Asset Allocation and Managerial Assumptions in

Corporate Pension Plans∗

Jawad M. AddoumDuke University†

Jules H. van BinsbergenStanford University‡

Michael W. BrandtDuke University§

and NBER

June 2010

Abstract

We empirically examine the effect of regulations on pension decision-making. Wefind that in the face of mandatory contributions, pension plans alter their assetallocations and increase their risk taking to avoid mandatory contributions. Thisbehavior resembles gambling for resurrection. We also examine the effect of reg-ulations on pension accounting assumptions affecting net income. We find thatplan sponsors increase their assumed rates of return on plan assets when subject topension-related costs. The evidence supports an earnings-management interpreta-tion. Finally, we examine whether pension fund managers are tactical in their assetallocations. We find that pension fund managers are active as an investor class, butdo not seem to time the market in a manner consistent with return predictability.

∗We thank Josh Rauh for providing the Pensions & Investments data. We also thank Alon Brav, HowardKung, Justin Murfin, and participants of the Duke Finance Brownbag Seminar for helpful comments.†Fuqua School of Business. Durham, NC 27708. Phone: 919-660-7628. Email: jawad.addoum@duke.edu.‡Graduate School of Business. Palo Alto, CA 94305. Phone: 650-721-1353. Email: jvb2@gsb.stanford.edu.§Fuqua School of Business. Durham, NC 27708. Phone: 919-660-1948. Email: mbrandt@duke.edu

1 Introduction

Pension plans account for a large fraction of global institutional investment holdings. In 2008,

$24.0 trillion of global institutional holdings was held by pension plans, making up 39% of the

total. $15.3 trillion of these holdings were held in U.S. sponsored plans. In comparison with

mutual and insurance funds, U.S. pension holdings comprise over 97% of the assets in these

classes combined.1 Given the importance of pension funds as an investor class, it is surprising

how little attention has been paid to unique features of pension funds in the academic literature.

We focus our analysis on privately sponsored U.S. defined benefit (DB) pension plans, a

group with $1.9 trillion in assets as of the end of 2003 (see Buessing and Soto (2006)). Our

analysis surrounds the determinants of decision-making in private DB pension plans. In doing

so, we examine a number of related questions.

First, we examine the effect of regulations on the investment choice of pension plans. We

focus our analysis on the effect of regulations on asset allocation decisions and managerial

assumptions. Exploiting within-firm funding status variation and precise knowledge of sharp

institutional discontinuities in the function determining plan sponsors’ mandatory contributions,

we obtain causal estimates of the effect of regulatory funding rules on asset allocation decisions.

Our approach is similar to the standard regression discontinuity design described by Hahn, Todd,

and van der Klaauw (2001), Imbens and Lemieux (2007), and Lee and Lemieux (2009), and

applied by Angrist and Lavy (1999), van der Klaauw (2002), Rauh (2006), Chava and Roberts

(2008), Lee (2008), and Roberts and Sufi (2009). We find that regulatory funding rules affect

asset allocation decisions in a statistically and economically significant way. Fund managers

appear to increase the riskiness of portfolios when approaching an underfunded status of 20% of

liabilities from below, a result we interpret as an attempt to increase the ex ante probability of

ending the plan year above the 20% threshold.2 We find similar results around the mandatory

funding threshold where plans go from overfunded to underfunded status. As in the latter case

a milder form of contributions are mandated, the effect we find is smaller.

We also apply the regression discontinuity approach to investigate whether regulations have

an observable effect on manager-controlled pension accounting assumptions. Specifically, we

examine the effects of the mandatory contribution rules described above, as well as accounting

rules dictating amortization charges, on the assumed rate of return on plan assets, an assumption

with a direct effect on firms’ income. We find that when plan sponsors are subject to mandatory

amortization charges that hurt income, there is an economically and statistically significant

positive effect on the assumed rate of return on pension assets when considering within-industry

variation. Considering only within-firm variation, we find that this effect is most pronounced

1Fund Management 2009, International Financial Services, London.2Having more than 20% of liabilities underfunded automatically subjects plan sponsors to relatively severe

mandatory additional contributions to the plan. For further details, see section 3.1.

2

when firms experience further decreases in funding status in the year following events leading

to income-hurting amortization charges. We find similar results when we consider the effect of

mandatory contribution function discontinuities. Namely, we find an effect on the assumed rate

of return that is consistent with income-smoothing manipulation only when we consider plans

around the institutionally critical 20% underfunded threshold.

Finally, we examine whether pension fund managers are tactical in their asset allocation

decisions and time the market. We find that investment managers do not seem to react to

changes in the investment opportunity set, as measured by the level of the price-dividend ratio.

Recent contributions examining mutual fund managers’ market timing ability include those of

Jiang, Yao, and Yu (2007) and Drish and Sagi (2008), with both papers coming to opposite

conclusions. For hedge funds, Fung, Xu, and Yau (2002) find no evidence of market timing abil-

ity, a conclusion shared by Graham and Harvey (1996) in the context of investment newsletter

recommendations. To our knowledge, just two studies address the question of market timing

ability in pension plans. First, Coggin, Fabozzi, and Rahman (1993) study the market timing

ability of pension fund managers using return-based measures on a small sample of U.S. pension

funds, with the conclusion that the average timing measure is negative. One major drawback

of their approach is that nonlinear relations between fund and market returns may be due to

reasons other than market timing, such as the dynamic trading effect proposed by Jagannathan

and Korajczyk (1986). By using holdings-based tests, we avoid this potential pitfall. Second,

Blake, Lehmann, and Timmermann (1999) study asset allocation dynamics using a sample of

monthly portfolio holdings for 306 U.K. pension plans. However, as pointed out by the authors

themselves, many of the conclusions of their analysis do not apply to U.S. pensions, where the

regulatory environment and competitiveness of the fund management industry are very different

than in the U.K.

Manipulation of the assumed rate of return on plan assets provides a possible explanation

for why underfunded pension plans underperform compared to overfunded plans, as obverved

by Franzoni and Marin (2006). Franzoni and Marin attribute their result to an anomaly similar

to post-earnings-announcement-drift3: market participants do not fully comprehend the auto-

correlated nature of mandatory contributions for firms with highly underfunded plans, therefore

delaying the adjustment of equity prices to proper relative values. Manipulation of the assumed

rate of return around the 20% underfunding discontinuity provides a channel for why the in-

formation in mandatory contributions may not be fully impounded into prices; firm managers

may be able to offset such adjustments by inflating the assumed rate of return on plan assets,

and in turn, net income.

There is a long standing, yet relatively sparse, literature on pension plan portfolio choice.

Sharpe (1976) and Treynor (1977) argue that in the context of DB pension plans, the portfolio

3See Ball and Brown (1968), Bernard and Thomas (1989, 1990).

3

choice problem is fraught with moral hazard issues. Both authors show that firm management

can maximize shareholder wealth by increasing the risk of asset holdings, through investments in

equity. Black (1980) and Tepper (1981) temper this motivation for equity investment, examining

the impact of taxes on optimal pension investment policy. In contrast to prior results, they

argue that the tax-exempt status of pension funds suggests use of pension arbitrage: firms

issuing debt to fund pension obligations, and investing pension assets entirely in debt. Rauh

(2009) examines these offsetting theories empirically, with the conclusion that, in general, risk

management incentives seem to dominate risk shifting overall.

More recently, van Binsbergen and Brandt (2007) consider a generalized asset liability man-

agement problem in which pension fund managers derive utility from their expected future

funding ratio, and experience disutility when their funds are subject to mandatory additional

funding contributions (AFCs) due to being underfunded. In the model, the presence of AFCs

leads to perverse investment behavior.

Another more recent strand of the literature utilizes data on private DB pension plans as a

laboratory for examining traditional issues in the finance literature. As described above, Rauh

(2006) relates mandatory pension contributions to sponsors’ capital expenditures. Franzoni

and Marin (2006) document an asset pricing anomaly attributable to heterogeneity in pension

funding status, and Bergstresser, Desai, and Rauh (2006) are the first to examine earnings

management through pension accounting assumptions.

The remainder of the paper proceeds as follows: Section 2 describes the data used in our

study. Section 3 examines asset allocation decisions in the face of mandatory contribution

discontinuities, while section 4 extends this analysis to pension accounting assumptions and

accounting rules. Section 5 examines the question of whether pension fund managers engage in

tactical asset allocation. Section 6 concludes the paper.

2 Data

Our study makes use of three data sets: (1) asset allocations from corporate plan sponsors’ IRS

Form 5500 filings, (2) Pensions & Investments survey-based asset allocations for the largest cor-

porate sponsors of defined benefit pension plans, and (3) Compustat’s Annual Pension database,

providing pension data from SEC filings. As in Rauh (2009), the two sets of pension asset al-

location data are almost mutually exclusive, for reasons that are outlined below.

2.1 IRS Form 5500 Data

The most comprehensive data on corporate pension plans are contained in the electronic

database comprised of plan sponsors’ IRS Form 5500 filings. Annual filing of the Form 5500

is mandatory for all firms with employer-sponsored benefit plans and at least one hundred em-

4

ployees. The data is made publically available through the United States Department of Labor

(DOL). A typical filing consists of the main Form 5500, numerous schedules, and in some cases,

a number of sponsor-prepared hard-copy attachments. The electronic database made available

by the DOL includes the contents of the main Form 5500 and of all corresponding schedules.

However, the contents of hard-copy attachments are available only for in-person viewing at the

Reading Room. At the time of writing, the DOL made available filings for plan years (corre-

sponding to calendar years) 1990 to 2007. However, the electronic files for plan years 1990 to

1991 do not contain all of the asset allocation variables requisite to our study, and so our sample

covers only plan years 1992 through 2007.

For plan years 1992 to 1998, asset allocations appears on the main Form 5500, where plan

assets at the beginning and end of the plan year are classified into standardized categories.

The same information on plan assets can be found in Schedule H of filings for plan years 1999

to 2007. The form contains many standardized asset classes. IRS filing regulations also allow

plan sponsors to categorize the assets in less transparent categories such as common/collective

trusts, pooled separate accounts, master trusts, 103-12 investment entities, or interests held

with registered investment companies.4 We find that, in general, it is the sponsors of the

largest pension plans that elect to categorize assets in these less transparent categories.

In constructing the IRS Form 5500 data set used in the study, we apply a series of filters.

Form 5500 filers include sponsors of defined benefit and defined contribution pensions, as well as

employee stock option and other forms of employee benefit plans. First, we only keep observa-

tions corresponding to defined benefit pension plans, the subject of our study. Next, we require

all plan year observations to have non-negative beginning-of-year (BOY) and end-of-year (EOY)

total assets and actuarial liability. Further, we impose the requirement that reported BOY and

EOY holdings in all asset class categories are non-negative, to account for pension plans’ in-

ability to take short positions. Finally, we require that all observations have information on

sponsor contributions to the plan during the year, as well as a determinate and non-negative

active share of participants.5

Table 1 presents summary statistics for the IRS Form 5500 data set. Panel A outlines the

statistics for the entire data set, subjected to those requirements in the preceding paragraph,

and for which the plan’s entire holdings are not composed of insurance contracts. Panel B

displays the same statistics as Panel A, but with the additional requirement that holdings in

4Sponsors are required to further categorize the assets held in these categories into more transparent as-set classes. However, these further categorizations are contained in sponsor-prepared hard-copy attachmentsunavailable in the electronic data.

5The active share of participants is calculated as the BOY total active participant count divided by the BOYtotal number of participants who are active, retired, separated from the company but entitled to future benefits,or widowers of one of the above categories. Therefore, an indeterminate calculated active share of participantsindicates a total participant count of zero, indicating either a recording error, or a plan in which we are notinterested.

5

opaque investment categories amount to less than 5% of total assets. It is the sample described

in Panel B that forms the basis for our tests in the remainder of the paper.

The full sample of IRS Form 5500 data consists of 150,697 plan-year observations, consisting

of 25,600 unique plans (identified by unique Employer Identification Number (EIN) and plan

number combinations) sponsored by 18,391 unique employers (identified by unique EIN). The

estimation sample consists of 34,364 plan-year observations, made up of observations on 7,864

unique plans sponsored by 7,235 unique employers.

Comparing the summary statistics across the samples, the mean pension asset observation

more than halves, from $113.28 million to $49.43 million, when removing from the sample

observations with more than 5% of pension assets in opaque investment categories. Mean plan

liabilities correspondingly decrease from $106.71 million to $47.32 million. The resultant mean

and median values of the plan funding status are relatively constant between the samples, with

the mean dropping from 0.084 to 0.078 and the median falling to 0.013 from 0.015.6 Consistent

with a drop in plan size when moving from the full to the estimation sample, contributions and

actuarial normal costs7 also drop, with the distribution of both variables tightening significantly.

In addition to funding status, Table 1 provides other descriptive statistics, including the

plan investment return (calculated as a plan’s investment income divided by BOY assets), ratio

of contributions to plan assets, and active share of participants. Like the funding status, the

distribution of these ratios remains fairly consistent across the two samples. Distributions of all

variables are winsorized at the 1% level in order to reduce the effects of outliers on our results.

Asset allocation statistics are also provided in Table 1. The allocation to corporate equity

is defined as holdings in both common and preferred stocks. Government debt includes all

government issued fixed-income securities, as well as certificates of deposit. Holdings in in-

surance company accounts represent arrangements in which insurance companies contract to

provide future annuity payments to plan participants, the initial price of which is recorded by

the plan sponsor as being held in the issuing insurance company’s general accounts. Cash hold-

ings include interest- and non-interest-bearing cash holdings, including cash held in checking,

savings, and money market accounts. Finally, all holdings in other asset classes are aggregated

and reported together. In panel A, these other asset class holdings, which include holdings

in opaque asset classes, make up 56.35% of holdings at the mean. In the estimation sample

outlined in panel B, this figure declines to 1.31% (0% at the median) after eliminating obser-

vations with more than 5% of holdings in opaque asset classes. Allocation statistics as a share

of non-insurance assets are also provided in Table 1, for purposes of comparability with the

Pensions & Investments data described in the next section.

6Plan funding status is calculated as: Plan Assets − Plan LiabilitiesPlan Assets

7Actuarial normal cost is the present value of pension benefits earned by plan participants during the year.

6

2.2 Pensions & Investments Data

Pensions & Investments (P&I ) is a biweekly magazine aimed at pension, portfolio, and invest-

ment management executives. Since 1974, the magazine has focused its second issue of every

calendar year on what has been dubbed the “P&I 1,000”: the largest 1,000 pension plans as

ranked by total assets under management. This special report details the investment practices

and experiences of these plans, both on an aggregate and individual basis, as of September 30

of the preceding year. Data on public and private pension funds’ asset allocations, investment

strategies, and investment managers are collected by sending questionnaires to over 1,200 plan

sponsors in P&I ’s database. Responses to these questionnaires are augmented with informa-

tion from follow-up emails and phone calls, as well as with data from Money Market Directories

Inc. Results of this data collection process for the period 1992 to 2004 were made available in

electronic format for purchase by P&I until 2004, after which the availability of all electronic

data was discontinued. It is the electronic data made available until 2004 that forms the basis

for the estimation sample in our study.

