outcome orientated investing for retirement · 2015. 3. 2. · outcome orientated investing for...

Outcome orientated investing for retirementFrom the DC scheme member’s perspective

For European professional investors only

2

Contents Page

Executive summary 4

1 Introduction 6

2 Literature review 10

3 A brief history of lifestyling 13

4 The future of lifestyling 19

4.1 Static lifestyle with full annuitisation at age 65 21

4.2 Static lifestyle with gradual annuitisation between ages 65 and 75 25

4.3 Dynamic asset allocation strategies 27

4.4 Liability driven asset allocation and ‘loss aversion’ 29

References 34

3

We believe there is a need for more innovative alternatives to the lifestyling approaches

that are typically employed in defined contribution (DC) pension schemes.

As we explored everything that has worked well, and not so well, with the traditional

lifestyling approaches, and considered the evolving role of target-date funds, we

questioned the application and ‘fitness for purpose’ of various existing solutions.

With this in mind, we sought the involvement and academic input of Cass Business School

to evaluate alternative approaches which might also consider the desired outcomes for

DC scheme members.

The past and present solutions treat people of a like age and/or number of years before

they retire as if they have the same income objectives in retirement. Moreover, and

most importantly, this approach fails to consider how close individuals are to achieving

their target retirement incomes. What this means in practice is that, in most existing

DC arrangements, two people of the same age, with entirely different retirement income

objectives, with one ‘on target’ and the other significantly ‘under target’, will have

identical asset allocation profiles. This is clearly wrong.

Much is made of the fact that DC is different from defined benefit (DB), and rightly so. DB

schemes treat members’ assets as a single pool with corresponding liabilities, whereas

DC schemes have historically focused solely on scheme members’ assets, with little

consideration to their needs in retirement. In view of this, we wanted to investigate the

extent to which aspects of the way in which DB schemes view and treat assets in the

context of liabilities could be applied to DC schemes.

Pension managers, trustees and their advisors will, we hope, find this paper to be both

interesting and challenging. We propose some highly original theories and approaches,

to which the asset management industry should now respond with workable products,

solutions and technology. We believe that these approaches would require the industry

to rethink how it engages with scheme members, and challenge assumptions on the key

inputs for future product developments.

David CalfoGroup head of DC strategy

BNY Mellon

[email protected]

Outcome orientated investing for retirementFrom the DC scheme member’s perspective

4

Few now dispute that the future of

pension provision, not just in the UK

but in other developed countries too,

seems to be the DC model1. In moving,

albeit gradually, from a DB to a DC world,

the burden of risk is also shifting from

employers and their shareholders, to

individuals.

However, unlike under DB arrangements,

under DC provision employers will not

be obliged to make up any pension

shortfalls, meaning that this risk is borne

by the member. Given this significant

shift to a scenario in which scheme

members must bear the risk that their

retirement income will not be at the

desired level, it is right to ask whether

the investment approach taken to DC

pension provision is appropriate.

The key findings from this paper include:

• ‘Traditional’ DC lifestyling approaches

are producing ever-lower eventual

pensions.

• This paper proposes a ‘dynamic’

investment strategy that is outcome-

driven (targeting the generation of an

income in retirement that will offer

a minimum acceptable replacement

ratio relative to the income earned

during employment), recognises

investors’ attitudes to risk and takes a

flexible approach to the decumulation

phase.

• We show that a more dynamic

investment and annuitisation strategy

produces a less uncertain outcome

with regard to the final DC-related

retirement income replacement ratio,

thereby helping greatly to reduce the

risk of future DC pension shortfalls.

Executive summary

1 Indeed, the National Employment Savings Trust (NEST), which is due to launch next year and which has been designed to provide pensions for potentially millions of low paid UK workers, has a DC structure, and within a few years is likely to become one of the largest DC pension schemes in the world.

5

The vast majority of DC members invest

their precious pension pots in the default

fund provided by the scheme. Given

that saving for a pension is a long-term

investment commitment for most people,

most (if not all) DC funds are heavily

weighted to equities, on the assumption

that, in the long-run, equities will out-

perform all other asset classes.

A second feature of a traditional default

DC investment strategy, is the lifestyling

that takes place, usually over the 10

years leading up to retirement and full

annuitisation, when investors’ pots

are automatically and mechanistically

switched out of equities and into

government bonds, with little reference

to the risk preferences of the member,

to the size of the investment fund

accumulated over this period, or, indeed,

to financial market developments.

In this paper we address some of

the shortcomings of the current DC

framework. In keeping with other studies

our empirical work shows the typical

approach to de-risking, or to lifestyling,

and how this mechanical strategy

has produced ever-lower eventual

pensions for a typical DC member over

the past 20 years. With annuity rates

at such depressed levels currently, it is

imperative that investment strategy is

more enlightened.

To examine these substantial investment

challenges we develop a model that

incorporates three important elements.

First, the asset allocation strategy is

dynamic and, crucially, it is driven

by the target replacement rate of the

representative DC member. The strategy

is not to generate the largest DC pot

possible, but, instead, to minimise the

likelihood of not achieving the target

replacement ratio.

The second feature of the model is that

we do not impose a constraint that forces

DC members to annuitise at the normal

retirement age – although we do impose

the constraint that they should be fully

annuitised by age 75. A crucial feature

of any dynamic DC investment strategy

should be the ability to bring forward or

delay the annuitisation process, or to

annuitise partially over time.

Finally, we adopt the framework

first proposed by Blake, Wright and

Zhang (2011) and suggest that the risk

preferences of each DC member should

be recognised and in particular the

notion that most individuals are actually

‘loss averse’, meaning that they are

generally more distressed about a loss

of a given amount, than they are happy

about a gain of the same amount.

Using this framework, it can be seen

that when compared with the traditional

approach to DC investment strategy,

the dynamic, outcome-oriented strategy

increases the probability of achieving

the desired pension significantly, while

greatly reducing the probability of

the replacement ratio falling below a

minimum ‘acceptable’ level.

In keeping with other studies our empirical work shows the typical approach to de-risking, or to lifestyling, and how this mechanical strategy has produced ever-lower eventual pensions for a typical DC member over the past 20 years.

6

IntroductionSection 1

The UK’s private sector pension

landscape has been dominated for many

years by the DB model. Until the early

part of this century, the amount of risk

that DB plan sponsors were assuming

was not widely appreciated. However, a

prolonged bear market in equities has

had a significant impact upon DB asset

portfolios over the past decade or so.

But DB balance sheets have also come

under pressure from continuing (and

recognised) improvements in longevity

and the move to marked-to-market

accounting practices at a time when the

discount rate used to market DB liabilities

to market, have fallen substantially.

Upwardly revised estimates of longevity

and low discount rates have together

pushed up the present value of DB

scheme liabilities. The net result of these

pressures is widespread DB deficits.

This widening of deficits put a sharp

focus on the scheme sponsor – arguably

the most valuable asset that a DB scheme

has2. Since the early part of this century,

DB plan sponsors have been trying to

plug the gap left behind by the weak

performance of high-risk asset classes

and the growth in the present value of

scheme liabilities. The burden has been,

and remains, quite considerable.

According to the Office for National

Statistics (ONS)3, the average contribution

made by employers on behalf of their DB

members was 16.6% of salary at the end

of 2008. It is, therefore, not uncommon

for some scheme sponsors to contribute

the equivalent of over 20% of a member’s

annual salary bill to his or her DB pension

fund. Some pay considerably more.

2 See for example Brigden et al (2008 and 2009)3 Pension Trends 2009, ONS

7

As DB trustees looked to their scheme

sponsors, finance directors, backed

by their boards, sought to reduce their

exposure to this risk. Consequently,

today, 79% of DB sponsors do not allow

new employees to join their DB scheme.

Many of these schemes have also

reduced the benefits that can be earned

by the remaining scheme members.

However, some scheme sponsors have

gone further still. 17% of DB schemes are

not only closed to new members, but are

also closed to ‘future accrual’. This means

that even active members cannot earn

any further pension benefits.4 Although

DB pension provision is no longer the

future, the liabilities are so long dated

that the ‘DB pension problem’ will be

with us for a very long time yet. To coin a

phrase, over the past few years we have

almost certainly witnessed the beginning

of the end of DB pension schemes.

So what about the future?Increasingly, new employees are not

permitted to enter existing DB plans;

instead they are offered an alternative

DC arrangement. For those schemes

that have closed to future accrual, their

existing members retain their pension

benefits accrued in the past under the DB

arrangements, but their future pension

accrual is offered on a DC basis. The

eventual pensions of these members will

therefore comprise a mixture of DB and

DC pension rights.

