Electronic copy available at: https://ssrn.com/abstract=3003624
Short-Termism and the Asset Allocation Decisions of DefinedBenefit Pension Plans∗
Kyriakos Chousakos† Garence Staraci‡
July, 2017
Abstract
We examine the presence of short-termism in the asset allocation decisions of U.S. private definedbenefit pension plans. We document an inverse U-shaped relationship between a plan’s allocation to fixedincome securities and its funding ratio, centered on a 80% funding ratio, and show that the relationship isstronger among plans sponsored by companies in financial distress, and whose CFOs have accumulated asubstantial amount of risky pension benefits. We then theoretically demonstrate that this relationshipemerges from loss-averse preferences of the plan’s investment committee (supervised by the CFO), withrespect to a 80% funding ratio. We additionally show that these preferences encompass both risk-shiftingand risk-management behaviors, and as such allow us to explain two empirical features of U.S. definedbenefit plans: a collapse in their average funding ratios over the past three decades, and the more recentshift toward fixed income securities in their allocation decisions. Assimilating these loss-averse preferenceswith short-termism, we conclude that plans without such preferences achieve a significant improvement intheir funding ratios over the long-run.
∗We thank Nicholas Barberis, James Choi, Gaston Gelos, Gary Gorton, Jonathan Ingersoll, Justin Murfin, Matthew Spiegel,Kate Tan, William Goetzmann, and seminar participants at Yale for helpful comments. Garence Staraci acknowledges supportfrom Whitebox Advisors.†Doctoral student at Yale School of Management. Email: [email protected]‡Doctoral student at Yale School of Management. Email: [email protected]
Electronic copy available at: https://ssrn.com/abstract=3003624
1 Introduction
U.S. Corporate defined benefit (DB) plans have experienced a large decline in their average funding
ratios over the past three decades. Starting at a peak level of 120% in the late 1980s’, the average funding
ratio has since then followed a downward trend to reach 80% in 2014. Meanwhile, the average allocation
of these plans to fixed income securities, which has historically been lower than that to equities, has risen
substantially over the past decade before recently closing the gap. This paper provides a rationale to explain
how such a rise in fixed income investments has occurred in spite of decreasing funding ratios, and shows
that the former has contributed to accelerate the latter. This rationale associates the investment behavior of
DB plans with a short-term objective, aiming to prevent the plan from becoming underfunded when funding
ratios decline, but with a trade-off of a long-term decline in the plan’s funding ratio.
Two main channels have been invoked in the literature to explain the pension plans’ investment decisions:
risk-shifting and risk-management. The former is induced by the presence of the Pension Benefit Guarantee
Corporation (PBGC), which by insuring the plans’ liabilities provides the sponsoring company with an
incentive to maximize wealth by investing in risky securities. The latter favors a reduction of a plan’s
investment risk exposure when the plan becomes underfunded, in order for the sponsor to avoid mandatory
contributions, which may increase the sponsor’s default risk on other non-pension obligations. In this paper,
we propose a unifying framework that encompasses both of these channels and fully describes the whole
investment behavior of DB plans.
This framework consists of an investment committee with a loss-averse investment behavior, in reference
to a 80% funding ratio. This reference level corresponds to a legal, actuarial and asset management consensus
on the funding ratio for which a DB pension plan is considered to be financially sound. Even though disputed
by the American Academy of Actuaries as a “mythic standard,” recent legislation requires sponsors to make
additional contributions to pension plans when their funding ratios fall below 80% or 90%.1 The incentive to
avoid a funding ratio below that level forces the investment committee of an underfunded plan to focus on
the short-term and links the investment decision to the current level of the funding ratio of the plan rather
than a longer term target.
We first empirically test our framework by focusing on the investment behavior of four categories
of pension plans grouped on the basis of their funding ratios evolution: (1) decreasing funding ratios
from the moderately overfunded region (0.9 < Funding Ratiot−1 < 1.1) to the moderately underfunded
region (0.8 < Funding Ratiot < 0.9), (2) decreasing ratios from the moderately underfunded region1Retirement Protection Act of 1994, Pension Protection Act of 2006.
1
(0.7 < Funding Ratiot−1 < 0.9) to the severely underfunded region (0.4 < Funding Ratiot < 0.7), (3)
increasing ratios from the severely underfunded region (0.1 < Funding Ratiot−1 < 0.7) to the moderately
underfunded region (0.7 < Funding Ratiot < 0.9), and (4) increasing ratios from the moderately overfunded
region (1 < Funding Ratiot−1 < 1.1) to the largely overfunded region (1.1 < Funding Ratiot < 1.5). We
find that the fixed income allocations of pension plans in the first category are, on average, higher by 1.209%
compared to those of the average plan in the sample. The allocations of plans in the second category are
lower by 0.938%, the allocations of plans in the third category are higher by 0.236%, and those of plans in
the fourth category are lower by 2.024%. The equities allocations exhibit the opposite pattern. Hence, we
show that the allocation to fixed income securities as a function of funding ratio takes the form of an inverse
U-shaped curve. Moreover, we show that plans within a given category are subject to various degrees of
loss aversion. For each plan, this degree is dependent on the financial soundness of the associated sponsor
company. Using a measure of distance-to-default as a proxy for financial soundness we show that plans
associated with sponsors in financial distress tend to be significantly more loss-averse in their investment
decisions. This result is shown to hold in a more general case of underfunded plans, since we document that
an underfunded plan is almost always associated with a financially distressed sponsor firm.
This loss-averse investment behavior centered around a funding ratio of 80% is a finding that can be
attributed to either the incentives structure around DB plans, or the preferences (utility function) of the
investment committee. The incentives structure is determined primarily by legislation, while preferences
dictate a risk/return relationship that is deemed acceptable by the involved agents, primarily the investment
committee. Focusing on the compensation scheme of corporate executives serving on the investment committee,
and especially on that of the CFO, the most influential figure on that committee, we find that plans whose
CFOs have the highest accumulated pension benefit as a percentage of their salary, exhibit a more pronounced
loss-averse investment behavior compared to similar plans whose CFOs have lower pension benefits. This
finding suggests that the observed loss-averse investment pattern is partly due to preferences. Our finding
does not completely rule out an incentives interpretation of the observed investment behavior, but strongly
suggests that CFOs’ preferences are an important element of the decision making process.
We then formalize our framework by showing that these asset allocation decisions are the optimal solution
to the portfolio problem of a loss-averse investment committee, whose expected utility is a function of the
plan’s funding ratio with respect to the 80% reference level. In this portfolio problem, the financial market
consists of both a risky and a riskless asset, and the committee decides on an optimal allocation to the
two assets. Assuming complete markets, we solve the problem in continuous time and obtain a closed-form
solution for the optimal portfolio allocation to the risky asset. In agreement with the data and our empirical
2
findings, the relationship between the optimal allocation to equities and the plan’s funding ratio is U-shaped.
We also explicitly show that this optimal allocation consists of two components: an insurance portfolio
which is a mean-variance contribution to the overall allocation, and a gambling portfolio which captures
the risk seeking behavior of the agent when faced with losses. As such, this model is able to unify both
risk-management and risk-shifting incentives.
Our empirical analysis shows that, on average, moderately underfunded pension plans choose to invest
in fixed income securities rather than equities, and that among these plans, the ones associated with non-
financially sound sponsors do so more aggressively. We associate this behavior with a short-term investment
objective. On the one hand, this strategy allows the plan’s investment committee to reduce the volatility
of the plan’s funding ratio by moving away from volatile investments. On the other, the yield provided by
fixed income investments is significantly lower than the growth rate of liabilities. The decision to invest in
fixed income therefore comes at a cost of a mismatch between assets and liabilities. By de-risking when
underfunded, the pension plans choose to lock-in their current funding ratios, focusing on the short-term, at
the cost of a significant long-term improvement of their funding ratios accomplished by re-risking strategies.
In our data, we measure this short-term gain (or long-term cost) as the difference in future funding ratios
between two groups of moderately underfunded plans. The first group comprises plans that increase their
fixed income allocations whereas, while the second plans that increase their equity allocations. We show that
plans that invested in equities achieved a 10% higher funding ratio compared to that of their counterparts
that invested in fixed income. We believe that this result calls for an overhaul of the incentives structure
created by the regulatory environment and the market. The incentives of the investment committee should
be aligned with the long-term goals of a pension plan. This entails a redesign of the regulatory framework so
that it favors investments to assets with returns closer to the growth rate of the plans’ liabilities.
This paper contributes to the literature on the investment behavior of DB pension plans in two ways.
First, it reconciles the risk-shifting incentive in pension plan investing with that of risk management. There
is an equal number of papers showing evidence in favor of both incentives. Harrison and Sharpe (1983)
show that the sponsor’s put option on the pension assets, which arises from the insurance provided on the
plan’s assets by the PBGC, can be valuable enough to incentivize the sponsor to invest all assets in equities.
Rauh (2009) shows that this is true for sponsors with well-funded pension plans and strong credit ratings,
whereas Anantharaman and Lee (2014) find that risk-shifting exists also within the most troubled sponsors.
However, the investment behavior of sponsors with underfunded pension plans and weak funding ratios is
consistent with risk management (Rauh (2009)). In this paper, we confirm the above findings and show, both
empirically and theoretically, that they are consistent with the decision making of a loss-averse investment
3
committee which holds as a reference point a specific funding ratio. Second, and to best of our knowledge,
this is the first paper which incorporates loss aversion into the preferences of a pension plan’s investment
committee. We divert from Merton’s standard optimal portfolio problem formulation (Merton (1969) and
Merton (1971)) by introducing loss aversion and unlike Barberis (2000) and Campbell and Viceira (1999) we
obtain lower demand for equities for specific levels of funding ratios.
This paper is organized as follows: Section 2 presents a number of facts regarding the funding ratio and
asset allocations of private defined pension plans in the U.S.. Section 3 reports empirical results that establish
the link between funding ratios and asset allocations. Section 4 theoretically shows that these empirical
results are consistent with the investment behavior of a loss-averse pension plan. Section 5 measures the
effect of loss-averse investing on the future funding ratio of plans in the underfunded region and discusses the
implications of a change in the incentive structure of the investment committee. Section 6 concludes the
paper.
2 De-Risking and The Decline of Aggregate Funding
In this section, we first document and explain both the decline in the average funding ratio of U.S.
private DB plans, and the associated rise in their asset allocation towards fixed income securities. We then
describe the two main channels that have been used in the literature to explain pension plans’ investment
decisions, namely risk-shifting and risk-management.
2.1 Current Trends among U.S. Defined Benefit Plans
Our full sample of plan-level data consists of 5,505 unique U.S. DB pension plans.2 All plans are
extracted from the Compustat North America Pension database and are private and single-employer, with
data available on an annual basis from 1986 to 2014. Summary statistics for our sample are available in
Table 1. On average, we work with 2000 plans per year which have asset and liability values of $1.59 billion
and $1.92 billion respectively. We compute the funding ratio of a plan as the ratio between total assets
and total liabilities.3 A funding ratio above 100% means that the pension plan is overfunded and the2as identified by unique EIN and plan number combinations3The funding ratios computed in this study are GAAP funding ratios, which might be lower than regulatory funding ratios as
calculated under ERISA regulations. Indeed, the Highway and Transportation Funding Act of 2014 extended the funding reliefthat was previously enacted under the Moving Ahead for Progress in the 21st Century Act back in 2012. This relief consisted inallowing sponsors to use a higher discount rate when calculating pension obligations, thereby resulting in a lower present valueof obligations and a higher funded status (IRS Notice 2014-53, http://www.gao.gov/assets/270/267150.pdf).
4
associated plan’s sponsor is not required to make additional contributions.4 Conversely, the plan is said to be
underfunded if the market value of its assets is less than the present value of the pension liabilities. In this
case, the sponsor is required to make additional contributions which are determined by a non-linear function
of the plan’s funding status.5 Therefore, a plan’s funding status is ultimately determined by the market
performance of the financial securities that the plan has invested in, the interest rate used to discount future
liabilities, voluntary financing decisions, and a possible change in the structure of benefits.
The evolution of our sample’s average funding ratio is represented in Figure 1a. We observe a sharp
downward trend in the level of funding over time. Starting at a relatively high level of about 120% in the late
1980s’, the average funding ratio steadily declines during the following decade before experiencing a sharp
increase in the late 1990s’, triggered by an above-average performance of equities. The occurrence of the
Dot-com bubble coincides with a collapse in funding. Plans become severely underfunded with an average
funding ratio reaching 80%. The years following the Dot-com bubble and preceding the last financial crisis
witnessed an improvement in the level of funding, once again fueled by a rebound in the performance of
equities. The financial crisis severely hit the DB plans and contributed to restore the post Dot-com bubble
underfunded status. The subsequent recession resulted in asset values tumbling and liabilities soaring. A
modest recovery, paced by equities, subsequently occurred in 2013 and 2014. Due to a combination of falling
long-term interest rates and increased life expectancies, through the adoption of new mortality assumptions,
kept overwhelming a strong asset performance.6 Liabilities have grown at a pace faster than that of assets
(Figure 11). We thus observe that, on average, DB pension plans’ funding ratios have been subject to a
steady decline over the last three decades which, as a consequence, has led a large proportion of them to an
underfunded status.
On the asset allocation side, Figure 1b represents the average percentage of assets which are, across
all plans within our sample, allocated to four distinct asset classes: equities, fixed income, real estate, and
other (including alternatives).7 Figure 10 (Appendix A) shows these percentages decomposed into quartiles
on the basis of the plans’ funding ratios. The class of fixed income assets comprises fixed income, cash,4The sponsor may however choose to still make contributions up to a certain funding level, above which no favorable tax
treatment applies (Black (1980) and Tepper (1981)).5The levels of contributions have changed significantly over time. The provision to make additional contributions was
introduced by ERISA (1974) and ever since a number of legislative acts (Pension Protection Act (1987), Retirement ProtectionAct (1994), and Pension Protection Act (2006)) have set specific funding rules for sponsors to avoid underfunding of their plans.