The detail provided in the P&I asset allocation data is dichotomous between the periods

1992 to 1997 and 1998 to 2004, with much greater asset class detail reported during the latter

period. To take advantage of this greater detail, as well as intertemporal consistency in asset

class detail, we focus our estimation sample on the period 1998 to 2004.

Our analysis requires merging of the P&I data with the Compustat Annual Fundamentals

database. We therefore remove those observations in the data for which the plan sponsor is

either a public (governmental) entity or a union. We then hand-match observations to Form 10-

Q filings, by sponsor name, using the SEC’s EDGAR database. Making note of plan sponsors’

EINs, we are able to match P&I and Compustat observations on this basis.

Our analysis using the P&I data builds on the results of Rauh (2009). Integral to his

analysis is a numerical measure of firms’ S&P credit ratings. To maintain consistency with his

analysis, we construct this measure in accordance with that in the original paper. We scale plan

sponsors’ S&P ratings, obtained from Compustat, so that the credit rating variable for those

sponsors with a D rating takes a value of 0.036; the credit rating variable for those sponsors

with an AAA rating takes a value of 0.929. Each of the ratings in between takes a value that

incrementally raises the rating variable by 0.036 for each increase in the qualitative S&P rating.

Table 2 presents summary statistics for the final P&I data set. The sample consists of 1,902

plan-year observations, consisting of 411 unique plan sponsors (identified by unique EIN). We

eliminate observations lacking defined benefit asset allocation data, as well as those for which

the plan sponsor is not incorporated in the United States. Application of these criteria leads to

an aggregate loss of 745 observations. We also eliminate observations for which all Compustat

variables requisite to the analysis in Rauh (2009) are not available. Observations for which the

plan sponsor does not have a S&P credit rating in Compustat are assigned a numerical credit

7

rating value of zero, but are accounted for using an indicator variable for firms without S&P

rated debt. This indicator has a mean value of 0.089 in the sample, indicating that 91.1% of

the observations in our sample belong to firms with a Compustat credit rating.8

Other firm characteristics are obtained from the Compustat Annual Fundamentals file. Firm

assets are measured using the Compustat Xpressfeed data code at. Altman’s Z-score, a pop-

ular measure (control variable) of financial distress in the literature (Altman(1968)), is calcu-

lated using the following function of Xpressfeed codes: 3.3*ebit/at + sale/at + 1.4*re/at +

1.2*wcap/at. The firm investment return measures the income earned on pension assets during

the fiscal year, net of plan contributions, scaled by BOY pension assets. Pension assets are

measured using Xpressfeed data code pplao, while pension liabilities are measured using the

Compustat projected benefit obligation (data code pbpro). Pension funding status is calculated

as in the IRS 5500 data (pension assets net of pension liabilities, divided by pension liabilities).

Plans in the sample have mean assets of $3.395 billion, and mean liabilities of $3.326 billion,

corresponding to a mean funding status of 1.9%, with the median fund underfunded by 3.5%

of liabilities.

Asset allocation statistics are also provided in Table 2. With respect to the composition of

fixed-income holdings, the P&I data is coarser than that of the IRS data, since P&I survey

respondents are not asked to classify total holdings into government and corporate debt. We are

therefore restricted to observing only the total plan allocation to debt. Reported allocations are

free of holdings in insurance company general accounts, which are aggregated into an ”other”

category in survey responses. From Table 2, we can see that equity investments make up 61.84%

of holdings at the mean, debt investments represent 28.13%, while cash holdings make up 2.03%.

The remaining 8.00% of mean asset holdings are held in other asset classes, including mortgages,

private equity, and real estate investments.

2.3 Compustat Annual Pensions Data

Data on private pension plans for North American sponsors is also made available in the Com-

pustat Annual Pensions file. For our study, we draw data on pension assets and liabilities,

investment returns, and assumed long-term rates of return on plan assets. The variables req-

uisite for our study are all available beginning in 1994, and up to 2007. After removing data

on plans with non-U.S. based sponsors, we are left with a data sample of 12,946 observations,

covering 2,418 unique sponsors. Table 3 provides summary statistics for this full sample, as well

as for restricted samples using only observations with funding ratios falling within a specified

interval. We postpone further discussion of this sample to Section 4 of the paper.

8As noted in Rauh (2009), this is not representative of the general Compustat universe, where approximatelyjust one quarter of observations have a non-missing S&P credit rating.

8

3 Regulatory Funding Rules and Asset Allocation

Defined benefit pension fund managers are charged with not only allocating assets in a fashion

leading to favorable excess returns, but also with safeguarding the assets backing the pension

liabilities of plan sponsors. In the literature, van Binsbergen and Brandt (2007) consider a

generalized asset liability management (ALM) problem in which pension fund managers derive

utility from their expected future funding ratio, and experience disutility when their funds are

subject to mandatory additional funding contributions (AFCs) due to being underfunded. In

the model, the presence of AFCs leads to perverse investment behavior around the funding

status at which AFCs are required.9

Armed with data on pension plans’ asset allocations and funding ratios over time, we ask

the question of whether asset allocations are affected by the presence of mandatory funding

contribution requirements. Our method of inquiry centers around investigating the asset al-

location dynamics of pension funds around critical funding ratios. For clarity, we provide a

brief overview of the relevant regulations surrounding funding requirements and mandatory

contributions before proceeding.

3.1 Institutional Background and Methodology

In general, U.S. pension plan sponsors are regulated by the Employee Retirement Income Secu-

rity Act (ERISA) of 1974, a federal statute establishing minimum standards for private pension

plans. Among the minimum standards mandated by ERISA were those with respect to funding

requirements. Specifically, for underfunded private plans ERISA mandated the payment of the

plan’s normal costs (present value of benefits accrued by plan participants during the year), as

well as amortization payments toward the unfunded portion of pension liabilities. Typically,

the amortization period for these payments was between 5 and 30 years.10 Over time, several

additional federal acts affecting funding requirements have been passed, for our purposes the

most important being the Pension Protection Act (PPA) of 1987 and the Retirement Protection

Act (RPA) of 1994.

The PPA of 1987 introduced much stricter funding requirements, mandating amortization

periods of just 3 to 5 years for unfunded liabilities. The PPA also mandated varying first-year

contributions, wherein sponsors of underfunded plans were required to make cash payments that

increased in the level of the plan’s underfunding (as a percentage of pension liabilities), therefore

more heavily penalizing those plans that experienced large funding status drops, perhaps due

to ignoring the effect of plans’ pension liabilities in making investment decisions.

9We refer to such a point, a funding status above which no mandatory AFC is required and below whichmandatory AFCs are required, as a critical funding ratio or critical funding status.

10See Munnell and Soto (2003) for further discussion of ERISA funding requirements, as well as examples ofmandatory contributions under ERISA.

9

Affecting plan years 1995 and onward, the RPA of 1994 added additional mandatory funding

contributions for those plans deemed to be critically underfunded. Added to the IRS Form 5500

that private plans must file each year was an additional section entitled Additional required

funding charge, in which an additional funding charge on top of that already required under

the PPA of 1987, was calculated. However, this additional funding charge was required to be

calculated and paid by only those plans which were more than 20% underfunded, as a percentage

of pension liabilities.11

Our empirical tests of how pension asset allocations are affected by mandatory funding

contributions center around exploiting the sharp discontinuities in mandatory funding contri-

butions at the critical funding ratios of 0% (fully funded), the point at which normal costs and

mandatory amortization of underfunding must be paid, and 20% underfunded, where plan spon-

sors are subject to additional funding charges after 1995. Our approach shares many features

with the standard regression discontinuity (RD) design, as described in Hahn, Todd, and van

der Klaauw (2001), Imbens and Lemieux (2007), and Lee and Lemieux (2009), and applied in

Angrist and Lavy (1999), van der Klaauw (2002), Rauh (2006), Chava and Roberts (2008), Lee

(2008), and Roberts and Sufi (2009).12 The RD design provides an ideal causal identification

strategy when treatment status is a function of some forcing variable, and the econometrician

has both detailed knowledge of the function determining treatment, as well as the ability to

observe the forcing variable. In our example of plan sponsors’ mandatory funding contributions

to a corporate pension plan, the forcing variable is given by the plan’s funding status. We are

able to observe this quantity, and given the above discussion, have detailed knowledge of the

functions determining treatment.

Denoting as T0,j the indicator for whether or not plan sponsor j is subject to mandatory

funding contributions, the treatment status can be written as:

T0,j =

{1 if xj < 0

0 if xj ≥ 0

where xj represents pension plan j’s funding status. Similarly, denoting as T20,j the indicator

for plans being subject to the additional funding requirement (for plan years 1995 and later),

the treatment status can be written as:

T20,j =

{1 if xj < −20%

0 if xj ≥ −20%.

11Plans with 10-20% underfunding could also be subject to the additional funding charge. However, this wouldrequire three consecutive years of being more than 10% underfunded. Even then, plan sponsors could apply forhardship exemptions to the additional funding charge, which were usually granted (see Rauh (2006) for furtherdetail).

12Lee and Lemieux (2009) provide a comprehensive discussion of the regression discontinuity design, as well asa detailed listing of papers in the various economic disciplines that make use of the technique.

10

One of the great advantages of the RD design commonly cited in the broader economic

literature is its relatively mild set of identification assumptions. In addition to those outlined

above, there is one assumption that remains critical to validating use of the RD design. As

explained by Lee and Lemieux (2009), inferences from the RD design can be invalid if agents

are able to precisely manipulate the forcing variable. Importantly, as shown by Lee (2007) in

the context of non-random selection in U.S. House elections, even if individuals do have some

control over the forcing variable, as long as this control is not precise, variation in treatment

near the threshold will still be as though from a randomized experiment, or as good as random.

More recently, McCrary (2009) has developed a statistical test of whether individuals are able

to control the forcing variable with the precision necessary to invalidate RD inferences.

This discussion is extremely relevant to our setting, in which pension fund investment man-

agers, all else equal, are surely interested in maximizing their plan’s funding status, and in

avoiding the payment of mandatory contributions by the plan sponsor. We therefore leverage

the recent contributions to the RD literature in showing that the RD design is valid in our

study.

Figure 1 shows smoothed density plots of plans across funding status bins, a graphical

diagnostic suggested by McCrary (2008) and Lee and Lemieux (2009). Construction of the

density plot follows the algorithm developed in McCrary (2008). Briefly, the dots in the plots

represent a very undersmoothed histogram, where the bins are designed carefully enough to

ensure that no bin contains points both to the left and right of the discontinuity point. The

bin-width of this first-step histogram is chosen according to the following expression:

b = 2σn−1/2,

where σ is the sample standard deviation of the forcing variable, the funding status. Using this

first-step histogram, we then estimate separate fourth-order polynomials on each side of the

discontinuity point. Letting X1, X2, ..., XJ represent the discretized grid covering the support

of the funding status for the first-step histogram, and labeling the fourth-order polynomial

f(Xj), we calculate on each side of the discontinuity point the following expression:

3.348[σ2(b− a)/Σf ′′(Xj)2]1/5,

where σ2 is the mean-squared error of the regression, b − a equals XJ − c for the right-side

regression and c−X1 for the left-side regression (where c is the discontinuity point), and f ′′(Xj)

is the estimated second-derivative implied by the estimated polynomial model. Then, we set

h equal to the average of the calculated quantities. Using h as the bin-size for a second-step

histogram, we again estimate a fourth-order polynomial on each side of the discontinuity using

the second-step bin heights. The plotted curves in Figure 1 are produced using the fitted values

of the estimated polynomials.

11

Panel A of Figure 1 shows a density plot constructed around the −20% funding status

discontinuity in the P&I sample. Similarly, panel B shows a density plot for the 0% funding

status discontinuity. In both of the density plots there does not appear to be qualitative evidence

of a discontinuity in the density of plans near the critical funding ratios.

Table 4 presents statistical evidence supporting the null hypothesis that plan sponsors and

fund managers are unable to manipulate the forcing variable in our setting. In the table, we con-

struct log discontinuity estimates using fitted values of the fourth-order polynomials estimated

on each side of the respective discontinuity points. From the estimates and asymptotically nor-

mal standard errors detailed in the table, it is evident that there is no statistical evidence against

the null hypothesis of a consistent density of plans on both sides of the discontinuity points.

Hence, we have both qualitative and quantitative evidence that the regression discontinuity

approach is appropriate in the setting of interest.13

3.2 Empirical Specification

Having established that the RD design is appropriate in our setting, we now return to our orig-

inal goal of investigating the effect of sharp mandatory contribution discontinuities on pension

funds’ asset allocations. In the context of pension funds, the results of Rauh (2009) provide an

ideal starting point for the further study of factors affecting asset allocations. Rauh’s analysis

focuses on the cross-sectional effect of variation in funding status and S&P ratings on risk taking

in pension funds, with risk taking defined as the level of funds’ allocations to equity. In the

process, he identifies and makes use of a set of independent variables that serve as a baseline in

our regression analysis, where we first consider panel regressions of the following form:

wi,j,t = α+ θicriticalj,t + εi,j,t,

where criticalj,t is an indicator variable that takes the value 1 if pension plan j takes on a

funding status in the critical region of interest in the current year, and is 0 otherwise. We will

characterize the critical regions of interest shortly. wi,j,t is defined to be the allocation to asset

class i in pension fund j at time t.

In regressions of the above form, one may be concerned that the coefficient of interest,θi, is

driven by passive changes in plan allocations, resulting from inertial investing. While we can

include controls such as time indicators and plan-specific investment returns in order to absorb

some of these effects, one may still be concerned that asset-class-specific passive effects are not

fully accounted for when using comparatively coarse controls at the year- and portfolio-level.

13We also test sponsor contributions in the Form 5500 sample directly. Voluntary contributions, over andabove those mandated by funding rules, are the channel through which sponsors can exert precise control overthe funding ratio. In unreported tests, we find no evidence that firms approaching the critical funding ratiosfrom above avoid going past the critical point by making such voluntary contributions.

12

To temper such concerns, we construct a measure of active reallocations across asset classes,

denoted wactivei,j,t , and instead consider regressions of the following form:

wactivei,j,t = α+ θicriticalj,t + εi,j,t,

where all independent variables and their respective coefficients are as described before.

Substituting active reallocations as the dependent variable effectively amounts to ensuring

our results are robust to the effects of controlling for specific asset class returns within each

of the four general asset classes. We follow the algebra of Brandt, Santa-Clara, and Valkanov

(2009) in generating these active reallocations, details of which we briefly reproduce next for

clarity.

3.2.1 Active Portfolio Reallocations

Suppose a fund manager starts with an initial portfolio, in which the weight of asset class i is

given by the previously optimal investment policy:

wi,0 = wi,0 + θTxi,0,

where wi,0 represents the weight of asset class i at date 0 in some benchmark portfolio,14 xi,0

represents the characteristics of asset class i affecting the fund manager’s allocation decision at

time 0, and θ is a vector of coefficients.

