3.1 Cross-sectional regressions

In our first set of cross-sectional results, we examine the relationship between a proxy for the risk-taking and ownership:

(1)$$\eqalign{ \tab {{Risk \minus taking_{ij} \equals \sum {\beta _{{\rm \setnum{0}\comma }t} D_{t} } \plus \beta _{\rm \setnum{1}} PubliclyTraded_{j} \plus \beta _{\rm \setnum{2}} FundedStatus_{ij} \plus }}\beta _{\rm \setnum{3}} Contributions_{ij} \cr \tab \hskip70pt \plus \beta _{\rm \setnum{4}} Vested_{ij} \plus \beta _{\rm \setnum{5}} Benefits_{ij} \plus \beta _{\rm \setnum{6}} Age_{ij} \cr\tab \hskip70pt \plus \beta _{\setnum{7}} ActiveParticipants_{ij} \plus Controls_{ij} \plus e_{ij}} $$

where our two measures of risk-taking are either Volatility_ij or Range_ij. The first one, Volatility_ij is the standard deviation of the returns on the beginning of year pension plan assets for plan i of sponsor j computed when at least five (year) observations are available, i.e., ${\sigma _{ij} \equals \sqrt {{{\rm 1} \over {T \minus {\rm 1}}}\sum {\left( {r_{ij\comma t} \minus {{\rm 1} \over T}\sum {r_{ij\comma t} } } \right)^{\rm \setnum{2}} } } \vert T\geqslant {\rm 5}}\comma {{\rm 1} \over T}\sum {r_{ij\comma t} } \geqslant r_{risk \minus free} $, where r_ij,t is the annual plan return for plan i of sponsor j in year t, calculated using data from the IRS form 5500 and defined as investment income divided by beginning-of-year pension assets. The second measure, Range_ij is the difference between the maximum and minimum returns for plan i of sponsor j computed when at least five (year) observations are available, i.e., Δr_ij = (max(r_ij,t) − min(r_ij,t))|T ≥ 5. The main advantage of the range measure is that it does not require an estimate (potentially very noisy) of the expected return of the plan.

The main explanatory variables of interest are: first, the PubliclyTraded_j indicator variable equals one if sponsor j is a publicly traded company and zero otherwise; FundedStatus_ij, which is calculated as the sample mean of the ratio of plan assets to liabilities based on the beginning-of-year assets and the RPA’94 current liabilitiesFootnote ¹³ reported in the 5500 forms; and Contributions_ij, which is a dummy variable that equals one if sponsor's contribution is positive and zero otherwiseFootnote ¹⁴.

Petersen (Reference Petersen, Fernandez, Turner and Hinz1996)provides evidence that more mature pension plans, with a greater proportion of the pension liabilities coming due in the near future, invest more of the pension plan assets in bonds in order to better match the duration of the pension obligation. The variables Vested_ij, Benefits_ij and Age_ij measure the duration of pension plan's liabilities. They are calculated as follows. The plan Age_ij is measured as the log of one plus the plan age in years. The variable Vested_ij is the percentage of the RPA ’94 current liability vested and Benefits_ij is the benefit payments made by pension plan i of sponsor firm j divided by the average pension plan assets. Finally, the share of ActiveParticipants_ij is a proxy for hedging demand by sponsors who hedge future wage growth as in Sundaresan and Zapatero (Reference Sundaresan and Zapatero1997)and Lucas and Zeldes (Reference Lucas and Zeldes2006).

The controls include the plan Size_ij measured as the log of plan assets at the beginning of the year, and the net FSA balances (scaled by beginning of year assets)Footnote ¹⁵. Current ERISA and IRC funding rules for DB pension plans permit sponsors of underfunded plans with FSA credit balances to forgo making contributions, even for severely underfunded plans. Comprix and Muller (Reference Comprix and Muller2006)show that pension plans with high net FSA balances take higher investment risk. Finally, we include a dummy variable that equals one if the ith plan was terminated during the sample period and zero otherwise. Because of differences in the level of market movements across years, we include year-effects, an indicator D_t that equals one if the data from that year was used to calculate that observation and zero otherwise.

