1. Introduction
Ever since the severe stock market decline in 2000, state and local public-pension plans in the USA have been under close public scrutiny. This scrutiny has intensified after the meltdown in the financial market in 2008. The financing of public-pension benefits has become one of the most discussed public finance issues at the state and local levels. The focus of this scrutiny over public-pension financing is best captured by two numbers: funded ratio and unfunded pension liability. Funded ratio of a pension plan refers to the percentage of benefits promised to public employees (representing liability to the government making the promise) covered by financial assets in the pension plan. Unfunded pension liability is the translation of the funded ratio into actual dollars. If a plan's funded ratio is 100%, its unfunded liability is zero. Any funded ratio under 100% yields a positive unfunded liability in terms of dollar.
Since 2001, the first and foremost trend in the public-pension world has been a fairly steady decline in the average funded ratio of public-pension plans. According to the public-pension survey conducted by the National Association of State Retirement Administrators (NASRA, 2016), the average funded ratio was 100% in 2001. This ratio declined gradually and reached a nadir of 72% in 2013, before showing a slight uptick in 2014 to 74% (see Figure 1).
The gradual decline in the funded ratio since 2001 corresponds to a gradual increase in unfunded pension liability. For the 99 large state-level public plans in the NASRA survey, the total unfunded liability at the end of 2014 was about $1 trillion. The total unfunded liability for all state and local pension plans, of which there are over 6,000 according to the US Census Bureau, is certainly higher than that amount. This increase in unfunded pension liability leads to a significant increase in the amount of government pension contributions, both in absolute terms and as a percentage of government revenue (Peng and Wang, Reference Peng and Wang2017). Consequently, pressure on government budgets increases.
This declining trend in funded ratio has occurred for many reasons. The most important by far is that the public-pension plans' average investment return over this period failed to meet expectations. Pension plans accumulate and invest assets now so as to pay for pension benefits in the future. Pension asset accumulation is through both a return on the plan's investments and annual contributions to the plan. Assumptions about the future returns on the plan's investment are made so as to determine the amount of the current annual contribution. The higher the expected future return, the lower the amount of the current annual contribution. However, if the actual return fails to meet those expectations in a given year, then not enough assets have been accumulated, potentially leading to a decrease in funded ratio and an increase in unfunded liability. While public-pension plans expected to earn on average between 7.5% and 8% a year on their investments from 2001 to 2014, the actual annualized return over this period was lower, due to the two stock market downturns (Brainard, Reference Brainard2011). Wang and Peng (Reference Wang and Peng2016) also found that the main reason for the variation in change in funded ratio among pension plans between 2001 and 2009 was investment return.
Given the importance of investment to public pensions, a second major trend in public-pension financing has also become significant in terms of asset allocation. The portfolio allocated to all alternative investments (hereafter referred to as AI), including private equity, hedge funds, and other asset types, has increased from about 3–17%, with a corresponding decrease in allocation to traditional investments, including both fixed-income securities and public equity, as can be seen in Figure 2. The magnitude of this shift in asset allocation over this period has major implications for investment returns and thus has made AI a hotly debated issue in pension investment and financing.
Asset allocation trend 2001–2014.
Note: Based on annual average numbers calculated from the Public Pension Database 2001–2014, maintained by Boston College's Center for Retirement Research, available at http://publicplansdata.org/; ‘Private Equity’ may include a small amount of other alternative assets that cannot be separated from this category. Data on hedge funds allocation were collected by the authors from each pension plan's annual comprehensive annual financial report.
These two salient trends over the same period of time – a gradual decrease in funded ratio and a gradual increase in allocation to AI – spark two research questions: (1) how the asset allocation shift to AI-affected investment returns over this period for public-pension plans and (2) if the trend of asset allocation shift was affected by the trend of declining funded ratio over this time period, among other factors. This research addresses these two questions. The findings of this research have important policy implications for pension plan investment and the financing of public-pension benefits in the future. The rest of the paper is structured as follows. Section 2 provides a brief introduction to AI. A literature review is presented in Section 3. Research methodology and data are discussed in Section 4. Empirical results are presented in Section 5. And, the final section concludes with the policy implications of our research.
2. Alternative investment
AI is at the center of this research, but it is also a relatively new development in public-pension investment. As such, it makes sense to describe what it is, and the role it plays in an investment portfolio.
To understand AI, it is best to start with its opposite: traditional investment. Traditional investment consists primarily of fixed-income securities, such as treasury securities and corporate bonds, and public equity, such as stocks traded on the New York Stock Exchange. The most important feature of traditional investment is that it can be bought and sold easily on the open financial market for very low transaction costs. Added to that, the value of such an investment is known to the public at any given time, due to frequent trading. AI, in comparison, refers to any asset class other than fixed-income security and public equity. It includes financial assets such as private equity (equity in a company that has been taken private), hedge funds (funds that apply any kind of investment strategy to take advantage of market inefficiency or earn an absolute return regardless of the market condition), and venture capital, as well as real assets such as real estate, timber, and precious metals. The market for such investments is rather illiquid, and it usually involves a financial intermediary such as a private equity firm or a hedge funds company, thus increasing transaction costs. Another consequence of the illiquid market for AI is that the value of such investment is not readily known.
