# Heterogeneity in Target Date Funds: Strategic Risk-taking or Risk Matching?

Heterogeneity in Target Date Funds: Strategic Risk-taking or Risk Matching? Abstract The use of target date funds (TDFs) as default options in 401(k) plans increased sharply following the Pension Protection Act of 2006. We document large differences in the realized returns and ex ante risk profiles of TDFs with similar target retirement dates. Analyzing fund-level data, we find evidence that this heterogeneity reflects strategic risk-taking by families with low market share, especially those entering the TDF market after 2006. Analyzing plan-level data, we find little evidence that 401(k) plan sponsors consider, to any economically meaningful degree, the risk profiles of their firms when choosing among TDFs. Received June 13, 2013; editorial decision March 20, 2018 by Editor Laura Starks. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online. A common implication of normative optimal portfolio models is that, as investors age, it is optimal for them to shift their financial wealth away from stocks and toward bonds.1 This normative implication found its way into the design of target date funds (TDFs). Wells Fargo introduced the first TDFs in 1994. According to Seth Harris, Deputy Secretary of the Department of Labor (DOL), TDFs “were designed to be simple, long-term investment vehicles for individuals with a specific retirement date in mind.”2 Investors who plan to retire in 2030, for example, could invest all of their 401(k) assets in the Wells Fargo LifePath 2030 fund. The innovation, relative to traditional balanced funds (BFs), is that TDFs relieve investors of the need to make asset allocation decisions or rebalance their portfolios. When the target date is far away, the TDF invests primarily in domestic and foreign equity, but as the number of years to the target date declines, the TDF automatically reduces its exposure to risky assets.3 The promise of a simple, long-term retirement investment prompted the DOL, through the Pension Protection Act of 2006 (PPA), to allow firms to adopt TDFs as default investment vehicles in employer-sponsored defined contribution (DC) retirement plans. Shortly thereafter, however, policy makers began to worry about the return characteristics of TDFs. In 2009, Herb Kohl, chairman of the Senate Special Committee on Aging, wrote: “While well-constructed target date funds have great potential for improving retirement income security, it is currently unclear whether investment firms are prudently designing these funds in the best interest of the plan sponsors and their participants” (Special Committee on Aging 2009, p. 4). Our goals in this paper are to examine changes in the return characteristics of TDFs between 2000 and 2012, and to relate these changes to the incentives of mutual fund families and retirement plan sponsors. Our motivation comes from the fact that assets under management (AUM) in TDFs increased from $\$$8 billion to \$$480 billion over our sample period and currently exceed$\$$1.1 trillion.4 We begin by establishing two stylized facts. The first is that it is common for TDFs with similar target dates to earn significantly different realized returns and exhibit significantly different levels of ex ante risk. Consider the 67 TDFs in 2009 with target dates of 2015 or 2020. The average annual return within this sample is$$25.1\%$$, the cross-sectional standard deviation is$$4.4\%$$, and the range is$$23.5\%$$, with realized returns varying between 11.9% and 35.4%. When we control for cross-sectional dispersion in glide paths (i.e., betas and realized factor returns), we find that a similar pattern holds for the idiosyncratic component of realized returns, the “alpha.” The cross-sectional standard deviation of five-factor alphas is$$3.1\%$$, and the range is$$12.9\%$$. These reflect economically meaningful differences in realized returns. To measure differences in ex ante risk, we focus on the time-series standard deviation of monthly five-factor alphas and five-factor model$$R^2$$and betas. Consistent with our prior that these measures capture portfolio characteristics under the control of TDF managers, we find that they are highly persistent. For the same 67 TDFs in 2009, the average standard deviation of alphas is 2.4%, the minimum is 0.9%, and the maximum is 5.6%, indicating large differences in the level of idiosyncratic risk. The$$R^2$$s, a measure of the relative importance of systematic risk, are similarly dispersed, with an average of$$97.3\%$$, but a minimum of$$84.8\%$$. Finally, the standard deviation of the beta on U.S. equity is$$0.12$$, and the range is$$0.64$$. The second stylized fact is that dispersion in TDF risk profiles increases following the PPA. When we compare the distribution of risk profiles in 2000–2006 (Pre-PPA) to those in 2007–2012 (Post-PPA), we find that idiosyncratic volatility and cross-sectional dispersion in monthly net returns, monthly five-factor alphas, and U.S. equity betas all increase in the post-PPA period. When we switch to difference-in-differences specifications that compare TDFs to BFs, we find even stronger evidence of increased risk-taking by TDFs during the post-PPA period. Importantly, none of these findings are being driven by the financial crisis. Although the financial crisis was associated with increased return dispersion among TDFs and (especially) BFs, we obtain similar results when we exclude 2008 and 2009. In fact, difference-in-differences specifications that exclude the financial crisis yield the strongest evidence of increased dispersion in the risk profiles of TDFs with similar target dates, including reductions in$$R^2$$. We hypothesize two reasons that dispersion in risk profiles may have increased following the PPA, based on two strategies that mutual fund families could plausibly pursue to increase the market shares of their TDFs. First, there is a large literature on risk-taking by mutual funds to attract investor flows (e.g., Brown, Harlow, and Starks 1996; Chevalier and Ellison 1997; Sirri and Tufano 1998; Evans 2010). Under the “strategic risk-taking” hypothesis, families increased their TDF risk exposures to achieve greater expected performance and thereby potentially increase their market shares. Second, beginning with Davis and Willen (2000a), academic studies have emphasized the role of labor-income heterogeneity in the construction of optimal portfolios. Under the “risk-matching” hypothesis, families may offer TDFs with increasingly different risk profiles so that plan sponsors can choose TDFs that better offset the risk from being employed in a given firm or industry (“human-capital risk matching”) or better match the overall risk preferences of the employees covered by their DC plans (“risk-preference matching”). Note that these hypotheses need not be mutually exclusive. An entrant could choose a glide path with a persistently high allocation to international equity, for example, with the twin goals of earning higher net returns and benefiting from risk-preference matching. Nevertheless, it is important to understand whether the data favor one hypothesis over the other. If the heterogeneity in TDF returns and risk exposures is primarily driven by families strategically responding to risk-taking incentives, then it could prove harmful to TDF investors, especially those who are limited to the TDFs from a single family.5 Alternatively, if the heterogeneity is primarily driven by risk-matching considerations, it could prove beneficial to TDF investors. We base our risk-taking predictions on four observations. First, by increasing the expected market share of TDFs inside retirement plans, the PPA increased the incentive for families to enter this market. Indeed, between 2006 and 2012, assets under management in TDFs more than quadrupled, increasing from \$$116.0 billion to $\$$480.2 billion, and the number of mutual fund families offering TDFs jumped from 27 to 44, before falling back down to 37. Second, because TDF flows are likely driven by the choices of plan sponsors (Sialm, Starks, and Zhang 2015), we expect—and provide supporting evidence—that TDF flows respond primarily to alphas. Competing on alphas can encourage TDFs to load up on idiosyncratic risk. Third, the fact that entrants—and incumbents with low market share—have few assets under management to lose adds convexity to the flow-performance relation and, thereby, an additional incentive to engage in risk-taking. Fourth, families that enter the market after the PPA are likely to be less constrained in terms of investment behavior than families that chose their glide paths and underlying set of funds before the PPA. Collectively, these observations lead us to predict that increased risk-taking during the post-PPA period is being driven by families with low market share, especially those families entering the TDF market after 2006. Our findings are broadly consistent with strategic risk-taking. After confirming that flows into TDFs respond primarily to alphas, we estimate a series of regressions that relate TDF return characteristics to family-level market share and date of entry. To control for time-series variation in both market returns and market structure, each regression includes a full set of target date-by-time period fixed effects. We find strong evidence of higher risk-taking by TDFs from families with Low market share (i.e., families with total TDF market shares$$\le 1\%$$) relative to TDFs from families with High market share (i.e.,$$> 5\%$$). TDFs from families with low market share exhibit more diverse net returns and five-factor alphas, higher levels of idiosyncratic volatility, lower$$R^2$$s, and more diverse betas on U.S. equity, global equity, and global debt.6 All of these differences are statistically significant at the 5% level or below. While the higher diversity in betas may be interpreted as the result of product differentiation, the higher levels of idiosyncratic volatility and lower$$R^2$$s of TDF returns are more likely consistent with higher risk-taking. We find the strongest evidence of higher risk-taking when we compare TDFs from post-PPA families with low market share to TDFs from families with high market share. This finding is broadly consistent with our conjecture that the PPA incentivized risk-taking by entrants, and is robust to (1) controlling for the return characteristics of BFs in the same family, (2) limiting our tests to the post-PPA sample period, and (3) excluding observations around the financial crisis. When the comparison group is TDFs from pre-PPA families with low market share, estimated differences in diversity remain economically large but often are only statistically significant at the 10% level. For example, the five-factor alphas of TDFs from post-PPA families differ from those of TDFs from pre-PPA families by approximately$$3\%$$annually, an economically meaningful difference that is statistically significant at the 10% level. To investigate the risk-matching hypothesis, we exploit data from BrightScope on the investment menus of thousands of DC retirement plans in 2010, when plan sponsors have a large set of TDFs from which to choose. For firms with publicly traded equity, we regress the systematic (idiosyncratic) risk of the TDFs offered in each plan on the systematic (idiosyncratic) risk of the firm’s equity. To expand our sample to include private firms, we also regress the risk of the TDFs offered in each plan on the median risk of public firms within the same industry. Regardless of whether we focus on systematic or idiosyncratic risk, we find little evidence of economically meaningful risk matching. This remains true when we focus on the subset of plans with automatic enrollment. Moreover, the$$R^2$$s of our regressions remain low when we include industry fixed effects to control for differences in the volatility of employment and other time-invariant differences across industries. Instead, within the sample of TDFs included in investment menus in 2010, the variables with the most explanatory power are those that measure the market share of the plan’s recordkeeper and that indicate whether the TDF is from a family with low TDF market share. Because we find that risky firms are no more or less likely to choose risky TDFs than safe firms, we conclude that the increased heterogeneity in TDF return characteristics during our sample period is unlikely to reflect growing demand from plan sponsors for new TDF risk profiles. 