As the world’s third largest pensions

market by assets – accounting for

8.6% of global pension assets,5 the

UK occupational pension industry is

huge. Indeed, total UK pension assets

(excluding those in personal and

stakeholder pensions) are estimated

to be US$2,279 billion (£1,381 billion),

equivalent to 101% of UK GDP, or national

output. According to the ONS, at the end

of 2008, 9 million people were active

members of either an occupational DB

or DC scheme, comprising 3.6 million in

the private sector and 5.4 million in the

public sector.6 Furthermore, the ONS

estimated that 8.8 million people in

the UK were receiving a DB and/or DC

occupational pension.

According to the ONS, at the end of 2008, 9 million people were active members of either an occupational DB or DC scheme, comprising 3.6 million in the private sector and 5.4 million in the public sector. Furthermore, the ONS estimated that 8.8 million people in the UK were receiving a DB and/or DC occupational pension.

4 Source of statistics: NAPF, March 20115 Only the US and Japan are bigger, accounting for 57.8% and 13.1% of global pension assets respectively. Towers Watson Global Pension Asset Study 20116 Remember that many public sector pension plans are run in the same way as private sector DB plans

8

The membership split between DB and

DC plans is difficult to estimate, and

indeed, as we explained earlier, many

employees may be members of both a

DB and a DC scheme. However, in a more

recent report by the Pensions Regulator 7,

it was estimated that:

• 2.3millionpeoplecurrentlycontribute

to a private sector DB pension scheme

(compared to 5.5 million in the early

1980s);

• 1 million active members currently

contribute to DC schemes;

• 2.5millionpeopleintotalhavesavings

in DC schemes;

• annual contributions to schemes

with 12 or more members amount to

approximately £2.2 billion, or £4,200

per active member, where 75% of these

contributions come from the employer;

and

• around half of all DC membership is

concentrated in 130 large schemes,

while most DC schemes (around

44,000) are very small, with less than

12 members, accounting for just 5% of

total DC membership.

In this paper we focus on DC pension

provision. In Section 2, we briefly

review the relevant academic literature

on this topic and identify some of the

key parameters and issues. The basic

conclusion of the recent literature is

that a more dynamic approach to DC

asset allocation is required. However,

the majority of DC members invest in

default funds that have historically been

heavily weighted towards equities, and

are then usually shifted mechanically

from equities into government bonds

over the 10-year period leading up to

their chosen retirement date, such that

they are fully invested in government

bonds when they annuitise their pension

pot. The approach typically taken to DC

asset allocation then is very static – and

is therefore unlikely to be optimal for all,

or for even any single individual.

In Section 3, we take a look at the

history of lifestyling, that is, the all-

important few years prior to retirement

and full annuitisation, which gradually

moves DC members from high- to low-

risk asset classes in a mechanical and

deterministic fashion. We believe that

our results in this section are the first full

examination of the performance of this

de-risking process.

7 The Pensions Regulator, DC Trust 2010

9

One of the key parameters of our model with regard to the asset allocation decision is the target replacement ratio, that is, the representative DC member in the scheme adopts a strategy towards achieving a certain level of pension relative to his or her final salary. That investment decision is driven largely by the extent to which the individual is likely to meet this target or not.

In Section 4, we develop and describe

a theoretical, whole-of-life model of DC

accumulation and decumulation for a

representative DC member. One of the

key parameters of our model with regard

to the asset allocation decision is the

target replacement ratio, that is, the

representative DC member in the scheme

adopts a strategy towards achieving

a certain level of pension relative to

his or her final salary. That investment

decision is driven largely by the extent

to which the individual is likely to meet

this target or not. It is in this sense

then that the DC member in our model

adopts a Liability Driven Investment (LDI)

strategy, a strategy that has become

very common for DB schemes in recent

years. Our LDI-based model allows us to

explore a number of important issues.

First, it allows us to consider whether it

is optimal to annuitise at a single point in

time. Would it instead be more beneficial

for DC members to annuitise partially

as they approach, and then pass, the

normal retirement age?

Secondly, we explore the possible

benefits of adopting a more dynamic

approach to asset allocation in both the

pre- and post-retirement periods. We

look at both momentum and contrarian-

based investment strategy, where the

DC member chooses between a risky

and risk-free asset class. Finally, we

consider DC member attitudes to risk

and, in so doing, introduce some of the

latest academic research in this area

that emanates from behavioural finance

literature.

10

Literature reviewSection 2

A number of authors have investigated

the performance of DC pension provision

in the past from a historical perspective.

The focus has generally been on the

‘replacement rate’, which is defined

as the annual pension divided by the

individual’s final salary. Using US

data from 1872 and assuming that an

individual’s fund was invested 100% in

US equities, Burtless (2009a and 2009b)

found that the highest replacement rate

was 89% in 1999, while the lowest was

12% in 1920. In a related study using

UK data from 1948 to 2007, Cannon and

Tonks (2009) found that the size of the

average DC fund relative to final salary

was 17.9 times, although the average for

the lowest decile of outcomes was 7.3

times – again indicating a wide range of

possible outcomes. This result and others

have shown how variable the resulting

DC pension can be when the fund is left

essentially unmanaged (with 100% of

the assets being invested, for example,

in equities, with no discretionary

management techniques being applied).

Other studies have investigated the

importance of the asset allocation

decisions taken by DC members. Blake

et al (2001) showed that the major

determinant of final DC pensions was

asset allocation, rather than stock

selection. However, all the evidence

shows that members typically show very

little interest in the asset allocation of

their fund – perhaps not surprisingly

given that most are not investment

experts. This is why the asset allocation

of the default fund is so important.

11

Levy (2009) reported that, in 2008,

96% of UK DC members used their

default fund, and yet these funds are

typically heavily tilted towards equities.

This is generally corrected in the last

10 years before the member’s chosen

retirement, with a default, mechanical

lifestyling asset allocation process. This

process involves the gradual reduction

of members’ equity allocation and

gradual proportionate increase in their

investment in government bonds. This

mechanical process is designed so that,

by the end of a typical 10-year lifestyling

period, they are entirely invested in

government bonds and ready to purchase

their annuity. But few would now argue

that heavy reliance on equity returns,

followed by a mechanical de-risking

strategy, would be ‘optimal’ for any DC

member.

Given the evidence of how important

asset allocation is to the eventual DC

pension, and the widespread use of

default funds and their associated

mechanical approach to de-risking, a

consensus has been building for some

time, in the academic literature and

within the pensions industry, that a more

dynamic approach to investment, and, in

particular, to asset allocation, is needed.

In a recent paper Basu et al (2010)

argue for a more dynamic investment

strategy. However, not one based upon

the number of years until retirement, or

even on the fund value at each point in

time, but instead upon a target, or hurdle

rate of return on the DC fund. Through

simulations they show that a dynamic

strategy with an investment hurdle rate

of 10% out-performed what they refer

to as the ‘Rip Van Winkle’, traditional

approach to asset allocation, particularly

over the 10 years prior to retirement.

The rule that they propose for the final

accumulation years involves investing

60% of assets in equities and 40% in

bonds each year whenever the target

return has been met or achieved. In

years where it has not been met, the

fund is allocated 100% to equities. This

rule therefore relies heavily on the idea

that equity prices tend to trend up over

time. It also requires a sensible hurdle

rate of return. Setting a hurdle rate that

is too high could result in an investment

portfolio that is always invested in

equities; setting it too low could result

in a fixed 60/40 equity bond allocation.

But there is another issue with this

rule, which the authors acknowledge,

which is that it does not pay sufficient

attention to individual attitudes to risk.

For example, suppose with three years to

retirement, that the investment fund had

under-performed its hurdle rate, the rule

would switch or keep the entire DC pot

invested in equities. It seems unlikely

that any individual so close to retirement

would be comfortable with 100% of his

or her funds invested in equities at any

time, let alone at a time when they had

been performing poorly and had possibly

generated substantial losses. Equally, no

responsible adviser would recommend

such a strategy either.

Given the evidence of how important asset allocation is to the eventual DC pension, and the widespread use of default funds and their associated mechanical approach to de-risking, a consensus has been building for some time in that a more dynamic approach to investment, and, in particular, to asset allocation, is needed.

12

Blake, Wright and Zhang (2011) address

this issue of risk aversion in their model

of DC investment accumulation and

integrate it with a dynamic investment

strategy. In particular, they integrate

one of the main findings from the

behavioural finance literature, which is

that individuals (investors) tend to be

loss averse. This means that they are

more upset about a loss of £20, than

they are happy about a gain of £20. In

other words, they do not view gains and

losses in a symmetric manner; it is in this

sense that we say individuals are ‘loss

averse’. By integrating loss aversion into

a dynamic DC asset allocation strategy

the authors arrive at some very intuitive

results.

