horizon (40 years in their study).23 Also, conservative bond-based

asset allocation strategies require much higher contributions to match the

outcomes of equity-based strategies.

Hibbert and Mowbray (2002) investigate various asset allocation strategies

including various forms of lifecycle strategies using a stochastic model. Like

most other studies, their results show that 100% equity strategy generates the

highest expected retirement income although the range of potential outcomes is

very wide. Lifecycle strategies are useful in reducing the dispersion of outcomes

in their study but they do so at the cost of lowering the expected value. Vigna

and Haberman (2002), among others, uses dynamic programming techniques to

determine an optimal investment strategy for DC plan participants. They find

that the conventional lifecycle strategy is optimal for a risk-averse investor

while for a risk-neutral investor the optimal allocation is 100% equities without

any switch. However, the different downside risk measures used in their study 22 VaR, a measure of tail risk, is discussed in the next section. 23 This strategy resembled the average allocation of UK pension funds in 1998 with 5% in treasury bills, 51% in UK equities, 20% in international equities, 15% in UK bonds, 4% in international bonds, and 5% in UK property.

49

give conflicting indications about optimality of the various strategies considered

in their study.

Using actual lifetime earnings data for a large sample of households to model

plan contributions and combining these with simulated patterns of asset returns,

Poterba, Roth, Venti, and Wise (2006) examine the distribution of retirement

wealth for DC plan participants to evaluate lifecycle strategies vis-à-vis age-

invariant strategies that hold the fraction of portfolio allocated to each asset class

constant. Their analysis shows that the distribution of retirement wealth for

lifecycle strategies is similar to age-invariant strategies which hold equal

proportion of stocks as the average stock holding in the lifecycle strategies.

They also find that expected utility associated with these strategies and their

relative rankings is very sensitive to the expected equity premium, the plan

participant’s risk aversion and the presence of wealth outside the DC plan.

In contrast to the above studies which discuss theoretical allocation strategies

and their impact on retirement outcomes, Blake et al. (2004) focuses directly on

asset allocation structures of default funds actually offered in pension schemes.

According to their findings, an allocation strategy with high fixed income

content, which is conventionally regarded as a low risk-low return approach,

produces worse VaR outcomes for pension ratios at 5% level than some other

strategies with higher allocation to equities. This shows that conservative

strategies may not be synonymous with ‘low risk’ strategies for retirement

investors with long horizons as returns from these may fail to keep pace with

that of equities as well as long term wage growth of the individual. Their results

indicate that lifecycle strategies are effective in reducing risk but at the cost of

reducing the terminal wealth outcome of the retiree. Also, they find very little

benefit in holding long gilts over cash in the final year before retirement.

50

Shiller (2005a) observes that lifecycle funds currently offered in the U.S. market

are not exactly the same. This shows that considerable difference in opinion

exists about the optimality of their asset allocation structure to investors with

similar horizon. For example, as of September 30, 2004, the Vanguard Target

Retirement 2045 fund (aimed at investors in their twenties who are expecting to

retire around 2045), allocates 89% to stocks (domestic and international), and

the remaining 11% to fixed income securities. This, according to their

prospectus, would gradually change to a target allocation of approximately 30%

in stocks, 65% in fixed income, and 5% in cash at the time of retirement (target

date). About 5 years after the target date, the allocation would resemble that of

Vanguard Target Retirement Income Fund (aimed at current retirees) which

allocates 20% to stocks, 50% to bonds, 5% to money market instruments, and

25% to inflation-protected securities. In contrast, T. Rowe Price Retirement

2045 Fund currently invests 93.5% in stocks and 6.5% in bonds. This allocation

gradually changes to approximately 50% stocks, 40% bonds, and 10% short

term investments at the point of retirement. The proportion of stocks would

continue to decline gradually for another 30 years after target date when it

would reach 20% and would remain fixed at that level.

An important issue that has been drawing attention from researchers recently is

the switching criteria for lifecycle strategies. As discussed above, most lifecycle

strategies currently in practice adopt a deterministic switching policy where shift

of allocations from equities to bonds and cash is done gradually following a

preset rule. Ludvik (1994) argues for a ‘self-modifying’ strategy that increases

allocation to safer assets when the accumulated fund is ahead of some specified

‘target’. Arts and Vigna (2003) proposes a dynamic switching criterion from

equities to bonds which takes into consideration actual realisations of returns on

assets (equities and bonds). The switching from equities to bonds occurs earlier

if returns from equities in the initial part of the accumulation phase are high and

vice versa. Among theoretical models for switching in lifecycle strategies,

51

Cairns, Blake, and Dowd (2006) use the stochastic properties of the asset class

returns and member’s salary progression to derive optimal solutions while Vigna

and Haberman (2002) include risk aversion and time to retirement as key

switching parameters.

Arts and Vigna (2003) also develop an alternative to the conventional lifecycle

investment strategy which gradually switches the DC account accumulations

from equities to bonds. In their model, the individual initially invests

contributions to equities for a certain time. Thereafter, further (new)

contributions are allocated to bonds while the previous accumulation in the

account is allowed to remain invested in equities until retirement when it is

converted into bonds. They compare their new switch strategy with conventional

lifecycle strategy and find that while the mean for the latter is higher it also has

higher probability of falling below the target outcome.

It is evident from the above studies that there is no consensus on the optimal

asset allocation for DC plan investors although there seems to be some

agreement about the superiority of portfolios with high allocation to stocks over

bonds and cash, which is a result of the return differential between these asset

classes. Also, lifecycle strategies do not find the same amount of support from

academic researchers as they do from investment practitioners. Although most

of the research cited above considers conventional lifecycle strategies where

investors switch investments from stocks to bonds and cash as they approach

retirement, some academics allude to other possibilities. Shiller (2005b) argues

that since young people have relatively less income than older workers, a

lifecycle portfolio would be prone to investing less money in stocks. Similarly,

at middle and old ages when their earnings tend to peak, lifecycle strategies

would actually move investments out of stocks to assets which are less risky and

generate lower returns. In that case the lifecycle investment approach would

actually undermine the investment objective of maximizing retirement wealth

52

and DC plan participants would do better by following a strategy that does just

the opposite– invest funds in bonds and cash during early years when their

earnings (and therefore, contributions) are low and to stocks in the middle and

late years when their earnings are high. However, this type of investment

strategy has not been developed and empirically tested so far. The third and

fourth essays in this dissertation examine some of these unorthodox asset

allocation approaches discussed in this section to maximize the welfare of the

DC plan participant.

2.6 Strategic Asset Allocation: Role of Equity Premium

The role of equity premium is central to our research in evaluating alternative

approaches to asset allocation.24 This is because the investment outcomes of any

strategy which invests in equities would undoubtedly be very sensitive to the

equity premium used by the researcher. The estimation about the exact long-run

equity premium is often a determinant of the weighting assigned to equities

(relative to other asset classes) in the portfolio of the DC plan participant.

According to Utkus (2005), one of the investment principles that are part of

most participant education programs in United States is an expectation that

positive equity risk premium would continue in the future. This, he points out,

can influence the plan sponsors’ choice of default options. Historical evidence

supports the existence of a positive equity risk premium, more so, over long

holding periods. Investment horizons of DC plan participants can be considered

as long, since these are typically well in excess of thirty years. This should call

for an allocation policy which is tilted towards stocks. There is also an implicit

24 The concept of equity risk premium i.e. excess returns of common stocks over fixed income and cash investments is well documented and debated in finance literature.

53

assumption that the expected equity risk premium is an adequate compensation

for the volatility of stock returns.

Mehra and Prescott (1985) study asset returns in US market for the 1889-1978

period and find that investment in stocks, on average, generated 6.2 % additional

return over investment in short-term government debt. According to them, such

a high premium, even when one considers the higher risk associated with stocks,

is puzzling. Siegel (1992) analyses returns for a longer period (1802-1990) and

finds that equity premium is actually not as large when one considers this

extended time span. He observes that real returns on bonds have been

particularly lower in the middle part of the twentieth century resulting in higher

equity premiums. But bond returns during the 1980-1990 period, the last ten

years of his study, bounced back to their highest levels for more than a century,

Siegel cautions that it is likely that the premium associated with holding equity

is likely to decline in future although he agrees that equities may still prove to be

the best route to long term wealth accumulation.

Dimson et al. (2002) study returns of different asset classes in USA over 25, 50,

75 and 100 year sub-periods during the last century. Their results indicate that

although real return on equities has increased continuously during the twentieth

century, so has real returns for bonds and bills. The gap between real returns on

equities and bonds has actually decreased for the 25 year sub-period compared

to 50 year sub-period to 2001. In fact, over the ten years until the end of 1990,

US bonds generated an annualized return of 13.7% to outperform equities which

returned 12.6% annually during the same period.

While the US investors enjoyed large positive equity premium (geometric risk

premium of 5.8% relative to bills and 5% relative to bonds) over the last

century, one needs to consider whether the experience has been similar in other

important markets outside US before drawing any definitive conclusion. Jorion

54

and Goetzmann’s (1999) report returns for 39 financial markets for the 1921-

1996 period and find real return for US equities to be the highest. They argue

that the high premium obtained for US is likely to be the exception rather than

the rule. However, not all commentators agree with their view. Dimson et al.

(2002) document the returns from equities, bonds and bills across 16 countries

during twentieth century. They find that while the equity risk premium relative

to bills differs across countries, the 101 year averages fall within a narrow range.

The average equity risk premium relative to bills for the world index is 4.9%,

which is 0.9% below the same premium for US. The equity premium relative to

bills for Australia is 7.1% which exceeds that for US (5.8%) and UK (4.8%).

The equity premium relative to bonds for most countries, expectedly, is lower

than that relative to bills. The world average of 4.6% is 0.4% lower than that of

US. Once again, the premium for Australia (6.3%) exceeds both US (5%) and

UK (4.4%).

While the equities had a good run in recent history, bond investors had a very

rough time for most of the time. Davis (1995) points out that not only bonds in

most countries offered a much lower return, but returns were also marked with

high degree of volatility. He finds that during the period 1967-1990 mean real

return for bonds has been negative for many countries including US (-0.5%),

UK (-0.5%), Sweden (-0.9%), and Australia (-2.7%). The corresponding

standard deviation of returns for these four countries has been 14.3%, 13%,

8.5%, and 14.7% respectively. Remarkably, for USA, the standard deviation of

real returns for bonds almost matched that for equities (14.4%) during this

period.

Given the existence of an equity premium for most of the last century and very

little probability of it turning negative when one considers a longer holding

period (Siegel, 2003), some commentators feel that retirement plan participants

should invest nearly all of their contributions in equities, especially when they

55

are young and therefore, have a long investment horizon25. Using US market

data for the 1926-1997 period, Hickman et al. (2001) examine relative

performance of bills, bonds, and stocks by employing sampling with

replacement and estimating period-by-period return differentials. They conclude

that for investors with holding periods of 20 years or more, investing in any

asset class other than equity results in substantially less expected terminal

wealth, while imparting little risk reduction benefits in compensation.

By examining the case of college and university endowment funds that

traditionally hold a 60:40 mix of stocks and bonds, Thaler and Williamson

(1994) demonstrates that an allocation of 100% of their assets to equities with

some tactical adjustments is likely to provide superior results most of the time.

Although individual retirement accounts under defined contribution pension

plans do not have a quasi-infinite investment horizon as enjoyed by university

endowment funds, a holding period of 30-40 years, as is the case for most

employees may be considered sufficiently long to warrant more aggressive

allocation than currently chosen by most plan sponsors for their default

investment options. An examination of the international evidence presented by

Dimson et al. (2002) seems to validate this point. The real returns for equities

for every 30-year and 40-year period starting at 1900 and observed at 10 year

intervals thereafter till 2000 has always been positive for most countries

including US, UK, and Australia. The equity premium has also been positive for

all the corresponding periods. However, the same cannot be said about the real

returns for bond and bills since both of these asset classes generated negative

returns for some of the observed 30-year and 40-year holding periods during the

last century. For example, real returns for Australian bonds were negative for 3

out of 8 observed 30-year periods (1940-1969, 1950-1979, and 1960-1989) and

2 out of 7 observed 40-year periods (1940-1979 and 1950-1989). Bills in

Australia fared even worse with 3 out of 8 observed 30-year periods (1930-

25 The theoretical basis for this argument is discussed later in this chapter.

56

1959, 1940-1969, and 1950-1979) and 4 out of 7 observed 40-year periods

(1920-59, 1930-69, 1940-1979 and 1950-1989) yielding negative real returns

and 1 observed 40-year period (1910-1949) yielding zero real return to the

investors.

2.7 Measures of Risk

An analysis of the arguments used in the previous sections reveal that differing

perceptions and definitions of risk used by the opposing camps lie at the heart of

the debates related to the superiority of equities for long term investors and time

diversification. In investment management, risk plays a central role along with

expected return in analysis the desirability of different outcomes. According to

Ludvik (1994), the perception of risk and its measurement is critical to the

choice of an investment strategy. Since this research seeks to evaluate the risk-

return trade-off of alternative asset allocation strategies, it would be appropriate

to review some of the important risk measures which can be employed by our

study.

The Oxford Dictionary describes risk as ‘hazard, chance of bad consequences,

loss etc’. Traditionally, the standard deviation (or its square, the variance) has

been the most widely used measure of risk in finance. In his seminal work,

Markowitz (1952) adopted the use of standard deviation to measure portfolio

risk and it has been used as a general measure of risk by finance researchers ever

since. Variance is given by

∑=

−=k

r

rk 1

22 )(1 µσ (19)

where � is the mean return, r is the return for a particular period and k is the

number of periods. This is used under the assumption that higher the variance

(or standard deviation), higher is the risk. If return distributions are normally

57

distributed or the investors have quadratic utility functions, variance or standard

deviation is a suitable measure of asset or portfolio risk (Oberuc, 2004).

By its very definition, standard deviation captures the dispersion on both sides

of the mean and therefore serves as a good statistical measure of variability. In

case of investment returns, it measures the volatility of returns over a given

period of time. But according to many academics and practitioners, volatility or

uncertainty is not necessarily risk because most people think about risk as the

possibility of unpleasant outcome (Balzer, 1994; Dowd, 2002). Their criticism

of standard deviation is principally based on the fact that it treats upside and

downside deviations equally. Therefore, if standard deviation (or variance) is

used as a risk measure, above-average performance (causing upside deviations)

are penalised as much as below-average performance (causing downside

deviations). Most investors may find this counterintuitive to their perception of

risk since they are likely to be more concerned about the below-average

performance of their investment. Among other shortcomings of standard

deviation as a measure of investment risk is that it leads to misleading

propositions when return distributions are not normal (Balzer, 1994, 2005).

It has long been recognized that investors view risk as the possibility of not

being able to meet their investment objectives i.e. chance of failing to meet their

target outcome.26 In such case, risk is only influenced by the returns below the

target and therefore, below-target losses are weighed more heavily by investors

than gains. This view of ‘downside’ risk has been noted by many researchers in

finance, economics, and psychology.27 Roy’s (1952) concept that an investor

may prefer the safety of principal first when facing uncertainty first drew the

26 For institutional investors, this may mean the risk of underperforming a particular benchmark index like ASX All Ordinaries and for pension plan participants it can be the risk of underperforming the rate of inflation. 27 For a comprehensive review of early literature, see Libby and Fishburn (1979).

58

attention of academic community towards downside risk measures. Markowitz

(1959) recognized the importance of minimizing downside risk in a portfolio

selection context if (i) returns are not normally distributed (as assumed in mean-

variance framework) or (ii) only downside risk or safety first is relevant to an

investor. He suggested using a semivariance computed from mean return

(below-mean semi-variance) in the first case and a semi-variance computed

from a target return (below-target semivariance).28 The theoretical superiority of

semi-variance over variance as measure of risk has later been demonstrated by

several researchers (Quirk & Saposnik, 1962; Ang & Chua, 1979). Mao (1970)

also argues strongly that investors are only interested in downside risk and

therefore semivariance is the relevant measure of risk.

Research on downside risk measures received boost from the development of

the lower partial moment (LPM) risk measure by Bawa (1975) and Fishburn

(1977). This risk measure could accommodate different forms of known Von

Neumann-Morgenstern utility functions unlike variance or semi-variance where

investor’s utility function always needs to be quadratic. The LPM can represent

different attitudes of human beings towards risk like risk averse, risk seeking,

and risk neutral. In other words, with LPM there is no limitation on the value of

the risk aversion coefficient used in investment analysis. If λ denotes the risk

tolerance of the investor, then lower partial moment is given by:

λ

λ ∑=

−=K

TTRtMax

KtLPM

1

)](,0[1

),( (20)

where k is the number of periods, t is the target return, TR is the actual return

during the time period T, and Max is the maximization function that selects the

larger between the numbers 0 and )( TRt − . The term λ , which is known as the

degree of lower partial moment (LPM), differentiates LPM from variance or

28 Although different terminologies exist for different semivariance measures like relative semivariance and downside deviation, we would use below-mean and below-target semivariance as these describe the measures more accurately (Nawrocki, 1999).

59

semivariance (and their square root counterparts) because in case of former it

can theoretically assume any value (even fractions) whereas in case of the latter

it is restricted to a single value i.e. 2.

For λ = 0, LPM gives the probability of shortfall i.e. how often the return can

fall below the target although it does not consider how severe the shortfall is

likely to be. If λ = 1, LPM weighs shortfalls (target return less below target

returns) with linear weighting. This is also defined as expected shortfall. For λ

= 2, as explained above, LPM is same as below-target semi-variance. Bawa

(1975) shows that LPM is mathematically related to stochastic dominance when

risk tolerance (λ ) is 0, 1 or 2. For example, for λ = 0, LPM is equivalent to

first order stochastic dominance and therefore investors with common von

Neumann-Morgenstern utility can use LPM (0) to evaluate the return

distribution of investment portfolios. The choice of appropriate shortfall

measure may be guided by the investor’s degree of risk aversion (Bawa, 1978;

Harlow and Rao, 1989) with risk averse investors choosing LPM with λ > 0.

One of the psychological concepts which is increasingly used in economic

analysis is loss aversion. Kahneman and Tversky (1979) first proposed this in

the framework of prospect theory and later also defined for choice under

uncertainty by Tversky and Kahneman (1991). An important aspect of loss

aversion is the fact that it can resolve several paradoxes in traditional choice

theory as well as the criticism of expected utility put forward by Rabin (2000)

and Rabin and Thaler (2001) who showed that reasonable degrees of risk

aversion for small and moderate stakes imply unreasonable high degrees of risk

aversion for large stakes. If DC plan participants are believed to be loss averse

towards the value of their retirement assets, which can be considered as a ‘large

stake’, the plan sponsors may decide to select asset allocation strategies that

have more chance of avoiding the most disastrous outcomes. In other words, DC

60

plans would select strategies that lower the estimates of tail risk of the

probability distribution of retirement wealth as their default investment option.

A popular measure of tail risk increasingly used by academics and practitioners

is value at risk (VaR). Pioneered by JP Morgan, it was originally used as a

single aggregate measure of risks across different trading positions of an

institution which gave the management an estimate of maximum likely loss for

the next trading day (Dowd, 2005).

In a portfolio context, if p represents the probability of worst percentage of

outcomes the investor is concerned about, α is the confidence level and p is set

such that α−= 1p , and if qpis the p-quantile of a portfolio’s prospective

profit/loss over some holding period, then the portfolio VaR at that confidence

level is given by

VaR = -qp (21)

In other words, VaR is represented by the negative of the qpquantile of the

profit/loss distribution. The parameter α indicates the likelihood that the

investor would not get an outcome worse than VaR. The VaR, therefore, is

critically dependent on the choice of confidence level (α ) as well as the length

of the holding period (Dowd, 2005).

The concept of VaR is simple and straightforward and easy to understand.

Losses greater than VaR are suffered only in extreme circumstances the

probability of occurrence of which can be specified by the user. Therefore, VaR

for time period T is given by TR such that Probability (TR <VaR) = α , where

α is set by the investor according to his or her degree of risk aversion. The

higher the degree of risk aversion, higher is the value of α and vice versa. In

case of distributions that are not normal or lognormal, where standard deviation

61

is not a good indicator for volatility especially downside risk, VaR can be

effectively used because one can empirically determine at what point in the data

set probability ( TR <VaR) equals α (Messina, 2005).

VaR, as a risk measure, is not without distinctive shortcomings. Although it

specifies the amount at risk at a particular probability level, it gives the users no

idea about the amount at risk at higher or lower levels of probability (Balzer,

1994). The failure of VaR to consider magnitude of losses greater than itself can

lead to serious underestimation of risk. Dowd (2005) points out that investors

may be exposed to extremely unfavourable outcomes if they use VaR as the

only measure of risk since they may accept any investment that increases

expected return regardless of the possible loss provided that such loss is only

insufficiently probable. A more serious drawback of VaR is that it is not

subadditive29 and therefore cannot fulfil a necessary axiom of being qualified as

a coherent risk measure (Acerbi, 2004).

While VaR has its use as a quantile measure, expected shortfall (ES) or expected

tail loss (ETL) is often forwarded as a better candidate for risk measurement

since it overcomes the limitation of VaR in satisfying the axioms of coherency.

Dowd (2005) defines it as the probability weighted average of tail losses. This

can be formally represented by

∫−=

1

1

1

αα α

dpqETL p (22)

Therefore, ETL is actually the average of the worst 100(1- )α % of the

outcomes. Risk-return decision rules based on ETL are valid under more

general conditions and consistent with expected utility maximisation where risks

29 The theory of coherent risk measures proposed by Artzner et al. (1997, 1999) postulates that the axioms of coherency includes the property of subadditivity, which means that aggregating risks does not increase overall risk. This is consistent with investment theory that diversification leads to reduction of risk when assets are not perfectly correlated. If assets are perfectly correlated, diversification would leave level of risk unchanged.

62

are rankable by second-order stochastic dominance, whereas decision rules

based on VaR are valid under more stringent conditions and only consistent with

expected utility maximization if risks are rankable by first order stochastic

dominance (Yoshiba & Yamai, 2002). Apart from being theoretically superior as

a risk measure, expected shortfall also offers an important practical advantage

over VaR because it tells the user about the potential exposure to losses for

outcomes that are worse than VaR (Dowd, 2005). However, Yoshiba and Yamai

(2002) show that expected shortfall fails to take into account extreme loss events

and may lead to incorrect selection for investments not ranked by second-order

stochastic dominance. They find the second lower partial moment to be more

effective in such cases.

2.8 Measures of Investment Performance

Measuring investment outcomes is critical to the current research since this

would form the basis of evaluating different asset allocation strategies. There are

two general approaches that have been most used by researchers to evaluate the

attractiveness of investment return distributions. The first approach is to select a

preference function and use its expected value as decision criterion. The

classical route to model preferences in finance theory is by means of a utility

function, the shape of which represents the risk attitude of the individual. The

modern portfolio theory developed by Markowitz (1952) uses expected return of

individual assets and their variance-covariance to derive an efficient frontier

such that every portfolio lying on it maximised the expected return for a given

variance of the portfolio. Selecting a portfolio from those lying on the efficient

frontier is a risk-return trade-off problem for the investor which according to

Markowitz is accomplished by maximising his or her quadratic utility function

of the following form:

63

2)( kwwwU −= (23)

where w is the wealth level and 0>k

Hicks (1962) and Arrow (1971) has pointed out this implies increasing absolute

risk aversion (IARA). But this contradicts with research evidence that indicates

decreasing absolute risk aversion (DARA) is more consistent with observed

human behaviour (Pratt, 1964; Arrow, 1971). In such a scenario, mean-variance

paradigm can only be valid if returns are normally distributed (Cass & Stiglitz,

1970). But this assumption is not acceptable to most analysts and practitioners

(Michaud, 1998).

Behavioural research in recent times also point out that preferences of

individuals cannot be characterised by one global degree of risk aversion.

Kahneman and Tversky (1979) show that an individual may demonstrate

different degrees of risk aversion at different future wealth levels relative to

current wealth. According to them, for values of future wealth below current

wealth, the investors would be risk-seeking in their behaviour while for values

above current wealth, they are likely to show risk aversion.

Because of the lack of specificity in investors’ utility functions (e.g. Rubinstein,

1973) and complexity involved in dealing with them, there have been attempts

to depart from the utility based framework and use more objective criteria to

rank portfolios. This has given birth to risk-adjusted performance measures

which combine a return and a risk measure into a composite measure to rank

investment alternatives. Unlike preference functions, they do not involve any

explicit modelling of the investors’ risk attitudes. These measures are generally

devised by dividing the return measure by the risk measure or by subtracting the

latter from the former (Platinga & De Groot, 2005).

64

Traditionally, both academics and practitioners in investment management have

favoured use of reward-to-risk ratios as measures of portfolio performance. The

best example of this is the Sharpe (1966) measure, popularly known as the

Sharpe Ratio (SR). This is given by

pfp RRSR σ/)( −= (24)

where pR is the return on the portfolio, fR is the riskless rate of return, and

pσ is the standard deviation of the portfolio.

A similar reward to risk ratio has also been given by Treynor (1965) which is

exactly the same as Sharpe Ratio except that it employs beta, a measure of

systematic risk of the portfolio, instead of standard deviation in its denominator.

This is represented mathematically as

pfp RRTreynor β/)( −= (25)

In addition to the Sharpe and Treynor measures, a number of other performance

measures have been developed from the modern portfolio theory and the capital

asset pricing model (CAPM). Most of these measures employ a benchmark

portfolio to calculate the performance outcome. Most well known of this

measures is given by Jensen (1968) which is based on CAPM and evaluates the

performance of the portfolio relative to that of the market index.

However, not all performance measures strictly work within the risk-return

framework of Portfolio theory. As discussed in 2.7, researchers have

increasingly questioned the concept of risk given by mean-variance paradigm of

Markowitz. Roy (1952) proposes an alternative known as safety first principle.

According to this an investor is concerned about limiting the risk of

unfavourable outcomes and therefore, specifies a minimum acceptable rate of

return30. According to Roy, the investor would prefer the investment which has

lowest probability of producing return below such specified floor rate. This

30 Roy refers to this as ‘disaster level’

65

leads to the formulation of an alternative reward to variability ratio (also known

as safety first ratio) mathematically represented by

Roy’s Reward-to-variability Ratio = ptp RR σ/)( − (26)

where tR is the minimum acceptable return (MAR) to the investor. The investor

would choose the investment which maximizes the safety first ratio which is

equivalent to minimizing the probability of returns below the minimum

acceptable level. A closer look at the safety first criterion would reveal that it is

very similar to the previously discussed reward-risk ratios. For example, if the

minimum acceptable return (tR ) for the investor is equal to the riskless rate of

return ( fR ), the safety first ratio becomes identical to the Sharpe ratio. In fact, it

has been mathematically proven that the portfolio that maximizes Roy’s safety

first criterion must lie along the efficient frontier in the mean-variance space

(Elton and Gruber, 1995).

Since the above performance measure depends on the assumption of normal

distribution of returns, researchers have questioned their validity. Klemkosky

(1973), and Ang and Chua (1979) demonstrate that these measures can lead to

incorrect rankings of performance and suggest the reward-to-semivariance

(R/SV) ratio as an alternative. While the numerator in this ratio represents the

excess return above target i.e. ( tp RR − ), the semivariance used in the

denominator is usually the ‘below target semivariance’.

The concept of downside deviation has been used to suggest several risk-

adjusted performance measures, especially in practitioner literature. The most

well-known among these is the Sortino ratio introduced by Sortino and Price

(1994). This is given by

δtp RR

Sortino−

= (27)

66

where δ denotes downside deviation. Thus, the Sortino ratio constructs a risk-

adjusted performance measure by replacing the standard deviation with the

downside risk measure and therefore, is equivalent to the Sharpe ratio but in a

mean-downside deviation space. Due to this formulation, it does not penalise

performance for volatility above the target rate of return for the investor unlike

the Sharpe ratio.

Recent research in behavioural finance suggests that, contrary to the

prescriptions of the portfolio theory, individuals may not be seeking the highest

return for a given level of risk. Statman and Shefrin (1998) claim that investors

seek upside potential with downside protection. According to the normative

utility function of Fishburn (1977), individuals are risk averse below a minimum

acceptable rate of return and risk neutral above it. Sortino, Van der Meer, and

Platinga (1999) propose a performance statistic that accommodates the above

suggestions. They do so by suggesting that the return should be replaced with

the upside potential of an investment relative to MAR. This is known as the

upside potential ratio (UPR) and measures upside potential relative to the

downside variance. Mathematically,

( )

( )2

1

2

−

−=

∑

∑

∞−

∞

t

t

R

tp

Rtp

RR

RR

UPR (28)

The numerator of the UPR is the probability weighted summation of returns

above the minimum acceptable rate and therefore represents the upside

potential. The denominator is same as the downside risk calculated by Sortino

and Van der Meer (1991).

Nawrocki (1999) is critical of the popular performance measures based on

downside risk because they do not include the different levels of the investor’s

67

risk aversion. For example the UPR only uses the square root of the below target

semivariance (when risk tolerance parameter a=2) and therefore, ignores other

levels of risk aversion that are available to the users of lower partial moment.

This problem may be overcome by employing more general reward-to-LPM

ratio and setting the value of n to match the degree of risk aversion of the

investor.

In evaluation of investment alternatives, whether based on maximization of

expected utility or risk-adjusted performance, it is generally assumed that the

investor is only exposed to the ‘risk’ which is inherent in the returns and

therefore can successfully trade this off against expected rewards. However,

Ellsberg (1961) among others, argues that the investors may not have all of the

information required to form such expectations because of uncertainty about the

future state of the world. In this situation of ambiguity, investors may

demonstrate loss aversion (as discussed in 2.7) where they want to make sure

that they would be able to provide for themselves if the future conditions fall

short of their expectations. Savage (1951) discusses the minmax principle and

suggests an alternative- the minmax-regret principle.31 Among recent work,

Shirland and Gatti (2005) propose a ‘maxi-min’ and ‘mini-max’ framework for

portfolio choice. The former selects the alternative which maximises the worst n

percentile of outcomes, where n is set by the investors according to their risk

tolerance level. Alternatively, the ‘mini-max’ rule chooses the strategy which

minimizes regret.32 Quantile risk measures like VaR, which ensures that the

investor’s wealth does not fall below a certain specified level qpwith a

probability level of at least α (as shown in 2.7 ) can be used in this kind of

framework to rank alternative asset allocation strategies.

31 Minmax is a well accepted technique in the statistical decision making literature (see e.g. Wald, 1950). 32 The authors measure this as difference between the pay-off from maxi-min strategy and the highest pay-off that would prevail in some better state of the world.

68

3. Methodology and Data

3.1 Model Description

We follow the steps outlined in Dowd (2005) in applying the simulation

methodology to the retirement wealth problem. The first of these involves

designing a model to generate retirement wealth outcomes which accommodates

the stochastic variable(s) of interest and other variables embedded in DC plans.

It is important to bear in mind that this model for generating retirement wealth

outcomes is distinct from the asset return generating model described in 3.2.

3.1.1 General Structure

We develop a DC plan accumulation model which uses stochastic simulation to

determine the expected distribution of retirement wealth outcome for the

accumulation phase, which is measured in terms of the ratio of the terminal

wealth at the point of retirement to the final salary of the plan participant.

The terminal value of DC plan portfolio is given by

∏∑−

+=

−

=++−=

1

1

1

0

)1()1()1(R

tuut

R

ttt rrSpkW (29)

where W = value of plan assets accumulated at the point of retirement

k = plan contribution rate

=tp probability of unemployment in year t

=tS annual salary in year t

=tr rate of investment return earned in year t

=R number of years in the plan before retirement

69

To estimate W, we need to model the (i) contribution cash flows and (ii)

investment returns for each period. The contribution cash flows primarily

depend on two variables: annual salary and contribution rate. The annual salary

for any year depends on starting salary, salary growth rate, and the number of

years elapsed since commencing employment. This is given by

10 )1( −+= t

t gSS (30)

where =0S starting salary of the plan participant

=g annual salary growth rate

To model the contribution cash flows, we have also included probability of

unemployment as a variable in our model, because the flow of plan

contributions is likely to be affected by the employment state.

Investment returns are dependent on returns on individual asset classes (included

in the portfolio) and the weights assigned to them. The latter is determined by

the asset allocation strategy of the plan. Mathematically,

∑= titit rwr ,, (31)

where =tiw , weight assigned to the thi asset in year t

=tir , return on the thi asset in year t

While asset allocation strategy is our primary variable of interest, we need to

assign values to other variables in the DC plan accumulation model for

modelling retirement wealth outcomes. Assumptions of DC plan researchers on

simulation model parameters have ranged from illustrative and arbitrary

suppositions (Johnston et al. 2001) to hypothetical estimates based on modelling

with historical data (Blake et al. 2001). For our baseline case, we assign values

that can be considered as reasonable in the current economic context. Although

there is some degree of arbitrariness involved in the process, this is not likely to

70

influence our investigation of the research issue focus on the outcomes of

alternative asset allocation strategies while holding other factors constant.