Next, we examine the interactions of sponsor's ownership type with the other theoretically-motivated variables to determine empirically if the ownership type is relevant for existing theories (see discussion below). Our cross-sectional regression has the specification:

(2)$${\eqalign{Risk \minus taking_{ij} \equals \tab \sum {\beta _{{\rm \setnum{0}\comma }t} D_{t} } \plus \beta _{\rm \setnum{1}} PubliclyTraded_{j} \cr\tab \plus \beta _{\rm \setnum{2}} FundedStatus_{ij} \plus \beta _{\rm \setnum{3}} FundedStatus_{ij} \ast PubliclyTraded_{j} \cr \tab \plus \beta _{\rm \setnum{4}} Contributions_{ij} \plus \beta _{\rm \setnum{5}} Contributions_{ij} \ast PubliclyTraded_{j} \cr\tab \plus \beta _{\rm \setnum{6}} Vested_{ij} \plus \beta _{\rm \setnum{7}} Benefits_{ij} \plus \beta _{\setnum{8}} Age_{ij} \plus \beta _{\rm \setnum{9}} ActiveParticipants_{ij} \cr\tab\plus Controls_{ij} \plus e_{ij} \cr} }$$

We test whether the funded status of a pension plan has significant effect on the risk-taking by testing the hypothesis that β₂ ≠ 0. In particular, the literature (e.g., see Rauh Reference Rauh2009), has proposed alternative explanations, and we test for risk-shifting, β₂ < 0, versus risk-management, β₂ > 0. The hypothesis that pension plan managers minimize the contributions of the plan sponsor implies that we expect to find a significant coefficient β₄ < 0. The literature (see, e.g., Petersen (Reference Petersen, Fernandez, Turner and Hinz1996)) also suggests that shorter duration of pension liabilities on average implies lower risk-taking, and if any of the individual hypotheses β₆ = 0, β₇ = 0 and β₈ = 0 are rejected, then we expect to find β₆ < 0, β₇ < 0 and β₈ < 0 respectively. The hypothesis that employers hedge future wage growth of their employees, as suggested in Sundaresan and Zapatero (Reference Sundaresan and Zapatero1997)and Lucas and Zeldes (Reference Lucas and Zeldes2006), is tested for β₉≠0, and if this coefficient is significant, we expect to find β₉ > 0.

Finally, we expect that there is a significant difference between publicly-held and privately-held sponsor's plans, due to different managerial incentives to manipulate earnings. Any evidence of significant coefficients on interaction terms with ownership can be interpreted to indicate that there are important differences in incentives for pension plan risk-taking between private and public sponsors.

3.2 Public sponsor characteristics

We consider the sub-sample of publicly traded sponsors. Equation (1) is modified to include sponsor's characteristics:

(3)$$\eqalign{ Volatility_{ij} \equals \tab \sum {\beta _{{\rm \setnum{0}\comma t}} D_{t} } \plus \beta _{\rm \setnum{1}} Funded_{ij} \plus \beta _{\rm \setnum{2}} Contributions_{ij} \plus \beta _{\rm \setnum{3}} Vested_{ij} \plus \beta _{\rm \setnum{4}} Benefits_{ij} \cr \tab \plus \beta _{\rm \setnum{5}} Age_{ij} \plus \beta _{\setnum{6}} ActiveParticipants_{ij} \plus \beta _{\rm \setnum{7}} CashFlow_{j} \plus \beta _{\rm \setnum{8}} CreditRating_{j} \cr\tab\plus Controls \plus e_{ij} \cr} $$

Friedman (Reference Friedman, Bodie and Shoven1983), Petersen (Reference Petersen, Fernandez, Turner and Hinz1996), Frank (Reference Frank2002)and Comprix and Muller (Reference Comprix and Muller2006)provide evidence that sponsors offset their (non-pension) business risk by reducing the investment risk of the pension plan assets. We include CreditRating_j to capture this incentive. We expect CreditRating to be positively associated with risk-taking, consistent with sponsors with lower business risk-taking on relatively higher investment risk with their pension plan assetsFootnote ¹⁶.

Petersen (Reference Petersen1992)provides evidence that sponsors’ ability to generate funds internally influences the operation of DB plans. He finds that sponsor firms’ inability to generate resources internally result in reduced plan contributions, more favorable actuarial assumptions to reduce required cash contributions, and in extreme cases, termination of overfunded pension plans. We include CashFlow_j, calculated as cash flow from operations divided by total assets, to capture the ability of sponsor firms to generate resources internally. We expect risk-taking and CashFlow to be positively associated for sponsors that manage liquidity risk, as in Petersen (Reference Petersen1992). Finally, in addition to the pension plan controls we include sponsors’ controls. These are the sponsor's size and leverage.

In our first three sets of tests, we examine the differences in the volatility of individual pension plans computed using between five and twelve observations for each plan. We cannot calculate annualized variance of return estimates computed using higher frequency data since only annual return data for DB pension plans are available from the IRS5500 formsFootnote ¹⁷. Our panel regressions below use our third measure of risk-taking, the realized volatility of daily asset-class benchmark returns.