6The key factor was the change in mortality tables finalized by the Society of Actuaries in October 2014 (https://www.soa.org/Research/Experience-Study/pension/research-2014-rp.aspx). This change led to an upward revision to reported grosspension obligations for some plans. Plan sponsors were not required to explicitly break out any increase to pension liabilitiesfrom adjustments to mortality assumptions, although the SEC did encourage such disclosures when any impact resulted in asignificant change in the benefit obligation. Moreover, large plans have a large enough population of participant data to createtheir own actuarial tables upon which to base their plan’s mortality assumptions. Hence they may not have adopted the tablesand projections of SOA in full.
7Among all available data sources (IRS 5500 form data, CEM Benchmarking, Pensions and Investments database), assetallocation data is not available on a consistent basis before 2003.
5
Figure 1: Panel (a) summarizes the average funding ratio among all DB plans in the data. Panel (b)Percentage of total assets, across all plans within our sample, that is allocated in Fixed Income and Equities.The data are from Compustat, and are represented on an annual basis from 1986 until 2014 for funding ratiosand from 2003 until 2014 for asset allocations.
.6.8
11.
21.
4A
sset
s/Li
abili
ties
1986 1990 1994 1998 2002 2006 2010 2014Year
Recession Funding Ratio
(a) Funding Ratio
3540
4550
5560
Allo
catio
n (%
)
2003 2005 2007 2009 2011 2013Year
Recession Fixed Income (%)Equity (%)
(b) Asset Allocations
short-term, U.S. government, corporate bonds, notes, and mortgages securities. The equities class involves
domestic and international equities, venture capital, and investments in the company’s own stock.8 Across
all of our sample’s plans, we observe a reallocation of assets from equities towards fixed income since the
inception of the last financial crisis. On an aggregate level, the average allocations to equities and fixed
income in the plans’ portfolios, which have started to be about 35% and 60% respectively, have converged
to an approximate 45% over the last few years (Figure 1a). This reallocation towards fixed income assets,
which is mainly associated with a reduced exposure in equities, is not only particularly significant in terms of
magnitude, but also a general pattern across all studied pension plans. Figure 10 shows that this reallocation
mechanism has always been associated with the very unfunded plans whereas the well-funded plans have
started to adopt it since the beginning of the last financial crisis.
The rise in fixed income investments over the past decade, observed in Figure 1b, has occurred in spite of
a large proportion of plans being significantly underfunded (Figure 1a), and a low interest rate environment
with rates expected to rise in the short to medium-term. At first, this investment behavior reflects the
willingness of pension managers to flee from the volatility of the stock market, and thus reduce the volatility
of funding ratios, in the hope of preventing a further decline in funding ratios. Moreover, the vast majority of
our plans are closed to new workers, who are offered 401(k) retirement savings plans instead. This could
shift the incentives of pension managers from generating an above market return towards locking a stream of
future income to meet their annual payout.8The class of real estate includes real estate investments and timberlands. The class of other comprises assets which are not
equity, debt, or real estate such as alternative investments (hedge fund assets).
6
More broadly, pension plans implementing this shift to fixed income investments (especially treasuries,
agency debt and corporate bonds) are said to be “de-risking”. This shift is mainly performed through an
increased reliance on the so-called liability-driven investment strategies. One of these strategies consists of
reducing the exposure to equities and increasing the exposure to bonds, long-duration fixed income securities,
or long-maturity interest rate swaps, even when market conditions would seem to dictate otherwise. The
purpose of this strategy is to match and balance the risk of the fixed income exposure with the interest-rate
risk of liabilities. This asset-liability matching additionally reduces the pension plan’s exposure to market
volatility, which is often undesirable since it can impact the income statement and cash flow of the sponsor
companies via unexpected mandatory contributions to underfunded plans. Such a strategy solely focuses
on the cash flows needed to fund future liabilities and differs in its objectives with a benchmark-driven
strategy. Moreover, any funding improvement can provide further incentives for pension managers to take
the de-risking path. With interest rates currently expected to rise in the near future, we can thus expect the
pace of de-risking to accelerate over the next several years.
2.2 Risk-Management versus Risk-Shifting
To understand the origins of de-risking strategies, we first recall the distinction between the two channels
used to describe pension plans’ investment decisions: risk-shifting and risk-management.
The risk-shifting or moral hazard incentive has originally been discussed in Sharpe (1976) and Treynor
(1977). These authors argue that a DB plan creates an obligation similar to long-term debt, with pension
beneficiaries and the sponsoring firm representing the debtholders and stockholders, respectively. Stockholders
are required to set aside assets to fund pension obligations whereas debtholders are bound to accept the
minimum between the assets of the plan and the level of liabilities if the sponsoring firm goes bankrupt.
Under this framework, the sponsoring firm owns the right to sell pension assets to the beneficiaries at a price
equal to the value of pension liabilities. The contract underlying the DB plan can thus be assimilated to a
put option on the pension assets, written by the beneficiaries (debtholders) and with a strike price equal to
the value of the pension liabilities. This option feature immediately implies that sponsors have incentives
to increase pension risk, either by increasing plan leverage or by investing in risky instruments. Choosing
the former means increasing the moneyness and thus the intrinsic value of the put option, while the later
increases the fair value of the option through increased assets volatility. The put option may even be, under
some conditions, valuable enough to lead to a solution in which the firm makes minimal contributions to
the fund and invests all assets in equities (Harrison and Sharpe (1983)). Moreover, a sponsoring company
7
approaching bankruptcy has further incentives to underfund the pension plan or make risky investments: if
the investment is successful and the firm survives, stockholders benefit from a lesser contribution into the
plan while a bankruptcy event primarily impacts beneficiaries.
The regulatory framework governing DB plans in the U.S. also exacerbates these moral hazard incentives.
The Employee Retirement Income Security Act of 1974 (ERISA) requires corporate plans to be insured
by PBGC which is expected to cover a portion of a pension plans’ liabilities towards its beneficiaries if
the sponsoring company is financial distress or goes bankrupt. In the former situation, the sponsor can
apply for distress termination of the plan if they can justify to a bankruptcy court that they cannot avoid
bankruptcy unless the plan is terminated. The PBGC will then take over the plan and pay benefits using the
remaining assets and its own funds to make up the deficit, up to a limit. If the sponsoring company of an
underfunded plan goes bankrupt, the PBGC also takes over the plan and provides plan recipients with their
annual pensions up to a statutory maximum amount.9
The introduction of the PBGC has contributed to exacerbate the moral hazard problem in pension plans’
asset allocation as it provided both the pension beneficiaries a disincentive to monitor the corporation’s
pension investment policy, and the sponsoring company an incentive to maximize wealth by investing in
risky securities. This is further exacerbated by the little control that the PBGC exerts over the sponsoring
company when it is a going concern, besides the contribution requirements and the collection of the insurance
premia. Those premia are flat-rates and, as such, are not adjusted for the plan sponsor’s creditworthiness or
plan asset risk, over which ERISA does not place direct restrictions.
The risk management hypothesis arises as a limitation on the risk-shifting incentive. Indeed, if a sponsor
firm which has followed a risky investment strategy ends up with a severely underfunded pension plan, it
must by law devise a schedule of payments in order to fund their pension assets using its own financial
resources. These mandatory contributions are part of the sponsor’s incurring costs and may even increase the
sponsor’s default risk on other non-pension obligations if its liquid assets become exhausted as a consequence
of that. This idea has been formalized in Smith and Stulz (1985) who show that if financial distress is
costly, a risk management incentive can increase shareholder value by reducing the likelihood of financial
distress. This would predict that as firms get closer to bankruptcy, they would reduce their investment
risk exposure. The mandatory contributions may additionally prevent financially constrained sponsors to
undertake profitable investment projects (Almeida et al. (2011), Froot et al. (1993), and Rauh (2006)). When
a plan is underfunded below a minimum level set by ERISA and subsequent regulations, the associated9The maximum insurance benefit level for 2016 for a 65-year-old retiree in a single-employer plan was $60, 136 (http:
//www.pbgc.gov/news/press/releases/pr15-11.html).
8
sponsor cannot legally make capital expenditures, invest in projects or distribute dividends before fulfilling
the mandatory contribution requirements. The risk management incentive can also be partially motivated
under a tax perspective. One of the factors that motivate employers to sponsor DB plans is the favorable
tax treatment of these plans. The tax status of these induces deductibility of pension contributions and tax
exemption on the fund’s investment earnings. There is therefore a natural incentive of the sponsors to invest
in highly taxable securities to achieve higher tax benefits, and these are generally bonds and other fixed
income instruments in comparison with equities (Black (1980) and Tepper (1981)).
Previous studies have empirically examined which of the risk-shifting or risk management incentives play
a role in corporate DB plans’ asset allocations. Rauh (2009) finds that sponsoring firms with underfunded
pension plans and weak credit ratings allocate a greater share of pension fund assets to safer securities,
whereas sponsoring firms with well-funded pension plans and strong credit ratings invest more heavily in
equities. A consequence of this result is that, on average, risk management dominate risk-shifting incentives. It
also implies that the moral hazard incentive created by the PBGC’s insurance is not of first order importance.
Anantharaman and Lee (2014) confirm these findings but also find that some risk-shifting exists within the
most troubled sponsors. They show that the moral hazard created by PBGC’s insurance can be seen within
firms in which the plan’s manager and stockholder risk preferences are closely aligned. The authors identify
executive compensation structure as a driver of pension policy and show that a stronger contractual alignment
between pension plan’s managers and stockholders exacerbates risk-shifting.10 An et al. (2013) additionally
find that pension fund risk-taking is also affected by labor unionization and sponsor incentives to maximize
tax benefits, restore financial slack or justify the accounting choices of pension assumptions. Their empirical
study reveals that sponsors shift toward an aggressive risk strategy when their pension plans emerge from
underfunding, bankruptcy risk is reduced, or marginal tax rate decreases.
3 Loss Aversion and Asset Allocation: Empirical Insights
3.1 Hypothesis Development
In this paper, we propose another channel to describe pension plans’ investment decisions which
encompasses both risk-shifting and risk management incentives: a loss aversion preference on the funding10Specifically, the authors find that risk-shifting through pension underfunding is stronger with compensation structures that
create high wealth-risk sensitivity and weaker with high wealth-price sensitivity. They show that top managers’ compensationstructure is an important driver of corporate pension policy. Their study highlights the fact that while diversified stockholdershave incentives to increase firm risk at the expense of debt-holders, most corporate decision making is in the hands of managers,who prefer less risk than stockholders, out of concern for their reputation or private benefits of control. The stockholder-managerconflict on risk could thus offset risk-shifting incentives arising from the stockholder-debtholder conflict.
9
ratio of the plan, in reference to a 80% funding ratio benchmark. This benchmark has been proposed by
accounting standards as the level above which a DB plan is considered financially sound. The American
Academy of Actuaries refers to this level as a “mythic standard”. This 80% benchmark also appeared in
a 2007 Government Accountability Office (GAO) report stating: “a funded ratio of 80% or more is within
the range that many public sector experts, union officials and advocates view as a healthy pension system”.11
Moreover, under the Pension Protection Act (PPA) of 2006, multiemployer plans use 80% as a level below
which stricter funding rules come into effect. This threshold also appears in state pension legislation. For
instance, the New Jersey pension legislation of 2011 mentions that the “proposed changes allow all pension
plans to reach an 80% funding ratio, which is the ERISA and GAO standard for a healthy pension system”.12
Under our proposed mechanism, an underfunded pension plan approaching the 80% threshold would have
a risk management incentive to cut the plan’s assets volatility in order to avoid a drop of its funding ratio
below that benchmark. This reflects the willingness of the sponsor to avoid providing additional contributions,
which are required by law when the funding ratio of the plan falls below a specific level.13 The likelihood of
such a mandatory, additional contribution would create an incentive to reduce the equities’ allocation and an
increase in less volatile fixed income investment. On the other hand, a pension plan with a funding ratio
which is significantly less, or significantly more than 80%, would have an incentive to invest more aggressively
into equities, hence the predominance of risk-shifting.
Indeed, funding ratios far below the 80% threshold imply that the pension plan needs immediate
contributions from the sponsor, who might not be able to provide those because of financial constraints.14 A
loss-averse investment committee would then have an incentive to increase the risk of the portfolio of assets
by investing more aggressively in equities.15 In the opposite case when funding ratios are far above the 80%
threshold, the overfunded pension plan does not need further contributions. The investment committee of
these plans will seek to achieve an even higher funding ratio to ensure that across all possible future market
realizations, the plan will be adequately funded. This will be implemented by investing in traditionally high
return generating assets, such as equities. Since the plan is well funded, the induced increase in volatility will11State and Local Government Retiree Benefits - Current Status of Benefit Structures, Protections, and Fiscal Outlook for
Funding Future Costs, prepared by the United States Government Accountability Office in 2007 (http://www.gao.gov/assets/270/267150.pdf).
12New Jersey pension legislation passed in 2011 (http://blogs.app.com/capitolquickies/files/2011/06/S-2937-Summary-revised.pdf).
13According to the Retirement Protection Act of 1994, plans with funding ratios larger than 90%, as well as certain plans withfunding ratios between 80% and 90%, were exempt from deficit reduction contributions, whereas plans with funding ratios lessthan 80% were required to make contributions according to a specified formula. According to the Pension Protection Act of2006, funding rules raise required funding from 90% to 100% of liabilities, require funding shortfalls to be amortized over sevenyears, and introduce the concept of at-risk plans which are subject to stricter funding requirements.
14It is very likely that the plan’s funding ratio declined over time since the sponsor did not have the financial strength toprovide the required contributions. Figure 2b shows that underfunded plans are more likely to be associated with sponsors infinancial distress.
15This behavior resembles that of gambling for resurrection (Thaler and Johnson (1990)).
10
be tolerated and the benefits of this shift will outweight its costs.