1. Institutional Background and Review of TDF Literature Although only four fund families offered TDFs in 2000, the PPA allowed firms to offer TDFs as default investment options within 401(k) retirement plans. The regulatory goal was to redirect investors from money market funds—the dominant default investment option—to age-appropriate, long-term investment vehicles. To accomplish this goal, the PPA relieves plan sponsors of liability for market losses when they default employees into a qualified default investment alternative (QDIA). The set of QDIAs is limited to TDFs, BFs, and managed accounts. While TDFs were perceived to be an important innovation in the market for retirement products, some commentators began expressing concerns about the lack of transparency regarding risk.7 The Investment Company Institute (ICI) reports that the share of 401(k) plans offering TDFs increased from$$57\%$$in 2006 to$$74\%$$in 2014.8 Similarly, the share of 401(k) plan participants offered TDFs increased from$$62\%$$to$$73\%$$. At year-end 2014,$$48\%$$of 401(k) participants held at least some plan assets in TDFs, up from$$19\%$$at year-end 2006. The fraction of mutual fund assets in DC plans that are invested in TDFs rose from 4% to 13% between 2006 and 2014 (and to 16% in 2016); according to both ICI and our sample of investment menus from BrightScope, it was 10% in 2010. However, ICI reports that 401(k) plan participants in their twenties collectively allocated 42.4% of their retirement assets to TDFs in 2014. Therefore, employees just entering the labor force appear likely to finance their retirement through a combination of TDF returns and Social Security benefits.9 Interestingly, mutual fund families have taken different approaches to the design of their TDF products. While some offer indexed TDFs with a relatively small number of underlying funds (4 or 5), others offer actively managed TDFs, sometimes with a large number of underlying funds (as many as 27). Whether one approach is better for investors than the other is an open question, but these diverse approaches highlight a significant source of heterogeneity in how TDFs are constructed. This is the first paper to focus on the heterogeneity of TDFs realized returns and risk profiles and to study changes in the population of TDFs around the time of the PPA. The existing literature mainly compares TDFs to other investment vehicles and studies the factors driving individual demand for TDFs.10 The paper most closely related to our own is Sandhya (2011), who compares TDFs to BFs offered within the same mutual fund family. While Sandhya (2011) focuses on average differences in fund expenses and returns, our paper links heterogeneity in idiosyncratic risk to risk-taking incentives arising from the PPA. Also related is Elton et al. (2015), who use data on underlying mutual fund holdings to study both the level of TDF fees and how deviations from TDF glide paths affect fund-level returns. The finding that TDFs have become increasing likely to invest in emerging markets, real estate, and commodities complements our findings related to heterogeneity in TDF betas. However, they do not investigate risk-taking by entrants. In addition, none of the existing papers explores the extent to which plan sponsors consider measures of TDF risk when constructing their investment menus.11 2. Data We obtain data on mutual fund names, characteristics, fees, and monthly returns from the CRSP Survivor-Bias-Free U.S. Mutual Fund Database. CRSP does not distinguish TDFs from other types of mutual funds, but they are easily identified by the target retirement year in the fund name (e.g., AllianceBernstein 2030 Retirement Strategy). Through much of the paper, our unit of observation is family$$i$$’s mutual fund with target date$$j$$in month$$t$$. For example, T. Rowe Price offers twelve distinct TDFs in December 2012, with target dates of 2005, 2010, ..., 2045, 2055, plus an income fund. As with other types of mutual funds, TDFs typically offer multiple share classes. To calculate a fund’s size, we sum the assets under management at the beginning of month$$t$$across all of its share classes. To calculate a fund’s expense ratio, we weight each share class’s expense ratio by its assets under management at the beginning of the month. To calculate a fund’s age, we use the number of months since its oldest share class was introduced. To identify families that enter the market after December 31, 2006, we use the year when each mutual fund family offered its first TDF. Because we find that CRSP data on the holdings of equity, debt, and cash are unreliable for TDFs, we infer investment strategies from the betas estimated in factor models.12 Table 1 presents summary statistics on the evolution of the TDF market over the 1994–2012 period. Wells Fargo introduced the first TDFs in 1994. Between 1994 and 2012, the number of TDFs grew from five to 368 and the number of mutual fund families offering TDFs grew from one to 37, with total assets under management going from \$$278 million to$\$$480 billion, a seventeen-hundred-fold increase.13 In particular, 20 families entered the market after 2006, allowing us to study differences between the TDFs of new entrants and more established mutual fund families. While Wells Fargo was the market leader until 1997, Fidelity took the lead in 1998. Fidelity’s dominant position has been eroded, though, dropping from a maximum market share of$$88.1\%$$in 2002, to$$32.7\%$$in 2012. Similarly, although the market for TDFs remains quite concentrated, the market share of the top three firms has fallen gradually from$$97.8\%$$in 2002, to$$75.1\%$$in 2012. Firms that entered the market after 2006 (and remained in the market through 2012) have a combined market share of 4.4%. However, note that seven of the ten families that exit the TDF market between 2009 and 2012 also entered the market after 2006. These include Goldman Sachs and Oppenheimer. Table 1 Summary statistics # Families offering one or more TDF within target date range Market share Income & 2005 & 2015 & 2025 & 2035 & 2045 & 2055 & # Families Market Market Top 3 Post-PPA 2000 2010 2020 2030 2040 2050 2060 Total Enter Exit AUM leader leader families entrants 1994 1 1 1 1 1 1 1 278.4 Wells Fargo 100.0% 100.0% 1995 1 1 1 1 1 1 590.1 Wells Fargo 100.0% 100.0% 1996 3 3 3 3 2 3 2 894.2 Wells Fargo 63.9% 100.0% 1997 2 3 3 3 2 3 1,499.4 Wells Fargo 42.7% 100.0% 1998 2 3 3 3 2 3 4,159.2 Fidelity 65.9% 100.0% 1999 4 4 4 4 3 4 1 6,525.5 Fidelity 76.6% 99.5% 2000 4 4 4 4 4 4 8,215.1 Fidelity 80.4% 99.4% 2001 4 5 5 5 5 1 5 1 11,828.8 Fidelity 85.1% 99.1% 2002 6 6 6 6 6 1 6 1 14,509.5 Fidelity 88.1% 97.8% 2003 9 9 9 9 9 2 9 3 25,632.2 Fidelity 85.1% 92.6% 2004 12 11 12 12 12 4 13 4 43,729.2 Fidelity 71.0% 85.3% 2005 17 17 20 20 19 7 20 7 70,211.3 Fidelity 61.5% 85.3% 2006 20 21 27 27 25 12 1 27 7 115,958.0 Fidelity 54.9% 84.0% 2007 24 28 35 35 32 22 2 35 8 174,647.8 Fidelity 50.5% 81.0% 1.5% 2008 31 33 44 44 43 35 3 44 9 159,717.1 Fidelity 42.8% 79.5% 2.7% 2009 28 31 40 40 40 34 3 40 1 5 254,826.0 Fidelity 39.0% 77.5% 3.7% 2010 27 27 39 39 39 36 8 39 1 339,879.4 Fidelity 36.7% 76.3% 4.2% 2011 27 26 40 40 40 38 15 40 1 375,686.1 Fidelity 34.6% 75.7% 4.5% 2012 28 22 37 37 37 35 19 37 1 4 480,162.4 Fidelity 32.7% 75.1% 4.4% # Families offering one or more TDF within target date range Market share Income & 2005 & 2015 & 2025 & 2035 & 2045 & 2055 & # Families Market Market Top 3 Post-PPA 2000 2010 2020 2030 2040 2050 2060 Total Enter Exit AUM leader leader families entrants 1994 1 1 1 1 1 1 1 278.4 Wells Fargo 100.0% 100.0% 1995 1 1 1 1 1 1 590.1 Wells Fargo 100.0% 100.0% 1996 3 3 3 3 2 3 2 894.2 Wells Fargo 63.9% 100.0% 1997 2 3 3 3 2 3 1,499.4 Wells Fargo 42.7% 100.0% 1998 2 3 3 3 2 3 4,159.2 Fidelity 65.9% 100.0% 1999 4 4 4 4 3 4 1 6,525.5 Fidelity 76.6% 99.5% 2000 4 4 4 4 4 4 8,215.1 Fidelity 80.4% 99.4% 2001 4 5 5 5 5 1 5 1 11,828.8 Fidelity 85.1% 99.1% 2002 6 6 6 6 6 1 6 1 14,509.5 Fidelity 88.1% 97.8% 2003 9 9 9 9 9 2 9 3 25,632.2 Fidelity 85.1% 92.6% 2004 12 11 12 12 12 4 13 4 43,729.2 Fidelity 71.0% 85.3% 2005 17 17 20 20 19 7 20 7 70,211.3 Fidelity 61.5% 85.3% 2006 20 21 27 27 25 12 1 27 7 115,958.0 Fidelity 54.9% 84.0% 2007 24 28 35 35 32 22 2 35 8 174,647.8 Fidelity 50.5% 81.0% 1.5% 2008 31 33 44 44 43 35 3 44 9 159,717.1 Fidelity 42.8% 79.5% 2.7% 2009 28 31 40 40 40 34 3 40 1 5 254,826.0 Fidelity 39.0% 77.5% 3.7% 2010 27 27 39 39 39 36 8 39 1 339,879.4 Fidelity 36.7% 76.3% 4.2% 2011 27 26 40 40 40 38 15 40 1 375,686.1 Fidelity 34.6% 75.7% 4.5% 2012 28 22 37 37 37 35 19 37 1 4 480,162.4 Fidelity 32.7% 75.1% 4.4% This table provides annual snapshots of the market for TDFs, between 1994 and 2012. All of the data used to calculate the numbers in this table comes from the CRSP Survivorship-Bias-Free U.S. Mutual Fund Database. The first seven columns indicate the number of mutual fund families that offer at least one TDF with a target retirement date of now (income fund) or 2000, 2005, 2010, ..., 2055, or 2060 at the end of each year. The next three columns indicate the number of distinct mutual fund families that offer at least one TDF at the end of each year, the number of families that enter the market, and the number of families that exit the market. AUM measures total assets under management in TDFs at the end of the year (in  millions), summed across all mutual fund families. The last four columns indicate the name of the mutual fund family with the largest market share (based on AUM) at the end of the year, the market share of the market leader, the combined market share of the three families with the largest market shares, and the combined market share of families entering the market in 2007 and later. Through 2000, the only market participants were American Independence Financial Services, Barclays Global Fund Advisors, Fidelity Management and Research, and Wells Fargo. Table 1 Summary statistics # Families offering one or more TDF within target date range Market share Income & 2005 & 2015 & 2025 & 2035 & 2045 & 2055 & # Families Market Market Top 3 Post-PPA 2000 2010 2020 2030 2040 2050 2060 Total Enter Exit AUM leader leader families entrants 1994 1 1 1 1 1 1 1 278.4 Wells Fargo 100.0% 100.0% 1995 1 1 1 1 1 1 590.1 Wells Fargo 100.0% 100.0% 1996 3 3 3 3 2 3 2 894.2 Wells Fargo 63.9% 100.0% 1997 2 3 3 3 2 3 1,499.4 Wells Fargo 42.7% 100.0% 1998 2 3 3 3 2 3 4,159.2 Fidelity 65.9% 100.0% 1999 4 4 4 4 3 4 1 6,525.5 Fidelity 76.6% 99.5% 2000 4 4 4 4 4 4 8,215.1 Fidelity 80.4% 99.4% 2001 4 5 5 5 5 1 5 1 11,828.8 Fidelity 85.1% 99.1% 2002 6 6 6 6 6 1 6 1 14,509.5 Fidelity 88.1% 97.8% 2003 9 9 9 9 9 2 9 3 25,632.2 Fidelity 85.1% 92.6% 2004 12 11 12 12 12 4 13 4 43,729.2 Fidelity 71.0% 85.3% 2005 17 17 20 20 19 7 20 7 70,211.3 Fidelity 61.5% 85.3% 2006 20 21 27 27 25 12 1 27 7 115,958.0 Fidelity 54.9% 84.0% 2007 24 28 35 35 32 22 2 35 8 174,647.8 Fidelity 50.5% 81.0% 1.5% 2008 31 33 44 44 43 35 3 44 9 159,717.1 Fidelity 42.8% 79.5% 2.7% 2009 28 31 40 40 40 34 3 40 1 5 254,826.0 Fidelity 39.0% 77.5% 3.7% 2010 27 27 39 39 39 36 8 39 1 339,879.4 Fidelity 36.7% 76.3% 4.2% 2011 27 26 40 40 40 38 15 40 1 375,686.1 Fidelity 34.6% 75.7% 4.5% 2012 28 22 37 37 37 35 19 37 1 4 480,162.4 Fidelity 32.7% 75.1% 4.4% # Families offering one or more TDF within target date range Market share Income & 2005 & 2015 & 2025 & 2035 & 2045 & 2055 & # Families Market Market Top 3 Post-PPA 2000 2010 2020 2030 2040 2050 2060 Total Enter Exit AUM leader leader families entrants 1994 1 1 1 1 1 1 1 278.4 Wells Fargo 100.0% 100.0% 1995 1 1 1 1 1 1 590.1 Wells Fargo 100.0% 100.0% 1996 3 3 3 3 2 3 2 894.2 Wells Fargo 63.9% 100.0% 1997 2 3 3 3 2 3 1,499.4 Wells Fargo 42.7% 100.0% 1998 2 3 3 3 2 3 4,159.2 Fidelity 65.9% 100.0% 1999 4 4 4 4 3 4 1 6,525.5 Fidelity 76.6% 99.5% 2000 4 4 4 4 4 4 8,215.1 Fidelity 80.4% 99.4% 2001 4 5 5 5 5 1 5 1 11,828.8 Fidelity 85.1% 99.1% 2002 6 6 6 6 6 1 6 1 14,509.5 Fidelity 88.1% 97.8% 2003 9 9 9 9 9 2 9 3 25,632.2 Fidelity 85.1% 92.6% 2004 12 11 12 12 12 4 13 4 43,729.2 Fidelity 71.0% 85.3% 2005 17 17 20 20 19 7 20 7 70,211.3 Fidelity 61.5% 85.3% 2006 20 21 27 27 25 12 1 27 7 115,958.0 Fidelity 54.9% 84.0% 2007 24 28 35 35 32 22 2 35 8 174,647.8 Fidelity 50.5% 81.0% 1.5% 2008 31 33 44 44 43 35 3 44 9 159,717.1 Fidelity 42.8% 79.5% 2.7% 2009 28 31 40 40 40 34 3 40 1 5 254,826.0 Fidelity 39.0% 77.5% 3.7% 2010 27 27 39 39 39 36 8 39 1 339,879.4 Fidelity 36.7% 76.3% 4.2% 2011 27 26 40 40 40 38 15 40 1 375,686.1 Fidelity 34.6% 75.7% 4.5% 2012 28 22 37 37 37 35 19 37 1 4 480,162.4 Fidelity 32.7% 75.1% 4.4% This table provides annual snapshots of the market for TDFs, between 1994 and 2012. All of the data used to calculate the numbers in this table comes from the CRSP Survivorship-Bias-Free U.S. Mutual Fund Database. The first seven columns indicate the number of mutual fund families that offer at least one TDF with a target retirement date of now (income fund) or 2000, 2005, 2010, ..., 2055, or 2060 at the end of each year. The next three columns indicate the number of distinct mutual fund families that offer at least one TDF at the end of each year, the number of families that enter the market, and the number of families that exit the market. AUM measures total assets under management in TDFs at the end of the year (in  millions), summed across all mutual fund families. The last four columns indicate the name of the mutual fund family with the largest market share (based on AUM) at the end of the year, the market share of the market leader, the combined market share of the three families with the largest market shares, and the combined market share of families entering the market in 2007 and later. Through 2000, the only market participants were American Independence Financial Services, Barclays Global Fund Advisors, Fidelity Management and Research, and Wells Fargo. To obtain our comparison sample of traditional BFs, we drop all of the funds that we identify as TDFs, and then restrict the sample to funds where the Lipper objective (as reported in CRSP) is “Balanced Fund.” This sample includes four Lipper classifications: Flexible Portfolio Funds (FX), Mixed-Asset Target Allocation Conservative Funds (MTAC), Mixed-Asset Target Allocation Moderate Funds (MTAG), or Mixed-Asset Target Allocation Growth Funds (MTAM). 