First, in agreement with Basu et al,

they confirm that a dynamic strategy

is preferable to a static, Rip Van Winkle

strategy. They also show that it is optimal

to increase weightings in equities when

the fund is either significantly below the

target (with the aim of making good the

deficit) or significantly above the target

(as the resulting cushion allows for more

risk to be accepted). However, when the

fund is close to the target, it is optimal to

reduce significantly the equity weighting

to minimise the risk of falling below

the target in future years. The degree of

adjustment is shown to be dependent

upon the degree to which individuals

are loss averse. Overall, they conclude

that when compared to the Rip Van

Winkle approach – which is the common

approach taken to asset allocation by

many DC members today – a dynamic,

target-driven approach to investment,

with the assumption of loss aversion,

produces a much greater degree of

certainty in retirement planning.

Blake, Wright and Zhang (2011) address this issue of risk aversion in their model of DC investment accumulation and integrate it with a dynamic investment strategy. In particular, they integrate one of the main findings from the behavioural finance literature, which is that individuals (investors) tend to be loss averse.

13

A brief history of lifestylingSection 3

In a DC scheme, regular contributions

by the member, and usually also their

employer, gradually build up over time.

Each DC member effectively builds

up his or her own fund over time. The

contributions attributable to each DC

member are invested, so that the size

of the eventual fund will be determined

by the size of regular contributions over

time, and the rate of return achieved

on the invested funds. At retirement,

the entire value of a member’s fund is

usually used to purchase an annuity,

that is, a regular income that is paid until

death. Clearly, other things being equal,

the larger the fund at this time, the larger

the pension will be.

When a DC member is relatively young,

his or her fund will usually be invested

predominantly in high-risk, growth

asset classes, normally equities. This

is because these asset classes are

normally expected to produce a higher

return on average over time. However,

equity markets can be very volatile. For

example, in October 1987 the UK equity

market fell by 27% and by a further 10%

during November 1987. Imagine having

one’s entire DC fund invested in equities

in October 1987 immediately prior to

one’s intended retirement. The resulting

collapse in the value of the fund would

have led to a commensurate decline

in the value of the pension. It’s for this

reason that DC plans (and many personal

pension plans) have a lifestyling option,

that is, a mechanistic asset allocation

process that starts to move the member’s

funds out of equities and progressively

into gilts, until the plan is 100% invested

in gilts just prior to the member’s chosen

retirement date.

-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Max

imum

ann

ual d

raw

dow

n

Year lifestyling begins

£0

£5,000

£10,000

£15,000

£20,000

£25,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Gro

ss a

nnua

l sal

ary


Starting salary

Final salary

£0

£5,000

£10,000

£15,000

£20,000

£25,000

£30,000

£35,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Sta

rtin

g va

lue

of D

C fu

nd


0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Annu

ity

rate

s


RPI-linked payment Level payment

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Pens

ion

as a

pro

port

ion

of fi

nal s

alar

y


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot


0.0

2.0

4.0

6.0

8.0

10.0

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot a

s pr

opor

tion

of s

alar

y


0%

5%

10%

15%

20%

25%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Aver

age

annu

al re

turn


Pension/Final salary (Level)

Pension/Final salary (RPI)

Necessary DC pot at 55

Necessary DC pot at 55 as % of salary at 55

-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Max

imum

ann

ual d

raw

dow

n


£0

£5,000

£10,000

£15,000

£20,000

£25,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Gro

ss a

nnua

l sal

ary


Starting salary

Final salary

£0

£5,000

£10,000

£15,000

£20,000

£25,000

£30,000

£35,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Sta

rtin

g va

lue

of D

C fu

nd


0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Annu

ity

rate

s



0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Pens

ion

as a

pro

port

ion

of fi

nal s

alar

y


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot


0.0

2.0

4.0

6.0

8.0

10.0

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot a

s pr

opor

tion

of s

alar

y


0%

5%

10%

15%

20%

25%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Aver

age

annu

al re

turn






Panel A: Average annual returns

Source: Centre for Asset Management Research, Cass Business School

Panel B: Maximum annual draw-downs

Figure 1: 10-yearly lifestyling return performance

15

This lifestyling often begins 10 years

before a member’s chosen retirement

date, and assumes that the member

wishes to have his or her DC fund fully

annuitised at this point in time. In this

section of the paper we look at how

this mechanical approach to asset

allocation and eventual annuitisation

has performed historically. What sort of

pension has this static approach to asset

allocation produced for lifestylers?

In Panel A of Figure 1 we present the

average 10-yearly returns that any

investor would have achieved from being

100% invested in UK equities at the

start of each 10-year period, and 100%

invested in gilts at the end of this period.

We assume a ‘straight line’ reallocation

of funds at the end of each year so, for

example, half way through this 10-year

period the investor has a 50% allocation

to equities and a 50% allocation to gilts.

The equity investment is represented

by the total return on the FTSE All-

Share Index, while the return on the gilt

portfolio is based upon the total return

on the IBOXX £ Gilts All Maturities Index.

The figure shows how the nominal returns

achievable from this asset allocation

strategy have declined over time. This, of

course, is largely a function of the equity

bear market that began in the early part

of the noughties. In Panel B we present

the maximum annual drawdown in each

10-year period, that is, the worst annual

return in each 10-year period.

As you can see from Panel A Figure 1,

early on, the worst year still produced a

positive return. Clearly, greater equity

market volatility has been a significant

problem for all DC members that have

adopted this lifestyling approach in

more recent years, as evidenced by the

negative draw-downs for most of this

sample period.

Any DC member, or indeed any investor,

adopting this approach to asset

allocation over each 10-year period

would have achieved these investment

returns. However, the question we wish

to address here is: what pension might

have been bought with the accumulated

DC pot at the end of each 10-year period?

To answer this question we hypothesise

a representative UK DC member, who

adopts the mechanistic lifestyling

approach at the beginning of each 10-

year period from 1980.

At the start of each 10-year period the representative worker:

• is a male aged 55 and has ten years

to go until retirement;

• earnsanaverageannualsalary;

• makes an annual contribution

equivalent to 6% of his annual

salary to the DC default fund, and

has an employer that matches this

contribution; and

• has a DC fund comprising 100%

equities and 0% in UK government

bonds, but by the time he retires his

investment pot comprises 100% UK

government bonds. This is achieved

over the 10 years by selling equal

amounts of his equity holding at the

end of every year, using the proceeds

to increase his holdings of UK

government bonds.

When a DC member is relatively young, his or her fund will usually be invested predominantly in high-risk, growth asset classes, normally equities. This is because these asset classes are normally expected to produce a higher return on average over time. However, equity markets can be very volatile.

16

-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Max

imum

ann

ual d

raw

dow

n


£0

£5,000

£10,000

£15,000

£20,000

£25,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Gro

ss a

nnua

l sal

ary


Starting salary

Final salary

£0

£5,000

£10,000

£15,000

£20,000

£25,000

£30,000

£35,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Sta

rtin

g va

lue

of D

C fu

nd


0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Annu

ity

rate

s



0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Pens

ion

as a

pro

port

ion

of fi

nal s

alar

y


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot


0.0

2.0

4.0

6.0

8.0

10.0

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot a

s pr

opor

tion

of s

alar

y


0%

5%

10%

15%

20%

25%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Aver

age

annu

al re

turn






-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Max

imum

ann

ual d

raw

dow

n


£0

£5,000

£10,000

£15,000

£20,000

£25,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Gro

ss a

nnua

l sal

ary


Starting salary

Final salary

£0

£5,000

£10,000

£15,000

£20,000

£25,000

£30,000

£35,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Sta

rtin

g va

lue

of D

C fu

nd


0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Annu

ity

rate

s



0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Pens

ion

as a

pro

port

ion

of fi

nal s

alar

y


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot


0.0

2.0

4.0

6.0

8.0

10.0

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot a

s pr

opor

tion

of s

alar

y


0%

5%

10%

15%

20%

25%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Aver

age

annu

al re

turn






Panel A: SalaryFigure 2: Representative DC member’s salary and DC pot at age 55

Panel B: DC fund at start of lifestyling


Panel A of Figure 2 uses historic wage

and salary data collected by the ONS to

show how the representative worker’s

salary has progressed over time. The

two bars in this chart show the value of

the annual (pre-tax) salary at the start

of each 10-year period and at the end,

that is, at the point of retirement and

annuitisation. Panel B of Figure 2 shows

the value of the pension pot accumulated

by the representative DC member at

the start of each 10-year period, which

we set at twice his annual salary at that

point in time. If our representative worker

started making contributions along with

his employer at the age of 40 equivalent

to 12% of his gross salary, and achieved

an average real return of around 5% on

his investment fund up until age 55, the

DC pot would be around twice his annual

salary at age 55. It is for this reason that

we choose this value for the starting

value of the DC pot. We will return to

this issue later, but, for the moment, it’s

important for the calculations to have a

starting value for the DC fund.