3.2 Empirical Design
To empirically test our proposed mechanism, we use our full sample of plan-level data merged with stock
level data from CRSP. Summary statistics for variables of interest are provided in Table 1. All variables are
winsorized on an annual basis at the 1% level to discard outliers. We work with an average of 1,400 plans
per year from 2003 to 2014 which have an average funding ratio of 80%.16 In this time frame, the average
allocation to fixed income is 38% and to equities is 54%. The assets’ returns are calculated as investment
income divided by beginning-of-year assets and therefore incorporate the assumption that contributions are
not made until the end of the year.
Table 1: Summary statistics. The table summarizes means, standard deviations, min, and max values for allvariables of the sample. The data are from Compustat and span a period from 1985 until 2014. All data arewinsorized at the 1% level.
Count Mean StDev Min MaxFixed Income Allocation (%) 17376 38.14 16.45 0.00 100.00Equities Allocation (%) 17376 54.24 17.67 0.00 98.00Real Estate Allocation (%) 16896 1.50 3.14 0.00 19.00Other Assets Allocation (%) 17355 5.99 11.38 0.00 97.50∆(Fixed Income) 16192 1.05 8.96 -42.00 50.00∆(Equities) 16219 -1.40 8.98 -50.90 42.00∆(Real Estate) 15683 0.04 1.06 -7.00 5.10∆(Other Assets) 16204 0.38 5.56 -33.00 44.00Funding Ratio 17376 0.80 0.21 0.09 2.80Assets (bil.$) 17376 1.59 3.81 0.01 26.95Liabilities (bil. $) 17376 1.92 4.56 0.00 34.19Total Assets (tril.$) 17376 2.34 0.51 1.11 3.04Total Liabilities (tril. $) 17376 2.83 0.63 1.34 3.80Assets′ Return 16701 0.08 0.11 -0.41 0.361/V ol 13202 3.41 1.53 0.43 8.68∆(1/V ol) 11375 0.06 1.11 -5.61 4.90Employer Contributions (mil. $) 17145 0.07 0.16 0.00 1.20Participant Contributions (mil. $) 16635 0.00 0.01 0.00 0.08No. of Plans 17376 1466.69 139.87 937.00 1614.00
We use, as a proxy for a sponsor firm’s financial soundness, a measure of distance to insolvency as
approximated by the inverse of the volatility of a firm’s equity returns (1/V ol) (Atkeson et al. (2013)). The
distance to insolvency is a measure of a firm’s leverage relative to the volatility of its assets, and as such
an indicator of the financial soundness of the firm. We compute this measure at the firm level using data
on equity volatility for the plans’ sponsoring firms. The data are from CRSP and the measure is computed
on an annual basis. Low values of 1/V ol indicate firms with high leverage or high volatility of assets. The
values of this measure vary between 0.43 and 8.68 with an average of 3.41 (Table 1) and most of the values
are within the [1.5,5] interval (Figure 2a). We chose distance to insolvency over credit ratings for reasons16The final number of pension plans in the sample is smaller than the Compustat Pension Plans data since plans without a
value for 1/Vol for their sponsor are removed from the final dataset.
11
related to availability of data and information aggregation. Several firms in the sample do not have long
enough histories of credit ratings and due to this, equity volatility data not only allows us to include such
firms in our analysis, but also captures additional information incorporated into stock returns that is not
incorporated in credit ratings in a timely manner.
Figure 2: Frequency distributions of the distance to default (1/V ol) for the sponsors of the plans in terms ofassets for (1) all plans, (2) plans with funding ratio less than 80% for two consecutive years versus plans withfunding ratio more than 80% for two consecutive years. The data are from Compustat, and span a period oftwelve years from 2003 until 2014.
0.0
5.1
.15
.2.2
5F
requ
ency
0 2 4 6 81/Vol
(a) All plans
0.1
.2.3
Fre
quen
cy
0 2 4 6 81/Vol
Overfunded Underfunded
(b) 1/Vol for Overfunded vs. Undefunded
The level of assets of a pension plan is the outcome of all past investment returns, in addition to decisions
of the sponsor for periodical contributions to the plan after benefits have been returned to beneficiaries. Well
funded plans are likely to be associated to financially healthy sponsors, and vice-versa. This is shown in
Figure 2b, where the mass of the distribution of plans with two consecutive years of less than 80% funding
ratios is to the left of the one of plans with two consecutive years of exceeding 80% funding ratios. This is
consistent with the known results that firms decrease their contributions to defined pension plans when their
default risk is increased (Coronado and Liang (2006); Cheng and Michalski (2011), and with studies that
show that distress is positively associated with underfunding (Anantharaman and Lee (2014)).
We now explore the relationship between the percentage portfolio allocations of the four asset classes
within our sample (fixed income, equities, real estate, other) and pension plan variables related to the level
of the funding ratio and the distance to insolvency of the sponsoring firm. Figure 3 shows the average
evolution of fixed income and equities allocations of three groups of pension plans formed on the basis of
their funding ratios and the distance to insolvency of their sponsors. The funding ratio groups are: (i)
underfunded (funding ratiot < 0.7), (ii) adequately funded (0.8 < funding ratiot < 1), and (iii) overfunded
12
(1.1 < funding ratiot).17 In Figure 3 we only consider plans associated with sponsors with the lowest distance
to insolvency. These are the plans for which the loss aversion channel is expected to be more pronounced. We
observe that plans in the adequately funded group consistently allocate a higher proportion of their assets to
fixed income securities (Figure 3a), whereas plans in the other two categories choose to invest more heavily in
equities (Figure 3b). We notice that this effect becomes more pronounced after the Pension Protection Act of
2006 went into effect in 2008.18
Figure 3: Time evolution of average plans’ allocation weights in fixed income (figure a) and equities(figure b) for plans with funding ratios: (i) funding ratiot < 0.7, (ii) 0.8 < funding ratiot < 1, and (iii)1.1 < funding ratiot, and which are associated with sponsoring companies that exhibit low distance toinsolvency (companies in the first quintile when sorted on the basis of their 1/V ol measure). The data arefrom Compustat, and span a period of twelve years from 2003 until 2014.
2530
3540
45A
lloca
tion
(%)
2004 2007 2010 2013yr
Recession Funding Ratio<0.7
0.8<Funding Ratio<1 Funding Ratio>1.1
(a) Fixed Income
4550
5560
6570
Allo
catio
n (%
)
2004 2007 2010 2013yr
Recession Funding Ratio<0.7
0.8<Funding Ratio<1 Funding Ratio>1.1
(b) Equities
Using a linear regression design, we then investigate the relationship between changes in a plan’s funding
ratio and its asset allocation decisions. We regress asset allocations on plan characteristics related to changes
in funding ratios after controlling for a set of variables such as the level of assets, contributions made by
the sponsor, contributions made by employees, and investment returns. Year and plan fixed effects are
introduced. Linear and logarithmic controls are also employed to absorb size effects. We focus on the
investment behavior of four groups of pension plans based on the evolution of their funding ratios: (i)
decreasing ratios from the moderately overfunded region (0.9 < Funding Ratiot−1 < 1.1) to the moderately
underfunded region (0.8 < Funding Ratiot < 0.9), (ii) decreasing ratios from the moderately underfunded
region (0.7 < Funding Ratiot−1 < 0.9) to the severely underfunded region (0.4 < Funding Ratiot < 0.7),
(iii) increasing ratios from the severely underfunded region (0.1 < Funding Ratiot−1 < 0.7) to the moderately17We ensure that there is a difference of at least 0.1 between the funding ratios of the three groups so that there is a clear
distinction between the funding ratios among groups.18The Pension Protection Act of 2006 tightened funding requirements and raised required funding from 90% to 100% of
liabilities, required funding shortfalls to be amortized over seven years, and introduced the concept of at-risk plans which aresubject to stricter funding requirements thereby inducing a more pronounced loss aversion behavior to plans with funding ratiosin the ballpark of 80%-100%.
13
underfunded region (0.7 < Funding Ratiot < 0.9), and (iv) increasing ratios from the moderately overfunded
region (1 < Funding Ratiot−1 < 1.1) to the largely overfunded region (1.1 < Funding Ratiot < 1.5).
3.3 Estimation Results
Table 2 reports the regression coefficients and standard errors of our first test which focuses on the
investment decisions of plans that enter the underfunded region (group (i)). In column (1), we observe
a positive relationship between the weight allocated to fixed income investments and a dummy variable
capturing the set of plans within (i). Thus, a plan in this group exhibits, on average, a higher allocation
to fixed income securities of 1.209% and a lower allocation to equities of equal magnitude compared to an
average plan in any other group. This result reflects a risk management tendency for plans in this group,
consistent with a loss aversion preference in reference to the 80% benchmark.
We also observe a positive relationship between the fixed income weight and value of the funding
ratio. A 10% increase in funding ratio is associated with a 0.828% increase in fixed income allocations. As
expected, Column (2) reflects the opposite results for future changes in equity allocations and suggests that a
deteriorating funding ratio induces an increase in the allocation to equity. As we later show, this result is
consistent with loss-averse plans moving from the moderately underfunded region to the severely underfunded
region and supports the risk-shifting hypothesis. This contradicts the findings of Rauh (2009), who however
uses asset allocation data from 1990 until 2003.
In the first two columns of Table 2, pensions asset values are positively correlated with fixed income
allocations and a negatively correlated with future changes in equity allocations. The Assets’ returns, however,
are negatively correlated with fixed income allocations. On average, a 10% return of the asset portfolio is
associated with a 1.413% decrease in the fixed income allocation of a given plan. This finding is consistent
with a loss-averse investment behavior since positive returns are associated with increasing funding ratios
which, as we show in the following section, lead to more risk seeking investment strategies for plans in the
overfunded region.
Next, we empirically investigate the effect of the remaining three directional changes in funding ratios
on asset allocations. Table 3 summarizes the variables of interest from these regressions and Tables 7, 8, 9
(Appendix B.1) provide the full results.
In the second row of Table 3, we focus on plans with decreasing funding ratios from the moderately under-
funded region (0.7 < Funding Ratiot−1 < 0.9) to the severely underfunded region (0.4 < Funding Ratiot <
0.7). Such plans show a decrease in their fixed income allocation of 0.938% along with an increase of equal
14
Table 2: Explanatory power of the level of funding ratio and a dummy 1(0.9 < Funding Ratiot−1 <1.1 ∩ 0.8 < Funding Ratiot < 0.9), on the percentage asset allocation of the current year ((%)Allocationt).We introduce time-dummies for 2007 (1(t = 2007)), 2008 (1(t = 2008)) and 2009 (1(t = 2009)), and controlfor the level of assets (in bil.), the logarithm of assets, the return on assets, the level of 1/V olt and one yearlags for the last three quantities. Data are from the Compustat private pension plans database and spana period eleven years from 2003 until 2014. All specifications include year and plan fixed effects. Robustt-statistics adjusted for firm-level clustering are reported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
Funding Ratiot 8.276∗∗∗ -6.686∗∗ -0.598∗∗ -0.840(4.13) (-3.20) (-2.91) (-0.77)
Funding Ratiot−1 -1.457 1.149 0.564∗ -0.849(-0.67) (0.47) (2.54) (-0.75)
Assetst 0.097 -0.221 -0.006 0.119(0.68) (-1.54) (-0.21) (1.39)
ln(Assets)t -2.222∗∗ 1.186 0.180∗ 0.952∗(-3.12) (1.60) (2.21) (2.18)
Assets Returnt -14.131∗∗∗ 15.713∗∗∗ 0.154 -2.423+
(-6.68) (6.85) (0.63) (-1.91)Assets Returnt−1 -3.220∗ 2.722+ 0.418+ -1.199
(-2.16) (1.85) (1.83) (-1.18)1(0.9 < FRt−1 < 1.1 ∩ 0.8 < FRt < 0.9) 1.209∗ -1.163∗ 0.034 -0.040
(2.33) (-2.09) (0.56) (-0.15)1/V olt -0.153 0.189 -0.013 -0.037
(-1.05) (1.29) (-0.66) (-0.44)1/V olt−1 0.102 -0.097 0.039+ -0.075
(0.71) (-0.66) (1.85) (-0.87)Employer Contributionst 3.768∗∗∗ -3.594∗∗ -0.511∗∗ 0.100
(3.53) (-3.11) (-2.82) (0.14)Participant Contributionst -2.075 55.003 -2.634 -60.996∗
(-0.06) (1.27) (-0.53) (-2.49)1(t = 2007)t 1.445∗ -2.164∗∗∗ 0.136+ 0.326
(2.53) (-3.63) (1.89) (0.87)1(t = 2008)t 4.531∗∗∗ -5.934∗∗∗ 0.224∗ 0.709
(5.46) (-6.72) (2.13) (1.41)1(t = 2009)t 3.437∗∗∗ -4.282∗∗∗ 0.022 0.217
(4.11) (-4.90) (0.20) (0.38)Constant 8.511∗∗∗ 35.345∗∗∗ 0.767∗∗ 6.038∗∗∗
(3.36) (13.33) (3.15) (4.18)N 10741 10741 10368 10733R2 0.34 0.40 0.31 0.22F 79.19 129.07 29.91 20.92FE (Year) YES YES YES YESFE (Plan) YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
magnitude in its equity allocations. Plans with increasing ratios from the severely underfunded region
(0.1 < Funding Ratiot−1 < 0.7) to the moderately underfunded region (0.7 < Funding Ratiot < 0.9) exhibit
a slight increase/decrease in their fixed income/equity allocations, whereas plans with increasing ratios
from the moderately overfunded region (1 < Funding Ratiot−1 < 1.1) to the largely overfunded region
(1.1 < Funding Ratiot < 1.5) show a decrease/increase in their fixed income/equities allocation of 2.024%.
These coefficients suggest that the relationship between allocation to (riskier) equity securities as a function
of the plan’s funding ratio is U-shaped .