3.3 Public sponsor panel regressions

The final set of results reports estimates from panel regressions of the annualized conditional volatility of daily returns on the pension plans’ asset-allocation benchmark portfolio on funded status, and other explanatory variables and controls. The panel regression has the following specification:

(4)$$\eqalign{ Volatility_{jt} \equals \tab \beta _{\rm \setnum{0}} \plus \beta _{\rm \setnum{1}} Funded_{j\comma t \minus \setnum{1}} \plus \beta _{\rm \setnum{2}} Contributions_{j\comma t \minus \setnum{1}} \plus \beta _{\rm \setnum{3}} Vested_{j\comma t \minus \setnum{1}} \cr \tab \plus \beta _{\rm \setnum{5}} Benefits_{j\comma t \minus \setnum{1}}\plus \beta _{\rm \setnum{6}} Age_{j\comma t \minus \setnum{1}} \plus \beta _{\setnum{7}} ActivePartcpant_{j\comma t \minus \setnum{1}} \cr \tab \plus \beta _{\rm \setnum{8}} CashFlow_{j\comma t \minus \setnum{1}} \plus \beta _{\rm \setnum{9}} CreditRating_{j\comma t \minus \setnum{1}} \plus Controls \plus e_{jt} \cr} $$

Our measure of risk (Volatility_jt) is the year t annualized volatility of daily returns on a portfolio invested in benchmark indexes with portfolio weights the jth sponsor's asset-class holdings, i.e., ${\sigma _{jt} \equals \sqrt {\omega {\prime}_{j} \Sigma _{t} \omega } {}_{j}}$ where ω_j is a (k × 1) vector of portfolio weights for the jth sponsor and Σ_t is the time t annualized covariance matrix of daily benchmark return for k asset classes. The main explanatory variable of interest is FundingStatus _j,t − 1, which is now calculated as the ratio of plan assets to liabilities based on the beginning-of-year assets and liabilities. The controls include the plan Size_jt, which is measured as the log of plan assets and the sponsor leverage. All specifications include time dummies and fixed effects or industry effects.

As before, we test the null hypothesis that the funded status of a pension plan has significant effect on the risk-taking, β₁≠0, with alternatives for risk-shifting, β₁ < 0, versus risk-management, β₁ > 0. Next, the hypothesis that pension plan managers minimize the contributions of the plan sponsor implies a significant coefficient β₂ < 0. Similarly, the hypotheses that longer duration of the pension liabilities is associated with higher risk-taking and that sponsors hedge future wages growth, etc. imply that we expect to find significant coefficients with signs as discussed above.

6.1 Endogenous ownership type, risk-taking and sponsor characteristics

In this section, we address the possibility that ownership may be determined by firm and industry characteristics that are correlated with risk-taking, i.e., ownership may be endogenous. For example, the scope for moral hazard may be greater for riskier firms so these firms remain private as their managers should hold greater ownership stakes to align incentives (Demsetz and Lehn, Reference Demsetz and Lehn1985).

In our set up, the endogenous variable is a dummy variable and applying directly 2SLS estimation is not appropriate. Angrist and Pischke (Reference Angrist and Pischke2008)coin this set up ‘the forbidden regression’Footnote ²⁹. In this case, the usual OLS first-stage is only an approximation to the underlying nonlinear model. If we use a nonlinear first stage (for example a Probit model), the forbidden regression in this case is the second stage equation created by plugging in nonlinear fitted values. The problem is that only OLS estimation of the first stage is guaranteed to produce first-stage residuals that are uncorrelated with fitted values and covariates.

Angrist and Pischke (Reference Angrist and Pischke2008)suggest using the nonlinear fitted values as instruments. In general, using fitted values as instruments is the same as plugging in fitted values when the first-stage is estimated by OLS. Nonlinear fits-as-instruments has the further advantage that, if the nonlinear model gives a better approximation than the linear model, the resulting 2SLS estimates will be more efficient than those using a linear first stage regression.

Firm-level variable such as profitability, growth and size are likely to be correlated with both ownership and firm risk-taking. We use the four-digit SIC industry average Tobin Q as an instrumental variable. Since we cannot observe the Q of private firms, we use an estimate of Q for public companies as a proxyFootnote ³⁰. Industry Q is a market signal of the perceived investment opportunities. Previous studies have argued that firms are more likely to be public when the market valuations in their industry are much higher than valuations in other industries. For example, Pastor and Veronesi (Reference Pastor and Veronesi2005) find that insiders tend to go public after observing improving market conditions and Lowry and Schwert (Reference Lowry and William Schwert2002) show that more firms go public after periods of high underpricingFootnote ³¹.

We examine the robustness of our results with respect to endogenous choice of ownership. The results of the IV regressions are reported in Table 7.

Table 7.

Cross-sectional regression: ownership endogeneity (IRS 5500 & ORBIS Data, 2000–2006)

Columns (1)–(3): the dependent variable (volatility) is the standard deviation of pension plan returns on the beginning of year pension plan assets. Columns (4)–(6): the dependent variable (range) is the difference between the maximum and minimum pension plan returns. Column (1) and (2) and (4)–(6): we use nonlinear fitted values from a probit model (ownership dummy is regressed on industry Tobin's Q and covariates) as an instrument for Public dummy in 2SLS regressions. Column (3) and (6): in addition to instrumenting the ownership dummy, the realized returns and the share of active participants are used as instruments for funded status and contributions. Fixed-year effects (an indicator Dt that equals one if the data from that year was used to calculate that observation and zero otherwise) are included but not reported. Standard errors robust to sponsor cluster effects are reported in parentheses.