Had DC members begun their lifestyling in 1980, and assuming that they did not take any tax-free lump sum from their fund, they would have been able to purchase a level payment annuity equivalent to 73% of their final salary, or an RPI-linked annuity equivalent to 40% of their final salary.

17

-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Max

imum

ann

ual d

raw

dow

n


£0

£5,000

£10,000

£15,000

£20,000

£25,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Gro

ss a

nnua

l sal

ary


Starting salary

Final salary

£0

£5,000

£10,000

£15,000

£20,000

£25,000

£30,000

£35,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Sta

rtin

g va

lue

of D

C fu

nd


0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Annu

ity

rate

s



0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Pens

ion

as a

pro

port

ion

of fi

nal s

alar

y


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot


0.0

2.0

4.0

6.0

8.0

10.0

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot a

s pr

opor

tion

of s

alar

y


0%

5%

10%

15%

20%

25%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Aver

age

annu

al re

turn






-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Max

imum

ann

ual d

raw

dow

n


£0

£5,000

£10,000

£15,000

£20,000

£25,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Gro

ss a

nnua

l sal

ary


Starting salary

Final salary

£0

£5,000

£10,000

£15,000

£20,000

£25,000

£30,000

£35,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Sta

rtin

g va

lue

of D

C fu

nd


0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Annu

ity

rate

s



0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Pens

ion

as a

pro

port

ion

of fi

nal s

alar

y


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot


0.0

2.0

4.0

6.0

8.0

10.0

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot a

s pr

opor

tion

of s

alar

y


0%

5%

10%

15%

20%

25%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Aver

age

annu

al re

turn






Panel A: Historic annuity rates

Panel B: Annual pension for typical DC member


The last part of the jigsaw puzzle needed

to calculate the annual pension of our

representative DC member is the annuity

rate that prevailed at the end of each 10-

year lifestyling period. Panel A of Figure 3

shows both level and RPI-linked annuity

rates over time for a 65 year-old, non-

smoking man. Annuity rates are closely

related to government bond yields. This

is because annuity providers (mainly

insurance companies) back these

annuities with government bonds, so,

as bond yields have fallen over the past

30 years, so have annuity rates. Panel B

of Figure 3 shows the value of both the

level and inflation-linked pension that

could be bought given all the elements

discussed above, that would be the end-

result of each 10-year lifestyling period.

The results in Panel B are quite

astounding. Had DC members begun

their lifestyling in 1980, and assuming

that they did not take any tax-free lump

sum from their fund, they would have

been able to purchase a level payment

annuity equivalent to 73% of their

final salary, or an RPI-linked annuity

equivalent to 40% of their final salary.

Contrast this with the fortunes of the

equivalent individuals beginning their

lifestyling journey in 2001.

These unfortunate individuals can only

afford a level payment annuity equivalent

to 21% of their final salary, or a RPI-linked

payment equivalent to a measly 12% of

their final salary.

Figure 3: Annuity rates and pensions

18

In Figure 4 we present the results of a

further experiment. The figure shows the

necessary size of the DC pot at the start of

the lifestyling process, that is, at age 55,

that would have been required to produce

a level annual pension equivalent to two-

thirds of the representative DC member’s

salary at 65. Remember that the pension

achieved and shown in Panel B of Figure

3 is based upon an assumption that the

DC pension pot was only twice the size of

the value of the individual’s salary at the

start of the 10-year de-risking process.

The results should not come as too much

of a surprise given the earlier analysis.

In cash terms Panel A of Figure 4 the size

of the required DC pot at 55 has increased

massively. A DC member beginning the

lifestyling, or de-risking process in 1980,

required a DC pot of £5,766 to achieve

a replacement ratio of two-thirds of his

or her final salary; by 2001 this figure

had risen to a staggering £152,986. To

put this into a real context, as shown in

Panel B, in 1980 our representative DC

member would have needed a DC pot

equivalent to just under twice his annual

salary at 55; by 2001 the necessary pot

size would have needed to be just over

nine times his annual salary at 55.

In the next section of this paper we

will explore how the sort of standard

lifestyling strategy described here might

be expected to perform in the future

and to see whether we can design

an alternative approach that may be

more successful in providing a desired

income in retirement. We will do this by

developing a forward-looking model of

DC pension provision and applying this

model to the situation of a representative

individual.

-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Max

imum

ann

ual d

raw

dow

n


£0

£5,000

£10,000

£15,000

£20,000

£25,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Gro

ss a

nnua

l sal

ary


Starting salary

Final salary

£0

£5,000

£10,000

£15,000

£20,000

£25,000

£30,000

£35,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Sta

rtin

g va

lue

of D

C fu

nd


0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Annu

ity

rate

s



0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Pens

ion

as a

pro

port

ion

of fi

nal s

alar

y


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot


0.0

2.0

4.0

6.0

8.0

10.0

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot a

s pr

opor

tion

of s

alar

y


0%

5%

10%

15%

20%

25%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Aver

age

annu

al re

turn






Figure 4: DC pot at age 55 necessary to produce a level annual pension of two-thirds of salary on retirement at age 65

Panel A: DC pot in cash terms

Panel B: DC pot as proportion of salary at age 55


-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Max

imum

ann

ual d

raw

dow

n


£0

£5,000

£10,000

£15,000

£20,000

£25,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Gro

ss a

nnua

l sal

ary


Starting salary

Final salary

£0

£5,000

£10,000

£15,000

£20,000

£25,000

£30,000

£35,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Sta

rtin

g va

lue

of D

C fu

nd


0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Annu

ity

rate

s



0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Pens

ion

as a

pro

port

ion

of fi

nal s

alar

y


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot


0.0

2.0

4.0

6.0

8.0

10.0

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Siz

e of

DC

pot a

s pr

opor

tion

of s

alar

y


0%

5%

10%

15%

20%

25%

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Aver

age

annu

al re

turn






19

The future of lifestylingSection 4

We will begin by considering an

individual who is currently aged 25, who

has an annual salary of £20,000 and

who has no previous pension savings. In

order to project this individual’s pension

entitlement in the future we first need a

model for future salary growth.

We will assume that future salary growth

for this individual will consist of two

components:

• general salary inflation of 2% per

annum, representing the real growth in

the economy over time; and

• promotional salary increases, based

on the Office for National Statistics

2005 Annual Survey of Hours and

Earnings.

The assumed future salary pattern is

shown in Figure 5. We can see that

income can be expected to fall slightly in

the years immediately before retirement.

This is a typical age-earnings profile

for an average UK worker. The decline

in age-related pay towards the end of

individuals’ working lives is typically

brought about because they undertake

less overtime, and perhaps do less

demanding work as they approach

retirement.8

Our representative DC member

contributes to his or her DC pension

pot over time. These contributions will

be invested in return-generating asset

classes. For simplicity, we will assume

that the individual invests in just two

asset classes:

• a risk-free asset (for example, an

index-linked government bond), which

provides a guaranteed real return of

2% per annum; and

• ariskyasset(forexample,adiversified

portfolio of equities), which produces

a real average return of 6% per annum

(that is, an equity risk premium of

4% per annum) and with standard

deviation of 20% per annum

Finally, we assume that, on retirement,

annuity prices are calculated using the

risk-free real return of 2% per annum and

a suitable standard mortality table used

by the actuarial profession.9

8 For ‘white-collar’ occupations, it may be appropriate to assume a slightly different pattern of promotional salary growth, although this will not make much difference to the results shown below.9 The mortality table used is PMA92C20, which is based on the experience of male pension annuitants over the period 1991-94 projected to the calendar year 2020. Thus, the annuity price at

retirement is fixed and the model does not explicitly include annuity risk. In practice, the price of annuity will depend on the prevailing interest rate environment at retirement and then current mortality projections (which are likely to be lower than those in use today, leading to higher annuity prices).