15
Table 3: Explanatory power of four different regions of funding ratios: (1) 1(0.9 < Funding Ratiot−1 <1.1 ∩ 0.8 < Funding Ratiot < 0.9), (2) 1(0.7 < Funding Ratiot−1 < 0.9 ∩ 0.4 < Funding Ratiot < 0.7) ,(3) 1(0.1 < Funding Ratiot−1 < 0.7 ∩ 0.7 < Funding Ratiot < 0.9), and (4) 1(1 < Funding Ratiot−1 <1.1∩1.1 < Funding Ratiot < 1.5) on the percentage asset allocation of the current year ((%)Allocationt). Thereported coefficients are from four different regression specifications with controls that include Funding Ratiot,dummies for each of the years 2007 (1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level ofassets (in bil.), the logarithm of assets, the return on assets, the level of 1/V olt, and one year lags for thelast three quantities. Data are from the Compustat private pension plans database and span a period elevenyears from 2003 until 2014. All specifications include year and plan fixed effects. Robust t-statistics adjustedfor firm-level clustering are reported in parentheses.
Funding Ratio Indicator Variable FIt EQt REt OTHt1(0.9 < F Rt−1 < 1.1 ∩ 0.8 < F Rt < 0.9) 1.209∗ -1.163∗ 0.034 -0.040
(2.33) (-2.09) (0.56) (-0.15)1(0.7 < F Rt−1 < 0.9 ∩ 0.4 < F Rt < 0.7) -0.938∗ 0.918∗ 0.031 0.007
(-2.37) (2.20) (0.55) (0.02)1(0.1 < F Rt−1 < 0.7 ∩ 0.7 < F Rt < 0.9) 0.236 -0.622+ 0.049 0.300
(0.62) (-1.65) (0.95) (1.35)1(1.0 < F Rt−1 < 1.1 ∩ 1.1 < F Rt < 1.5) -2.024∗∗ 1.704∗ 0.022 0.403
(-3.03) (2.38) (0.22) (0.84)t-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
3.4 The Origins of Loss Aversion: Firm’s Financial Status and Corporate Pen-
sion Benefits
We interpret the results of Table 3 as being consistent with the investment behavior of a loss-averse agent,
in reference to a 80% benchmark. However, not all of the plans in our sample are expected to exhibit the
same level of loss aversion. Intuitively, in a moderately underfunded region, a plan sponsored by a company
in financial distress is expected to be more loss-averse in comparison with a plan with the same funding ratio
but associated with a financially sound sponsor. We thus explore the effect that the distance to insolvency of
the sponsor has on the asset allocations of the associated plans. We conjecture that the effect of loss aversion
on investment decisions is stronger for plans with funding ratios in the underfunded region and with sponsors
in financial distress. To test this hypothesis, we use a similar specification as in Table 3: we rank sponsor
firms on the basis of their distance to insolvency, group them into quintiles, and interact the top and bottom
quintile with one of our four funding ratio groups.
Table 4 summarizes the regression coefficients for the first group (moderately overfunded to moderately
underfunded). Column (1) shows that pension plans associated with non-financially sound sponsors tend to
increase their fixed income allocations by 4.691% whereas plans in the same group associated with financially
sound sponsors do not alter their fixed income allocations. This effect is much stronger compared to that
of Table 2 (1.209%). Column (2) shows a similar but inverse effect on changes in equity allocations. The
investment decisions of plans in this group are thus directly related to the levels of financial soundness of
16
Table 4: Explanatory regressions. The table summarizes the explanatory power of the level of funding ratio, andthe interaction between a plan’s funding ratio (1(0.9 < Funding Ratiot−1 < 1.1 ∩ 0.8 < Funding Ratiot <0.9)) with the quintile of its distance to insolvency (∆(1/V ol)t) on the percentage asset allocation of thecurrent year ((%)Allocationt). The controls are dummies for each of the years 2007 (1(t = 2007)), 2008(1(t = 2008)), and 2009 (1(t = 2009)), the level of assets (in bil.), the logarithm of assets, the return onassets, the level of 1/V olt, and one year lags for the level of assets (in bil.), the level of allocation, the returnon assets, and the level of 1/V olt. Data are from the Compustat private pension plans database and spana period eleven years from 2003 until 2014. All specifications include year and plan fixed effects. Robustt-statistics adjusted for firm-level clustering are reported in parentheses. Robust t-statistics adjusted forfirm-level clustering are reported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
Funding Ratiot 8.046∗∗∗ -6.553∗∗ -0.598∗∗ -0.781(4.03) (-3.17) (-2.93) (-0.72)
Funding Ratiot−1 -1.193 1.020 0.566∗∗ -0.942(-0.55) (0.43) (2.58) (-0.84)
Assetst 0.080 -0.208 -0.006 0.121(0.56) (-1.45) (-0.21) (1.42)
ln(Assets)t -2.224∗∗ 1.202 0.180∗ 0.942∗(-3.12) (1.62) (2.20) (2.16)
Assets Returnt -13.973∗∗∗ 15.591∗∗∗ 0.156 -2.448+
(-6.62) (6.84) (0.64) (-1.94)Assets Returnt−1 -3.185∗ 2.696+ 0.419+ -1.205
(-2.14) (1.83) (1.83) (-1.18)1(0.9 < FRt−1 < 1.1 ∩ 0.8 < FRt < 0.9)× 1((1/V ol)t−1 ∈ Bin-1) 4.691∗ -5.478∗∗ 0.029 0.775
(2.45) (-2.96) (0.22) (0.70)1(0.9 < FRt−1 < 1.1 ∩ 0.8 < FRt < 0.9)× 1((1/V ol)t−1 ∈ Bin-5) -0.131 -0.536 0.089 0.321
(-0.16) (-0.59) (1.00) (0.74)1/V olt -0.153 0.187 -0.012 -0.036
(-1.05) (1.28) (-0.65) (-0.43)1/V olt−1 0.135 -0.128 0.038+ -0.074
(0.95) (-0.88) (1.80) (-0.85)Employer Contributionst 3.753∗∗∗ -3.604∗∗ -0.510∗∗ 0.115
(3.53) (-3.11) (-2.81) (0.16)Participant Contributionst -0.175 53.700 -2.643 -61.317∗
(-0.00) (1.24) (-0.53) (-2.51)1(t = 2007)t 1.375∗ -2.107∗∗∗ 0.136+ 0.332
(2.42) (-3.55) (1.88) (0.89)1(t = 2008)t 4.527∗∗∗ -5.937∗∗∗ 0.225∗ 0.712
(5.45) (-6.72) (2.13) (1.41)1(t = 2009)t 3.459∗∗∗ -4.303∗∗∗ 0.022 0.218
(4.15) (-4.93) (0.19) (0.39)Constant 8.417∗∗∗ 35.404∗∗∗ 0.767∗∗ 6.032∗∗∗
(3.32) (13.35) (3.15) (4.17)N 10741 10741 10368 10733R2 0.34 0.40 0.31 0.22F 76.59 124.01 28.69 20.04FE (Year) YES YES YES YESFE (Plan) YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
their sponsors.19 This finding is again consistent with the hypothesis of a loss-averse investment behavior.
Plans with non-financially sound sponsors realize that they cannot rely on contributions from their sponsors
in order to meet the level of their liabilities. Hence, they choose to invest in fixed income securities to remove
some of the volatility associated with their funding ratios and thus lock-in their current funding ratios. This
would also prevent the PBGC from undertaking any action, which would signal that both the sponsoring
firm and the pension plan are in a bad financial condition.
Table 5 summarizes the variables of interest from the regressions of the three remaining directional19The remaining control variables have similar coefficients and standard errors with our prior specifications.
17
changes in funding ratios interacted with the 1/Vol quintile of the sponsoring company. Tables 10, 11 and 12
(Appendix B.2) provide the full results.
Table 5: Explanatory power of four different regions of funding ratios: (1) 1(0.9 < Funding Ratiot−1 <1.1 ∩ 0.8 < Funding Ratiot < 0.9), (2) 1(0.7 < Funding Ratiot−1 < 0.9 ∩ 0.4 < Funding Ratiot < 0.7) ,(3) 1(0.1 < Funding Ratiot−1 < 0.7 ∩ 0.7 < Funding Ratiot < 0.9), and (4) 1(1 < Funding Ratiot−1 <1.1 ∩ 1.1 < Funding Ratiot < 1.5) interacted with the quintile of its distance to insolvency (∆(1/V ol)t) onthe percentage asset allocation of the current year ((%)Allocationt). The reported coefficients are from fourdifferent regression specifications with controls that include Funding Ratiot, dummies for each of the years2007 (1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level of assets (in bil.), the logarithmof assets, the return on assets, the level of 1/V olt, and one year lags for the last three quantities. Data arefrom the Compustat private pension plans database and span a period eleven years from 2003 until 2014. Allspecifications include year and plan fixed effects. Robust t-statistics adjusted for firm-level clustering arereported in parentheses.
Funding ratio region interacted with 1/Vol quintile FIt EQt REt OTHt1(0.9 < F Rt−1 < 1.1 ∩ 0.8 < F Rt < 0.9)× 1((1/V ol)t−1 ∈ Bin-1) 4.691∗ -5.478∗∗ 0.029 0.775
(2.45) (-2.96) (0.22) (0.70)1(0.9 < F Rt−1 < 1.1 ∩ 0.8 < F Rt < 0.9)× 1((1/V ol)t−1 ∈ Bin-5) -0.131 -0.536 0.089 0.321
(-0.16) (-0.59) (1.00) (0.74)1(0.7 < F Rt−1 < 0.9 ∩ 0.4 < F Rt < 0.7)× 1((1/V ol)t−1 ∈ Bin-1) -1.086+ 0.789 -0.012 0.248
(-1.74) (1.07) (-0.10) (0.45)1(0.7 < F Rt−1 < 0.9 ∩ 0.4 < F Rt < 0.7)× 1((1/V ol)t−1 ∈ Bin-5) -1.225+ 1.220+ 0.296∗ -0.420
(-1.75) (1.83) (2.21) (-0.83)1(0.1 < F Rt−1 < 0.7 ∩ 0.7 < F Rt < 0.9)× 1((1/V ol)t−1 ∈ Bin-1) 0.057 -0.330 0.153+ 0.009
(0.08) (-0.51) (1.69) (0.02)1(0.1 < F Rt−1 < 0.7 ∩ 0.7 < F Rt < 0.9)× 1((1/V ol)t−1 ∈ Bin-5) -0.240 -1.387 -0.214+ 1.716∗
(-0.31) (-1.60) (-1.89) (2.27)1(1.0 < F Rt−1 < 1.1 ∩ 1.1 < F Rt < 1.5)× 1((1/V ol)t−1 ∈ Bin-1) 1.850 -1.724 0.032 0.257
(1.08) (-0.86) (0.25) (0.39)1(1.0 < F Rt−1 < 1.1 ∩ 1.1 < F Rt < 1.5)× 1((1/V ol)t−1 ∈ Bin-5) -2.359∗ 0.855 0.044 1.777∗
(-2.53) (0.87) (0.20) (2.33)t-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Again, pension plans starting from the moderately overfunded region and going to the moderately
underfunded region, with non-financially sound sponsors, increase on average their fixed income allocations of
4.691% and decrease their equility allocations in the same proportion. In the second row of Table 5, we focus
on plans starting from the moderately underfunded region and going to the severely underfunded region,
with non-financially sound sponsors. Such plans decrease their fixed income allocations of 1.086% on average,
matched by an increase of equal magnitude in equity allocations. Plans with increasing funding ratios, going
from the severely underfunded region to the moderately underfunded region, and with solvent sponsors exhibit
a significant increase/decrease in their other investments/equity allocations. Finally, plans going from the
moderately overfunded region to the largely overfunded region, with solvent sponsors, decrease/increase their
fixed income/other allocations of 2.359%. The coefficients of the first two groups suggest that loss aversion is
more pronounced for plans in the underfunded region.
So far, we have shown that DB pension plans exhibit a loss-averse investment behavior centered around
a funding ratio of 80%, and that this behavior is more pronounced for underfunded plans associated with
insolvent sponsors. This finding can be attributed to either the incentives structure around DB plans, or
18
preferences (utility function) of the investment committee. The incentives structure is determined primarily
by legislation, which describes the scope of action and responsibilities of the relevant parties (sponsor,
beneficiaries, investment committee, regulators). Preferences, on the other hand, determine a risk/return
relationship that is deemed acceptable by the involved agents, primarily the investment committee.
In the exercise that follows we attempt to look further into the origins of this loss-averse behavior, by
focusing on the compensation scheme of corporate executives serving on the investment committee of the
sponsored pension plan. Anantharaman and Lee (2014) show that executives’ compensation structure is
a significant driver of the asset allocation decisions of pension plans. Among corporate executives, CFOs
are usually the ones with a leading role in the investment committee of the plan the company sponsors.
RBC Group (2016) and Anantharaman and Lee (2014) confirm that the pension’s policy falls under the
CFO’s domain. This finding implies that if preferences of the members of the investment committee played a
role in the asset allocation decisions of the plan, then the observed allocations should be correlated with the
level of personal wealth (in the form of accumulated pension benefit claims) of the committee members. We
conjecture that plans associated with sponsors whose CFO’s have accumulated high pension benefits exhibit
a more pronounced loss-averse investment behavior.