Despite the potential drawbacks of AI – the lack of liquidity and higher transaction costs – there are also potential benefits associated with it. First, the inclusion of AI has the potential to reduce the volatility of the investment return over time as the returns on alternative and traditional investments are not highly correlated from year to year. Second, some types of AI have the potential to earn a higher return in the long run than traditional investments. For example, the allure of private equity is that it has potential to earn a long-term higher return than public equity. Due to these perceived benefits, especially the potential for a higher return compared with a traditional investment, we have witnessed a more dramatic increase in allocation to AI since 2001, particularly since 2007. Two specific aspects of this trend bear further discussion.
The first is the variation in allocation to different types of AIs over time. While real estate has long been a part of AI, it is typically in its own subcategory separate from the other AI types, as is the case in the database maintained by Boston College's Center for Retirement Research. This distinction, probably due to the unique nature of real estate, provides additional insight into the allocation to AI over this period. As can be seen from Figure 2, real estate saw a very modest increase in allocation over this period. The dramatic increase in allocation to the broad AI class over this period was primarily accounted for by other asset types in this category, such as investments in private equity and hedge funds. Thus, to better understand the change in allocation to AI over this period, we define AI more narrowly in this study by excluding the real estate component. According to the survey of about 100 state pension plans by Cliffwater LLC (2012) when real estate was excluded, AI primarily consisted of private equity and hedge funds in 2011. As such, this paper will focus on private equity and hedge funds.
The second aspect is the variation in allocation to AI among public-pension plans. The increase in average allocation to AI shown in Figure 2 conceals significant variation among pension plans. Instead, Figure 3 shows the box plots of private equity and hedge funds allocation for 2001–2014. As can be seen from the box plot of private equity on the left, the median allocation to private equity had climbed from about 2% in 2001 to about 12% in 2014. There were many plans/years with zero allocation to AI whereas several plans/years allocated more than 40% to private equity. Similarly, the box plot on the right clearly shows that the median allocation to hedge funds had remained at zero from 2001 to 2008 but climbed significantly since the Great Recession. More importantly, the relatively extreme values greater than the upper adjacent values became fewer as time went by, meaning that more plans had invested a higher percentage of their assets in hedge funds.
Box plots of private equity and hedge funds: (1) private equity and (2) hedge funds.
Due to this significant variation in AI allocation among individual pension plans from year to year, and also due to significant variation in the funded ratio around the national average among pension plans, we can use data at the individual plan level to address this paper's two research questions: the impact of AI on investment returns and the effects of a lower funded ratio on investment allocation to AI.
3. Literature review
This section reviews the existing literature on investment return and asset allocation, and the determinants of these two key components of pension investment.
3.1 Investment return
The literature on investment return can be divided into two categories: the general factors affecting investment return, and, more specifically, the contribution of AI to investment return. Brinson et al. (Reference Brinson, Hood and Beebower1986) found that investment policy (the selection of asset classes and their normal weights) dominates investment strategy (market timing and security selection), and it explains 94% of the variation in total plan return. A follow-up research by Brinson et al. (Reference Brinson, Hood and Beebower1991) confirmed that asset allocation policy, however determined, is the dominant contributor to total return. In the same vein, Amir and Benartzi (Reference Amir and Benartzi1998) found empirical evidence that the percentage of equity is related both to the expected rate of return and future pension returns. Schneider and Damanpour (Reference Schneider and Damanpour2001) examined the determinants of public-pension plan investment return and concluded that strategies such as asset allocation have a much greater impact on plan performance than do public choice influences.
More specifically to the contribution of AI to investment returns, Robertson and Wielezynski (Reference Robertson and Wielezynski2008) examined one large pension plan from each state and found public-pension plans with at least 10% of their assets allocated to AI had significantly higher annual returns in 2004, 2005, and 2006. However, these same plans had lower returns, though not significantly so, in 2002 and 2003. Parisant and Bhatti (Reference Parisant and Bhatti2016) analyzed 11 public-pension funds' experience with investing in hedge funds. By conducting a simple year-by-year comparison of hedge funds net returns and total fund net returns, the authors found that hedge funds’ investments failed to deliver any significant benefits to the pension funds studied.
3.2 Pension asset allocation
While there is no literature specifically on the factors influencing the allocation to AI for public-pension plans, there is still a body of literature on the determinants of allocation to other risky investments such as public equity in public-pension plans. These factors can generally be divided into two categories: plan governance and plan characteristics.