Then, for each period t, we let the fund manager have an optimal investment policy defined by

a function of the same form:

wi,t = wi,t + θTxi,t

where all components are as defined above, but at time t.

We operate under the assumption that the sequence of events is as follows: the fund observes

returns based on time t− 1 weights, after which trading occurs such that the weights at time t

are set to their optimal level wi,t for each asset class i. We label the intermediate weights, after

returns have been observed but before rebalancing trades have occurred, as passive weights.

These passive weights are given by:

wpassivei,t = wi,t−1 ∗

1 + ri,t1 + rp,t

,

14In the context of pension funds, this could be interpreted as a target allocation mandated by the plansponsor’s pension committee. For a more generalized interpretation, see Brandt et. al. (2009).

13

where ri,t and rp,t are the observed returns on asset class i and the entire portfolio, respectively.

Finally, we define the active reallocation in asset class i at time t as:

wactivei,t = wi,t − wpassive

i,t .

Active asset class reallocations are calculated using both the IRS Form 5500 and the P&I asset

allocation data. Of course, in doing so, we must take a stand on what the appropriate returns

are between times t−1 and t for each asset class i. Table 5 outlines for both of the data sets the

asset classes for which we observe allocations, and the benchmark indices we choose for each

observable asset class.

Table 6 presents summary statistics of the active reallocations used in this paper. For

comparability with those from the P&I data, active reallocations for the Form 5500 sample are

calculated using the allocations as a share of noninsurance assets described in Panel b of Table

1.

3.3 Asset Allocation Results

One way of constructing the critical indicator is by considering only the funding status of the

pension plan, setting criticalj,t equal to 1 if the funding status of plan j falls in some specific

neighborhood of a contribution discontinuity point. However, this unconditional approach fails

to truly take into account the motivations of pension fund managers. After all, the manager

of a pension fund with an improving funding status just above a discontinuity point (ie. the

funding status is moving away, in a good way, from the discontinuity point) does not have a

strong motivation to adopt a special asset allocation strategy in order to avoid falling below the

discontinuity point. Similarly, the manager of a fund with funding status just below a disconti-

nuity point with deteriorating funding ratio will act differently than the manager of a fund with

the same funding status, but one which is improving. We hypothesize that in the neighborhood

of a discontinuity point, if a plan’s funding status is moving toward the discontinuity point, then

asset allocations will be adjusted so as to minimize the ex-ante probability of falling on the side

of a critical funding ratio requiring the payment of additional contributions. Therefore, our

tests are performed by running the following conditional regression, splitting critical as defined

above into the indicators criticalup and criticaldn:

wactivei,j,t = α+ θi,upcriticalup,j,t + θi,dncriticaldn,j,t + εi,j,t,

where criticalup,j,t = criticalj,t ∗ fundstatincrease,j,tand criticaldn,j,t = criticalj,t ∗ (1 − fundstatincrease,j,t).

14

In the above, we set fundstatincrease,j,t equal to 1 if the expression fundstatj,t − fundstatj,t−1

is positive, and 0 otherwise. That is, fundstatincrease,j,t is an indicator measuring whether a

plan’s funding status improves during the current year, due to plan asset returns, interest rate

movements, or both.15

Figures 2 and 3 display the coefficients on criticalup and criticaldn from running regressions

of the above form. Figure 2 displays the results of these tests using the P&I sample, while

Figure 3 is generated using the IRS Form 5500 sample.16 In all regressions, we include controls

adapted from Rauh (2009)17, as well as time fixed effects in the form of year indicator variables.

Additionally, we also control for plans’ investment returns in year t, as a control for the effects

of plan-specific variation in returns on top of the effects absorbed by time indicators. We also

restrict consideration to specifications with plan fixed effects, since we are inherently interested

in examining within-firm variation in asset allocation decisions, as a given plan’s funding ratio

varies and moves around the contribution discontinuity points. Figures 2 and 3 are each split

into four panels, one for each of the general asset classes we consider: equity, debt, cash and all

others. Coefficient estimates for θup are shown using green bars, while those for θdn are given

by bars in red. Coefficients from the unconditional specification are given by bars in blue. We

split the support of plans’ funding ratios so as to best capture the motivations of pension fund

managers around the -20% and 0% funding ratio discontinuities. Specifically, on the lower side

of a discontinuity we group plans with funding ratios within 10% of the discontinuity. The

intuition behind this is that we wish to capture the discontinuous behavior of fund managers

altering asset allocations in an attempt to increase the ex-ante probability of improving their

funding ratios to the point that they are past the discontinuity. Of course, even within this

grouping, fund managers facing funding ratios that are relatively closer to the discontinuity point

will plausibly have a larger incentive to alter plan allocations. Therefore, while decreasing the

range of funding ratios within the grouping could lead to more consistent coefficient estimates,

doing so would also have the negative effect of decreasing the precision of our estimates. On the

upper side of discontinuities, we group plans with funding ratios within 5% of the discontinuity

point. As above, we wish to measure the behavior of fund managers altering asset allocations

when attempting to increase the ex-ante probability of maintaining a funding ratio above the

15A plan’s funding status can also be improved via voluntary contributions by the plan sponsor. However,Rauh (2006) shows that, as a general rule, plan sponsors make only those contributions mandated by fundingregulations. In addition, voluntary contributions by sponsors would lead to a large jump in the density of sponsorsaround critical funding ratios. Our density plots in Figure 1 and formal statistical tests in Table 4 indicate thatthis is not the case. Therefore, fundstatincrease,j,t is a reasonable measure of plans’ exogenously determinedfunding status trajectory during year t.

16For clarity, Figures 2 and 3 restrict attention to only those funding status bins surrounding the respectivecritical funding ratios. For completeness, Figures 4 and 5 repeat this analysis for a set of funding status binscovering the entire spectrum of funding ratios.

17Specifically, in the P&I sample, we control for the pension funding status, the S&P credit rating of thesponsor, the sponsor’s operating assets and the plan’s assets, both in logs, as well as Altman’s Z-score. In theForm 5500 sample, we control for the pension funding status, the active share of employees, and the size of thepension at time t− 1, both in levels and logs.

15

discontinuity.

We first examine the 20-30% underfunded funding ratio grouping. We first consider Figure

2, displaying results from the P&I active reallocation sample. As alluded to earlier, examining

the unconditional results (blue bars), we can see that there is not a large or significant departure

from zero in active reallocations to equity or debt. Unconditional active reallocations to cash are

positive at the 10% significance level, suggesting that as plans move into the funding ratio just

below the -20% contribution discontinuity, there is a precautionary motive to hold cash in order

to avoid falling further away from the discontinuity point. This interpretation is supported

when we look at the conditional results: at the 10% significance level, plans in the 20-30%

underfunded grouping actively move out of equity and into cash holdings when their funding

ratio deteriorates during the year (red bars). The same does not hold for plans in this grouping

with improving funding ratios (green bars). Instead, our results appear to show that as plans

move toward the -20% discontinuity, they make active reallocations, significant at the 5% level,

into equity and out of debt. Economically, the magnitude of these reallocations is quite large:

3.04% into equity and -2.81% out of debt, with the balance made up of insignificant reallocations

to cash and out of other asset classes.

Continuing to focus on the 20-30% underfunded grouping, but shifting consideration to the

results for the IRS Form 5500 data in Figure 3, we can see that this result is robust. That is,

as plans move toward the -20% contribution discontinuity, fund managers actively reallocate

1.43% of plan assets into equity, and 1.08% out of debt, with statistical significance at the 5%

level. Collectively, this behavior is consistent with our hypothesis of fund managers attempting

to increase the ex-ante probability of ending the year on the high side of the funding ratio

discontinuity, thereby avoiding mandatory additional contributions.

Shifting our focus to the 15-20% underfunded funding status grouping, in which plans end

the year just above the -20% discontinuity, we first consider the results from the P&I sample

in Figure 2. Examining the conditional results, we can see that those plans with deteriorating

funding ratios (red bars) during the year appear to make active reallocations into debt, and out

of equity. Switching consideration to the IRS Form 5500 sample in Figure 3, we can see active

reallocations that are similar in spirit. Plans deteriorating toward the -20% discontinuity appear

to move out of equity and into cash, while those plans in this grouping with improving funding

ratios do the opposite, moving into equity and out of cash. In both samples, the coefficients of

interest are not estimated with enough precision to allow us to make statistical inference.

The difference in coordination of action between plans above and below the -20% discon-

tinuity is worth noting. Such a difference is consistent with fund managers generally taking a

reactionary, as opposed to anticipatory, approach to the mandatory additional contributions at

a funding ratio of -20%. Since filing of the Form 5500, on which detail of these additional con-

tributions appears, is the responsibility of the plan sponsor, a plausible reason for the difference

16

in observed coordination of action is that fund managers are not fully informed of this discon-

tinuity until their plans’ funding ratios fall past -20%, subjecting the sponsor to the additional

contributions.

We next examine the 0-10% underfunded funding ratio grouping, first considering results

from the P&I sample, contained in Figure 2. Again, we can see that unconditional results (blue

bars) give very little insight into allocations just below the 0% discontinuity. However, the results

when we consider conditional coefficients are, once again, much richer. Considering plans with

improving funding ratios (green bars), moving toward the discontinuity point from below, we

can see that active reallocations to cash and debt are negative, at the 5% and 10% significance

levels, respectively. Reallocations to equity and the other asset classes, comparatively riskier

asset classes with higher mean expected returns, are both positive with near-5% statistical

significance. These results are consistent with those described above among plans approaching

the -20% discontinuity from below. That is, among plans in the P&I sample approaching the 0%

discontinuity from below, we can see behavior consistent with our hypothesis of fund managers

actively reallocating assets in an attempt to increase the ex-ante probability of garnering returns

sufficient to avoid being subject to mandatory contributions at the end of the year.

Focusing on the results from the Form 5500 sample in Figure 3, we can see that, contrary

to the results for the -20% discontinuity, the results for funds approaching the discontinuity

from below are inconsistent with those in panel a. From panel b, we can see that the small-

to medium-sized plans in the Form 5500 sample do not appear to make active reallocations

that are unexplained by the controls, and time and firm fixed effects described earlier. That is,

approaching the 0% discontinuity from below appears to have no causal effect on active asset

class reallocations in the Form 5500 sample.

We can see a similar difference when shifting our focus to the 0-5% overfunded grouping.

Again, the results for the P&I sample in Figure 2 suggest behavior consistent with managers of

funds approaching the 0% discontinuity from above making reallocations in an attempt to avoid

falling below the critical ratio. In general, fund managers in the P&I sample actively move into

debt and out of equity, with significance at the 5% level, when experiencing a deteriorating

funding ratio just above the discontinuity point. However, there is no indication fund managers

in the Form 5500 sample in Figure 3 take a similar form of coordinated active reallocations just

above the 0% discontinuity.

This inconsistency between the two samples around the 0% discontinuity can be interpreted

in a number of ways. One explanation is that plans in the Form 5500 sample differ from those

in the P&I with respect to their size. Our results would then suggest that larger plans are more

averse to mandatory contributions at the 0% discontinuity. Another related explanation for

why larger plans may shift allocations around both discontinuity points is that larger plans are

more likely to have internally managed funds that can be quickly reallocated, whereas smaller

17

plans with funds invested wholly with managers external to the firm will have a harder time

making such reallocations.

All of this is not to say that plans in the Form 5500 sample do not react to the 0% disconti-

nuity. In fact, it appears that they simply react differently. Examining plans with deteriorating

funding ratios in the 0-10% underfunded grouping in Figure 3, we can see that these plans ac-

tively reallocate into debt, at the 5% significance level, with the offsetting reallocation coming

from equity. This is consistent with plans attempting to stop the bleeding as they move away

from the funding ratio representing fully funded status.

All things considered, the results of this section suggest that controlling for a number of

sources of observable plan- and firm-level heterogeneity, time fixed effects, and unobservable

sources of cross-sectional heterogeneity, proximity to regulatory mandatory contribution func-

tion discontinuities indeed affects the asset allocation decisions of defined benefit pension plans.

It is also apparent, in the results for both samples, that the -20% discontinuity has stronger

effects on asset allocation than those around the 0% discontinuity.

4 Regulations and Pension Assumptions

Accounting rules provide corporate managers with leeway when it comes to establishing and

reporting estimates affecting the firm’s financial position, as reported in the financial statements.

In this respect, the accounting for corporate pension plans, wherein managers are charged with

setting an assumed long-term rate of return on plan assets, is no exception. Since the assumed

return has a direct effect on a firm’s net income, the process of deciding on an appropriate

assumption is fraught with moral hazard issues. Bergstresser, Desai, and Rauh (2006) show

that managers appear to manipulate corporate earnings through aggressive increases of the

assumed rate of return when preparing to acquire other firms, when near critical earnings

thresholds, and when managers exercise stock options.

In the previous section, we established the effect of mandatory contribution regulations on

the asset allocations of defined benefit pension funds. A natural follow-up question, tieing to-

gether this result and those of Bergstresser, Desai, and Rauh (2006), is whether regulations have

an effect on managerial assumptions concerning pension plans at the firm-level. We will focus

our analysis on both the funding regulations already considered, and accounting regulations

to be outlined below. Before proceeding, we provide a brief overview of accounting rules for

private defined benefit pension plans in the United States.

4.1 Pension Accounting Background

Pension accounting rules in the United States essentially concern calculation of the pension

expense appearing on the income statement. Table 7 outlines the components contributing to

18

the calculation of this quantity.

The first component increasing the pension expense is the service cost. The service cost

is the expense caused by the increase in pension benefits payable due to services rendered by

employees during the fiscal year. The service cost is calculated as the actuarial present value

of these benefits payable, a calculation that takes into account expected future compensation

levels, as well as expected workforce attrition and mortality rates.

The second component adding to a firm’s pension expense is the interest expense. Since

pension obligations represent amounts payable in the future, they are recorded on a discounted

basis. Hence, as the time of payment approaches, the difference between discounted and undis-

counted amounts must be accrued for; the interest expense is precisely this accrual.

The third component of pension expense is the amortization of unrecognized prior service

costs. When defined benefit pension plans are either initiated or amended, it is often the case

that employees are credited for service in years prior to the date of initiation or amendment.

Amendments can either increase or (rarely) decrease pension benefits for plan participants.

Under the rationale that employers will derive future benefits from retroactively applying in-

creased plan benefits, plan sponsors are not required to recognize the entire actuarial present

value of the retroactive component of liability increase. Instead, sponsors are encouraged to

amortize the cost of retroactive benefits over the expected remaining service lives of benefitting

employees.

The fourth and fifth components of pension expense, amortization of unexpected actuarial

gains/losses and the assumed return on plan assets, are interrelated. In order to smooth the

volatility of pension expense that would result if actual quarterly and annual returns on plan

assets were used, the Financial Accounting Standards Board (FASB) has instead pronounced

the use of an assumed long-term rate of return on plan assets in offsetting the costs of defined

benefit plans. Of course, cases in which actual returns to plan assets match this assumed return

are exceedingly rare, and so the difference between the two returns is accounted for using

an unrecognized net gain/loss off-balance-sheet account, with no income statement impact.