Table 6: Explanatory power of four different regions of funding ratios: (1) 1(1.2 < Funding Ratiot−1 ∩ 0.8 <Funding Ratiot < 1.2), (2) 1(0.8 < Funding Ratiot−1 < 1.2 ∩ 1.2 < Funding Ratiot) , (3) 1(0.7 <Funding Ratiot−1 < 0.8 ∩ 0.4 < Funding Ratiot < 0.7), and (4) 1(0.4 < Funding Ratiot−1 < 0.7 ∩ 0.7 <Funding Ratiot < 0.8) interacted with the quintile of CFO’s accumulated pension benefits as a percentageof their salary (pensCFO) on the percentage asset allocation of the current year ((%)Allocationt). Thereported coefficients are from four different regression specifications with controls that include Funding Ratiot,dummies for each of the years 2007 (1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level ofassets (in bil.), the logarithm of assets, the return on assets, the level of 1/V olt, and one year lags for thelevel of assets (in bil.), the level of allocation, the return on assets, and the level of 1/V olt. Data are fromthe Compustat private pension plans database and span a period eleven years from 2003 until 2014. Allspecifications include year and plan fixed effects. Robust t-statistics adjusted for firm-level clustering arereported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
1(1.2 < FRt−1 ∩ 0.8 < FRt < 1.2)× 1((pensCFO)t−1 ∈ Bin-1) 6.819∗∗∗ -6.444∗∗∗ -0.209+ -0.184(5.16) (-4.98) (-1.80) (-0.45)
1(1.2 < FRt−1 ∩ 0.8 < FRt < 1.2)× 1((pensCFO)t−1 ∈ Bin-5) 3.175∗∗ -1.585 -2.416∗∗∗ 0.391(3.30) (-1.50) (-12.62) (0.49)
1(0.8 < FRt−1 < 1.2 ∩ 1.2 < FRt)× 1((pensCFO)t−1 ∈ Bin-1) -1.157 1.552 0.209 -0.736(-0.25) (0.34) (1.08) (-1.00)
1(0.8 < FRt−1 < 1.2 ∩ 1.2 < FRt)× 1((pensCFO)t−1 ∈ Bin-5) -18.444∗∗∗ 16.333∗∗∗ 0.549∗ 3.434∗∗∗(-6.85) (5.96) (2.49) (3.49)
1(0.7 < FRt−1 < 0.8 ∩ 0.4 < FRt < 0.7)× 1((pensCFO)t−1 ∈ Bin-1) -1.387 3.271 -0.080 -1.551(-0.60) (1.27) (-0.49) (-1.31)
1(0.7 < FRt−1 < 0.8 ∩ 0.4 < FRt < 0.7)× 1((pensCFO)t−1 ∈ Bin-5) -3.625∗ 1.581 0.029 1.558(-2.42) (0.98) (0.16) (0.83)
1(0.4 < FRt−1 < 0.7 ∩ 0.7 < FRt < 0.8)× 1((pensCFO)t−1 ∈ Bin-1) -3.604 -2.722 0.137 5.504+
(-1.36) (-0.86) (0.90) (1.70)1(0.4 < FRt−1 < 0.7 ∩ 0.7 < FRt < 0.8)× 1((pensCFO)t−1 ∈ Bin-5) 0.351 -1.347 0.170 1.077
(0.31) (-1.27) (0.77) (1.59)t-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
19
To test this conjecture, we compute the CFOs’ accumulated (risky) pension benefits as a percentage of
their salary (pensCFO) and we study its correlation with asset allocations across four different ratios. 20 In
Table 6, we find that plans whose CFOs have the highest accumulated pension benefit as a percentage of
their salary, exhibit a more pronounced loss-averse investment behavior compared to similar plans whose
CFOs have lower pension benefits. This finding is in line with our conjecture and suggests that the observed
loss-averse investment pattern is partly due to preferences. Of course with this test we cannot rule out the
possibility that this investment pattern is also partially driven by incentives, but we can clearly state that
CFO’s preferences are an important element of the decision making process.
4 Loss Aversion and Asset Allocation: Theoretical Insights
In this section, we show that the asset allocations outlined in the previous section constitute the optimal
solution to the asset allocation problem of a loss-averse investor. This investor has to decide on how much of
their assets they will invest in a risk asset versus a riskless bond, in order to maximize their expected utility,
expressed as a function of the funding ratio, at a given maturity.
Let us consider a time interval [0, T ] with finite time horizon 0 < T < +∞. We let (Ω,F ,P) denote a
probability space on which we define a one-dimensional Wiener process Wt (0 ≤ t ≤ T ). We assume that the
process Wt is adapted to the augmented filtration Ft; 0 ≤ t ≤ T.
We start by modeling the assets of the pension plan. We consider a financial market in which two assets
are available: a money market account asset (riskless bond) with value S0t at time t and an equity account
(risky) asset with value S1t . There are no transaction costs. The riskless bond bears a constant interest rate r.
We assume the following asset prices dynamics:
dS0t = rS0
t dt (1)
dS1t = S1
t µdt+ S1t σdWt (2)
where r < µ. Let uit denote the fraction of total assets which is invested by a pension plan in asset i ∈ 0, 1.20We compute CFOs’ accumulated pension benefits as a percentage of their salary (pensCF O) using the methodology described
in Anantharaman and Lee (2014) Table B1 of the Appendix. We estimate an annual post-retirement payout from the executives’ERISA-qualified pensions account (we use the at-risk portion only) and scale it by the annual base salary of the executive. Weobtain the data from ExecuComp, and assume a retirement age of 65 and a gender-specific life expectancy (75 for men, 81 forwomen).
20
We have∑1i=0 u
it = 1. Next, we define At as the value of total assets held by the plan at time t:
At = a0tS
0t + a1
tS1t (3)
where ait is the plan’s holding amount of asset i and satisfies:
a1t = ut
AtS1t
(4)
a0t = (1− ut)
AtS0t
(5)
We consider a self-financing strategy from which (3) can be used to write:
dAt = a0tdS
0t + a1
tdS1t
Using (4) and (5) within the latter expression, we obtain the following dynamics for the total asset dynamics:
dAtAt
= (r + (µ− r)ut) dt+ (utσ) dWt (6)
where ut is the fraction of total assets invested in the risky asset.
We next define Lt as being the value of total liabilities held by the plan at time t. Specifically, we
assume:dLtLt
= µLdt (7)
which is a pure drift process, motivated by the lack of volatility associated with the observed dynamics of the
total liabilities process (see Figure 11 in Appendix A). We also assume µL > µ based on empirical evidence.
In this project, we are ultimately interested in the funding ratio Ft of the pension plan. As defined in
Section 2, we have Ft = AtLt
.
Lemma 1. The value Ft of the pension plan’s funding ratio is given by:
dFtFt
= (r − µL + (µ− r)ut) dt+ (utσ) dWt (8)
We assume that the portfolio process ut is square-integrable and is admissible if it satisfies (8). We
further assume the completeness of markets which implies that there exists a unique state-price deflator πt
21
for t ∈ [0, T ] which can be expressed as:
πt = e−(r−µL)t dQ
dP= e−(r−µL)t− 1
2
∫ t0θ2sds−
∫ t0θsdWs (9)
where we define the market price of risk:
θt = θ = σ−1 (µ− r) (10)
The state-price deflator thus satisfies π0 = 1 and has the following dynamics:
dπtπt
= −(r − µL)dt− θdWt (11)
The pension’s problem is given by:
Suput
EU(FT )
s.t dFtFt
= (r + (µ− r)ut) dt+ (utσ) dWt
F0 given
Ft ≥ 0,∀t ∈ [0, T ]
(12)
We consider the following utility specification:
U(x) =
−λ (K − x)β if x ≤ K
(x−K)α if x > K
where λ > 1 and 0 ≤ α ≤ β ≤ 1. The reference level (or kink in the utility function) corresponds to the
parameter K which is assumed to be constant. Based on Section 3, this reference level will take the value
of 80% and as such will distinguish, for the pension plan, what is considered to be a loss and a gain in
terms of funding ratio. The choice the utility specification is motivated by prospect theory. The complete
markets assumption and the fact that the process πtFtt≥0 is a martingale allows to rewrite the pension’s
problem as one of choosing an optimal portfolio of Arrow-Debreu securities in each state of the world at
maturity. This martingale methodology, which allows to transform the dynamic portfolio problem into a
static optimization problem, has been used in Karatzas et al. (1987) and Karatzas and Shreve (1998). The
22
pension plan’s problem (12) can thus be written as:
SupFT
EU(FT )
s.t E
πTπ0FT
≤ F0
FT ≥ 0
(13)
where we assume a maximization over expected rather than prospective values, hence not using subjective
decision weights as introduced in Kahneman and Tversky (1979). This assumption is also retained in Barberis
et al. (2001) in an asset pricing context. Problem (13) is a non-concave optimization problem since the chosen
utility specification is concave for gains and convex for losses. It is also non-differentiable at the kink point,
and since this point K is not equal to 0 then Ft has a non-zero probability of reaching this value within the
considered time horizon. As a consequence, we cannot use dynamic programming and solve the optimization
problem through a HJB equation. Moreover, the utility function is not quasi-concave, which implies that
the first-order conditions of the problem only represent local maxima. However, the function U is strictly
increasing, hence pseudo-concave, which implies that the martingale’s optimization problem (13) has a global
optimum.
Proposition 1. Solution Pension Plan’s Problem (13) The optimal solution FT of the pension plan’s problem
(13) is given by:
FT =
K +
(αδπT
) 11−α if πT < π
0 if πT ≥ π
where π solves: ( αδπ
) α1−α (1− α)− δπK + λKβ = 0 (14)
and δ solves:
E
πTπ0FT
= F0 (15)
In Proposition 1, the expression for the optimal funding ratio at maturity is made of two contributions.
The first is K, which makes the solution similar to a binary (cash) call option written on the state-price
deflator at maturity and with payoff the reference level. The second contribution,(
αδπT
) 11−α , also shares some
similarities with a binary call option. In Merton’s standard optimal portfolio problem (Merton (1969) and
Merton (1971)), the inverse of the state-price deflator is equal to the mean-variance efficient, optimal growth
portfolio. The term(
αδπT
) 11−α is the inverse of the state-price deflator but however scaled by the coefficient
of risk aversion from the concave part of the utility function. It can thus be interpreted as mean-variance
23
efficient insurance portfolio. Finally, the value of π is dependent on the preferences of the pension plan. If
the first-order risk aversion(−λβα
)or the risk aversion over gains increase, π increases, leading to a higher
likelihood of a non zero outcome at maturity.
Next, the knowledge of FT allows us to determine the value of Ft for t ∈ [0, T ] using the martingale
property of the process πtFtt≥0.
Proposition 2. The optimal funding ratio Ft of the pension plan for t ∈ [0, T ] is given by:
Ft = Ke−(r−µL)(T−t)Φ(d1) +(δπtα
) 1α−1
e−αα−1 (r−µL+ 1
2 θ2)(T−t)+ 1
2 ( θαα−1 )2(T−t)Φ(d2) (16)
with:
d1 =ln(ππt
)+(r − µL − θ2
2
)(T − t)
θ√T − t
d2 = d1 −θ√T − t
α− 1
Finally, we can determine the optimal control for the problem (12).
Proposition 3.
ut = σ−1θ
Ft
(Ke−(r−µL)(T−t)φ(d1)
θ√
(T − t)+(δπtα
) 1α−1
e−αα−1 (r−µL+ 1
2 θ2)(T−t)+ 1
2 ( θαα−1 )2(T−t)
(φ(d2)
θ√
(T − t)− Φ(d2)α− 1
))(17)
which can also be written as:
ut = u1t + u2
t (18)
where,
u1t = θ
σ
(α
1− α
)(Ft −Ke−(r−µL)(T−t)Φ(d1)
Ft
)u2t = θ
σFt
(Ke−(r−µL)(T−t)φ(d1)
σ√T − t
+(δπtα
) 1α−1
e−αα−1 (r−µL+ 1
2 θ2)(T−t)+ 1
2 ( θαα−1 )2(T−t)
(φ(d2)
θ√
(T − t)
))
In Proposition 3, the optimal portfolio allocation ut in the risky asset is decomposed into two portfolios
u1t and u2
t . The first portfolio u1t constitutes a mean-variance contribution to the overall allocation, for which
the term(Ke−(r−µL)(T−t)Φ(d1)
)is the present value of the reference level K discounted at the state price
density. The second portfolio u2t is a gambling portfolio which translates the risk seeking behavior over
losses. Indeed, we can observe that limπt→∞Φ(d1) = 0 while limπt→∞ φ(d1) = limπt→∞ φ(d2) = 1 which
24
implies that as the funding ratio Ft deteriorates below the reference level, the contribution of the gambling
component within the total allocation in the risky asset becomes predominant.
We then perform a number of simulations of the model in order to illustrate its dynamics and predictions.
In Figure 4, we simulate the model for a set of representative parameters and report, for each time t, the
median values of the processes Ft and ut from a total of 500,000 simulations. In Figures 4a and 4b, maturities
of T = 5 and T = 25 years are chosen respectively and the same initial funding ratio is shared (F0 = 1).
In Figure 4a, we observe the previously documented shift from equity to fixed income investment which
occurs when the funding ratio deteriorates towards the 80% reference level. Figure 4b illustrates the case of
a longer maturity, during which the funding ratio keeps decreasing in a monotonic fashion due to the high
liability drift value. This figure instead outlines the role of the gambling allocation u2t . Unlike Figure (4a) in
which the insurance strategy dictates a decreasing stock position as the funding ratio decreases towards the
reference level (u1t is predominant), shortly before the maturity the pension plan will massively rebalance
towards stock in the hope of breaking-even to the reference level at maturity. The pension plan will proceed
to this rebalancing even if this implies a tremendous increase in the volatility of the funding ratio, which
might even push the ratio further down. As we get closer to maturity with a funding ratio lower that the
reference level, the gambling portfolio u2t will dominate.
Figure 4: Time evolution of median funding ratios and associated equity allocations for two time horizons(T = 5, 25 years) and a number of 500,000 simulations. The simulation parameters are : µ = 6%, µl = 8%,σ = 30%, α = 0.8, β = 0.9, K = 0.8, λ = 2, r = 2%.
0 1 2 3 4 50.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
t
Ft
0 1 2 3 4 50.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
t
Equ
ity A
lloca
tion t
(a) T = 5 years
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
1.4
t
Ft
0 5 10 15 20 250
2
4
6
8
10
12
t
Equ
ity A
lloca
tion t
(b) T = 25 years
In Figure 5, we keep the same parameters as in Figure 4 but instead represent the median values of
ut versus Ft, for t = 0.5 and two different maturities (T = 5 in Figure 5a and T = 25 in Figure 5b). The
U-shape in stock allocation, which is generated by the model, is in perfect agreement with the empirical
findings of Section 3. As the funding ratio moves away from the region around the reference point of 80%,
25
the allocation to equities increases.
Figure 5: Median equity allocation versus median funding ratio for two time horizons (T = 5, 25 years) and anumber of 500,000 simulations. The simulation parameters are: µ = 6%, µl = 8%, σ = 30%, α = 0.8, β = 0.9,K = 0.8, λ = 2, r = 2%.
