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: kyriakos.chousakos@yale.edu‡Doctoral student at Yale School of Management. Email: garence.staraci@yale.edu

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.

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(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

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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

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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.

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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).

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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

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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).

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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.

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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)).

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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

References

Addoum, Jawad M, Jules H Van Binsbergen, and Michael W Brandt, 2010, Asset allocation and managerial

assumptions in corporate pension plans, Available at SSRN 1710902 .

Almeida, Heitor, Murillo Campello, and Michael S Weisbach, 2011, Corporate financial and investment

policies when future financing is not frictionless, Journal of Corporate Finance 17, 675–693.

An, Heng, Zhaodan Huang, and Ting Zhang, 2013, What determines corporate pension fund risk-taking

strategy?, Journal of Banking & Finance 37, 597–613.

Anantharaman, Divya, and Yong Gyu Lee, 2014, Managerial risk taking incentives and corporate pension

policy, Journal of Financial Economics 111, 328–351.

Atkeson, Andrew G, Andrea L Eisfeldt, and Pierre-Olivier Weill, 2013, Measuring the financial soundness of

us firms, 1926-2012, Technical report, National Bureau of Economic Research.

Barberis, Nicholas, 2000, Investing for the long run when returns are predictable, The Journal of Finance 55,

225–264.

Barberis, Nicholas, Ming Huang, Tano Santos, et al., 2001, Prospect theory and asset prices, The Quarterly

Journal of Economics 116, 1–53.

Black, Fischer, 1980, The tax consequences of long-run pension policy, Financial Analysts Journal 36, 21–28.

Campbell, John, George Chacko, Jorge Rodriguez, and Luis Viceira, 2004, Strategic asset allocation in a

continuous-time var model, Journal of Economic Dynamics and Control 28, 2195–2214.

Campbell, John Y., and Luis M. Viceira, 1999, Consumption and portfolio decisions when expected returns

are time varying, The Quarterly Journal of Economics 114, 433–495.

Cheng, Qiang, and Laura Michalski, 2011, Contributions to defined benefit pension plans: Economic and

accounting determinants, American Accounting Association Annual Meeting. Research Collection School

Of Accountancy .

Coronado, Julia, and Nellie Liang, 2006, Chapter: The influence of pbgc insurance on pension fund finances,

Restructuring Retirement Risks 88–108.

Froot, Kenneth A, David S Scharfstein, and Jeremy C Stein, 1993, Risk management: Coordinating corporate

investment and financing policies, the Journal of Finance 48, 1629–1658.

Harrison, J Michael, and William F Sharpe, 1983, Optimal funding and asset allocation rules for defined-

31

benefit pension plans, in Financial aspects of the United States pension system, 91–106 (University of

Chicago Press).

Kahneman, Daniel, and Amos Tversky, 1979, Prospect theory: An analysis of decision under risk, Economet-

rica: Journal of the econometric society 263–291.

Karatzas, Ioannis, John P Lehoczky, and Steven E Shreve, 1987, Optimal portfolio and consumption decisions

for a small investor on a finite horizon, SIAM journal on control and optimization 25, 1557–1586.

Karatzas, Ioannis, and Steven E Shreve, 1998, Methods of mathematical finance, volume 39 (Springer Science

& Business Media).

Merton, Robert C., 1969, Lifetime portfolio selection under uncertainty: The continuous-time case, The

Review of Economics and Statistics 51, 247–257.

Merton, Robert C., 1971, Optimum consumption and portfolio rules in a continuous-time mode, Journal of

Economic Theory 3, 373–413.

Rauh, Joshua D, 2006, Investment and financing constraints: Evidence from the funding of corporate pension

plans, The Journal of Finance 61, 33–71.

Rauh, Joshua D, 2009, Risk shifting versus risk management: investment policy in corporate pension plans,

Review of Financial Studies 22, 2687–2733.

RBC Group, USA Wealth Management, 2016, Establishing an investment committee for your company’s

retirement plan, Technical report, RBC Wealth Management.

Sharpe, William F, 1976, Corporate pension funding policy, Journal of financial Economics 3, 183–193.

Smith, Clifford W, and Rene M Stulz, 1985, The determinants of firms’ hedging policies, Journal of financial

and quantitative analysis 20, 391–405.

Tepper, Irwin, 1981, Taxation and corporate pension policy, The Journal of Finance 36, 1–13.

Thaler, R. H., and E. J. Johnson, 1990, Gambling with the house money and trying to break even: The

effects of prior outcomes on risky choice, Management Science 36, 643–660.

Treynor, Jack L, 1977, The principles of corporate pension finance, Journal of Finance 32, 627–38.

van Binsbergen, Jules, and Michael W. Brandt, 2016, Chapter: Optimal asset allocation in asset liability

management, Handbook of Fixed-Income Securities 147–166.

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