However, in order to control for systematic positive or negative differences between the two

returns, the FASB also requires firms to amortize the balance of the off-balance-sheet account

if its balance ever exceeds 10% of the maximum of pension assets and liabilities, known as the

pension corridor. Specifically, if unrecognized net gains/losses exceed the bounds of the corridor

at the end of fiscal year t, then amortization will be required at the end of fiscal year t+ 1.

Of the components of pension expense detailed above, only the assumed return on plan

assets is truly under the control of management. The service cost is calculated by independent

actuaries and the amortization schedules for unrecognized prior service costs and unrecognized

net gains/losses are prescribed by the FASB. Even the discount rate, and hence rate of accrual,

for pension liabilities is required by the FASB to reflect rates implicit in insurance company

annuity contracts, at which the company could effectively settle pension liabilities, or rates

19

on high-quality fixed income instruments. Moreover, this rate is also controlled by the firm’s

actuaries. However, the guidance surrounding establishment of a plan sponsor’s assumed long-

term rate of return on plan assets is considerably less detailed. According to paragraph 45 of

FASB Statement No. 87:

The expected long-term rate of return on plan assets shall reflect the average rate

of earnings expected on the funds invested... In estimating that rate, appropriate

consideration should be given to the returns being earned by the plan assets in the

fund and the rates of return expected to be available for reinvestment.

Given the latitude afforded corporate managers apparent in the above quote, we follow Bergstresser,

Desai, and Rauh (2006) in concentrating our analysis on the long-term assumed rate of return

as a potential source of managerial manipulation in the face of accounting regulations.

4.2 Funding Regulations and the Assumed Rate of Return

We begin our analysis of effects on the long-term assumed rate of return by examining dis-

continuities in the mandatory contribution function considered earlier. We are interested in

determining whether these discontinuities lead to observable effects on the assumed rate of re-

turn. We engage a testing strategy similar to those employed in section 3.3 and by Bergstresser,

Desai, and Rauh (2006). That is, we consider regressions of the following form:

pprorj,t = α+ ηlevelcriticalj,t−1 + ηslope(criticalj,t−1 ∗ psensitivityj,t) + ψpsensitivityj,t + εj,t,

where pprorj,t represents plan j’s long-term assumed rate of return at time t, and criticalj,t is

an indicator variable, as before, indicating pension plan j’s funding status being in a critical

region in the previous year. We adopt the pension sensitivity measure of Bergstresser, Desai,

and Rauh (2006), denoted psensitivityj,t, which we calculate as follows:

psensitivityj,t = log

(ppassetsj,toibdpj,t

),

where ppassetsj,t and oibdpj,t represent pension plan assets and operating income before depre-

ciation, respectively, for plan sponsor j at time t.

The psensitivity measure captures the effect that a given change in ppror has on oibdp for a

given plan sponsor. Mathematically, a given change in ppror will have the following effect on

oibdp:

%∆oibdp = %∆ppror ∗ exp(psensitivity).

Hence, plan sponsors with higher psensitivity measures will have greater incentives to set higher

assumed rates of return on plan assets, and inclusion of psensitivity in our specifications will

control for this phenomenon.

20

While we control for psensitivity, we include the interaction term given by critical ∗psensitivity in order to measure if those firms with more to gain from increases in ppror react

more strongly to being in a critical funding status grouping (ie. critical being equal to 1).

Table 8 displays the results of running regressions of the above form. In all regressions, we

include time fixed effects in the form of year indicator variables. Additionally, we also control

for plans’ investment returns in year t, as a control for plan-specific variation in returns on

top of the effects absorbed by time indicators, as well as for the plans’ funding ratios at time

t− 1, and changes in funding ratios between times t− 1 and t. Table 8 is split into two panels

horizontally. The left panel contains specifications with 4-digit Global Industry Classification

Standard (GICS) industry fixed effects18, while the right panel replaces industry fixed effects

with those at the firm level. Within each horizontal panel, we run two variants of the above

regression. The first, corresponding to columns (1) and (3) and which we label unconditional

specifications, are the same as the specification outlined above. The second, corresponding to

columns (2) and (4) and which we label conditional specifications, are a conditionally modified

version of the specification outlined above:

pprorj,t =

α+ ηup,levelcriticalup,j,t−1 + ηdn,levelcriticaldn,j,t−1 +

ηup,slope(criticalup,j,t−1 ∗ psensitivityj,t) + ηdn,slope(criticaldn,j,t−1 ∗ psensitivityj,t) +

ψpsensitivityj,t + εj,t,

where criticalup,j,t−1 and criticaldn,j,t−1 are defined precisely as in section 4.2.

Vertically, Table 8 is again split into two panels. In panel a, we restrict the sample to

plan-years with lagged funding ratios in the range of -40% (40% underfunded) to 0%. Similarly,

we restrict the sample to plan-year observations where the lagged funding status falls in the

range of -20% to 20% in panel b. Again, we do this in order to capture the behavior of

corporate managers with respect to the assumed return on pension assets around the -20% and

0% mandatory contribution discontinuities. In both panels, we define criticalj,t−1 equal to 1

if plan j’s funding ratio falls in the lower 20% of the range of consideration, and 0 otherwise.

That is, if the time t− 1 funding status falls below the discontinuity point, such that the plan

sponsor is subject to additional mandatory contributions, we set criticalj,t−1 equal to 1, and 0

otherwise.19

184-digit GICS industry codes correspond to a total of 68 different industries. In using GICS industry codes,we follow the work of Bhojraj, Lee, and Oler (2003), who find that the GICS performs significantly better thanboth SIC and NAICS codes in explaining stock return comovements and cross-sectional variation of various keyfinancial figures and ratios.

19In untabulated results, we perform the same analysis without restricting the samples in the vertical panels.The results remain consistent and, in fact, are even stronger due to significantly lower average assumed rates ofreturn for those firms with plans that are under/overfunded by a magnitude of more than 40% of BOY pensionliabilities. We report results using restricted samples in order to abstract from, and eliminate, this issue.

21

We first examine panel a of Table 8. From specification (1), we can see that the coefficient

ηlevel is significantly positive at the 1% level, with a point estimate of 10.20 basis points. This

indicates that firms subject to mandatory additional contributions (due to time t − 1 funding

status below -20%) assume long-term rates of return that are 10.20 basis points higher than

their industry peers not subject to additional contribution requirements. In addition, ηslope is

estimated to be 3.97 basis points, significant at the 10% level. This indicates that for each

additional unit of log pension sensitivity, plan sponsors past the -20% discontinuity assumed

rates of return are 3.97 basis points higher compared to within-industry counterparts. Another

way of interpreting ηslope is that a firm in the 90th percentile of log pension sensitivity (1.19)

will have a 13.30 basis point higher reaction to being below the 20% discontinuity point than a

firm in the 10th percentile of log pension sensitivity (-2.16) in the same industry.

Examining the conditional results in specification (2) of panel a, we can further explore

the results from specification (1) described above. Our first observation is that the estimates

for ηup,level and ηdn,level, 10.70 and 9.15 basis points, respectively, with both significant at the

1% level, are very similar. However, the interaction-term estimates for ηup,slope and ηdn,slope

do differ, with ηup,slope insignificant and ηdn,slope significantly positive at the 5% level, with an

effect of 7.43 basis points for each unit of log pension sensitivity. Together, we can interpret

this difference as evidence that within an industry, and holding time fixed, firms facing the

combination of being subject to mandatory contributions and a deteriorating funding status

in the current year will have higher assumed returns that vary positively with log pension

sensitivity. That is, restricting attention to firms facing this combination, a firm in the 90th

percentile of log pension sensitivity will have a 24.89 basis point higher reaction to being below

the 20% discontinuity point than a firm in the 10th percentile.

Shifting our focus to specifications with firm fixed effects, we can see from specification (3)

in panel a that when considering only within-firm variation, there is no statistical evidence

in support of higher assumed rates of return for sponsors subject to additional contributions.

However, considering the conditional results in specification (4), it becomes apparent that the

result of interest is concentrated among those firms experiencing a deteriorating funding status

during the year. For these firms, the estimates for both ηdn,level and ηdn,slope are significantly

positive at the 5% level.

We next examine panel b of Table 8, detailing results for the 20% underfunded to 20%

overfunded sample, where critical is set equal to 1 for those plans with funding ratios below

the 0% discontinuity. Specification (1) offers no evidence that firms subject to mandatory

contributions assume higher rates of return on plan assets than their industry peers with lagged

funding ratios above the 0% discontinuity. In fact, at the 10% significance level, the estimate

of ηlevel indicates that firms below the discontinuity point actually have lower assumed rates of

return, in contrast to the results seen above for the -20% discontinuity.

The conditional results in specification (2) offer further insight into this result, where we can

22

see that the driving force is a highly significant negative ηdn,level estimate of -12.30 basis points.

While it appears that being subject to mandatory contributions is not associated with a within-

industry difference in assumed rates of return for sponsors of plans with improving funding

ratios, sponsors of plans with deteriorating funding ratios actually assume rates of return that

are 12.30 basis points lower than industry peers above the discontinuity point.

Focusing on specifications (3) and (4), we can see that in both unconditional and conditional

specifications, being subject to mandatory contributions is not associated in a statistically

detectable way with any difference in assumed rates of return on plan assets when considering

only within-firm variation.

The results in this section echo those of section 3.3, where we considered the effect of

contribution function discontinuities on plans’ asset allocation decisions. Namely, the results

surrounding the -20% discontinuity are much stronger in both settings. Here, our results indicate

manipulation of the assumed rate of return not by firms subject to mandatory contributions

at the 0% discontinuity, but by firms subject to additional mandatory contributions past the

-20% discontinuity for both within-industry and within-firm specifications. Together with the

asset allocation results, this lends credence to our earlier interpretation that those in charge

of pension plans, in general, pay much more attention to, and have their decisions affected

much more by, additional contributions coming into effect at the -20% discontinuity than initial

contributions mandatory once a fund falls below fully funded status.

4.3 Accounting Regulations and the Assumed Rate of Return

Having examined the effect of funding regulations on the assumed long-term rate of return,

we now examine the effects of accounting regulations. Specifically, we examine the effects of

unrecognized gains/losses and prior service costs that must be amortized in the subsections that

follow.

4.3.1 Unrecognized Gains and Losses

As described in section 4.1, the FASB requires firms to amortize the balance of the unrecognized

gains/losses account if it exceeds 10% of the maximum of pension assets and liabilities. Our

goal is to measure the effect that unexpectedly having to incur such amortization charges has on

the assumed long-term rate of return on plan assets.20 Hence, we focus our attention on plans

that experience large funding status gains and losses, specifically those that amount to at least

10% of the maximum of pension assets and liabilities.21 In doing so, we consider unconditional

20We focus on firms subject to unexpected amortization charges, since firms that steadily approach the bound-aries of the pension corridor may incrementally change their assumed rates of return over time, possibly renderingsuch changes undetectable in our econometric framework.

21We perform sensitivity analysis with smaller and larger cutoffs of 5% and 15%, with no change in the spiritof the results.

23

regressions of the following form:

pprorj,t =

α+ ηgain,levelgainj,t−1 + ηgain,slope(gainj,t−1 ∗ psensitivityj,t) +

ηloss,levellossj,t−1 + ηloss,slope(lossj,t−1 ∗ psensitivityj,t) +

ψpsensitivityj,t + εj,t,

where gainj,t−1 (lossj,t−1) is set equal to 1 if plan j experiences a large unexpected gain (loss)

at time t− 1 leading to amortization charges at time t.

We also consider conditional regressions of the following form:

pprorj,t =

α+ ηgainup,levelgainupj,t−1 + ηgainup,slope(gainupj,t−1 ∗ psensitivityj,t) +

ηgaindn,levelgaindnj,t−1 + ηgaindn,slope(gaindnj,t−1 ∗ psensitivityj,t) +

ηlossup,levellossupj,t−1 + ηlossup,slope(lossupj,t−1 ∗ psensitivityj,t) +

ηlossdn,levellossdnj,t−1ηlossdn,slope(lossdnj,t−1 ∗ psensitivityj,t) +

ψpsensitivityj,t + εj,t,

where gainupj,t−1 = gainj,t−1 ∗ fundstatincrease,t,gaindnj,t−1 = gainj,t−1 ∗ (1 − fundstatincrease,t),

lossupj,t−1 = lossj,t−1 ∗ fundstatincrease,t,lossdnj,t−1 = lossj,t−1 ∗ (1 − fundstatincrease,t),

and fundstatincrease,t is defined as in section 3.3.

Table 9 displays the results of running the regressions detailed above. Table 9 is organized in

a very similar fashion to that in Table 8, with columns (1) and (3) corresponding to unconditional

specifications, and columns (2) and (4) corresponding to conditional specifications. Again, the

left panel of the table reports the results of specifications with GICS industry fixed effects,

while the right panel does the same for specifications with fixed effects at the firm level. We

also include controls for plans’ investment returns in year t, plans’ funding ratios at time t− 1,

and changes in funding ratios between times t− 1 and t.

Specification (1) in Table 9 provides strong evidence in support of the hypothesis that firms

subject to amortization charges assume higher rates of return on pension assets in order to

offset impact on net income. We estimate a large positive ηloss,level coefficient of 19.70 basis

points, at a significance level of 1%, while the estimate of ηgain,level is insignificant, indicating

that assumed rates of return for firms experiencing large gains that lead to income-helping

amortization are not statistically different from the baseline sample of industry peers without

24

large swings in funding status. The coefficients on the interaction terms are also insignificant

for losses, and mildly significant in the negative direction for sponsors of plans experiencing

large gains.

Examining the results of specification (2) provides further insight into the source of the

mildly significant ηgain,slope coefficient in specification (1). From specification (2) we can see

that this result is driven by a -15.10 basis point estimate of ηup. This is offset by a 10.10 basis

point estimate of ηdn, with both estimates significant at the 5% level. This can be interpreted

as evidence that it is only sponsors of plans that experience large lagged gains and improved

funding ratios in the current year that have lower assumed rates of return than industry coun-

terparts not subject to amortization of gains or losses. Focusing on the estimates of ηlossup

and ηlossdn, we can see that the result from the unconditional specification is largely driven by

sponsors of plans subject to income-hurting amortization and with funding ratio deterioration

in the current year.

Shifting focus to regressions with firm fixed effects, we can see from specification (3) that

when considering only within-firm variation, it is only firms experiencing income-hurting amor-

tization charges that increase the assumed rate of return at a statistically significant level. In

the conditional specification (4), we can again see that this result is strongest for firms subject

to the combination of amortization charges and a falling funding ratio in the current year.