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.8
1
1.2
1.4
1.6
1.8
2
Ft
Equ
ities
t
t=0.5
(a) T = 5 years
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
1.46
1.48
1.5
1.52
1.54
1.56
1.58
1.6
Ft
Equ
ities
t
t=0.5
(b) T = 25 years
In Figure 6 we repeat the exercise of Figure 4, but keep a fixed maturity of 5 years, set the mean of
liabilities µL at 8% (Figure 6), and consider various initial funding ratios from 40% to 120% in steps of 20%.
Changing the initial funding ratio amounts to modifying the time at which the funding ratio will reach the
reference level. For initially well funded plans (funding ratios of 100% and 120%), which will experience
a decrease in their funding ratio due to the high rate of liabilities increase, the insurance allocation will
dominate the gambling one and the plan will increase its allocation in the risk free asset in order to make sure
it will stay above the reference level at maturity. This pattern is also observed for an initial funding ratio of
80%, albeit at lesser extent since the plan will need a higher allocation in the risky asset to prevent a further
declining funding ratio. Only when the plan will be close to maturity, hence sure of locking in a funding ratio
above 80%, it will move away from the risky security in order to lock in the ratio. Finally, the trajectories
associated with an initial funding ratio of 60% and 40% will see their risky allocation mostly associated with
a gambling incentive. For the trajectory associated with F0 = 60%, the gambling incentive is moderate and
allows to reach the reference level at maturity while de-risking in the last time periods. However, the extreme
gambling incentive of the F0 = 40% trajectory will fail to reach its goal, as a consequence of an extreme
increase in the volatility of the funding ratio. In that case, the volatility will work against the pension plan.
26
Figure 6: Time evolution of median funding ratio and equity allocation for a set of starting funding ratios(F0 = 0.4, 0.6, 0.8, 1.0, 1.2) and a number of 500,000 simulations. The simulation parameters are: T = 5,µ = 6%, µl = 8%, σ = 30%, α = 0.8, β = 0.9, K = 0.8, λ = 2, r = 2%.
0 1 2 3 4 50
0.2
0.4
0.6
0.8
1
1.2
1.4
t
Ft
0 1 2 3 4 50
0.5
1
1.5
2
2.5
3
tE
quity
Allo
catio
n t
5 The Cost of Short-Termism
Our findings in Section 3 suggest that pension plans with declining funding ratios below the 80%level
of funding choose, on average, to invest in fixed income securities over equities. More specifically, we find
that that among these plans, the ones associated with non-financially sound sponsors, and with CFOs whose
accumulated (risky) pension benefits constitute a large part of their compensation, do so in a more pronounced
way. In Section 4, we show that this investment behavior is consistent with a loss-averse one, in reference to
a 80% funding benchmark, which we associate with short-termism. On the one hand, this strategy allows the
plan’s investment committee to reduce the volatility in the value of assets caused by equities. On the other
hand, the yield from fixed income investments does not emulate the increase of liabilities over time. This
means that the decision of investing in fixed income comes at a cost which takes the form of a mismatch
between assets and liabilities. In this section we attempt to measure this cost, and we offer a number of
suggestions to minimize it.
In Figure 7, we compare the effect that two distinct investment strategies have on the funding ratio of
pension plans adopting them within our sample. Both strategies consist of an increase in the allocations to
either fixed income or equities securities for two consecutive years.21 We focus on plans with funding ratios
between 80% and 100% prior to implementing these strategies, and we monitor the evolution of funding21∆F It > 0% and ∆F It−1 > 0% for the fixed income strategy, and ∆EQt > 0% and ∆EQt−1 > 0% for the one based on
equities. The results are robust to alternative thresholds of 1%, and 2%.
27
ratios until five years after the beginning of the investment strategy.
Figures 13 and 14 (Appendix A) show the evolution of funding ratios and asset allocations five years
before and after implementing the two strategies. Figures 13a and 14a show a significant decline in funding
ratios prior to the implementation of both. However, the evolution of funding ratios differs between the two
categories. Figure 7a shows that pension plans that invested in equities exhibit, on average, higher funding
ratios compared to their counterparts that invested in fixed income assets. This difference amounts to more
than 10% in the fifth year after the beginning of the strategy. Pension plans which choose equity strategies
are associated with sponsors that are more financially sound compared to sponsors of plans choosing fixed
income strategies (Figure 7b).
Figure 7: The figure summarizes the change (%) in the average funding ratio and the average 1/V ol measureof the sponsor until five years after the implementation of a fixed income or an equities strategy marked byan increase in the allocation to fixed income (∆FIt+1 > 0% and ∆FIt+2 > 0%) and equities (∆EQt+1 > 0%and ∆EQt+2 > 0%) respectively. The focus is on the plans that are in the underfunded region (f -ratiot > 0.8and f -ratiot < 1.0) and for which there are more than nine annual observations. Panel (a) shows thecumulative change (%) in the average funding ratio, and Panel (b) shows the 1/V ol measure. The data arefrom Compustat, and span a period of eleven years from 2003 until 2014.
−15
−10
−5
05
Cha
nge
(%)
in F
undi
ng R
atio
0 1 2 3 4 5Year
Fixed Income strategy Equity strategy
(a) Change in funding ratio
2.5
33.
54
1/V
ol
0 1 2 3 4 5Year
Fixed Income strategy Equity strategy
(b) 1/V ol
DB pension plans face an assets-liabilities management (ALM) problem with a long horizon. Strategic
asset allocation is one of the most popular portfolio strategies designed to tackle this problem. It consists
of target allocations for a number of asset classes and portfolio rebalancing which allow the portfolio to
maintain the target allocations. In our data, we observe significant heterogeneity in terms of these target
allocations ranging from high allocations to fixed income assets, to high allocations to equities. The equity
strategy clearly outperforms the fixed income strategy both in the medium and the long-term investment
horizons (Figure 7a). The choice to invest more heavily into equities is consistent with that of a risk-averse
investor who solves a dynamic portfolio problem incorporating return predictability and rebalancing at regular
28
intervals (Barberis (2000)).22 A higher demand for equities is also consistent with the portfolio choice decision
of an infinitely lived investor with Epstein-Zin-Weil utility who faces a constant riskless interest rate and
a time-varying equity premium (Campbell and Viceira (1999), and Campbell et al. (2004)). Both investor
profiles match that of DB pension plans, which typically have investment horizons that typically span over
one or two decades.
The portfolio choice problem of a pension plan significantly differs from that of other investors. First,
the plan has a constant negative (minus one) exposure to its liabilities. Second, the regulatory framework
governing DB plans, as discussed in Section 2, exacerbates the moral hazard problem in pension plans’
asset allocation. Third, the investment management industry, regulation, and stakeholders have created
a “mythic standard” of funding ratio (80%) below which a plan is deemed underfunded and immediate
action is required from its sponsor. A number of papers show that the regulatory framework along with the
beliefs of stakeholders can have a direct impact on the plan’s investment strategy (Addoum et al. (2010)
and van Binsbergen and Brandt (2016)). We provide evidence that the loss-averse behavior exhibited by
the majority of the pension plans of our sample can be at least partially attributed to the preferences of the
investment committee. However, we cannot rule out the conjecture that this investment behavior is a result
of the incentive structure created by the regulatory environment and the market. The prospect of additional
contributions from the sponsor along with the signal sent to the market that the pension plan might be in
trouble forces the investment committee of the plan to switch its allocation from equities to fixed income,
thus making it impossible for the plans’ assets to keep up with the increase of its liabilities.
Figure 7a shows that an increase in the holdings of equities can lead to a higher funding ratio compared
to that of a fixed income strategy. We believe that a more detailed study of the institutional details that
affect asset allocation decisions in pension plans is required. The incentives of the investment committee
should be aligned with the long-term goals of a DB pension plan. This entails a redesign of the regulatory
framework so that it takes into account both the incentives structure and the preferences of the investment
committee favoring investments to assets whose expected return is closer to the rate of increase of the plans’
liabilities.22More specifically, investors have higher allocations to equities at longer horizons, when they are more risk-averse than
investors with log utility.
29
6 Conclusion
In this paper we document that short-term incentives in the investment process of private DB pension
plans affect their asset allocations and future funding ratios. We propose and test a framework that reconciles
the long-term decline in average funding ratios with the long-term increase in fixed income allocations.
We establish both empirically and theoretically that the allocation to fixed income assets as a function
of a plan’s funding ratio is inverse U-shaped, with increasing allocations around a reference funding ratio
equal to 80%, suggested by the current regulatory environment and market consensus. This effect is more
pronounced for plans associated with sponsors in financial distress, and with CFOs that have significant
accumulated (risky) pension benefits. The documented relation between asset allocations and funding ratios
reconciles the initially paradoxical empirical evidence in favor of both a risk-shifting and a risk management
incentive, as we show that the two incentives affect asset allocations in separate regions of the continuum of
possible funding ratios.
Finally, the observation that the yield from fixed income investments is smaller than the growth rate of
liabilities motivated our analysis for the cost of a possible future mismatch between assets and liabilities. We
find that plans that adopted an equities strategy achieved a significantly higher funding ratio in the medium-
and long-term compared to that of plans that adopted a fixed income strategy. We believe that this result
calls for an overhaul of the incentive structure created by the regulatory environment and the market. The
incentives of the investment committee should be aligned with the long-term goals of a pension plan. This
entails a redesign of the regulatory framework so that it favors investments to assets with returns closer to
the rate of increase of the plans’ liabilities.
30
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32
Appendices
A Figures
Figure 8: The figure summarizes the evolution of the number of defined benefit pension plans in the sample.The data are from Compustat, and span a period of twenty years from 1986 until 2014.
500
1000
1500
2000
2500
# of
Pla
ns
1986 1990 1994 1998 2002 2006 2010 2014Year
Figure 9: The figure summarizes the evolution of the average funding ratio of defined benefit pension plansalong with the evolution of the 5th and 95th percentile. The data are from Compustat, and span a period oftwenty years from 1986 until 2014.
.51
1.5
2A
sset
s/Li
abili
ties
1986 1990 1994 1998 2002 2006 2010 2014Year
Recession Funding Ratio
Funding Ratio (5th percentile) Funding Ratio (95th percentile)
33
Figure 10: Percentage allocation of total assets in fixed income (panel a) and equities (b) within pensionplan’s quartiles determined on the basis of their funding ratios. The data are from the Compustat database,and are represented on an annual basis from 2003 until 2014. Over the whole period, the minimum, second,third and maximum quartiles have an average funding ratio of 60%, 75%, 90% and 115% respectively.
3035
4045
50A
lloca
tion
(%)
2003 2005 2007 2009 2011 2013Year
Recession Quartile 1 (min)Quartile 2 Quartile 3Quartile 4 (max)
(a) Fixed Income45
5055
6065
Allo
catio
n (%
)
2003 2005 2007 2009 2011 2013Year
Recession Quartile 1 (min)Quartile 2 Quartile 3Quartile 4 (max)
(b) Equities
Figure 11: The figure summarizes the level in bil. $ of total assets and liabilities for private defined benefitplans. The data are from Compustat, and span a period of twelve years from 1986 until 2014.
010
0020
0030
0040
00Le
vels
1986 1990 1994 1998 2002 2006 2010 2014Year
Recession Assets
Liabilities
34
Figure 12: Percentage of total assets, across all plans within our sample, that is allocated in four asset classes(Fixed Income, Equities, Real Estate and Other). The data are from Compustat, and are represented on anannual basis from 1986 until 2014 for funding ratios and from 2003 until 2014 for asset allocations.
020
4060
Allo
catio
n (%
)
2003 2005 2007 2009 2011 2013Year
Recession Fixed Income (%)Equity (%) Other (%)Real Estate (%)
Figure 13: The figure summarizes the evolution of funding ratio and fixed income and equity allocations beforeand after LDI for plans which at the time when LDI was implemented (∆FIt+1 > 0% and ∆FIt+2 > 0%)where in the underfunded region (f -ratiot > 0.8 and f -ratiot < 1.0). The data are from Compustat, andspan a period of eleven years from 2003 until 2014.
0.78
0.80
0.82
0.84
0.86
0.88
Fun
ding
Rat
io
−5 −4 −3 −2 −1 0 1 2 3 4 5Time
(a) Funding Ratio
3040
5060
70A
lloca
tion
(%)
−5 −4 −3 −2 −1 0 1 2 3 4 5Time
Fixed Income (%) Equities (%)
(b) Asset Allocations
35
Figure 14: The figure summarizes the evolution of funding ratio and fixed income and equity allocationsbefore and after an increase in the allocation to equities (∆EQt+1 > 0% and ∆EQt+2 > 0%) where in theunderfunded region (f -ratiot > 0.8 and f -ratiot < 1.0). The data are from Compustat, and span a period ofeleven years from 2003 until 2014.
0.86
0.88
0.90
0.92
0.94
Fun
ding
Rat
io
−5 −4 −3 −2 −1 0 1 2 3 4 5Time
(a) Funding Ratio30
4050
60A
lloca
tion
(%)
−5 −4 −3 −2 −1 0 1 2 3 4 5Time
Fixed Income (%) Equities (%)
(b) Asset Allocations
Figure 15: The figure summarizes the evolution of funding ratio and equity holdings for a set of startingfunding ratios (funding ratiot=0 = 0.4, 0.6, 0.8, 1.0, 1.2). Parameters: T = 25, µ = 4%, µl = 5%, σ = 30%,α = 0.8, β = 0.9, K = 0.8, λ = 2, ρ = 2%, iterations = 500, 000.