3.1.2 Control Variables

The model includes three control variables that are set either by the plan

provider or the plan participant.

a) Asset Allocation Strategy ( )iw :

This is the key variable of interest in the model which decides the weights of

different asset classes in the portfolio. For examining our first research question,

we consider actual fixed weight asset allocation strategies used by Australian

superannuation funds in chapter 4. These allocations would be maintained by

annual rebalancing. In chapter 6, we would examine lifecycle and contrarian

asset allocation strategies. In addition to conventional lifecycle strategies,

chapter 7 considers a dynamic asset allocation whereiw would be modified

according to past portfolio performance.

b) Employment Life (R):

The starting age is the age when the employee commences employment and

therefore, becomes a member of the DC plan. In our baseline case, the DC plan

participant joins the plan at the age of 25 years.33 The retirement age is the age

when the contribution to the DC plan ceases. For our baseline case, this is set at

65 years, the current age for Australian males to be eligible for Age Pension.

The employment life (25-65 years) for our baseline case is consistent with

standard assumptions in DC plan literature (e.g. Blake et al., 2001; Dowd, 2005) 33 Although many job starters in Australia belong to the 15-24 years age group, a bulk of such employment is part-time or casual and labour force participation rate is lower compared to those aged 25 years and above. However, the participant rate is also low for 55 years and above category (Australian Bureau of Statistics Year Book Australia, 2006).

71

c) Contribution Rate (k)

For our baseline case, the contribution rate is assumed to be fixed at 9% of the

member’s annual salary, which under Superannuation Guarantee legislation, is

the mandatory minimum rate for employer contributions on behalf of

employees. A more general analysis could consider the possibility of including

voluntary contributions from members as well as future changes in mandatory

contribution rate. For the sake of simplicity, we assume that contributions are

made annually at the end of the year.

3.1.3 Other Variables

a) Asset Class Returns (tir , ):

For chapters 4 and 5, annual real returns for Australian asset classes such as

equities, bonds, and bills are employed. Real returns from US equities and bonds

are used to proxy those from international stocks and bonds respectively. For

chapters 6 and 7, we use nominal returns on US stocks, bonds, and bills. Details

of the dataset are reported in 3.4.1.

b) Earnings ( 0S , g):

Except in chapter 5, where we confront the gender inequity problem in

retirement savings, the earning estimates used in this research are hypothetical.

However this is certainly not going to have any bearing on the results of our

analysis as we hold the estimate constant for all competing allocation strategies

discussed within a chapter. In chapter 4, we assume that the starting annual

salary for the employee to be $25,000. The annual salary is assumed to grow at a

constant real rate of 2%, which closely follows Australia’s growth in real GDP

per person of 2.6% between 1994 and 2004 (Australian Bureau of Statistics

72

[ABS], 2005). In chapter 5, we use actual salary estimates for male and female

Australian workers from ABS. Chapters 6 and 7 use an arbitrary starting salary

estimate of $25,000 and a constant nominal growth rate of 4% for hypothetical

employees enrolled in DC plans in USA.

c) Probability of Unemployment (tp ):

For our simulation experiments in chapters 4 and 5, unemployment is modelled

as a binary variable (1 if employed, 0 if unemployed). The probability of

unemployment during any period of the baseline employee’s working life is

assumed to be constant at 5%. This is equal to the unemployment rate among

Australian workers with post-school qualifications (Kryger, 1999; Richardson,

2006). However we ignore this variable in modelling wealth outcomes in

chapters 6 and 7 since it is not relevant to the concerned research problems.

3.2 Asset Class Return Generating Process

To generate simulated returns for our trials, we employ both Monte Carlo and

bootstrap resampling methods in this thesis. The latter is our preferred return

generating process, the reasons for which are explained later in this section.

However they have two important similarities. First, in our research, both the

processes are modelled under the assumption that asset class return during any

period is serially uncorrelated to its own past returns. In other words, we assume

asset class returns are randomly distributed over time. Second, both methods use

the past returns data of different asset class returns to generate future return

scenarios. The appropriateness of our assumptions and return generation

approach is briefly discussed below.

73

Our assumption that asset class returns follow random walk has its roots in the

well accepted notion of efficiency of financial markets as shown by Samuelson

(1965) and Fama (1965, 1970).34 According to Samuelson, in an information-

efficient market, price changes cannot be predicted if they fully incorporate

information and expectations of all market participants. Fama encapsulated this

idea of efficient markets succinctly- prices fully reflect all available

information.35 Though subsequent empirical research has presented conflicting

evidence on this issue, the random walk still remains arguably the dominant

paradigm for researchers in this field.

Several studies like Goetzmann (1990) and Kim, Nelson, and Startz (1988) have

modelled serial independence of monthly and annual stock returns and have

rejected the notion of mean reversion of long term stock returns in favour of the

more parsimonious random walk model. Poterba and Summers (1988), who find

evidence that financial markets may be subject to time-varying expected returns,

admit that the lack of enough independent observations makes it difficult to

draw convincing conclusions about predictability of returns for low frequency

data. Most empirical studies which have found evidence against the random

walk (for example, Lo and Mackinlay, 1988) have used high frequency data like

daily and weekly returns. Since all the studies included in this dissertation use

annual returns from different asset categories, this is obviously not a major

concern in our case. Also, in recent times, many researchers (for example, Ang

and Bekaert, 2005; Campbell and Yogo, 2006) have shown that predictability in

returns is mainly a short horizon phenomenon and not a long horizon

34 An early version of the random walk hypothesis was proposed in 1900 by French mathematician Louis Bachelier in his doctoral thesis Théorie de la Spéculation. Bachelier’s pioneering work on behaviour of security prices is widely acknowledged by Samuelson and others (Bernstein, 1992) 35 The notion of efficient market hypothesis, however, is distinct from random walk hypothesis. As LeRoy (1973) and many others have shown, random walk is neither a necessary nor a sufficient condition for rationally determined security prices.

74

phenomenon.36 Therefore, the issue may not be of significant importance for

strategic asset allocation decisions of long horizon investors in our research.

3.2.1 Monte Carlo Simulation

This first essay (chapter 4) in this dissertation employs Monte Carlo simulation

(MCS) methodology to evaluate alternative asset allocation strategies by

estimating the DC plan outcomes. MCS was first introduced by Metropolis and

Ulam (1949) and, since then, have been used in several different fields like

physics, biology, and engineering to solve complex problems. This method has

been employed by finance researchers since late 1970s to price derivatives (e.g.

Boyle, 1977) and more recently to estimate VaRs and other financial risk

measures (e.g. Picoult, 1998). It has also been favoured by academics and

actuaries in evaluating risk of both DC and DB type pension plans (Blake et al.,

2001, 2005; Scott, 2002; Johnston, Forbes & Hatem, 2005). The MCS method is

appropriate for this research because it can handle complex and

multidimensional problems like those encountered in investigating DC plans,

where the retirement outcome is dependent on more than one risk variable. It

can address problems related to factors like path dependency, non-linearity, and

optionality, which most analytical approaches have difficulty in dealing with.

MCS is a general method of modelling stochastic processes by simulating them

using random numbers drawn from probability distributions that are assumed to

describe accurately the uncertain elements of the processes being modelled.

Unlike historical simulation, which does not assume any theoretical distribution,

36 Campbell (2003) reports long horizon predictability for UK, France, and Germany. But Ang and Baekart (2005) points out that this conclusion is critically dependent on their use of Newey-West (1987) standard errors and disappears when Hodrick (1992) standard errors, more appropriate for small samples as argued by the authors, are employed. Using other error correction methods like Richardson and Smith (1991) also supports their conclusions.

75

MCS estimates statistical parameters (like standard deviation and correlation)

from historical data series and then expose these to random changes to simulate

future outcomes. In its common form, the one which would be used in this

research, MCS assumes that returns from different asset classes are normally

distributed and their correlations are stable over time.37

The general idea for Monte Carlo studies as described in Kennedy (2003) is to

(i) model the data generating process, (ii) generate several sets of artificial data,

(iii) employ the data and estimator to create several estimates, and (iv) use these

estimates to gauge the sampling distribution properties of the estimator. We

briefly describe these stages below in relation to our study.

The key objective of this study is to draw comparisons between retirement

wealth outcomes of alternative asset allocation strategies. In doing so, perhaps

the most critical step is to develop a model which generates returns for different

asset classes over multiple periods. In Monte Carlo methods, a sample size of N

is considered to fix the parameters at certain values and then draw repeated

samples from the distribution of the error term. Since we follow standard Monte

Carlo simulation assuming that asset returns are drawn from a multivariate

normal distribution, the implication is that mean and standard deviation of asset

returns are time invariant and the returns are independent over the time horizon.

At each stage of the simulation horizon, the random shocks generated by the

multivariate normal model are adjusted so as to follow the average cross-

sectional correlation observed in the historical data. The correlation-based

dependence structure for Monte Carlo analysis is derived through either

Cholesky decomposition or principal component analysis (Picoult, 1998). The

former method is used in this research. If ijlL =1 is the lower-triangular

37 Incorporating complex features like fat tails, skewness, and dynamic correlations is desirable for accurate estimates of outcomes. But since in this research, we are primarily concerned with evaluating outcomes of alternative strategies to comment on their relative appeal, the basic Monte Carlo method is expected to adequately serve the purpose.

76

Cholesky decomposition of the correlation matrix ,C iµ be mean return on the

asset ,i and iσ be the standard deviation of return on asset ,i then for a

portfolio of n assets, the multivariate normal Monte Carlo model dictates that

∑=

=n

jjiji lZ

1

ξ (32)

where ξ denotes an independent standard normal random variable

(i.i.d. ))1,0(N≈ and where iZ represents a correlated standard normal variable

for asset i . The simulated return on asset i is then obtained as

iiii Zr σµ += (33)

Having selected the model, we estimate the parameters of asset classes – mean,

standard deviations, correlations – on the basis of historical return data, which is

described in 3.3.1. With the model of the data generating process already built in

MATLAB, we can generate several sets of artificial data sets for asset class

returns using random numbers. The MATLAB function MVNRND (MU,

SIGMA) returns an n-by-d matrix R of random vectors chosen from the

multivariate normal distribution with mean vector MU and covariance matrix

SIGMA. MU is an n-by-d matrix, and MVNRND generates each row of R

using the corresponding row of MU. SIGMA is d-by-d symmetric positive

semi-definite matrix, or a d-by-d-by-n array. These simulated return paths are

then combined with individual asset class weightings to obtain simulated

portfolio returns under each asset allocation strategy under investigation for

every period of the investment horizon.

The above portfolio returns are applied to contribution flows for the

corresponding periods to derive hypothetical retirement wealth outcomes

according to the simulation model for retirement wealth described in 3.1.1. The

simulation trials are then repeated many times to be reasonably confident that

the simulated distribution would be sufficiently close to the actual distribution.

77

The Monte Carlo simulation method as described above is not free from

shortcomings. The major concern for the researcher is that it requires strict

assumptions about the probability distribution of asset class returns. Although

we generate returns for the asset classes under the standard assumption that they

follow a multivariate normal distribution, the presence of skewness and fat tail

to some degree in data for different sample periods cannot be ruled out.38

Second, the simulation method assumes that the asset class returns are

independently distributed over time i.e. there is no correlation of returns of any

asset class with its own past returns. This disregards the possibility of any return

persistence or mean reversion in asset class returns. Finally, the assumption that

cross-asset correlation is constant over time may be inaccurate and simplistic if,

for instance, the equity risk premium is believed to be time-varying.

3.2.2 Bootstrap Resampling

The Monte Carlo method relies on strong assumptions about the distribution of

returns. In any Monte Carlo study errors must be drawn from a known

distribution. For instance, we assume asset class return distributions over long

horizons are multivariate normal. However, imposing such explicit distributional

assumptions on the return generating process is open to question and may at

times pose a serious threat to the acceptance of the results of such exercise by

the research community. This is a major drawback of the traditional Monte

Carlo method. Therefore, to adjust for this problem, we resort to an alternative

non-parametric method of return generation namely bootstrap resampling which

does not require the researcher to make such an onerous assumption.

38 However, this is more of a problem with high frequency data (for example, daily or weekly returns). In general, research suggests that monthly returns are well described by normal distributions (for example, Hagerman (1978))

78

The basic idea of resampling is to pick repeated samples at random from a

hypothetical population of interest. Very often this is based on the data sample

in hand. Since authentic data on past returns goes back to little more than the last

hundred years, it can be considered as a sample of the whole unknown

population. Hence we have to take several samples out of this sample as a way

of understanding the consequences of sampling variability for making inferences

about the unknown population based on our dataset, which itself is a sample of

the whole population. This, in essence, is resampling.

There are several methods of drawing random samples from a given sample of

data. Two well-known methods are the jackknife introduced by Quenouille

(1956) and the bootstrap introduced by Efron (1979). In both these methods, the

given data sample is reused many times to generate further samples. The

jackknife method, which deletes a number of datapoints at each cycle of

computation, is not commonly used in econometrics (Maddala, 2002). The

bootstrap method, which is frequently used in this research to generate asset

class returns, is briefly described below.

The bootstrap procedure is a popular econometric technique generally employed

to estimate sampling distributions by using only the original data and so “pulls

itself by its own bootstrap” (Kennedy, 2003). The asset class return data in our

sample are randomly drawn, with replacement, every period to create new return

samples over the investment horizon. If ( ),....., 21 irrr be the given sample and we

draw a sample of size n (= number of periods) with replacement, then

),......,( 21 nj RRRB = represents a bootstrap sample if each iR is randomly

selected from ( ),....., 21 irrr . The process is repeated for mj ,......2,1= where m is

the number of simulation trials.

79

It is no trivial matter that we choose to resample with replacement. It has to be

borne in mind that the actual population of interest is much bigger than our

sample of data ( ),....., 21 irrr . For example, in our dataset, i = 105 whereas the

sample size usually used in our simulation experiments is given by n = 40 (often

the length of investment horizon of the retirement plan participant) which means

there are only 2 complete non-overlapping samples in the dataset. In order to

make the dataset appear larger than it is, we need to draw repeated samples of

size n = 40 from the dataset with replacement. This allows for creation of

virtually unlimited number of samples to enable inferences to be drawn about

the unknown parameter of interest. To conduct bootstrap resampling with

replacement, we employ a MATLAB program called resamp developed by

Kaplan (1999). When applied to a data in the form of a matrix p x q, resamp (n,

data) randomly draws row by row n times i.e. n number of vectors (if the chosen

sample size is n). In other words, the random sampling process continues until

the number of drawn observations corresponds to the length of the investment

horizon. For M number of trials, the resampling process is repeated M times.

Since the given data can be rearranged in numerous different combinations,

bootstrapping can generate a dramatically larger number of future scenarios

compared to historical simulations which sample data sequentially. Since we

allow for resampling with replacement, the possibility of observing a wider

range of scenarios is also considerably larger which is informative in assessment

of extreme downside risk. Like the Monte Carlo method, the bootstrap

resampling destroys any serial correlation that may exist in the return data for

individual asset classes.39 This does not allow the researcher to capture any

positive (persistence) or negative (mean reversion) serial correlation in asset

39 Resampling can also be conducted using a ‘moving block bootstrap’ method introduced by Carlstein (1986) and Künsch (1989) which aim to capture any time dependence structure in the dataset as well as preserve cross-sectional correlation within the block, the length of which has to be specified by the researcher. However, as discussed earlier, we assume that asset class returns are serially uncorrelated and therefore, refrain from employing such approach in generating future returns from historical data.

80

class returns. However, the row-by-row resampling permits preservation of the

cross-asset correlation.

For the first study in this dissertation, we use both MCS and bootstrap

resampling separately to simulate asset class returns which are then used to

estimate potential wealth outcomes. Since the results after many trials are found

to be extremely close in the two cases, we use the latter method only in the

subsequent chapters (5, 6, and 7). Our preference for the bootstrap resampling

method is obviously influenced by its relative advantage (over MCS) in not

requiring the researcher to make any kind of assumption about the distribution

of future asset class returns.

3.3 Data

To evaluate the retirement wealth outcomes of different asset allocation

strategies using the simulation model discussed in 3.1.1, it has to be provided

with two key inputs. These are return data and the respective weight of each

asset class. Historical data for asset class returns would be used to generate

simulated investment return for each asset class for every period of the

investment horizon. The weights of the individual asset classes, which depend

on the allocation strategy, would be multiplied by their respective simulated

returns and then added up to generate the portfolio return for every period.

3.3.1 Asset Class Returns

As many authors have indicated, the issue of strategic asset allocation for long

horizon investors like DC plan participants should be based on historical

81

observations of asset class returns over decades rather than short periods.40 This

is essential to neutralise the undue influence that recent investment performance

(of these asset classes) may have on long-term risk assessment and asset

allocation decisions. Ceteris paribus, a longer period of data has a higher chance

of capturing the wide-ranging effects of favourable and unfavourable events of

history on returns of individual asset classes.

The source of the asset class return for this research program is the dataset of

global returns compiled by Dimson et al. (2002) and commercially available

through Ibbotson Associates, Chicago. An updated version of this dataset which

provides global returns from 1900 to 2004 has been used in this dissertation.

This is the only authentic dataset available for long term nominal and real

returns from bills, bonds, and equities in 16 countries including Australia. It is

unique in the sense that it covers a period of more than 100 years starting from

1900. Apart from returns on Australian asset classes, the returns for US

equities, bonds, and bills used in this thesis are also sourced from this dataset.

All returns are annual and include reinvested income and capital gains. Return

data is available in the domestic currency (Australian dollars for Australian asset

classes) as well as in US dollars. For chapters 4 and 5, returns in Australian

Dollars are used while for chapters 6 and 7, we use return data measured in US

Dollars.

The above dataset has used equity return data compiled by Officer which is

described in Ball, Brown, Finn, and Officer (1989). Officer uses a variety of

indexes in his work including Lamberton’s (1958) classic study to calculate

Australian equity return data for the early period. This is linked for the period

over 1958-74 to an accumulation index of fifty shares from the Australian

Graduate School of Management (AGSM) and for 1975-1979 to the AGSM

40 Short term return data, however, is useful if the focus is on short term volatility (Dimson et al. 2002)

82

value-weighted accumulation index. The Australia All-Ordinaries index is used

thereafter.

For bonds, the returns are based on the yields on New South Wales government

securities for 1900-1914, Commonwealth Government Securities of at least five

years maturity for 1915-1949, and ten-year Commonwealth Government Bonds

during 1950-1986. From 1987, JP Morgan Australian Government Bond Index

has been used to compute returns.

The dataset uses a 3-month time deposit rate to calculate cash returns for 1900-

1928. Then onwards, the Treasury bill rate has been used. Inflation rate has been

based on the GDP deflator (1900-01), retail price index (1902-48), and

consumer price index (1949 onwards). The switch from Australian pounds to

Australian dollars in 1966 has also been taken into account while computing

returns.

For computing the returns for US stocks, the dataset uses the Wilson-Jones

index data for the period 1900-25. For 1926-1961, the returns are obtained using

the University of Chicago’s Center for Research in Security Prices (CRSP)

capitalisation-weighted index of all stocks listed in New York Stock Exchange

(NYSE). For 1962-70, the dataset uses the CRSP capitalisation-weighted index

of NYSE and Amex stocks. The Wiltshire 5000 index is employed from 1971

onward.41 All the indices include reinvested dividends.

To compute returns from US bonds, the dataset uses 4 percent government

bonds for 1900-18 period. Returns for 1919-25 are based on Federal Reserve

ten-to-fifteen year bond index. Thereafter, the Ibbotson Associates’ long bond

index is used to calculate bond returns.

41 By end of 2000, this index included over 7000 stocks listed in NYSE, Amex, Nasdaq, and other exchanges.

83

The US bill returns are based on commercial bills during 1900-18. From 1919

onward, the return series is based on US treasury bills.

3.3.2Asset Allocation of Default Strategies

For our analysis in chapter 4, we examine several asset allocation strategies that

are actually used as default choices by superannuation funds in Australia. We

select funds that have been highly rated for their performance by SuperRatings,

an independent research organisation which rates Australian superannuation

funds annually. Details of the data used in this research are provided in 4.3.

3.3.3 Earnings Data

The earnings data for Australian male and female workers by age categories

used in chapter 5 are sourced from Australian Bureau of Statistics (ABS) 2001

Census of Population and Housing. Details of the dataset are available in 5.3.1.

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4. Evaluation of Fixed Weight Strategies as Default Options

4.1 Introduction

4.1.1 Background

In most developed countries policymakers are encouraging funded private

retirement plans (generally sponsored by employers or other private providers)

known as defined contribution (DC) plans, where employee participants build

up retirement savings through mandatory or voluntary contributions in their

individual retirement accounts. Retirement benefits of participants in these

plans are entirely dependent on the accumulation of plan contributions and

investment returns earned on those assets. A growing trend in DC plans is to

give the individual participants more control over investment of their plan

assets. For instance, DC plan participants are expected to select an investment

option from a menu of investment choices provided by the plan sponsor. This

investment decision is critical because it determines future investment returns on

their plan assets, and therefore, influences the wealth accumulated in the

retirement account at the end of the participant’s working life.

A substantial body of recent research demonstrates that although members of

retirement plans have the option to exercise choice, most accept the default

arrangements offered by their plans. The work of Choi et al. (2003) finds that

American employees tend to accept default arrangements in their plans for

critical features like contribution rate and investment choice. In their study, up

to 80 % of assets in different plans are invested in the default fund. In a recent

study conducted by Beshears et al. (2006), around 9 out of 10 existing

85

employees who were subject to automatic enrolment in the company retirement

plan were found to have some of their assets invested in default fund, with

around two-thirds having all their assets in the default fund.

The apparent reluctance of the plan participants to exercise active investment

choice is corroborated by international evidence. According to consulting firm

Hewitt Bacon and Woodrow, around 80 % of group personal pension scheme

members in UK accept the default option provided by their plans (Bridgeland,

2002). Similarly, Cronqvist and Thaler (2004) find that since 2003 only 10% of

the new participants in Swedish retirement plans actually made any choice. In

Australia, about two-thirds of all retirement plan assets are invested in default

investment options (APRA, 2005). It seems that for a large majority of DC plan

participants worldwide, the investment of plan contributions are dictated by the

default arrangement of their respective plans.

Given that most plan participants tend to accept default investment options in

their plans, perhaps it is more important, from a practical standpoint, to question

whether these default investment options are appropriately designed to meet the

retirement goals of the participants. This issue has received little research

interest, which is surprising because financial well being for a majority of plan

participants after retirement is directly linked to the performance of the default

options. Moreover, international evidence like Blake, Byrne, Cairns, and Dowd

(2006) indicates that there is serious lack of agreement on this subject which is

reflected in the wide disparity in benchmark asset allocation of default funds

chosen by different plan providers.

The question of appropriateness of the default options is no less pertinent for

countries where these are less heterogeneous in terms of strategic asset

allocation. For instance, Utkus (2004) points out that majority of the plans in

the United States choose a money market or stable value fund as default

86

investment option although such arrangements are inconsistent with two of the

‘prudent investor’ principles on asset allocation underlying most participant

education programs: first, the existence of positive equity risk premium; and,

second, the change in the investor’s risk-taking capacity with age.42

4.1.2 Research Description

In this chapter, we examine the appropriateness of various asset allocation

strategies adopted by DC plans in Australia as default options. The importance

of asset allocation in influencing investment performance has been well

demonstrated by many researchers (Brinson et al., 1986; Blake et al., 1999).

Therefore, one would expect that the asset allocation strategies of default

options are decided with utmost care - not only because a majority of

participants passively accept the default options offered by their plans - but also

considering that there is evidence (Beshears et al., 2006) to suggest that many

individuals perceive the default choice as recommendation or endorsement of a

particular course of action by the provider.

To investigate the issue of appropriateness of asset allocation strategies used as

default investment vehicles, we find Australian DC plans provide an interesting

avenue for research for three reasons. First, Australia has a well established

private retirement system with nine out of ten employees currently members of

DC plans (APRA, 2005). Since 1992, the Australian Government has made it

compulsory for all employers to make contributions to these plans (known as

‘superannuation funds’) on behalf of their employees (members) at a minimum

42 Utkus (2004) also observes that extant legal provisions permit investments that result in short-term losses to pursue long term gains and do not require the trustees to invest in ‘safe’ assets.

87

specified rate (currently nine % of wage and salary).43 Contribution rates

remaining equal, the differences in the accumulated value of the plan assets for a

vast majority of the members with similar earnings profile is largely reliant on

the investment returns generated by the default investment strategy, which in

turn is heavily influenced by its benchmark asset allocation.

Second, members in Australian superannuation funds directly confront the

classical portfolio choice problem as they are expected to choose an asset

allocation strategy (or a combination of strategies) from a menu of pre-selected

asset allocation strategies provided by the plan providers to invest plan

contributions. This is different from say 401 (k) plans in USA where

participants are offered a choice of mutual funds rather than actual asset classes.

The default investment choice of every Australian superannuation fund clearly

specifies the target allocation among available asset classes; there is no scope for

the researcher to make any conjecture about the precise classification of mutual

funds and commit any error in the process.

Finally, to examine the issue of effectiveness of any strategic asset allocation

policy in the context of wealth accumulation in DC plans, we need to consider

its optimality from the perspective of an investor with long horizon, typically

equalling the participant's employment life. Many plans like 401 (k) may allow

distribution of account balances for participants who change jobs as well as

include loan features against account balances, the investment horizon relevant

to many participants may actually be much shorter. Superannuation funds in

Australia, on the other hand, are prohibited from permitting withdrawal of

superannuation assets by members before they reach the preservation age

(currently 60 years for those born after June 1964).44 These funds also do not

offer any loan feature to members against balance in their individual

43 Many employees are employed under awards that require them to contribute an additional three % of wage to superannuation. 44 Restricted withdrawals are permitted in some extreme circumstances.

88

superannuation accounts. Therefore, the asset allocation structure of the default

options offered by Australian pension funds can be expected to be designed

from a truly long term perspective and less concerned with the impact of short

term volatility in returns on the participant's account balance.

Past research on DC plan investment choices have mostly examined

hypothetical asset allocation strategies. In contrast, our study considers asset

allocation strategies which are actually used by plan providers as default

investment choices. We use more than a hundred years of data for real returns

on different asset classes to simulate the retirement wealth outcomes for a

typical participant whose plan contributions are invested following the default

asset allocation strategies of the top rated superannuation funds in Australia.

For the benefit of analysis, we also simulate wealth outcomes under two

hypothetical allocation strategies: (i) 100% stocks; and, (ii) default option

average (DOA) strategy. The outcomes are then compared to assess their

relative appeal to be nominated as default investment option in DC plans. To

capture the possibility that past returns on any asset class may not represent the

complete range of its expected future returns, we use both parametric and non-

parametric methods in this study to generate simulated returns for the asset

classes.

Poterba et al. (2006) attempt to rank wealth outcomes associated with different

asset allocation strategies for 401(k) plans by using a utility function of

retirement wealth. However, we use risk-adjusted performance measures in lieu

of a utility-based framework to avoid making specific assumptions about the

form of the utility function of DC plan participants. Also, in contrast to most

other studies, we consider downside risk (the risk of the participants falling short

of reaching their target wealth accumulation at retirement) as an important

criterion in selecting an appropriate default strategy for DC plans.

89

To evaluate alternative allocation rules in terms of their ability to meet the

wealth accumulation objective of the plan participants, we employ lower partial

moments as robust measures of downside risk and performance measures which

are adjusted for downside risk. This study also considers the possibility that the

risk of extreme events can influence the plan providers’ choice of default

strategy. We compare these risk estimates under each asset allocation strategy

to rank them in terms of their ability to reduce the potential and severity of the

most adverse outcomes. We also measure variability of outcomes for every

strategy under consideration and compare these estimates as this can form the

basis for selection of default in case plans aim to reduce the disparity in wealth

outcomes between different employee cohorts.

4.1.3 Summary of Findings

Our study reports several key findings. First, asset allocation strategies with

higher allocation to stocks can be expected to result in higher wealth outcomes

for participants. At the same time, the range of wealth outcomes generated by

such strategies can also be expected to be wider. Second, the downside risk of

falling short of the participant’s target wealth outcome is reduced with increased

allocation to stocks in terms of probability as well as magnitude of shortfall.

This holds for participants with different levels of risk tolerance. Our results

also indicate that on most occasions a strategy which invests entirely in stocks

offers highest upside potential and lowest downside risk in relation to retirement

wealth accumulated by participants. Third, contrary to popular belief, we find

that the potential and severity of the most extreme outcomes for DC plan

participants do not seem to increase much with increasing allocation to stocks.

In fact, there is little evidence that the extreme downside or tail-related risks of

DC plan outcomes are sensitive to the choice of asset allocation strategies.

Fourth, the lifecycle strategies which are currently used as defaults by a few

90

Australian plans seem to impart little or no protection to participants from

downside risk. On the other hand, these strategies are found to considerably

erode the value of expected retirement wealth the participants can potentially

accumulate by keeping the initial asset allocation unchanged till retirement.

Therefore, like Booth and Yakoubov (2000), we find little basis for plans

switching assets as participants approach retirement.45

Our findings, although based on simulated wealth outcomes using historical

return data for Australian asset classes, may have important implications for

default investment options for retirement plans in other industrialised nations.

This is because the returns on various asset classes in many of these markets

have displayed broadly similar trend over the last century (Dimson et al., 2002).

4.2 Metrics for Evaluating Retirement Wealth Outcomes

To evaluate asset allocation strategies and assess their appropriateness as default

investment options in DC plans, we need to make plausible assumptions about

the rationale that may guide the selection of a specific asset allocation strategy

as a default option from many competing candidates. The basic motivation

behind instituting retirement savings plans is to generate adequate income for

the participating employees after retirement. In that case, performance of DC

plans should be measured in terms of their ability to generate sufficient

retirement income (Baker et al., 2005). Therefore, it is assumed that the

principal investment objective of such plans is to maximize the terminal value of

plan assets at the point of retirement since that would directly determine the

amount of annuity the retiring employees are able to purchase for sustenance

45 We desist from drawing any general conclusion on lifecycle strategies since we have very few funds in our sample using such strategies and the mode of switching is also different from that of typical lifecycle funds in other countries.

91

during post-retirement life. Past studies have mainly considered the absolute

value of the participant’s accumulated assets at retirement. However, we

employ a ratio which compares the terminal wealth of the participant’s

retirement account to their terminal income because it is very likely that the

participant’s post-retirement income expectations are closely linked to their

immediate income before retirement.46 We call this measure the ‘retirement

wealth ratio’ (RWR). To evaluate asset allocation strategies on the basis of

terminal wealth outcomes we consider the mean, the median, and the quartiles of

the RWR distribution.

Higher estimates of different measures of RWR outcomes do not automatically

qualify a particular strategy to be selected as default option. The trustees also

need to consider the risk associated with investment of plan assets since

participants would want a better exploitation of trade-off between risk and

reward. In finance, the optimal trade-off between reward and risk is generally

determined through Markowitz’s (1952) mean-variance analysis. Yet it can be

shown that in the presence of time-varying investment opportunities, predictable

variation in expected equity risk premium, or mean reversion in stock returns,

risk can be viewed differently by long-term investors than short-term investors

(Campbell and Viciera, 2002). They also point out that mean-variance model

also do not allow for periodic rebalancing of portfolio which is essential for

long-term investors to maintain their strategic asset allocation. Finally, the use

of variance as a measure of risk is questionable especially for long-term

investors like DC plan participants. McEnally (1985) shows that the appropriate

measure for investment risk is the variability of the terminal wealth outcomes

that arise by holding an asset for the intended investment horizon and not the

variability of periodic returns of the asset around its average return. This study

46 This is supported by Booth and Yakoubov (2000), who employ a similar benchmark, that is, the value of accumulated fund at retirement in terms of employee’s salary. In addition, this study uses a broader range of metrics in evaluating the risk-reward characteristics of the outcomes.

92

uses measures of terminal wealth to compute risk (and reward) associated with

different asset allocation strategies. However, we consider shortfall below target

outcome instead of variability of terminal wealth outcomes as measure of risk.