Figure 6 provides visual evidence of the results considering within-industry variation in a

time-series sense. The figure shows long-term rate of return assumptions around large funding

status losses (panel a) and gains (panel b) leading to mandatory amortization in the following

year. Each point in the figure corresponds to the coefficient on an indicator variable (with ±2

standard error bands) in a separate regression fitting the assumed rate of return on controls

outlined above, industry fixed effects, and the indicator capturing gains or losses. Panel c

displays the difference between losses and gains (panels a and b) at corresponding times. The

indicator variable for time 0 is set equal to 1 if the sponsor of a plan is subject to amortization

charges during the current year, due to a large gain or loss in the prior year. Likewise, the

-5 time indicator variable is set equal to 1 if the plan sponsor will be subject to mandatory

amortization charges in 5 years, due to a large gain or loss in 4 years, but is not subject to

amortization in the current year.

From panel a of Figure 6, we can see that for times -5 through -1, the coefficient on the loss

indicator is statistically insignificant. However, at time 0, when amortization payments first

become due, we can see a statistically significant positive coefficient, as seen in Table 12. We

also see continued positive significance in the loading on indicator variables for years after the

initial amortization payment. However, this is unsurprising if firms adopt higher assumed rates

of return in order to offset income-hurting amortization charges, since these charges persist over

time.

Panel b of Figure 6 shows that, for the most part, the coefficient on the gain indicator

25

is statistically insignificant for periods prior to time 0, the date of the first income-helping

amortization entry. At time 0, as seen in specification (1) of Table 12, the coefficient on

the indicator is negative, with slight statistical significance and small magnitude. However,

indicator coefficients for times after 0 do not move further in the negative direction, but instead

turn significantly positive, in a very similar fashion those seen in panel a.

Panel c highlights the difference between coefficients for losses and gains. At time 0, the

difference between the coefficients spikes upward, becoming positive and statistically significant.

Before time 0, when no amortization charges are due, the differences are statistically insignifi-

cant. After time 0, the differences are either insignificant, or marginally significant with smaller

magnitude than the difference at time 0.

Together, the results of Table 9 and Figure 6 provide support for the hypothesis that plan

sponsors adjust the assumed rate of return on plan assets in such a way as to offset income-

hurting amortization charges, effectively smoothing income.

4.3.2 Unrecognized Prior Service Costs

When defined benefit pension plans credit plan participants for service in periods prior to

an amendment to, or initiation of, the plan, sponsors are required to begin amortizing the

unrecognized portion of service costs immediately. Our goal is to measure the effect of incurring

these amortization charges on the assumed long-term rate of return. To examine whether plan

sponsors smooth the net income effects of these charges through manipulation of the assumed

rate of return, we utilize a similar testing strategy to that employed in the previous subsection.

Specifically, we consider regressions of the following form:

pprorj,t = α+ ηhurt,levelhurtj,t + ηhelp,levelhelpj,t + ψpsensitivityj,t + εj,t,

where hurtj,t (lossj,t) is set equal to 1 if plan j has a positive (negative) balance of unrecognized

gains/losses, leading to amortization that will hurt (help) net income in year t.

Table 10 presents the results of running this regression. The left panel again contains a GICS

industry fixed effect specification, while the right panel presents results with firm fixed effects.

In both specifications, we include time indicators and control for plan investment returns over

year t, the funding ratio at time t, and the change in funding status between time t− 1 and t.

Specification (1) in Table 10 again shows that considering within-industry variation, we

estimate large positive coefficients on hurt and help, significant at the 1 and 5% levels, respec-

tively. However, these coefficients are significantly different from one another, with ηhurt,level

estimated at 46.30 basis points, versus ηhelp,level at a comparatively small 18.20 basis points.

Interpreting this difference, we can see that firms amortizing unrecognized prior service costs,

be they positive or negative, assume higher rates of return on plan assets than industry peers

without such prior service costs. However, the large differential in coefficient estimates for hurt

26

and help once again provides support for the hypothesis that plan sponsors subject to income-

hurting amortization adjust the assumed rate of return on plan assets in a fashion consistent

with income smoothing.

Examining specification (2) with firm fixed effects, we can see that compared to the baseline

of having no unrecognized prior service costs, there is statistical evidence that plan sponsors

increase the assumed rate of return upon recognizing such prior service costs. Considering only

within-firm variation, it appears that the sign of such prior service costs is of no consequence.

Figure 7 provides visual evidence, similar to that in Figure 6, of the above results considering

within-industry variation. The figure displays long-term rate of return assumptions around

periods with positive (income-hurting) and negative (income-helping) unrecognized service costs

in panels a and b, respectively. Each point in the figure corresponds to the coefficient on an

indicator variable (with ±2 standard error bands) in a separate regression fitting the assumed

rate of return on the controls listed above, industry fixed effects, and an indicator for positive or

negative unrecognized prior service costs. Panel c displays the difference in coefficients between

positive and negative unrecognized service costs (panels a and b) at corresponding times. The

indicator variable for time 0 is set equal to 1 if a plan has outstanding unrecognized prior service

costs to be amortized in that year. That is, consecutive plan-years can be assigned time 0 status,

if in both of those years the plan sponsor is subject to amortization of prior service costs. The

-5 time indicator variable is set to 1 if the plan sponsor will be subject to amortization of prior

service costs in 5 years, and is not currently, and will not in the intervening period be, subject

to such amortization charges.

From panel a of Figure 7, we can see a large spike in the coefficient on the indicator at

time 0, during the period in which firms are subject to amortization charges with a negative

effect on income. We can again see a positive spike at time 0 in panel b, but with a much

smaller magnitude, echoing the within-industry results of Table 10. It is interesting to note

that coefficients on indicators for post-time 0 periods are upward sloping in both panels.

Examining the difference between coefficients for positive and negative service costs in panel

c, we can see that at time 0, the difference between the coefficients spikes upward, becoming

positive and statistically significant. Before and after time 0, when no amortization charges are

due, the differences are either insignificant, or marginally significant.

Like previous results, the setting of unrecognized prior service costs yields results suggestive

of the hypothesis that plan sponsors adjust the assumed rate of return on plan assets in such a

way as to offset amortization charges with negative income effects.

5 Expected Returns and Asset Allocation

We now turn to an examination of whether pension fund managers actively time the market.

First, we examine whether or not fund managers are passive or active in rebalancing asset

27

allocations in response to changes in investment opportunities. Second, we examine whether

fund managers are able to successfully time investment opportunities, in the sense of return

predictability by the price-dividend ratio.

As in section 3, Rauh’s (2009) set of independent variables serve as a baseline in our re-

gression analysis. In order to measure time-independent effects of the variables of interest in

his study, Rauh includes time fixed effects in all specifications. However, in light of the return

predictability literature discussed above, it is interesting to examine the effect that variations

in the investment opportunity set have on professional money managers’ asset allocations, in

general; in this study, we examine the specific case of pension fund managers.

In order to examine pension fund managers’ responses to changes in the investment oppor-

tunity set, we require a proxy representing such changes. The return predictability literature

provides a natural candidate, in the price-dividend (PD) ratio. Pension fund managers can

essentially pursue one of three strategies in response to the level of the PD ratio:

1. Passive: Fund managers do not follow a strategy of portfolio rebalancing in response to

the level of the PD ratio.

2. Active Value: Fund managers actively rebalance into equity investments when the PD

ratio is low, and actively rebalance away from equity investments when the PD ratio is

high.

3. Active Momentum: Fund managers actively rebalance away from equity investments

when the PD ratio is low, and actively rebalance into equity investments when the PD

ratio is high.

We perform a series of tests in order to distinguish which of these strategies, if any, is

pervasively followed by pension fund managers.22 The first of these tests examines the broader

question of whether pension fund managers are active or passive investors, in the face of changes

in the level of the PD ratio.23 In order to tackle this question, we utilize the active reallocations

across asset classes outlined in section 3.2.1.

5.1 Are pension fund managers active or passive?

Table 11 presents the results of pooled specifications (ie. without plan-fixed effects), regressing

active asset class reallocations from Table 6 on the variable of interest, the lagged change in the

log-PD ratio. Panel a displays the results of these tests using the IRS Form 5500 sample, while

22We recognize the difficulty of concluding the Passive strategy is followed in our study design, since doing sorequires the satisfaction of a joint hypothesis: that fund managers are acting in a consistent manner and thatfund managers are passive. We avoid this joint hypothesis problem, in that our results do not support the Passivestrategy.

23We use the log-PD ratio in our empirical specifications, consistent with return predictability regression resultsoutlined in Campbell, Lo, and MacKinlay (1997).

28

panel b is generated using the P&I sample. The table is also split into four panels from left

to right, with each horizontal panel corresponding to active reallocations to a separate general

asset class. The general asset classes considered are equity, debt, cash, and the other category

described in Table 6. Within each of these horizontal panels, we consider two specifications.

The first column is a regression of the active reallocation into the respective general asset classes

on just the lagged change in the log-PD ratio. The independent variable in this regression is

calculated as:

∆pdt−1 = pdt−1 − pdt−2 = log(PDt−1) − log(PDt−2),

where PDt represents the price-dividend ratio at time t, pdt is equal to log(PDt), and the

regressand is wactivei,t .

The second column adds controls adapted from Rauh (2009). For the Form 5500 regressions,

these controls include the pension funding status, the active share of employees, and the size

of the pension at time t− 1, both in levels and logs. For the P&I panel, these controls include

the pension funding status, the S&P credit rating of the sponsor, the sponsor’s operating assets

and the plan’s assets, both in logs, as well as Altman’s Z-score.

Although our method of calculating active reallocations is essentially a control in itself for

the portfolio return of each fund, given its asset allocations at times t−1 and t, it is nevertheless

a noisy one. We therefore also include in the second column, where available, each fund’s actual

investment return over the period from time t − 1 to t. Including this return should capture

the idiosyncratic component of individual funds’ asset reallocations caused by idiosyncratic

deviations from the portfolio return we would expect, rp,t, based on their asset class allocations

at time t− 1.

The return predictability literature discussed above suggests that the level of the log-PD

ratio is a good predictor of future equity returns at horizons of one year and longer. However,

since we wish to examine the question of whether fund managers actively rebalance their port-

folios after exogenous shocks to their asset class weights, it is instead the change in the log-PD

ratio which is of interest as a regressor. Since passive equity allocations are increasing in the

log-PD ratio(ie. if prices are increasing), then we would expect active managers to move out

of equity, and hence for the coefficients of interest in the equity panel of Table 11 (columns (1)

and (2)) to be negative. By the same token, we would expect a positive coefficient of interest

in the debt panel of Table 11 (columns (3) and (4)) if pension fund managers are indeed active.

The results in Table 11 demonstrate that the lagged change in the log-PD ratio is negatively

correlated with active reallocations to equity, and positively correlated with active reallocations

to debt. These coefficients can be interpreted as follows: when changes in the PD ratio move

portfolio allocations away from the fund manager’s chosen optimum for each asset class, the

fund manager actively moves capital into and out of asset classes such that allocations move

29

toward the previously optimal levels. This result is also robust to controlling for the fund’s

investment return in the year of active reallocations, as well as other measures of plan sponsor

heterogeneity.24

From Table 11, we can also see that the lagged change in the log-PD ratio is positively

correlated with active reallocations to cash, and negatively correlated with active reallocations

to other asset classes. These results are consistent with and without the inclusion of control

variables, and are statistically stronger in Panel a (IRS Form 5500 sample). Similar coefficient

magnitudes between the two samples suggest that the difference in estimation precision may be

due to the difference in sample sizes. Qualitative interpretation of these coefficients is consistent

with that for equity and debt active reallocations: an increase in the PD ratio alone will have no

effect on the level of cash holdings, but will drive down the percentage of pension assets that cash

holdings represent. Therefore, a positive active reallocation to cash will restore cash holdings

to their previous level, as a percentage of plan assets. The value of asset classes composing

the other category (ie. private equity, mortgages) will plausibly have a positive correlation with

changes in the PD ratio, indicating that negative active reallocations will be necessary to restore

previous allocation levels after an increase in the PD ratio.

Table 12 repeats the analysis of Table 11, but with plan fixed effect specifications. The

results with plan fixed effects indicate a very similar relation between lagged changes in the PD

ratio and active asset class reallocations, as we would expect with a regressor that is invariant

in the cross-section. Therefore, the active reallocation discussion extends to the case where we

consider only variation within plans over time, and fully control for unobserved heterogeneity

between plans in a given year. Positive (negative) lagged changes lead to active reallocations

out of (into) equity and active reallocation into (out of) debt.

While the direction of active reallocations in response to changes in the investment oppor-

tunity set are consistent for the equity and debt asset classes across the samples, the estimated

magnitudes of response differ markedly. However, examining the distributions of debt and eq-

uity allocations for the respective samples in Tables 1b and 2, we know that P&I plans invest a

much higher proportion of assets in equity, and a much lower proportion in debt, than those in

the Form 5500 sample.25 Hence, higher magnitudes should be expected when considering active

reallocations if fund managers are rebalancing toward previously optimal asset class weights,

since changes in the PD-ratio will have a larger effect on the allocations of those plans with

higher initial allocations to equity. Whether the larger coefficients should be interpreted as a

causal story of changes in the investment opportunity set leading P&I plans to change their

optimal portfolio allocations is not the focus of our investigation in this section. We consider

24In untabulated results, we run separate regressions including each of the control variables individually. Theresults do not change.

25At the mean, P&I plans invest 61.84% of assets in equity and 28.13% in debt, versus respective allocations of44.87% and 14.67% for Form 5500 sponsors. Median allocations to equity (debt) are also largely higher (lower)for P&I plans.

30

this important question in the next section.

5.2 Do pension fund managers time the market?

The previous section examined whether pension fund managers are active or passive in response

to changes in the investment opportunity set, with the conclusion that fund managers are indeed

active. This section considers how fund managers’ asset allocation decisions are affected by the

level of the PD ratio; in other words, whether or not they successfully time the market.

5.2.1 Methodology

The return predictability literature has shown that, for horizons of one to four years, the log

PD ratio (or, equivalently, the log dividend yield) is a strong predictor of future returns (ie.

Fama and French (1988)). Indeed, the log PD ratio can be written as a linear function of

expected equity market returns and the expected dividend growth rate, as originally shown

by Campbell and Shiller (1988). Given these results, we hypothesize that fund managers will

follow the Active Value strategy outlined earlier. That is, all else equal, sophisticated pension

fund managers should increase fund allocations to equity when they observe a relatively low

PD ratio (expected returns to equity are high), and decrease their allocations to equity when

the PD ratio is relatively high (expected returns to equity are low).

Our empirical tests of this hypothesis center around measuring the direction and strength

of the correlation between the log PD ratio at time t − 1 and the levels of asset class hold-

ings measured at time t. However, before embarking on our testing strategy, it is important to

consider a very important potential source of omitted variables bias (OVB) that may be present.

Denoting the weight at time t in asset class i, for fund j, as wi,j,t, consider the following

two regressions:

wi,j,t = α1 + φ1pdt−1 + ε1,i,j,t, and

wi,j,t = α2 + φ2pdt−1 + γrequity,j,t + ε2,i,j,t,

where pdt represents the log PD ratio at time t−1, and requity,j,t represents the return on equity

holdings between times t− 1 and t for fund j.