3. Characterizing Cross-Sectional Heterogeneity in TDFs We establish two stylized facts in this section. First, TDFs with similar target dates exhibit significant cross-sectional dispersion in realized returns and estimated ex ante risk profiles. Second, this dispersion increases following the PPA. Table 2 summarizes the return characteristics of TDFs and BFs, before and after the PPA. We begin by testing for differences in the diversity of realized monthly net returns, defined as squared deviations from cross-sectional average returns.14 For TDFs, diversity is measured as the squared deviation relative to the average TDF within the same target date range (e.g., 2015 and 2020). For BFs, it is measured as the squared deviation relative to the average BF with the same Lipper classification. Among the sample of TDFs operating during 2000–2006, our measure of diversity in monthly net returns averages 0.212, and we can reject the hypothesis of no cross-sectional dispersion during this period at the 1% level. Among the (much larger) sample of TDFs operating during 2007–2012, we find that average diversity of returns increases more than threefold, to 0.748, and we can reject the hypothesis of no increase in diversity at the 5% level.15 When we exclude monthly observations from 2008 and 2009, to minimize any impact of the financial crisis, the post-PPA increase is still more than double the value (0.536 vs. 0.252), but we can only reject the hypothesis of no increase in diversity at the 10% level. To measure economic significance, we calculate changes in the cross-sectional standard deviations of realized annual net returns within each target date range (see Internet Appendix Table B.1). Across the five target date ranges, we find that equally weighted standard deviations increase between 0.9% and 1.8%, while value-weighted standard deviations increase between 0.4% and 1.3%.16 Table 2 Benchmarking TDFs against BFs Dependent variable: Cross-sectional dispersion in Monthly net return Cross-sectional dispersion in Monthly 5-factor alpha Cross-sectional dispersion in U.S. equity beta Idiosyncratic volatility$$R^2$$from 5-factor model Fund type: BFs TDFs BFs TDFs BFs TDFs BFs TDFs BFs TDFs Frequency: Monthly Monthly Monthly Monthly Annual Annual Annual Annual Annual Annual Pre-PPA 1.272*** 0.212*** 0.365*** 0.066*** 0.027*** 0.005*** 1.636*** 0.991*** 0.935*** 0.966*** Post-PPA 1.240*** 0.748*** 0.490*** 0.232*** 0.016*** 0.011*** 2.110*** 1.944*** 0.951*** 0.971*** Post-PPA (excl. crisis) 0.558*** 0.464*** 0.269*** 0.145*** 0.012*** 0.012*** 1.635*** 1.615*** 0.954*** 0.968*** Difference –0.032 0.536** 0.106 0.166*** –0.011*** 0.005** 0.474 0.953*** 0.016** 0.005 Difference (excl. crisis) –0.714** 0.252* –0.105* 0.079** –0.015*** 0.006** –0.001 0.624*** 0.019** 0.003 Diff.-in-diff. 0.567* 0.061 0.016*** 0.479* –0.011 Diff.-in-diff. (excl. crisis) 0.966*** 0.185*** 0.021*** 0.625*** –0.016* Dependent variable: Cross-sectional dispersion in Monthly net return Cross-sectional dispersion in Monthly 5-factor alpha Cross-sectional dispersion in U.S. equity beta Idiosyncratic volatility$$R^2$$from 5-factor model Fund type: BFs TDFs BFs TDFs BFs TDFs BFs TDFs BFs TDFs Frequency: Monthly Monthly Monthly Monthly Annual Annual Annual Annual Annual Annual Pre-PPA 1.272*** 0.212*** 0.365*** 0.066*** 0.027*** 0.005*** 1.636*** 0.991*** 0.935*** 0.966*** Post-PPA 1.240*** 0.748*** 0.490*** 0.232*** 0.016*** 0.011*** 2.110*** 1.944*** 0.951*** 0.971*** Post-PPA (excl. crisis) 0.558*** 0.464*** 0.269*** 0.145*** 0.012*** 0.012*** 1.635*** 1.615*** 0.954*** 0.968*** Difference –0.032 0.536** 0.106 0.166*** –0.011*** 0.005** 0.474 0.953*** 0.016** 0.005 Difference (excl. crisis) –0.714** 0.252* –0.105* 0.079** –0.015*** 0.006** –0.001 0.624*** 0.019** 0.003 Diff.-in-diff. 0.567* 0.061 0.016*** 0.479* –0.011 Diff.-in-diff. (excl. crisis) 0.966*** 0.185*** 0.021*** 0.625*** –0.016* The dependent variable in each ordinary least squares (OLS) regression is a measure of cross-sectional dispersion. The unit of observation is fund$$i$$offered by family$$k$$in month or year$$t$$. The comparison group is the sample of BFs offered by families that offer TDFs. We compute cross-sectional dispersion in monthly net returns in month$$t$$as$$(r_{ijt} - \overline{r}_{jt})^2$$, where$$j$$is either the TDF’s target date or the BF’s Lipper classification (Flexible Portfolio Funds (FX), Mixed-Asset Target Allocation Conservative Funds (MTAC), Mixed-Asset Target Allocation Moderate Funds (MTAG), or Mixed-Asset Target Allocation Growth Funds (MTAM)). The cross-sectional dispersion in monthly five-factor alphas in month$$t$$is computed similarly. Each month, we estimate the five-factor model for fund$$i$$using daily excess returns between month$$t-11$$and month$$t$$. The five factors are the daily excess returns of the CRSP U.S. value-weighted market index, MSCI World Index excluding the United States, Barclays U.S. Aggregate Bond Index, Barclays Global Aggregate excluding the United States, and GSCI Commodity Index. The five-factor alpha of fund$$i$$in month$$t$$is defined as the difference between realized excess return in month$$t$$and the predicted component of the excess returns from the five-factor model in month$$t$$(i.e., the “systematic” component of the return), where factor loadings are estimated using daily returns between month$$t-12$$and month$$t-1$$. The cross-sectional dispersion in U.S. equity beta is computed as$$(\beta_{ijt} - \overline{\beta}_{jt})^2$$, where we focus on betas estimated using daily returns for calendar year$$t$$. Idiosyncratic volatility is the nonannualized standard deviation of monthly five-factor alphas earned by fund$$i$$in calendar year$$t$$.$$R^2$$from five-factor model is the$$R^2$$estimated using daily returns for calendar year$$t$$. We report the average value of each measure separately for BFs and TDFs for three time periods. Pre-PPA includes 2000–2006 for cross-sectional dispersion in monthly net returns, 2002–2006 for idiosyncratic volatility, and 2001–2006 for the other three measures. Post-PPA includes 2007–2012. Post-PPA (excl. crisis) includes 2007 and 2010–2012. We also report the coefficients from regressions that test for changes in each measure for TDFs or BFs (“difference”) and for TDFs relative to each sample of BFs (“diff.-in-diff.”). Standard errors are simultaneously clustered by family and time (month or year). *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. Table 2 Benchmarking TDFs against BFs Dependent variable: Cross-sectional dispersion in Monthly net return Cross-sectional dispersion in Monthly 5-factor alpha Cross-sectional dispersion in U.S. equity beta Idiosyncratic volatility$$R^2$$from 5-factor model Fund type: BFs TDFs BFs TDFs BFs TDFs BFs TDFs BFs TDFs Frequency: Monthly Monthly Monthly Monthly Annual Annual Annual Annual Annual Annual Pre-PPA 1.272*** 0.212*** 0.365*** 0.066*** 0.027*** 0.005*** 1.636*** 0.991*** 0.935*** 0.966*** Post-PPA 1.240*** 0.748*** 0.490*** 0.232*** 0.016*** 0.011*** 2.110*** 1.944*** 0.951*** 0.971*** Post-PPA (excl. crisis) 0.558*** 0.464*** 0.269*** 0.145*** 0.012*** 0.012*** 1.635*** 1.615*** 0.954*** 0.968*** Difference –0.032 0.536** 0.106 0.166*** –0.011*** 0.005** 0.474 0.953*** 0.016** 0.005 Difference (excl. crisis) –0.714** 0.252* –0.105* 0.079** –0.015*** 0.006** –0.001 0.624*** 0.019** 0.003 Diff.-in-diff. 0.567* 0.061 0.016*** 0.479* –0.011 Diff.-in-diff. (excl. crisis) 0.966*** 0.185*** 0.021*** 0.625*** –0.016* Dependent variable: Cross-sectional dispersion in Monthly net return Cross-sectional dispersion in Monthly 5-factor alpha Cross-sectional dispersion in U.S. equity beta Idiosyncratic volatility$$R^2$$from 5-factor model Fund type: BFs TDFs BFs TDFs BFs TDFs BFs TDFs BFs TDFs Frequency: Monthly Monthly Monthly Monthly Annual Annual Annual Annual Annual Annual Pre-PPA 1.272*** 0.212*** 0.365*** 0.066*** 0.027*** 0.005*** 1.636*** 0.991*** 0.935*** 0.966*** Post-PPA 1.240*** 0.748*** 0.490*** 0.232*** 0.016*** 0.011*** 2.110*** 1.944*** 0.951*** 0.971*** Post-PPA (excl. crisis) 0.558*** 0.464*** 0.269*** 0.145*** 0.012*** 0.012*** 1.635*** 1.615*** 0.954*** 0.968*** Difference –0.032 0.536** 0.106 0.166*** –0.011*** 0.005** 0.474 0.953*** 0.016** 0.005 Difference (excl. crisis) –0.714** 0.252* –0.105* 0.079** –0.015*** 0.006** –0.001 0.624*** 0.019** 0.003 Diff.-in-diff. 0.567* 0.061 0.016*** 0.479* –0.011 Diff.-in-diff. (excl. crisis) 0.966*** 0.185*** 0.021*** 0.625*** –0.016* The dependent variable in each ordinary least squares (OLS) regression is a measure of cross-sectional dispersion. The unit of observation is fund$$i$$offered by family$$k$$in month or year$$t$$. The comparison group is the sample of BFs offered by families that offer TDFs. We compute cross-sectional dispersion in monthly net returns in month$$t$$as$$(r_{ijt} - \overline{r}_{jt})^2$$, where$$j$$is either the TDF’s target date or the BF’s Lipper classification (Flexible Portfolio Funds (FX), Mixed-Asset Target Allocation Conservative Funds (MTAC), Mixed-Asset Target Allocation Moderate Funds (MTAG), or Mixed-Asset Target Allocation Growth Funds (MTAM)). The cross-sectional dispersion in monthly five-factor alphas in month$$t$$is computed similarly. Each month, we estimate the five-factor model for fund$$i$$using daily excess returns between month$$t-11$$and month$$t$$. The five factors are the daily excess returns of the CRSP U.S. value-weighted market index, MSCI World Index excluding the United States, Barclays U.S. Aggregate Bond Index, Barclays Global Aggregate excluding the United States, and GSCI Commodity Index. The five-factor alpha of fund$$i$$in month$$t$$is defined as the difference between realized excess return in month$$t$$and the predicted component of the excess returns from the five-factor model in month$$t$$(i.e., the “systematic” component of the return), where factor loadings are estimated using daily returns between month$$t-12$$and month$$t-1$$. The cross-sectional dispersion in U.S. equity beta is computed as$$(\beta_{ijt} - \overline{\beta}_{jt})^2$$, where we focus on betas estimated using daily returns for calendar year$$t$$. Idiosyncratic volatility is the nonannualized standard deviation of monthly five-factor alphas earned by fund$$i$$in calendar year$$t$$.$$R^2$$from five-factor model is the$$R^2$$estimated using daily returns for calendar year$$t$$. We report the average value of each measure separately for BFs and TDFs for three time periods. Pre-PPA includes 2000–2006 for cross-sectional dispersion in monthly net returns, 2002–2006 for idiosyncratic volatility, and 2001–2006 for the other three measures. Post-PPA includes 2007–2012. Post-PPA (excl. crisis) includes 2007 and 2010–2012. We also report the coefficients from regressions that test for changes in each measure for TDFs or BFs (“difference”) and for TDFs relative to each sample of BFs (“diff.