In the governance category, the main factor is the makeup of the governing board, i.e., whether board members are appointed by plan sponsors or elected from pension participants. Pennacchi and Rastad (Reference Pennacchi and Rastad2011) hypothesized that when there are more plan participants on the pension board, they are more likely to take risk and allocate more to equity in a desire to gamble for higher benefits with higher returns. The study used a sample of 125 plans over the period between 2000 and 2009. However, Dobra and Lubich (Reference Dobra and Lubich2013) argued that the higher the percentage of board members who are active participants in the system, the lower the percentage of assets in riskier investments.
The second category relates to the characteristics of the pension plan itself. The first characteristic is the discount rate (investment return assumption). A lower discount rate should be correlated with a less risky portfolio. Lucas and Zeldes (Reference Lucas and Zeldes2009) found that there is almost no correlation between the equity share, a proxy for the riskiness of investment, and the assumed rate of return. Park (Reference Park2009) found that public plan sponsors using discount rates greater than 8% were 3.6 percentage points more likely to invest in higher risk assets than those using low discount rates. Pennacchi and Rastad (Reference Pennacchi and Rastad2011) found that pension plans that select a relatively high rate tend to choose riskier portfolios. Stalebrink (Reference Stalebrink2014) provided empirical evidence that adopted investment return assumptions are partly determined by the investment board's affiliation with the political process, and are correlated with asset allocations. The second characteristic is the plan's funded ratio. The generally accepted hypothesis is that the lower the ratio, the more risk the pension plan needs to take on to earn higher returns to increase the ratio. Nevertheless, Lucas and Zeldes (Reference Lucas and Zeldes2009) found that the opposite is true. These two factors are directly related to the second research question in our study.
The third characteristic is the ratio of current workers to retirees. The rationale is that when the ratio decreases, the pension plan needs to pay relatively more in benefits and thus needs to take on more risk in its allocation. Lucas and Zeldes (Reference Lucas and Zeldes2009) found that this ratio has no significant impact on a portfolio's equity share. However, Andonov et al. (Reference Andonov, Bauer and Cremers2015) found that when the ratio increases, US public-pension funds increased their allocation to risky assets. The fourth characteristic is the size of plan. Pope (Reference Pope1986) contended that there are significant economies of scale among public-employee pension plans and a larger plan is more likely to invest in risky assets. Weller and Wenger (Reference Weller and Wenger2009) also hypothesized that larger pension plans are more likely to invest in risky assets. Finally, a pension plan's benefit level may also play a role in asset allocation. If a plan provides more generous benefits to its retirees, it will face greater liability and may have to allocate more assets to riskier investments to earn higher returns. Several empirical studies found a significant relationship between pension benefit provisions and the pension plan's funded ratio (Johnson, Reference Johnson1997; Munnell et al., Reference Munnell, Haverstick and Aubry2008).
Based on this brief literature review, we can see that there is general agreement on the relationship between investment return and asset allocation: (a) asset allocation policy is a dominant contributor to total return and (b) allocation to riskier asset classes such as public equity and AI is the primary driver of better pension investment performance. However, there has been no systematic analysis of the impact of AI on public-pension plan investment returns over the entire period in our study. While there are studies showing AI had a positive impact on investment returns prior to 2009, it is not clear whether this continued to be the case after 2009. This is important because, as can be seen in Figure 2, much of the increase in allocation to our narrowly defined AI occurred after 2007. The literature review also reveals that there is no clear consensus as to what causes the asset allocation to differ among plans, although several important determinants are frequently mentioned and analyzed.
4. Methodology and data
In this section, we present empirical models, explain data sources, and discuss descriptive statistics of dependent and independent variables.
4.1 Empirical models
The literature review in the previous section as well as classic studies on portfolio performance, including Sharpe (Reference Sharpe1966), Treynor (Reference Treynor1965), and Jensen (Reference Jensen1968), all point to selectivity, or some slight variant thereof, as the most important measure of fund performance. Selectivity measures how well the chosen portfolio did relative to a naively selected portfolio with the same level of risk (Fama, Reference Fama1972).
Using these studies as guidelines, our study will use two methods to answer the first research question. We first follow the methodology adopted by Amir and Benartzi (Reference Amir and Benartzi1998) and Robertson and Wielezynski (Reference Robertson and Wielezynski2008), and test whether allocating more AI as a whole (including private equity, hedge funds, etc.) to the pension portfolio earns AI benefit, incurs AI loss, or makes no difference. In particular, we will conduct a two-sample t test to compare the sample means of high-AI and low-AI groups relative to the difference of their standard deviation for each of the sample years.