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
1.4
t
Ft
0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
t
Equ
ity A
lloca
tion t
36
B Regressions
B.1 Levels
Table 7: Explanatory regressions. The table summarizes the explanatory power of the level of fundingratio, and a dummy 1(1 < Funding Ratiot−1 < 1.1 ∩ 1.1 < Funding Ratiot < 1.5) on the percentageasset allocation of the current year ((%)Allocationt). The controls are dummies for each of the years 2007(1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level of assets (in bil.), the logarithm ofassets, the return on assets, the level of 1/V olt, and one year lags for the level of assets (in bil.), the level ofallocation, the return on assets, and the level of 1/V olt. Data are from the Compustat private pension plansdatabase and span a period eleven years from 2003 until 2014. All specifications include year and plan fixedeffects. Robust t-statistics adjusted for firm-level clustering are reported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
Funding Ratiot 8.310∗∗∗ -6.676∗∗ -0.610∗∗ -0.901(4.14) (-3.20) (-2.98) (-0.84)
Funding Ratiot−1 -1.129 0.814 0.579∗∗ -0.834(-0.52) (0.34) (2.66) (-0.75)
Assetst 0.081 -0.206 -0.006 0.119(0.57) (-1.44) (-0.23) (1.40)
ln(Assets)t -2.206∗∗ 1.170 0.181∗ 0.953∗(-3.09) (1.58) (2.22) (2.19)
Assets Returnt -14.002∗∗∗ 15.579∗∗∗ 0.160 -2.416+
(-6.64) (6.81) (0.66) (-1.91)Assets Returnt−1 -3.207∗ 2.704+ 0.420+ -1.192
(-2.15) (1.83) (1.84) (-1.17)1(1 < FRt−1 < 1.1 ∩ 1.1 < FRt < 1.5) -2.024∗∗ 1.704∗ 0.022 0.403
(-3.03) (2.38) (0.22) (0.84)1/V olt -0.153 0.189 -0.013 -0.038
(-1.05) (1.29) (-0.66) (-0.45)1/V olt−1 0.108 -0.103 0.039+ -0.075
(0.75) (-0.70) (1.85) (-0.88)Employer Contributionst 3.794∗∗∗ -3.612∗∗ -0.514∗∗ 0.088
(3.56) (-3.13) (-2.84) (0.13)Participant Contributionst -0.245 53.237 -2.584 -61.053∗
(-0.01) (1.23) (-0.52) (-2.49)1(t = 2007)t 1.416∗ -2.133∗∗∗ 0.134+ 0.322
(2.49) (-3.59) (1.86) (0.87)1(t = 2008)t 4.551∗∗∗ -5.951∗∗∗ 0.224∗ 0.705
(5.48) (-6.73) (2.13) (1.40)1(t = 2009)t 3.444∗∗∗ -4.288∗∗∗ 0.022 0.215
(4.12) (-4.90) (0.20) (0.38)Constant 8.301∗∗ 35.492∗∗∗ 0.768∗∗ 6.074∗∗∗
(3.26) (13.37) (3.16) (4.20)N 10741 10741 10368 10733R2 0.34 0.40 0.31 0.22F 79.38 128.59 29.84 21.04FE (Year) YES YES YES YESFE (Plan) YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
37
Table 8: Explanatory regressions. The table summarizes the explanatory power of the level of fundingratio, and a dummy 1(0.7 < Funding Ratiot−1 < 0.9 ∩ 0.4 < Funding Ratiot < 0.7) on the percentageasset allocation of the current year ((%)Allocationt). The controls are dummies for each of the years 2007(1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level of assets (in bil.), the logarithm ofassets, the return on assets, the level of 1/V olt, and one year lags for the level of assets (in bil.), the level ofallocation, the return on assets, and the level of 1/V olt. Data are from the Compustat private pension plansdatabase and span a period eleven years from 2003 until 2014. All specifications include year and plan fixedeffects. Robust t-statistics adjusted for firm-level clustering are reported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
Funding Ratiot 7.476∗∗∗ -5.909∗∗ -0.591∗∗ -0.826(3.71) (-2.85) (-2.87) (-0.77)
Funding Ratiot−1 -0.714 0.431 0.569∗∗ -0.867(-0.33) (0.18) (2.60) (-0.78)
Assetst 0.080 -0.205 -0.006 0.119(0.57) (-1.43) (-0.23) (1.40)
ln(Assets)t -2.204∗∗ 1.169 0.181∗ 0.951∗(-3.09) (1.58) (2.22) (2.18)
Assets Returnt -14.345∗∗∗ 15.927∗∗∗ 0.173 -2.427+
(-6.73) (6.87) (0.70) (-1.88)Assets Returnt−1 -3.155∗ 2.661+ 0.419+ -1.201
(-2.11) (1.80) (1.84) (-1.18)1(0.7 < FRt−1 < 0.9 ∩ 0.4 < FRt < 0.7) -0.938∗ 0.918∗ 0.031 0.007
(-2.37) (2.20) (0.55) (0.02)1/V olt -0.150 0.186 -0.013 -0.037
(-1.03) (1.27) (-0.67) (-0.44)1/V olt−1 0.110 -0.105 0.039+ -0.075
(0.76) (-0.71) (1.85) (-0.87)Employer Contributionst 3.754∗∗∗ -3.581∗∗ -0.514∗∗ 0.101
(3.52) (-3.10) (-2.84) (0.14)Participant Contributionst 0.345 52.673 -2.609 -61.061∗
(0.01) (1.21) (-0.52) (-2.49)1(t = 2007)t 1.393∗ -2.114∗∗∗ 0.134+ 0.328
(2.44) (-3.55) (1.86) (0.88)1(t = 2008)t 4.552∗∗∗ -5.954∗∗∗ 0.223∗ 0.709
(5.49) (-6.74) (2.12) (1.41)1(t = 2009)t 3.492∗∗∗ -4.337∗∗∗ 0.021 0.216
(4.17) (-4.96) (0.19) (0.38)Constant 8.695∗∗∗ 35.177∗∗∗ 0.759∗∗ 6.037∗∗∗
(3.44) (13.28) (3.12) (4.18)N 10741 10741 10368 10733R2 0.34 0.40 0.31 0.22F 79.54 128.88 29.96 21.13FE (Year) YES YES YES YESFE (Plan) YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
38
Table 9: Explanatory regressions. The table summarizes the explanatory power of the level of fundingratio, and a dummy 1(0.1 < Funding Ratiot−1 < 0.7 ∩ 0.7 < Funding Ratiot < 0.9) on the percentageasset allocation of the current year ((%)Allocationt). The controls are dummies for each of the years 2007(1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level of assets (in bil.), the logarithm ofassets, the return on assets, the level of 1/V olt, and one year lags for the level of assets (in bil.), the level ofallocation, the return on assets, and the level of 1/V olt. Data are from the Compustat private pension plansdatabase and span a period eleven years from 2003 until 2014. All specifications include year and plan fixedeffects. Robust t-statistics adjusted for firm-level clustering are reported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
Funding Ratiot 7.856∗∗∗ -6.122∗∗ -0.626∗∗ -0.949(3.91) (-2.94) (-3.06) (-0.88)
Funding Ratiot−1 -0.787 0.195 0.616∗∗ -0.629(-0.36) (0.08) (2.78) (-0.56)
Assetst 0.082 -0.211 -0.006 0.122(0.58) (-1.47) (-0.21) (1.43)
ln(Assets)t -2.198∗∗ 1.171 0.180∗ 0.944∗(-3.08) (1.58) (2.21) (2.17)
Assets Returnt -13.966∗∗∗ 15.605∗∗∗ 0.154 -2.469+
(-6.61) (6.83) (0.63) (-1.95)Assets Returnt−1 -3.176∗ 2.696+ 0.417+ -1.216
(-2.13) (1.83) (1.83) (-1.20)1(0.1 < FRt−1 < 0.7 ∩ 0.7 < FRt < 0.9) 0.236 -0.622+ 0.049 0.300
(0.62) (-1.65) (0.95) (1.35)1/V olt -0.154 0.187 -0.012 -0.036
(-1.05) (1.28) (-0.64) (-0.42)1/V olt−1 0.108 -0.106 0.039+ -0.073
(0.74) (-0.71) (1.87) (-0.85)Employer Contributionst 3.702∗∗∗ -3.493∗∗ -0.518∗∗ 0.072
(3.48) (-3.03) (-2.86) (0.10)Participant Contributionst -0.609 54.196 -2.663 -61.523∗
(-0.02) (1.25) (-0.53) (-2.51)1(t = 2007)t 1.382∗ -2.099∗∗∗ 0.134+ 0.323
(2.42) (-3.53) (1.85) (0.87)1(t = 2008)t 4.507∗∗∗ -5.875∗∗∗ 0.220∗ 0.681
(5.41) (-6.63) (2.09) (1.35)1(t = 2009)t 3.417∗∗∗ -4.231∗∗∗ 0.019 0.193
(4.08) (-4.84) (0.17) (0.34)Constant 8.382∗∗ 35.588∗∗∗ 0.745∗∗ 5.911∗∗∗
(3.29) (13.33) (3.08) (4.07)N 10741 10741 10368 10733R2 0.34 0.40 0.31 0.22F 79.40 128.72 30.14 20.93FE (Year) YES YES YES YESFE (Plan) YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
39
B.2 Interraction with 1/Vol Quintiles
Table 10: Explanatory regressions. The table summarizes the explanatory power of the level of funding ratio,and the interaction between a plan’s funding ratio (1(1 < Funding Ratiot−1 < 1.1∩1.1 < Funding Ratiot <1.5)) with the quintile of its distance to insolvency (∆(1/V ol)t) on the percentage asset allocation of thecurrent year ((%)Allocationt). The controls are dummies for each of the years 2007 (1(t = 2007)), 2008(1(t = 2008)), and 2009 (1(t = 2009)), the level of assets (in bil.), the logarithm of assets, the return onassets, the level of 1/V olt, and one year lags for the level of assets (in bil.), the level of allocation, the returnon assets, and the level of 1/V olt. Data are from the Compustat private pension plans database and spana period eleven years from 2003 until 2014. All specifications include year and plan fixed effects. Robustt-statistics adjusted for firm-level clustering are reported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
Funding Ratiot 8.035∗∗∗ -6.379∗∗ -0.610∗∗ -0.931(4.02) (-3.09) (-3.00) (-0.86)
Funding Ratiot−1 -1.014 0.687 0.579∗∗ -0.818(-0.47) (0.29) (2.66) (-0.73)
Assetst 0.078 -0.204 -0.006 0.120(0.55) (-1.42) (-0.23) (1.41)
ln(Assets)t -2.199∗∗ 1.160 0.181∗ 0.955∗(-3.08) (1.56) (2.22) (2.20)
Assets Returnt -13.963∗∗∗ 15.527∗∗∗ 0.160 -2.398+
(-6.60) (6.79) (0.66) (-1.90)Assets Returnt−1 -3.181∗ 2.669+ 0.420+ -1.183
(-2.13) (1.81) (1.84) (-1.16)1(1 < FRt−1 < 1.1 ∩ 1.1 < FRt < 1.5)× 1((1/V ol)t−1 ∈ Bin-1) 1.850 -1.724 0.032 0.257
(1.08) (-0.86) (0.25) (0.39)1(1 < FRt−1 < 1.1 ∩ 1.1 < FRt < 1.5)× 1((1/V ol)t−1 ∈ Bin-5) -2.359∗ 0.855 0.044 1.777∗
(-2.53) (0.87) (0.20) (2.33)1/V olt -0.152 0.190 -0.013 -0.039
(-1.05) (1.29) (-0.66) (-0.46)1/V olt−1 0.121 -0.109 0.039+ -0.083
(0.84) (-0.73) (1.84) (-0.97)Employer Contributionst 3.788∗∗∗ -3.580∗∗ -0.514∗∗ 0.060
(3.56) (-3.10) (-2.84) (0.09)Participant Contributionst -0.086 53.226 -2.590 -61.258∗
(-0.00) (1.23) (-0.52) (-2.50)1(t = 2007)t 1.398∗ -2.114∗∗∗ 0.134+ 0.322
(2.45) (-3.55) (1.86) (0.87)1(t = 2008)t 4.541∗∗∗ -5.937∗∗∗ 0.224∗ 0.701
(5.47) (-6.71) (2.13) (1.39)1(t = 2009)t 3.462∗∗∗ -4.295∗∗∗ 0.022 0.203
(4.13) (-4.90) (0.20) (0.36)Constant 8.384∗∗∗ 35.374∗∗∗ 0.768∗∗ 6.118∗∗∗
(3.30) (13.31) (3.16) (4.23)N 10741 10741 10368 10733R2 0.34 0.40 0.31 0.22F 76.96 123.31 28.93 20.41FE (Year) YES YES YES YESFE (Plan) YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
40
Table 11: Explanatory regressions. The table summarizes the explanatory power of the level of fund-ing ratio, and the interaction between a plan’s funding ratio (1(0.7 < Funding Ratiot−1 < 0.9 ∩ 0.4 <Funding Ratiot < 0.7)) with the quintile of its distance to insolvency (∆(1/V ol)t) on the percentage as-set allocation of the current year ((%)Allocationt). The controls are dummies for each of the years 2007(1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level of assets (in bil.), the logarithm ofassets, the return on assets, the level of 1/V olt, and one year lags for the level of assets (in bil.), the level ofallocation, the return on assets, and the level of 1/V olt. Data are from the Compustat private pension plansdatabase and span a period eleven years from 2003 until 2014. All specifications include year and plan fixedeffects. Robust t-statistics adjusted for firm-level clustering are reported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