As previously discussed, we assume that the ultimate goal of the DC plan

participants is to attain a specific amount of wealth in DC plan accounts in terms

of their terminal income, which we call the target retirement wealth

ratio )( TRWR . Under this assumption, the investment risk most relevant to

participants is that of failure of their chosen asset allocation strategy to

generate TRWR . This type of ‘downside risk’ is not new to economics or

finance literature. Roy (1952) developed the target rate of return approach in a

portfolio selection context where the investor is concerned about minimizing the

probability of falling below the disaster level or minimum acceptable rate of

return. Mao (1970) presents evidence to show that decision makers conceive

risk as the possibility of outcomes below target. Olsen (1997) also finds that

two of the most important attributes of perceived investment risk are potential

for below target returns and potential for large loss. We capture these two risk

attributes by employing downside risk and tail-related risk metrics respectively.

In this essay, we employ the LPM (Bawa, 1975; Fishburn, 1977) to measure

downside risk of different asset allocation strategies. The relative advantages of

using LPM as a measure of risk have already been enumerated in 2.7. In the

retirement portfolio context, if λ denotes the risk tolerance of the plan

participant, then lower partial moment of retirement wealth outcomes is given

by

λ

λ ∑=

−=n

ttT RWRRWRMax

nLPM

1

)](,0[1

(34)

where TRWR is the target outcome, tRWRis the outcome for the t-th

observation, n is the number of observed RWR outcomes, and Max is the

93

maximization function that selects the larger between the numbers 0

and )( tT RWRRWR − . The termλ , which is known as the degree of lower partial

moment (LPM) can theoretically assume any value depending on the risk

aversion of the participant.

We compute the lower partial moments for wealth outcomes under different

asset allocation strategies for participants with λ = 0, 1, and 2. For λ = 0,

0LPM gives the probability of shortfall, that is, how often the actual RWR can

fall below the target. If λ = 1, 1LPM weighs shortfalls ( TRWR less ‘below

TRWR ’ outcomes in the context of our problem) with linear weighting.47 This

provides an estimate of how severe the shortfall can be. Forλ = 2, 2LPM gives

the below-target semi-variance.

We also use Sortino and UPR as performance measures which are adjusted for

downside risk in evaluating alternative asset allocation strategies. These have

already been discussed in 2.8. In the context of our problem, the Sortino Ratio is

given by

Sortino 2

1

2 ][LPM

RWRRWR TM −= (35)

where MRWR denotes the mean RWR. The denominator in (2) denotes the

downside deviation of wealth outcomes.

The UPR, which measures the upside potential relative to the downside risk, can

be denoted in the context of our problem as

( )

[ ] 21

2LPM

RWRRWR

UPR TRWRT∑

∞

−= (36)

Next, we consider the risk of extremely adverse wealth outcomes for plan 47 This is also referred by some as the expected shortfall.

94

participants. If DC plan participants are believed to be loss averse towards the

value of their retirement assets, which can be considered as a ‘large stake’ as

discussed in Rabin and Thaler (2001), the plan sponsors may decide to select

asset allocation strategies that have more chance of avoiding the most disastrous

outcomes. In other words, DC plans would select strategies that lower the

estimates of tail risk of the probability distribution of retirement wealth as their

default investment option.

To evaluate the extreme retirement wealth outcomes of alternative asset

allocation strategies, we use two common measures of estimating tail risk -

value at risk (VaR) and expected tail loss (ETL). The use of VaR in risk

management is widespread (Jorion, 2000). In the context of our problem,

if p represents the probability of worst percentage of RWR outcomes that the

participants are concerned about,α is the confidence level and p is set such that

α−= 1p , and if pRWR represents the p-quantile of the RWR distribution, then

from equation (21) VaR at that confidence level is given by

pRWRVaR= (37)

An outcome worse than VaR can occur only in extreme circumstances, the

probability of which can be specified by the user by specifyingα , which

indicates the likelihood that the investor would not get an outcome worse than

VaR. The higher the degree of risk aversion, higher is the value of α and vice

versa.

As VaR at a given probability gives us no idea about the amount at risk at higher

or lower levels of probability (Balzer, 1994) and suffers from lack of sub-

additive feature (Artzner, Delbaen, Eber, and Heath, 1999), we also employ

expected tail loss (ETL), which is often proposed as a better candidate as a

coherent measure of risk (Yoshiba and Yamai, 2002; Dowd, 2005). ETL gives

the probability weighted average of estimates that fall below VaR. In our case,

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if iRWR is the i th outcome and i is the probability of the i th outcome, then

iRWRETLi

i .1

1

0∑

=−=

α

α α (38)

Therefore, in the context of wealth accumulation of participants, ETL is actually

the average of the worst 100(1- α ) % of the RWR outcomes.

Finally, employee participants belonging to the same plan and following an

identical investment strategy but retiring a few years apart can face widely

different wealth outcomes (Burtless, 2003). Plan providers may feel that it is

important to minimize the disparity in real retirement wealth among different

employee cohorts whose investments are governed by the same default

strategy.48 In that case, they would be prompted to select such an asset

allocation strategy as default which results in least variation in real retirement

wealth outcomes between different employee cohorts, in other words, the real

retirement wealth outcomes under different investment return scenarios fall

within a narrow range. Our simulations produce a range of possible RWR

outcomes for every strategy. The terminal wealth outcome in every case is

dependent on the simulated path for asset class returns. Which of these return

paths would actually govern the investments of participants following a specific

strategy would entirely depend on the future state of the world. The future

return path, however, would be identical for participants belonging to the same

cohort while it is likely to be different for participants belonging to different

cohorts.49 Therefore participants from different cohorts may have different

terminal wealth outcomes even when their investments are directed by identical

default option.

48 Cross-cohort differences in retirement preparedness as a result of variation in wealth accumulated through retirement plans may also not be desirable from a policy perspective. 49 It is easy to see that parts of the return paths experienced by different cohorts would be overlapping for the cohorts who share overlapping employment periods.

96

To compare the variability of retirement wealth outcomes under different asset

allocation strategies, we use two common measures of dispersion. First, we

estimate coefficient of variation (CV) for simulated retirement wealth outcomes

under every strategy which is the standard deviation of RWR outcomes divided

by the mean RWR. To supplement this metric, we also estimate the inter-

quartile range ratio (IQRR) which is obtained by dividing the difference

between the 75th percentile RWR and the 25th percentile RWR by the median

RWR for each strategy under consideration.

4.3 Methodology

To analyse the wealth outcomes generated by different asset allocation

strategies, we use the DC plan accumulation model described in 3.1 which uses

stochastic simulation of asset class returns to determine the expected distribution

of wealth outcome at retirement. As discussed in previous section, the wealth

outcome is measured as retirement wealth ratio (RWR).

We base our analysis on simulated wealth outcomes for an employee who joins

the plan at the age of 25 years and retires at the age of 65 years. The starting

salary of the employee is assumed to be 25,000 Australian Dollars and the

growth in real wages to be 2% per year, which closely follows growth rate of

Australia's real GDP per capita of 2.6% per annum from 1994 through 2004

(Australian Bureau of Statistics, 2005). The contribution rate is fixed at 9%

which is the legislated minimum prescribed by the Australian government. No

contribution is made during periods of unemployment, the probability of which

is assumed to be 5%. This is equal to the unemployment rate among Australian

workers with post-school qualifications (Kryger, 1999; Richardson, 2006). For

the sake of simplicity, we assume that the contributions are credited annually to

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the accumulation fund at the end of every year (in practice, the Australian

Government has recently legislated that contributions needs to be made, at a

minimum, on a quarterly basis). The portfolios are also rebalanced at the end of

each year to maintain the target asset allocation. We assume that plan

contributions and investment returns are not subject to any tax. We also ignore

any transaction cost that may be incurred in managing the investment of the plan

assets.

For generating asset class returns, we initially employ Monte Carlo simulation

which estimates statistical parameters from historical data series under a

theoretical distribution and then exposes these to random changes in simulating

future outcomes. Following standard Monte Carlo simulation methodology, we

assume that asset class returns are drawn from a multivariate normal

distribution. This implies that mean and standard deviation of asset class returns

are time invariant and the returns are independent over the time horizon. At

each stage of the simulation horizon, the random shocks generated by the

multivariate normal model are adjusted so as to follow the average cross-

sectional correlation observed in the historical data. The Monte Carlo method

employed in this study is discussed further in 3.2.1.

Since Monte Carlo simulation imposes explicit distributional assumptions in

generating asset class returns, we run a parallel test for generating wealth

outcomes using non-parametric bootstrapping which draws asset class returns

from the empirical return distribution. Here the historical return data series for

the asset classes is randomly resampled with replacement to generate portfolio

returns for every period of the 40 year investment horizon of the DC plan

participant. In other words, each bootstrap sample is a random sample of asset

class returns for a particular period drawn with replacement from historical

observations over several periods. Thus we retain the cross-correlation between

the asset class returns as given by the historical data while assuming that asset

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class return series is independently distributed over time. More details about the

resampling method employed in this study are provided in 3.2.2.

4.4 Data

To investigate the issue of strategic asset allocation for long horizon investors

like DC plan participants, it is essential that we generate simulated returns based

on historical observations of asset class returns over several decades. This is

done to minimize the undue influence that recent investment performance (of

these asset classes) may have on long-term risk assessment and asset allocation

decisions. Moreover, it is often argued that a longer period of data has greater

chance of capturing wide-ranging effects of favourable and unfavourable events

of history on returns of individual asset classes. Since participants are likely to

be concerned with the effect of inflation on the value of their retirement wealth,

we need to use real investment returns to simulate terminal wealth outcomes for

different asset allocation strategies. This study uses an updated version of the

dataset of returns on stocks, bonds, and bills originally compiled by Dimson et

al. (2002) and commercially available through Ibbotson Associates for 16

countries including Australia for a period of 105 years spanning from 1900 to

2004. All returns are annual real returns and include reinvested income and

capital gains.

For the full 105 year period from 1900 to 2004, the mean annual real return for

Australian stocks has been 9.09% while the same for Australian bonds and bills

has been 2.27% and 0.72% respectively. When we consider only data after the

Second World War, from 1947 through 2004, the mean annual real returns for

the three asset classes were smaller, recorded at 8.05%, 1.08%, and 0.62% for

stocks, bonds, and bills respectively. However, real returns for all three classes

seem to have been significantly higher in recent times. During the most recent

99

30 year period in our dataset, 1975 through to 2004, mean annual real returns for

stocks, bonds, and bills have been 10.93%, 4.97%, and 3.20% respectively.

Going by the higher mean real returns produced by stocks, one would also

expect much higher standard deviation for stocks in comparison to that for

bonds and bills. This has certainly been the case with the standard deviation of

annual real returns on stocks, bonds, and bills being 17.74%, 13.36%, and

5.51% from 1900 through 2004. The corresponding estimates for post war

period (1947-2004) were 21.06%, 11.47%, and 5.09% while those most recent

30-year period (1975-2004) were 20.54%, 11.13%, and 3.76%.

Since DC plan participants have long investment horizons, typically between 30

and 40 years, asset class returns for long holding periods would be of more

interest in examining their case. From asset class return data between 1900

through 2004, we find that the real returns from bonds have been negative for 29

of the 76 observed 30 year holding periods and 20 out of 66 observed 40-year

holding periods. Bills recorded further underperformance with 32 of the 76

observed 30-year holding periods and 20 of the 66 observed 40-year holding

periods yielding negative real returns for the investors. In contrast, the real

returns from Australian stocks for every 30-year and 40-year holding period

between 1900 and 2004 were positive. The real equity premium over bond and

bills has also been positive for each of these holding periods.

We also use data on default investment strategy for major Australian

superannuation funds. In Australia, it is a regulatory requirement for trustees to

identify a default strategy where investment choice is offered to standard

employer-sponsored members. Most superannuation funds offer a balanced

diversified investment strategy to their member participants as the default

investment choice. The guidelines for trustees provided by the regulatory

authority emphasises the benefits of diversification as, according to them, it

would ‘result in a lower overall level of risk to achieve desired return’ (APRA,

100

1999). At the end of June 2004, the majority of default strategy assets of

superannuation funds were held in stocks: 33% in Australian stocks and 21% in

international stocks. A further 15% was invested in Australian fixed interest,

6% in international fixed interest, 7% in cash, 6% in property, and 12% in other

assets (APRA, 2005).

In 2005-06, SuperRatings, an independent research house, conducted a

comprehensive analysis of 120 superannuation funds including major industry,

corporate, and public sector funds as well as commercial master trusts, most of

which hold more than $500 million of assets.50 Together, the funds cover in

excess of $300 billion of retirement savings on behalf of nearly 10 million

member accounts. The funds are rated on the basis of their performance by

aggregating several factors including investment methodology, returns, fees,

administration and governance/risk framework. A total of seventeen of these

funds (representing the top 15% of their universe) received the highest or

‘platinum’ rating. We limit our study to these ‘platinum’ rated funds since most

of these funds can be expected to have default investment strategies that are

relatively well designed compared to those of funds with lower ratings. The

asset allocation data for individual default investment strategies is collected

from the product disclosure statements available in the respective websites of

these funds as at March 2006.

In our study, only 3 of the 17 default investment options change their allocation

with the age of the participant. But unlike typical ‘target retirement funds’ in

the US and elsewhere where the benchmark asset allocation is changed

continuously and gradually to achieve a more conservative asset allocation as

the members grow older and approach retirement, the change in asset allocation

here is done instantaneously when the members reach specified age threshold(s).

50 More details of the survey and rankings are available on SuperRating’s website, www.superratings.com.au

101

For each of these three default options, we examine two different allocation

rules: one assuming that their initial asset allocation remains unchanged till the

retirement of the participant (which is equivalent to a fixed weight strategy) and

another following the exact switch in allocations given by the actual default

option i.e. lifecycle strategy. This enables us to directly compare the results and

determine whether this type of lifecycle strategies can be expected to produce

superior outcomes for the participants, particularly in terms of reducing risk. In

addition, we examine two hypothetical strategies: (i) default option average

(DOA) strategy whose allocation is the same as the average allocation of default

options for all Australian superannuation funds as of June 2004; and, (ii) 100%

stocks strategy.

Initially we conduct our analysis under the assumption that the DC plan assets

are invested in Australian stocks, bonds, and bills. Allocations of the default

options to international stocks and international bonds are, therefore, included in

domestic stocks and bonds respectively. We, later, repeat the simulations by

including international stocks and international bonds as separate asset classes

but do not present the results in Appendix 4C since these lead to very similar

conclusions.51 Although ‘property’ is an important asset class for investment by

these funds, we do not include it as a separate asset class in our analysis because

of the paucity of reliable long-term return data. Similarly ‘alternative

investments’ which mainly comprise investments in infrastructure, hedge funds,

and commodities, cannot be included because of the lack of specific information

on their composition and therefore of any reliable index to measure returns.

While examining investment strategies of Australian superannuation funds, we

handle their allocation component to ‘properties’ and ‘alternative investments’

in a manner similar to that of other well-known studies like Brinson et al., 51 This may be due to the reason that we use US stocks and US bonds, which are highly correlated with their Australian counterparts, as proxies for international stocks and international bonds.

102

(1986) and Arshanapalli, Coggin, and Nelson (2001), where the percentage

allotted to ‘others’ is divided between equities, bonds and bills on a pro-rata

basis. However, we choose to direct the allocations against ‘property’ and

‘alternative investments’ only to equities and bonds (and not bills) on a pro-rata

basis, because we believe that the risk-return profile of these asset classes is far

removed from that of bills (cash). The asset allocation data for every strategy

included in our analysis are provided in Table 4.1.

Out of the seventeen ‘platinum’ rated funds used in our analysis, eight funds

have their default option’s initial allocation to stocks ranging between 60% and

70% which typically represents a balanced diversified fund. The DOA strategy

also has an asset allocation profile similar to these strategies. Of the remaining

funds, four funds have their default strategy’s initial allocation to stocks between

70% and 80% while the default strategies of other five funds are highly

aggressive with more than 80% of assets invested to stocks. Only three of the

default strategies (#18, #19, and #20) change their initial asset allocation with

the age of the member. To examine the efficacy of these lifecycle strategies, we

devise three corresponding fixed weight strategies (#6, #7, and #16) by

assuming that their initial asset allocations remain constant throughout the

investment horizon. Therefore, we have seventeen fixed weight strategies

(fourteen actual and three devised), three lifecycle strategies, and two

hypothetical strategies, that is, twenty-two strategies in total available for our

analysis.

103

Table 4.1: Asset Allocation of Default Investment Options The following table reports the asset allocation structure of default investment options of seventeen superannuation funds in Australia which received ‘platinum rating from SuperRatings Australia in 2005-2006. For three of these funds that have age-based lifecycle strategy as default option, we treat their initial asset allocation as a separate strategy in addition to the original lifecycle strategy. We also include a default option average asset allocation strategy as given by APRA. Allocation to international stocks and bonds are included in stocks and bonds respectively. Allocation to alternative asset classes is proportionately split between stocks and bonds.

Stocks (%) Bonds (%) Cash (%) FIXED WEIGHT STRATEGIES

A. Conservative (Stocks w < 70% stocks) 66 29 5 1. UniSuper Balanced 64 36 0 2. Equipsuper Balanced Growth 65 30 5 3. HOSTPlus Balanced 66 32 2 4. Sunsuper Balanced 66 32 2 5. REST Core 66 24 10 6. Telstra Balanced* 67 33 0 7. First State Super Diversified# 68 17 15 8. CARE Super Balanced 69 26 5

B. Moderate Agg. (Stocks 70% ≥ w < 80%) 76 22 2

9. Westcheme Trustee's Selection 73 27 0

10. Vision Balanced Growth 74 23 3 11. HESTA Core Pool 77 21 2 12. NGS Diversified 79 18 3 C. High Aggressive (Stocks w ≥ 70%) 85 13 2 13. ARF Balanced 80 18 2

14. STA Balanced 83 15 2

15. Cbus Super 83 14 3 16. Health Long Term Growth^ 88 12 0 17. MTAA 93 4 3

L IFECYCLE STRATEGIES

18. Telstra: Under 60 years (Balanced) 67 33 0 60 years and above (Conservative) 32 48 20 19. First State Super: Up to 56 years (Diversified) 68 17 15 Above 56 years (Balanced) 47 28 25 20. Health: Less than 50 years (Long Term Grow.) 88 12 0 50 to 60 years (Medium Term Growth) 64 36 0 Above 60 years (Balanced) 41 59 0

HYPOTHETICAL STRATEGIES 21. Default Option Average 67 26 7 22. 100% Stock 100 0 0

* Initial allocation of lifecycle strategy #18; # Initial allocation of lifecycle strategy #19; ^ Initial allocation of lifecycle strategy #20

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4.4 Results and Discussion

Based on the wealth accumulation model described in 3.1, we simulate RWR

outcome for all the twenty-two asset allocation strategies. We conduct two

separate sets of simulation experiments using the Monte Carlo and bootstrap

resampling methods for return generation respectively. For both sets of

experiments, we conduct 5,000 iterations for every asset allocation strategy

under consideration to generate 5,000 different investment return paths over 40-

year periods. These simulated returns are applied every year on corresponding

cash flows in the participant’s account to produce a range of 5,000 RWR

outcomes under every strategy at the end of the 40-year horizon. Each set of

experiments is initially conducted based on historical asset class returns for the

entire period of available data, 1900 through 2004. However, it is quite possible

that structural changes in the domestic and the international economy may

render data from the very distant past, especially before the Second World War,

less relevant in projecting future asset class returns. Therefore, we repeat the

simulations using two more recent datasets: one for the entire post-war period

(1947-2004) and another for the most recent 30 year period (1975-2004). Since

the estimates obtained by the Monte Carlo and the bootstrap resampling

experiments are very similar, we report only the results of the former in Tables

4.2, 4.3, and 4.4.52

We set the wealth accumulation target TRWR for the plan participant at 8.0 i.e.

800% of salary at retirement. Booth and Yakoubov (2000) uses a target wealth

of 500% of salary at retirement which translates into a TRWR of 5.0. Although

there is no consensus on what can be considered as an adequate wealth to

income ratio for Australian retirees, we choose to set TRWR at a higher level for

52 Summary results of trials using the bootstrap resampling method to generate asset class returns are provided in Appendix 4B.

105

two reasons. First, several commentators consider the current wealth to income

levels as grossly inadequate in view of increasing life expectancy and growing

health care costs. Second, since our study ignores the taxes on retirement

savings and investment returns as well as transaction costs while modelling

terminal wealth outcomes, we feel the need to compensate it by setting the target

wealth outcome on the higher side. However, setting TRWR at a different value

is not expected to alter the relative ranking of asset allocation strategies as long

as we hold it constant for all the simulations.

4.4.1 RWR Distribution

The distribution of RWR for each asset allocation strategy provides us with the

range of wealth outcomes the participant may expect to confront at the point of

retirement. In addition to mean and median RWR, we estimate the first and

third quartile estimates of the distribution for every allocation strategy to assess

their relative appeal. For any of these parameters, a higher value would

generally make a strategy more attractive. Table 4.2 provides the distribution

parameters of RWR for each of the asset allocation strategies. The results

indicate that RWR varies significantly across asset allocation strategies. The

mean and the median RWR seem to increase for strategies with higher allocation

to stocks and are highest for the strategy which invests entirely in stocks. The

median RWR for the 100% stocks strategy is over 50% higher than that of DOA

strategy, which only has two-thirds of assets invested in stocks. Although in a

few cases, the mean and median RWR are not higher for the strategy with higher

proportion of stocks, we find that the allocations to stocks in these cases are very

close, and the difference in outcome seems to be more influenced by the

difference in their allocation splits between bonds and cash.

Table 4.2: Distribution Parameters of Retirement Wealth Ratio (RWR)

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Table 4.2 reports the distribution of RWR from the Monte Carlo simulation (multivariate normal). A total of 5,000 iterations for every asset allocation strategy under consideration to generate different investment return paths over 40-year periods. Max., Min., Q1, and Q3 denote maximum, minimum, first quartile, and third quartile RWR outcomes respectively. CV and IQRR measure the dispersion of RWR outcomes and stands for coefficient of variation and interquartile range ratio for the distribution of RWR outcomes respectively.

PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA Mean Median Max. Min. Q1 Q3 CV IQRR FIXED WEIGHT STRATEGIES

A. Conservative (Avg.) 9.87 8.34 81.11 1.38 5.80 12.17 0.62 0.76 1. UniSuper Balanced 9.73 8.21 75.73 1.19 5.70 12.05 0.62 0.77 2. Equipsuper Bal.

Growth 9.61 8.16 82.63 1.46 5.69 11.90 0.60 0.76

3. HOSTPlus Balanced 9.85 8.24 73.28 1.44 5.72 12.10 0.64 0.77 4. Sunsuper Balanced 9.98 8.33 99.95 1.50 5.84 12.34 0.63 0.78 5. REST Core 9.56 8.17 74.64 1.56 5.70 11.70 0.60 0.73 6. Telstra Balanced 10.06 8.54 82.95 1.44 5.83 12.36 0.65 0.76 7. First State Super Div. 9.70 8.33 66.52 1.17 5.82 12.05 0.59 0.75 8. CARE Super Balanced 10.43 8.77 93.14 1.25 6.06 12.84 0.64 0.77

B. Moderate Agg. (Avg.) 11.63 9.49 92.89 1.26 6.34 14.51 0.69 0.86 9. Westscheme Trustee's

Sel. 11.32 9.19 98.41 1.27 6.18 14.15 0.69 0.87

10. Vision Balanced Growth

11.12 9.14 67.29 1.33 6.20 14.02 0.65 0.86

11. HESTA Core Pool 11.83 9.61 89.89 1.26 6.38 14.72 0.69 0.87 12. NGS Diversified 12.24 10.03 115.97 1.19 6.58 15.13 0.72 0.85 C. High Aggressive (Avg.) 13.71 10.91 129.16 1.38 6.98 16.98 0.75 0.92 13. ARF Balanced 12.54 10.17 153.85 1.32 6.55 15.58 0.72 0.89

14. STA Balanced 13.24 10.50 133.49 1.31 6.76 16.22 0.77 0.90 15. Cbus Super 13.16 10.57 114.17 1.47 7.00 16.37 0.73 0.89 16. Health Long Term

Growth 14.31 11.24 136.11 1.28 7.12 17.71 0.74 0.94

17. MTAA 15.28 12.07 108.19 1.50 7.49 19.03 0.78 0.96 L IFECYCLE STRATEGIES

18. Telstra 9.02 7.78 49.18 1.56 5.46 11.12 0.58 0.73 19. First State Super 8.64 7.56 47.90 1.31 5.40 10.66 0.54 0.70 20. Health 9.47 8.12 65.26 1.49 5.66 11.54 0.61 0.72

HYPOTHETICAL STRATEGIES 21. Default Option

Average 9.90 8.37 72.27 1.69 5.84 12.34 0.62 0.78

22. 100% Stock 17.37 12.88 194.55 1.13 7.78 21.48 0.90 1.06

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Table 4.2 (cont’d): Distribution Parameters of Retirement Wealth Ratio (RWR)

PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA

Mean Median Max. Min. Q1 Q3 CV IQRR FIXED WEIGHT STRATEGIES


Growth 7.53 6.14 56.56 0.77 4.17 9.30 0.68 0.84

3. HOSTPlus Balanced 7.75 6.32 70.14 0.90 4.14 9.52 0.71 0.85 4. Sunsuper Balanced 7.73 6.28 114.36 0.90 4.17 9.55 0.73 0.86 5. REST Core 7.80 6.45 47.83 1.02 4.30 9.66 0.67 0.83 6. Telstra Balanced 7.83 6.33 73.43 0.97 4.20 9.59 0.73 0.85 7. First State Super Div. 7.88 6.45 67.46 0.88 4.34 9.67 0.69 0.82 8. CARE Super Balanced 8.01 6.45 66.90 0.88 4.30 9.77 0.72 0.85

B. Moderate Agg. (Avg.) 9.09 6.98 101.60 0.90 4.51 11.31 0.81 0.98 9. Westscheme Trustee's

Sel. 8.90 6.90 77.26 0.97 4.53 11.05 0.79 0.95


8.86 6.86 159.40 0.98 4.52 10.94 0.83 0.94

11. HESTA Core Pool 9.15 7.11 87.00 0.75 4.45 11.45 0.81 0.98 12. NGS Diversified 9.43 7.06 82.73 0.90 4.53 11.81 0.82 1.03 C. High Aggressive (Avg.) 10.76 7.81 179.96 0.74 4.75 13.07 0.96 1.06 13. ARF Balanced 9.47 7.25 87.65 0.94 4.58 11.50 0.84 0.95 14. STA Balanced 10.58 7.57 269.15 0.87 4.76 12.69 1.08 1.05 15. Cbus Super 10.49 7.71 210.27 0.76 4.69 12.78 0.93 1.05 16. Health Long Term

Growth 11.26 8.14 167.64 0.58 4.83 13.72 0.96 1.09

17. MTAA 12.01 8.38 165.10 0.57 4.90 14.64 0.99 1.16

L IFECYCLE STRATEGIES 18. Telstra 6.92 5.78 60.38 0.79 4.01 8.53 0.63 0.78 19. First State Super 7.03 5.87 59.13 1.15 4.07 8.53 0.65 0.76 20. Health 7.44 6.07 47.68 0.88 4.13 9.15 0.68 0.83


Average 7.77 6.31 87.21 0.99 4.29 9.49 0.71 0.82

22. 100% Stock 13.63 8.92 228.03 0.76 5.11 16.54 1.14 1.28

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Table 4.2 (cont’d): Distribution Parameters of Retirement Wealth Ratio (RWR)

PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA

Mean Median Max. Min. Q1 Q3 CV IQRR FIXED WEIGHT STRATEGIES


Growth 16.21 13.36 135.89 1.82 9.05 19.80 0.68 0.80

3. HOSTPlus Balanced 16.82 13.64 131.48 1.90 9.24 20.75 0.69 0.84 4. Sunsuper Balanced 16.88 13.90 154.42 1.90 9.26 21.21 0.69 0.86 5. REST Core 15.81 13.15 149.30 2.25 8.91 19.76 0.66 0.82 6. Telstra Balanced 16.57 13.69 173.81 1.87 9.08 20.54 0.69 0.84 7. First State Super Div. 15.92 13.24 161.27 1.61 8.87 19.88 0.66 0.83 8. CARE Super Balanced 17.18 13.75 147.68 1.69 9.04 21.70 0.73 0.92 B. Moderate Agg. (Avg.) 19.29 15.09 249.66 1.48 9.60 23.84 0.81 0.94 9. Westscheme Trustee's

Sel. 18.52 14.55 148.00 1.74 9.52 22.77 0.76 0.91


18.81 14.96 197.04 1.44 9.51 23.22 0.77 0.92

11. HESTA Core Pool 19.49 15.05 223.53 1.31 9.61 23.93 0.84 0.95 12. NGS Diversified 20.33 15.79 430.06 1.42 9.76 25.42 0.85 0.99 C. High Aggressive (Avg.) 22.45 16.42 346.70 1.31 9.90 27.76 0.92 1.08 13. ARF Balanced 20.47 15.64 331.79 1.39 9.73 25.57 0.86 1.01 14. STA Balanced 21.31 15.96 278.44 1.70 9.94 26.65 0.85 1.05 15. Cbus Super 21.91 16.03 276.49 1.47 9.89 26.91 0.90 1.06 16. Health Long Term

Growth 23.67 17.11 375.28 1.01 9.97 29.19 0.95 1.12

17. MTAA 24.88 17.34 471.52 0.98 9.95 30.50 1.04 1.18


18. Telstra 15.16 12.67 107.95 1.75 8.70 18.76 0.63 0.79

19. First State Super 14.64 12.45 146.95 2.27 8.71 17.83 0.63 0.73

20. Health 16.01 13.29 136.60 2.07 8.99 19.67 0.91 0.80


Average 16.32 13.42 130.57 1.71 8.97 20.40 0.68 0.85

22. 100% Stock 28.15 18.17 460.72 1.34 9.78 33.45 1.19 1.30

109

The first and third quartile outcomes also tend to increase as we move from

strategies with lower proportion of stocks to those with higher proportion of

stocks. The difference between first quartile outcomes of different strategies are

relatively smaller compared to the spread between the third quartile outcomes.

For example, the first quartile outcomes for the strategy with the lowest and

highest allocation to stocks are 5.70 and 7.48 respectively. The corresponding

estimates for their third quartile outcomes are 12.04 and 19.02. Again, the

100% stocks strategy results in the best first and third quartile RWR outcomes.

The increasing trend in RWR outcomes with aggressiveness of the asset

allocation strategy is graphically demonstrated in Figure 4.1. Generally, more

aggressive is the strategy, higher (lower) is the maximum (minimum) RWR

outcome. Also, the minimum outcomes for different strategies lie within a

narrow range (0.57 to 1.13) which shows that there is not much to choose

between the strategies on the basis of their worst outcomes.

Figure 4.1 RWR distribution parameters of Asset Allocation Strategies

The plot uses results of simulation using full period (1900-2004) data. IQRR denotes the interquartile range ratio which is used as a measure of dispersion of RWR outcomes. RWR distribution parameters for lifecycle strategies are not included since these have changing allocation to stocks over time.

110

The results of Monte Carlo simulations using returns data for 1947-2004 and

1975-2004 give similar indications about the effect of asset allocation strategies

on terminal wealth outcomes. While the RWR estimates for various strategies

vary when we use data for different periods, strategies with higher allocations to

stocks consistently dominate those with lower allocation to stocks in terms of

mean, median, first quartile, and third quartile outcomes. As before, the 100%

stocks strategy result in the best outcomes for all these parameters except the

first quartile outcome for the simulations using 1975-2004 data. The best result,

in this case, is produced by a strategy which invests 88% of assets in stocks and

remaining in bonds.

Our simulations produce a range of possible RWR outcomes for every strategy.

It is important to measure the dispersion of RWR outcomes for each strategy in

order to form a view on possible future retirement wealth disparity among

different cohorts following that strategy. The estimates for both CV and IQRR

indicate that the dispersion of RWR outcomes tends to increase with increase in

allocation to stocks although the rate of increase seems to be very small. For

instance, the IQRR for the strategy with lowest stock allocation (64%) is 0.7725

while that for the strategy with highest allocation to stocks (93%) is 0.9559. The

hypothetical 100% stocks strategy produces an IQRR of 1.0631. These

estimates indicate that the disparity in wealth outcomes between the cohorts who

meet very positive investment return scenarios and those who confront relatively

unfavourable investment returns during their employment life while being

enrolled in the same default option may be dependent on the allocation policy of

the plan. Nevertheless, the difference in disparity across cohorts for strategies

with different proportions of stocks may not be very large. This is well

demonstrated by the flatness of the IQRR curve when plotted against strategies

with changing allocation to stocks. The simulation results using data for recent

periods also support these findings.