While two-sample means test suggests a relationship between pension investment return and AI allocation, it is not a causal analysis. In order to test the hypothesis that more AI allocation leads to higher investment return of pension portfolio, we further conduct a panel vector autoregression (PVAR) analysis, a time-series vector autoregression (VAR) model in panel data settings. Generally, a k-variate homogeneous PVAR of order p with panel-specific fixed effects can be written in reduced form as:
$$Y_{it} = Y_{it-1}A_1 + \cdots + Y_{it-p}A_p + X_{it}B + u_i + e_{it}$$
$$i\in \{ 1,2,...,N\}, \;t\in \{ 1,2,...,T_i\} $$where Y it is a k × 1 vector of variables; X it is a (l × 1) vector of exogenous covariates if any; A is a k × k matrix of regression coefficients; B is a k × l matrix of parameters; p is the number of lagged values of Y it included in the estimation, and u i and e it are (k × 1) vectors of dependent variable-specific panel fixed-effects and idiosyncratic errors.Footnote 1
PVARs are desirable for assessing the causality relationship between pension investment return and allocation to AI in three senses. First, they capture the lagged effects of one variable on another, allowing one to analyze the causal dynamic relationships among variables. The reason is that time-series data represent the results of a unique data-generation process. Conducting an analysis of the relationship between a predictor variable and that data series isolates the unique effect of that variable on the data-generation process. The second aspect of time-series analysis is that it enables a uniquely robust method of detecting and modeling endogeneity because of the simultaneous nature of the model (Sims, Reference Sims1980). One challenge in carrying out this research is the possible simultaneity between the two study variables. PVARs, however, can help assess whether changes in AI allocation preceded changes in investment return, whether the two series changed together, or whether the changes in AI allocation occurred after changes in return. Third, in contrast to simple VARs, PVARs can make full use of our pension data and improve estimation results with increased sample size.
For the second research question regarding the effect of funded ratio on AI allocation, we first set up a panel regression model on AI allocation. While funded ratio is our main variable of interest in this model, we also need to control for the impact of other pension plan variables and financial market conditions on asset allocation. Based on theory and our prior literature review, we constructed the following panel regression model with predicted signs on top of each explanatory variable:
$$\eqalign{AI = &\mathop {\,f\,(invassump\_1}\limits^ +, \,\mathop {\,fundedratio\_1}\limits^-, \,\mathop {arcpaid\_1}\limits^-, \,\mathop {actratio\_1}\limits^-, \mathop {size\_1}\limits^ +, \mathop {cola\_1}\limits^ + \cr &\mathop {ss{\mathop{\rm cov}} \_1}\limits^-, \mathop {invcl\_1}\limits^ +, \mathop {\,participants\_1}\limits^ \pm, \mathop {sp500\_1}\limits^ \pm, \mathop {bondind\_1}\limits^ \pm )} $$One problem with the panel regression model is a possible mechanical relationship between the funded ratio and the allocation to AI.Footnote 2 It is possible the return on traditional investments is negative in 1 year whereas that on AI is positive (since they are not highly correlated), then we can have a lower funded ratio (as traditional investments still account for the majority of assets) and a larger allocation to AI in the next year (holding other things constant). In this case, if there was no active rebalancing of portfolio weights, the funded ratio and AI allocation tend to be negatively related to each other.
To deal with this problem, we next construct an event history model to investigate the factors that drove pension plans to initiate investments in alternative assets. Since the first-time investment in alternatives definitely represents an active policy decision, the event history analysis of AI will not suffer from the mechanical effects as described above. In specific, we are interested to answer whether pension plans are more likely to initiate AI when the funded ratio is low? Therefore, the event for this study is defined as the initiation of AI, and a general event history model with both constant and time-varying explanatory variables can be written as follows:
$$\log h(t) = a(t) + b_1x_1 + \cdots + b_kx_k + b_{k + 1}x_{k + 1}(t-1) + \cdots + b_px_p(t-1)$$where a(t) may be any function of time, X 1 through X k are constant variables in the sample (i.e., social security coverage, existence of investment council, etc.), and X k+1 through X p are time-varying explanatory in the sample (i.e., investment return assumption, funded ratio, the percentage of actuarially required contribution paid, active to retirement member ratio, etc.). This model says that the hazard rate of the event at time t depends on the value of X 1 − X k and also on the value of X k+1 − X p at time t − 1. In estimating equation (3), we will use the same set of variables as in equation (2) and apply a standard Cox's regression method that can model both the occurrence and the duration of the events (Allison, Reference Allison2014).
4.2 Variables
The dependent variable to be used in the PVAR model (equation (1)) is annual investment return and the independent variable is AI as percentage of total pension assets for each pension plan. The dependent variable for the panel regression model (equation (2)) is AI as percentage of total pension assets, which is the same as the independent variable in the PVAR model. And the dependent variable for the event history model (equation (3)) is the log of the hazard ratio of the event as defined above (the percent of AI switched from 0 to a positive number). To make the result more robust and meaningful, we will also investigate the two major components of AI for all models: private equity and hedge funds as percentage of total assets.