The regressor requity,j,t in the second regression serves to control for the passive change in asset

class weights that occurs when requity,j,t varies. We consider requity,j,t instead of1+ri,j,t1+rp,j,t

for each

asset class i (as described earlier) since it is largely variation in requity,j,t that drives variation

in this quantity, capturing the effect of passive changes for all asset classes.

In this framework of equations, the so-called OVB Formula relating the coefficients of inter-

31

est in the above regressions, φ1 and φ2, is given by26:

φ1 = φ2 + γδ,

where δ is the coefficient from the following regression:

requity,j,t = α3 + δpdt−1 + ε3,j,t.

This regression bears a strong resemblance to those considered in the long-horizon predictability

literature (ie. Fama and French (1988)), the conclusions of which suggest that there is a strong

negative correlation between requity,j,t and pdt−1, and hence, that φ1 will be biased downward

from its true value if we neglect to control for requity,j,t.

Since we do not observe requity,j,t for each fund j and time t pairing, we appeal to the use

of a proxy variable. Given the large proportion of pension asset holdings that are composed of

equity, it is reasonable that variation in rp,j,t is largely driven by variation in requity,j,t, making

rp,j,t a good proxy variable.27

5.2.2 Results

Table 11 presents the results of plan fixed effect specifications, regressing asset class allocations

on the lagged log-PD ratio. Panel a displays the results of these tests using the IRS Form

5500 sample, while panel b is generated using the P&I sample. As in Tables 11 and 12, Table

13 is also split into four panels from left to right, with each horizontal panel corresponding to

allocations in a separate general asset class. The asset class classifications are as before: equity,

debt, cash, and the other category. Within each of these horizontal panels, we consider three

specifications. The first column is a regression of asset class weights on just the lagged log-PD

ratio. The second column adds the proxy variable identified in the previous section, the fund’s

portfolio return between times t − 1 and t, in order to control for the OVB discussed earlier.

Finally, the third column adds the controls adapted from Rauh (2009) discussed earlier.

Comparing columns (1) and (2) of Table 13, we can see that, as expected from the discussion

in the Methodology section above, inclusion of the portfolio investment return as a control in the

regression leads to a large increase in the coefficient of the lagged log-PD ratio in both samples.

Mechanically, since debt, for the most part, makes up the residual allocation after equity, it

is natural that the OVB is in the opposite (upward) direction to that for equity allocations.

Again, this is evident when comparing columns (4) and (5) of Table 13. Once again, inclusion

of the portfolio investment return leads to large changes, this time in the downward direction,

of the coefficient of interest, that on the lagged log-PD ratio. The results for the cash and other

26See Wooldridge (2002) or Angrist and Pischke (2009) for further details.27The correlation coefficients (p-values) between rp,j,t and pdt−1 are -0.211 (0.000) and -0.482 (0.000) in the

Form 5500 and P&I samples, respectively.

32

asset class categories are economically insignificant, and therefore we forgo their discussion but

nevertheless include them for completeness and transparency.

The results in columns (3) and (6) of Table 13 demonstrate that, after controlling for the

portfolio return, a host of firm- and plan-level regressors, and even unobserved sources of cross-

sectional heterogeneity (plan fixed effects), the lagged PD ratio is positively correlated with

equity allocations, and negatively correlated with the allocation to debt securities. The coeffi-

cients of interest can be interpreted as follows: when the lagged PD ratio is high, controlling

for other sources of variation, pension fund managers tend to increase their equity allocations

and decrease their debt allocations. Referring back to our earlier discussion of pension fund

managers’ candidate strategies, these results indicate that fund managers pervasively follow

what we labeled the Active Momentum strategy.

In light of our earlier discussion of the return predictability literature, this result is striking,

since it indicates that with a high degree of statistical and economic significance, pension fund

managers’ investment decisions in response to the level of the PD ratio is exactly the opposite

of what we would expect. Fund managers increase their allocations to equity and decrease those

to debt precisely when the expected returns to equity are lowest, and move out of equity and

increase weights in debt when the expected returns to equity are highest.

Anecdotal evidence, in the form of the authors’ conversations with pension industry insiders,

suggests that the observed response to the level of the PD ratio may be due to time-varying in-

vestment constraints placed on fund managers. After long equity market runups, fund managers

may be able to convince investment boards that larger allocations to equity are necessary in

order to avoid a continued sense of missing out on favorable returns. However, this is precisely

the time when PD ratios are highest, and when, according to the predictability literature, these

funds should be decreasing allocations to the equity market.

6 Conclusion

In this paper, we studied two related issues, with the ultimate goal of further explaining the

determinants of decision-making in private DB pension plans. First, we examined the effect

of pension regulations on both fund managers’ asset allocation decisions, and firm managers’

pension accounting assumptions. In both cases, we found evidence that regulations had econom-

ically and statistically significant effects. Second, we examined whether pension fund managers

are tactical in their asset allocation decisions, with the conclusion that while pension fund man-

agers are indeed active, their portfolio holdings do not indicate an ability to successfully time

the market, in the sense of exploiting the results of return predictability.

33

References

[1] Altman, E.I., 1968, Financial Ratios, Discriminant Analysis and the Prediction of Corpo-

rate Bankruptcy, The Journal of Finance 23, 589-609.

[2] Angrist, J.D., and Pischke, J., 2009, Mostly Harmless Econometrics: An Empiricist’s Com-

panion, Princeton University Press, Princeton, NJ.

[3] Ball, R., and Brown, P., 1968, An Empirical Evaluation of Accounting Income Numbers,

Journal of Accounting Research 6, 159-178.

[4] Bergstresser, D., Desai, M., and Rauh, J., 2006, Earnings Manipulation, Pension Assump-

tions, and Managerial Investment Decisions, The Quarterly Journal of Economics 121,

157-195.

[5] Bernard, V.L., and Thomas, J.K., 1989, Post-Earnings-Announcement Drift: Delayed Price

Response or Risk Premium?, Journal of Accounting Research 27, 1-36.

[6] Bernard, V.L., and Thomas, J.K., 1990, Evidence that stock prices do not fully reflect the

implications of current earnings for future earnings, Journal of Accounting and Economics

13, 305-340.

[7] Bhojraj, S., Lee, C.M.C., and Oler, D.K., 2003, What’s My Line? A Comparison of Indus-

try Classification Schemes for Capital Market Research, Journal of Accounting Research

41, 745-774.

[8] van Binsbergen, J.H., and Brandt, M.W., 2007, Optimal Asset Allocation in Asset Liability

Management, NBER working paper 12970.

[9] van Binsbergen, J.H., and Koijen, R.S.J., forthcoming, Predictive Regressions: A Present-

Value Approach, The Journal of Finance.

[10] Black, F., 1980, The Tax Consequences of Long-Run Pension Policy, Financial Analysts

Journal 36, 21-28.

[11] Blake, D., Lehmann, B.N., and Timmermann, A., 1999, Asset Allocation Dynamics and

Pension Fund Performance, Journal of Business 72, 429-461.

[12] Brandt, M.W., Santa-Clara, P., and Valkanov, R., forthcoming, Parametric Portfolio Poli-

cies: Exploiting Characteristics in the Cross-Section of Equity Returns, Review of Financial

Studies.

[13] Breon-Drish, B., and Sagi, J.S., 2008, Do fund managers make informed asset allocation

decisions?, Vanderbilt University working paper.

34

[14] Buessing, M., and Soto, M., 2006, The State of Private Pensions: Current 5500 Data,

Center for Retirement Research Issue in Brief 42.

[15] Campbell, J.Y., and Viceira, L.M., 2006, Strategic Asset Allocation for Pensions, Oxford

Handbook of Pensions and Retirement Income, Oxford University Press, Oxford.

[16] Chava, S., and Roberts, M.R., 2008, How Does Financing Impact Investment? The Role

of Debt Covenants, The Journal of Finance 63, 2085-2121.

[17] Coggin, D.T., Fabozzi, F.J., and Rahman, S., 1993, The Investment Performance of U.S.

Equity Pension Fund Managers: An Empirical Investigation, The Journal of Finance 48,

1039-1055.

[18] Financial Accounting Standards Board, 2007, Statement of Financial Accounting Standards

No. 87 Employers’ Accounting for Pensions, Original Pronouncements as Amended.

[19] Franzoni, F., and Marin, J.M., 2006, Pension Plan Funding and Stock Market Efficiency,

The Journal of Finance 61, 921-956.

[20] Fung, H., Xu, X.E., and Yau, J., 2002, Global Hedge Funds: Risk, Return, and Market

Timing, Financial Analysts Journal 58, 19-30.

[21] Graham, J.R., and Harvey, C.R., 1996, Market timing ability and volatility implied in

investment newsletters’ asset allocation recommendations, Journal of Financial Economics

42, 397-421.

[22] Hahn, J., Todd, P., and van der Klaauw, W., 2001, Identification and Estimation of Treat-

ment Effects with a Regression-Discontinuity Design, Econometrica 69, 201-209.

[23] Imbens, G.W., and Lemieux, T., 2008, Regression discontinuity designs: A guide to prac-

tice, Journal of Econometrics 142, 615-635.

[24] International Financial Services London, 2009, Fund Management 2009.

[25] Jagannathan, R., and Korajczyk, R.A., 1986, Assessing the Market Timing Performance

of Managed Portfolios, Journal of Business 59, 217-235.

[26] Jiang, G.J., Yao, T., and Yu, T., 2007, Do mutual funds time the market? Evidence from

portfolio holdings, Journal of Financial Economics 86, 724-758.

[27] Kandel, S., and Stambaugh, R.F., 1996, On the Predictability of Stock Returns: An Asset-

Allocation Perspective, The Journal of Finance 51, 385-424.

[28] Kieso, D.E., Weygandt, J.J., and Warfield, T.D., 2007, Intermediate Accounting: Twelfth

Edition, John Wiley & Sons, Hoboken, NJ.

35

[29] Lee, D.S., 2008, Randomized experiments from non-random selection in U.S. House elec-

tions, Journal of Econometrics 142, 675-697.

[30] Lee, D.S., and Lemieux, T., 2009, Regression Discontinuity Designs in Economics, NBER

working paper 14723.

[31] McCrary, J., 2008, Manipulation of the running variable in the regression discontinuity

design: A density test, Journal of Econometrics 142, 698-714.

[32] Munnell, A., and Soto, M., 2003, The Outlook for Pension Contributions and Profits in

the U.S., Boston College Center for Retirement Research Working Paper.

[33] Rauh, J.D., 2006, Investment and Financing Constraints: Evidence from the Funding of

Corporate Pension Plans, The Journal of Finance 61, 33-71.

[34] Rauh, J.D., 2009, Risk Shifting versus Risk Management: Investment Policy in Corporate

Pension Plans, Review of Financial Studies 22, 2687-2733.

[35] Samuelson, W., and Zeckhauser, R., 1988, Status Quo Bias in Decision Making, Journal

of Risk and Uncertainty 1, 7-59.

[36] Sharpe, W.F., 1976, Corporate Pension Funding Policy, Journal of Financial Economics

3, 183-193.

[37] Tepper, I., 1981, Taxation and Corporate Pension Policy, The Journal of Finance 34, 1-13.

[38] Thaler, R., 1980, Toward a Positive Theory of Consumer Choice, Journal of Economic

Behavior and Organization 1, 39-60.

[39] Treynor, J.L., 1977, The Principles of Corporate Pension Finance, The Journal of Finance

32, 627-638.

[40] Wooldridge, J., 2002, Econometric Analysis of Cross Section and Panel Data, MIT Press,

Cambridge, MA.

36

Figure 1: Funding status density plots

0.0

05.0

1.0

15.0

2D

ensi

ty E

stim

ate

−.5 0 .5 1Funding Status

Panel a: −20% discontinuity

0.0

05.0

1.0

15.0

2D

ensi

ty E

stim

ate

−.5 0 .5 1Funding Status

Panel b: 0% discontinuity

This figure displays smoothed density plots of plans across funding status bins. Constructionof the density plots follows the algorithm developed in McCrary (2008). Panel a concentratesaround the -20% funding status discontinuity, while panel b focuses on the 0% funding statusdiscontinuity.

37

Fig

ure

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38

Fig

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41

Figure 6: Assumed long-term rate of return: Unrecognized gains and losses

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel a: Large losses

Loss '‐1.96StdErr '+1.96StdErr

0 2

0.3

0.4

0.5

0.6 Panel b: Large gains

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel a: Large losses

Loss '‐1.96StdErr '+1.96StdErr

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel b: Large gains

Gain '‐1.96StdErr '+1.96StdErr

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel c: Losses minus gains

L G i ' 1 96StdE '+1 96StdE

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel a: Large losses

Loss '‐1.96StdErr '+1.96StdErr

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel b: Large gains

Gain '‐1.96StdErr '+1.96StdErr

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel c: Losses minus gains

Loss ‐ Gain '‐1.96StdErr '+1.96StdErr

This figure displays long-term rate of return assumptions around large funding status losses(panel a) and gains (panel b) leading to mandatory amortization in the following year. Eachpoint corresponds to the coefficient on an indicator variable (with ±2 standard error bands) ina separate regression fitting the assumed rate of return on controls (see text), industry fixedeffects, and the indicator for gains or losses. Panel c displays the difference in coefficientsbetween losses and gains (panels a and b) at corresponding times. The indicator for time 0 isset equal to 1 if the sponsor of a plan is subject to amortization charges during the current year,due to a large gain or loss during the prior year. The -5 time indicator variable is set equal to 1if the plan sponsor will be subject to mandatory amortization in 5 years, but not in the currentyear. Standard errors are heteroskedasticity robust and clustered by plan sponsor.

42

Figure 7: Assumed long-term rate of return: Unrecognized prior service costs

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel a: Positive unrecognized service costs

Hurt '‐1.96StdErr '+1.96StdErr

0.4

0.5

0.6

0.7Panel b: Negative unrecognized service costs

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel a: Positive unrecognized service costs

Hurt '‐1.96StdErr '+1.96StdErr

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel b: Negative unrecognized service costs

Help '‐1.96StdErr '+1.96StdErr

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel c: Positive minus negative unrecognized service costs

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel a: Positive unrecognized service costs

Hurt '‐1.96StdErr '+1.96StdErr

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel b: Negative unrecognized service costs

Help '‐1.96StdErr '+1.96StdErr

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5

Panel c: Positive minus negative unrecognized service costs

Hurt‐ Help '‐1.96StdErr '+1.96StdErr

This figure displays long-term rate of return assumptions around periods with positive (income-hurting) and negative (income-helping) unrecognized service costs in panels a and b, respectively.Each point corresponds to the coefficient on an indicator variable (with ±2 standard error bands)in a separate regression fitting the assumed rate of return on controls (see text), industry fixedeffects, and the indicator for positive or negative unrecognized service costs. Panel c displays thedifference in coefficients between positive and negative unrecognized service costs (panels a andb) at corresponding times. The indicator for time 0 is set equal to 1 if a plan has outstandingunrecognized prior service costs to be amortized in that year. The -5 time indicator variableis set equal to 1 if the plan sponsor will be subject to amortization of prior service costs in 5years, but not in the current year. Standard errors are heteroskedasticity robust and clusteredby plan sponsor.