The table shows that the ownership remains robust determinants of pension plan risk-taking. In addition, the positive coefficient on funded status and the negative coefficient of Contributions are significant in all regression specifications. The coefficients of the Public interaction variables have the same sign and magnitude to those in Table 4 but they have larger standard error reflecting the smaller sample size. These findings confirm our previous results that for plans with public sponsors, better funding levels are associated with increased plan risk-taking but changes in contributions are important for the investment risk of plans with private sponsorsFootnote ³².

We also address the concerns that our results are driven by fundamental differences between the sample of plans with public sponsors and the sample of plans with private sponsors (e.g., Table 1 shows that these samples differ with respect to size, age, funding, and shares of active participants, i.e., characteristics associated with risk-taking).We performed a propensity score matching procedure where we first calculated propensity scores derived from a probit model where the dependent variable Public ownership dummy variable is regressed on plan characteristics (size, age, funding, and shares of active participants), sponsor characteristics (size, profitability, industry Tobin's Q), and other controls. We then matched each pension plan with private sponsor, one-to-one, with the public sponsor pension plan with the closest propensity scoreFootnote ³³. The results based on the propensity score matched samples confirm that public sponsor pension plans take more risk-than private sponsor pension plans.

6.2 Ex-post returns and ex-ante risk-taking

Panel C of Table 1 shows that during our sample period the realized equity premium was about 12%. This highlights the fact that ex-ante (expected) and ex-post (realized) returns differ. It is common, however, to use ex-post market-based measures of risk (such as fluctuations in stock returns) or accounting-based measures of risk (fluctuation in accounting earnings). Examples from the literature on bank risk-taking include Esty (Reference Esty1997), Saunders et al. (Reference Saunders, Strock and Travlos1990), and Emmons et al. (Reference Emmons, Gilbert and Yeager2004)and from the literature on mutual funds risk-taking, Chevalier and Ellison (Reference Chevalier and Ellison1997), Coles et al. (Reference Coles, Daniel and Naveen2006), and Ma and Tang (Reference Ma and Tang2012).

In this section, we re-examine our result using the conventional measure for ex-ante pension plan risk-taking, the proportion of funds allocated to risky assets. Data on asset allocation are only available for public pension plans so we are only able to replicate the regression results from Table 6. Table 8 presents the robustness regression results. Our main findings remain the same. The coefficient of funded status is significantly positive and the coefficient of contributions is not statistically significant in all specifications.

Table 8.

Panel regression for publicly traded sponsors (IRS 5500, COMPUSTAT & P&I Data, 1996–2002)

The table reports OLS estimates. Columns (1) and (2): the dependent variable is the percentage invested in equity; Columns (3) and (4): the dependent variable is the percentage invested in alternative assets (private equity, real estate and mortgages); Columns (5) and (6): the dependent variable is the percentage invested in international assets; Year effects are included in all regressions but are not reported. Robust standard errors are reported in parenthesis.

6.3 Additional robustness tests

We estimated specifications that employ an alternative measure of pension plan risk-taking. The likelihood that the pension plan is frozen or terminated can be interpreted as a proxy for risk-taking, since higher risk is associated with a lower probability of pension plan survival. The relationship between plan closure and the asset–liability structure also captures differences in the incentives of public and private sponsors to terminate or freeze the pension plans.

The results (not reported here, available upon request) show that the probability of pension plan closure increases with underfunding for plans with public sponsors, but not for plans with private sponsors. Moreover, contributions, vested liabilities, benefits and the share of active participant are significant drivers of pension plan closures for both public and private pension plans in this specification. In particular, higher contributions, vested liabilities and benefits lead to increased likelihood of plan closures, while a higher share of active participants implies a lower probability of plan closure.

In our panel regressions, we have considered additional specifications with industry controls as well as fixed effects that include different combinations of control variables. The main findings reported above are robust across the specifications. For example, including the lagged return in specification (4) decreases the statistical significance because we lose about 40% of the observations but the results are qualitatively similar with coefficients that have the same sign and are of similar magnitude.

Overall, our robustness tests suggest that the empirical relationships documented in this paper are robust, while the testable predictions of the theoretical models in the current literature, when taken individually, cannot explain the rich empirical pattern of pension plan risk-taking. Instead, the existing theoretical models can be viewed as complementary and need to be incorporated into a more general framework that highlights the multiple trade-offs of sponsors and agents when they optimize pension plan investments.