For the independent variables of equations (2) and (3), the first category of plan characteristics is captured by investment return assumption, funded ratio, the percentage of actuarially required contribution paid, active to retirement member ratio, plan size, cost of living provision, and social security coverage. As discussed previously, higher investment return assumption should provide plans with stronger incentives to invest in AI. Contrarily, better funded plans should have less incentive to invest in AI. The percentage of actuarially required contribution paid and active to retirement member ratio are two important indicators of the employer contribution. If state and local pension plans pay the required contribution fully and on time or if they have higher active to retirement member ratio, they should have less need to rely on more uncertain assets such as AI to earn high returns. Therefore, the predicted sign of these two variables is negative. Additionally, larger pension plans have greater need to diversify their assets and also have more ability to afford investment losses. Therefore, plan size is predicted to have a positive relationship with AI investment. Moreover, plans with more generous cost of living adjustment (COLA) provision are costlier to maintain, so these plans also tend to have more AI. Last, plans whose participants are covered by social security pay less in retirement benefits than those plans without social security coverage, other things being equal.Footnote 3 Such plans, therefore, should be less likely to invest a high percentage of their assets in AI.
The second category of independent variables – pension plan governance – is represented by the existence of an independent investment council and the percentage of plan participants on the pension board. Professional investment managers usually have deeper understanding of AI, so plans with an investment council are more likely to include AI so to achieve an optimal portfolio and better investment performance. However, literature provides conflicting hypotheses and empirical evidence about the role of active plan participants, so the predicted sign on this variable is unclear.
Additionally, Standard & Poor's 500 index and bond index are measures of general financial market conditions. On the one hand, a boom market will increase the return on private equity, a major component of AI, and therefore attract more allocation to AI, so there could be a positive relationship between these two indices and AI allocation. On the other hand, the high return on stocks and bonds could also lead to a diversion of pension assets from AI to equities and bonds. As a result, the composite impact of the two marked indices on AI allocation is unclear.
All independent variables are lagged one period for both panel regression model and event history model, as a decision on asset allocation for the current period is typically made on the basis of information from the previous period(s).
4.3 Data
The main data analyzed in this study were drawn from the new Public Plans Database (PPD) collected and regularly updated by the Center for Retirement Research at Boston College. The PPD currently contains comprehensive financial, governance, and plan design information from 2001 through 2014 for the majority of state-administered defined benefit plans and some of the largest locally-administered plans. This sample covers 90% of public-pension membership and assets nationwide.
A comparability issue arose because pension plans included in the PPD have different ending dates for their fiscal years. Many plans in the sample use June 30 as the ending date, but others use March 31, August 31, September 30, or December 31. For a comparison of investment return and other related variables to make sense, the observations included in the sample have to cover the same time period. Since the majority of the pension plans in our sample adopt a fiscal year ending on June 30, and an accurate matching between investment variables and fiscal period is virtually impossible without more detailed information, in this study we limited our analysis to those plans with fiscal year ending on June 30. Doing this and removing a few other plans with missing data reduced the total sample to 92 plans, among which 80 are state-administered plans and 12 are administered by counties, cities, or school districts.
The PPD data, however, did not separate allocations to hedge funds and private equity from allocations to other types of AI (i.e., venture capital, commodities, etc.). To obtain the data on these two main components of AI, we searched the Comprehensive Annual Financial Reports (CAFRs) for each pension plan between 2001 and 2014. While we managed to find accurate data of hedge funds, we were not able to get the precise percentages of private equity for some plans. This was because these plans simply reported an aggregate number typically labeled as ‘other alternatives’ and there was no further information. According to Cliffwater LLC (2012), in 2011, when real estate and hedge funds are excluded, private equity accounted for 88.2% of the remaining portion of AI. Therefore, this research employed the total percentage of all remaining AI (excluding real estate and hedge funds) as an approximate number for private equity for those plans without accurate subcategory data.
In addition to the PPD and data from the CAFRs, this study also utilized benchmark indices of two major types of assets as controls for general market conditions. The S&P 500 index was retrieved from the Federal Reserve Bank of St. LouisFootnote 4 and the bond index data is retrieved from Deutsche Bank.Footnote 5 Both indices are widely used in financial studies. Table 1 has definitions of all the variables used in the two-sample t test and multiple regression analysis.
Variable specification
4.4 Descriptive statistics
Table 2 provides summary statistics of all variables to be used in this study.
Descriptive statistics
The first dependent variable is annual investment return for each public-pension plan from 2001 to 2014.Footnote 6 Figure 4 is a box plot of annual investment returns for all plans in the 2001–2014 period. It clearly shows, as indicated by the median and adjacent values, there was great variability from year to year. During the two economic downturns of 2001 and 2008, almost all of the plans recorded negative returns; the opposite was true when the US economy recovered from these two recessions. More importantly, there is also considerable difference among pension plans within each year. In 2013 for example, the best performing plan gained 22.5% of total assets (Delaware State Employees), while the worst performer suffered about 0.1% loss (Hawaii ERS).
Box plot of annual investment return 2001–2014.
