Asset Allocation and Managerial Assumptions in Corporate Pension Plans

Transcription

1 Asset Allocation and Managerial Assumptions in Corporate Pension Plans Jawad M. Addoum Duke University Jules H. van Binsbergen Stanford University June 2010 Michael W. Brandt Duke University and NBER Abstract We empirically examine the effect of regulations on pension decision-making. We find that in the face of mandatory contributions, pension plans alter their asset allocations and increase their risk taking to avoid mandatory contributions. This behavior resembles gambling for resurrection. We also examine the effect of regulations on pension accounting assumptions affecting net income. We find that plan sponsors increase their assumed rates of return on plan assets when subject to pension-related costs. The evidence supports an earnings-management interpretation. Finally, we examine whether pension fund managers are tactical in their asset allocations. We find that pension fund managers are active as an investor class, but do 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, Howard Kung, Justin Murfin, and participants of the Duke Finance Brownbag Seminar for helpful comments. Fuqua School of Business. Durham, NC Phone: jawad.addoum@duke.edu. Graduate School of Business. Palo Alto, CA Phone: jvb2@gsb.stanford.edu. Fuqua School of Business. Durham, NC Phone: mbrandt@duke.edu

2 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 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 to 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 1 Fund Management 2009, International Financial Services, London. 2 Having more than 20% of liabilities automatically subjects plan sponsors to relatively severe mandatory additional contributions to the plan. For further details, see section

3 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% 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 ability, 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 pension plans underperform compared to plans, as obverved by Franzoni and Marin (2006). Franzoni and Marin attribute their result to an anomaly similar to post-earnings-announcement-drift 3 : market participants do not fully comprehend the autocorrelated nature of mandatory contributions for firms with highly 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 information 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 3 See Ball and Brown (1968), Bernard and Thomas (1989, 1990). 3

4 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 management 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. 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 corporate 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 allocation 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

5 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 (corresponding to calendar years) 1990 to 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 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 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, 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 observations 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 inability 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 4 Sponsors are required to further categorize the assets held in these categories into more transparent asset classes. However, these further categorizations are contained in sponsor-prepared hard-copy attachments unavailable in the electronic data. 5 The active share of participants is calculated as the BOY total active participant count divided by the BOY total 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 participants indicates a total participant count of zero, indicating either a recording error, or a plan in which we are not interested. 5

6 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 $ 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 $ 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 to and the median falling to from Consistent with a drop in plan size when moving from the full to the estimation sample, contributions and actuarial normal costs 7 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 issued fixed-income securities, as well as certificates of deposit. Government debt includes all Holdings in insurance 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 holdings 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 observations 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. 6 Plan funding status is calculated as: Plan Assets Plan Liabilities Plan Assets 7 Actuarial normal cost is the present value of pension benefits earned by plan participants during the year. 6

7 2.2 Pensions & Investments Data Pensions & Investments (P&I ) is a biweekly magazine aimed at pension, portfolio, and investment 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 information from follow-up s 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 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 Each of the ratings in between takes a value that incrementally raises the rating variable by 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

8 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 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 popular measure (control variable) of financial distress in the literature (Altman(1968)), is calculated 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 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 Compustat 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 requisite for our study are all available beginning in 1994, and up to 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. 8 As noted in Rauh (2009), this is not representative of the general Compustat universe, where approximately just one quarter of observations have a non-missing S&P credit rating. 8

9 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. 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 allocation 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 Security 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 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 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 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. 9 We refer to such a point, a funding status above which no mandatory AFC is required and below which mandatory AFCs are required, as a critical funding ratio or critical funding status. 10 See Munnell and Soto (2003) for further discussion of ERISA funding requirements, as well as examples of mandatory contributions under ERISA. 9

10 Affecting plan years 1995 and onward, the RPA of 1994 added additional mandatory funding contributions for those plans deemed to be critically. 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%, 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 contributions 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%, where plan sponsors are subject to additional funding charges after 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 T 0,j the indicator for whether or not plan sponsor j is subject to mandatory funding contributions, the treatment status can be written as: T 0,j = { 1 if x j < 0 0 if x j 0 where x j represents pension plan j s funding status. Similarly, denoting as T 20,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: T 20,j = { 1 if x j < 20% 0 if x j 20%. 11 Plans with 10-20% underfunding could also be subject to the additional funding charge. However, this would require three consecutive years of being more than 10%. Even then, plan sponsors could apply for hardship exemptions to the additional funding charge, which were usually granted (see Rauh (2006) for further detail). 12 Lee and Lemieux (2009) provide a comprehensive discussion of the regression discontinuity design, as well as a detailed listing of papers in the various economic disciplines that make use of the technique. 10