43

Tab

le 1

IRS

Form

550

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mm

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stat

istic

s (19

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007)

: (a)

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ple

and

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44

Tab

le 1

(con

tinue

d)M

ean

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ian

Stan

dard

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nM

inim

umM

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um

Leve

ls (i

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45

Table 2Pensions & Investments summary statistics (1998-2004)

Mean Median Standard deviation Minimum Maximum

Firm characteristicsS&P credit rating (0-1) 0.633 0.679 0.224 0.000 0.929No S&P credit rating 0.089 0.000 0.285 0.000 1.000Sponsor assets ($ billions) 30.640 8.628 93.348 0.314 1264.032Ln(Sponsor assets in $ millions) 9.156 9.063 1.335 5.749 14.050Altman's Z-score 1.485 1.384 0.931 -0.409 4.090

Pension characteristicsPension assets ($ billions) 3.395 1.172 8.327 0.025 99.909Ln(Pension assets in $ millions) 7.177 7.066 1.218 3.219 11.512Pension liabilities ($ billions) 3.326 1.191 8.033 0.043 108.816Pension funding status 0.019 -0.035 0.315 -0.808 2.068Investment return* 0.065 0.094 0.122 -0.525 0.750

Asset allocation (%)Equity 61.84 63.00 13.55 0.00 100.00Debt 28.13 28.00 11.22 0.00 94.00Cash 2.03 1.00 4.38 0.00 100.00Other 8.00 4.00 12.95 0.00 100.00

Total observations 1902Total unique firms 411

Pension asset allocation data come from the annual Pensions & Investments 1000 survey of the largest pensionplans as ranked by assets under management. Firm characteristics come from the Compustat AnnualFundamentals file. Pension characteristics are from the Compustat Annual Pension Plans file. The S&P credit ratingvariable take a calue of 0.036 for sponsors with a D rating, and a value of 0.929 for those with an AAA rating. Eachrating in between takes value that incrementally raises the rating variable by 0.036. Altman's Z-score is calculatedusing the following function of Compustat Xpressfeed codes: 3.3*ebit/at + sale/at + 1.4*re/at + 1.2*wcap/atPension assets are measured using Compustat code pplao , and pension liabilities are measured using pbproPension funding status is calculated as the difference between pension assets and liabilities, all divided by pensionliabilities. Pension investment return is calculated as pension investment income divided by BOY pension assets.*The number of observations for this variable is only 1,777.

46

Table 3Compustat Pension Plans summary statistics (1994-2007)

Mean Median Standard deviation Minimum Maximum

Full sampleAssumed long-term rate of return (%) 8.24 8.50 1.26 3.00 10.50Pension sensitivity -0.434 -0.316 1.351 -4.344 2.773Funding status -0.118 -0.146 0.286 -0.736 0.868Gain indicator 0.120 0.000 0.325 0.000 1.000Loss indicator 0.277 0.000 0.447 0.000 1.000Hurt indicator 0.680 1.000 0.466 0.000 1.000Help indicator 0.145 0.000 0.352 0.000 1.000

Total observations 12946Total unique firms 2418

-40% to 0% restricted funding status sampleAssumed long-term rate of return (%) 8.12 8.25 1.09 3.00 10.50Pension sensitivity -0.386 -0.307 1.280 -4.344 2.773Funding status -0 188 -0 183 0 105 -0 399 0 000Funding status -0.188 -0.183 0.105 -0.399 0.000Critical funding status indicator 0.391 0.000 0.488 0.000 1.000

Total observations 8386Total unique firms 2013

-20% to 20% restricted funding status sampleAssumed long-term rate of return (%) 8.23 8.50 1.18 3.00 10.50Pension sensitivity -0.258 -0.174 1.256 -4.344 2.773Funding status -0.050 -0.068 0.103 -0.200 0.200Critical funding status indicator 0.490 0.000 0.500 0.000 1.000

Total observations 6608Total unique firms 1885

All data come from the Compustat Annual Pension Plans dataset. Pension sensitivity is calculated as the log ratioof pension assets to net operating income before depreciation. Pension funding status is calculated as thedifference between pension assets and liabilities, all divided by pension liabilities. The gain (loss) indicator is setequal to 1 if in the prior year a plan experienced a large gain (loss), leading to amortization in the current year. Thehurt (help) indicator is set equal to 1 if a plan sponsor has a positive (negative) balance of unrecognized priorservice costs to be amortized in the current year. The critical funding status indicator is set equal to 1 if a plan-yearobservation's funding status is between -40% and -20% (-20% and 0%) in the -40% to 0% (-20% to 20%)restricted sample. Other than indicators, all variables are winsorized at the 1% level to avoid the effects of outliers.

47

Table 4McCrary funding status density test

0% discontinuity -20% discontinuityLog discontinuity estimate 0.0494 -0.0051

(0.0489) (0.0447)

N 1033 1033

This table presents the results of a statistical density test developed byMcCrary (2008). The sample is composed of funding ratios for plan-yearobservations in the Pensions & Investments sample for which we there existactive asset class reallocations. The log discontinuity estimate is calculated asthe difference in the log of fitted densities using fourth-order polynomialsestimated on each side of the discontinuity point. Standard errors of logdiscontinuity estimates are reported in parentheses, and are calculated usingan asymptotically normal formula detailed by McCrary (2008). ***Statisticallysignificant at the 1% level, **statistically significant at the 5% level, *statisticallysignificant at the 10% level.

48

Table 5Asset class benchmark return indices

Asset Class Return Index Datastream Mnemonic(if applicable)

IRS Form 5500 sampleEquity 80%: CRSP S&P500 w/Dividend, 20%: MSCI World ex-US Government Debt JP Morgan US Government Bond Index JPMUSU$Corporate Debt Citigroup US Broad Investment Grade Bond Index USBBIG..Real Estate Dow Jones US Select REIT Index WILDJRTMortgages Datastream US Mortgage Index MORTFUS

Pensions & Investments sampleDomestic Equity CRSP S&P500 w/Dividend IndexInternational Equity MSCI World ex-US Index MSWXUSLDomestic Fixed Income Merrill Lynch US Domestic Index MLDOMEMInternational Fixed Income JP Morgan Broad ex-US Index JPMBXUSReal Estate Dow Jones US Select REIT Index WILDJRTMortgages Datastream US Mortgage Index MORTFUSPrivate Equity Post Venture Capital Index PVCINDX

This table outlines the indices we use as a source for benchmark returns for each asset class in calculating the passiveallocations, and in turn, active reallocations used in the paper. See section 3.1 for further details.

49

Table 6Active asset class reallocations summary statistics

Mean Median Standard deviation Minimum Maximum

IRS Form 5500 sample active reallocations (%)Equity 0.61 0.00 12.29 -51.39 42.86Debt -1.31 -0.14 12.84 -47.99 39.99Cash 0.80 0.00 14.92 -48.28 74.88Other -0.10 0.00 2.59 -4.63 2.41

Total observations 34139Total unique firms 411Total unique firms 411

Pensions & Investments sample active reallocations (%)Equity 1.54 0.32 8.50 -14.44 21.59Debt -1.36 -0.06 8.41 -21.15 17.21Cash -0.19 0.00 3.07 -9.67 6.19Other 0.00 0.00 2.94 -9.06 9.00

Total observations 1051Total unique firms 7158

This table presents summary statistics of the active asset class reallocations used in this paper. Activereallocations for each asset class are calculated following the algebra in Brandt, Santa-Clara, and Valkanov(forthcoming), outline in section 3.1 of this paper. Active reallocations for the IRS Form 5500 sample arecalculated using allocations as a share of noninsurance assets.

50

Table 7Calculation of Pension Expense for Defined-Benefit Corporate Plans

Component of Pension Expense DescriptionService cost for benefits earned Increase in pension benefits payable due to services

rendered in the current year

+ Interest cost on benefit obligation Accrual for discounting of pension obligations

+ Unrecognized prior service cost amortization Amortization of cost of retroactive benefits credited to employees for prior years of service at time of plan initiation or amendment

+ Net actuarial gain/loss amortization Amortization of accumulated unrecognized gains/losses in excess of pension corridor in magnitude

Less: Assumed return on plan assets Product of assumed long-term rate of return and pension assets

= Pension expense

51

Table 8Pension fund assumed rate of return around critical funding ratios

Specification

Dependent variable

(1) (2) (3) (4)

Critical funding status indicator 0.102*** 0.0168(0.0315) (0.0156)

Critical funding status indicator interacted with pension 0.0397* 0.00557 sensitivity (0.0221) (0.0125)

Critical funding status indicator with improvement 0.107*** 0.0106(0.0330) (0.0167)

Critical funding status indicator with improvement 0.0249 -0.00181 interacted with pension sensitivity (0.0228) (0.0133)

Critical funding status indicator with deterioration 0.0915** 0.0398**(0.0431) (0.0202)

Critical funding status indicator with deterioration 0.0743** 0.0292** interacted with pension sensitivity (0.0330) (0.0146)

Pension sensitivity 0.143*** 0.143*** -0.000826 -0.00157(0.0189) (0.0189) (0.0175) (0.0175)

Observations 8386 8386 8386 8386Firms 2013 2013 2013 2013R-squared 0.247 0.247 0.345 0.346

GICS Industry fixed effects Firm fixed effects

Assumed long-term rate of return on plan assets

Assumed long-term rate of return on plan assets

Panel a: 0% to 40% underfunded sample

Critical funding status indicator -0.0513* -0.00389(0.0283) (0.0151)

Critical funding status indicator interacted with pension 0.00125 0.00391 sensitivity (0.0224) (0.0137)

Critical funding status indicator with improvement -0.0163 -0.000660(0.0304) (0.0161)

Critical funding status indicator with improvement 0.00722 -0.000796 interacted with pension sensitivity (0.0237) (0.0147)

Critical funding status indicator with deterioration -0.123*** -0.00828(0.0370) (0.0180)

Critical funding status indicator with deterioration -0.00983 0.0143 interacted with pension sensitivity (0.0292) (0.0162)

Pension sensitivity 0.131*** 0.130*** 0.00426 0.00391(0.0205) (0.0204) (0.0206) (0.0207)

Observations 6608 6608 6608 6608Firms 1885 1885 1885 1885R-squared 0.297 0.298 0.430 0.431

This table presents the results of specifications regressing the long-term assumed rate of return on pension assets on funding statusindicators, in levels and interacted with pension sensitivity. Panel a displays results using the restricted sample of plan-year observationswith funding status between -40% and 0%, and funding status indicator equal to 1 if funding status is less than -20%. Panel b reportsresults using the restricted sample of observations with funding status between -20% and 20%, and funding status indicator equal to 1 iffunding status is less then 0%. Pension sensitivity is calculated as the log ratio of pension assets to net operating income beforedepreciation. See Table 3 for summary statistics. The table is split into two horizontal panels. The left panel displays results ofspecifications with GICS industry level fixed effects (68 industries). The right panel displays results of specifications with plan fixed effects.

Panel b: 20% underfunded to 20% overfunded sample

All variables are calculated from the Compustat Annual Pension Plans dataset and are measured as of the beginning of the plan year.Additional control variables in all specifications that are unreported are the lagged funding status, change in funding status over the currentyear, and portfolio return over the current year. Standard errors are heteroskedasticity robust and clustered by plan sponsor. ***Statisticallysignificant at the 1% level, **statistically significant at the 5% level, *statistically significant at the 10% level.

52

Table 9Pension fund assumed rate of return following large gains/losses

Specification

Dependent variable

(1) (2) (3) (4)

Gain indicator -0.0238 0.0105(0.0494) (0.0172)

Gain indicator interacted with pension sensitivity -0.0478* -0.0221(0.0262) (0.0135)

Loss indicator 0.197*** 0.0308**(0.0298) (0.0138)

Loss indicator interacted with pension sensitivity 0.00798 0.0204***(0.0175) (0.00781)

Gain_up indicator -0.155** -0.00311(0.0774) (0.0232)

Gain_up indicator interacted with pension sensitivity -0.0456 -0.0236(0.0402) (0.0177)

Gain_dn indicator 0.101** 0.0221(0.0422) (0.0220)

GICS Industry fixed effects Firm fixed effects

Assumed long-term rate of return on plan assets

Assumed long-term rate of return on plan assets

Gain_dn indicator interacted with pension sensitivity -0.0442 -0.0197(0.0301) (0.0191)

Loss_up indicator 0.146*** 0.0274*(0.0323) (0.0166)

Loss_up indicator interacted with pension sensitivity 0.00799 0.00631(0.0216) (0.00977)

Loss_dn indicator 0.249*** 0.0321*(0.0392) (0.0172)

Loss_dn indicator interacted with pension sensitivity 0.00989 0.0332***(0.0217) (0.0100)

Pension sensitivity 0.172*** 0.171*** 0.0117 0.0104(0.0187) (0.0187) (0.0173) (0.0174)

Observations 12946 12946 12946 12946Firms 2418 2418 2418 2418R-squared 0.284 0.285 0.348 0.348

This table presents the results of specifications regressing the long-term assumed rate of return on pension assets on large gain andloss indicators, in levels and interacted with pension sensitivity. The gain indicator is set equal to 1 when a fund experiences a large gainin the prior year, leading to mandatory income-helping amortization in the year of observation. The loss indicator is equal to 1 when afund experiences a large loss in the previous year, leading to mandatory income-hurting amortization in the year of observation. Pensionsensitivity is calculated as the log ratio of pension assets to net operating income before depreciation. See Table 3 for summarystatistics. The table is split into two horizontal panels. The left panel displays results of specifications with GICS industry level fixedeffects (68 industries). The right panel displays results of specifications with plan fixed effects. All variables are calculated from theCompustat Annual Pension Plans dataset and are measured as of the beginning of the plan year. Additional control variables in all

ifi ti th t t d th l d f di t t h i f di t t th t d tf li tspecifications that are unreported are the lagged funding status, change in funding status over the current year, and portfolio return overthe current year. Standard errors are heteroskedasticity robust and clustered by plan sponsor. ***Statistically significant at the 1% level,**statistically significant at the 5% level, *statistically significant at the 10% level.