111

By comparing the RWR distribution parameters of each of the lifecycle

strategies (#18, #19, and #20) with those of the corresponding strategy that

maintains its initial asset class weighting (#6, #7, and #16 respectively), we find

that former produces lower mean, median, first quartile, and third quartile

outcomes in every case. Yet the minimum outcome in almost all cases is

slightly higher for the lifecycle strategies.53 Since the CV and IQRR are also

always lower for lifecycle strategies, it seems that switching to a conservative

allocation as the employee approaches retirement may actually reduce the

dispersion in RWR outcomes. In other words, if these strategies do not switch

their asset allocation with the members approaching retirement, the range of

expected wealth outcomes gets wider.

4.4.2 Downside Risk and Risk-Adjusted Performance Estimates

We use lower partial moments with risk aversion parameters 0, 1, and 2 so that

the investors with different levels of risk tolerance can use these estimates to

evaluate alternative asset allocation strategies. Table 4.3 reports the downside

risk estimates for RWR under different asset allocation strategies.

Estimates for all the LPM measures steadily increase with decrease in allocation

to stocks indicating a clear inverse relationship. For instance, the 0LPM for the

strategy with 64% allocation to stocks is 0.4826 which indicates that there is a

48.26% probability that the RWR would fall below TRWR (close to the toss of a

fair coin). In comparison, the probability of shortfall for the strategy with 77%

stocks is 38.58% and for the strategy with 93% stocks is 28.06%. Interestingly,

the 100 % stocks strategy has only 26.22%, or around one-in-four, probability of

53 However, the minimum outcome may not serve as a useful evaluation criterion because there is only a 1 in 5,000 chance of getting that outcome.

112

falling below TRWR , which is the lowest of all strategies, while DOA strategy

has almost 47 % chance of underperforming that target.

Similar trends are also observed for measures of magnitude of shortfall

)( 1LPM and below target semivariance )( 2LPM indicating that the downside

risk is reduced by increasing allocation to stocks in the portfolio. Figure 4.2

graphically depicts this trend. The slopes of LPM curves reveal that the rate of

decline of downside risk gets higher with increasing risk aversion, that is, more

averse the participants are to the downside risk of failing to meet their wealth

accumulation objective, more appealing would the aggressive strategies relative

to balanced or conservative strategies.

Figure 4.2 Downside risk estimates of Asset Allocation Strategies Lower partial moments for RWR outcomes have been computed for simulation using full period

(1900-2004) data using three different degrees of risk aversion: 0, 1, and 2. TRWR is set at 8.0. Lifecycle strategies are not included since these have changing allocation to stocks over time.

113

Table 4.3: Estimates for Downside Risk and Performance Measures

Table 4.3 reports estimates for downside risk and performance measures from the Monte Carlo simulation.

OLPM , 1LPM , and 2LPM measure downside risk and represent lower partial moment with

degree )(λ 0, 1, and 2 respectively. The downside risk adjusted performance measures SR and UPR

denote Sortino ratio and upside potential ratio respectively. A target retirement wealth ratio ( TRWR ) of

8.0 has been used in the simulations to estimate these measures.

PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA

0LPM 1LPM 2LPM SR UPR

FIXED WEIGHT STRATEGIES A. Conservative (Avg.) 0.4719 1.1608 3.9099 0.9465 1.5335

1. UniSuper Balanced 0.4826 1.2058 4.1128 0.8544 1.4490 2. Equipsuper Balanced Growth 0.4864 1.1960 4.0210 0.8014 1.3978 3. HOSTPlus Balanced 0.4812 1.1992 4.0933 0.9149 1.5076 4. Sunsuper Balanced 0.4708 1.1609 3.9432 0.9979 1.5825 5. REST Core 0.4858 1.1813 3.9251 0.7862 1.3825 6. Telstra Balanced (Under 60) 0.4580 1.1329 3.8144 1.0571 1.6371 7. First State Super Div. (Up to 56) 0.4722 1.1514 3.8447 0.8673 1.4544 8. CARE Super Balanced 0.4384 1.0589 3.5243 1.2927 1.8567

B. Moderate Aggressive (Avg.) 0.3920 0.9510 3.2046 2.0339 2.5650

9. Westscheme Trustee's Selection 0.4094 0.9874 3.2778 1.8359 2.3812

10. Vision Balanced Growth 0.4108 1.0025 3.4088 1.6925 2.2355 11. HESTA Core Pool 0.3858 0.9287 3.1060 2.1707 2.6977 12. NGS Diversified 0.3620 0.8855 3.0256 2.4365 2.9456

C. High Aggressive (Avg.) 0.3240 0.7813 2.6410 3.5427 4.0229 13. ARF Balanced 0.3554 0.8721 2.9170 2.6610 3.1716

14. STA Balanced 0.3408 0.8280 2.8008 3.1317 3.6264

15. Cbus Super 0.3302 0.7711 2.6087 3.1931 3.6705 16. Health LT Growth (Less than

50) 0.3132 0.7531 2.5702 3.9329 4.4027

17. MTAA 0.2806 0.6820 2.3084 4.7946 5.2435 L IFECYCLE STRATEGIES

18. Telstra 0.5194 1.3100 4.4336 0.4855 1.1076

19. First State Super 0.5438 1.3565 4.5678 0.3001 0.9348

20. Health 0.4868 1.2202 4.196 0.7189 1.3146

HYPOTHETICAL STRATEGIES

21. Default Option Average 0.4696 1.1455 3.8546 0.9681 1.5516 22. 100% Stock 0.2622 0.6415 2.2062 6.3074 6.7393

114

Table 4.3 (cont’d): Estimates for Downside Risk and

Performance Measures



FIXED WEIGHT STRATEGIES A. Conservative (Avg.) 0.6520 2.0445 8.2208 -0.0840 0.6290

1. UniSuper Balanced 0.6758 2.1418 8.6593 -0.1588 0.5690 2. Equipsuper Balanced Growth 0.6708 2.1008 8.3474 -0.1627 0.5644 3. HOSTPlus Balanced 0.6500 2.0645 8.4223 -0.0869 0.6244 4. Sunsuper Balanced 0.6520 2.0616 8.3608 -0.0927 0.6203 5. REST Core 0.6422 1.9866 7.9223 -0.0719 0.6339 6. Telstra Balanced (Under 60) 0.6508 2.0519 8.2799 -0.0606 0.6525 7. First State Super Div. (Up to 56) 0.6404 1.9645 7.8222 -0.0420 0.6604 8. CARE Super Balanced 0.6342 1.9842 7.9524 0.0034 0.7070



10. Vision Balanced Growth 0.5904 1.8280 7.3254 0.3192 0.9946 11. HESTA Core Pool 0.5688 1.7991 7.3513 0.4231 1.0867 12. NGS Diversified 0.5644 1.7707 7.1433 0.5332 1.1957

C. High Aggressive (Avg.) 0.5179 1.6236 6.6785 1.0751 1.7032 13. ARF Balanced 0.5610 1.7444 7.1135 0.5523 1.2063

14. STA Balanced 0.5328 1.6290 6.5471 1.0092 1.6458 15. Cbus Super 0.5236 1.6430 6.7266 0.9618 1.5953 16. Health LT Growth (Less than

50) 0.4936 1.5611 6.4333 1.2868 1.9023


18. Telstra 0.7112 2.2890 9.2494 -0.3543 0.3983

19. First State Super 0.7160 2.2379 8.8958 -0.3265 0.4239

20. Health 0.6768 2.1413 8.6017 -0.1900 0.5401

HYPOTHETICAL STRATEGIES 21. Default Option Average 0.6512 2.0240 8.0674 -0.0794 0.6333 22. 100% Stock 0.4494 1.4613 6.2095 2.2612 2.8477

115

Table 4.3 (cont’d): Estimates for Downside Risk and

Performance Measures



FIXED WEIGHT STRATEGIES A. Conservative (Avg.) 0.1892 0.3738 1.0884 8.0830 8.4413 1. UniSuper Balanced 0.1976 0.4018 1.1840 7.3444 7.7136 2. Equipsuper Balanced Growth 0.1846 0.3588 1.0403 8.0477 8.3995 3. HOSTPlus Balanced 0.1838 0.3705 1.0869 8.4585 8.8138 4. Sunsuper Balanced 0.1788 0.3502 1.0037 8.8621 9.2116 5. REST Core 0.1948 0.3725 1.0416 7.6533 8.0183 6. Telstra Balanced (Under 60) 0.1890 0.3810 1.1402 8.0291 8.3859 7. First State Super Div. (Up to 56) 0.1982 0.3824 1.1074 7.523 7.8864 8. CARE Super Balanced 0.1868 0.373 1.1027 8.7461 9.1013



10. Vision Balanced Growth 0.1738 0.3691 1.1365 10.1426 10.4888 11. HESTA Core Pool 0.1768 0.3871 1.2170 10.419 10.7699 12. NGS Diversified 0.1734 0.3799 1.2054 11.2307 11.5767 C. High Aggressive (Avg.) 0.1688 0.3856 1.2764 12.7748 13.116 13. ARF Balanced 0.1694 0.3691 1.1599 11.5822 11.9249

14. STA Balanced 0.1626 0.3547 1.1071 12.6542 12.9913 15. Cbus Super 0.1700 0.3774 1.2588 12.3981 12.7345 16. Health LT Growth (Less than

50) 0.1680 0.3949 1.3534 13.4668 13.8062


18. Telstra 0.2038 0.3566 0.9211 7.4590 7.8306

19. First State Super 0.2014 0.3639 0.9836 6.6922 7.0592

20. Health 0.1876 0.3591 1.0184 7.9387 8.2945

HYPOTHETICAL STRATEGIES 21. Default Option Average 0.1868 0.3744 1.1073 7.9102 8.2659 22. 100% Stock 0.1812 0.4641 1.6793 15.551 15.9092

116

Simulation results using post-war data also suggest that LPM estimates are

generally smaller for strategies with higher allocation to stocks. However, the

results are not as conclusive when we use recent 30-year returns data as

simulation input. While the 0LPM estimates are still lower for more aggressive

strategies, albeit by a much smaller margin, this is not true for 1LPM and

2LPM . The estimates for 1LPM do not exhibit any clear trend with similar

estimates observed for strategies with significantly different proportion of

stocks. For 2LPM , the estimates are generally lower for strategies holding a

lower proportion of stocks. The evidence for lifecycle strategies also follows

the same pattern. The simulation results using full period and post-war period

data shows that the downside risk actually increases by making lifecycle

switching whereas results with the recent 30-year returns data indicates mixed

trends - 0LPM estimates are higher (higher downside risk) while 1LPM and

2LPM estimates are lower (suggesting lower downside risk) for lifecycle

strategies compared to corresponding strategies where the initial asset

weightings remain unchanged.

While the terminal wealth outcomes and associated risks involved with each

allocation strategy under consideration can be assessed from the parameters of

the simulated RWR distribution and various measures of LPM, composite

performance measures are essential to rank the strategies based on overall risk-

reward profile. We compute estimates for Sortino and UPR, performance

measures that are adjusted for downside risk and also produce these results in

Table 4.3. For simulations using full period data, Sortino and UPR are generally

found to increase with rising proportion of stocks in the strategy. This is almost

always the case with strategies with more than 70% allocation to stocks. The

100% stock strategy results in the highest Sortino and UPR.

117

The above results come as no surprise since we earlier found strategies with

higher stock allocation to be superior in terms of terminal wealth outcomes as

well as downside risk based on our simulation with the full period data. Of

more interest is the performance estimates for simulations using data for the

other two sub-periods because downside risk estimates in these cases lead to

conclusions that were different from those of simulation with the full period

data, particularly for 1LPM and 2LPM . However, we find that the risk-adjusted

performance estimates for the sub-periods are supportive of the rankings

indicated by the full-period simulation. Estimates for both Sortino and UPR in

these cases indicate that an allocation rule dominated by stocks results in better

risk adjusted performance and therefore, are consistent with the findings based

on simulation using full period data. Also, lifecycle strategies produce inferior

risk-adjusted performance estimates in all cases compared to their fixed weight

counterparts.

4.4.3 Tail-Related Risk Estimates

As discussed in 4.2, it is plausible that plan participants may care more about the

most adverse outcomes that can occur for a given strategy which makes it

important to analyse the risk of these extreme events. Plan providers in that case

are likely to use ‘maxi-min’ rule to select a strategy which maximizes the worst

‘n’ percentile of outcomes. In this study, we estimate VaR and ETL at 95%

confidence level, which means we assume that the participants are concerned

about the worst 5 % of RWR outcomes. While it is theoretically possible that

some participants may demonstrate an even greater degree of risk aversion, that

is, they may only consider RWR outcomes that are below an even lower

threshold (say 1%), we believe that in reality the 5th percentile outcome would

118

serve as an adequate indicator of extreme risk for majority of participants.

Moreover, for participants who are concerned about outcomes falling below 5th

percentile, the ETL measure provides the expected value of such an outcome.

The results for VaR and ETL estimates are produced in Table 4.4. The results

for simulations using full period data indicate that the VaR estimates, in general,

tend to increase with aggressiveness of the asset allocation strategy although

strategies with a higher proportion of stocks do not always result in better

outcomes than a strategy with a slightly lower proportion of stocks. More

importantly, it is observed that the difference between the VaR estimates of

different asset allocation strategies is very small.

The lowest observed VaR estimate is 3.3936 given by the strategy with lowest

allocation to stocks. This means that by employing this strategy there is a 5% (or

one-in-twenty) chance of the RWR falling below that level. The highest VaR

estimate (4.0033) is produced by the 100% stock strategy, which goes against

the conventional logic that stocks, being most volatile among the asset classes,

can potentially result in the most adverse outcomes. The results for ETL also

support these conclusions.

119

Table 4. 4: Tail Risk Estimates for RWR Distribution Table 4.4 reports tail risk estimates for the RWR Distribution from the Monte Carlo simulation. Value at Risk (VaR) and Expected Tail Loss (ETL) for RWR outcomes are estimated at 95% confidence level. Therefore, there is a 5% probability of the RWR falling below the VaR estimate. Conditional to the RWR falling below VaR i.e. for the worst 5% of RWR outcomes, the expected value is given by ETL.

PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA VaR ETL FIXED WEIGHT STRATEGIES

A. Conservative (Avg.) 3.4926 2.8843 1. UniSuper Balanced 3.3936 2.8416 2. Equipsuper Balanced Growth 3.4528 2.8546 3. HOSTPlus Balanced 3.3961 2.7940 4. Sunsuper Balanced 3.4546 2.8623 5. REST Core 3.5509 2.9596 6. Telstra Balanced (Under 60) 3.5407 2.8946 7. First State Super Diversified (Up to 56) 3.5439 2.9209 8. CARE Super Balanced 3.6079 2.9467 B. Moderate Aggressive (Avg.) 3.6832 2.9878 9. Westscheme Trustee's Selection 3.6781 3.0074 10. Vision Balanced Growth 3.6085 2.9194 11. HESTA Core Pool 3.7601 3.0432 12. NGS Diversified 3.6860 2.9813 C. High Aggressive (Avg.) 3.8715 3.0732 13. ARF Balanced 3.8085 3.0626 14. STA Balanced 3.8493 3.0136 15. Cbus Super 3.8785 3.0489 16. Health Long Term Growth (Less than

50) 3.8527 3.0394

17. MTAA 3.9685 3.2016


18. Telstra 3.3876 2.8527

19. First State Super 3.3596 2.8547

20. Health 3.4053 2.7809

HYPOTHETICAL STRATEGIES 21. Default Option Average 3.4616 2.8893 22. 100% Stock 4.0033 3.2043

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Table 4.4 (cont’d): Tail Risk Estimates for RWR Distribution


VaR ETL FIXED WEIGHT STRATEGIES


50) 2.5301 1.9845

17. MTAA 2.3603 1.7973


18. Telstra 2.4083 2.0388


20. Health 2.4494 1.973

HYPOTHETICAL STRATEGIES 21. Default Option Average 2.5196 2.028 22. 100% Stock 2.4100 1.8323

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Table 4.4 (cont’d): Tail Risk Estimates for RWR Distribution


FIXED WEIGHT STRATEGIES VaR ETL


50) 4.8043 3.6031

17. MTAA 4.6138 3.512


18. Telstra 5.4205 4.5456


20. Health 5.2157 4.3255

HYPOTHETICAL STRATEGIES

21. Default Option Average 5.1974 4.1088 22. 100% Stock 4.3970 3.2636

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The simulation results based on data for other periods present a slightly different

picture but do not alter the fundamental conclusion of the previous simulation.

Using data for 1947-2004 period, the VaR estimates of individual strategies are

found to lie within a very close range (2.3603-2.6014) and do not seem to follow

any clear pattern. The 100% stock strategy produces a VaR estimate of 2.41

which is almost the same as that of the strategy with the lowest stock allocation

(64%) but slightly lower than that of DOA strategy which has 67% allocation to

stocks and produces a VaR estimate of 2.5196. Similarly, the ETL estimates are

generally higher for the balanced strategies but only marginally, as with VaR

estimates.

Figure 4.3 Tail Risk Estimates of Asset Allocation Strategies VaR and ETL estimated at 95 % confidence level for simulations using asset class returns data for full period (1900-2004), post-war period (1947-2004), and most recent 30-year period (1975-2004). Lifecycle strategies are not included since these have changing allocation to stocks over time.

Simulation with data for 1975-2004 period results in higher VaR and ETL

estimates for balanced strategies compared to the more aggressive strategies.

Generally, VaR and ETL estimates seem to gradually deteriorate with increasing

123

stock allocation. This is quite the opposite of our results using 1900-2004 data

but the range of VaR estimates is still very narrow. The lowest estimate of

4.3970 is given by the 100% stocks strategy, which means that the participants

who invest in this strategy have a 5% chance of accumulating wealth that is less

than 4.39 times their final annual salary. The highest estimate of 5.4205 is

produced by lifecycle strategy #18 which invests two-thirds in stocks for

participants below 60 years and one-third thereafter. By adopting this strategy,

participants would have a 5% chance of having their plan account balance at

retirement less than 5.42 times their final annual salary. It is easy to see that the

gap between these two situations can hardly be considered as the difference

between a ruinous and a non-ruinous outcome. This is confirmed by the ETL

estimates which range from 3.2636 to 4.5456 indicating even the below 5%

outcomes are not very different between different allocation strategies. Thus our

evidence clearly implies that the risk of confronting extremely poor retirement

wealth outcomes may not be very sensitive to the choice of asset allocation

strategy.

The evidence on the most adverse outcomes for lifecycle strategies and their

corresponding fixed weight strategies is mixed. While simulations using data

for the full period and the post-war period result in lower VaR estimates for

lifecycle strategies compared to corresponding fixed weight strategies, the

results are quite the opposite for simulations based on the most recent 30 year

period (1975-2004) when all three lifecycle strategies are found to slightly

improve the VaR estimates. The ETL estimates also follow the same pattern

except for simulations with post war data where two of the three lifecycle

strategies produce higher estimates than their corresponding fixed weight

strategies. Based on this evidence, the claim of lifecycle strategies reducing the

risk of most unfavourable outcomes does not appear to be strong. Even in cases

where they reduce the severity of the extreme outcomes, the benefits appear to

be marginal.

124

4.5 Conclusion

Given the fact that Australian stocks have significantly outperformed fixed

income securities over long horizons in the past, it is no surprise that differences

between default investment options with respect to their exposure to stocks

result in large differences in simulated terminal wealth outcomes for DC plan

participants. More revealing is our finding that very high allocations to stocks

may actually prove to be less risky on most occasions if risk is viewed in the

context of falling short of the participant’s wealth accumulation target, in terms

of both probability and magnitude of shortfall.

At present, regulators in most countries, including Australia, do not prescribe

any asset allocation structure for default investment options. But very often they

emphasise the importance of diversification in coping with risk by optimizing its

trade-off with returns. Our results, however, raise serious questions about the

benefits of diversification for very long term investors like DC plan participants,

who seem to have higher likelihood of being better off by concentrating their

investments in stocks alone. We have demonstrated that the strategies that are

heavily tilted towards stocks not only reduce the chance of failure in meeting the

participants’ wealth accumulation target but also seem to diminish the extent of

shortfall in case the participants fail to achieve such objective. At the same

time, they seem to offer strong upside potential of generating terminal wealth

outcomes that outperform the participant's accumulation target at retirement.

Past research in this area like Booth and Yakoubov (2000) and Blake et al.

(2001) argue that a diversified portfolio with high equity content would yield

best results for the retirement plan investors. While our results are supportive of

their findings to the extent of their recommending a tilt towards equities in the

investors’ portfolios, we do not see much benefit arising from diversification.

The most powerful evidence against selecting balanced diversified strategies or

125

even moderately aggressive strategies as default options is provided by our

results for tail-related risk. As stock returns are essentially considered to be

more volatile than other asset class returns, one would have normally expected

their presence in the portfolio to cause more extreme outcomes. However, our

results indicate that the extreme wealth outcomes occur mostly at the upper tail

of the wealth distribution, which is actually favourable to the plan participant.

The measures for the extreme outcomes at the lower tail of retirement wealth

distribution suggest that higher allocation to stocks do not necessarily increase

the risk of confronting these adverse outcomes and in some cases, may even

reduce their severity. In our study, the risk of extremely adverse outcomes does

not seem to vary considerably with change of asset allocation which implies that

extreme loss aversion should have minimal role to play in the asset allocation

decision for default investment options.

Turning specifically to the issue of investment horizon, Thaler and Williamson

(1994) demonstrate that, for college and university endowment funds, who

traditionally hold a 60:40 mix of stocks and bonds, an allocation entirely to

stocks is likely to provide superior results most of the time. Although individual

retirement accounts under DC plans do not have a quasi-infinite investment

horizon as enjoyed by university endowment funds, it appears that the typical

DC plan participant’s holding period of 30 to 40 years may be considered

sufficiently long to warrant more aggressive allocation than what is currently

chosen by most plan sponsors for their default investment options. Like Poterba

et al. (2006) we find that 100% allocation of stocks is optimal for DC retirement

investors but we do not find this optimal allocation rule to change with the

degree of risk aversion of the plan participant, especially when we consider

performance adjusted for downside risk. Even when the participants demonstrate

an unreasonably high degree of risk aversion like when they care only about the

worst 5% outcomes, the case for plan providers nominating a conservative or

balanced strategy as default option does not appear to be strong.

126

Trustees using conservative or balanced diversified strategies as defaults may

argue that these strategies tend to reduce the variability of outcomes and

therefore can potentially minimize the problems associated with disparity in

wealth accumulated by different employee cohorts. But selection of defaults

primarily on this criterion can be deemed as flawed given that the trade-off

involves much lower accumulation of retirement wealth and therefore, defeats

the very purpose of instituting these plans. By nominating such ‘safe’ strategies

as defaults, plan providers may actually be instrumental in creating future

generations of retirees who are ‘more equal’ but ‘poorer’ instead of retiree

cohorts who are ‘less equal’ but nevertheless ‘wealthier’. This is also the case

with the lifecycle strategies considered in our study which reduce the variability

of wealth outcomes but at the cost of producing much lower retirement wealth

on average than what the participants could potentially achieve by not switching

to a relatively conservative allocation rule as they near retirement.

Shiller (2003) opines that merely defining and implementing the default option

correctly for individual accounts within social security can prove to be the most

effective tool for intervention. It appears that the same also applies to individual

accounts in DC plans. This study strongly suggests the possibility of widely

different wealth outcomes confronting many DC plan participants simply as a

result of the existing disparity in asset allocation structure between their plans'

default investment options. It demonstrates that the balanced diversified

strategies nominated by many plan providers in Australia as default investment

options may not be well suited to optimise the retirement benefits of the

participants. The problem may be even more serious for countries like the US,

where DC plans typically adopt an even more conservative approach towards

asset allocation.

127

Annexure 4A

Figure 4A.1: Simulated RWR Distribution



128


129

Annexure 4B: Bootstrap Simulation Results

Table 4B.1 Distribution Parameters for RWR We run a parallel test for generating wealth outcomes using non-parametric bootstrapping which draws asset class returns from the empirical return distribution. Here the historical return data series for the asset classes is randomly re-sampled with replacement to generate portfolio returns for every period of the 40 year investment horizon of the DC plan participant. A total of 5,000 iterations for every asset allocation strategy under consideration to generate different investment return paths over 40-year periods. We report the results from the various fixed weight strategies: conservative average, moderate average, and high aggressive average, the default option average and the 100 % stock options.

SIMULATION RESULTS BASED ON 1900-2004 DATA

Mean Median Max. Min. Q1 Q3 CV IQRR A. Conservative (Avg.) 9.87 8.36 71.50 1.24 5.79 12.18 0.61 0.76

B. Moderate Agg. (Avg.) 11.59 9.48 101.57 1.28 6.30 14.39 0.70 0.85

C. High Aggressive (Avg.) 13.67 10.87 137.58 1.33 6.96 17.05 0.76 0.93 Default Option Average 10.02 8.42 88.29 1.47 5.91 12.20 0.64 0.75 100% Stock 17.44 13.26 138.81 1.38 7.92 22.19 0.84 1.08

SIMULATION RESULTS BASED ON 1947-2004 DATA A. Conservative (Avg.) 7.79 6.35 80.92 0.92 4.22 9.65 0.70 0.85

B. Moderate Agg. (Avg.) 9.08 7.09 83.30 0.78 4.54 11.26 0.78 0.95

C. High Aggressive (Avg.) 10.67 7.79 150.19 0.89 4.75 13.05 0.93 1.06 Default Option Average 7.78 6.40 54.48 0.90 4.26 9.62 0.69 0.84 100% Stock 13.46 8.98 313.09 0.51 5.07 16.21 1.12 1.24

SIMULATION RESULTS BASED ON 1975-2004 DATA A. Conservative (Avg.) 16.57 13.69 128.54 2.11 9.25 20.54 0.67 0.82 B. Moderate Agg. (Avg.) 19.18 15.22 244.04 1.95 9.77 23.82 0.77 0.92 C. High Aggressive (Avg.) 22.14 16.46 297.49 1.70 10.04 27.50 0.89 1.06 Default Option Average 16.73 13.89 116.11 2.05 9.24 20.75 0.67 0.83 100% Stock 28.31 18.78 577.66 1.32 10.65 34.82 1.13 1.29

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Table 4B.2 Estimates for Downside Risk & Performance Measures



A. Conservative (Avg.) 0.47 1.16 3.96 0.94 1.52

B. Moderate Agg. (Avg.) 0.39 0.98 3.34 1.97 2.50 C. High Aggressive (Avg.) 0.33 0.81 2.82 3.42 3.90 21. Default Option Average 0.46 1.11 3.71 1.05 1.63 22. 100% Stock 0.25 0.63 2.26 6.27 6.70

SIMULATION RESULTS BASED ON 1947-2004 DATA A. Conservative (Avg.) 0.65 2.04 8.25 -0.07 0.64

B. Moderate Agg. (Avg.) 0.57 1.79 7.28 0.40 1.06

C. High Aggressive (Avg.) 0.52 1.64 6.75 1.03 1.66 Default Option Average 0.65 2.01 8.07 -0.08 0.63 100% Stock 0.44 1.46 6.22 2.19 2.77




B. Moderate Agg. (Avg.) 0.16 0.33 0.97 11.34 11.68

C. High Aggressive (Avg.) 0.16 0.33 1.02 13.98 14.31 Default Option Average 0.18 0.33 0.91 9.16 9.50 100% Stock 0.15 0.36 1.19 18.66 18.99

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Table 4B.3 Tail Risk Estimates


VaR ETL A. Conservative (Avg.) 3.47 2.87 B. Moderate Agg. (Avg.) 3.57 2.89 C. High Aggressive (Avg.) 3.72 2.97 Default Option Average 3.56 2.96 100% Stock 3.89 3.05

PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA A. Conservative (Avg.) 2.44 1.99 B. Moderate Agg. (Avg.) 2.44 1.95 C. High Aggressive (Avg.) 2.44 1.95 Default Option Average 2.52 2.07 100% Stock 2.39 1.85

PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA A. Conservative (Avg.) 5.41 4.45 B. Moderate Agg. (Avg.) 5.31 4.28 C. High Aggressive (Avg.) 5.21 4.16 Default Option Average 5.45 4.42 100% Stock 5.01 3.88

132

Annexure 4C: Monte Carlo Simulation Results with 5 Asset Classes

Table 4C.1 Asset Allocation for Default Investment Options

Stocks (%) Int’l

Stocks Bonds (%) Int’l

Bonds Cash (%) A. Conservative (Stocks w < 70% stocks) 43 23 17 12 5

UniSuper Balanced 39 25 21 15 0 Equipsuper Balanced Growth 45 20 17 13 5 HOSTPlus Balanced 43 23 19 13 2 Sunsuper Balanced 43 23 19 13 2 REST Core 46 20 15 9 10 Telstra Balanced* 44 23 23 10 0 First State Super Diversified# 38 29 5 12 16 CARE Super Balanced 49 20 16 10 5

B. Moderate Agg. (Stocks 70% ≥ w < 80%) 51 25 14 8 2 Westcheme Trustee's Selection 55 18 18 9 0 Vision Balanced Growth 46 28 14 9 3 HESTA Core Pool 52 25 14 7 2 NGS Diversified 49 30 11 8 2

C. High Aggressive (Stocks w ≥ 80%) 60 26 8 4 2 ARF Balanced 57 23 11 7 2 STA Balanced 58 25 10 5 2 Cbus Super 58 25 9 5 3 Health Long Term Growth^ 53 35 7 5 0 MTAA 72 21 3 1 3

Default Option Average 46 21 20 6 7 100% Stock 100 0 0 0 0

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Table 4C.2 Distribution Parameters of Retirement Wealth Ratio (RWR)

PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA Mean Median Max. Min. Q1 Q3 CV IQRR A. Conservative (Avg.) 10.40 8.36 112.30 1.18 5.52 12.82 7.56 0.87

UniSuper Balanced 10.22 8.35 95.48 1.32 5.49 12.66 7.18 0.86 Equipsuper Bal. Growth 10.24 8.20 107.17 1.17 5.50 12.44 7.56 0.85 HOSTPlus Balanced 10.51 8.30 218.11 1.38 5.56 13.01 7.98 0.90 Sunsuper Balanced 10.52 8.52 106.61 1.01 5.51 13.13 7.48 0.89 REST Core 10.42 8.27 97.39 1.15 5.41 12.98 7.73 0.92 Telstra Balanced 10.70 8.44 115.72 1.13 5.56 13.04 8.29 0.89 First State Super Div. 9.88 8.27 68.18 1.08 5.55 12.24 6.40 0.81 CARE Super Balanced 10.71 8.55 89.77 1.22 5.61 13.07 7.83 0.87

B. Moderate Agg. (Avg.) 12.35 9.59 146.57 1.04 6.04 15.32 9.86 0.97 Westscheme Trustee's Sel. 12.13 9.35 170.50 1.25 5.86 14.83 10.10 0.96 Vision Balanced Growth 11.70 9.29 103.28 1.01 5.95 14.51 8.72 0.92 HESTA Core Pool 12.67 9.70 157.90 0.92 6.07 15.82 10.34 1.00 NGS Diversified 12.90 10.01 154.62 0.97 6.27 16.13 10.30 0.98

C. High Aggressive (Avg.) 14.41 10.65 204.57 1.01 6.52 17.79 13.05 1.06 ARF Balanced 12.96 9.87 145.79 1.29 6.22 16.01 10.88 0.99 STA Balanced 13.85 10.26 206.34 0.90 6.39 17.09 12.53 1.04 Cbus Super 14.05 10.68 168.29 0.82 6.38 17.56 11.87 1.05 Health Long Term Growth 14.43 10.92 196.98 1.22 6.78 17.74 12.46 1.00 MTAA 16.73 11.49 305.47 0.84 6.83 20.55 17.53 1.19

Default Option Average 10.49 8.35 132.04 0.85 5.43 12.75 8.03 0.88 100% Stock 18.59 12.99 229.71 0.56 7.54 22.97 18.78 1.19

134

Table 4C.2 (cont’d): Distribution Parameters of Retirement Wealth Ratio (RWR)

PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA Mean Median Max. Min. Q1 Q3 CV IQRR

A. Conservative (Avg.) 10.49 8.91 78.41 1.50 6.16 12.97 6.52 0.76





135

Table 4C.2 (cont’d): Distribution Parameters of Retirement Wealth Ratio (RWR)

PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA Mean Median Max. Min. Q1 Q3 CV IQRR A. Conservative (Avg.) 16.74 14.03 148.72 2.08 9.58 20.78 10.76 0.80





136

Table 4C.3 Estimates for Downside Risk and Performance Measures




UniSuper Balanced 0.4698 1.2793 4.6107 1.036 1.6318 Equipsuper Balanced Growth 0.4846 1.2929 4.6551 1.0395 1.6388 HOSTPlus Balanced 0.4732 1.2399 4.3872 1.1986 1.7906 Sunsuper Balanced 0.4632 1.2599 4.6015 1.1733 1.7607 REST Core 0.4788 1.3261 4.9029 1.0919 1.6908 Telstra Balanced (Under 60) 0.4646 1.2598 4.5816 1.2625 1.8511 First State Super Div. (Up to 56) 0.477 1.2654 4.53 0.8827 1.4772 CARE Super Balanced 0.4584 1.2358 4.4993 1.2753 1.8579

B. Moderate Agg. (Avg.) 0.3948 1.0633 3.8659 2.2210 2.7616 Westscheme Trustee's Selection 0.4142 1.1255 4.106 2.0385 2.5939 Vision Balanced Growth 0.4044 1.091 3.984 1.8556 2.4022 HESTA Core Pool 0.387 1.052 3.8452 2.3818 2.9182 NGS Diversified 0.3734 0.9846 3.5284 2.608 3.1322

C. High Aggressive (Avg.) 0.3497 0.9377 3.4481 3.4684 3.9732 ARF Balanced 0.3778 1.0121 3.7071 2.5778 3.1035 STA Balanced 0.368 0.9698 3.531 3.1148 3.6309 Cbus Super 0.3542 0.9764 3.617 3.1834 3.6968 Health LT Growth (Less than 50) 0.3244 0.8528 3.077 3.6651 4.1513 MTAA 0.3242 0.8776 3.3086 4.8011 5.2836

Default Option Average 0.4752 1.3274 4.9693 1.1173 1.7128 100% Stock 0.2744 0.7414 2.7468 6.3868 6.8341

137

Table 4C.3 (cont’d): Estimates for Downside Risk and Performance Measures








138

Table 4C.3 (cont’d): Estimates for Downside Risk and Performance Measures








139

Table 4C.4 Tail Risk Estimates for RWR Distribution


VaR ETL A. Conservative (Avg.) 3.1612 2.5772

UniSuper Balanced 3.1546 2.5424 Equipsuper Balanced Growth 3.2471 2.6534 HOSTPlus Balanced 3.1508 2.5849 Sunsuper Balanced 3.0615 2.5037 REST Core 3.1525 2.5135 Telstra Balanced (Under 60) 3.2125 2.6559 First State Super Diversified (Up to 56) 3.1294 2.5206 CARE Super Balanced 3.1809 2.6428

B. Moderate Agg. (Avg.) 3.3492 2.6766 Westscheme Trustee's Selection 3.3103 2.6026 Vision Balanced Growth 3.2708 2.6484 HESTA Core Pool 3.3348 2.6747 NGS Diversified 3.4809 2.7806

C. High Aggressive (Avg.) 3.3961 2.6699 ARF Balanced 3.3741 2.6405 STA Balanced 3.3645 2.6669 Cbus Super 3.3218 2.6495 Health Long Term Growth (Less than 50) 3.5917 2.7977 MTAA 3.3286 2.595

Default Option Average 2.9724 2.366 100% Stock 3.6058 2.827

140

Table 4C.4 (cont’d): Tail Risk Estimates for RWR Distribution







141

Table 4C.4 (cont’d): Tail Risk Estimates for RWR Distribution







142

5. Gender-sensitive Contribution and Asset Allocation Strategies in Superannuation Plans

5.1 Introduction

5.1.1 Background

A common concern expressed in pension literature is that the retirement system in

most developed countries is biased against women. With the concept of welfare state

in many of these countries taking a backseat in the last few decades, as evidenced by

policies aimed at retrenchment of public pension coupled with growing emphasis on

private savings for retirement, the problem of gender inequity in pensions is bound

to erupt like never before.54 Private retirement systems are designed to reward long

and continuous periods of employment and penalize breaks. While this benefits the

typical male worker with uninterrupted working life, the retirement provisions of the

female workforce, whose participation in the labour market is often constrained by

their child bearing and family care responsibilities, is adversely affected. Career

profiles of most working women in Australia are characterised by a broken

employment pattern in early and middle years. Even where women work full-time,

their earnings are significantly lower compared to men. The result is a significantly

lower level of superannuation for women at retirement. How the relative

disadvantage in labour market would result in inferior retirement wealth outcomes

for women is well documented by several authors (see Rosenman & Winocur, 1994;

Sharp, 1995 among others).