Figure 5: Assumed future salary progression of a representative individual with current salary of £20k

Probability of replacement ratio

of greater than 66.7% = 20% (cf. 12%)

Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio

Replacement ratio = 50%


Replacement ratio = 66.7%




Replacement ratio

Replacement ratio

Replacement ratio

Age

Ratio of current fund to current ‘target’ fund


of greater than 66.7% = 12%

Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000

General salary inflation

Promotional increases

Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%

Static lifestyle asset allocation (to age 65) Static lifestule asset allocation (to age 75)

0%756555453525

Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0



6% contributionfrom age 25


10% contribution from age 25


Static lifestyle asset allocation (to age 65)Static lifestyle asset allocation (to age 75)

Static lifestyle asset allocation (to age 75)Dynamic asset allocation (to age momentum)Dynamic asset allocation (contrarian)

Opt

imal

allo

cati

on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

Opt

imal

allo

cati

on in

equ

itie

s

20%

0%706050403020

Static lifestyle asset allocation (to age 75)Loss aversion


21

Using these parameters we will begin

by investigating the suitability of a

standard ‘static’ lifestyle investment

strategy for this individual. That is, the

traditional approach to lifestyling and

annuitisation described in Section 3.

As with the experiments in Section 3

with historic data, we assume that the

representative DC member’s investment

fund is 100% invested in equities from

age 25 to age 55 and then the equity

allocation is reduced by 10% each year

(by switching to risk-free government

bonds) to give an equity allocation of

0% on retirement at age 65. We refer

to this strategy as ‘static’ because the

asset allocation at each age is set in

advance and does not vary according to

either current economic conditions or to

the individual’s personal circumstances.

Initially, we assume a contribution

rate of 8% of salary per annum prior to

retirement. This is consistent with the

minimum National Employment Savings

Trust (NEST) contribution.10 We assume

that the accumulated fund is used to

purchase an annuity at age 65 and

we define the ‘replacement ratio’ on

retirement as in the equation below.

When we apply these parameters to the

case of our representative DC member,

simulating the outcome 10,000 times

based on different realisations of the

random return on the risky asset each

year prior to retirement, we find that the

mean replacement ratio is 43%, that is,

on average the accumulated fund at

retirement is sufficient to purchase an

RPI-linked pension income of 43% of

salary immediately prior to retirement.

This is significantly lower than the

‘desired’ replacement ratio of two-thirds

(or 66.7%) that has been traditionally

targeted by members of both DC and

DB pension plans.11 However, when

analysing the effectiveness of a particular

investment strategy, it is more useful to

consider the range of possible outcomes.

The distribution for the replacement ratio

on retirement is shown in Figure 6.

Replacement ratio =Annual income immediately before retirement

10 From 2017 onwards, NEST will be introduced in October 2012 and lower minimum contribution rates will apply initially.11 Some of the most generous DB pension schemes provide a pension of 1/60th of final salary on retirement for each

year of service. With a ‘typical’ working lifetime of 40 years, this led to a pension of 40/60th of final salary being considered by many as standard. While it is true to say that, with the demise of DB schemes as discussed previously, very few individuals currently in employment can expect to achieve a pension on this scale, it can be considered as a desirable goal.

4.1 Static lifestyle with full annuitisation at age 65

Annual income immediately after retirement

12 We include this for comparison purposes as it is increasingly common for individuals to postpone retirement savings until age 40 (or, indeed, even later).

Figure 6: Distribution of replacement ratio on retirement assuming standard lifestyle investment strategy and annual contributions of 8% of salary



Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio







Replacement ratio

Replacement ratio

Replacement ratio

Age




Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000



Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%


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Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0









Opt

imal

allo

cati

on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

Opt

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allo

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equ

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s

20%

0%706050403020



In the event of very high investment

returns, particularly prior to age 55 (when

the fund is invested entirely in equities),

then a replacement ratio of 120% of

final salary (or more) can be achieved.

However, because equity returns are

very volatile in our experiment, it can

also be seen from Figure 6 that a very

low replacement ratio (perhaps of 20%

or less) is also a distinct possibility.

The default lifestyle strategy then is

not very effective at ensuring that the

income after retirement will be consistent

with the income before retirement.

The probability of achieving or exceeding

the desired replacement ratio of two-

thirds of salary at retirement is only

12%. And, equally as important, there

is a probability of 72% of failing even to

achieve what we might consider to be an

acceptable replacement ratio of 50% of

salary at retirement.

For comparison purposes, we will also consider what happens if:

a the annual contribution rate is reduced

to 6% per annum,

b the annual contribution rate is

increased to 10% per annum, and

c the individual does not begin

contributing until age 40 (rather than

at age 25) and then contributes at 15%

of salary per annum until retirement.12



Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio







Replacement ratio

Replacement ratio

Replacement ratio

Age




Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000



Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%


0%756555453525

Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0









Opt

imal

allo

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on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

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20%

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Figure 7: Distribution of replacement ratio on retirement assuming a standard lifestyle investment strategy and annual contributions of 6%, 8%, 10% and 15% of salary

Table 1: Replacement ratio on retirement assuming standard lifestyle investment strategy and annual contributions of 6%, 8%, 10% and 15% of salary

Annual contribution rate

6% of salary 8% of salary 10% of salary 15% of salary from age 25 from age 25 from age 25 from age 40Mean replacement ratio 32% 43% 54% 43%

Probability of replacement ratio > 66.7% 4% 12% 24% 7%

Probability of replacement ratio < 50.0% 88% 72% 55% 73%

Figure 7 shows the distribution of the

replacement ratio on retirement for the

parameters defined in (a), (b) and (c)

above (again, obtained empirically using

10,000 simulations), as well as for the

baseline version of the model shown in

Figure 6.

These results are summarised in

Table 1. Unsurprisingly, contributing a

higher percentage of salary each year

increases the probability of achieving the

desired replacement ratio of two-thirds

of salary at retirement (from 12% with

a contribution rate of 8% per annum,

to 24% with a contribution rate of 10%

per annum) and reduces the probability

of failing to achieve an acceptable

minimum replacement ratio of 50% of

salary at retirement (from 72% with a

contribution rate of 8% per annum, to

55% for a contribution rate of 10% per

annum). It can also be seen from Table

1 that, for a ‘typical’ individual with a

salary of £20,000 per annum at age 25,

an additional contribution of 2% of salary

a year (that is, £400 or just over £30 a

month) can be expected to result in an

average replacement ratio of around 11

percentage points higher, corresponding

to an additional annual pension income

of around £2,200 in current prices. While

it may be difficult for a 25 year-old earning

£20,000 a year to find an additional £30

a month to save (particularly those with

a young family), doing so will make a

significant difference to the standard of

living in retirement.

While it may be difficult for a 25 year-old earning £20,000 a year to find an additional £30 a month to save (particularly those with a young family), doing so will make a significant difference to the standard of living in retirement.

Finally, given that many individuals

appear to be unwilling (or unable) to

begin pension savings at age 25, we

have also considered the effect of

delaying contributions until age 40 (and

contributing at a higher rate of 15% per

annum thereafter). In this case, the

mean replacement ratio is similar to that

achieved by contributing 8% of salary per

annum from age 25. The probability of

failing to achieve a ‘minimum’ acceptable

replacement ratio is also similar.

However, while it may seem desirable for a

25 year-old to delay saving for retirement,

it should be noted that if saving does not

begin until age 40, individuals will be

required to pay almost twice as much as

they would have to pay had they started

contributing at 25, at a time when other

commitments – mortgage, school and

university fees etc – may be high too.

Also, given that the funds are invested

fully in higher-risk equities for only 15

years (as compared to 30 years if saving

begins at age 25), the upside potential

is lower, meaning that the probability of

achieving the desired replacement ratio

is commensurately lower too.

From this analysis we can conclude that

the standard, static lifestyle approach

to retirement planning can produce a

highly variable outcome for a typical DC

member.

So, can we do better?

25

Suppose that, rather than purchasing

an annuity on retirement at age 65, the

DC member gradually annuitises the

accumulated pension fund between

age 65 and age 7513, with the remainder

of the fund invested in equities. How

would this affect the distribution of the

replacement ratio? Figure 8 shows the

asset allocation to equities for each age

under this strategy (and for the standard

static lifestyling with full annuitisation on

retirement at age 65 considered above).

To shed some light on this issue, we

again assume that the asset allocation

is 100% in equities from age 25 to age

55 which then reduces linearly to 0%

at age 75.14 Then, prior to age 65, funds

not invested in equities are assumed

to be invested in the risk-free asset

(that is, index-linked government bonds)

and, after age 65, funds not invested

in equities are assumed to be used to

purchase an annuity (to benefit from the

‘mortality drag’ effect).15

13 From 6 April 2011, the government removed the requirement to annuitise fully accumulated pension wealth by age 75. However, as a result of the ‘mortality drag’ inherent in annuity products, it remains optimal for most individuals to annuitise fully from about age 75.