Funding Ratiot 7.754∗∗∗ -6.207∗∗ -0.586∗∗ -0.835(3.88) (-3.00) (-2.87) (-0.78)
Funding Ratiot−1 -0.870 0.600 0.570∗∗ -0.870(-0.40) (0.25) (2.62) (-0.78)
Assetst 0.080 -0.205 -0.006 0.118(0.56) (-1.43) (-0.21) (1.39)
ln(Assets)t -2.204∗∗ 1.167 0.180∗ 0.952∗(-3.09) (1.57) (2.21) (2.19)
Assets Returnt -14.195∗∗∗ 15.752∗∗∗ 0.191 -2.451+
(-6.68) (6.85) (0.78) (-1.93)Assets Returnt−1 -3.148∗ 2.654+ 0.416+ -1.195
(-2.11) (1.80) (1.82) (-1.18)1(0.7 < FRt−1 < 0.9 ∩ 0.4 < FRt < 0.7)× 1((1/V ol)t−1 ∈ Bin-1) -1.086+ 0.789 -0.012 0.248
(-1.74) (1.07) (-0.10) (0.45)1(0.7 < FRt−1 < 0.9 ∩ 0.4 < FRt < 0.7)× 1((1/V ol)t−1 ∈ Bin-5) -1.225+ 1.220+ 0.296∗ -0.420
(-1.75) (1.83) (2.21) (-0.83)1/V olt -0.152 0.190 -0.012 -0.040
(-1.04) (1.29) (-0.60) (-0.48)1/V olt−1 0.105 -0.104 0.036+ -0.068
(0.73) (-0.70) (1.74) (-0.79)Employer Contributionst 3.741∗∗∗ -3.569∗∗ -0.517∗∗ 0.107
(3.50) (-3.08) (-2.86) (0.15)Participant Contributionst 0.296 52.735 -2.698 -60.930∗
(0.01) (1.22) (-0.54) (-2.49)1(t = 2007)t 1.381∗ -2.101∗∗∗ 0.137+ 0.322
(2.42) (-3.53) (1.91) (0.87)1(t = 2008)t 4.515∗∗∗ -5.917∗∗∗ 0.229∗ 0.701
(5.44) (-6.69) (2.18) (1.39)1(t = 2009)t 3.462∗∗∗ -4.309∗∗∗ 0.015 0.230
(4.13) (-4.92) (0.14) (0.41)Constant 8.590∗∗∗ 35.276∗∗∗ 0.755∗∗ 6.039∗∗∗
(3.39) (13.29) (3.11) (4.17)N 10741 10741 10368 10733R2 0.34 0.40 0.31 0.22F 76.00 123.24 28.72 20.01FE (Year) YES YES YES YESFE (Plan) YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
41
Table 12: Explanatory regressions. The table summarizes the explanatory power of the level of fund-ing ratio, and the interaction between a plan’s funding ratio (1(0.1 < Funding Ratiot−1 < 0.7 ∩ 0.7 <Funding Ratiot < 0.9)) with the quintile of its distance to insolvency (∆(1/V ol)t) on the percentage as-set allocation of the current year ((%)Allocationt). The controls are dummies for each of the years 2007(1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level of assets (in bil.), the logarithm ofassets, the return on assets, the level of 1/V olt, and one year lags for the level of assets (in bil.), the level ofallocation, the return on assets, and the level of 1/V olt. Data are from the Compustat private pension plansdatabase and span a period eleven years from 2003 until 2014. All specifications include year and plan fixedeffects. Robust t-statistics adjusted for firm-level clustering are reported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
Funding Ratiot 7.956∗∗∗ -6.265∗∗ -0.614∗∗ -0.915(3.97) (-3.03) (-3.02) (-0.85)
Funding Ratiot−1 -0.994 0.449 0.576∗∗ -0.639(-0.46) (0.18) (2.64) (-0.57)
Assetst 0.079 -0.210 -0.007 0.125(0.56) (-1.47) (-0.25) (1.47)
ln(Assets)t -2.191∗∗ 1.163 0.184∗ 0.939∗(-3.07) (1.57) (2.26) (2.16)
Assets Returnt -13.924∗∗∗ 15.601∗∗∗ 0.166 -2.516∗(-6.59) (6.83) (0.68) (-1.99)
Assets Returnt−1 -3.166∗ 2.673+ 0.417+ -1.199(-2.12) (1.81) (1.82) (-1.18)
1(0.1 < FRt−1 < 0.7 ∩ 0.7 < FRt < 0.9)× 1((1/V ol)t−1 ∈ Bin-1) 0.057 -0.330 0.153+ 0.009(0.08) (-0.51) (1.69) (0.02)
1(0.1 < FRt−1 < 0.7 ∩ 0.7 < FRt < 0.9)× 1((1/V ol)t−1 ∈ Bin-5) -0.240 -1.387 -0.214+ 1.716∗(-0.31) (-1.60) (-1.89) (2.27)
1/V olt -0.155 0.189 -0.012 -0.037(-1.06) (1.29) (-0.63) (-0.44)
1/V olt−1 0.110 -0.090 0.044∗ -0.095(0.76) (-0.60) (2.09) (-1.10)
Employer Contributionst 3.743∗∗∗ -3.472∗∗ -0.496∗∗ -0.010(3.52) (-3.01) (-2.74) (-0.01)
Participant Contributionst -0.101 54.142 -2.485 -62.109∗(-0.00) (1.25) (-0.50) (-2.53)
1(t = 2007)t 1.385∗ -2.106∗∗∗ 0.132+ 0.330(2.43) (-3.54) (1.83) (0.89)
1(t = 2008)t 4.536∗∗∗ -5.885∗∗∗ 0.228∗ 0.656(5.45) (-6.65) (2.16) (1.30)
1(t = 2009)t 3.450∗∗∗ -4.208∗∗∗ 0.036 0.121(4.12) (-4.81) (0.33) (0.22)
Constant 8.482∗∗∗ 35.403∗∗∗ 0.755∗∗ 5.984∗∗∗(3.34) (13.32) (3.11) (4.12)
N 10741 10741 10368 10733R2 0.34 0.40 0.31 0.22F 76.03 123.11 28.70 20.34FE (Year) YES YES YES YESFE (Plan) YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
42
Table 13: Explanatory power of four different regions of funding ratios: (1) 1(1.2 < Funding Ratiot−1∩0.8 <Funding Ratiot < 1.2), (2) 1(0.8 < Funding Ratiot−1 < 1.2 ∩ 1.2 < Funding Ratiot) , (3) 1(0.7 <Funding Ratiot−1 < 0.8 ∩ 0.4 < Funding Ratiot < 0.7), and (4) 1(0.4 < Funding Ratiot−1 < 0.7 ∩ 0.7 <Funding Ratiot < 0.8) interacted with the quintile of CEO’s accumulated pension benefits as a percentageof their salary (pensCEO) on the percentage asset allocation of the current year ((%)Allocationt). Thereported coefficients are from four different regression specifications with controls that include Funding Ratiot,dummies for each of the years 2007 (1(t = 2007)), 2008 (1(t = 2008)), and 2009 (1(t = 2009)), the level ofassets (in bil.), the logarithm of assets, the return on assets, the level of 1/V olt, and one year lags for thelevel of assets (in bil.), the level of allocation, the return on assets, and the level of 1/V olt. Data are fromthe Compustat private pension plans database and span a period eleven years from 2003 until 2014. Allspecifications include year and plan fixed effects. Robust t-statistics adjusted for firm-level clustering arereported in parentheses.
(1) (2) (3) (4)FIt EQt REt OTHt
1(1.2 < FRt−1 ∩ 0.8 < FRt < 1.2)× 1((pensCEO)t−1 ∈ Bin-1) 10.321+ -8.615 0.210 -1.770(1.88) (-1.51) (0.27) (-1.32)
1(1.2 < FRt−1 ∩ 0.8 < FRt < 1.2)× 1((pensCEO)t−1 ∈ Bin-5) -3.170 -0.201 -0.852∗ 4.422∗∗(-0.81) (-0.05) (-2.06) (2.69)
1(0.8 < FRt−1 < 1.2 ∩ 1.2 < FRt)× 1((pensCEO)t−1 ∈ Bin-1) -0.744 2.807 -0.021 -1.995+
(-0.41) (1.22) (-0.08) (-1.82)1(0.8 < FRt−1 < 1.2 ∩ 1.2 < FRt)× 1((pensCEO)t−1 ∈ Bin-5) -4.405 6.679∗ 0.422 -2.984
(-1.30) (2.17) (1.62) (-0.98)1(0.7 < FRt−1 < 0.8 ∩ 0.4 < FRt < 0.7)× 1((pensCEO)t−1 ∈ Bin-1) -0.279 -0.481 0.151 0.568
(-0.16) (-0.29) (0.42) (0.71)1(0.7 < FRt−1 < 0.8 ∩ 0.4 < FRt < 0.7)× 1((pensCEO)t−1 ∈ Bin-5) -2.939 1.175 -0.118 2.053
(-1.50) (0.62) (-0.87) (1.27)1(0.4 < FRt−1 < 0.7 ∩ 0.7 < FRt < 0.8)× 1((pensCEO)t−1 ∈ Bin-1) -2.231∗ 1.996∗ -0.108 0.289
(-2.53) (1.97) (-0.53) (0.39)1(0.4 < FRt−1 < 0.7 ∩ 0.7 < FRt < 0.8)× 1((pensCEO)t−1 ∈ Bin-5) -1.012 -2.833 -0.358 3.970+
(-0.65) (-1.54) (-1.22) (1.89)t-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
43
C Mathematical Proofs
Proof of Lemma 1: We define Ft = AtLt
. Using Ito’s Lemma, and the dynamics (6) and (7) we obtain:
dFt =(∂F
∂t
)dt+
(∂F
∂At
)dAt +
(∂F
∂Lt
)dLt
+ 12
(∂2Ft∂A2
t
)(dAt)2 + 1
2
(∂2Ft∂L2
t
)(dLt)2 +
(∂2Ft∂At∂Lt
)dAtdLt
= Ft
((dAtAt
)−(dLtLt
)+(dLtLt
)2−(dAtAt
)(dLtLt
))
Since in our specification(dLtLt
)2=(dAtAt
)(dLtLt
)= 0, we immediately obtain the stated result.
Proof of Proposition 1: Let UB(x) = −λ (K − x)β denote the value of the utility function below K and
UA(x) = (x−K)α the value of the utility function above K.
We first consider the case x < K. Since UB(x) is convex in x, a corollary of the Weirestrass theorem
implies that UB(x) reaches its maximum value at one of the boundaries of the interval ]0,K]. If we let xb
denote the optimal solution of (13) when x ≤ K, then xb = 0 or xb = K.
Next, we consider the case x ≥ K. The function UA(x) is concave. Let L : R −→ R be the Legendre-
Fenchel transform of the pension plan’s problem (13). L is thus defined as:
L(πT ) = Supx≥0U(x)− δπTx (19)
for δ > 0. Let xa denote the optimal solution of (19). The KKT conditions of (19) are given by
U′
A(xa) = δπT − γ
γxa = 0
for γ > 0 being the Lagrange multiplier associated with the non-negativity constraint x ≥ 0. Solving the
system immediately leads to
xa = K +(
α
δπT
) 1α−1
It remains to determine which of xa and xb corresponds to the global optimum. Let LA and LB stand for
44
the values of the function L associated with xa and xb respectively. If xb = K, then
LA − LB = (U(xa)− δπTxa)− (U(xb)− δπTxb)
=(
α
δπT
) α1−α
(1− α)
> 0
where the last inequality follows from the fact that since 0 < α < 1, πT > 0 and δ > 0. Next, let xb = 0. The
same procedure leads to:
LA − LB = (U(xa)− δπTxa)− (U(xb)− δπTxb)
= f(πT ;α, γ,K, β, λ)
where
f(πT ;α, γ,K, β, λ) =(
α
δπT
) α1−α
− δπTK + λKβ
We first observe that f(πT ) > 0 when πT ≤ λδK
β−1. Moreover, since f ′(πT ) < 0 we know that f is a
decreasing function of πT . If we further observe that limπT→∞ f(πT ) = −∞, then by Bolzano’s Theorem we
know that there exists a unique π ∈ R+ such that f(π) = 0. That is, π must satisfy
( αδπ
) α1−α (1− α)− δπK + λKβ = 0
It follows that if we let F ∗T be the global optimum argument of the convex conjugate problem (19), we have
F ∗T =
K +
(αδπT
) 11−α if πT < π
0 if πT ≥ π
where π solves: ( αδπ
) α1−α (1− α)− δπK + λKβ = 0 (20)
and δ solves:
E
πTπ0F ∗T
= F ∗0 (21)
To finish the proof, it remains to show that F ∗T also corresponds to the global optimum of the original pension
45
plan’s problem (13). Let us assume that FT is any optimal solution of (13). We have
E U(F ∗T )− U(FT ) = E U(F ∗T )− U(FT )+ δπTF0 − δπTF0
≥ E U(F ∗T )− U(FT )+ δE πTFT + δE πTF ∗T
= 0
which concludes the proof.
Proof of Proposition 2: Indeed, we have
Ftπt = Et FTπT
Ft = Et
πTπtFT
= E
πTπt
(K +
(πT δ
α
) 1α−1)
1πT<π
(22)
Next, from (9) we know that
πTπt
= exp
(−(r − µL)(T − t)− 1
2
∫ T
t
θ2sds−
∫ T
t
θsdWs
)
and it thus follows that log(πT )− log(πt) is normally distributed as:
log(πT )− log(πt) ∼ N(−(r − µL + 1
2θ2)(T − t), θ2(T − t)
)
Using this result, we can compute the two terms of (22) as:
KEt
πTπt
1πT<π
= Ke−(r−µL)(T−t)Φ(d1) (23)
with
d1 =ln(ππt
)+(r − µL − θ2
2
)(T − t)
θ√T − t
(24)
and
Et
πTπt
(πT δ
α
) 1α−1
1πT<π
=(δπtα
) 1α−1
e−αα−1 (r−µL+ 1
2 θ2)(T−t)+ 1
2 ( θαα−1 )2(T−t)Φ(d2) (25)
with
d2 = d1 −θ√T − t
α− 1 (26)
46
Combining (23) and (25) in (22), we obtain the stated result.
Proof of Proposition 3: By Ito’s lemma, we have
dFt =(∂Ft∂t
+ 12∂2Ft∂π2
t
)dt+
(∂Ft∂πt
)dπt
=(∂Ft∂t
+ 12∂2Ft∂π2
t
− (r − µL)πt)dt−
(∂Ft∂πt
)πtθdWt
We also have
dFt = Ft (r − µL + (µ− r)ut) dt+ Ft (utσ) dWt
from which we obtain
ut = −σ−1θ
Ft
(∂Ft∂πt
)πt
which can be explicitely computed using (16), providing the stated result.
47