The body of work looking into the problem confronting Australian women in

retirement is vast.55 Several authors focus specifically on the issue of gender

54 The dependence of female Australian workers on age pension in the face of lower superannuation outcomes has been demonstrated in earlier papers like Preston and Austen (2001). 55 Jefferson (2005) reviews this literature.

143

inequity in accumulation outcomes at retirement (Brown, 1994; Donath, 1998;

Preston & Austen, 2001). But much of this work stops at pointing out the

inadequacies of the current private superannuation plans in ensuring sufficient

accumulation for female workers in their accounts to maintain their lifestyle after

retirement. Some authors suggest changes to the existing arrangements but the

proposals put forward are often too subjective and imprecise to bring about any

significant change to the accumulation level of female workers within the current

superannuation framework. For example, Olsberg (2004) argues for greater equity

for women in workforce, more education on superannuation and investments, and

increasing female representation in governance of superannuation funds. One cannot

discount the impact of some of these proposals in addressing the problem of low

retirement income for Australian women. But the precise manner in which they

would impact retirement savings (and to what extent) is not clear.


This essay aims to demonstrate the impact of gender sensitive savings and asset

allocation policies in alleviating differences between superannuation wealth

accumulation outcomes for male and female workers of Australia. While one would

expect higher contribution rates for female workers would result in minimizing the

gender-based inequality in superannuation outcomes, the role of asset allocation in

addressing the inequality problem is not obvious. The importance of asset allocation

as a key determinant of long term investment performance has been universally

acknowledged since the publication of the seminal work by Brinson, Hood, and

Beebower (1986). In a study conducted among pension funds in UK, it was found

that more than 99% of the total return generated could be explained by the long-run

asset allocation specified by the plan sponsors (Blake, Lehmann, and Timmerman,

1998). Surprisingly, the possibility of using asset allocation to reduce the gender gap

144

in retirement wealth has not yet been considered by academic researchers or

policymakers in any country. We address this issue in this study.


We show that the current policy of having gender-neutral savings and investment

options for the workforce is almost always bound to result in lower superannuation

for the average female worker compared to her male counterpart. Specifically, the

distribution of superannuation assets for the average male member exhibits first

degree stochastic dominance over that for the average female member. However, we

find that establishing a different default arrangement (by superannuation funds) for

female workers may significantly alter this situation.56 This can be achieved through

either changing the mandatory contribution rate or changing the default asset

allocation strategy of the plans (or a combination of both) for the female member.

5.2 Methodology

This study uses stochastic simulation methods to compare the expected distributions

of superannuation accumulation outcomes of an average female plan member to that

of her male counterpart under several alternative savings and investment strategies.

We assume that the average male and female member joins the superannuation plan

at the age of 20 years and stays in the plan till their retirement at the age of 65 years.

56 We focus on default savings and investment arrangements since a vast body of contemporary scholarly work (for example, Choi et al., 2004; Cronqvist & Thaler, 2004) indicates that majority of employees passively accept the default contribution rates and investment strategies chosen by the trustees of their respective funds. In the Australian superannuation context, the importance of default choices is highlighted in Gallery, Gallery, and Brown (2004). As per the estimate of Australian Prudential Regulatory Authority, nearly two-third of all superannuation assets are invested in default investment options of various plans (APRA, 2005).

145

Our baseline case represents an average male worker with no voluntary break from

employment whose superannuation contribution is 9% of earnings which is equal to

the mandatory contribution rate for all Australian workers. The contributions of this

hypothetical male worker is assumed to be invested in a balanced fund holding 60%

of the assets in shares, 30% in bonds and the remaining 10% in cash. The asset

allocation structure of this classic balanced fund is akin to that of the average default

investment option offered by superannuation funds in Australia.57 The accumulation

outcome of the baseline male is then compared with those of an average female

worker under three alternative assumptions: (i) no voluntary break from

employment, (ii) a voluntary break of 5 years duration between the age of 26 and 30

and (iii) a voluntary break of 5 years between the age of 31 and 35. Under each of

these alternative scenarios, we use different contribution and asset allocation rules

for modeling the wealth outcomes at retirement. The details of these are discussed in

the section 5.4.

To estimate the terminal wealth outcomes for different contribution rates and asset

allocation strategies, we use a simple accumulation model which uses stochastic

simulation of asset class returns to determine the expected distribution of wealth

outcome at retirement. This has already been described in 3.1.1. In this chapter, we

assume uninterrupted contributions are made into the superannuation accounts the

male and female worker as long as they are not unemployed or not having voluntary

breaks from employment. For the sake of simplicity, we assume that the

contributions are credited annually to the accumulation fund at the end of every

year.58 The portfolios are also rebalanced at the end of each year to maintain the

target asset allocation. We also assume that plan contributions and investment

57 At the end of June 2004, the average default investment option had 33 % of assets held as Australian shares and 21 % in international shares. A further 15 % was invested in Australian fixed interest, 6 % in international fixed interest, 7 % in cash, 6 % in property, and 12 % in other assets (APRA, 2005). 58 In practice, the Australian Government has recently legislated that contributions need to be made, at a minimum, on a quarterly basis.

146

returns are not subject to any tax. Any transaction cost that may be incurred in

managing the investment of the plan assets is not considered.

For generating asset class returns, this study employs non-parametric bootstrapping

which draws asset class returns from the empirical return distribution.59 Here the

historical return data series for the asset classes is randomly resampled with

replacement to generate portfolio returns for every period of the 45 year investment

horizon of the male or female employee. In other words, each bootstrap sample is a

random sample of asset class returns for a particular period drawn with replacement

from historical observations over several periods. Thus we retain the cross-

correlation between the asset class returns as given by the historical data while

assuming that asset class return series is independently distributed over time. More

details about the resampling method employed in this study are provided in 3.2.2.

The asset class return vectors are then combined with the weights accorded to the

asset classes in the portfolio (which is governed by the asset allocation strategy) to

generate portfolio returns for each year in the 45 year horizon. The simulated

investment returns are applied to the retirement account balance at the end of every

year to arrive at the terminal wealth in the account. Each set of simulation

experiment is iterated 5,000 times for both the male and the female worker under

different employment scenarios resulting in a range of wealth outcomes confronting

the employee at the point of retirement.

To compare the distribution of terminal superannuation wealth outcomes of the

women under different assumptions about employment breaks, contribution rates,

and asset allocation strategies with that of the baseline male worker, we compute the

mean, median, and the quartiles of the distribution in every case. Comparing these

parameter estimates would give us some idea about the relative standing of different

59 We feel that this approach is superior to alternative parametric methods as the latter make strong assumptions about the empirical distribution of asset class returns. For example, Blake et al. (2001) assume annual asset returns are generated following multivariate normal stochastic process.

147

savings and asset allocation rules in improving superannuation outcomes for women.

However we are more interested in finding out how effective these strategies are in

offsetting the gender inequality in superannuation. To be effective any strategy

should be able to reduce the chance of the female worker underperforming the

baseline male worker. Also, as long as a strategy does not diminish that chance of

underperformance to zero, we need to estimate the magnitude of such

underperformance.

We compute a statistic called the probability of shortfall which represents the chance

of a female worker ending with less accumulated wealth than the baseline male

worker. This probability of shortfall is given by

0

1

)](,0[1∑

=−=

n

tfms WWMax

nP (39)

where mW and fW represents the terminal superannuation wealth for the male and

female worker respectively, and n the number of trials. While SP estimates the odds

of the hypothetical woman worker doing worse than the baseline male worker in

different situations, it does not describe the how large the shortfall in wealth

outcome for the former would be compared to that of the latter. To estimate the

magnitude of underperformance of the woman worker, we measure the expected

shortfall which is given by

∑=

−=n

tfms WWMax

nE

1

)](,0[1

(40)

SP and SE are equivalent to LPM of degree 0 and 1 respectively discussed in 2.7

and equations (39) and (40) are derived by modifying equation (20) in the context of

this problem.

To compare the most adverse outcomes for various strategies, we compute the VaR

estimates at 95% confidence level for the baseline male worker who uses a relatively

conservative allocation strategy with those generated by the more aggressive

148

strategies used by the hypothetical female worker. Further, we also compare ETL at

95% level of confidence for different allocation strategies which is the probability

weighted average of all outcomes which are below 5th percentile of the wealth

distribution.60 This statistic, in other words, considers all outcomes that are below

the 5th percentile outcome and provides the average of such conditional outcomes.

Details on VaR and ETL as measures of tail risk have already been discussed in 2.7.

5.3 Data

5.3.1 Earnings Data

For modeling wage and contributions, we employ weekly income data for

individuals from Australian Bureau of Statistics (ABS) 2001 Census of Population

and Housing. The dataset reports weekly individual incomes of Australian males and

females over 15 years in the following age ranges: 15-19 years, 20-24 years, 25-34

years, 35-44 years, 45-54 years, 55-64 years, 65-74 years, and above 75 years. In

this study, we base our analysis on simulated wealth outcomes for a male and a

female employee who joins the plan at the age of 20 years and retires at the age of

65 years. In other words, we ignore the ‘15-19 years’, ‘65-74 years’, and ‘above 75

years’ categories in building the wage profile of a typical male and a typical female

employee. This is done because a vast majority of the population in the ‘15-19

years’ range is reported to have either little (below $80 a week) or no income while

those above 65 years possibly derive most of their income from outside the labour

market. Table 5.1 provides the truncated income data used in this chapter.

60 Expected tail loss is an important risk measure used in actuarial science (see Dowd, 2005) and satisfy the criteria of coherent risk measures proposed by Artzner et al (1997, 1999)

149

Table 5.1: Weekly Individual Income of Australian Men and Women by Age

Income Category

20-24 years

25-34 years

35-44 years

45-54 years

55-64 years

MEN

Negative/Nil income

36,821 34,224 30,192 32,397 28,416

$1-$39 4,909 3,153 3,763 4,320 4,314 $40-$79 10,083 4,087 4,602 5,759 6,415 $80-$119 24,508 10,355 9,658 11,110 12,785 $120-$159 37,662 40,180 35,754 35,659 49,087 $160-$199 46,783 63,915 62,539 66,639 101,199 $200-$299 58,687 68,197 74,341 77,068 92,803 $300-$399 65,853 69,107 69,638 65,950 68,532 $400-$499 85,475 116,578 104,420 94,418 74,028 $500-$599 75,387 154,635 135,571 119,605 80,621 $600-$699 50,153 135,630 120,395 99,925 59,914 $700-$799 35,185 125,427 115,388 94,215 50,237 $800-$999 30,418 174,725 178,586 147,618 66,713 $1,000-$1,499 15,919 169,907 228,868 204,720 77,062 $1,500 or more 4,349 81,317 150,719 142,083 58,447

WOMEN

Negative/Nil income

35,351 77,744 85,450 100,419 67,002

$1-$39 5,817 19,376 26,253 18,673 12,696 $40-$79 14,258 44,375 45,163 23,418 16,078 $80-$119 28,565 53,367 51,468 29,647 24,552 $120-$159 38,865 60,141 63,989 58,617 70,625 $160-$199 45,537 70,180 82,906 97,987 150,701 $200-$299 77,057 135,167 166,293 142,454 149,838 $300-$399 82,885 150,200 175,262 130,954 83,128 $400-$499 79,570 137,611 160,047 132,643 62,363 $500-$599 69,610 129,242 128,658 117,193 48,556 $600-$699 45,414 106,851 93,661 85,681 32,422 $700-$799 27,891 90,659 73,497 66,452 24,187 $800-$999 16,504 114,820 94,653 89,650 29,458 $1,000-$1,499 5,667 80,605 87,967 88,792 27,156 $1,500 or more 1,399 28,580 36,612 29,726 11,622

Source: Australian Bureau of statistics 2001 Census of Population and Housing

150

However, one has to exercise caution about several limitations of modelling the

career wage profile of individuals using the above ABS dataset. First, to accurately

model career wage profiles the researcher would need a longitudinal dataset which

tracks earnings of individuals through their working lives - from commencement of

employment to retirement. But the ABS data gives the average weekly earnings for

individuals in different age ranges at a particular point in time (2001 in this case)

and therefore does not show the actual career wage experience of a particular

generational cohort throughout their working life. Second, between the

commencement of employment and retirement of our typical male and female

employee in this chapter (20 and 64 years respectively), the ABS data provides

income data for only 5 age ranges (20-24 years, 25-34 years, 35-44 years, 45-54

years, and 55-64 years). This leaves us with only 5 data-points or observations to

construct their career wage profiles. Also, we ignore any growth in real wages due to

economy wide productivity gains that individuals may experience over the next 45

years.

Another shortcoming of the dataset is that it provides number of individuals of

different age categories whose weekly incomes are within ranges which, in some

cases, can be as large as $500 (i.e. $1,000 to $1,499). This does not allow for correct

estimation of the average earning of individuals in a particular range because one

has no idea how evenly the actual individual earnings are spread within such income

range. For the purpose of simplicity, we take the midpoint of each income range as

the average income of the individuals in that range. Finally for all age groups, the

dataset aggregates all individuals earning more than $1,500 into a single income

category. In our modeling, we use $1,500 as the average income for individuals in

this range. Although this is bound to result in underestimating the average income

for individuals belonging to the highest income range in this dataset, the

consequences may not be very severe on our modeling of career wage profile given

151

that the size of this group is relatively small in most cases compared to those of the

lower income categories.

Figure 5.1: Income Distribution of Australian Population

Income Distribution of Australian Pouplation Betwee n 20 and 64 years

0100,000200,000300,000400,000500,000600,000700,000800,000

Negativ

e/Nil i

ncome

$1-$3

9

$40-$

79

$80-$

119

$120

-$15

9

$160

-$19

9

$200

-$29

9

$300

-$39

9

$400

-$49

9

$500

-$59

9

$600

-$69

9

$700

-$79

9

$800

-$99

9

$1,00

0-$1,499

$1,50

0 or m

ore

Number of Men

Number of Women

Several interesting observations can be made from the income data for individuals.

The income distribution of the male and female population between the age of 20

and 64 years are shown in Figure 5.1. For income categories below $500 per week,

women on aggregate outnumber men. This is also true when we compare the

genders across different age categories. However, as we move towards higher

income categories, number of women steadily declines relative to men. For the

highest income category in our dataset i.e. above $1,500, women are outnumbered

by men by a ratio greater than 4:1. The highest number of women workers fall

within the income category of $200-$299 per week closely followed by number of

women with weekly earnings in the $300-$399 and $400-$499 categories

respectively. Together these three categories account for almost one-third of all

women income earners. In contrast, the highest number of male income earners fall

within income category of $1000-$1499 followed by the income categories of $800-

152

$999 and $500-$599. Also noteworthy is the fact that the number of women with nil

or negative income is more than double the corresponding number of men.

Figure 5.2: Earnings Profile of Australian Population by Age

Earnings Profile of Average Male and Female Between 20 and 64 Years

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

20-24 years 25-34 years 35-44 years 45-54 years 55-64 years

Age

Inco

me

($)

Male

Female

Figure 5.2 plots the earnings profile of the average male and female worker between

the age of 20 and 64 years. Both demonstrate a hump-shaped pattern with earnings

growing in the initial years, reaching a plateau in the middle years and then

declining in later years although the hump is more pronounced in the case of the

average male worker. Earnings for the typical Australian female worker grow at a

relatively slower pace in the initial years. They also appear to peak much sooner

(between 25 to 34 years) compared to that of the male counterpart and then drop

slightly only to recover between 45 and 54 years. Thereafter the rate of decline is

similar to that of a male worker. Apparently the data not only lends support to the

existence of a substantial gender wage gap in Australia across all categories but also

reveals the differences between the lifetime earnings profiles of men and women.

153

5.3.2 Asset Class Returns

To resample asset class returns, this study uses an updated version of the dataset of

real returns for Australian stocks, bonds, and bills reported by Dimson, Marsh, and

Staunton (2002) and commercially available through Ibbotson Associates. This

annual return data series covers a period of 105 years between 1900 and 2004. Since

the dataset spans over several decades, it captures wide-ranging effects of favourable

and unfavourable events of history on returns of individual asset classes within our

test. The returns include reinvested income and capital gains. The descriptive

statistics for this data is provided in Appendix A. During this 105 year period, the

mean annual real return for Australian stocks has been 9.09% while the same for

Australian bonds and bills has been 2.27% and 0.72% respectively. The standard

deviation for stocks has also been higher at 17.74% compared to that for bonds

(13.36%) and bills (5.51%).


5.4.1 Contribution Rate

Initially, we focus on the impact of changing the superannuation contribution rate in

addressing the gender inequity in accumulation outcomes. Therefore, we need to

hold the asset allocation strategy constant for the male and female worker. We

assume that all superannuation contributions are invested in the balanced fund

described in 5.2. For the hypothetical male worker, which represents our baseline

case, the contribution rate is 9%. For the hypothetical female worker, we examine

the impact of a continuous career as well as that of a voluntary career break of 5

years. In our simulation model, we assume that this break occurs either at the age of

25 years or at 30 years although we acknowledge that these breaks can happen at

154

different ages for different woman. Also, our assumption of a continuous break for 5

years may not be representative of many women who may experience more than one

career break at different stages of their career. The contribution rates for the female

workers range from 9% to 16%. For every trial for the hypothetical female worker

under alternative assumptions about employment breaks, a parallel trial is conducted

for the baseline male worker. The results are given in Table 5.2.

For the female worker with no career break (Panel A), the results indicate the stark

differences between the accumulation outcomes of Australian men and women. In

case the contribution rate is same for both the genders, the projected outcomes for

the male dominate those of the females for all 5000 simulation trials i.e. there is

stochastic dominance of the first order. The mean and median accumulation of the

male worker exceeds that of his female counterpart by more than $186,000 and

$156,000 respectively. This result is significant as it gives an idea about the quantum

of shortfall in accumulation that would be experienced by an average woman worker

under the current regime of gender-blind superannuation plans even if she does not

take any voluntary break during her career.

The gap in accumulation between the genders grows even further if the hypothetical

woman worker has a voluntary career break, a distinct possibility confronted by

most Australian women. Every outcome for female worker under this condition is

dominated by the corresponding outcome of the male worker. A 5-year break from

employment at the age of 25 (Panel B) results in a mean accumulation for the

average female worker that is almost $300,000 less compared to that of the average

male worker. The median account balance for the former is also less than that of the

latter by a staggering amount of more than $ 237,000. The average wealth

differential between the male and the female worker also increases to $288,485. If

the female worker defers this career break till she is 30 (Panel C), the probability of

underperforming the baseline outcome still remains at 100%. However, the average

shortfall in this case declines slightly to $263,981.

155

Table 5.2 Accumulation Outcomes for Different Female contribution Rates

Table 5.2 reports the superannuation accumulation results of simulation trials for a hypothetical male and female worker in Australia who join the workforce at the age 20 and retire at the age of 64 for different contribution rates of the latter. The accumulation outcomes of the male worker are compared to those for a female with no voluntary break in employment (Panel A), with a voluntary break in employment between 25 and 30 years (Panel B) and with a voluntary break in employment between 30 and 35 years (Panel C).

SP represents the probability of the accumulation of the female worker falling below that of the male worker.

SE is the expected shortfall of the female accumulation outcome i.e. the probability weighted average of the amount by which the accumulation for the female worker falls short of that of the male worker. Contribution Rate Mean Median

25th Percentile

75th Percentile SP

SE

PANEL A

Male: 9% 660,322 551,392 373,595 820,129 Female: 9% 476,274 395,222 265,286 591,562 100% 184,047 Male: 9% 656,535 552,043 378,813 820,179 Female: 12% 622,897 520,463 354,068 781,262 100% 33,638 Male: 9% 656,127 554,317 371,646 814,304 Female: 12.5% 647,603 544,548 362,465 806,628 86% 9,974 Male: 9% 659,953 546,966 367,199 831,464 Female: 12.75% 663,940 547,558 364,778 837,870 49% 2,850

PANEL B Male: 9% 654,039 544,186 361,446 822,651 Female: 9% 365,554 306,831 205,162 459,603 100% 288,485

Male: 9% 662,048 559,897 370,630 822,965 Female: 12% 492,761 420,946 282,163 610,859 100% 169,287 Male: 9% 660,129 554,277 368,665 825,380 Female: 15% 614,193 520,776 349,338 762,904 92% 46,630 Male: 9% 669,069 561,338 373,178 835,128 Female: 16% 663,421 564,586 378,691 828,662 47% 15,993

PANEL C

Male: 9% 660,051 555,442 369,869 820,576 Female: 9% 396,069 331,281 222,340 492,675 100% 263,981 Male: 9% 666,186 555535 368005 838751 Female: 12% 533,711 442640 294861 664923 100% 132,475

Male: 9% 655,380 545769 362952 821870 Female: 15% 655,179 542623 363448 816312 49% 12,000

156

The above results spring no surprise given the existence of the gender wage gap in

the Australian labour market. Lower earnings for women over the lifecycle are

bound to result in lower superannuation contributions which in turn produce less

terminal wealth at retirement relative to male workers in the same cohort as both the

sexes experience the same investment return path. The likelihood of longer absence

from paid work for women further widens the mismatch. One way of reducing the

imbalance in wealth outcomes would be to increase the superannuation contribution

rate for women. But the key question is to what extent it needs to be increased. Our

simulation results throw light on this issue. For the woman worker with no voluntary

break from employment, increasing the contribution rate to 12% reduces the average

size of the terminal wealth shortfall to $33,638 (compared to $184087 in case of 9%

contribution). But still every accumulation outcome falls short of the corresponding

outcome for the baseline male worker. However, if the contribution rate for the

female worker goes up further to 12.5%, the probability of underperforming male

accumulation outcomes at retirement comes down to 86% and the size of

underperformance dramatically decreases to below $10,000. A further increase of

female contribution rate to 12.75% actually turns the odds slightly in favour of the

female workers. The probability of underperforming the male baseline is now only

49% i.e. there is now a 51% chance of the female worker retiring with a higher

superannuation balance. The corresponding average shortfall is now below $3000.

At a contribution rate of 13%, the female accumulation outcomes dominate

corresponding male projected outcomes in 86% of cases.

While a contribution rate of 12.5% would give the woman worker with continuous

employment almost an even chance of doing as well as men in superannuation, this

is not a realistic scenario for most Australian women who spend less time in paid

work than typical men. To assess the amount of contribution for women with broken

employment record required to match the outcome of the baseline male worker, we

look at the results presented in panels B and C of Table 5.2. As expected an increase

in female contribution rate to 12% does not lead to a dramatic reduction in the size

157

of average shortfall. A break for 5 years at the age of 25 would lead to an expected

shortfall of $169,287 relative to the male worker with no break in employment. If

the break is experienced at the age of 30, the expected shortfall would be still very

large at $132,475. A contribution rate of 16% (if break occurs at 25) or 15% (if

break occurs at 30) would be necessary for the female worker to bring down the

probability of shortfall relative to the baseline male worker below 50%. But the

average size of shortfall at $15993 and $12000 respectively in these cases are still

higher than that of the woman with no career break and contribution rate of 12.75%.

5.4.2 Asset Allocation

While the above results underlines the significance of higher contributions for

Australian women workers to reduce the gender disparity in retirement wealth

outcomes, a novel alternative approach to tackling this issue may lie in the

investment strategy chosen by the worker participants. Since the only investment

decision made by superannuation fund members in Australia is asset allocation i.e.

how to divide the contributions in their account among various asset classes, we

examine the impact of changing the asset allocation strategy on terminal wealth at

retirement.61 Empirical evidence for most developed nations overwhelmingly

suggests that the probability of growth assets like stocks underperforming less

volatile assets like bonds over longer holding periods is extremely low.62 However,

the average default investment strategy for superannuation funds in Australia

allocates only about 54% of their assets to shares (APRA, 2005). If one includes

investments in asset categories like property, the total allocation to growth assets for

the average default fund increases to 60%. Given the long investment horizon of 61 American workers, in contrast, have the option to choose between an array of funds offered by different fund managers in investing their plan contributions. 62 The literature on this subject is vast. Siegel (1994) provides a good account in the US market while Jorion and Goetzmann’s (1999) studies this phenomenon in international markets.

158

superannuation members and the large equity premium prevalent in Australian and

major international markets over last several decades, this asset allocation strategy

may be regarded as unduly conservative.63 Therefore, it as an attractive option for

the researcher to investigate whether resorting to a more aggressive investment

strategy can actually help Australian women to overcome the gender inequity in

retirement wealth outcomes.

For all simulation trials conducted in this part of our investigation, we hold the

contribution rate for both the male and female worker constant at the current

mandatory rate of 9%. For the sake of simplicity, we assume investments are made

only in Australian shares, bonds, and bills.64 The asset allocation strategy adopted by

the baseline male worker always resembles a balanced fund holding 60% of its

assets in shares, 30% in bonds and the remaining 10% in cash. For the woman

worker, in addition to the classic balanced fund described above, we explore wealth

outcomes under alternative strategies with increasing allocation to growth assets i.e.

shares. This is compensated by an equal reduction in the proportion of assets

invested in bonds and cash. However, to meet liquidity requirements of the fund, the

allocation to cash is assumed to never go below 5% (apart from the extreme case

where allocation to share is 100%). For example, a 10% increase in allocation to

shares from 60 to 70% is matched by a 5% decline in allocation to bonds (from 30 to

25%) and 5% decline in allocation to cash (from 10% to 5%). But a further increase

of share investments to 80% leads to a 10% decline in allocation to bonds (from

25% to 15%) while the allocation to cash remains unchanged at 5%.

63 This is also supported by our findings in chapter 4. 64 Most Australian superannuation funds, obviously, would invest in international shares and bonds. But this is not expected to alter our results significantly since a majority of these assets are held in US and UK markets, the returns of which are highly correlated with those in Australian domestic market. We also ignore properties and alternative assets in our analysis because of the paucity of reliable long run data on their returns.

159

Table 5.3: Accumulation Outcomes for Different Female Asset Allocation Strategies

Table 5.3 reports the superannuation accumulation results of simulation trials for a hypothetical male and female worker in Australia who join the workforce at the age 20 and retire at the age of 64 for different asset allocation strategies employed by the latter. The accumulation outcomes of the male worker are compared to those for a female with no voluntary break in employment (Panel A), with a voluntary break in employment between 25 and 30 years (Panel B) and with a voluntary break in employment between 30 and 35 years (Panel C). The allocation of the male worker to shares is constant at 60 % while allocation to shares for the female worker is changed for each set of simulation experiment consisting of 5000 trials.

SP represents the probability of the accumulation of

the female worker falling below that of the male worker. SE is the expected shortfall of the female

accumulation outcome i.e. the probability weighted average of the amount by which the accumulation for the female falls short of that of the male worker.

Allocation to Shares Mean Median

25th Percentile

75th Percentile

SP SE

PANEL A

Male: 60% 664,015 561,477 372,063 830,892 Female: 70% 597,295 480,357 301,116 746,496 94% 71,427 Male: 60% 668,332 559,850 372,673 832,108 Female: 75% 669,681 518,907 323,422 840,281 69% 38,036

Male: 60% 659,571 553,586 368,400 823,700 Female: 80% 726,348 559,311 343,222 909,111 49% 24,081

PANEL B

Male: 60% 662,048 559,897 370,630 822,965 Female: 70% 455,140 372,421 239,193 571,582 100% 206,908

Male: 60% 660,129 554,277 368,665 825,380 Female: 80% 550,210 432,049 272,157 687,667 93% 117,130 Male: 60% 669,069 561,338 373,178 835,128 Female: 90% 686,090 508,750 303,123 856,292 66% 61,792 Male: 60% 650,186 540,071 359,247 814,638 Female: 95% 729,388 521,922 306,261 905,812 56% 50,834

Male: 60% 653,648 540,748 376,424 804,847 Female: 100% 824,474 577,415 335,566 999,982 43% 35,733

160

Table 5.3 (Cont’d): Accumulation Outcomes for Different Female Asset Allocation Strategies


25th Percentile

75th Percentile

SP SE

PANEL C



The results under different asset allocation rules adopted by the female worker vis-à-

vis the baseline male worker is presented in Table 5.3. For the woman who does not

go through any voluntary break in employment, an increase in allocation to shares to

70% slightly reduces the chance of underperforming the male outcome to 94%

(compared to 100% in case both the genders follow the same balanced allocation

strategy). But it leads to a remarkable decline in the average size of the

underperformance. The average size of shortfall relative to the accumulation

outcome for the baseline male worker is now $71,427 which is less than 40% of

what it would be ($184,087) had the female worker invested in the same balanced

strategy chosen for the male worker. If the allocation to shares is increased by

another 5% to 75%, the impact is a dramatic drop in the probability of shortfall to

69%. In other words, there is almost a 1 in 3 chance now that the female worker

would outperform the baseline male worker. A further increase in allocation to

shares to 80% for the former gives her more than an even (1 in 2) chance of ending

with a higher superannuation account balance in retirement than the latter.