14 For consistency, we assume that, after age 65, the accumulated fund provides the same level of income as before. However, in this case, the income consists of both an annuity instalment and a “draw-down” of funds from the remaining equity investments.

15 Even though we assume that annuities are priced using the risk-free interest rate (of 2% per annum), the annual return achieved on an annuity investment exceeds the risk-free interest rate, assuming that the individual survives to receive the next instalment. The additional return arises from the redistribution of annuity wealth from annuitants who died during the year to those who survived, and is known as the “mortality drag”. A consequence of this is that it is sub-optimal to invest directly in the risk-free asset after retirement (and, indeed, the effect of this mortality drag is so strong that, by age 75 or so, the return achieved on annuity investment even exceeds that available on the risky equity investment, so that it is usually optimal to invest the entire amount of the pension wealth in annuities from this age).

Figure 8: Asset allocation strategy assuming lifestyle investment strategy with full annuitisation by age 75



Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio







Replacement ratio

Replacement ratio

Replacement ratio

Age




Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000



Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%


0%756555453525

Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0









Opt

imal

allo

cati

on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

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imal

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on in

equ

itie

s

20%

0%706050403020



4.2 Static lifestyle with gradual annuitisation between ages 65 and 75

26

Figure 9: Distribution of replacement ratio on retirement assuming lifestyle investment strategy with full annuitisation by age 75



Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio







Replacement ratio

Replacement ratio

Replacement ratio

Age




Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000



Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%


0%756555453525

Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0









Opt

imal

allo

cati

on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

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20%

0%706050403020




replacement ratio (that is, the pension

income received as a percentage of

the final salary immediately before

retirement) compared with the standard

static lifestyle approach shown in

Figure 6. In both cases, we have used

a contribution rate of 8% of salary

per annum (consistent with the NEST

requirements).

From Figure 9 we can conclude that a

more gradual approach to de-risking

and the maintenance of some equity

allocation (as a proxy for allocation

to risky asset classes generally) after

age 65 (with full annuitisation at age

75 only) is more effective than the

standard lifestyle approach above.

The mean replacement ratio of 49% is

significantly higher than that assuming

full annuitisation immediately on

retirement at age 65 (as would be

expected given that some equity

investment is now held between age 65

and age 75).

However, crucially, the strategy is also

less risky – the probability of achieving

the desired replacement ratio of two-

thirds is also significantly higher (that

is, 20% compared with 12%) and the

probability of failing to achieve an

acceptable replacement ratio of 50%

is also significantly lower (that is, 63%

compared with 72%).

Thus, as a first step to improve DC pension

outcomes, we propose extending the

standard static lifestyle investment

strategy offered to most DC members to

allow for a more gradual annuitisation

after retirement, rather than using the

full accumulated fund on retirement to

purchase an annuity immediately.

However, can we improve further on this?

27

So far, we have considered only static

asset allocation strategies, with 100%

invested in equities prior to age 55 and

full annuitisation either immediately

on retirement at age 65 or gradually

between age 65 and 75. We now consider

the effect of two simple dynamic asset

allocation strategies – a ‘momentum’

approach and a ‘contrarian’ approach. As

full annuitisation at age 75 is significantly

better than immediately on retirement at

age 65, we will use this as the ‘underlying’

driver for asset allocation and the basis

for comparison. However, in addition we

implement the following two dynamic

investment strategies:

A momentum strategy• if equities performed well in the

previous year, then we increase the

allocation for the coming year;16

• iftheequityreturninthepreviousyear

is greater than 16% (that is, risk-free

real return + equity risk premium + 0.5

* volatility of equity return), then we

increase the equity allocation by 5%

(subject to a maximum of 100%);


is less than -4% (that is, risk-free real

return + equity risk premium – 0.5 *

volatility of equity return), then we

decrease the equity allocation by 5%

(subject to a minimum of 0%); and

• if the equity return in the previous

year is between -4% and 16%, then

we follow the standard static lifestyle

allocation above.

A contrarian strategy• if equities performed well in the

previous year, then we decrease the

allocation for the coming year;17


is greater than 16% per annum, then

we decrease the equity allocation by

5% (subject to a minimum of 0%);


is less than -4%, then we increase the

equity allocation by 5% (subject to a

maximum of 100%); and

• if the equity return in the previous

year is between -4% and 16%, then

we follow the standard static lifestyle

allocation above.

16 The rationale for this being that, as we now have a higher fund (as a result of the previous year’s high returns), we can afford to take on some extra risk. While this runs counter to the efficient markets hypothesis, Jegadeesh and Titman (1993) report that, over the period from 1965 to 1989, such a strategy would have produced significant positive returns over 3 to 12-month holding periods.

17 The rationale for this being that we choose to protect some of the previous year’s gains by de-risking.

4.3 Dynamic asset allocation strategies

28


replacement ratio on retirement for both

the momentum and contrarian strategies,

as well as for the static lifestyle approach

from Section 4.2 (that is, with full

annuitisation by age 75). These results

are summarised in Table 2.

We can conclude from this experiment

that a contrarian asset allocation

strategy is an improvement on the static

lifestyle strategy, in that the probability

of meeting the desired two-thirds

replacement ratio is increased slightly

from 20% to 21% and the probability of

failing to achieve even the acceptable

50% replacement ratio is reduced from

63% to 61%. This is because a contrarian

strategy protects previous gains by

switching out of equities when returns in

the previous year have been significantly

above average, and increases the

opportunity to recover previous losses

by increasing the equity allocation when

returns in the previous year have been

significantly below average. However,

on the downside, this approach gives

a slightly lower mean replacement

ratio due to de-risking following high

investment returns. The momentum

strategy is the more risky giving the

highest mean replacement ratio, but

at the cost of both a lower probability

of meeting the desired two-thirds

replacement ratio (that is, 19% compared

with 21% for the contrarian approach)

and a higher probability of failing to

achieve the acceptable 50% replacement

ratio (of 65% compared with 61% for the

contrarian approach). However, it does

improve the mean replacement ratio in

retirement, as a result of taking on more

risk following high investment returns in

the previous year.

Figure 10: Distribution of replacement ratio on retirement assuming momentum and contrarian investment strategies

Table 2: Replacement ratio on retirement assuming momentum and contrarian investment strategies

Investment strategy

Static lifestyle (to age 75) Momentum ContrarianMean replacement

ratio 49% 50% 48%

Probability of replacement

ratio > 66.7% 20% 19% 21%

Probability of replacement

ratio < 50.0% 63% 65% 61%



Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio







Replacement ratio

Replacement ratio

Replacement ratio

Age




Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000



Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%


0%756555453525

Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0









Opt

imal

allo

cati

on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

Opt

imal

allo

cati

on in

equ

itie

s

20%

0%706050403020



29

The results presented in Table 2 (page

28) and in Figure 9 (page 26) lead Blake,

Wright and Zhang (2011)18 to suggest

that a ‘loss aversion’ framework may

be suitable for DC pension plan asset

allocation. The concept of ‘loss aversion’

was first proposed by Kahneman and

Tversky (1979) within the framework

of prospect theory, one of the building

blocks of behavioural finance.19 Loss

aversion is defined in terms of the

satisfaction (utility)20 of gains and

losses in wealth relative to a pre-defined

reference or endowment point, rather

than in terms of the satisfaction derived

from the absolute level of total wealth, as

it is in traditional finance theory.

In particular, it states that, relative to

the chosen reference point, individuals

prefer avoiding losses to acquiring

equivalently sized gains (that is, they are

loss averse). The degree of loss aversion

varies from person to person, although

studies suggest that individuals can

be somewhere between two and five

times more sensitive to a particular

loss (relative to the chosen reference

point) than to a corresponding gain.21

The standard loss aversion framework

suggests that individuals exhibit ‘typical’

risk aversion with respect to gains

(relative to the pre-defined reference

point) – thus, the satisfaction of a gain

of $200 is less than twice that of a gain of

$100. However, because individuals are

loss averse, they prefer risks that might

reduce a loss, leading to risk-seeking

behaviour with regard to losses. Thus,

the investment behaviour that results

from loss aversion is similar to the sort

of investment decision making that a

contrarian investor might follow.