11 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 managers, 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: ˆb = 2ˆσn 1/2, where ˆσ 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 X 1, X 2,..., X J represent the discretized grid covering the support of the funding status for the first-step histogram, and labeling the fourth-order polynomial f(x j ), we calculate on each side of the discontinuity point the following expression: 3.348[ σ 2 (b a)/σf (X j ) 2 ] 1/5, where σ 2 is the mean-squared error of the regression, b a equals X J c for the right-side regression and c X 1 for the left-side regression (where c is the discontinuity point), and f (X j ) is the estimated second-derivative implied by the estimated polynomial model. Then, we set ĥ equal to the average of the calculated quantities. Using ĥ 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

12 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 construct 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 normal 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 Empirical Specification Having established that the RD design is appropriate in our setting, we now return to our original 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: w i,j,t = α + θ i critical j,t + ε i,j,t, where critical j,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. w i,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,θ i, 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. 13 We also test sponsor contributions in the Form 5500 sample directly. Voluntary contributions, over and above those mandated by funding rules, are the channel through which sponsors can exert precise control over the funding ratio. In unreported tests, we find no evidence that firms approaching the critical funding ratios from above avoid going past the critical point by making such voluntary contributions. 12

13 To temper such concerns, we construct a measure of active reallocations across asset classes, denoted wi,j,t active, and instead consider regressions of the following form: w active i,j,t = α + θ i critical j,t + ε i,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 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: w i,0 = w i,0 + θ T x i,0, where w i,0 represents the weight of asset class i at date 0 in some benchmark portfolio, 14 x i,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: w i,t = w i,t + θ T x i,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 w i,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: w passive i,t = w i,t r i,t 1 + r p,t, 14 In the context of pension funds, this could be interpreted as a target allocation mandated by the plan sponsor s pension committee. For a more generalized interpretation, see Brandt et. al. (2009). 13

14 where r i,t and r p,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: w active i,t = w i,t w passive 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 Asset Allocation Results One way of constructing the critical indicator is by considering only the funding status of the pension plan, setting critical j,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 discontinuity 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 critical up and critical dn : w active i,j,t = α + θ i,up critical up,j,t + θ i,dn critical dn,j,t + ε i,j,t, where critical up,j,t = critical j,t fundstat increase,j,t and critical dn,j,t = critical j,t (1 fundstat increase,j,t ). 14

15 In the above, we set fundstat increase,j,t equal to 1 if the expression fundstat j,t fundstat j,t 1 is positive, and 0 otherwise. That is, fundstat increase,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 critical up and critical dn 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 θ up are shown using green bars, while those for θ dn 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. 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 15 A 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 funding regulations. In addition, voluntary contributions by sponsors would lead to a large jump in the density of sponsors around critical funding ratios. Our density plots in Figure 1 and formal statistical tests in Table 4 indicate that this is not the case. Therefore, fundstat increase,j,t is a reasonable measure of plans exogenously determined funding status trajectory during year t. 16 For clarity, Figures 2 and 3 restrict attention to only those funding status bins surrounding the respective critical funding ratios. For completeness, Figures 4 and 5 repeat this analysis for a set of funding status bins covering the entire spectrum of funding ratios. 17 Specifically, in the P&I sample, we control for 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. In the Form 5500 sample, we control for the pension funding status, the active share of employees, and the size of the pension at time t 1, both in levels and logs. The 15

16 discontinuity. We first examine the 20-30% 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% 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% 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% 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% discontinuity 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 contributions appears, is the responsibility of the plan sponsor, a plausible reason for the difference 16

17 in observed coordination of action is that fund managers are not fully informed of this discontinuity until their plans funding ratios fall past -20%, subjecting the sponsor to the additional contributions. We next examine the 0-10% 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 smallto 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% 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