-in-diff.”). Standard errors are simultaneously clustered by family and time (month or year). *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. There are two features of these initial comparisons worth noting. First, we are not yet comparing the return characteristics of TDFs from high market share families and low market share families, or from pre-PPA families and post-PPA families. Second, economic and statistically significance both increase when we estimate difference-in-differences between TDFs and BFs offered by families that offer TDFs during our sample period.17 The reason is that, while cross-sectional diversity in monthly net returns of BFs is essentially constant before and after the PPA, cross-sectional diversity of BFs during the post-PPA period drops sharply when we exclude the monthly observations from 2008 and 2009. Next, we study the drivers of the diversity in monthly alphas. To control for the effect of systematic factors on TDF (and BF) returns, we estimate monthly alphas using a five-factor model. Each month, we estimate the five-factor model for fund$$i$$using daily excess returns between month$$t-11$$and month$$t$$. The five factors are the daily excess returns of the CRSP U.S. value-weighted market index, MSCI World Index excluding the United States, Barclays U.S. Aggregate Bond Index, Barclays Global Aggregate excluding the United States, and GSCI Commodity Index. The five-factor alpha of fund$$i$$in month$$t$$is defined as the difference between the realized excess return in month$$t$$and the variable component of the predicted excess returns from the five-factor model in month$$t$$(i.e., the “systematic” component of the excess return), where factor loadings are estimated using daily returns between month$$t-12$$and month$$t-1$$. We again measure diversity as the squared deviation relative to the average TDF within the same target date range (or the average BF with the same Lipper category). We find that diversity in TDF alphas is significantly higher in the post-PPA period, even when we exclude 2008 and 2009. However, that the pre-PPA and post-PPA magnitudes are approximately one-third of those estimated for net returns implies that a significant fraction of the diversity in net excess returns is being driven by diversity in factor loadings and the absolute magnitude of factor excess returns, which plausibly reflects product differentiation by entrants. In the third set of columns, we test for changes in the cross-sectional diversity of U.S. equity betas. We find that the average diversity in the U.S. equity betas of TDFs doubles between the pre-PPA and post-PPA periods, regardless of whether we exclude observations from 2008 and 2009. Again, economic and statistical significance both increase when we estimate difference-in-differences between TDFs and BFs. To shed additional light on changes in ex ante TDF risk profiles, we test for changes in the time-series volatility of alphas and in the level of$$R^2$$s in factor models. We measure the idiosyncratic volatility of TDF$$i$$in calendar year$$t$$as the annualized—scaled by$$\sqrt{12}$$—within-TDF standard deviation of monthly five-factor alphas during that calendar year. When we compare the pre-PPA period to the full post-PPA period, we find that idiosyncratic volatility has essentially doubled, from 0.991 to 1.944, an increase that is statistically significant at the 1% level. While we estimate smaller increases in idiosyncratic volatility when we exclude 2008 and 2009 from the post-PPA period (or when we benchmark TDFs relative to BFs), the increases remain economically and statistically significant. The serial correlation in idiosyncratic volatilities is 0.480, which is both economically and statistically significant.18 The persistence in realized idiosyncratic volatilities increases our confidence that we are capturing ex ante differences in risk-taking across TDFs. The final set of columns focus on the$$R^2$$s of the five-factor model. We estimate the serial correlation in the annual$$R^2$$s of TDFs to be near$$0.9$$, confirming our prior that TDF-level investment policies are highly persistent.19 We cannot reject the hypothesis that average$$R^2$$s were stable between the pre-PPA and post-PPA periods, except when we focus on difference-in-differences between TDFs and BFs that exclude 2008 and 2009, and then only at the 10% level. The interesting caveat is that when we focus on the distribution of$$R^2$$s within each target date range, we find a small number of TDFs with especially low$$R^2$$s. For example, for the 2005–2010 TDFs, the lowest$$R^2$$is$$95.3\%$$in 2001, but only$$64.8\%$$in 2012. More generally, the drop in the minimum$$R^2$$is especially pronounced during the last three years of our sample, after the financial crisis.20 Overall, Table 2 reveals that cross-sectional dispersion in realized returns, idiosyncratic volatility, and factor loadings all increased in the post-PPA period, that the increased dispersion was not driven by the financial crisis and, by comparing TDFs to BFs, that it was unique to TDFs.21 In the remainder of the paper, we examine whether the increased dispersion in the realized returns and estimated ex ante risk profiles of TDFs, following the PPA of 2006, is driven by the risk-taking incentives of mutual fund families or the risk-matching incentives of plan sponsors. 4. Does TDF Heterogeneity Reflect Strategic Risk-taking? 4.1 The role of risk-taking incentives We base our strategic risk-taking predictions on four observations related to the incentives of mutual fund families. First, by increasing demand for TDFs as default investment options, the PPA significantly increased the future share of retirement plan assets that will be invested in TDFs. As a result, the PPA increased the incentive for mutual fund families to place their TDFs on DC investment menus. Because we cannot observe the counterfactual market structure, we cannot quantify the strength of this incentive. TDFs were, after all, gaining market share before the PPA. Nevertheless, the passage of the PPA likely helps to explain why, in Table 1, we observe 17 families entering the TDF market in 2007 and 2008, increasing the total from 27 to 44. The large number of entrants is likely to have intensified competition for market share. Second, because flows into TDFs are likely to be driven by plan sponsor decisions about the TDFs to include in their investment menus, and because plan sponsors are likely to be more sophisticated than the typical individual investor (e.g., Pool, Sialm, and Stefanescu 2016; Sialm, Starks, and Zhang 2015), we expect (and provide supporting evidence) that flows into TDFs load on TDF alphas. Third, a well-established literature shows that mutual funds facing more convex payoffs are more likely to engage in risk-taking (e.g., Brown, Harlow, and Starks 1996; Evans 2010). In our setting, convexity arises from the fact that entrants and incumbents with low market share have fewer assets—and therefore fewer management fees—to lose if they underperform their peers. Fourth, we expect families entering the TDF market after the PPA to be less constrained with respect to their choice of glide path and set of underlying funds than incumbents, who made these choices before the PPA and disclosed them to existing investors. The first three observations lead us to predict that increased dispersion in TDF return characteristics would reflect increased risk-taking by families with low market share in the TDF market. To be able to distinguish increased risk-taking from increased product differentiation—whereby entrants offer different glide paths than incumbents, perhaps for reasons related to risk matching—it is important for us to focus on dispersion in alphas and differences in the level of idiosyncratic risk. The last observation leads us to predict that the link between low market share and risk-taking will be strongest among families that enter the market after 2006. This second prediction is consistent with two different types of behavior. Following the PPA, entrants may be more likely to assign funds pursuing more idiosyncratic strategies to their TDFs. Alternatively, families pursuing more idiosyncratic strategies may have been more likely to enter the TDF market after the PPA. While this is not a crucial distinction from the investor’s perspective, we are able to shed light on the origin of any change in risk-taking by comparing specifications that do and do not control for the investment behavior of a family’s BFs. A separate issue is that families face a choice about when to enter the market and pursue an idiosyncratic investment strategy. To the extent that pursuing the volatility option this year prevents families from pursuing it next year, the incentives of entrants and other families with low market share to pursue idiosyncratic strategies may be weaker than we claim. Our conjecture is that mutual fund families not yet in the TDF market viewed the passage of the PPA as a unique opportunity to gain market share and quickly designed new products to pursue this opportunity. One piece of suggestive evidence is that we observe 17 entrants between 2007 and 2008, and only 3 entrants between 2009 and 2012. Another piece of suggestive evidence is that many of the families that exit the TDF market towards the end of our sample period entered the market after 2006. However, the extent to which entrants are responsible for the increased level of risk-taking is one of the empirical questions that we seek to answer in this section. 4.2 Flows and performance The existing literature finds that DB and DC plan sponsors are more sophisticated than the typical individual mutual fund investor (e.g., Del Guercio and Tkac 2002; Sialm, Starks, and Zhang 2015). These findings lead us to predict that TDF flows respond primarily to alphas. In Table 3, we estimate the following flow-performance model: \begin{eqnarray} \mbox{flow}_{ijt} = a_j + b_t + c^\top X_{jt} + d^\top Z_{ijt} + \epsilon_{ijt}, \end{eqnarray} (1) where$$\mbox{flow}_{ijt}$$is the one-year net flow, measured as a percentage of assets under management at the beginning of the period. The specification is motivated by the flow-performance regression in Del Guercio and Reuter (2014), who run a horse race between raw and risk-adjusted returns. However, following Barber, Huang, and Odean (2016), we decompose net returns into alphas and systematic returns, which are the product of betas and factor realizations. We also extend the specification to capture features of the TDF market. The$$X_{jt}$$vector includes the natural logarithm of the total number of funds with target date$$j$$in year$$t$$, which is a measure of the degree of competition for flows. The$$Z_{ijt}$$vector includes: the one-year systematic fund return in year$$t-1$$; the one-year alpha in year$$t-1$$; the volatility of monthly systematic fund returns in year$$t-1$$; the volatility of monthly alphas in year$$t-1$$; the net flow into fund$$i$$in year$$t-1$$; a dummy equal to one if the fund was introduced after December 2006; a dummy equal to one if the fund was introduced by a family that entered the TDF market after December 2006; the fund-level expense ratio measured in year$$t$$; the natural logarithm of fund assets under management in year$$t-1$$; and the natural logarithm of family assets under management in year$$t-1$$. To capture potential convexities in the flow-performance relation (Sirri and Tufano 1998), one specification includes dummy variables that indicate whether fund$$i$$’s one-year alpha was in the first, second, third, or fourth quartile of alphas earned by TDFs with the same target date in year$$t-1$$. Specifications with TDF flows as the dependent variable include calendar-year fixed effects and target date fixed effects. For comparison, we also estimate comparable flow-performance specifications for BFs. These specifications include calendar-year fixed effects and Lipper classification fixed effects. In all regressions, standard errors are simultaneously clustered by mutual fund family and year. Table 3 Flows and performance Dependent variable: Net flow, year$$t$$Sample: TDFs BFs Systematic return, year$$t-1$$0.331 –0.006 0.122 0.366*** (0.397) (0.227) (0.247) (0.104) 5-factor alpha, year$$t-1$$2.784** 2.425*** 2.497*** 1.483*** (1.286) (0.905) (0.669) (0.342) 5-factor alpha in fourth quartile? 