So, when it comes to a DC pension, how

do we determine a suitable reference

point? The Blake, Wright and Zhang

(2011) framework assumes that the

representative DC member wishes to

retire on a pension equivalent to two-

thirds of his final salary. The authors

then use this ‘desire’ to determine the

required fund at retirement based on the

current salary and expected salary growth

up to retirement. Then, at each age

prior to retirement, they can determine

a fund target by discounting this final

amount to allow for future investment

18 The intellectual property for the loss aversion framework discussed in this section belongs to the authors of the original Blake, Wright and Zhang (2011) paper and we are grateful to them for allowing its inclusion here.

19 Kahneman & Tversky (1979) developed this theory to remedy the descriptive failures of subjective expected utility theories of decision-making in the face of uncertainty, thereby leading the way for the development of the field of behavioural finance.

20 In economics, utility is a measure of relative satisfaction or happiness. Given this measure, economists then try to explain an individual’s economic behaviour, including decisions regarding investment, in terms of attempting to maximise satisfaction or utility.

21 Tversky & Kahneman (1992) suggest that individuals are 2.25 times more sensitive to a loss than to a corresponding gain (that is, a loss aversion parameter of λ=2.25). However, this was based on a study of decisions made under uncertainty by a group of only 25 graduate student in the US, so may not representative of the typical DC plan member. Hwang and Satchell (2005) propose a long-term loss aversion parameter of λ=3, but suggest that a value as high as 4.5 may be appropriate in some circumstances.

4.4 Liability-driven asset allocation and ‘loss aversion’

30

returns (and for future contributions to

be paid into the fund). In this framework,

the current ‘target’ fund serves as the

reference point and is used to determine

the current ‘optimal’ asset allocation

needed to achieve it. This approach to DC

retirement planning works like this if the

actual fund is:

• closetothecurrentdiscountedtarget,

the asset allocation in the risky

asset (that is, equities) is reduced to

minimise the risk of a loss (relative to

the current target) in future.

• significantly higher than the current

target, then the asset allocation in the

risky asset can be increased again,

because the likelihood of a loss,

relative to the current target, falls

because of the bigger cushion held;

and crucially,

• iftheactualfundissignificantlylower

than the target, the asset allocation in

the risky asset will rise in order that the

shortfall can be made up.

The key parameter controlling the asset

allocation over time is the loss aversion

parameter. A typical loss aversion

parameter might be around 4, with a

lower value appropriate for a member

who is more risk (or, strictly speaking,

loss) tolerant and a higher value

appropriate for a member who is risk (or

loss) averse.

In this model the DC member’s focus on

the target replacement ratio is analogous

to the liability-driven approach to

investment strategy which many DB

plans have adopted over the past few

years. That is, all investment decisions

are made with a view to maximising

the likelihood of meeting the targeted

replacement ratio.

Integrating this loss aversion behaviour

and the liability-driven approach to

asset allocation allows us, once again, to

generate a distribution of the replacement

ratio. But before we do this it’s worth

considering the impact of this framework

on the optimal asset allocation of our DC

member at each age. The optimal asset

allocation at each age will depend only

upon the ratio of the current fund level to

the current target fund, which is simply

a function of the current salary. For

example, consider the way in which the

optimal asset allocation can vary when

our DC member reaches age 64. Under

the assumptions used by Blake, Wright

and Zhang (2011), the target fund at this

time is about 10 times the current salary,

that is, he needs to have accumulated

a fund 10 times his salary at age 64 to

be confident of achieving the desired

target replacement ratio of two-thirds on

retirement at age 65.

It is clear from these results that a loss aversion strategy is much more successful in meeting the desired replacement ratio of two-thirds of salary at retirement.

31

Figure 11 shows how the optimal asset

allocation varies according to the ratio of

the current fund to the target fund. In this

case, the individual is assumed to have

a ‘typical’ loss aversion parameter of 4,

although in practice this will vary from

individual to individual. We can see that

a higher allocation to equities is optimal

if the current fund is significantly lower

than the target (with 100% in equities for

ratios of about 80% or less). This higher

allocation to equities is made in the hope

of increasing the fund accumulated at

retirement to that required to achieve the

target replacement ratio of two-thirds at

retirement. Also, a higher allocation to

equities is also made if the actual fund

is significantly higher than the target,

with 100% in equities for ratios of about

120% or above. This is because the risk

of the fund accumulated at retirement

falling below that required to achieve

the target replacement ratio at retirement

is sufficiently low. However, if the ratio

is between 80% and 120%, then the

optimal allocation to equities is lower

to reduce the risk of a significant loss at

retirement, relative to the target.

Figure 11 could be reproduced for a DC

member at each age from 25 to 75, and

Blake, Wright and Zhang (2011) shows

that the younger the DC member, the

more optimal it will be to be invested in

equities, or at least high-risk, high-return

asset classes. That is, the younger the

DC member, the shallower will be the ‘V’

shape shown in Figure 11. The optimal

asset allocation varies then, with age,

with the ratio of the actual to the targeted

DC fund, and the individual’s aversion to

losses.

Figure 11: Determining optimal asset allocation within loss aversion framework for a 64 year-old



Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio







Replacement ratio

Replacement ratio

Replacement ratio

Age




Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000



Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%


0%756555453525

Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0









Opt

imal

allo

cati

on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

Opt

imal

allo

cati

on in

equ

itie

s

20%

0%706050403020



32

Figure 12: Distribution of replacement ratio on retirement assuming loss aversion



Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio







Replacement ratio

Replacement ratio

Replacement ratio

Age




Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000



Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%


0%756555453525

Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0









Opt

imal

allo

cati

on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

Opt

imal

allo

cati

on in

equ

itie

s

20%

0%706050403020




replacement ratio at retirement for the

loss aversion framework, as well as for

the static lifestyle approach, with full

annuitisation by age 75. These results

are also summarised in Table 3. It is clear

from these results that a loss aversion

strategy is much more successful in

meeting the desired replacement ratio

of two-thirds of salary at retirement.

This is unsurprising because, unlike the

other dynamic asset allocation strategies

above, the asset allocation at each

age is set with reference to the current

discounted value of this target – that is,

it is outcome driven. Compared with the

static lifestyle asset allocation with full

annuitisation by age 75, the probability

of meeting the desired replacement ratio

of two-thirds increases significantly from

20% to 34% and, equally as important,

the probability of failing to achieve

an acceptable minimum replacement

ratio of 50% of salary at retirement

is substantially lower, that is, 48%

compared to 63%.

The asset allocation strategy at each

age is dynamic and will depend on the

individual circumstances prevalent at the

time (and, in particular, the level of the

current accumulated fund relative to the

current target fund).

Table 3: Replacement ratio on retirement assuming loss aversion framework

Investment strategy

Static lifestyle (to age 75) Loss aversionMean replacement ratio 49% 49%

Probability of replacement ratio > 66.7% 20% 34%

Probability of replacement ratio < 50.0% 63% 48%

33

Figure 13: Mean optimal allocation in equities assuming a loss aversion framework



Probability of

replacement ratio

of less than

50% = 63%

(cf. 72%)

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

0.6

0.5

0.4

0.3

0.2

0.1

0

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

0% 140%20% 40% 60% 80% 100% 120%

Replacement ratio

Replacement ratio







Replacement ratio

Replacement ratio

Replacement ratio

Age




Probability of

replacement ratio

of less than

50% = 72%

30,000

40,000

50,000

60,000

70,000



Total salary

Sal

ary

20,00025 30 35 40 45 50 55 60 65

Age

0.6

0.5

0.4

0.3

0.2

0.1

0

100%

80%

60%

40%

Equi

ty a

lloca

tion

20%


0%756555453525

Age

0.6

0.5

0.4

0.3

0.2

0

0.1

0.6

0.5

0.4

0.3

0.2

0

0.1

100%

80%

60%

40%

20%

0%0% 25% 50% 75% 100% 125% 150% 175% 200%

0.5

0.4

0.3

0.2

0.1

0









Opt

imal

allo

cati

on to

equ

itie

s



Probability of

replacement

ratio of less

than 50%

= 48%

(cf. 63%)



(cf. 20%)

100%

80%

60%

40%

Opt

imal

allo

cati

on in

equ

itie

s

20%

0%706050403020



In particular, from Figure 11 (page 31), the

actual allocation in the risky asset will be

much lower if the current fund is close

to the current target. As such, it is useful

to compare the mean asset allocation

strategy under the loss aversion

framework with that for the static lifestyle

strategy. From Figure 13, we can see

that, based on the 10,000 outcomes

generated, loss aversion can be expected

to lead to an earlier switch out of equities

(from around age 40, although in any

particular realisation, this will depend

on the level of the current fund relative

to the current target), but can also lead

to a significantly higher equity weighting

at older ages (particularly if the current

fund is significantly above or significantly

below the current target).