Total percentage of AI allocation, the percentage of private equity and the percentage of hedge funds will also be used as dependent variables in later analyses. Similar to investment return, AI as well as its two major components also varied widely in the sample: total AI ranged from 0% to 60.8% with the mean at 8.97%; private equity ranged from 0% to 51.4% with the mean at 7.85%; and hedge funds ranged from 0% to 23% with the mean at 1.56%. It should be noted that a considerable number of plans/years invested nothing in private equity, hedge funds, or other alternative assets at all, so our sample was left-censored at zero. This reveals that many pension plans remained highly cautious about AI, especially during the early years of the sample.
A few other independent variables worth noting include funded ratio, the ratio of active to retired members, and the investment assumption. The average funded ratio was 81.8%, ranging from 197.4% to only 19.1%. This large gap between the best and worst funded plans reflected many crises and changes that had occurred to public-pension plans during this tumultuous period. Active to retired members' ratios in our sample fluctuated from 0.02 to 179.7, with the mean at 2.85. This ratio for most ongoing pension plans was actually bounded between one and five, but a few plans that had already been closed to new members had a particularly low ratio (e.g., Washington LEOFF Plan 1) while some newly-established plans had a very high ratio (e.g., Washington School Employees Plan). Finally, investment return assumptions ranged from 6% to 9%, with the mean at 7.9%. The average return dropped slightly since 2009 from 8% to 7.8% in 2014 (NASRA, 2014).
5. Empirical results
How did AI affect pension fund performance? To answer this question, we first conducted two-sided t-tests to compare mean investment returns of pension plans with varying percentages of assets dedicated to total AI including both private equity and hedge funds in the previous year. First, we compared mean investment returns of pension plans with AI allocation greater than zero to plans with no AI allocation. We then examined the results of two sample t-tests comparing mean returns as we increased the AI allocation, using 10% and 15% as the thresholds that separate the two groups. The results of the performance comparisons are presented in panel (a) through panel (c) of Appendix.
As panel (a) of Appendix shows, compared with pension plans with no AI allocations, pension funds investing in AI had significantly higher annual returns in 2004–2007. However, this same group of plans had significantly lower returns in 2003, 2009, and 2012. As we increased the AI allocation threshold that separated the two groups, the mean return comparison results remain almost the same though the significance and standard deviation vary. Panel (b) of Appendix shows that plans with higher levels (⩾10%) of AI had significantly higher returns for the years 2004 through 2007, and 2010, but they fared worse in 2009 and 2014. When the AI threshold increased to 15%, as shown in panel (c), we found that the higher-AI plan group earned significantly higher returns only in 2004 and 2007 but earned significantly lower returns in 2009 and 2014. Because only a few plans invested more than 15% of their assets in AI prior to 2009, we need more seasoned data before being able to come to any strong conclusions.
The two-sample means tests above provided some initial evidence that pension investment return might be related to the allocation to AI: overall, plans with higher allocation to AI seemed to have better or no worse investment performance for most years of the sample period. However, as explained in the methodology section, such a relationship was not meant to be causal. Therefore, we went on to estimate the PVAR model as specified in equation (1). Following the standard procedures outlined in Abrigo and Love (Reference Abrigo and Love2016), we first identified the number of lags to include in the model, then fitted a PVAR model using the generalized method of moments estimation method, and last checked the stability of PVAR and conducted a series of other necessary tests.
The results of the PVAR of annual investment return (invreturn_1yr) and total alternatives as well as its two major components are shown in Table 3 (only the estimators for investment return are presented; full results are available upon request). Based on the minimum value of moment model selection criteria (MMSC)-Bayesian information criterion (MBIC), MMSC-Akaike information criterion (MAIC), and MMSC-Hannan and Quinn information criterion (MQIC), the appropriate lag length was determined to be three lags. The individual regression coefficients are less important than the F-tests of joint significance of the variables (Granger causality tests). The F-tests of joint significance suggest that private equity Granger-causes annual investment return and so do total alternatives, but hedge funds do not Granger-cause investment return.
Results from PVAR analysis, t = 14 (dependent variable = annual investment return)
Note. *p < 0.10; **p < 0.05; ***p < 0.01. Standard errors are given in parentheses. Lag length (=3) was determined by MBIC, MAIC, and MQIC. All three models satisfied the eigenvalue stability condition.
The more common way to present the results of PVAR is to present impulse response functions (IRFs). IRFs predict the response of one variable to an ‘impulse’ or ‘shock’ in another variable. The basic idea is that if there were no changes in a given variable, then another variable would stay in the same time path as it would if the other variable was not present. When one changes the predictor variable (impulse), however, the IRF plots project changes in the time path of the predicted variable. Since there is no significant relationship between hedge funds and investment return, we only show the IRFs for the change in annual return given a one-unit shock in private equity (left graph) and in total alternatives (right graph) in Figure 5. The confidence interval was estimated using 200 Monte Carlo simulation draws.
Orthogonalized IRFs for the response of annual investment return to private equity and total alternatives: (1) response of return to private equity and (2) response of return to total alternatives.
Note: Response of return to hedge funds was insignificant, and therefore was not shown here.