0.076** (0.037) 5-factor alpha in third quartile? 0.014 (0.034) 5-factor alpha in second quartile? — 5-factor alpha in first quartile? –0.095*** (0.032) Volatility of monthly systematic –3.372** –3.635*** –3.568*** –0.687**$$\quad$$returns, year$$t-1$$(1.318) (0.744) (0.790) (0.287) Volatility of monthly 1.277 2.245 2.256 1.091*$$\quad$$5-factor alphas, year$$t-1$$(2.389) (2.717) (3.287) (0.603) Net flow, year$$t-1$$0.305*** 0.300*** 0.438*** (0.020) (0.020) (0.036) ln(number of funds with –0.074 0.070 0.051$$\quad$$target date$$j$$in year$$t$$) (0.065) (0.074) (0.066) Fund introduced after 2006? 0.352*** 0.093 0.081 0.109 (0.064) (0.056) (0.061) (0.180) Fund managed by family entering –0.197** –0.058 –0.048 –0.008$$\quad$$TDF market after 2006? (0.086) (0.056) (0.063) (0.022) Expense ratio, year$$t$$–0.046 –0.011 –0.005 –0.009 (0.040) (0.028) (0.028) (0.012) ln(fund size), year$$t-1$$0.003 0.006 0.002 –0.010* (0.019) (0.010) (0.010) (0.006) ln(family size), year$$t-1$$0.022 0.008 0.010 0.002 (0.022) (0.012) (0.013) (0.009)$$H_0$$: Predicted return = 5-factor alpha 0.009*** 0.000*** 0.000*** 0.029**$$H_0$$: Volatility predicted = Volatility alpha 0.144 0.049** 0.112 0.002*** Calendar year fixed effects? Yes Yes Yes Yes Yes Target date fixed effects? Yes Yes Yes Yes — BF classification fixed effects? — — — — Yes$$N$$1,285 1,105 1,076 1,076 1,158$$R^2$$15.00% 26.50% 52.22% 52.28% 39.22% Dependent variable: Net flow, year$$t$$Sample: TDFs BFs Systematic return, year$$t-1$$0.331 –0.006 0.122 0.366*** (0.397) (0.227) (0.247) (0.104) 5-factor alpha, year$$t-1$$2.784** 2.425*** 2.497*** 1.483*** (1.286) (0.905) (0.669) (0.342) 5-factor alpha in fourth quartile? 0.076** (0.037) 5-factor alpha in third quartile? 0.014 (0.034) 5-factor alpha in second quartile? — 5-factor alpha in first quartile? –0.095*** (0.032) Volatility of monthly systematic –3.372** –3.635*** –3.568*** –0.687**$$\quad$$returns, year$$t-1$$(1.318) (0.744) (0.790) (0.287) Volatility of monthly 1.277 2.245 2.256 1.091*$$\quad$$5-factor alphas, year$$t-1$$(2.389) (2.717) (3.287) (0.603) Net flow, year$$t-1$$0.305*** 0.300*** 0.438*** (0.020) (0.020) (0.036) ln(number of funds with –0.074 0.070 0.051$$\quad$$target date$$j$$in year$$t$$) (0.065) (0.074) (0.066) Fund introduced after 2006? 0.352*** 0.093 0.081 0.109 (0.064) (0.056) (0.061) (0.180) Fund managed by family entering –0.197** –0.058 –0.048 –0.008$$\quad$$TDF market after 2006? (0.086) (0.056) (0.063) (0.022) Expense ratio, year$$t$$–0.046 –0.011 –0.005 –0.009 (0.040) (0.028) (0.028) (0.012) ln(fund size), year$$t-1$$0.003 0.006 0.002 –0.010* (0.019) (0.010) (0.010) (0.006) ln(family size), year$$t-1$$0.022 0.008 0.010 0.002 (0.022) (0.012) (0.013) (0.009)$$H_0$$: Predicted return = 5-factor alpha 0.009*** 0.000*** 0.000*** 0.029**$$H_0$$: Volatility predicted = Volatility alpha 0.144 0.049** 0.112 0.002*** Calendar year fixed effects? Yes Yes Yes Yes Yes Target date fixed effects? Yes Yes Yes Yes — BF classification fixed effects? — — — — Yes$$N$$1,285 1,105 1,076 1,076 1,158$$R^2$$15.00% 26.50% 52.22% 52.28% 39.22% The unit of observation is the TDF offered by family$$i$$with target date$$j$$. The dependent variable is estimated percentage net flow, measured over the 12 months ending in December of year$$t$$. The sample period covers 2003–2012. We use the approach described in Table 2 to decompose the realized excess return of fund$$i$$in month$$t$$into a systematic component and alpha. We calculate annual systematic returns (alphas) by compounding monthly systematic returns (alphas) over the calendar year. We calculate the (annualized) standard deviation of monthly systematic returns (alphas) as the standard deviation of the monthly systematic returns (alphas) times$$\sqrt{12}$$. The full set of independent variables includes: the lagged predicted return, measured over the 12 months ending in December of year$$t-1$$; the lagged five-factor alpha, measured over the same 12-month period; dummy variables that equal one if the lagged five-factor alpha are in the first, second, third, or fourth quartiles of the distribution for target date$$j$$in year$$t-1$$; the annualized standard deviation of monthly systematic returns in year$$t-1$$; the annualized standard deviation of monthly five-factor alphas in year$$t-1$$; the lagged net flow in year$$t-1$$; the natural logarithm of the number of funds with target date$$j$$in December of year$$t$$; a dummy equal to one if the fund was introduced after December 2006; a dummy equal to one if the fund was offered by a family that entered the TDF market after December 2006; the fund-level expense ratio measured in year$$t$$(reported by CRSP); the natural logarithm of the fund assets in December of year$$t-1$$; and the natural logarithm of the family assets in December of year$$t-1$$. The sample in the first four columns includes all TDFs with target dates between 2005 and 2050 for which we observe the dependent and independent variables. The sample in the fifth column includes all BFs offered by families that offer at least one TDF in year$$t$$. Estimation performed via OLS. We include calendar year fixed effects and either target date fixed effects or BF classification fixed effects. Standard errors are simultaneously clustered by family and year. *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. Table 3 Flows and performance Dependent variable: Net flow, year$$t$$Sample: TDFs BFs Systematic return, year$$t-1$$0.331 –0.006 0.122 0.366*** (0.397) (0.227) (0.247) (0.104) 5-factor alpha, year$$t-1$$2.784** 2.425*** 2.497*** 1.483*** (1.286) (0.905) (0.669) (0.342) 5-factor alpha in fourth quartile? 0.076** (0.037) 5-factor alpha in third quartile? 0.014 (0.034) 5-factor alpha in second quartile? — 5-factor alpha in first quartile? –0.095*** (0.032) Volatility of monthly systematic –3.372** –3.635*** –3.568*** –0.687**$$\quad$$returns, year$$t-1$$(1.318) (0.744) (0.790) (0.287) Volatility of monthly 1.277 2.245 2.256 1.091*$$\quad$$5-factor alphas, year$$t-1$$(2.389) (2.717) (3.287) (0.603) Net flow, year$$t-1$$0.305*** 0.300*** 0.438*** (0.020) (0.020) (0.036) ln(number of funds with –0.074 0.070 0.051$$\quad$$target date$$j$$in year$$t$$) (0.065) (0.074) (0.066) Fund introduced after 2006? 0.352*** 0.093 0.081 0.109 (0.064) (0.056) (0.061) (0.180) Fund managed by family entering –0.197** –0.058 –0.048 –0.008$$\quad$$TDF market after 2006? (0.086) (0.056) (0.063) (0.022) Expense ratio, year$$t$$–0.046 –0.011 –0.005 –0.009 (0.040) (0.028) (0.028) (0.012) ln(fund size), year$$t-1$$0.003 0.006 0.002 –0.010* (0.019) (0.010) (0.010) (0.006) ln(family size), year$$t-1$$0.022 0.008 0.010 0.002 (0.022) (0.012) (0.013) (0.009)$$H_0$$: Predicted return = 5-factor alpha 0.009*** 0.000*** 0.000*** 0.029**$$H_0$$: Volatility predicted = Volatility alpha 0.144 0.049** 0.112 0.002*** Calendar year fixed effects? Yes Yes Yes Yes Yes Target date fixed effects? Yes Yes Yes Yes — BF classification fixed effects? — — — — Yes$$N$$1,285 1,105 1,076 1,076 1,158$$R^2$$15.00% 26.50% 52.22% 52.28% 39.22% Dependent variable: Net flow, year$$t$$Sample: TDFs BFs Systematic return, year$$t-1$$0.331 –0.006 0.122 0.366*** (0.397) (0.227) (0.247) (0.104) 5-factor alpha, year$$t-1$$2.784** 2.425*** 2.497*** 1.483*** (1.286) (0.905) (0.669) (0.342) 5-factor alpha in fourth quartile? 0.076** (0.037) 5-factor alpha in third quartile? 0.014 (0.034) 5-factor alpha in second quartile? — 5-factor alpha in first quartile? –0.095*** (0.032) Volatility of monthly systematic –3.372** –3.635*** –3.568*** –0.687**$$\quad$$returns, year$$t-1$$(1.318) (0.744) (0.790) (0.287) Volatility of monthly 1.277 2.245 2.256 1.091*$$\quad$$5-factor alphas, year$$t-1$$(2.389) (2.717) (3.287) (0.603) Net flow, year$$t-1$$0.305*** 0.300*** 0.438*** (0.020) (0.020) (0.036) ln(number of funds with –0.074 0.070 0.051$$\quad$$target date$$j$$in year$$t$$) (0.065) (0.074) (0.066) Fund introduced after 2006? 0.352*** 0.093 0.081 0.109 (0.064) (0.056) (0.061) (0.180) Fund managed by family entering –0.197** –0.058 –0.048 –0.008$$\quad$$TDF market after 2006? (0.086) (0.056) (0.063) (0.022) Expense ratio, year$$t$$–0.046 –0.011 –0.005 –0.009 (0.040) (0.028) (0.028) (0.012) ln(fund size), year$$t-1$$0.003 0.006 0.002 –0.010* (0.019) (0.010) (0.010) (0.006) ln(family size), year$$t-1$$0.022 0.008 0.010 0.002 (0.022) (0.012) (0.013) (0.009)$$H_0$$: Predicted return = 5-factor alpha 0.009*** 0.000*** 0.000*** 0.029**$$H_0$$: Volatility predicted = Volatility alpha 0.144 0.049** 0.112 0.002*** Calendar year fixed effects? Yes Yes Yes Yes Yes Target date fixed effects? Yes Yes Yes Yes — BF classification fixed effects? — — — — Yes$$N$$1,285 1,105 1,076 1,076 1,158$$R^2$$15.00% 26.50% 52.22% 52.28% 39.22% The unit of observation is the TDF offered by family$$i$$with target date$$j$$. The dependent variable is estimated percentage net flow, measured over the 12 months ending in December of year$$t$$. The sample period covers 2003–2012. We use the approach described in Table 2 to decompose the realized excess return of fund$$i$$in month$$t$$into a systematic component and alpha. We calculate annual systematic returns (alphas) by compounding monthly systematic returns (alphas) over the calendar year. We calculate the (annualized) standard deviation of monthly systematic returns (alphas) as the standard deviation of the monthly systematic returns (alphas) times$$\sqrt{12}$$. The full set of independent variables includes: the lagged predicted return, measured over the 12 months ending in December of year$$t-1$$; the lagged five-factor alpha, measured over the same 12-month period; dummy variables that equal one if the lagged five-factor alpha are in the first, second, third, or fourth quartiles of the distribution for target date$$j$$in year$$t-1$$; the annualized standard deviation of monthly systematic returns in year$$t-1$$; the annualized standard deviation of monthly five-factor alphas in year$$t-1$$; the lagged net flow in year$$t-1$$; the natural logarithm of the number of funds with target date$$j$$in December of year$$t$$; a dummy equal to one if the fund was introduced after December 2006; a dummy equal to one if the fund was offered by a family that entered the TDF market after December 2006; the fund-level expense ratio measured in year$$t$$(reported by CRSP); the natural logarithm of the fund assets in December of year$$t-1$$; and the natural logarithm of the family assets in December of year$$t-1$$. The sample in the first four columns includes all TDFs with target dates between 2005 and 2050 for which we observe the dependent and independent variables. The sample in the fifth column includes all BFs offered by families that offer at least one TDF in year$$t$$. Estimation performed via OLS. We include calendar year fixed effects and either target date fixed effects or BF classification fixed effects. Standard errors are simultaneously clustered by family and year. *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. We find that flows into TDFs respond primarily to alphas, whereas flows into BFs respond to both systematic returns and alphas. For BFs, a 1-standard-deviation increase in systematic return increases flows by 4.0% vs. 5.8% for a 1-standard-deviation increase in alpha. Both effects are statistically significant at the 1% level. In the comparable specification for TDFs (in the third column), the corresponding estimates are a statistically insignificant 2.0% for systematic returns ($$p$$-value of .622) and a statistically significant 7.7% for alpha ($$p$$-value of .000). A possible explanation for this difference in results is that the beta of a BF might be perceived as being more discretionary, so investors are rewarding the BF both for choosing betas and for picking securities. In the TDF context, if investors perceive the beta as being nondiscretionary, there is no basis for rewarding managers based on beta timing.22 In the fourth column, the difference in flows between the top quartile and bottom quartile of TDFs is an economically and statistically significant 17.1%. When we simultaneously include the volatilities of systematic returns and alphas, the coefficient on the volatility of systematic returns is large and negative and statistically significant at the 5% level and below. A 1-standard-deviation increase in the volatility of systematic returns is associated with a 21.7% decrease in flows. The coefficients on the volatility of alpha, on the other hand, are positive but statistically indistinguishable from zero. (In Column 3, which includes the largest set of control variables, we can reject the hypothesis that the coefficients on systematic volatility and idiosyncratic volatility are equal.) In other words, flows into TDFs are lower when those TDFs have larger factor loadings and more volatile factor returns, but not when they have more volatile alphas. These patterns are consistent with plan sponsors believing that managers with lower$$R^2$$s are more skilled (Amihud and Goyenko 2013). In summary, the patterns in Table 3 are consistent with the hypothesis that TDFs are primarily rewarded for generating higher alphas. 