53

Table 10Pension fund assumed rate of return and prior service costs

Specification GICS Industry fixed effects Firm fixed effects

Dependent variable Assumed long-term rate of return on plan assets

Assumed long-term rate of return on plan assets

(1) (2)

Hurt indicator 0.463*** 0.0548*(0.0482) (0.0313)

Help indicator 0.182** 0.0645*(0.0753) (0.0386)

Pension sensitivity 0.142*** 0.0138(0.0171) (0.0164)

Observations 12946 12946Firms 2418 2418R-squared 0.301 0.347

This table presents the results of specifications regressing the long-term assumed rate ofreturn on pension assets on indicators for the presence of unrecognized prior service coststhat hurt and help income. The hurt indicator is set equal to 1 when a fund has positiveunrecognized prior service costs, leading to mandatory income-hurting amortization in theyear of observation. The help indicator is equal to 1 when a fund has negative unrecognizedprior service costs, leading to mandatory income-helping amortization in the year ofobservation. Pension sensitivity is calculated as the log ratio of pension assets to netoperating income before depreciation. See Table 3 for summary statistics. The table is splitinto two horizontal panels. The left panel displays results of specifications with GICS industrylevel fixed effects (68 industries). The right panel displays results of specifications with planfixed effects. All variables are calculated from the Compustat Annual Pension Plans datasetand are measured as of the beginning of the plan year. Additional control variables in allspecifications that are unreported are the lagged funding status, change in funding statusover the current year, and portfolio return over the current year. Standard errors areheteroskedasticity robust and clustered by plan sponsor. ***Statistically significant at the 1%level, **statistically significant at the 5% level, *statistically significant at the 10% level.

54

Table 11Pension fund active asset reallocations and Price-Dividend ratios, pooled specifications

(1) (2) (3) (4) (5) (6) (7) (8)

Lag Change PD ratio -2.727*** -2.577*** 2.363*** 2.202*** 0.761 0.784 -0.396*** -0.409***(0.455) (0.475) (0.472) (0.490) (0.547) (0.565) (0.0915) (0.0893)

Investment Return -1.655*** 2.864*** -1.171 -0.0387(0.609) (0.659) (0.742) (0.117)

Pension funding status -1.541*** 0.303 1.192*** 0.0463(0.208) (0.220) (0.252) (0.0486)

Active Share of Employees 2.591*** 0.843** -3.407*** -0.0264(0.378) (0.408) (0.505) (0.127)

Pension Assets BOY 0.00390 0.0277 0.0361 -0.0678(0.110) (0.107) (0.112) (0.0525)

Ln(Pension assets BOY) -0.0243 0.189*** -0.155*** -0.0104(0.0423) (0.0456) (0.0514) (0.0150)

Observations 34139 34072 34139 34072 34139 34072 34139 34072Firms 7158 7151 7158 7151 7158 7151 7158 7151R-squared 0.001 0.004 0.001 0.002 0.000 0.003 0.000 0.001

Active Equity Reallocation (%)

Active Debt Reallocation (%)

Active Cash Reallocation (%)

Active Other Reallocation (%)

Panel a: IRS Form 5500 sample

Lag Change PD ratio -22.66*** -22.65*** 22.11*** 22.89*** 0.841 0.924 -0.285 -1.158(1.286) (1.685) (1.327) (1.592) (0.758) (0.856) (0.657) (0.756)

Investment Return 11.19*** -8.282*** -1.731** -1.174(1.809) (1.907) (0.759) (0.816)

S&P credit rating (0-1) 1.507 -2.242 -0.293 1.028(1.798) (1.619) (0.791) (0.647)

No S&P credit rating 0.161 -0.259 -0.0339 0.133(1.434) (1.400) (0.534) (0.561)

Ln(Operating assets) -0.302 0.415 0.0955 -0.209***(0.370) (0.313) (0.0967) (0.0789)

Ln(Pension assets) 0.257 -0.480 0.000414 0.222***(0.359) (0.303) (0.0992) (0.0780)

Altman's Z-score 0.173 0.00920 -0.0169 -0.165(0.217) (0.237) (0.0640) (0.104)

Pension funding status (level) -1.836*** 0.956* 0.159 0.721***(0.628) (0.520) (0.279) (0.232)

Observations 1050 1023 1050 1023 1050 1023 1050 1023Firms 311 305 311 305 311 305 311 305R-squared 0.171 0.204 0.166 0.191 0.002 0.008 0.000 0.017

This table presents the results of pooled specifications, regressing active asset class reallocations on the lagged change in the log-PD ratio. Panel a displays results using the IRS Form 5500 sample. Panel b reports results using the P&I sample. See Table 5 forsummary statistics of active reallocations. Within each horizontal asset class panel, the second specification adds controls adaptedfrom Rauh (2009). All variables in panel a are calculated from the IRS Form 5500 dataset and are measured as of the beginning ofthe plan year. Control variables in panel b are calculated using Compustat data and are measured as of the end of the fiscal year.The investment return in both panels is calculated using investment income earned during the year for which the active reallocation is

Panel b: Pensions & Investments sample

The investment return in both panels is calculated using investment income earned during the year for which the active reallocation iscalculated. Standard errors are heteroskedasticity robust and clustered by plan sponsor. ***Statistically significant at the 1% level,**statistically significant at the 5% level, *statistically significant at the 10% level.

55

Table 12Pension fund active asset reallocations and Price-Dividend ratios, fixed effect specifications

(1) (2) (3) (4) (5) (6) (7) (8)

Lag Change PD ratio -2.218*** -4.616*** 3.821*** 3.274*** -1.281** 1.650** -0.322*** -0.308***(0.500) (0.538) (0.519) (0.574) (0.595) (0.659) (0.0993) (0.102)

Investment Return -4.649*** 4.037*** 0.491 0.121(0.718) (0.730) (0.829) (0.109)

Pension funding status -0.513 1.541*** -1.079** 0.0503(0.435) (0.441) (0.531) (0.0864)

Active Share of Employees 10.52*** 3.963*** -14.67*** 0.186(1.209) (1.304) (1.700) (0.192)

Pension Assets BOY 0.179 0.896 -1.617** 0.542*(0.435) (0.558) (0.639) (0.283)

Ln(Pension assets BOY) -2.817*** 1.387*** 1.335*** 0.0946(0.308) (0.289) (0.378) (0.0599)

Observations 34139 34072 34139 34072 34139 34072 34139 34072Firms 7158 7151 7158 7151 7158 7151 7158 7151R-squared 0.001 0.016 0.002 0.005 0.000 0.014 0.000 0.001

P l b P i & I t t l

Active Equity Reallocation (%)

Active Debt Reallocation (%)

Active Cash Reallocation (%)

Active Other Reallocation (%)

Panel a: IRS Form 5500 sample

Lag Change PD ratio -23.15*** -18.41*** 23.04*** 18.94*** 0.950 0.938 -0.845 -1.474(1.648) (2.645) (1.613) (2.433) (0.905) (1.182) (0.757) (1.071)

Investment Return 12.36*** -11.77*** -0.464 -0.119(2.511) (2.536) (0.744) (1.079)

S&P credit rating (0-1) 10.37** -9.934** -0.865 0.426(4.347) (4.450) (1.763) (1.544)

No S&P credit rating 5.531* -4.956* -0.698 0.123(2.954) (2.893) (1.022) (1.113)

Ln(Operating assets) -3.785** 2.756* 1.105* -0.0759(1.481) (1.523) (0.585) (0.583)

Ln(Pension assets) 0.618 3.325 -1.774** -2.168***(2.849) (2.597) (0.814) (0.641)

Altman's Z-score -0.247 0.361 -0.102 -0.0123(0.979) (1.060) (0.318) (0.566)

Pension funding status (level) -8.998*** 6.675*** 1.122 1.201*(1.665) (1.600) (0.768) (0.626)

Observations 1050 1023 1050 1023 1050 1023 1050 1023Firms 311 305 311 305 311 305 311 305R-squared 0.182 0.230 0.178 0.220 0.002 0.010 0.002 0.020

This table presents the results of specifications with plan fixed effects, regressing active asset class reallocations on the laggedchange in the log-PD ratio. Panel a displays results using the IRS Form 5500 sample. Panel b reports results using the P&I sample.See Table 5 for summary statistics of active reallocations. Within each horizontal asset class panel, the second specification addscontrols adapted from Rauh (2009). All variables in panel a are calculated from the IRS Form 5500 dataset and are measured as ofthe beginning of the plan year. Control variables in panel b are calculated using Compustat data and are measured as of the end ofthe fiscal year. The investment return in both panels is calculated using investment income earned during the year for which theactive reallocation is calculated Standard errors are heteroskedasticity robust and clustered by plan sponsor ***Statistically

Panel b: Pensions & Investments sample

active reallocation is calculated. Standard errors are heteroskedasticity robust and clustered by plan sponsor. Statisticallysignificant at the 1% level, **statistically significant at the 5% level, *statistically significant at the 10% level.

56

Tabl

e 13

Pens

ion

fund

ass

et a

lloca

tions

and

Pric

e-D

ivid

end

ratio

s, fi

xed

effe

ct s

peci

ficat

ions

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Lag

PD

ratio

11.9

9***

14.3

5***

9.65

8***

-12.

71**

*-1

4.81

***

-10.

41**

*1.

405*

**1.

211*

*1.

499*

*-0

.683

***

-0.7

50**

*-0

.744

***

(0.5

71)

(0.6

04)

(0.6

86)

(0.5

78)

(0.6

20)

(0.7

61)

(0.4

65)

(0.4

92)

(0.6

74)

(0.1

43)

(0.1

57)

(0.1

82)

Inve

stm

ent R

etur

n16

.44*

**19

.59*

**-1

4.63

***

-15.

07**

*-1

.353

-4.0

62**

*-0

.460

**-0

.457

**(0

.900

)(0

.918

)(0

.868

)(0

.874

)(0

.872

)(0

.860

)(0

.232

)(0

.221

)P

ensi

on fu

ndin

g st

atus

-0.8

212.

614*

**-1

.724

***

-0.0

692

(0.6

29)

(0.6

06)

(0.5

61)

(0.1

22)

Act

ive

Sha

re o

f Em

ploy

ees

4.80

1**

12.3

0***

-17.

04**

*-0

.063

4(1

.970

)(1

.821

)(2

.154

)(0

.372

)P

ensi

on A

sset

s B

OY

-1.5

68**

0.71

81.

335*

*-0

.485

(0.7

10)

(0.9

15)

(0.5

90)

(0.4

87)

Ln(P

ensi

on a

sset

s B

OY)

7.25

8***

-3.1

48**

*-4

.106

***

-0.0

0375

(0.6

15)

(0.6

37)

(0.6

49)

(0.1

68)

Obs

erva

tions

3436

434

364

3429

734

364

3436

434

297

3436

434

364

3429

734

364

3436

434

297

Firm

s72

3572

3572

2872

3572

3572

2872

3572

3572

2872

3572

3572

28R

-squ

ared

0.05

00.

069

0.08

70.

055

0.07

00.

085

0.00

10.

001

0.02

00.

002

0.00

30.

003

Equ

ity A

lloca

tion

(%)

Deb

t Allo

catio

n (%

)C

ash

Allo

catio

n (%

)O

ther

Allo

catio

n (%

)

Pan

el a

: IR

S F

orm

550

0 sa

mpl

e

Lag

PD

ratio

0.62

54.

834*

**4.

734*

-2.1

75*

-5.6

60**

*-5

.302

**0.

684

0.68

7-1

.058

0.88

7*0.

171

1.66

2*(1

.225

)(1

.622

)(2

.626

)(1

.224

)(1

.631

)(2

.556

)(0

.826

)(1

.138

)(1

.273

)(0

.505

)(0

.638

)(0

.958

)In

vest

men

t Ret

urn

9.93

5***

6.31

3**

-8.2

48**

*-5

.994

**-0

.132

-0.8

23-1

.527

**0.

530

(1.5

87)

(2.7

57)

(1.4

86)

(2.6

02)

(0.7

86)

(0.8

64)

(0.7

12)

(1.0

60)

S&

P c

redi

t rat

ing

(0-1

)2.

707

-2.9

73-1

.786

2.06

2(3

.061

)(3

.282

)(1

.513

)(1

.409

)N

o S

&P

cre

dit r

atin

g1.

913

-2.0

70-1

.146

1.30

5(2

.001

)(2

.131

)(1

.020

)(0

.874

)Ln

(Ope

ratin

g as

sets

)0.

0459

-0.2

29-0

.421

0.59

5(1

.061

)(1

.025

)(0

.765

)(0

.497

)Ln

(Pen

sion

ass

ets)

2.82

7**

-1.6

46-0

.242

-0.9

38*

(1.2

22)

(1.1

05)

(0.4

93)

(0.5

29)

Altm

an's

Z-s

core

1.33

3**

-0.9

61*

-0.2

34-0

.137

(0.5

76)

(0.5

13)

(0.2

77)

(0.3

11)

Pen

sion

fund

ing

stat

us (l

evel

)-1

.039

0.41

51.

684*

*-1

.068

(1.5

30)

(1.5

21)

(0.6

62)

(0.6

72)

Obs

erva

tions

1498

1426

1426

1498

1426

1426

1498

1426

1426

1498

1426

1426

Firm

s37

837

037

037

837

037

037

837

037

037

837

037

0R

-squ

ared

0.00

00.

042

0.06

10.

004

0.03

50.

044

0.00

10.

001

0.00

90.

003

0.00

90.

024

This

tabl

epr

esen

tsth

ere

sults

ofsp

ecifi

catio

nsw

ithpl

anfix

edef

fect

s,re

gres

sing

asse

tcla

ssal

loca

tions

onth

ela

gged

log-

PD

ratio

.Pan

ela

disp

lays

resu

ltsus

ing

the

IRS

Form

5500

sam

ple.

Pan

elb

repo

rtsre

sults

usin

gth

eP

&I

sam

ple.

See

Tabl

e5

for

sum

mar

yst

atis

tics

ofac

tive

real

loca

tions

.W

ithin

each

horiz

onta

lass

etcl

ass

pane

l,th

ese

cond

spec

ifica

tion

adds

aco

ntro

lfor

the

portf

olio

inve

stm

entr

etur

n.Th

eth

irdsp

ecifi

catio

nad

dsco

ntro

lsad

apte

dfro

mR

auh

(200

9).

All

varia

bles

inpa

nela

are

calc

ulat

edfro

mth

eIR

SFo

rm55

00da

tase

tand

are

mea

sure

das

ofth

ebe

ginn

ing

ofth

epl

anye

ar.

Con

trolv

aria

bles

inpa

nelb

are

calc

ulat

edus

ing

Com

pust

atda

taan

dar

em

easu

red

asof

the

end

ofth

e

Pan

el b

: Pen

sion

s &

Inve

stm

ents

sam

ple

fisca

lyea

r.Th

ein

vest

men

tret

urn

inbo

thpa

nels

isca

lcul

ated

usin

gin

vest

men

tinc

ome

earn

eddu

ring

the

year

for

whi

chth

eac

tive

real

loca

tion

isca

lcul

ated

.Sta

ndar

der

rors

are

hete

rosk

edas

ticity

robu

st a

nd c

lust

ered

by

plan

spo

nsor

. ***

Stat

istic

ally

sig

nific

ant a

t the

1%

leve

l, **

stat

istic

ally

sig

nific

ant a

t the

5%

leve

l, *s

tatis

tical

ly s

igni

fican

t at t

he 1

0% le

vel.

57