161

For the alternative scenario of the woman worker experiencing 5-year breaks from

employment, the impact of pursuing more aggressive investment strategies is far less

spectacular in terms of reducing the chance of underperforming the baseline male

worker. If the break happens at the age of 25, even an investment strategy with 80%

allocation to stocks would result in a modest improvement in shortfall probability to

93%. The results indicate that unless the entire superannuation contribution is

invested in a portfolio with almost 100% allocation to shares, this female worker has

less than an even chance to match the accumulation of the baseline male worker. If

the break happens later in her career at the age of 30, a similar result is achieved

with an allocation of 95% to shares, which is still very high. The aggressive asset

allocation strategies, however, prove effective in trimming down the magnitude of

underperformance relative to the baseline male case. For example, by employing an

allocation rule which invests 90% of assets in shares, the female worker with 5 year

employment break at the age of 25, reduces the expected shortfall to $61,792 which

is less than a quarter of the expected shortfall she would be exposed to if she invests

using the same allocation rule as the baseline male.

However employing highly aggressive asset allocation strategies to improve

terminal wealth outcomes for female workers (or reducing the expected shortfall)

may have pitfalls. The higher volatility of returns from share market is the key

concern here. While mean reversion is a well demonstrated feature of past history of

stock market returns (Poterba and Summers, 1988; Fama and French, 1988),

theoretically, the chance of many consecutive years of low or negative returns from

investments in shares in future cannot be ruled out. In the case of such an

occurrence, the wealth outcome for a highly aggressive strategy can be extremely

adverse. A large number of simulation trials (5000 in this study) which resample

past returns, positive and negative, with replacement can potentially capture these

extremely adverse outcomes at the lower end of the wealth distribution for each

investment strategy. The results for these extremely adverse outcomes are presented

in Table 5.4.

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Table 5.4: Extreme Adverse Outcomes for Different Female Asset Allocation Strategies

Table 5.4 reports estimates of the most adverse outcomes for different asset allocation strategies employed by a hypothetical female worker in Australia who join the workforce at the age 20 and retire at the age of 64. The Value-at-Risk (VaR) estimate is computed at 95% level of confidence. The Expected Tail Loss is a conditional measure given by the probability weighted average of all accumulation outcomes that are below VaR. Panels A, B, and C represents the accumulation outcomes for a female with no voluntary break in employment with a voluntary break in employment between 25 and 30 years and with a voluntary break in employment between 30 and 35 years respectively.

Allocation to Shares VaR ETL

PANEL A

60% 150,557 121,550 70% 160,141 130,509 75% 170,147 133,984 80% 169,519 131,978

PANEL B

60% 122,870 100,646 70% 131,662 107,764 80% 137,945 109,093 90% 150,471 116,962

PANEL C

60% 129,018 104,652 70% 136,643 109,155 80% 150,902 117,670 90% 152,912 117,752

Contrary to expectations, they show that the risk of encountering extremely adverse

outcomes by pursuing a more aggressive strategy is not significantly different from

following a less aggressive one. For the female employee with continuous

employment record, the VaR estimates are actually better for strategies with higher

allocation to shares. For example, allocating 70% to shares results in a VaR estimate

of $160,141 whereas increasing the allocation of shares to 75% produces a

corresponding estimate ($170,147) which is higher by more than $10,000.

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Increasing the allocation to shares further to 80%, however, results in a slightly

lower VaR estimate at $169,519. The ETL estimates are also extremely close for

different asset allocation strategies. When we look at the woman worker with

breaks, the results indicate that more aggressive strategies generally produce better

outcomes at the lower tail of the wealth distribution. This is clear from the

increasing trends in both the VaR and the ETL estimate with an increase in

allocation to stocks. This is apparently confounding due to their inconsistency with

the conventional notion of risk and return going hand in hand. Yet our results are

well supported by the empirical evidence showing that the risk of investing in shares

over less volatile assets like bond and cash decrease over longer holding periods.

This is demonstrated to be true both under assumptions that future returns are

random drawings from distribution of past returns (Butler and Domian (1991)) and

mean reversion of returns in the long run (Thaler and Williamson (1994)).

5.4.3 Combination

So far we have demonstrated the effectiveness of increasing contribution rates and

adopting aggressive asset allocation approaches in mitigating the gender inequality

in superannuation outcomes. Yet one cannot discount the fact that prescriptive

changes of this scale are difficult to implement in practice. To give the female

worker, who has a very high chance of experiencing a career break for childbearing

and caring requirements, an even chance of accumulating as much in superannuation

as the baseline male worker, her contributions have to be raised to 15% or 16% from

the current 9% level. To fill this gap is no easy task for the policymakers as it is

bound to meet with strong opposition from employers or the employees depending

on who is made to pay for this increase in contributions. If the mandatory employer

contribution rates are increased significantly for female workers, it may give rise to

discrimination against employing women by many employers. On the other hand, if

the female workers themselves are subjected to a compulsory or voluntary

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contribution regime to fill this gap, it is unlikely to find much favour as it involves

substantial trade-off with their current consumption needs.

The alternative solution of setting aggressive portfolio strategies for female workers

may be even more controversial although this does not require any extra

contributions from the employer or the employees. International research evidence

finds women to be more risk averse than men and this is reflected in their preference

for relatively conservative investment strategies (see e.g. Bajtelsmit, Bernasek, &

Jianakoplos, 1999; Bernasek & Shwiff, 2001).65 Therefore, any default arrangement

that allocates more than 90% of female superannuation assets to the share market (as

our results suggest) in order to match male retirement outcomes could be viewed as

reckless by current standards.

A third approach to address the problem would be to use a combination of higher

contributions and aggressive asset allocation for the woman employee. We put this

to the test by conducting simulations that set female contribution at a slightly higher

level of 12% and then adjust the asset allocation to match the superannuation

outcomes of the baseline male worker. The results are reported in Table 5.5. For the

woman with no voluntary break in employment, the consequence is astounding.

With a modest increase in contribution rate (to 12%) and exposure to shares (to

70%), the accumulation outcomes for the woman now dominates those of her male

counterpart most of the time. The probability of the female doing worse than a male

is reduced to a meagre 9% with an expected shortfall of only $800. The median

outcome for the female worker outperforms that of the baseline male by nearly

$80,000.

65 In Australia, Gerrans and Clark-Murphy (2004) finds support for this assertion. Some researchers, however, find that with equal access to financial knowledge and information, there is little difference between the investment behaviour of men and women (see for instance Dwyer, Gilkeson & List, 2002). .

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Table 5.5: Accumulation Outcomes for Different Female Contribution Rates and Asset Allocation Strategies

Table 5.5 reports the superannuation accumulation results of simulation trials for a hypothetical male and female worker in Australia who join the workforce at the age 20 and retire at the age of 64. The contribution rate and asset allocation for male worker is constant while the female worker has a constant but higher contribution rate and employs a range of different asset allocation strategies. The accumulation outcomes of the male worker are compared to those for a female with no voluntary break in employment (Panel A), with a voluntary break in employment between 25 and 30 years (Panel B) and with a voluntary break in employment between 30 and 35 years (Panel C). The contribution rate of the male worker remains constant at 9 % and allocation to shares is also constant at 60 %.

SP represents the probability of the accumulation of the female worker falling below that of the male worker. SE is the expected shortfall of the female accumulation outcome.

Contribution Rate


25th Percentile

75th Percentile SP

SE

PANEL A

Male 9% 60% 661,619 558,777 371,128 819,093 Female 12% 70% 794,187 637,462 401,755 988,134 0.09 800

PANEL B

Male 9% 60% 660,322 551,392 373,595 820,129 Female 12% 70% 605,406 491,184 323,197 757,062 0.92 59,461 Male 9% 60% 656,535 552,043 378,813 820,179 Female 12% 80% 725,501 576,141 360,670 910,521 0.43 18,927

PANEL C Male 9% 60% 662,048 559,897 370,630 822,965 Female 12% 70% 648,023 524,302 333,364 809,337 0.75 33,693 Male 9% 60% 669,069 561,338 373,178 835,128 Female 12% 75% 730,192 570,722 360,411 916,911 0.44 15,581

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The above results for the female worker using a combination of ‘higher contribution

rate’ and ‘aggressive asset allocation’ are far superior to those obtained previously

when we employed these strategies individually (Tables A and B respectively). For

instance, with a contribution rate of 12% alone, the female with no voluntary break

in employment was always certain to accumulate less than the baseline male i.e.

probability of shortfall was 100%. The average size of the shortfall was also much

larger (more than $33,000). If on the other hand the female worker contributed the

same 9% as the baseline male worker but invested in a more aggressive portfolio of

70% of assets in shares, she would still be underperforming the male worker in 94%

of cases with an even larger expected shortfall exceeding $71,000.

The combination approach also seems to work well for the hypothetical woman with

voluntary breaks in employment although the break in contributions needs to be

compensated by holding a more aggressive portfolio if her contribution rate remains

unchanged at 12%. To give the woman worker a more than even chance to

outperform the baseline male accumulation at retirement (i.e. SP < 0.5), our results

indicate that her portfolio exposure to shares has to be between 75% and 80%

depending on the timing of the break. Again, had the female worker relied on an

increased contribution rate of 12% alone, she had little chance of matching the

accumulation of the baseline male. The expected shortfall, for the woman with

career breaks at the age of 25 and 30 years would be $169,287 and $132,475

respectively which is considerably higher compared to $18,927 and $15,581, the

value of expected shortfalls in case the same woman employed the combination

approach. Similarly by holding a portfolio with 80% of assets invested in shares

(without altering the contribution rate), she would have struggled to match the male

accumulation outcomes in most cases (93% and 82% respectively for breaks at the

age of 25 and 30) and confronting a higher expected shortfall ($117,130 and $79,834

respectively for breaks at the age of 25 and 30).

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5.5 Conclusion

Hill and Tigges (1995) like many other authors point out that pension systems were

historically developed ‘by men with men in mind’. The Australian superannuation

system, which is assuming a prominent place in the retirement income landscape of

the workforce, is no exception. Inequality in labour market performance is bound to

put Australian women at a serious disadvantage in retirement compared to men.

Many studies in the past have highlighted the problem of gender inequity in

retirement. But there has been little research done on examining the solutions to the

problem especially in terms of quantifying their precise impact on differences in

superannuation account balances of male and female workers. Among those like

Preston and Austen (2001) that have put forward proposals like increases in

contribution rates or removal of exemptions for employer contributions tax have not

explained how these measures would neutralise the relative disadvantage of women

to men in retirement plan accumulation.

In this chapter, we have examined the effectiveness of two alternative strategies –

higher contribution rates and aggressive asset allocation for female workers– in

addressing the inherent, albeit inadvertent, discrimination in the current

superannuation arrangement. Whilst our results suggest that both these approaches

are individually useful in mitigating the gender inequality in wealth outcomes at

retirement, we find that their effectiveness grows manifold when used in tandem. A

combined approach is also appealing from policymaker’s perspective since it

demands relatively modest changes to current mandatory contribution rates and

default asset allocation of the average superannuation fund.

As Thomson (1999) points out an equal treatment of the genders by the

superannuation system would result in unequal outcomes in presence of women’s

enduring disadvantage in the labour market. The evidence presented in this chapter

supports this contention and suggests that there is a compelling case for instituting

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gender specific contribution and investment strategies in superannuation plans. It

may be argued, perhaps not entirely without merit, that such a policy would actually

hope to nullify women’s inferior performance in one market (labour) partly by

increasing their exposure to the performance risk in another market (investment).

But while women’s relative disadvantage in the former market is almost certain to

continue for many years in future, our past experience on long term performance of

the latter provides strong ground for optimism.

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6. Portfolio Size Effect and Lifecycle Asset Allocation

6.1 Introduction

6.1.1 Background

Lifecycle funds have gained great popularity in recent years. Sponsors of defined

contribution (DC) plans offer more and more of these funds as investment options to

their participants. In many cases, these funds serve as default investment vehicles for

plan participants who do not make any choice about investment of their plan

contributions. The findings of the Mercer 2000 survey of DC plans in UK (as cited

in Blake, 2006) show that these funds were the most common default options

covering 55% of funds. As reported by Vanguard (2006), one of the largest pension

plan managers in USA, two thirds of their plans offered lifecycle options in 2005, up

from one-third in 2000. Assets under lifecycle funds amounted to $160 billion in

2005 compared to below $10 billion in 1996 (Gordon & Stockton, 2006).66 The

rapid growth in lifecycle investment programs in DC plans is often attributed to the

fact that they simplify asset allocation choice for millions of ordinary investors who

supposedly lack the knowledge or inclination to adjust their portfolios over time. For

them, the lifecycle fund offers an automatic one-step solution by modifying the asset

allocation of retirement investments periodically in tune with the investors’

changing capacity to bear risk.

66 Not all lifecycle funds change their asset allocation over time. Static allocation funds offered by various providers which have the same exposure to various asset classes throughout the investment horizon are also sometimes categorised as lifecycle or lifestyle funds. In contrast, the lifecycle funds we discuss in this and the next chapter change their allocation over time and therefore are often referred to as age-based or target retirement funds. It is this type of age-based lifecycle funds that has witnessed the highest growth in the last few years (Mottola and Utkus, 2005).

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The central theme of the lifecycle model of investing is that one’s portfolio should

become increasingly conservative with age (See, for example, Malkiel, 1996) In

retirement plans, this is done by switching investments from more volatile assets

(like stocks) to less volatile assets (fixed interest securities like bonds and cash) as

the participant approaches retirement. For example, the Vanguard Target Retirement

Funds prospectus states that ‘It is also important to realize that the asset allocation

strategy you use today may not be appropriate as you move closer to retirement. The

Target Retirement Funds are designed to provide you with a single Fund whose

asset allocation changes over time as your investment horizon changes. Each

Fund’s asset allocation becomes more conservative as you approach retirement.’

While lifecycle funds offered by different providers differ from one another with

respect to how and when they switch assets, there is total unanimity about the

overall direction of the switch – from stocks to bonds and cash.

The practitioners’ belief that one’s exposure to risky assets should decrease with age

(and consequent shortening of investment horizon) has been theoretically refuted by

Samuelson (1963) and more recently by Bodie (1995) among others. Their argument

holds under a ‘random walk’ model of stock returns, an assumption that is open to

question. On the other hand, there is no dearth of theoretical work that lends support

to the concept of horizon based investing (for example, Merrill and Thorley, 1996;

Levy and Cohen, 1998). The riskiness of stocks over longer horizons seem to reduce

much faster than what is predicted by the random walk model, a phenomenon which

can be attributed to mean-reverting behaviour of stock returns observed in empirical

data. In contrast, returns on fixed income securities like bonds and bills are found to

be mean-averting in many cases (Siegel, 2003).67

67 If asset returns follow a random walk, the annualized standard deviation over a holding period of n

years is given by nσ where σ is the standard deviation over one year. The fact that the shrinkage of standard deviation for stock returns over long horizon is higher than this prediction of random walk model is often cited as an evidence of mean reversion. For fixed income assets, the empirical evidence is quite the opposite i.e. the shrinkage is lower than the prediction of the model.

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More recently, Campbell and Viceira (1999, 2002) have studied this question under

the assumption of time-varying expected stock returns. They find it optimal for long

horizon investors to have a strategic tilt in their portfolio towards equities.68

However the idea of age-based investing focused on mean-reversion is a

controversial area in finance with ongoing debate about the robustness of the

statistical evidence on stock return predictability. Some research disputes this

evidence (Goyal & Welch, 2007), while others find it acceptable (Lewellen, 2004;

Campbell & Thomson, 2007).69

The relationship between horizons and investment risk has also been examined by

empirical researchers with different conclusions.70 Much of the empirical work,

however, considers the case of a multi-period investor who invests in a portfolio of

assets at the beginning of the first period and reinvests the original sum and the

accumulated returns over several periods in the investment horizon.71 The situation

of retirement plan participants, however, is more complex because they make fresh

additional investments in every period till retirement in the form of plan

contributions. As a result, the retirement plan participant’s terminal wealth is not

only determined by the strategic asset allocation governing investment returns but

also by the contribution amounts that go into the retirement account every period

since these alter the size of the portfolio at different points on the horizon.

68 However they argue against a buy and hold strategy in view of the mean reverting behaviour of stock prices. They recommend a periodic revision in allocation in response to change in market conditions. 69 A completely different justification for age-based lifecycle investing is provided by considerations about human capital (Bodie, Merton, and Samuelson, 1992). An excellent review of the literature on optimal asset allocation under different assumptions about riskiness of human capital is provided by Viceira (2007) 70 For example, McEnally (1985) and Butler and Domian (1991) examine the effect although they reach different conclusions. This is, however, a result of different measures of risk employed by the researchers. While the former views variability of terminal wealth as risk, the latter uses probability of stocks underperforming bonds and T-bills over long horizons as the risk measure. 71 An exception to this is Hickman et al. (2001) who model the terminal value of a retirement investor’s portfolio where contributions are made every month. However, they assume that contributions remain equal throughout the horizon.

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A recent observation by Robert Shiller (2005b) harps on this issue and questions the

intuitive foundation of conventional lifecycle switching for retirement investors.

Shiller argues that “a lifecycle plan that makes the percent allocated to stocks

something akin to the privately- offered lifecycle plans may do much worse than a

100% stocks portfolio since young people have relatively little income when

compared to older workers…... The lifecycle portfolio would be heavily in the stock

market (in the early years) only for a relatively small amount of money, and would

pull most of the portfolio out of the stock market in the very years when earnings are

highest.” The statement is remarkable in asserting that the portfolio size of plan

participants at different points of time is significant from the asset allocation

perspective. If the above is true, then lifecycle funds may be missing a trick by

ignoring the growing size of the participant’s portfolio over time while switching

assets.

The size of the participant’s retirement portfolio is likely to grow over time, not only

because of possible growth in earnings and size of contributions as Shiller indicates,

but also due to regular accumulation of plan contributions and investment returns. In

such case, it would make little sense for the investor to follow the prescriptions of

conventional lifecycle asset allocation. By moving away from stocks to low return

asset classes as the size of their funds grow larger, the investor in effect would be

foregoing the opportunity to earn higher returns on a larger sum of money invested.

But there is another side to this story. Advocates of lifecycle strategies point out that

a severe downturn in the stock market at later stages of working life can have

dangerous consequences for the financial health of a participant holding a stock-

heavy retirement portfolio, not only because it can significantly erode the value of

the nest egg but also because it leaves the participant with very little time to recover

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from the bad investment results. Lifecycle funds, on the other hand, are specifically

designed to preserve the nest egg of the investor nearing retirement. By gradually

switching investments from stocks to less volatile assets over time, they aim to

lessen the chance of confronting very adverse investment outcome during that

period.

In this chapter, we examine whether by reducing the allocation to stocks as the

participants approach retirement, the lifecycle investment strategy benefits or works

against the retirement plan participant’s wealth accumulation goal. We are

particularly interested to test whether growing size of the accumulation portfolio in

later years indeed calls for a higher allocation to stocks to produce better outcomes

despite the looming danger of facing sharp decline in stock prices close to

retirement. Since an important objective of lifecycle strategy is to avoid the most

disastrous outcomes at retirement, we examine various possible scenarios,

particularly the most adverse ones, to assess their efficacy as the investment vehicle

of choice for DC plan participants.


Using stochastic simulation, we report that the existence of a portfolio size effect in

retirement plan investments causes the terminal wealth to be more sensitive to the

asset allocation strategy employed closer to retirement than that followed in the

early years after joining the plan. Since lifecycle strategies systematically switch

investments away from growth assets during the years leading to retirement, they

seem to dampen the growth potential of the retirement investor’s portfolio. The

sooner the lifecycle strategy starts switching from stocks to bonds and cash, more

pronounced is the dampening effect. On the other hand, by switching to less volatile

assets lifecycle strategies appear to reduce the severity of disastrous wealth

outcomes in a few cases caused by stock market downturns within a few years prior

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to retirement. But, as we argue in this essay, the switching seems to be justified only

when the portfolio value matches or exceeds the participant’s target accumulation.

We further discuss the case against deterministic lifecycle switching in chapter 7.

6.2 Methodology

We examine the case of a hypothetical retirement plan participant with starting

salary of $25,000 and contribution rate of 9%. The growth in salary is taken as 4%

per year. The participant’s employment life is assumed to be 41 years during which

regular contributions are made into the retirement plan account. For the sake of

simplicity, we assume that the contributions are credited annually to the

accumulation fund at the end of every year and the portfolio is also rebalanced at the

same time to maintain the target asset allocation. Therefore, the first investment is

made at the end of the first year of employment followed by 39 more annual

contributions to the account.

A number of studies in recent years including Hickman et al. (2001) and Shiller

(2005a) compare terminal wealth outcomes of 100% stocks portfolios with those of

lifecycle portfolios and find little reason for investors to choose lifecycle strategies

for investing retirement plan contributions. But these studies are not specifically

designed to test whether the allocation towards stocks should be favoured during the

later stages of the investment horizon because of the growth in size of one’s

portfolio. This is because the competing strategies invest in different asset classes

for different lengths of time and therefore they are bound to result in different

outcomes simply because of the return differentials between the asset classes. For

example, one may argue that a 100% stocks portfolio may dominate a lifecycle

portfolio purely because the former holds stocks for longer duration. The role played

by the growing size of the portfolio over time and its interplay with the asset

allocation in influencing the final wealth outcome is not very clear from this result.

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6.2.1 Lifecycle and Contrarian Strategy Pairs

To find out whether the growth in size of contributions and overall portfolio with the

investor’s age renders the conventional lifecycle asset allocation model counter-

productive, as Shiller conjectures, we formulate a novel test. We consider

hypothetical strategies which invest in less volatile assets like bonds and cash when

the participants are younger and switch to stocks as they get older i.e. strategies that

reverse the direction of asset switching of conventional lifecycle models. These

strategies, which we call contrarian strategies in the remainder of this chapter, are

well placed to exploit the high returns offered by the stock market as the participants

accumulation fund grow larger during the later part of their career. Moreover, we

design these strategies in such a manner that they hold different asset classes for

identical lengths of time as corresponding lifecycle strategies. This is necessary to

ensure that we are not comparing apples to oranges which would be the case if we

compare the outcomes of any lifecycle strategy with a fixed weight strategy like one

holding 100% stocks throughout the horizon or even with another lifecycle strategy

which holds stocks (and other asset classes) for an unequal length of time.72

Initially we construct four stylised lifecycle strategies, all of which initially invest in

a 100% stocks portfolio but start switching assets from stocks to less volatile assets

(bonds and cash) at different points of time - after 20, 25, 30, and 35 years of

commencement of investment respectively.73 We make a simplified assumption that

the switching of assets takes place annually in a linear fashion in such a manner that

in the final year before retirement all four lifecycle strategies are invested in bonds

and cash only. The proportion of assets switched from stocks every year is equally

72 An exception would be the case where the average allocation of the lifecycle strategy to any asset class over the investment horizon exactly matches that of the fixed weight strategy it is compared with. 73 Blake (2006) observes that the most common switchover period among lifecycle funds offered in UK is 5 years prior to retirement followed by 10 years prior to retirement.

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allocated between bonds and cash.74 Next we pair each lifecycle strategy with a

contrarian strategy that is actually its mirror image in terms of asset allocation. In

other words, they replicate the asset allocation of lifecycle portfolios in the reverse

order. All four contrarian strategies invest in a portfolio comprising only bonds and

cash in the beginning and then switch to stocks linearly every year in proportions

which mirror the asset switching for corresponding lifecycle strategies. The four

pairs of lifecycle and contrarian strategies are described below.

Figure 6.1: Asset Allocation over Investment Horizon (Pair A)

74 Information about precise asset allocation of existing lifecycle funds at every point on the horizon is rarely made available in the providers’ prospectus. Our formulation follows the general direction of the switch and does not try to consciously replicate the allocation of any of the existing funds.

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Pair A. The lifecycle strategy (20, 20) invests only in stocks for the first 20 years

and then linearly switches assets towards bonds and cash over the remaining period.

At the end of the 40 years, all assets are held in bonds and cash. The corresponding

contrarian strategy (20, 20) invests only in bonds and cash in the initial year of

investment. It linearly switches assets towards stocks over the first 20 years at the

end of which the resultant portfolio comprises only of stocks. This allocation

remains unchanged for the next 20 years. Figure 6.1 graphically demonstrates this

allocation rule.

Figure 6.2: Asset Allocation over Investment Horizon (Pair B)

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Pair B. The lifecycle strategy (25, 15) invests only in stocks for the first 25 years




investment. It then linearly switches assets towards stocks over the first 15 years at

the end of which the resultant portfolio comprises only of stocks. This allocation

remains unchanged for the remaining 25 years. Figure 6.2 graphically demonstrates

this allocation rule.

Figure 6.3: Asset Allocation over Investment Horizon (Pair C)

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Pair C. The lifecycle strategy (30, 10) invests only in stocks for the first 30 years




investment. It linearly switches assets towards stocks over the first 10 years at the

end of which the resultant portfolio comprises only of stocks. This allocation

remains unchanged for the remaining 30 years. Figure 6.3 graphically demonstrates

this allocation rule.

Figure 6.4: Asset Allocation over Investment Horizon (Pair D)

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Pair D. The lifecycle strategy (35, 5) invests only in stocks for the first 35 years and

then linearly switches assets towards bonds and cash over the remaining period. At

the end of the 40 years, all assets are held in bonds and cash. The corresponding

contrarian strategy (5, 35) is initially invested 100% in bonds and cash. It linearly

switches assets towards stocks over the first 5 years at the end of which the resultant

portfolio comprises only of stocks. This allocation remains unchanged for the

remaining 35 years. Figure 6.4 graphically demonstrates this allocation rule.

The above test formulation allows us to directly compare wealth outcomes for a

lifecycle strategy to those of a contrarian strategy that invest in stocks (and

conservative assets) for the same duration but at different points on the investment

horizon. The allocation of any lifecycle strategy is identical to that of the paired

contrarian strategy in terms of length of time they invest in stocks (and conservative

assets). They only differ in terms of when they invest in stocks (and conservative

assets) - early or late in the investment horizon. For example, in case of pair A, both

lifecycle (20, 20) strategy and contrarian (20, 20) strategy invests in a 100% stocks

portfolio for 20 years and allocate assets between stocks, bonds, and cash for the

remaining 20 years in identical proportions. However, the former holds a 100%

stocks portfolio during the first 20 years of the horizon in contrast to the latter which

holds a 100% stocks portfolio during the last 20 years of the horizon. The same is

graphically demonstrated in Figures 6.1.


To generate investment returns under every strategy, we randomly draw with

replacement from the empirical distribution of asset class returns. The historical

annual return data for the asset classes over several years is randomly resampled

with replacement to generate asset class return vectors for each year of the 40 year

investment horizon of the DC plan participant. Thus we retain the cross-correlation

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between the asset class returns as given by the historical data series while assuming

that returns for individual asset classes are independently distributed over time. The

asset class return vectors are then combined with the weights accorded to the asset

classes in the portfolio (which is governed by the asset allocation strategy) to

generate portfolio returns for each year in the 40 year horizon. The simulated

investment returns are applied to the retirement account balance at the end of every

year to arrive at the terminal wealth in the account. For each lifecycle and contrarian

strategy the simulation is iterated 10,000 times. Thus, for each of the eight strategies,

we have 10,000 investment return paths that result in 10,000 wealth outcomes at the

end of the 40-year horizon. More details about the resampling method employed in

this study are provided in 3.2.2.

6.2.3 Data

To resample returns, this study uses an updated version of the dataset of nominal

returns for US stocks, bonds, and bills originally compiled by Dimson, Marsh, and

Staunton (2002) and commercially available through Ibbotson Associates. This

annual return data series covers a period of 105 years between 1900 and 2004. Since

the dataset spans several decades, we are able to capture the wide-ranging effects of

favourable and unfavourable events of history on returns of individual asset classes

within our test. The returns include reinvested income and capital gains. More

details about the data have been discussed in 3.3. The descriptive statistics for the

dataset is provided in Appendix C.

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6.3.1 Terminal Wealth Estimates

Comparing various parameters of the terminal wealth distribution for the lifecycle

strategies and their contrarian counterparts provide us with a fair view of their

relative appeal to the retirement investor. In particular, we look at the mean, the

median, and the quartiles of the terminal wealth distribution under the different asset

allocation strategies. These are reported in Table 6.1. Even a cursory glance reveals

that there are significant differences between these estimates under the lifecycle and

contrarian strategy in every pair.

For each of the four pairs, we observe that the contrarian strategies result in much

higher expected value (mean) than the lifecycle strategies. The difference is most

striking for pair A and pair B as the mean wealth at retirement for the contrarian

strategies exceed those for the corresponding lifecycle strategies by more than half a

million dollars. While the differences between expected values for the other two

lifecycle and contrarian pairs (C and D) are less spectacular, they are still very large.

However, it is important to note that the mean is not the most likely outcome or even

average likely outcome for any of the strategies. This is apparent from the skewness

of the terminal wealth distributions. The means of the distributions are much higher

than the medians indicating the probability of achieving the mean outcome is much

less than 50%. In other words, the participants should have ‘better than average’

luck to come up with the mean outcome at retirement. The average outcome in this

case is, therefore, much more accurately represented by the median of all outcomes.

But even when one looks at the median estimates, the story does not change at all.

For all pairs, the contrarian portfolios easily beat the lifecycle portfolios. For

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example, the contrarian (20, 20) strategy in pair A results in a median final wealth of

$1,425,387. The corresponding lifecycle (20, 20) strategy manages only $1,160,225

thus falling short by a whooping $265,162. The same margins for pair B, C, and D,

are $270,763, $176,531, and $121,584 respectively.

Table 6.1: Terminal Value of Retirement Portfolio in Nominal Dollars

Strategy

Mean

Median

25th

Percentile 75th

Percentile Pair A Lifecycle (20,20) 1,420,332 1,160,225 793,371 1,724,852 Contrarian (20,20) 1,959,490 1,425,387 838,796 2,435,856 CONT - LCYL (%) 38.0 22.9 5.7 41.2 Pair B Lifecycle (25,15) 1,645,154 1,275,577 825,149 2,004,439 Contrarian (15,25) 2,173,389 1,546,339 889,496 2,702,427 CONT - LCYL (%) 32.1 21.2 7.8 34.8 Pair C Lifecycle (30,10) 1,909,918 1,411,168 876,711 2,355,363 Contrarian (10, 30) 2,335,373 1,587,699 909,020 2,864,003 CONT - LCYL (%) 22.3 12.5 3.7 21.6 Pair D Lifecycle (35,5) 2,253,731 1,578,405 918,483 2,764,413 Contrarian (5,35) 2,491,247 1,699,990 964,222 3,032,984 CONT - LCYL (%) 10.5 7.7 5.0 9.7 CONT – LYCL = Contrarian Strategy Terminal Value – Lifecycle Strategy Terminal Value (Expressed as percentage of the lifecycle strategy terminal value)

We also compare the 75th percentile and 25th estimates which represent the mid-

point of the above average and the below average outcomes respectively. For the

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75th percentile estimates, which are practically the medians of the ‘above median’

outcomes, the differences between the lifecycle and the corresponding contrarian

portfolios grow even wider than those for median estimates. For pair A, the 75th

percentile outcome for the contrarian portfolio is about 41% larger than the lifecycle

portfolio which translates a wealth difference of more than $700,000 i.e. Even for

pair D, where the results for the two strategies are the closest, the contrarian

portfolio is still better off by more than a quarter million dollars.

For 25th percentile estimates, which represents the medians of the ‘below median’

outcomes, one would normally expect the lifecycle strategies to perform better given

they are specifically designed to protect the retirement portfolio against the adverse

market movements in the final years. Well, they certainly do better in terms of

closing the gap with but are still not able to outperform contrarian strategies for any

of the pairs. Even for pair C, where the two estimates are the closest, the result for

the contrarian (10, 30) strategy is almost 4% ($32,000) higher than that for the

corresponding lifecycle (30, 10) strategy.