4.3 Explaining cross-sectional dispersion in TDF returns and alphas and levels of idiosyncratic risk, alphas, and information ratios This section contains our first tests for strategic risk-taking. We begin with the regression model: \begin{eqnarray} (r_{ijt} - \overline{r}_{jt})^2 = a_{jt} + b^\top X_{ijt} + e_{ijt}, \end{eqnarray} (2) where$$r_{ijt}$$is the monthly return of TDF$$i$$and$$\overline{r}_{jt}$$is the cross-sectional average return of TDFs with target date$$j$$in month$$t$$;$$a_{jt}$$is a target date-specific fixed effect for month$$t$$; and$$X_{ijt}$$is a vector of covariates intended to capture family-level incentives and investment strategies.23 This vector includes: a dummy variable equal to one if the market share of family$$j$$’s TDFs was$$\le 1\%$$(Low Market Share) interacted with dummy variables equal to one if family$$k$$entered the TDF market before or after December 31, 2006 (Pre-PPA family vs. Post-PPA family); a dummy variable equal to one if the market share of family$$j$$’s TDFs was$$>1\%$$and$$\le 5\%$$(Medium Market Share) in month$$t-1$$; and a dummy variable equal to one if TDF$$i$$invests in index funds. In the second specification, we also include the average cross-sectional return dispersion for BFs in TDF$$i$$’s family in month$$t$$, where the cross-sectional return dispersion for each BF is measured within the full cross-section of BFs with the same Lipper classification, squared, and then averaged across all of the family’s BFs. These regression specifications allow us to test the prediction that TDFs from families with low market share contribute more to cross-sectional dispersion than TDFs from families with medium market share or high market share (the omitted category), and the prediction that increased cross-sectional dispersion following the PPA is being driven by the investment strategies of the post-PPA families with low market share.24 We expect TDFs investing in index funds to exhibit less cross-sectional return dispersion than TDFs based on actively managed funds. To the extent that some families pursue more volatile investment strategies across their full range of funds, we also expect the average cross-sectional return dispersion of a family’s BFs (relative to the universe of BFs with the same Lipper classification) to be positively correlated with the cross-sectional return dispersion of its TDFs. To control for time-series variation in the properties of market returns and in the number of TDFs offered with a particular target date, we include a separate fixed effect for each target date-month pair. As a result, the coefficients in equation (2) are being identified entirely by cross-sectional variation in the return dispersion of different TDFs with the same target date in the same month. Standard errors are two-way clustered by family and month. We find support for both risk-taking predictions in Table 4. In the first two columns, we find that TDFs from low market share families exhibit greater cross-sectional dispersion in monthly net returns than TDFs from other families. Both estimated coefficients are positive and statistically different from zero at the 10% level (and below), and we can reject the hypothesis that they are both equal to zero at the 5% level. Consistent with our second prediction, we also find that the estimated coefficient for post-PPA families with low market share is consistently larger than that for pre-PPA families with low market share.25 We can reject the hypothesis that these coefficients are equal at the 10% level. In terms of economic significance, TDFs from post-PPA families with low market share exhibit annualized cross-sectional dispersion in net returns that are 6.90% higher than TDFs from high market share families and 4.36% higher than TDFs from pre-PPA families with low market share.26 Controlling for the cross-sectional dispersion of a family’s BFs significantly increases the$$R^2$$(from 11.23% to 17.35%), but does not otherwise change our inference that TDFs from families with low market share exhibit greater cross-sectional dispersion in monthly net returns. This implies that these TDFs have more diverse betas (perhaps driven by product differentiation), higher levels of idiosyncratic risk, or both. Table 4 Cross-sectional dispersion in TDF returns and alphas and the level of idiosyncratic risk Dependent Variable: Cross-sectional dispersion in monthly net return Cross-sectional dispersion in monthly 5-factor alpha Idiosyncratic volatility Average monthly 5-factor alpha Alpha scaled by idiosyncratic volatility Frequency: Monthly Monthly Monthly Monthly Annual Annual Annual Annual Annual Annual Low market share$$\times$$0.849** 0.784** 0.347*** 0.275** 0.765*** 0.695*** –0.067** –0.036* –0.043* –0.030*$$\qquad$$Post-PPA family (0.368) (0.346) (0.131) (0.119) (0.249) (0.229) (0.032) (0.021) (0.022) (0.016) Low market share$$\times$$0.154* 0.120* 0.096** 0.077** 0.323*** 0.298** –0.014 –0.002 –0.022* –0.006$$\qquad$$Pre-PPA family (0.079) (0.070) (0.041) (0.036) (0.116) (0.138) (0.020) (0.016) (0.012) (0.011) Medium market share 0.091 0.086 0.044** 0.027 0.088 0.044 –0.020 –0.009 –0.035* –0.029* (0.085) (0.075) (0.018) (0.027) (0.103) (0.136) (0.028) (0.018) (0.020) (0.015) Index-fund-based TDF –0.078 –0.089 –0.001 0.001 –0.449*** –0.321*** –0.001 0.017 –0.024 –0.014 (0.068) (0.060) (0.023) (0.022) (0.145) (0.112) (0.036) (0.030) (0.022) (0.018) Average demeaned characteristic 0.157** 0.255*** 0.360*** 0.544*** 0.518***$$\qquad$$of family’s BFs (0.071) (0.046) (0.066) (0.040) (0.063)$$H_0$$: Low$$\times$$Post-PPA$$\qquad$$= Low$$\times$$Pre-PPA 0.016** 0.021** 0.004*** 0.013** 0.001*** 0.005*** 0.035** 0.067* 0.084* 0.114$$H_0$$: Low$$\times$$Post-PPA$$\qquad$$= Low$$\times$$Pre-PPA 0.059* 0.058* 0.056* 0.099* 0.085* 0.084* 0.226 0.021** 0.324 0.051* Target date-by-time fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$21,788 21,788 21,788 21,788 1,609 1,609 1,609 1,609 1,609 1,609$$R^2$$11.23% 17.35% 10.29% 21.82% 13.92% 26.76% 50.15% 63.21% 54.66% 63.17% Dependent Variable: Cross-sectional dispersion in monthly net return Cross-sectional dispersion in monthly 5-factor alpha Idiosyncratic volatility Average monthly 5-factor alpha Alpha scaled by idiosyncratic volatility Frequency: Monthly Monthly Monthly Monthly Annual Annual Annual Annual Annual Annual Low market share$$\times$$0.849** 0.784** 0.347*** 0.275** 0.765*** 0.695*** –0.067** –0.036* –0.043* –0.030*$$\qquad$$Post-PPA family (0.368) (0.346) (0.131) (0.119) (0.249) (0.229) (0.032) (0.021) (0.022) (0.016) Low market share$$\times$$0.154* 0.120* 0.096** 0.077** 0.323*** 0.298** –0.014 –0.002 –0.022* –0.006$$\qquad$$Pre-PPA family (0.079) (0.070) (0.041) (0.036) (0.116) (0.138) (0.020) (0.016) (0.012) (0.011) Medium market share 0.091 0.086 0.044** 0.027 0.088 0.044 –0.020 –0.009 –0.035* –0.029* (0.085) (0.075) (0.018) (0.027) (0.103) (0.136) (0.028) (0.018) (0.020) (0.015) Index-fund-based TDF –0.078 –0.089 –0.001 0.001 –0.449*** –0.321*** –0.001 0.017 –0.024 –0.014 (0.068) (0.060) (0.023) (0.022) (0.145) (0.112) (0.036) (0.030) (0.022) (0.018) Average demeaned characteristic 0.157** 0.255*** 0.360*** 0.544*** 0.518***$$\qquad$$of family’s BFs (0.071) (0.046) (0.066) (0.040) (0.063)$$H_0$$: Low$$\times$$Post-PPA$$\qquad$$= Low$$\times$$Pre-PPA 0.016** 0.021** 0.004*** 0.013** 0.001*** 0.005*** 0.035** 0.067* 0.084* 0.114$$H_0$$: Low$$\times$$Post-PPA$$\qquad$$= Low$$\times$$Pre-PPA 0.059* 0.058* 0.056* 0.099* 0.085* 0.084* 0.226 0.021** 0.324 0.051* Target date-by-time fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$21,788 21,788 21,788 21,788 1,609 1,609 1,609 1,609 1,609 1,609$$R^2$$11.23% 17.35% 10.29% 21.82% 13.92% 26.76% 50.15% 63.21% 54.66% 63.17% The unit of observation is TDF$$i$$offered by family$$k$$in month$$t$$. The dependent variables in the first three sets of regressions are measures of return diversity. When focusing on fund-level net returns, the dependent variable is$$(r_{ijt} - \overline{r}_{jt})^2$$. We compute a similar measure for monthly five-factor alphas, where the alpha of fund$$i$$in month$$t$$is calculated as the difference between the realized excess monthly return in month$$t$$and the systematic excess monthly returns, based on the five-factor model estimated using daily excess returns between month$$t-12$$and month$$t-1$$. The third dependent variable is idiosyncratic volatility, the nonannualized standard deviation of monthly alphas earned by fund$$i$$in calendar year$$t$$. The dependent variable in the fourth set of regressions is the average monthly five-factor alpha earned by fund$$i$$in calendar year$$t$$. The dependent variable in the final set of regressions is the average monthly five-factor alpha scaled by idiosyncratic volatility. The sample period covers 2001–2012 when we are examining cross-sectional dispersion in monthly net returns and five-factor alphas, and 2002–2012 when we are examining the other three measures. Independent variables include a dummy variable equal to one if the market share of family$$j$$’s TDFs was$$\le$$1% (Low market share) and family$$k$$entered the TDF market after December 31, 2006 (Post-PPA family); a dummy variable equal to one if the market share of family$$j$$’s TDFs was$$\le$$1% (Low market share) and family$$k$$entered the TDF market before December 31, 2006 (Pre-PPA family); a dummy variable equal to one if the market share of family$$j$$’s TDFs was between 1% and 5% (Medium market share); a dummy variable equal to one if TDF$$i$$invests in index funds; and the average demeaned value of the dependent variable for family$$k$$’s BFs (where BF return characteristics are demeaned within four Lipper classifications for BFs: Flexible Portfolio Funds (FX), Mixed-Asset Target Allocation Conservative Funds (MTAC), Mixed-Asset Target Allocation Moderate Funds (MTAG), or Mixed-Asset Target Allocation Growth Funds (MTAM)). Estimation performed via OLS. We include a separate fixed effect for each target retirement date (e.g., 2020), each time period (month or year). Standard errors are simultaneously clustered by family and time (month or year). *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. Table 4 Cross-sectional dispersion in TDF returns and alphas and the level of idiosyncratic risk Dependent Variable: Cross-sectional dispersion in monthly net return Cross-sectional dispersion in monthly 5-factor alpha Idiosyncratic volatility Average monthly 5-factor alpha Alpha scaled by idiosyncratic volatility Frequency: Monthly Monthly Monthly Monthly Annual Annual Annual Annual Annual Annual Low market share$$\times$$0.849** 0.784** 0.347*** 0.275** 0.765*** 0.695*** –0.067** –0.036* –0.043* –0.030*$$\qquad$$Post-PPA family (0.368) (0.346) (0.131) (0.119) (0.249) (0.229) (0.032) (0.021) (0.022) (0.016) Low market share$$\times$$0.154* 0.120* 0.096** 0.077** 0.323*** 0.298** –0.014 –0.002 –0.022* –0.006$$\qquad$$Pre-PPA family (0.079) (0.070) (0.041) (0.036) (0.116) (0.138) (0.020) (0.016) (0.012) (0.011) Medium market share 0.091 0.086 0.044** 0.027 0.088 0.044 –0.020 –0.009 –0.035* –0.029* (0.085) (0.075) (0.018) (0.027) (0.103) (0.136) (0.028) (0.018) (0.020) (0.015) Index-fund-based TDF –0.078 –0.089 –0.001 0.001 –0.449*** –0.321*** –0.001 0.017 –0.024 –0.014 (0.068) (0.060) (0.023) (0.022) (0.145) (0.112) (0.036) (0.030) (0.022) (0.018) Average demeaned characteristic 0.157** 0.255*** 0.360*** 0.544*** 0.518***$$\qquad$$of family’s BFs (0.071) (0.046) (0.066) (0.040) (0.063)$$H_0$$: Low$$\times$$Post-PPA$$\qquad$$= Low$$\times$$Pre-PPA 0.016** 0.021** 0.004*** 0.013** 0.001*** 0.005*** 0.035** 0.067* 0.084* 