The projected change in annual return given a shock to private equity is very similar to that given a shock to total alternatives. Initially, there was a significantly negative shock; however, at the third lag, the shock became positive and significant at the 0.05 α level. From the fourth lag, the shock mostly stayed positive and was significant for the seventh and 11th lag. Although it fell slightly under zero for the fifth and ninth lag, it was not significant at the 0.05 level in neither of the two cases. After the 12th lag, the shock gradually died out and became identical to zero. This shock pattern suggests that allocation to private equity may initially have a negative impact on investment return, but after 2–3 years, its positive effect will begin to emerge and continue to contribute to investment return for about 10 years. This result is consistent with the maturity theory which states that private equity investments usually sustain low returns (sometimes losses) in the initial years and earn increased return as the investment matures – the so-called J-curve (Grabenwarter and Weidig, Reference Grabenwarter and Weidig2005). The magnitude of the change is relatively small (ranging from one to three percentage points), but, given the importance of private equity to total AI and the importance of investment return to public-pension plans and the length of the effect, the results are very important.
One potential concern with any assessment of the relationship between investment return and AI allocation is reverse causality: that the direction of causality may be from the outcome variable – investment return to asset allocation. Although not reported here, the IRFs and Granger tests indicated no causal relationship in the opposite direction. Another concern is cointegration which refers to the situation in which the individual time series contain common trends. A Kao (Reference Kao1999) test was conducted. The results indicated no cointegration between the individual time series.Footnote 7
To explore the effect of funded ratio and other factors on private equity, hedge funds, and total alternatives, we estimated equation (2) using two different methods to ensure the robustness of the results. Since both panel heteroskedasticity and autocorrelation were detected, we first engaged a fixed-effect model with panel-corrected standard errors (PCSEs). To deal with the left-censoring problem in the dependent variable, we then estimated equation (2) using a panel Tobit method. The two sets of estimation results are reported in Table 4. Overall, the signs of the independent variables remained consistent across different estimation methods, though the magnitude of coefficients were larger in the Tobit model and the significance level fluctuated somewhat. As indicated in the lower right corner of Table 4, there was a severe left-censoring issue in our data. Therefore, we will mostly rely on the Tobit results for interpretations.
Panel regression models (dependent = private equity, hedge funds and total alternatives)
Note. *p < 0.10; **p < 0.05; ***p < 0.01. Robust standard errors are given in parentheses.
As Table 4 shows, investment return assumption was positively associated with allocation to private equity as well as total alternatives, but it had no relation with allocation to hedge funds. Holding other things constant, an increase in the return assumption of one percentage point was associated with an increase in allocation to private equity by 1.9–3.3 percentage points and to total AI by 1.6–3.0 percentage points. Conversely, the plan funded ratio was negatively associated with both the total AI and its two major components, indicating that well-funded plans are inclined to include more traditional assets in their portfolio, whereas poorly funded plans are more willing to take advantage of AI as a possible solution to their funding problem. Moreover, the asset size of pension plans had a positive and significant effect on AI allocations. Apparently, larger pension plans tend to include more alternatives in their portfolios, probably due to its economy of scale in achieving a higher level of diversification.
Plan governance structure also played a role in AI allocation decisions. If a plan had a separate investment council, it was more likely to reduce holdings of other assets in favor of private equity as hypothesized. However, the same could not be said to hedge funds, suggesting that professional investment managers held a more conservative attitude toward hedge funds than toward other types of alternatives. In contrast, a higher percentage of plan participants on retirement boards seemed to have no impact on allocation to private equity and total AI, but it showed a significant negative impact on allocation to hedge funds.
On the benefit front, automatic or consumer price index-linked COLA provision was positively correlated with private equity and total AI allocation, but was not correlated with hedge funds. It seems that plans with stricter COLA rules are under higher pressure to make more profits to cover the increased costs. Additionally, the active ratio was negative and significant for hedge funds, but it was positive and significant for private equity and total AI in the Tobit model. This indicates that plans with a higher percentage of active members relied less on hedge funds than on private equity to generate long-term higher investment return. Other independent variables were either statistically insignificant or highly inconsistent across different estimation methods.
Finally, the results of event history model seemed to reiterate the findings from the panel regression models, except that the significance level of the coefficients was generally lower. As Table 5 reports, investment return assumption was still positively associated with allocation to total alternatives, but it has no significant relation with private equity and hedge funds. Similarly, the plan funded ratio was still negatively associated with private equity, hedge funds, and total alternatives, but only the its negative relation with hedge funds reached the level of being statistically significant at the 0.05 level. This indicates that poorly funded plans are especially more likely to initiate investment in hedge funds than other types of AIs. Same as before, plans with a separate investment council were more inclined to begin investing in private equity and total alternatives, but not hedge funds. Social security coverage, which did not show any significant impact, now turned negative and significant for private equity and total alternatives. This result suggests that plans whose members are mostly covered by social security are less likely to embrace AI. In contrast, the pension asset size, the active-to-retired-members ratio and the percentage of plan participants on retirement boards, all of which were significant in the panel regression model, were no longer significant in the event history model.