Although the dominance of contrarian strategies over their lifecycle counterparts is

clearly visible for all pairs, the difference between the outcomes of the two strategies

gets monotonically smaller as we move from pair A to pair D. This is expected as

each subsequent pair of strategies has greater overlap in terms of holding the same

asset class at the same point on the horizon (i.e. identical allocation) than the

previous pair. For example, at no point of time do the lifecycle (20, 20) strategy and

the contrarian (20, 20) strategy in pair A have identical allocation to the asset

classes. In stark contrast, the lifecycle (35, 5) and the contrarian (5, 30) strategies in

pair D have identical allocation for 30 years (between 6th and 36th year), during

which both are invested in 100% stocks portfolio, thus resulting in final wealth

outcomes that are closer to one another than those produced by other pairs where the

lifecycle and contrarian strategies have shorter overlapping periods of identical

allocation.

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6.3.2 Accumulation Paths over Horizon

The above results indicate that if the plan participant’s objective is to maximise

wealth at the end of horizon, lifecycle strategies vastly underperform relative to the

contrarian strategies. Shiller’s emphasis on exposing the portfolio in later years to

higher returns offered by stock market seems to be a possible candidate in

explaining the superior 40-year performance of the contrarian strategies. But to have

proper understanding of the interaction between portfolio size and asset allocation, it

is necessary to track the accumulation paths of the lifecycle and corresponding

contrarian strategies in the early, middle, and final years. In other words, to obtain

more compelling evidence of the portfolio size effect, we need to plot the simulated

portfolios over the entire 40 year period. Figures 6.5 to 6.8 depict the accumulation

paths over 40 years for each pair of lifecycle and contrarian strategies.

It is evident from the figures that for every lifecycle and contrarian strategy, the

slopes of the accumulation curves generally steepen as they move along the horizon

which seems to indicate that the potential for rapid growth in retirement nest egg

comes only in the later years. What is most striking in this respect is that every

lifecycle strategy and its paired contrarian strategy display very similar

accumulation outcomes in the initial years despite the difference in their asset

allocation structures. In fact, till half way through the 40-year horizon, there is very

little to choose between the accumulation patterns of the lifecycle strategy and those

of the contrarian strategy. It is only when the accumulation plots move well beyond

the half-way mark they start looking markedly different.75 This seems to suggest

that, in the initial years, accumulation in the retirement account may not be very

sensitive to the asset allocation strategy chosen by the participant.

75 Two dimensional accumulation plots provided in the annexure to this chapter also make this very clear.

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Figure 6.5: Simulated Accumulation Paths over Investment Horizon (Pair A)

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Figure 6.6: Simulated Accumulation Paths over Investment Horizon

(Pair B)

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(Pair C)

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(Pair D)

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The slopes of the accumulation curves under lifecycle strategies and those of the

corresponding contrarian strategies become conspicuously different during the later

years. The lifecycle portfolios generally enjoy a smooth climb as they move along

the horizon while the contrarian portfolios have far steeper ascent. This clearly

demonstrates the effect of portfolio size on the terminal wealth outcome. By

allowing exposure of large portfolios to stock market in later years, the contrarian

strategies produce spectacular growth opportunities. A closer examination of the

plots would reveal that in many cases the contrarian portfolios leapfrog over the

lifecycle portfolios only at very late stages in the investment horizon but still

manage to result in huge differences in terminal balance. For example, accumulation

balances for the contrarian (20, 20) strategy in pair A lags behind those of the

lifecycle (20, 20) strategy for the best part of 40 years. However not only do they

manage to catch up the lifecycle portfolios in the final years before retirement but

actually leave them way behind by the time the investors reach the finishing line.

It does not escape our attention that the accumulation profiles for the contrarian

strategies get much rougher towards the end of the horizon. This is certainly

indicative of higher variability of outcomes. But does this indicate higher risk?

Looking at the skewness of the terminal wealth distributions under contrarian

strategies, it is clear that the higher variability is mainly the result of some extremely

large accumulation outcomes. If the plan participant’s goal is to avoid the possibility

of disastrous outcomes, this kind of variability would be of little relevance in

gauging actual risk.

6.3.3 Adverse Outcomes and Tail Risk

Looking at the lower tail of the distribution which comprises of the adverse wealth

outcomes however, would be more sensible to compare the riskiness of the

competing strategies. It is quite possible that higher volatility of returns for

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contrarian strategies in the later years can result in large losses and very poor

terminal accumulations at least in some cases. In other words, lifecycle strategies

may actually generate better outcomes at the lower tail of the terminal wealth

distribution compared to contrarian strategies. From results reported in Table 6.1, we

have already observed that the first quartile outcomes of contrarian strategies

dominate those for lifecycle strategies in every case. Now we compare various

percentiles of distribution within the first quartile range which may be considered as

the zone of most adverse outcomes for the plan participant. Table 6.2 tabulates the

VaR estimates at 99%, 95%, 90%, 85%, and 80% levels of confidence under

different lifecycle and contrarian strategies.

Table 6.2: VaR Estimates for Lifecycle & Contrarian Strategies

Asset Allocation Strategy VaR estimates at Differen t Confidence Levels ($) 99% 95% 90% 85% 80% Pair A Lifecycle (20,20) 370,049 483,800 577,066 654,132 728,573 Contrarian (20,20) 258,637 407,053 532,291 639,031 738,534 LCYL – CONT (%) 43.08 18.85 8.41 2.36 -1.35 Pair B Lifecycle (25,15) 343,326 466,203 571,193 662,194 744,045 Contrarian (15,25) 259,630 424,103 557,240 673,115 778,744 LCYL – CONT (%) 32.24 9.93 2.50 -1.62 -4.46 Pair C Lifecycle (30,10) 318,211 470,271 585,107 685,409 781,134 Contrarian (10, 30) 249,829 434,660 567,613 682,174 803,828 LCYL – CONT (%) 27.37 8.19 3.08 0.47 -2.82 Pair D Lifecycle (35,5) 301,184 455,267 589,409 700,323 817,011 Contrarian (5,35) 264,326 446,592 600,863 719,279 843,420 LCYL – CONT (%) 13.94 1.94 -1.91 -2.64 -3.13 LYCL - CONT = Lifecycle Strategy Terminal Value - Contrarian Strategy Terminal Value ((Expressed as percentage of the contrarian strategy terminal value)

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It is evident from comparing the VaR estimates that lifecycle strategies do produce

better outcomes than their contrarian counterparts when we consider only the

outcomes in the lowest decile (10th percentile or below) of the distribution. However

this is not without exception as we observe that the VaR estimate for the lifecycle

(35, 5) strategy in pair D at 90% confidence level is lower than that of the

corresponding contrarian strategy. The difference between the VaR estimates for

every pair is highest at 99% confidence level and reduces gradually as we decrease

the level of confidence. But what is remarkable is that the final wealth under the

contrarian strategies in the worst case scenarios falls short of the corresponding

lifecycle strategies by a margin which is far less significant relative to the size of the

overall accumulation. For the VaR estimates at confidence level of 99% (and 95%),

this ranges from a little more than $100,000 (and $75,000) for pair A to about

$37,000 (and $8,000) for pair D. The difference between the estimates seems to

become less significant around the 85% confidence level with the contrarian

strategies resulting in slightly higher estimates for pairs B and D. For estimates at

80% confidence level, the dominance of the contrarian strategies is clearly visible

for all the four pairs.

The above results show that lifecycle strategies do not always fare better than the

contrarian strategies even in terms of reducing the risk of adverse outcomes. Only

when we compare the VaR estimates at confidence level of 90% and above,

lifecycle strategies fare slightly better. A chance of encountering poorer outcomes is

less than 1 in 10. However, it is very unlikely that investors in reality would select a

lifecycle asset allocation model with the sole objective of minimizing the severity of

these extremely adverse outcomes, should they occur, because the cost of such

action is substantial in terms of foregone wealth. For example, if the 10th percentile

outcome (which is equivalent to the 90% VaR estimate) is confronted at retirement,

one could be better off only by about 8% by following the lifecycle (20, 20) strategy

rather than the contrarian (20, 20) strategy. But for the 90th percentile outcome,

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which is equally likely to happen, one would be 55% better off by following the

contrarian (20, 20) strategy instead of the lifecycle (20, 20) strategy.76 Choosing one

strategy over the other in this case can result in considerable difference in lifestyle

after retirement.

The opportunity for risk reduction varies considerably between various lifecycle

strategies. These are more visible for lifecycle strategies that start changing their

asset allocation relatively earlier in the investment horizon than those that do so

later. For example, the 95% VaR estimate for lifecycle (20, 20) strategy is almost

19% higher than the contrarian (20, 20) strategy. The same estimate for lifecycle

(25, 15), (30, 10), and (35, 5) strategies, which switch to conservative assets

relatively later, vis-à-vis corresponding contrarian strategies 10%, 8%, and 2%

respectively indicating declining risk reduction advantage for lifecycle strategies that

delay switching to conservative assets. Ironically, reducing the risk of extreme

outcomes by switching early to conservative assets involves a very heavy penalty in

terms of foregone accumulation of wealth. This becomes apparent from the variation

in terminal wealth outcomes for the four lifecycle strategies in question.

6.4 Conclusion

The apparently naïve contrarian strategies which, defying conventional wisdom,

switch to risky stocks from conservative assets produce far superior wealth outcomes

relative to conventional lifecycle strategies in all but the most extreme cases. This

demonstrates that the size of the portfolio at different stages of the lifecycle exerts

substantial influence on the investment outcomes and therefore should be carefully

considered while making asset allocation decisions. The evidence presented in this

chapter lends support to Shiller’s view that the growing size of the participants’

76 The 90th percentile terminal wealth estimates, although not provided in this chapter, are available from the author on request.

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contributions in the later years calls for aggressive asset allocation which is quite the

opposite of what is currently done by lifecycle asset allocation funds.

It is important to emphasize here that we are clearly not suggesting that one should

follow any of the contrarian asset allocation strategies to allocate retirement plan

assets. We have formulated and used them in this study only to conduct a fair test of

the hypothesis that by investing conservatively in middle and later years lifecycle

funds work against the participant’s investment objectives. Our results show that, in

most cases, the growth in portfolio size experienced in the later years of employment

seems to justify holding a portfolio which is at least as aggressive as that held in the

early years. For some participants, this may well mean holding 100% stocks

throughout the horizon.

By their own admission, financial advisors recommending lifecycle strategies focus

on two objectives: maximizing growth in the initial years of investing and reducing

volatility of returns in the later years. Our findings suggest that the bulk of the

growth in value of accumulated wealth actually takes place in the later years. The

first objective, therefore, has little relevance to the overarching investment goal of

augmenting the terminal value of plan assets. We do find some support for pursuing

the second objective of reducing volatility in later years to lessen the impact of

severe market downturns but this comes at a high cost of giving up significant

upside potential. In other words, the effect of portfolio size on wealth outcomes over

long horizons is so large that it outweighs the volatility reduction benefit of lifecycle

strategies in most cases. Therefore, switching to less volatile assets a few years

before retirement can only be rationalized if the employee participants have already

accumulated wealth which equals or exceeds their target accumulation at retirement.

Several studies in the past like Ludvik (1994), Booth and Yakoubov (2000), Blake et

al. (2001) have found lifecycle asset allocation strategies to be sub-optimal for

pension plan participants. The results of this chapter, therefore, are in agreement

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with these findings. However, unlike past studies, we have taken a step further to

reveal the specific reason why age based (but performance blind) lifecycle switching

causes inferior outcomes for the retirement plan investor. The portfolio size effect,

as has been demonstrated in this chapter, plays a major role behind the poor

performance of conventional lifecycle strategies.

If lifecycle strategies aim to preserve accumulated wealth, then it seems one has to

first ensure sufficient accumulation in the retirement investor’s account before

recommending switch towards conservative investments. Unfortunately, this is not

the case with lifecycle funds currently used in DC plans, where the asset switching is

done following a pre-determined mechanistic allocation rule and without giving any

cognizance to the actual accumulation in the account. It seems that retirement

investors would be better off by refraining from blindly adopting these age-based

investment strategies that are keen on preservation even when there is not much to

preserve.

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ANNEXURE 6A: Two Dimensional Accumulation Plots

Figure 6A.1: Two-Dimensional View of Accumulation Paths over Horizon (Pair A)

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Figure 6A.2: Two-Dimensional View of Accumulation Paths over Horizon (Pair B)

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Figure 6A.3: Two-Dimensional View of Accumulation Paths over Horizon (Pair C)

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Figure 6A.4 Two-Dimensional View of Accumulation Paths over Horizon (Pair D)

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7. A Dynamic Asset Allocation Framework for Lifecycle Investing in Retirement Plans

7.1 Introduction

7.1.1 Background

Lifecycle or target retirement funds have gained favour with retirement plan

investors in recent years. As a rule of thumb, these funds have high initial

concentration in stocks but gradually move towards less volatile assets like bonds

and cash. Thus, it is often argued, they offer the best of both worlds – robust

portfolio growth in the early years of employment and preservation of the

accumulated wealth as the investors approach retirement. Also, once enrolled there

is no need for the investors to keep constant vigil over their investment strategy. The

switching of assets (from stocks to fixed income) over the years happens

automatically following a preset glide path laid down by the plan provider.

But does the predisposition of lifecycle funds to systematically switch out of equities

benefit the investors of target retirement funds? Empirical research in the past has

generally found that a switch to low-risk assets prior to retirement can reduce the

risk of confronting the most extreme negative outcomes. Lifecycle strategies are also

said to reduce the volatility of wealth outcomes making them desirable to investors

who seek a reliable estimate of final pension a few years before retirement.77 On the

other hand, there is near unanimity among most researchers that these benefits come

at a substantial cost to the investor - giving up significant upside potential of wealth

accumulation offered by more aggressive strategies. Authors like Siegel (1992) and

77 For example, see Ludvik (1994) or Blake et al. (2001).

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Kim and Wong (1997) find that holding a portfolio heavily tilted towards stocks is

the optimal investment strategy for long horizon investors like retirement plan

participants.


This study questions the rationale of the deterministic nature of switching from

stocks to fixed income assets as is the prevalent practice among most lifecycle

funds. The most common argument cited by the proponents of the lifecycle strategy

in retirement plans is apparently straightforward – the probability that returns from

stocks would outperform (underperform) those from bonds and cash increases

(decreases) with the length of the investment horizon. If this is true, then long

horizon investors may prefer to have a higher allocation to stocks in their portfolio

compared to investors with shorter investment horizons.78 It is also argued that

younger investors in retirement plans should heavily invest in stocks not only

because of the prospect of higher returns but also for the reason that investors have

enough time to recover from stock market downturn(s) should that happen. On the

other hand, for older investors with a few years to retire, holding such an aggressive

portfolio can spell disaster. A major slump in the stock market just before retirement

can potentially wipe away years of investment gains with little time to salvage the

situation. But would this imply that investors should automatically reduce the

proportion of stocks in their retirement portfolio as years go by? The following

example would explain why the answer may not be always in the affirmative.

78 This is sometimes referred to as ‘time diversification’. Samuelson (1989, 1994) shows that if returns are independently and identically distributed such long horizon effect cannot exist. While Samuelson’s argument is mathematically sound, mean reversion in stock returns is a well documented empirical phenomenon. For example, Poterba and Summers (1988), provides evidence from the US market.

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Suppose an investor has a horizon of 40 years. Following popular lifecycle

strategies, she decides to invest her money in stocks for the initial 20 years and then

gradually switch to bonds and cash over the last 20 years. Once this allocation

decision is made, she puts it on an autopilot (like most lifecycle funds) for the next

40 years. However, the stock market returns following the investment decision do

not augur well for the investor. Due to a prolonged bear market there are several

years of negative returns eroding the value of her portfolio. After 20 years, the

balance in her account is next to nothing and this gets gradually switched to bonds

and cash. Subsequent returns in the account are stable but low. In this case, after 40

years the investor would find herself in a financial situation quite different from

what was anticipated while setting the investment strategy.79

Undoubtedly the above example is an extreme one and describes only one of the

several possibilities that an investor can expect to encounter over a long horizon. Yet

it reveals the Achilles’ heel of the lifecycle funds currently in market. These funds

follow a pre-determined performance-blind asset allocation strategy where not only

the switching of assets is always unidirectional – from stocks to fixed income –and it

is done in proportions that are pre-specified at the inception of the fund. In our

example, had the stock market offered very high returns during the last 20 years, the

investor would stand to gain very little because her investments were automatically

switched from stocks to bonds and cash during that period following the allocation

strategy she had set on autopilot. The pre-programmed lifecycle strategy was blind

to the fact that she had accumulated too little wealth in the initial years to necessitate

switching to conservative assets. The asset switching in that case virtually ensures

that she misses the only realistic chance she had to reverse her bad fortune.

The problem for the retirement plan members enrolled in lifecycle funds is more

complex than the hapless investor of our example. Typically the plan members make

79 It is not inconceivable that she even finds herself poorer in real terms than what she was 40 years ago.

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regular contributions to the retirement account as opposed to a single investment

made at the beginning of the 40 year period in our example. As contributions are

normally a fixed percentage of the members’ salaries, they are expected to grow

larger over time with growth in earnings. Therefore, as Shiller (2005b) points out,

the lifecycle strategy invests heavily in the stock market in the early years when the

contribution size is relatively small and switches out of it when earnings and

contributions grow larger in later years. This can be counterproductive as by moving

away from stocks to low return assets just when the size of their contributions (and

accumulation fund) are growing larger, the investor may be foregoing the

opportunity to earn higher returns on a larger sum of money invested. We have

already demonstrated this in chapter 6 of this thesis.

One cannot help question the fact that why lifecycle funds need to have their

benchmark asset allocation over the entire horizon cast in stone. A possible

alternative would be to switch to conservative assets a few years before retirement

when a plan member feels that the wealth in the retirement account adequately meets

his or her accumulation objective and therefore needs to be preserved. By the same

token, the plan member may be unwilling to switch to less volatile but low return

assets in case the past performance of the portfolio has been unsatisfactory, leaving

him or her with inadequate wealth relative to the accumulation target. Thus, the

decision to switch or not to switch and even how much to switch at any stage in this

case largely depends upon the cumulative performance of the retirement portfolio in

the preceding years.

In this chapter, we extend the abovementioned alternative approach by proposing a

dynamic lifecycle strategy which is flexible in adjusting its allocation between

growth and conservative assets while approaching retirement depending on the

extent that the plan member’s wealth accumulation objective has been achieved at

that time. In other words, this strategy is responsive to past performance of the

portfolio relative to the investor’s target return in determining the right mix of assets

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in future periods. While initially it invests heavily in equities just as any other

lifecycle strategy, the switching criterion is different in the sense that switch to fixed

income is not automatic. It only takes place if the investor has accumulated wealth in

excess of the target accumulation at the point of switch. Also, after switching to

conservative assets, if the accumulation falls below the target in any period, the

direction of switch is reversed by moving away from fixed income and towards

stocks. But does this strategy result in improved outcomes for the retirement plan

member? To find out we compare and contrast the outcomes of such a dynamic

strategy with those achieved by following a regular lifecycle strategy.

Blake et al. (2001) test a similar lifecycle strategy with performance feedback

although their benchmark is set in terms of a replacement ratio i.e. ratio of pension

to final salary. The similarity between their threshold strategy and the dynamic

lifecycle strategy proposed in this chapter is that both resort to an aggressive asset

allocation strategy if the portfolio underperforms the set benchmark (or lower

threshold in their case) and vice versa. However, their strategy switches assets

based on performance feedback right after the member joins the retirement plan

while in our case the asset switching starts a few years before retirement which is

more akin to the conventional lifecycle model.

Arts and Vigna (2003) also suggest an asset allocation model with a switch criterion

based on performance feedback. Switching from equities to bonds takes place only if

the cumulative returns on equities have been high prior to the switch and vice versa.

However, in their model the switching is irreversible i.e. once assets are switched to

bonds, they cannot be reallocated to equities. Moreover, the switching from stocks to

bonds is not gradual but total at the point of switch.80 Unlike their paper, the

switching criterion in our proposed allocation strategy is dynamically applied over

the horizon.

80 This is an extreme case and not encountered ordinarily among lifecycle funds in practice.

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In Chapter 6 we demonstrated that naive age-based lifecycle switching results in loss

of significant upside potential while the trade-off in terms of avoiding most adverse

outcomes at retirement appeared inadequate. In light of our findings in that study,

we conjectured that a better strategy might be one that periodically incorporates the

information on past portfolio performance on asset switching mechanisms. In this

chapter, we put this dynamic strategy to test. Our results clearly suggest that a

deterministic asset switching rule, following conventional lifecycle strategies

produce inferior wealth outcomes for the investor compared to strategies that

dynamically alter allocation between growth and conservative asset classes at

different stages based on cumulative portfolio performance relative to a set target.

The dynamic lifecycle strategies exhibit clear second-degree stochastic dominance

over conventional lifecycle strategies which switch assets unidirectionally without

cognizance to the portfolio performance.

7.2 Methodology

7.2.1 Conventional Versus Dynamic Lifecycle Strategy

In comparing conventional lifecycle and dynamic lifecycle strategies, we consider

the case of a hypothetical individual who joins the plan with starting salary of

$25,000. The earnings grow linearly at the rate of 4% per annum over the next 41

years, which is the duration of the individual’s employment life. Throughout this

period, the member makes regular annual contributions amounting to 4% of earnings

in the retirement plan account. We assume that the contributions are credited

annually to the member’s accounts at the end of every year. This means that the first

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contribution by the member is made at the end of first year followed by 39 more

contributions in as many years. No contribution is made in the final year of

employment.

Our hypothetical plan member can choose between a conventional lifecycle strategy

and a dynamic strategy to invest the contributions. We consider two variations of the

conventional lifecycle strategy, namely 20,20LC and 10,30LC , which invest in a 100%

stocks portfolio for 20 years and 30 years respectively following the first

contribution. Thereafter both of them linearly switch from stocks to bonds and cash

over the remaining 20 (and 10) years in such a manner that at the point of retirement

all assets are held in bonds and cash. This type of allocation is akin to that of a

typical lifecycle or target retirement funds which invest heavily in equities in the

initial years and gradually switch to fixed income instruments as they approach

maturity. Similarly the dynamic strategy has two variations, namely 20,20DLC and

10,30DLC , corresponding to the above lifecycle strategies. They invest in the same

100% stocks portfolio as the two lifecycle strategies during the first 20 (and 30)

years. Thereafter every year the strategies review how the portfolio has performed

relative to the investor’s accumulation objective. If the value of the portfolio at any

point is found to equal or exceed the investor’s target, the portfolio partially

switches to conservative assets. Otherwise, it remains invested 100% in stocks.

From our formulation of the strategies, it is clear that while 20,20DLC and 10,30DLC

uses performance feedback control in switching assets, 20,20LC and 10,30LC do not.

Although people may have different accumulation objectives on retirement, we need

to make a plausible assumption about the accumulation target set by the hypothetical

individual employing the dynamic allocation strategies in this study. Dimson,

Marsh, and Staunton (2002) have compiled returns for US stocks, bonds, and bills

from 1900. We use an updated version of their dataset and find the geometric mean

return offered by US stocks between 1900 and 2004 is 9.69%. We assume that the

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second individual sets a target of achieving a return close to this rate, say 9%, on the

retirement plan investments. In other words, the retirement portfolio under the

dynamic strategy aims to closely match the compounded accumulation of a fund

where contributions are annually reinvested at a 9% nominal rate of return.

For 20,20DLC which invests in 100% stocks portfolio for 20 years, we assume that

the individual sets a target of 9% compounded annually on investments for the initial

20 year period. At the end of 20 years, if the actual accumulation in the retirement

account exceeds the accumulation target, the assets are switched to a relatively

conservative portfolio comprising of 80% stocks and 20% fixed income (equally

split between bonds and cash). However, if the actual accumulation in the account is

found to fall below the target, the portfolio remains invested in 100% stocks. This

performance review process is carried out annually for the next 10 years and asset

allocation is adjusted depending on whether the holding period return outperforms or

underperforms the target. In the final 10 years the same allocation principle is

applied with only one difference. If the value of the portfolio in any year during this

period matches or exceeds the investor’s target accumulation at that point, 60% of

assets are invested in equities and 40% in fixed income (equally split between bonds

and cash). Failing to achieve the target return for the holding period, results in all

assets being invested in a 100% stocks portfolio.

For 10,30DLC , which invests in 100% stocks for the 30 years after making the first

contribution, the investor has the same target return of 9% compounded annually.

After 31 years, if the portfolio value in any year matches or exceeds the target

accumulation, 20% assets are switched to fixed income (equally split between bonds

and cash). A failure to achieve the target performance results in the portfolio being

invested in 100% equities. The performance of the portfolio relative to the target is

monitored annually and the asset allocation is adjusted accordingly. In the final 5

years before retirement, if the portfolio performance at any point matches or exceeds

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the target accumulation at that point, 40% of assets are switched to fixed income

(equally split between bonds and cash).


To generate simulated investment returns under the two conventional lifecycle

strategies (say 20,20LC and 10,30LC ) and their corresponding dynamic lifecycle

strategies ( 20,20DLC and 10,30DLC ) we use the same updated version of the dataset

of annual nominal returns for US stocks, bonds, and bills originally compiled by

Dimson et al. (2002) used in the previous chapters. The dataset spans a long period

of 105 years between 1900 and 2004 and thus capture both favourable and

unfavourable returns on the individual asset classes over the entire twentieth century

within our simulation trials. However, to examine holding period returns for assets

over horizons as long as 40 years, 105 years worth of returns data may not be

sufficient. There are only two independent, non-overlapping 40-year holding period

observations within our dataset. Any conclusion based on a sample of two

observations cannot be deemed reliable.

To get around the problem of insufficient data, we use bootstrap resampling. The

empirical annual return vectors for the three asset classes in the dataset is randomly

resampled with replacement to generate asset class return vectors for each year of

the 40 year investment horizon confronting the two hypothetical retirement plan

investors. Since we randomly draw rows (representing years) from the matrix of

asset class returns, we are able to retain the cross-correlation between the asset class

returns as given by the historical data series while assuming that returns for

individual asset classes are independently distributed over time. More details about

the resampling method employed in this study are provided in 3.2.2.

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As the resampling is done with replacement, a particular data point from the original

data set could appear multiple times in a given bootstrap sample. This is particularly

important while examining probability distribution of future outcomes. For example,

1931 is the worst year for stock market in our 105 year long dataset. In that year

return from stocks was -44% while bonds and bills offered returns of 1% and -5%

respectively. Although this is only one observation in the century long data, a

bootstrap sample of 40 annual returns can include this return observation for 1931

many times in any sequence. Similarly, return observations for other years, good or

bad, can also be repeated a number of times within a bootstrap sample. Since this

method allows for inclusion of such extreme possibilities (like a -44% return

occurring a number of times in a particular 40-year long return path), by obtaining a

large number of bootstrap samples from the observed historical data, one can capture

a much wider range of future possibilities.

The asset class return vectors obtained by bootstrap resampling are combined with

their respective weightings under each asset allocation strategy to generate portfolio

returns for each year in the 40 year horizon. The simulation trial is iterated 10,000

times for lifecycle strategy 20,20LC and its corresponding dynamic strategy 20,20DLC

thereby generating 10,000 independent 40 year return paths that would govern the

possible wealth outcomes for the individuals following them. A separate set of

experiment (comprising of another 10,000 trials) is conducted for the other pair of

lifecycle and dynamic strategies, 10,30LC and 10,30DLC . For the purpose of doing a

comparative analysis, we include two other allocation strategies – (i) a 100% stocks

strategy and (ii) a balanced strategy which allocates in the ratio of 60:30:10 between

stocks, bonds, and cash in both sets of experiments and provide the results in 7.3.

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7.2.3 Stochastic Dominance

While we compare the terminal wealth distribution parameters like the mean,

median, and the lower and upper quartile outcomes of the dynamic strategies

( 20,20DLC and 10,30DLC ) with their conventional lifecycle counterparts ( 20,20LC and

10,30LC ), the superiority of one over the other cannot be established with certainty

without comparing the entire range of outcomes under the two approaches.

Stochastic dominance is a well known criterion used in this type of situation to rank

investment alternatives because it relies on the entire distribution of outcomes.81 It

also places minimal restrictions on the investors’ utility functions and makes no

assumption (like normality) about the return distributions.82 We use this approach

here to find out whether investors would prefer terminal wealth distribution under

one asset allocation strategy over that of the other.

Bawa (1975) provides the necessary and sufficient conditions for various degrees of

stochastic dominance in the context of ranking portfolios. Formally, given utility of

wealth is a non-decreasing function i.e. 0)( ≥′ WU , if F and G represents

respectively the cumulative distributions of terminal wealth outcomes under the

dynamic lifecycle strategy and the conventional lifecycle strategy, the former

dominates the latter under the first degree stochastic dominance (FSD) rule if and

only if:

)()( WGWF ≤ W∀ (41)

This means that the dynamic lifecycle strategy would dominate the corresponding

conventional lifecycle strategy by the FSD criterion if the cumulative distribution of

terminal wealth outcomes under it always remains below the cumulative wealth

distribution of the conventional lifecycle strategy.

81 Since the distribution of wealth outcomes get increasingly asymmetric over long horizons, the mean-variance framework is not useful in this situation. We also refrain from making any strong assumption on the utility function (like quadratic) of the retirement plan members. 82 See Elton and Gruber (1995) for a thorough discussion on this subject.

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Due to the strong conditionality it imposes regarding the cumulative distributions

not intersecting each other even once, FSD cannot be applied in ordering

distributions in many cases. The second degree stochastic dominance criterion

(SSD) which is a weaker condition than FSD can be useful in these situations. SSD

can be applied to a large class of problems because it works within the framework of

risk aversion, an assumption widely used in finance literature (Hadar and Russell,

1969). Formally, given 0)( ≥′ WU and 0)( ≤′′ WU , the dynamic lifecycle strategy

dominates the conventional lifecycle strategy under the SSD criterion if and only if:

∫ ∫∞ ∞

≤0 0

)()( dWWGdWWF (42)

This implies that the area under F has to be equal or less than the area under G for

the dynamic strategy to dominate the conventional strategy by the SSD rule. Unlike

FSD, SSD allows for F and G to cross each other as long as the above condition is

met.

7.2.4 Shortfall Measures for Dynamic Strategy

We compute a statistic called the probability of shortfall which represents the chance

of the dynamic lifecycle strategy ending with less accumulated wealth than the other

strategies in our simulation trials. Using equation (20) in context of this problem,

this probability of shortfall is given by

0

1,0 )](,0[

1∑

=−=

n

tDLCXDLC WWMax

nLPM (43)

where n denotes the number of trials, XW represents the terminal wealth under any

strategy and DLCW represents the terminal wealth under the dynamic strategy. While

DLCLPM ,0 estimates the odds of the dynamic strategy doing worse (or better) than

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the other strategies in different future states of the world, it does not describe how

large the shortfall in wealth outcome for the former would be compared to that of the

latter. To estimate the magnitude of underperformance of the dynamic strategy

relative to other strategies, we measure the expected shortfall given by equation (20)

in the context of this problem as

∑=

−=n

tDLCXDLC WWMax

nLPM

1,1 )](,0[

1 (44)

The use of LPM family of downside risk measures has already been discussed in

2.7.


7.3.1 Terminal Wealth Estimates

The resampling method described above generates a range of terminal wealth

outcomes under the conventional lifecycle strategies and their corresponding

dynamic strategies. The parameter estimates for the wealth distribution under the

different strategies are reported in Table 7.1. From panel A, which provides the

results for the conventional lifecycle and dynamic lifecycle strategies which always

remain invested in 100% stocks for the first 20 years, the difference is stark. The

mean and the median outcome for the dynamic lifecycle strategy 20,20DLC exceeds

those for the conventional lifecycle strategy 20,20LC by more than half a million

dollars. The first quartile and the third quartile estimate for the former are also

greater than the latter by $245,033 and $704,324 respectively. For the lifecycle

strategies which always invest in the 100% stock portfolio for the first 30 years, the

results appear in Panel B. As in panel A, we find that the dynamic lifecycle strategy

10,30DLC produces much higher mean, median, first and third quartile outcomes than

the conventional lifecycle strategy 10,30LC . The gap between the outcomes in this

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case, however, is lower than what it was between 20,20DLC and 20,20LC . This is

expected as 10,30DLC and 10,30LC strategies invest in the same portfolio (100%

stocks) for ten more years.

Table 7.1: Terminal Value of Retirement Portfolio in Nominal Dollars

Table 7.1 reports the simulation estimates for terminal wealth under different asset allocation strategies. Panel A provides the results for the set of 10,000 trials where both the lifecycle and the dynamic strategy invest in a 100% stocks portfolio for the first 20 years and then commence switching. Panel B provides the results for the set of 10,000 trials where both the lifecycle and the dynamic strategy invest in a 100% stocks portfolio for the first 30 years and then switch assets.