The challenge in terms of applying this

asset allocation strategy is that no

individual will follow this ‘average’ path

of equity allocation. The average is high

at older ages because there will be some

scenarios when the equity weighting is

very high (for example, 100%, if the fund

is well above or well below the target),

but there will be many scenarios where

the allocation is very low (as the fund is

close to the target). Thus, the distribution

is very polarised (that is, either very high

or very low), so the ‘average’ is not really

very meaningful.

The asset allocation strategy at each age is dynamic and will depend on the individual circumstances prevalent at the time (and, in particular, the level of the current accumulated fund relative to the current target fund).

34

References

Basu, A., Byrne A. and Drew M. (2009),

‘Dynamic lifecycle strategies for target

date retirement funds’, University of

Edinburgh working paper.

Benartzi, S., and Thaler, R. (1995),

‘Myopic Loss Aversion and the Equity

Premium Puzzle’, Quarterly Journal of

Economics, 110, pp. 73-92.

Blake, D., Cairns, A.J.G. and Dowd, K.

(2001), ‘Pensionmetrics: Stochastic

Pension Plan Design and Value at

Risk During the Accumulation Phase’,

Insurance: Mathematics and Economics,

29, 2, October, pp. 187-215.

Blake, D., Wright D. and Zhang Y. (2011),

‘Optimal investment strategies in defined

contribution pension plans under loss

aversion’, Working Paper, Cass Business

School, London.

Brigden, A., A. Clare, R. Driver and M.

Selvaggi (2008), Coping with uncertainty

and the importance of the Sponsor’s

covenant: The case of defined-benefit

pension plans, ABI Research Paper No.

9, 2008.

Brigden, A., A. Clare, R. Driver and M.

Selvaggi (2009), The Road To Buyout,

Pensions, pp. 90-110.

Burtless, G. (2009a), ‘Financial Market

Turbulence and Social Security Reform.

In Pensions, Social Security and the

Privatization of Risk’, edited by M.A.

Orenstein, Columbia University Press,

pp. 72-85.

Burtless (2009b), ‘Lessons of the

Financial Crisis for the Design of National

Pension Schemes’, CESifo Working Paper

no. 2735, July.

Cannon, E. and Tonks, I. (2009), ‘The

Value and Risk of Defined Contribution

Pension Schemes: International

Evidence’, Working paper, University of

Exeter Business School, no. 09/03.

Hwang, S., and Satchell, S. (2005), ‘The

Magnitude of Loss Aversion Parameters

in Financial Markets’, unpublished

manuscript, Cass Business School.

Jegadeesh, N., and Titman, S. (1993),

‘Returns to buying winners and selling

losers: Implications for stock market

efficiency’, Journal of Finance, 48, 65-91.

Kahneman, D., and Tversky, A. (1979),

‘Prospect Theory: An Analysis of Decision

under Risk’, Econometrica, 47, pp. 263-

91.

Levy, S. (2009), Occupational Pension

Schemes Annual Report 2008, Office for

National Statistics, No. 16.

Mehra, R. and Prescott, E. (1985). ‘The

Equity Premium: A Puzzle’, Journal of

Monetary Economics, 15, pp. 145–161.

Tversky A., and Kahneman, D. (1992),

‘Advances in Prospect Theory: Cumulative

Representation of Uncertainty’, Journal of

Risk and Uncertainty, 5, pp. 297-323.

Contributors

David Calfo

David Calfo joined BNY Mellon in

September 2010 as the group’s head of

defined contribution (DC) strategy.

His role is to define the firm’s DC strategy

and business approach in the UK and in

other markets.

Prior to joining BNY Mellon, David was

at Ignis Asset Management (part of Pearl

Group Limited) where he had worked

since 2006 as chief operations officer

and, subsequently, as head of corporate

development and strategy.

In these roles, David was instrumental

in establishing the group’s asset

management business.

Before Pearl Group, David was founder

and director of his own strategic advisory

firm, specialising in investment and DC

pensions businesses across Europe.

He also spent a significant portion of his

career at Fidelity Investments, working in

both the US and UK, and is recognised for

establishing and running Fidelity’s UK DC

business.

Professor Andrew Clare

Andrew Clare is the Professor of Asset

Management at Cass Business School

and the Associate Dean responsible for

Cass’s MSc programme, which is the

largest in Europe.

He was a Senior Research Manager in the

Monetary Analysis wing of the Bank of

England which supported the work of the

Monetary Policy Committee. While at the

Bank, Andrew was responsible for equity

market and derivatives research.

Andrew also spent three years working

as the Financial Economist for Legal and

General Investment Management (LGIM),

where he was responsible for the group’s

investment process and where he began

the development of LGIM’s initial Liability

Driven Investment offering.

He has published extensively in both

academic and practitioner journals on

a wide range of economic and financial

market issues. In a recent survey Andrew

was ranked as the world’s ninth most

prolific finance author of the past fifty

years.

Andrew serves on the investment

committee of the GEC Marconi pension

plan, which oversees the investments

and investment strategy of this £3.2bn

scheme, and has recently been appointed

as a trustee to the Magnox Electric Group

Pension scheme.

Dr Douglas Wright

Dr Douglas Wright is a Senior Lecturer

in the Faculty of Actuarial Science and

Insurance at Cass Business School in

London.

Douglas joined Scottish Provident Life

Assurance in Edinburgh in October 1991,

after completing a BSc (Hons) in Actuarial

Science and Statistics at Heriot-Watt

University. He returned to Heriot-Watt

in October 1993 to begin a PhD entitled

“A Stochastic Approach to Pension

Scheme Funding and Asset Allocation”

under the supervision of Dr Mary Hardy.

After completion of the PhD, he joined

the Faculty of Actuarial Science and

Insurance at Cass Business School in

January 1997, specialising in financial

mathematics and investment, stochastic

modelling and life insurance.

Douglas is author (or co-author) of papers

published in, amongst others, the Journal

of Economic Dynamics and Control, the

Journal of Management Mathematics,

Insurance: Mathematics and Economics

and the British Actuarial Journal.

His current research interests include

the optimal asset allocation for defined

contribution pension schemes, the future

of defined benefit pension schemes and

applications of agent-based models in

non-life insurance.

The information listed in this white paper is not intended to serve as tax or legal advice. Please consult your own tax or legal advisor for advice particular to your circumstances. BNY Mellon is a corporate brand of The Bank of New York Mellon Corporation and may also be used as a generic term to reference the corporation as a whole or its various subsidiaries. Any services described herein are provided by subsidiaries or affiliates of The Bank of New York Mellon Corporation which includes The Bank of New York Mellon (each the “Bank”). The Bank of New York Mellon – Incorporated with limited liability in the State of New York, USA. Head Office: One Wall Street New York, NY 10286, USA. London Branch registered in England & Wales with FC005522 and BR000818 - Registered Office at One Canada Square, London E14 5AL, authorised and regulated in the UK by the Financial Services Authority. The Bank of New York Mellon, DIFC Branch (the “Authorised Firm”) is communicating these materials on behalf of The Bank of New York Mellon. The Bank of New York Mellon is a wholly owned subsidiary of The Bank of New York Mellon Corporation. This material is intended for Professional Clients only and no other person should act upon it. The Authorised Firm is regulated by the Dubai Financial Services Authority. This material is not intended for US persons. Material contained within this white paper is intended for the purposes of general information only. It is not intended to be a comprehensive study of the subject matter, nor provide any business, legal, professional counsel, tax or investment advice, and is not to be used as such. No statement or expression is an offer or solicitation to buy or sell any products or services mentioned. The views expressed herein are those of the contributors only and not those of the Bank or Cass Business School. The contents may not be comprehensive or up-to-date, and the Bank will not be responsible for updating any information, it makes no representation as to its accuracy, completeness, timeliness, merchantability or fitness for a specific purpose. The Bank recommends that professional consultation should be obtained before using any service offered. The Bank assumes no liability whatsoever for any action taken in reliance on the information contained herein, or for direct or indirect damages resulting from use of this white paper, its content, or services. Any unauthorised use of material is at the user’s own risk. Reproduction, distribution, republication and retransmission of material is prohibited unless the prior consent of the Bank and Cass Business School has been obtained. All references to assets under management, assets serviced and assets under custody and administration are correct as of 30th June 2011. The Bank assumes no responsibility or liability for access to or content of any website which is linked to or from this white paper. © 2011 The Bank of New York Mellon Corporation. All rights reserved. CP7157-31-08-2011 (6M) 19609 08/11

For more information please contact David Calfo on 020 7163 3951 or email [email protected]

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