Event history models for allocations to private equity, hedge funds, and total alternatives
Note. *p < 0.10; **p < 0.05; ***p < 0.01. Robust standard errors are given in parentheses. The Efron approximation method was used to handle ties in all three models. Schoenfeld residual tests for proportional hazards assumption were conducted for all three models, but no violations were found.
In a nutshell, there was a small but statistically significant and relatively long-lasting effect of AI on pension investment return. Generally, pension investment performance is improved by allocating more assets to private equity and a few other types of AI. The effect on investment return takes 2–3 years to set in, indicating the cost of assets reallocation and a lag in policy effectiveness. In contrast, hedge funds seemed to have little impact on investment return.Footnote 8 With respect to the determinants of AI allocation, investment return assumptions, funded ratio, active ratio, asset size, COLA, use of investment council, and plan participant percentage were the main drivers of the observed level of private equity, but only funded ratio, active ratio, asset size, and participant percentage were related to the observed level of hedge funds. Last, pension plans with higher investment assumption and a separate investment council were more likely to initiate AI, while plans with higher funded ratio and better social security coverage were less likely to do so.
6. Discussion and conclusion
The findings above answer the two questions we raised at the beginning. First, AI, except for hedge funds, generally provided higher returns for the period under study, although the benefit of including AI in the portfolio would roughly follow the J-curve and take a while to emerge. That is probably the main reason why public-pension plans flocked to AI over this period, especially after 2008. Second, plans with a lower funded ratio and a higher investment return assumption (plus higher benefit levels) are likely to invest more in private equity and other similar alternatives than otherwise. This answers the second question about whether the declining pension funded ratio since 2001 affected the upward trend in allocation to AI, especially private equity. Putting these two findings together, it is reasonable to say that such plans were counting on the expected higher returns from AI to help them realize higher expectations and pull up their funded ratio.
These findings lead to one very important question and its policy implications: will this investment strategy help generate enough investment income to increase the funded ratio? To answer this question, we need to examine the broader investment environment. In the aftermath of the Great Recession, interest rates have been reduced to zero, or close to zero, for the most developed nations. The economic growth rate has slowed significantly in the USA and across the developed world, for a variety of long-term factors such as the retirement of the baby boom generation, the aging of the population across the developed world and a slowdown in the productivity rate. Against such an economic background, for the foreseeable future, the investment return on fixed-income securities and public equity is unlikely to match the average return achieved in the 30-year period between 1980 and 2010. McKinsey Global Institute (2016) predicts that total real returns from US equities over a 20-year period beginning in 2016 could average 4–5%, and fixed-income real returns could be around 0–1%. In such an environment, an allocation to traditional assets such as public equity and fixed-income will have a low probability of achieving the expected return of at least 7.5% for an extended period of time.
It is then no wonder that pension plans with a lower funded ratio allocated a greater portion of their assets to AI in order to increase their odds of meeting or beating their (sometimes higher) expected rate of return. However, both empirical evidence and theoretical reasoning suggest that past performance in AI may not be sustainable. Empirically, we found in this study that even though the return on AI on average provided higher return, the extra return was relatively small and did not last very long. Theoretically, unlike the public equity market, which is deep and broad and thus can absorb a continuing flow of new funds, there are more limited investment opportunities to earn higher return over public equity without taking higher risk. When more and more funds from public-pension plans and other sources pour into AI to earn the extra return, it will become harder and harder to identify those investment opportunities that can earn a return higher than that of the broad public equity market. This poses a bigger problem for state-level public-pension plans as they tend to be large and have more funds to invest.
If AI is unlikely to earn a substantially higher return to offset the potentially below-average return on traditional assets over an extended period of time, then it will be difficult to meet the investment expectations embedded in public-pension financing, posing challenges to pension plans with relatively low funded ratios. That means there are only two other options to increase the average funded ratio from its current level: slow the growth rate of pension liability (to that below the investment return rate) or inject more pension contributions into the public plans or both. Since 2001, many state and local governments have already reduced pension benefits. However, as benefits for existing employees and retirees are protected by state constitutions or statutes, such changes only affect new employees. While in the long run this will reduce the growth of pension liabilities, its impact is still rather limited in the foreseeable future. That means pension contribution increase needs to play a major role in reducing the unfunded liability, potentially taking more resources away from other vital government services and thus putting pressure on government budget.
In all, even though AI has provided higher returns to public-pension plans in the past, it will be difficult to rely on it to achieve the expected rate of return in the foreseeable future. This leaves a difficult policy choice for sponsors of public-pension funds, especially those with a low funded ratio. With no easy solution, that means state and local governments will face financial pressure for many years to come.
Author ORCIDs
Qiushi Wang, 0000-0002-1780-1088
Appendix: Mean investment return comparison: alternatives >0%, >10%, >15%