Strategy Mean Median

25th

Percentile 75th

Percentile Panel A Dynamic( 20,20DLC ) 1,978,387 1,733,256 1,037,838 2,432,030 Lifecycle( 20,20LC ) 1,426,510 1,163,836 792,805 1,727,706 100% Stocks 2,523,681 1,715,014 981,005 3,040,650 Balanced 1,273,744 1,117,258 804,466 1,562,407

Panel B Dynamic( 10,30DLC ) 2,243,825 1,762,712 988,573 2,695,902 Lifecycle( 10,30LC ) 1,919,124 1,408,545 876,404 2,340,550 100% Stocks 2,547,867 1,716,608 965,411 3,102,896 Balanced 1,276,875 1,118,547 799,502 1,573,030

In addition to the conventional and the dynamic lifecycle strategies, which are of

primary interest to this study, we also simulate wealth outcomes for the 100% stock

and the balanced strategy. The mean outcomes for the 100% stock strategy are

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higher than both the conventional and dynamic strategy pairs. Given the existence of

large positive equity premium in our data, this result is unsurprising. While the

median and the first quartile outcomes for the 100% stocks strategy is higher than

those of 20,20LC and 10,30LC they fall short of both 20,20DLC and 10,30DLC . This

suggests that dynamic strategies are superior in protecting the investors from the risk

of adverse wealth outcomes than both the aggressive 100% stocks strategy and the

conventional lifecycle strategy which adopts a pre-determined conservative

allocation principle in later years.

The ineffectiveness of lifecycle switching in protecting investors from the risk of

confronting adverse wealth outcomes on retirement is clear when we look at the

balanced fund simulation results. The balanced fund, whose mean and median

outcomes are inferior to all the other three strategies, outperforms 20,20LC in terms

of the first quartile estimate. This apparently puts a question mark on the efficacy of

the conventional lifecycle strategies in improving the floor level of outcomes.

Dynamic lifecycle strategies, again, seem to produce better results in this respect.

But we take up this issue later in this chapter.

7.3.2 CDF and Stochastic Dominance Test

Figure 7.2 demonstrates the cumulative distributions of terminal wealth achieved

under 20,20LC and 20,20DLC strategies. Again for the purpose of comparison, we also

show cumulative wealth distributions for the 100% stocks and the balanced

strategies. The horizontal axis of the graph represents the nominal dollar value of

the portfolio at the point of retirement. As explained above, if the CDF for one

strategy lies under (or to the right of) other CDFs, it is likely to result in a superior

outcome relative to other strategies. Also, if CDF for a strategy is generally steeper

than the others, the strategy can be considered to result in less variable outcomes.

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Figure 7.1: Cumulative Distribution Plots for First Pair of Lifecycle and Dynamic Strategies ( 20,20LC and )20,20DLC

It is clear that except for a very small part on the left of the point X, the cumulative

distribution plot of 20,20DLC remains much under that of 20,20LC . Therefore,

although the dynamic lifecycle strategy does not dominate the conventional lifecycle

strategy by the strict FSD criterion, it does dominate under SSD because the area

under cumulative distribution F of the dynamic strategy is clearly far less than that

under cumulative distribution G of the conventional lifecycle strategy. Except for a

very small section on the left of point X representing wealth outcomes of about

$500,000 or less after 41 years, we can infer from the cumulative distributions that

the investor employing 20,20DLC has higher chance of achieving any particular

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accumulation outcome than the investor employing 20,20LC . For example, the former

has about 75% probability of accumulating more than one million dollars at

retirement whereas the later has got only a 60% chance of crossing that milestone. If

investors set a target of achieving a compounded return of 9% minimum on their

investments, which amounts to an accumulated wealth of at least $1.69 million at

retirement, our results indicate that the 20,20DLC strategy would achieve this goal

with almost 50% certainty. With 20,20LC strategy, this probability drops to only

25%. The gap between the cumulative distribution functions for the two strategies

widens as we move up further towards higher accumulation figures although after a

point (approximately around 2 million dollars) it starts to diminish gradually.

A comparison of the cumulative distributions of the lifecycle strategies 20,20LC and

20,20DLC with that of the 100% stock strategy reveals two important results. First,

we find that the distribution of conventional lifecycle strategy 20,20LC always

remains above that of 100% stock strategy except for the small section on the left of

point X (representing only about the worst 5% of outcomes). This undermines the

effectiveness of conventional lifecycle strategies in protecting the wealth of

investors from the vagaries of stock market downturns. Had it been the case, we

would have found X much to the right of its current location i.e. 20,20LC would have

dominated the 100% stock strategy for a much larger percentage of outcomes in the

lower end of the distribution. In contrast, we find the cumulative distribution of

20,20DLC remains below that of the 100% stock strategy for a much longer section

(the left side of Y). This clearly suggests its effectiveness in reducing the risk of

investor’s wealth breaching any floor level of wealth to the left of Y. Although it

does not dominate the 100% stocks strategy under the SSD criterion, it does much

better in terms of producing superior outcomes in the below median range, which is

likely to be viewed as the zone of risk for most investors. Remarkably it is obvious

from the diagram that our hypothetical investor has a slightly higher chance of

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achieving the target wealth outcome of $1.69 million by employing the 20,20DLC

instead of the 100% stocks strategy.

Now we turn our attention to the cumulative wealth distribution functions for the

other lifecycle and dynamic strategy pair - 10,30LC and 10,30DLC . This is presented in

Figure 7.2. As before, we also show cumulative wealth distributions for the 100%

stocks and the balanced strategies.

Figure 7.2: Cumulative Distribution Plots for Second Pair of Lifecycle and Dynamic Strategies ( 10,30LC and )10,30DLC

Apart from a small part in the extreme lower tail of the distributions representing

terminal wealth outcomes below $500,000, the cumulative wealth distribution

function of 10,30DLC (F) always remains below that of 10,30LC (G). Thus, there is

clear second degree stochastic dominance of 10,30DLC over 10,30LC indicating that

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any risk averse investor would find the former more appealing to the latter. As is the

case with 20,20LC and 20,20DLC pair, the distance between the CDF plots is larger in

the middle than in the extremes. In other words, the dynamic strategy dominates the

conventional strategy over for a vast range of outcomes by a staggering margin.

In relation to the target accumulation outcome of $1.69 million at retirement, Figure

7.2 indicates that the 10,30LC strategy would achieve this goal with about 40%

certainty. Although this is significant improvement compared to the performance

of 20,20LC , it still falls short of the corresponding dynamic strategy, 10,30DLC , which

surpasses the target on more than 50% of occasions. The reason behind 10,30LC

putting up a superior performance relative to 20,20LC strategy in attaining the target

may be attributed mainly to the fact that the former invests in a 100% stocks

portfolio for a longer duration (30 years) compared to that of the latter (20 years).

However to apply the same argument to explain the dominance of dynamic

strategies over corresponding lifecycle strategies appears too simplistic. Had this

been the only reason, 100% stocks strategy would have outperformed other

strategies in terms exceeding the target accumulation. But it is evident from Figure

7.2, the probability of achieving the target wealth outcome with 10,30DLC strategy is

clearly higher than that with 100% stocks strategy. Also, the median outcome for

10,30DLC strategy is larger than that of 100% stocks strategy.

7.3.3 Shortfall Estimates for Dynamic Strategy

But what is the success (or failure) rate of the dynamic strategy over other strategies

in different possible future states of the world? This knowledge is important to the

investor yet comparing cumulative probability distributions of terminal wealth under

different competing strategies would not provide a clear answer. This is because in

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doing so we are comparing the n-th percentile outcome of one strategy with the n-th

percentile outcome of the other. In plain words, the good scenarios under one

strategy are compared to the good scenarios under another and likewise the bad

outcomes are pitted against the bad outcomes. But for any particular future state of

the world (with a particular asset return path over the investment horizon), this

comparison may not be very useful. For example, if stock returns turn out to be very

poor compared to other assets in a particular state of the world, the 100% stocks

strategy would produce inferior outcome relative to a balanced strategy no matter

how attractive or dominating the wealth distribution of the former appears compared

to the latter.

Table 7.2: Shortfall Measures of Dynamic Strategies Relative to Other Asset Allocation Strategies

Asset Allocation Strategy

Shortfall Probability )( ,0 DLCLPM

Average Shortfall ($) )( ,1 DLCLPM

20,20DLC

Lifecycle ( 20,20LC ) 0.19 34,462 100% Stocks 0.51 582,815 Balanced 0.1 6,110

10,30DLC

Lifecycle ( 10,30LC ) 0.26 50,273 100% Stocks 0.43 343,890 Balanced 0.11 6,907

Recall that the asset class return path over the 41 year horizon is unique for each

trial in our simulation experiment. Each of those 10,000 trials represents a different

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possible future state of the world.83 Therefore, for each trial, we compare the wealth

outcomes under all four strategies, the main point of interest being how the dynamic

strategy performs vis-à-vis other strategies. To be specific, we compute the shortfall

probability (given by DLCLPM ,0 ) of 20,20DLC and 10,30DLC as well as their average

size of shortfall (given by DLCLPM ,1 ) compared to the other three strategies. These

shortfall measures are likely to constitute an important part of what the investors

view as downside risk of adopting the dynamic allocation strategy. The results

provided in Table 7.2 show that the dynamic strategy has small chance of

underperforming the conventional lifecycle strategy. For only 19% of trials the

wealth outcome of the dynamic strategy 20,20DLC falls short of that of the

corresponding lifecycle strategy 20,20LC . For 10,30DLC , the chance of it

underperforming the corresponding lifecycle strategy 10,30LC however increases to

26%, i.e. about one in four. However, the average size of the shortfall in both cases

is quite miniscule ($34462 and $50273) compared to the average size of terminal

wealth outcomes for both the strategies.

Further comparing individual trial outcomes, we find that the 20,20DLC strategy and

the 100% stocks strategy run close to each other in terms of dominance. The chance

of doing better with either strategy in different future states of the world is almost

even with the 100% stocks strategy emerging the winner in 51% of the trials. But

when compared with 10,30DLC , the 100% stocks strategy fares better only in 43% of

trials i.e. the dynamic strategy emerges the winner in a majority of cases. The

average size of the shortfall for the dynamic strategy in both cases, however, is quite

high at $582,815 and $343,890 respectively. This is not unexpected with the 100%

stocks strategy producing spectacularly large wealth outcomes in the above median

and particularly in the upper quartile range. Relative to the balanced strategy, the

chance of underperformance of the dynamic strategy is minimal. 20,20DLC and

83 The actual number of possibilities is obviously infinite.

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10,30DLC strategy underperforms the balanced strategy only in 10% and 11% of the

trials respectively. The average size of shortfall in both cases is extremely small at

$6,110 and $6,907 respectively.

7.3.4 Extreme Adverse Outcomes

While our evidence so far overwhelmingly suggests superiority of dynamic

strategies over conventional lifecycle strategies, the saving grace for the latter may

lie in the zone of most adverse outcomes. This is represented by the left portion of X

in the CDF plots in Exhibits 2 and 3 where the lifecycle strategies actually dominate

corresponding dynamic strategies. It is also apparent from the diagrams that this

zone is constituted by outcomes that are below the 10th percentile mark for every

strategy. To have some idea about how large the differences actually are between the

adverse outcomes under different strategies, we report the VaR estimates at

confidence levels of 99%, 95%, and 90% and ETL estimates at 95% confidence

level for both sets of simulation trials in Table 7.3.

As is evident in the CDF plots, both the lifecycle strategies 20,20LC and 10,30LC

produce higher 95% and 99% VaR estimates compared to their dynamic

counterparts (and 100% stocks strategy). The differences between the 95% VaR

estimates are less than $25,000. But when one compares the 99% VaR estimates, the

differences between the lifecycle and dynamic strategy grow considerably larger.

The 99% VaR estimate for 20,20LC strategy is almost $100,000 more than that of the

corresponding dynamic strategy 20,20DLC . Between 10,30LC and 10,30DLC , the

difference, however, is smaller than $50,000. The results are similar for ETL

estimates with the lifecycle strategy faring slightly better than the dynamic strategy

for both sets of trials. It is also to be noted that the dynamic strategy outperforms the

100% stocks strategy in terms of VaR and ETL estimates for both sets of trials.

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Table 7.3: VaR Estimates for Different Asset Allocation Strategies

Asset Allocation Strategy

VaR at Different Confidence Levels ETL at 95% Confidence Level

99% 95% 90%

Panel A Dynamic ( 20,20DLC ) 275,914 461,640 607,872 344,437 Lifecycle ( 20,20LC ) 375,810 486,156 578,814 417,804 100% Stocks 271,458 447,330 592,348 337,980 Balanced 361,326 505,209 597,506 422,350

Panel B Dynamic ( 10,30DLC ) 274,968 444,468 599,673 340,901 Lifecycle ( 10,30LC ) 321,875 468,598 581,526 377,114 100% Stocks 274,657 443,251 595,398 339,980 Balanced 369,362 501,541 599,863 423,124

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Yet one would be reluctant to declare lifecycle funds to be the preferred investment

strategy even under the unreasonable assumption that investors care only about the

zone of extremely adverse wealth outcomes (below 90% VaR in this case). This is

because the balanced fund produces better 95% VaR estimates than both 20,20LC and

10,30LC . In terms of 99% VaR estimate, the balanced fund outperforms 10,30LC but

underperforms 20,20LC . When we consider 95% ETL, the balanced fund produces

estimates that are higher than both 20,20LC and 10,30LC . These results suggest that if

the retirement plan investors are concerned about improving the floor level of

possible wealth outcomes or protection from extreme downside risk, they are more

likely to be better off by investing in a static balanced fund rather than a

conventional lifecycle fund.

7.4 Conclusion

The evidence presented in this chapter exposes the inherent weakness of traditional

lifecycle investing for members of retirement plans. While pulling out of volatile

assets like stocks while the plan member nears retirement is generally accepted as

sensible investment advice, traditional lifecycle funds appear to implement this

strategy in a dogmatic manner that completely disregards the investors’ wealth

accumulation objectives. As we have demonstrated in this study, the mechanistic

switching strategy from growth to conservative assets following any age based rule

of thumb is clearly sub-optimal to a dynamic strategy that considers the actual

accumulation in the retirement account before switching assets. We propose a

specific dynamic asset allocation strategy where the switching of assets at any stage

is based on cumulative investment performance of the portfolio relative to the

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investors’ set expectations at that stage. Unlike conventional lifecycle asset

allocation rules where the switching of assets is preordained to be unidirectional, this

dynamic strategy can switch assets in both directions: from aggressive to

conservative and vice versa. Using simple rules of stochastic dominance, we show

that such a dynamic lifecycle strategy vastly outperforms a conventional lifecycle

strategy in terms of accumulation outcomes over long horizon.

On comparing adverse outcomes in our trials, we find lifecycle strategies to do

better than the dynamic strategies only for ‘below 95%’ VaR outcomes. However,

the differences do not appear to be large enough to negate the appeal of dynamic

strategies to the average investor in view of their overall dominance over lifecycle

strategies. Even for these extremely adverse wealth outcomes in our trials, we find

that the static balanced asset allocation strategy generally does better than lifecycle

strategy. Therefore an investor whose sole concern is improving the floor level of

the extremely adverse wealth outcomes is likely to prefer investing in a balanced

fund rather than a lifecycle fund.

We have conducted a large number of trials in this study to capture different

possibilities about future asset class returns over the investment horizon of the

retirement plan investor. According to our results, the chance of the dynamic

strategy underperforming the lifecycle strategy at the end of such long horizon is

small (although not insignificant). Not only does the dynamic strategy produce

superior terminal wealth outcomes compared to the lifecycle strategy in a vast

majority (about 75% to 80%) of cases, it appears to have a fair chance of

outperforming an all equity strategy. In fact, the dynamic lifecycle strategy 10,30DLC

in this study which invests in an all equity portfolio for the first 30 years and then

adjusts asset allocation on an annual basis, seems to have more than even chance of

beating the strategy which invests in an all equity portfolio for the entire horizon.

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The only authoritative past study to have considered a dynamic allocation rule with

performance feedback for DC plan investments is Blake et al. (2001). Unlike this

research, their results for the UK market indicate that the dynamic strategy (called

‘threshold strategy’ by the authors) underperforms the conventional lifecycle

strategy. This, we suspect, is caused by the relatively conservative upper and lower

thresholds they originally set in their study to prompt switching of assets. When the

sensitivity of the dynamic strategy to changes in thresholds (equivalent to ‘target’ in

this chapter) is tested by those authors, they observe that setting aggressive

thresholds clearly leads to superior performance. By using annualised holding period

return offered by the US stocks over last century as the performance target, which

can be considered as very aggressive, we find that the dynamic lifecycle strategy

dominates the conventional lifecycle strategy for vast majority of outcomes.

Therefore our results are not in disagreement with the results of Blake et al. (2001)

Apart from its relative superiority over other allocation strategies from a risk-return

perspective, the dynamic strategy proposed in this chapter has another distinct

appeal for the retirement plan investors from the behavioural angle. Since the

allocation is responsive to performance feedback, it may provide them some sense of

control over their investment decision on a continual basis. Without giving up the

basic tenet of lifecycle investing - seeking reduced volatility in the value of the

accumulation fund as one gets closer to retirement – the dynamic strategy

overcomes its limitations to a large extent.

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8. Conclusion

8.1 Scholarly Contributions

This dissertation makes several important contributions to the field of pension fund

investments specifically to the area of strategic asset allocation for individual plan

participants in DC plans. Asset allocation choices offered in DC plans is a relatively

new area of research interest but has been drawing significant attention from

academics in the last few years. In sharp contrast to the existing body of work, we

have investigated various asset allocation strategies using estimates of upside

potential and downside risk, both of which rely on a target based approach to

investing to assess return and risk. The essays, therefore, in addition to uncovering

new evidence and providing new insight into specific asset allocation issues within

DC plans, put forward an alternative framework for researchers to assess investment

outcomes for long horizon investors. The following key findings that emerge from

this thesis would be informative to the existing literature.

The thesis presents strong evidence in support of holding stocks by retirement plan

participants. While few other studies in the past have indicated the superiority of

equity over other assets in the long term with respect to the probability of

underperforming the latter, the risk of extremely adverse outcomes for different

asset allocation strategies has remained a territory largely unexplored. This study,

for the first time to the best of our knowledge, has demonstrated that the extremely

adverse outcomes for retirement plan investors have very little sensitivity to their

asset allocation choices. This is a significant finding which contradicts the

commonly held notion among academics and practitioners that the risk of disastrous

outcomes is significantly higher for more aggressive strategies. Moreover, by using

the LPM family of risk measures, we have shown that the preference for aggressive

strategies remains unchanged for investors with different degrees of risk aversion.

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The existing literature on asset allocation in DC plans has mostly used data from the

USA or UK market in drawing conclusions. Using long run data for Australian asset

classes, we have shown that the default investment options for most of the highly

ranked funds may suffer from sub-optimal asset allocation choice for their members.

This can result in insufficient wealth outcomes for the vast majority of potential

retirees. The problem of inadequacy of retirement wealth, as many scholars have

pointed out in the past, is aggravated for female workers due to their relative

disadvantage in the labour market. This thesis has investigated the potential of a

gender sensitive asset allocation policy in reducing the gender gap in retirement

wealth accumulation. The results suggest that aggressive asset allocation strategies,

in addition to modest changes in default contribution rates, can have dramatic impact

on the wealth outcomes for female workers.

A major contribution of this dissertation emerges from its investigation of the role of

lifecycle funds in retirement plans. The current state of scholarship in this area is not

well developed with research studies mainly considering the relative standing of

lifecycle strategies vis-à-vis constant weight allocation strategies. One of the

important research questions we have explored in this thesis - the implication of

growing portfolio size over the horizon for portfolio choice decisions – provides

insight that is more fundamental to the understanding of lifecycle funds in the

context of retirement plans. In chapter 6 of this thesis, we have demonstrated that the

existence of portfolio size effect results in greater sensitivity of wealth outcomes to

asset allocation strategy adopted by the investors when they are nearer to retirement

than when they are farther from it. Thus lifecycle strategies may prove

counterproductive to the participant’s wealth accumulation objective since they

systematically switch away from stocks as the portfolio size becomes larger. This

explains findings of past research that lifecycle strategies tend to underperform fixed

weight strategies tilted towards equities. The sacrifice of portfolio growth

opportunity in the later part of the horizon by lifecycle strategies does not seem to be

228

compensated adequately in terms of reducing the risk of potentially adverse

outcomes at retirement.

Further to presenting new evidence to support past studies that find the lifecycle

asset allocation model inferior to many other static allocation models, our research

takes a major leap to address the shortcomings of conventional age-based lifecycle

investing in retirement plans. We propose a dynamic lifecycle model which

systematically incorporates past performance feedback in the asset allocation

decision. While dynamic strategies have been proposed and tested in the literature,

albeit sparingly, in chapter 7 of this thesis we have formally established the

stochastic dominance of the dynamic lifecycle strategy over deterministic lifecycle

strategies currently used by most retirement plans in terms of wealth accumulated at

the point of retirement. Moreover, the dynamic strategy is found to produce better

results compared to other strategies in achieving the target outcome of matching

historical returns offered by the stock market.

The current opinion of researchers on the subject of asset allocation over long

horizons is deeply divided. To support the long term case for holding more equity,

the proponents have mostly relied on the existence of mean reversion of returns, a

phenomenon which itself has been open to challenge. Without having to assume any

form of autocorrelation in historical returns on different asset categories, we are still

able to obtain results that broadly favour equity dominated allocation strategies for

individual participants. This, we believe, is mainly due to our use of target based

metrics that captures the DC plan participant’s perception of risk more effectively

than the measures of volatility often used by academics.

The evidence from different chapters, when synthesized, does not offer unqualified

support to the recommendation of holding an all equities portfolio by the DC plan

participant till retirement. Nor do we find any justification for deterministic lifecycle

switching of assets (from stocks to fixed income) for participants approaching

229

retirement. The results suggest that a dynamic lifecycle strategy that initially invests

heavily in equities but later uses performance feedback in switching assets would be

able to produce superior wealth outcomes to those of conventional lifecycle

strategies while reducing the risk of extremely adverse outcomes compared to an all

equity strategy. In other words, by not giving away too much of the upside the

dynamic lifecycle strategy provides downside risk protection at a lower cost to the

investor.

8.2 Relevance

The findings of this thesis have important implications for retirement plan sponsors,

investors, and policymakers. Since there is overwhelming global evidence that a vast

majority of plan participants are enrolled in the default investment options of their

respective plans, it is vital that the plan sponsors prudently design the default option

to meet the participant’s investment objective. The essays in this dissertation provide

useful insights in evaluating the appropriateness of different asset allocation

strategies as default options in defined contribution plans. The same applies for

investors who make active asset allocation choices within their plans. Without being

prescriptive, the research findings suggest that aggressive asset allocation strategies

are more likely to bear fruitful investment outcomes for the retirement plan

participants.

Despite their intuitive appeal conventional lifecycle asset allocation strategies do not

appear to yield any significant advantage according to our results. In relation to the

most adverse outcomes, the risk reduction benefit offered by a lifecycle fund is at

least matched if not bettered by a static diversified balanced fund. However, the

dynamic strategy proposed in this dissertation addresses the shortcomings of the

conventional lifecycle strategy and appears to result in superior wealth outcomes.

The dynamic strategy adopts a significantly different approach from asset allocation

230

strategies currently offered within pension plans as it considers past performance

(relative to a preset accumulation target) as an important input in asset allocation

decision. These findings have an important bearing on portfolio choice decisions not

only for retirement plan participants but for all long horizon investors. Our evidence

indicates that practitioners need to consider a target based approach to design

lifecycle funds.

The issue of adequacy of retirement wealth is of overwhelming concern to

policymakers all over the globe. Any study that aims to throw light in this area

would potentially draw their interest. Although the topic of retirement income

adequacy is beyond the scope of our dissertation, it is informative to public policy in

at least two ways. First, the study highlights the importance of default options

offered by retirement plan providers in ensuring the economic well being of future

generation of retirees. In light of our evidence, policymakers may consider

instituting optimal default investment option for new participants in retirement

plans. At the very least, guidelines on default asset allocation could be included for

trustees of these plans to help them in discharging their fiduciary responsibilities.

Second, the current system in most countries has resulted in the gender gap in

retirement wealth accumulation. Following the suggestion of this thesis, gender-

sensitive defaults could be considered in addressing this long-standing problem.

8.3 Limitations & Avenues for Future Research

Five issues related to our study deserve further attention. First, our results,

undoubtedly, have been influenced by the large premium that stocks have enjoyed

historically over bonds and bills in the Australian and the US market. By using long

run data for these asset classes over a hundred years, we have attempted to ensure

that our results are not biased by returns for any asset class in a particularly

favourable (or unfavourable) period. Yet, as many commentators have observed,

231

even a century of data may be inadequate to predict the entire scope of future

possibilities. Analysing the impact of potential fall in the real equity premium on the

appropriateness of default investment choice in DC plans can be an area which

future research would do well to investigate.

Second, the simulation experiments in this dissertation do not consider the

possibility of autocorrelation in future returns for different asset classes. As

discussed elsewhere in this thesis, some researchers have observed negative

autocorrelation in stock returns and positive autocorrelation in returns for fixed

income securities. For example, if mean reversion in stock returns is correct, then

the all equity portfolio, however tempting it may appear over long horizons, may not

be the optimal portfolio to hold for the retirement plan investor. In this case,

sufficiently high returns in the past would drive down expected future returns from

the stock market and the investors may actually reduce their allocation to equities. It

would be a fruitful exercise to investigate how these variations in asset class returns,

claimed to be predictable by some scholars, alters the level of appropriateness of

various asset allocation strategies in DC plans.

Third, we have not considered wealth outside retirement plan in this thesis. This may

be an important factor in portfolio choice decision for individuals particularly at

higher levels of income distribution who have substantial level of savings outside

retirement accounts. For them, tax efficiency of the investments may be important

consideration. Differential tax treatment of income derived from stocks and fixed

income assets held outside the plan would influence allocating funds between these

asset classes within the plan. Other factors like home ownership and social security

benefits also deserve attention as this may exert significant influence on investment

policy pursued by investors in relation to their retirement plan contributions.

Fourth, the role of human capital in allocation of retirement plan assets holds

considerable appeal for future investigation. If indeed, for most members in the

232

retirement plans, human capital is perceived to be of low risk and earnings are

uncorrelated to the stock market, a propensity towards holding more stocks when

young than when old could be justified. However, true riskiness of human capital as

well as correlation of labour market earnings with returns from financial asset

categories are topics of ongoing debate among economists. Therefore, the sensitivity

of optimal asset allocation rules under different sets of assumptions about human

capital needs to be examined.

Finally, while we have assumed annual rebalancing of portfolios, the impact of

associated transaction costs has been ignored in our analysis. To the extent these

transaction costs differ between different asset allocation strategies, the results of

this study can be affected. For example, an all equity strategy with no rebalancing

cost would be at a relative advantage vis-à-vis other fixed weight strategies, lifecycle

strategies, or even the dynamic strategies discussed in this thesis, all of which

involve substantial transaction cost on account of rebalancing.

233

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APPENDIX A: Real Return Data for Australian and US Asset classes

1900-2004 Data

I. Descriptive Statistics

Australian

Stocks US Stocks Australian

Bonds US

Bonds Bills Mean 0.090952 0.084571 0.022667 0.026000 0.007238 Median 0.110000 0.110000 0.020000 0.010000 0.010000 Maximum 0.510000 0.570000 0.620000 0.960000 0.180000 Minimum -0.380000 -0.380000 -0.270000 -0.350000 -0.160000 Standard Deviation 0.177426 0.203049 0.133627 0.183185 0.055131

Skewness -0.247029 -0.184646 0.663710 1.704195 -0.058101 Kurtosis 2.972500 2.575718 6.086779 9.529573 4.319608 Observations 105 105 105 105 105

II. Correlation Matrix (3 Asset Class)

Australian Stocks

Australian Bonds

Bills

Australian Stocks

1.0000

0.3389

0.2524

Australian

Bonds

0.3389

1.0000

0.6344

Bills

0.2524

0.6344

1.0000

III. Correlation Matrix (5 Asset Class)

Australian Stocks

US Stocks

Australian Bonds

US Bonds

Bills

Australian Stocks

1.0000

0.8217

0.3389

0.3010

0.2524

US Stocks

0.8217

1.0000

0.2698

0.6185

0.1252

Australian Bonds

0.3389

0.2698

1.0000

0.7403

0.6344

US Bonds

0.3010

0.6185

0.7403

1.0000

0.3787

Bills

0.2524

0.1252

0.6344

0.3787

1.0000

254

1947-2004 Data


Australian Stocks US Stocks

Australian Bonds US Bonds Bills

Mean 0.080517 0.089828 0.010862 0.021897 0.006207 Median 0.105000 0.120000 0.020000 0.020000 0.015000 Maximum 0.510000 0.510000 0.270000 0.340000 0.090000 Minimum -0.380000 -0.360000 -0.270000 -0.210000 -0.160000 Standard Deviation 0.210642 0.174170 0.114682 0.130914 0.050881 Skewness -0.140441 -0.233371 -0.464026 0.229548 -0.988497 Kurtosis 2.416410 2.804259 3.133224 2.346402 4.467748 Observations 58 58 58 58 58


Australian Stocks

Australian Bonds

Bills

Australian Stocks

1.0000

0.3237

0.2113

Australian Bonds

0.3237

1.0000

0.6406

Bills

0.2113

0.6406

1.0000


Australian Stocks

US Stocks

Australian Bonds

US Bonds

Bills

Australian Stocks

1.0000

0.4887

0.3237

0.2140

0.2113

US Stocks

0.4887

1.0000

0.2064

0.1679

0.0650

Australian Bonds

0.3237

0.2064

1.0000

0.6446

0.6406

US Bonds

0.2140

0.1679

0.6446

1.0000

0.3179

Bills

0.2113

0.0650

0.6406

0.3179

1.0000

255

1975-2004 Data


Australian Stocks US Stocks

Australian Bonds US Bonds Bills

Mean 0.109333 0.112667 0.049667 0.049000 0.032000 Median 0.115000 0.125000 0.090000 0.035000 0.030000 Maximum 0.510000 0.520000 0.270000 0.340000 0.090000 Minimum -0.230000 -0.280000 -0.190000 -0.180000 -0.060000 Standard Deviation 0.205358 0.233533 0.111308 0.142499 0.037637 Skewness 0.084032 0.067832 -0.414026 0.098392 -0.588575 Kurtosis 2.081935 1.910695 2.546260 2.025290 3.133234 Observations 30 30 30 30 30


Australian Stocks

Australian Bonds

Bills

Australian Stocks

1.0000

0.0542

-0.0671

Australian

Bonds

0.0542

1.0000

0.4207

Bills

-0.0671

0.4207

1.0000


Australian Stocks

US Stocks

Australian Bonds

US Bonds

Bills

Australian Stocks

1.0000

0.8519

0.0542

0.0178

-0.0671

US Stocks

0.8519

1.0000

-0.0601

0.3518

-0.1430

Australian Bonds

0.0542

-0.0601

1.0000

0.6102

0.4207

US Bonds

0.0178

0.3518

0.6102

1.0000

0.2041

Bills

-0.0671

-0.1430

0.4207

0.2041

1.0000

256

APPENDIX B: Nominal Returns Data for Australian Asset Classes (1900-2004)

1. Descriptive Statistics

Stocks Bonds Bills Mean 0.1329 0.0596 0.04629 Median 0.1400 0.0500 0.04000 Maximum 0.6700 0.5400 0.17000 Minimum -0.2700 -0.1900 0.01000 Standard Deviation 0.1800 0.1149 0.04022

Skewness 0.1677 0.6740 1.5183 Kurtosis 3.4080 4.9474 4.7790 Observations 105 105 105

2. Correlation Matrix

Stocks

Bonds

Bills

Stocks 1.000 0.199 0.044 Bonds 0.199 1.000 0.297 Bills 0.044 0.297 1.000

257

APPENDIX C: Nominal Returns Data for US Asset Classes (1900-2004)

1. Descriptive Statistics

Stocks Bonds Bills Mean 0.1162 0.05276 0.04057 Median 0.1400 0.04000 0.04000 Maximum 0.5800 0.40000 0.15000 Minimum -0.4400 -0.09000 0.00000 Standard Deviation 0.2000 0.08215 0.02875

Skewness -0.3177 1.5267 0.7212 Kurtosis 2.7793 6.6831 4.1836 Observations 105 105 105

2. Correlation Matrix

Stocks

Bonds

Bills

Stocks 1.000 0.102 -0.083 Bonds 0.102 1.000 0.213 Bills -0.083 0.213 1.000