0.114$$H_0$$: Low$$\times$$Post-PPA$$\qquad$$= Low$$\times$$Pre-PPA 0.059* 0.058* 0.056* 0.099* 0.085* 0.084* 0.226 0.021** 0.324 0.051* Target date-by-time fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$21,788 21,788 21,788 21,788 1,609 1,609 1,609 1,609 1,609 1,609$$R^2$$11.23% 17.35% 10.29% 21.82% 13.92% 26.76% 50.15% 63.21% 54.66% 63.17% Dependent Variable: Cross-sectional dispersion in monthly net return Cross-sectional dispersion in monthly 5-factor alpha Idiosyncratic volatility Average monthly 5-factor alpha Alpha scaled by idiosyncratic volatility Frequency: Monthly Monthly Monthly Monthly Annual Annual Annual Annual Annual Annual Low market share$$\times$$0.849** 0.784** 0.347*** 0.275** 0.765*** 0.695*** –0.067** –0.036* –0.043* –0.030*$$\qquad$$Post-PPA family (0.368) (0.346) (0.131) (0.119) (0.249) (0.229) (0.032) (0.021) (0.022) (0.016) Low market share$$\times$$0.154* 0.120* 0.096** 0.077** 0.323*** 0.298** –0.014 –0.002 –0.022* –0.006$$\qquad$$Pre-PPA family (0.079) (0.070) (0.041) (0.036) (0.116) (0.138) (0.020) (0.016) (0.012) (0.011) Medium market share 0.091 0.086 0.044** 0.027 0.088 0.044 –0.020 –0.009 –0.035* –0.029* (0.085) (0.075) (0.018) (0.027) (0.103) (0.136) (0.028) (0.018) (0.020) (0.015) Index-fund-based TDF –0.078 –0.089 –0.001 0.001 –0.449*** –0.321*** –0.001 0.017 –0.024 –0.014 (0.068) (0.060) (0.023) (0.022) (0.145) (0.112) (0.036) (0.030) (0.022) (0.018) Average demeaned characteristic 0.157** 0.255*** 0.360*** 0.544*** 0.518***$$\qquad$$of family’s BFs (0.071) (0.046) (0.066) (0.040) (0.063)$$H_0$$: Low$$\times$$Post-PPA$$\qquad$$= Low$$\times$$Pre-PPA 0.016** 0.021** 0.004*** 0.013** 0.001*** 0.005*** 0.035** 0.067* 0.084* 0.114$$H_0$$: Low$$\times$$Post-PPA$$\qquad$$= Low$$\times$$Pre-PPA 0.059* 0.058* 0.056* 0.099* 0.085* 0.084* 0.226 0.021** 0.324 0.051* Target date-by-time fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$21,788 21,788 21,788 21,788 1,609 1,609 1,609 1,609 1,609 1,609$$R^2$$11.23% 17.35% 10.29% 21.82% 13.92% 26.76% 50.15% 63.21% 54.66% 63.17% The unit of observation is TDF$$i$$offered by family$$k$$in month$$t$$. The dependent variables in the first three sets of regressions are measures of return diversity. When focusing on fund-level net returns, the dependent variable is$$(r_{ijt} - \overline{r}_{jt})^2$$. We compute a similar measure for monthly five-factor alphas, where the alpha of fund$$i$$in month$$t$$is calculated as the difference between the realized excess monthly return in month$$t$$and the systematic excess monthly returns, based on the five-factor model estimated using daily excess returns between month$$t-12$$and month$$t-1$$. The third dependent variable is idiosyncratic volatility, the nonannualized standard deviation of monthly alphas earned by fund$$i$$in calendar year$$t$$. The dependent variable in the fourth set of regressions is the average monthly five-factor alpha earned by fund$$i$$in calendar year$$t$$. The dependent variable in the final set of regressions is the average monthly five-factor alpha scaled by idiosyncratic volatility. The sample period covers 2001–2012 when we are examining cross-sectional dispersion in monthly net returns and five-factor alphas, and 2002–2012 when we are examining the other three measures. Independent variables include a dummy variable equal to one if the market share of family$$j$$’s TDFs was$$\le$$1% (Low market share) and family$$k$$entered the TDF market after December 31, 2006 (Post-PPA family); a dummy variable equal to one if the market share of family$$j$$’s TDFs was$$\le$$1% (Low market share) and family$$k$$entered the TDF market before December 31, 2006 (Pre-PPA family); a dummy variable equal to one if the market share of family$$j$$’s TDFs was between 1% and 5% (Medium market share); a dummy variable equal to one if TDF$$i$$invests in index funds; and the average demeaned value of the dependent variable for family$$k$$’s BFs (where BF return characteristics are demeaned within four Lipper classifications for BFs: Flexible Portfolio Funds (FX), Mixed-Asset Target Allocation Conservative Funds (MTAC), Mixed-Asset Target Allocation Moderate Funds (MTAG), or Mixed-Asset Target Allocation Growth Funds (MTAM)). Estimation performed via OLS. We include a separate fixed effect for each target retirement date (e.g., 2020), each time period (month or year). Standard errors are simultaneously clustered by family and time (month or year). *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. Our findings are quite similar when we study cross-sectional dispersion in monthly five-factor alphas. In this case, TDFs from post-PPA families with low market share exhibit annualized cross-sectional dispersion in alphas that are 4.16% higher than TDFs from high market share families and 2.20% higher than TDFs from pre-PPA families with low market share. In other words, we find that more than half of the increased cross-sectional dispersion in the net returns of TDFs from post-PPA families with low market share reflects increased cross-sectional dispersion in alphas.27 We estimate analogous fund-level specifications for the annualized idiosyncratic volatility of TDF$$i$$in year$$t$$, our first measure of ex ante risk-taking. Because the unit of observation switches from month to year, we focus on market shares calculated in month$$t-12$$. We find strong evidence that TDFs from low market share families have higher levels of idiosyncratic risk than their peers. The estimated coefficients on both low market share dummy variables are positive and statistically significant at the 5% level, and we can reject the hypothesis that both coefficients are equal to zero at the 1% level. Furthermore, because the estimated coefficients for TDFs from post-PPA families with low market share are approximately double those for TDFs from pre-PPA families with low market share, we can reject the hypothesis that these coefficients are equal at the 10% level. This remains true even when we control for the average (Lipper classification adjusted) idiosyncratic volatility of the family’s BFs, which has a strong positive correlation with the dependent variable. In other words, while the PPA may have drawn families with more idiosyncratic investment strategies into the TDF market (as reflected by the reduction in the coefficient on the low market share, post-PPA family dummy variable between Columns 5 and 6), when we control for this family-level trait, we continue to find significantly higher levels of idiosyncratic risk among TDFs from post-PPA families with low market share. We also find that TDFs based on index funds exhibit much lower levels of idiosyncratic risk than TDFs based on actively managed funds. In the remaining columns of Table 4, we estimate specifications that focus on the average monthly five-factor alpha during calendar year$$t$$, and the information ratio, defined as the average monthly five-factor alpha over the prior 12 months divided by idiosyncratic volatility in calendar year$$t$$. Our goal is to determine whether investors being exposed to higher levels of idiosyncratic risk are being compensated for this risk with higher average alphas. Our estimates imply that they are not. TDFs from post-PPA families with low market share, which have the highest levels of idiosyncratic risk, earn alphas that are 6.7 basis points per month lower than TDFs from families with high market share. When we control for the average (Lipper classification adjusted) monthly five-factor alpha of the family’s BFs, the coefficients on all three market-share dummy variables shrink towards zero, implying that some of the underperformance can be thought of as a family-level trait. Nevertheless, we continue to find the largest underperformance among TDFs from post-PPA families with low market share: 3.6 basis points per month ($$p$$-value of .086).28 Finally, we find that TDFs from post-PPA families with low market share and TDFs from families with medium market share both have lower information ratios than TDFs from families with high market share (because TDFs from families with medium market share have less negative alphas but also much lower levels of idiosyncratic risk). However, when we control for the average (Lipper classification adjusted) information ratios of the family’s BFs, we can reject the hypothesis that TDFs from post-PPA families with low market share have the same information ratios as TDFs from pre-PPA families with low market share at the 10% level. 4.4 Explaining differences in levels of factor model$$R^2$$s As an alternative measure of ex ante risk, we turn to factor model$$R^2$$s. We consider a single-factor model, with the U.S. equity excess return as the only factor (capital asset pricing model, or “CAPM”), and the five-factor model used throughout the paper. The dependent variable is the$$R^2$$of TDF$$i$$in year$$t$$, and the regression specifications mirror those introduced in the previous section. Since lower$$R^2$$s are associated with more variability in alphas, our predictions for the coefficients on the low market share dummy variables are the opposite of those for idiosyncratic risk. Consistent with the prediction that TDFs from low market share will exhibit lower$$R^2$$s than other TDFs, the estimated coefficients on both low market share dummy variables are negative and statistically significant across all four specifications in Table 5. We can reject the hypothesis that TDFs from low market share families have the same$$R^2$$s as TDFs from high market share families at the 5% level and below, whether or not we control for the average (Lipper classification adjusted)$$R^2$$s of the family’s BFs. Table 5 Differences in the level of factor model$$R^2$$s Dependent variable:$$R^2$$from CAPM$$R^2$$from 5-factor model Frequency: Annual Annual Annual Annual Low market share –0.072*** –0.066*** –0.035*** –0.035***$$\quad\times$$Post-PPA family (0.027) (0.025) (0.013) (0.013) Low market share –0.018* –0.016* –0.009*** –0.008***$$\quad\times$$Pre-PPA family (0.010) (0.009) (0.003) (0.003) Medium market share –0.019 –0.016 –0.005* –0.004 (0.012) (0.013) (0.003) (0.003) Index-fund-based TDF –0.008 –0.004 0.004* 0.004 (0.015) (0.015) (0.002) (0.003) Average demeaned$$R^2$$0.289** 0.136$$\quad$$of family’s BFs (0.134) (0.135)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.013** 0.010*** 0.001*** 0.000***$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.053* 0.048** 0.055* 0.061* Target date-by-year fixed effects? Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000$$R^2$$31.50% 34.12% 22.43% 23.35% Dependent variable:$$R^2$$from CAPM$$R^2$$from 5-factor model Frequency: Annual Annual Annual Annual Low market share –0.072*** –0.066*** –0.035*** –0.035***$$\quad\times$$Post-PPA family (0.027) (0.025) (0.013) (0.013) Low market share –0.018* –0.016* –0.009*** –0.008***$$\quad\times$$Pre-PPA family (0.010) (0.009) (0.003) (0.003) Medium market share –0.019 –0.016 –0.005* –0.004 (0.012) (0.013) (0.003) (0.003) Index-fund-based TDF –0.008 –0.004 0.004* 0.004 (0.015) (0.015) (0.002) (0.003) Average demeaned$$R^2$$0.289** 0.136$$\quad$$of family’s BFs (0.134) (0.135)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.013** 0.010*** 0.001*** 0.000***$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.053* 0.048** 0.055* 0.061* Target date-by-year fixed effects? Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000$$R^2$$31.50% 34.12% 22.43% 23.35% The unit of observation is TDF$$i$$offered by family$$k$$in December of year$$t$$. The dependent variable is fund$$i$$’s$$R^2$$in a one-factor or five-factor model estimated during calendar year$$t$$using daily returns. The sample period covers 2001–2012. The one-factor (CAPM) model is based on the excess daily returns on the CRSP U.S. value-weighted index. The five-factor model adds the excess daily return on the Barclay U.S. Aggregate Bond Index; the excess daily return on the MSCI World Index excluding the United States, Barclays Global Aggregate excluding the United States, and GSCI Commodity Index. The set of independent variables matches Table 4 except that we now control for the average demeaned$$R^2$$of the family’s BFs (where$$R^2$$s are demeaned within four Lipper classifications for BFs: Flexible Portfolio Funds (FX), Mixed-Asset Target Allocation Conservative Funds (MTAC), Mixed-Asset Target Allocation Moderate Funds (MTAG), or Mixed-Asset Target Allocation Growth Funds (MTAM)). Estimation performed via OLS. Standard errors are simultaneously clustered by family and year. *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. Table 5 Differences in the level of factor model$$R^2$$s Dependent variable:$$R^2$$from CAPM$$R^2$$from 5-factor model Frequency: Annual Annual Annual Annual Low market share –0.072*** –0.066*** –0.035*** –0.035***$$\quad\times$$Post-PPA family (0.027) (0.025) (0.013) (0.013) Low market share –0.018* –0.016* –0.009*** –0.008***$$\quad\times$$Pre-PPA family (0.010) (0.009) (0.003) (0.003) Medium market share –0.019 –0.016 –0.005* –0.004 (0.012) (0.013) (0.003) (0.003) Index-fund-based TDF –0.008 –0.004 0.004* 0.004 (0.015) (0.015) (0.002) (0.003) Average demeaned$$R^2$$0.289** 0.136$$\quad$$of family’s BFs (0.134) (0.135)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.013** 0.010*** 0.001*** 0.000***$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.053* 0.048** 0.055* 0.061* Target date-by-year fixed effects? Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000$$R^2$$31.50% 34.12% 22.43% 23.35% Dependent variable:$$R^2$$from CAPM$$R^2$$from 5-factor model Frequency: Annual Annual Annual Annual Low market share –0.072*** –0.066*** –0.035*** –0.035***$$\quad\times$$Post-PPA family (0.027) (0.025) (0.013) (0.013) Low market share –0.018* –0.016* –0.009*** –0.008***$$\quad\times$$Pre-PPA family (0.010) (0.009) (0.003) (0.003) Medium market share –0.019 –0.016 –0.005* –0.004 (0.012) (0.013) (0.003) (0.003) Index-fund-based TDF –0.008 –0.004 0.004* 0.004 (0.015) (0.015) (0.002) (0.003) Average demeaned$$R^2$$0.289** 0.136$$\quad$$of family’s BFs (0.134) (0.135)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.013** 0.010*** 0.001*** 0.000***$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.053* 0.048** 0.055* 0.061* Target date-by-year fixed effects? Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000$$R^2$$31.50% 34.12% 22.43% 23.35% The unit of observation is TDF$$i$$offered by family$$k$$in December of year$$t$$. The dependent variable is fund$$i$$’s$$R^2$$in a one-factor or five-factor model estimated during calendar year$$t$$using daily returns. The sample period covers 2001–2012. The one-factor (CAPM) model is based on the excess daily returns on the CRSP U.S. value-weighted index. The five-factor model adds the excess daily return on the Barclay U.S. Aggregate Bond Index; the excess daily return on the MSCI World Index excluding the United States, Barclays Global Aggregate excluding the United States, and GSCI Commodity Index. The set of independent variables matches Table 4 except that we now control for the average demeaned$$R^2$$of the family’s BFs (where$$R^2$$s are demeaned within four Lipper classifications for BFs: Flexible Portfolio Funds (FX), Mixed-Asset Target Allocation Conservative Funds (MTAC), Mixed-Asset Target Allocation Moderate Funds (MTAG), or Mixed-Asset Target Allocation Growth Funds (MTAM)). Estimation performed via OLS. Standard errors are simultaneously clustered by family and year. *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. However, we also find strong evidence that the lower$$R^2$$s of TDFs from low market share families are driven by the investment behavior of those TDFs offered by post-PPA families. The$$R^2$$s of TDFs from post-PPA families with low market share are between$$6.6\%$$and$$7.2\%$$lower than those of TDFs from families with high market share, when we focus on the one-factor model, and$$3.5\%$$lower, when we focus on the five-factor model. All of these differences are statistically significant from zero at the 1% level, and we can reject the hypothesis that TDFs from post-PPA families with low market share have the same$$R^2$$s as TDFs from pre-PPA families with low market share at the 10% level and below. 4.5 Explaining differences in levels and dispersion of five-factor model betas In this section, we test for differences in factor model betas, another measure of ex ante risk. To the extent that plan sponsors focus on alphas, we do not necessarily expect TDFs from entrants to offer systematically higher equity betas than TDFs from other families. Nor do we expect TDFs from incumbents with low market share, which have already publicized their glide paths, to increase their equity betas. Rather, because entrants may find it difficult to market their TDFs to plan sponsors if they have the same glide paths as incumbents, we expect entrants to differentiate themselves from incumbents through the weights placed on different asset classes along the glide path. The regressions in Table 6 mirror those in Tables 4 and 5. The dependent variable in panel A is the deviation of the beta of TDF$$i$$in year$$t$$from the equally weighted average of all TDFs with the same target date in year$$t$$. In this panel, positive coefficients imply positive tilts in beta. The dependent variable in panel B is the squared deviation for TDF$$i$$in year$$t$$, so that positive coefficients imply greater cross-sectional dispersion in beta. Table 6 Levels and dispersion in five-factor model betas Panel A Beta: U.S. equity U.S. debt Global equity Global debt Commodities Low market share$$\times$$–0.046 –0.040 0.079** 0.071** –0.003 –0.006 0.020*** 0.019*** 0.010 0.013**$$\quad$$Post-PPA family (0.040) (0.038) (0.037) (0.028) (0.009) (0.008) (0.006) (0.006) (0.009) (0.006) Low market share$$\times$$0.000 0.002 0.024 0.021 0.005 0.004 0.006** 0.006** –0.006 –0.001$$\quad$$Pre-PPA family (0.029) (0.028) (0.022) (0.014) (0.005) (0.004) (0.003) (0.003) (0.007) (0.003) Medium market share 0.002 0.003 0.058** 0.056*** –0.008* –0.006 0.015*** 0.016*** –0.013 –0.008** (0.030) (0.030) (0.025) (0.018) (0.004) (0.004) (0.005) (0.005) (0.008) (0.004) Index-fund-based TDF –0.019 –0.016 0.056 0.029 –0.014** –0.012*** 0.010*** 0.010*** –0.004 –0.001 (0.016) (0.015) (0.036) (0.027) (0.006) (0.002) (0.003) (0.003) (0.005) (0.003) Average demeaned beta tilt 0.230 0.401*** 0.456*** 0.425*** 0.733***$$\quad$$of family’s BFs (0.186) (0.091) (0.105) (0.094) (0.112)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.413 0.456 0.088* 0.031** 0.580 0.510 0.001*** 0.003*** 0.011** 0.022**$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.197 0.219 0.123 0.066** 0.444 0.297 0.024** 0.017** 0.004*** 0.007*** Target date-by-year fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000 2,000 2,000 2000 2,000 2,000 2,000$$R^2$$76.96% 77.51% 58.40% 63.89% 49.59% 59.54% 32.20% 39.71% 26.58% 42.40% Panel B Dispersion in beta: U.S. equity U.S. debt Global equity Global debt Commodities Low market share$$\times$$1.935* 1.959** 2.165* 1.663 0.102*** 0.069** 0.055*** 0.054*** 0.103* 0.105*$$\quad$$Post-PPA family (0.988) (0.971) (1.300) (1.158) (0.033) (0.031) (0.019) (0.019) (0.062) (0.060) Low market share$$\times$$0.360* 0.432** 0.047 0.012 0.075** 0.054** 0.010 0.010 –0.014 –0.010$$\quad$$Pre-PPA family (0.204) (0.210) (0.291) (0.266) (0.031) (0.022) (0.008) (0.008) (0.014) (0.014) Medium market share 0.030 0.053 –0.114 –0.259 0.011 0.013 0.043 0.044 –0.016 –0.013 (0.169) (0.151) (0.342) (0.328) (0.013) (0.009) (0.027) (0.027) (0.016) (0.016) Index-fund-based TDF –0.178 –0.198 –0.162 –0.320 –0.004 –0.016 –0.028* –0.027 0.014 0.016 (0.147) (0.171) (0.362) (0.278) (0.025) (0.017) (0.016) (0.017) (0.015) (0.013) Average dispersion in demeaned 0.000 0.160 0.000 0.193*** 0.000 0.285*** 0.000 0.027 0.000 0.043$$\quad$$beta of family’s BFs (0.105) (0.018) (0.039) (0.040) (0.111)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.023** 0.016** 0.252 0.344 0.002*** 0.016** 0.006*** 0.005*** 0.116 0.209$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.127 0.127 0.103 0.145 0.511 0.634 0.031** 0.036** 0.058* 0.078* Target date-by-year fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000$$R^2$$6.55% 7.56% 6.75% 15.22% 11.99% 39.93% 7.21% 7.33% 7.48% 7.52% Panel A Beta: U.S. equity U.S. debt Global equity Global debt Commodities Low market share$$\times$$–0.046 –0.040 0.079** 0.071** –0.003 –0.006 0.020*** 0.019*** 0.010 0.013**$$\quad$$Post-PPA family (0.040) (0.038) (0.037) (0.028) (0.009) (0.008) (0.006) (0.006) (0.009) (0.006) Low market share$$\times$$0.000 0.002 0.024 0.021 0.005 0.004 0.006** 0.006** –0.006 –0.001$$\quad$$Pre-PPA family (0.029) (0.028) (0.022) (0.014) (0.005) (0.004) (0.003) (0.003) (0.007) (0.003) Medium market share 0.002 0.003 0.058** 0.056*** –0.008* –0.006 0.015*** 0.016*** –0.013 –0.008** (0.030) (0.030) (0.025) (0.018) (0.004) (0.004) (0.005) (0.005) (0.008) (0.004) Index-fund-based TDF –0.019 –0.016 0.056 0.029 –0.014** –0.012*** 0.010*** 0.010*** –0.004 –0.001 (0.016) (0.015) (0.036) (0.027) (0.006) (0.002) (0.003) (0.003) (0.005) (0.003) Average demeaned beta tilt 0.230 0.401*** 0.456*** 0.425*** 0.733***$$\quad$$of family’s BFs (0.186) (0.091) (0.105) (0.094) (0.112)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.413 0.456 0.088* 0.031** 0.580 0.510 0.001*** 0.003*** 0.011** 0.022**$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.197 0.219 0.123 0.066** 0.444 0.297 0.024** 0.017** 0.004*** 0.007*** Target date-by-year fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000 2,000 2,000 2000 2,000 2,000 2,000$$R^2$$76.96% 77.51% 58.40% 63.89% 49.59% 59.54% 32.20% 39.71% 26.58% 42.40% Panel B Dispersion in beta: U.S. equity U.S. debt Global equity Global debt Commodities Low market share$$\times$$1.935* 1.959** 2.165* 1.663 0.102*** 0.069** 0.055*** 0.054*** 0.103* 0.105*$$\quad$$Post-PPA family (0.988) (0.971) (1.300) (1.158) (0.033) (0.031) (0.019) (0.019) (0.062) (0.060) Low market share$$\times$$0.360* 0.432** 0.047 0.012 0.075** 0.054** 0.010 0.010 –0.014 –0.010$$\quad$$Pre-PPA family (0.204) (0.210) (0.291) (0.266) (0.031) (0.022) (0.008) (0.008) (0.014) (0.014) Medium market share 0.030 0.053 –0.114 –0.259 0.011 0.013 0.043 0.044 –0.016 –0.013 (0.169) (0.151) (0.342) (0.328) (0.013) (0.009) (0.027) (0.027) (0.016) (0.016) Index-fund-based TDF –0.178 –0.198 –0.162 –0.320 –0.004 –0.016 –0.028* –0.027 0.014 0.016 (0.147) (0.171) (0.362) (0.278) (0.025) (0.017) (0.016) (0.017) (0.015) (0.013) Average dispersion in demeaned 0.000 0.160 0.000 0.193*** 0.000 0.285*** 0.000 0.027 0.000 0.043$$\quad$$beta of family’s BFs (0.105) (0.018) (0.039) (0.040) (0.111)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.023** 0.016** 0.252 0.344 0.002*** 0.016** 0.006*** 0.005*** 0.116 0.209$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.127 0.127 0.103 0.145 0.511 0.634 0.031** 0.036** 0.058* 0.078* Target date-by-year fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000$$R^2$$6.55% 7.56% 6.75% 15.22% 11.99% 39.93% 7.21% 7.33% 7.48% 7.52% The unit of observation is TDF$$i$$offered by family$$k$$in December of year$$t$$. In panel A, the dependent variable is the beta estimated for TDF$$i$$in a five-factor model using daily returns from year$$t$$. In panel B, the dependent variable is the squared deviation of each beta for TDF$$i$$in year$$t$$. The sample period covers 2001–2012. The set of independent variables matches Tables 4 and Table 5 except that we control for the average beta tilt of the family’s BFs in panel A and for the average squared deviation of the betas of the family’s BFs in panel B. Coefficients in panel B are multiplied by 100. Estimation performed via OLS. Standard errors are simultaneously clustered by family and year. *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. Table 6 Levels and dispersion in five-factor model betas Panel A Beta: U.S. equity U.S. debt Global equity Global debt Commodities Low market share$$\times$$–0.046 –0.040 0.079** 0.071** –0.003 –0.006 0.020*** 0.019*** 0.010 0.013**$$\quad$$Post-PPA family (0.040) (0.038) (0.037) (0.028) (0.009) (0.008) (0.006) (0.006) (0.009) (0.006) Low market share$$\times$$0.000 0.002 0.024 0.021 0.005 0.004 0.006** 0.006** –0.006 –0.001$$\quad$$Pre-PPA family (0.029) (0.028) (0.022) (0.014) (0.005) (0.004) (0.003) (0.003) (0.007) (0.003) Medium market share 0.002 0.003 0.058** 0.056*** –0.008* –0.006 0.015*** 0.016*** –0.013 –0.008** (0.030) (0.030) (0.025) (0.018) (0.004) (0.004) (0.005) (0.005) (0.008) (0.004) Index-fund-based TDF –0.019 –0.016 0.056 0.029 –0.014** –0.012*** 0.010*** 0.010*** –0.004 –0.001 (0.016) (0.015) (0.036) (0.027) (0.006) (0.002) (0.003) (0.003) (0.005) (0.003) Average demeaned beta tilt 0.230 0.401*** 0.456*** 0.425*** 0.733***$$\quad$$of family’s BFs (0.186) (0.091) (0.105) (0.094) (0.112)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.413 0.456 0.088* 0.031** 0.580 0.510 0.001*** 0.003*** 0.011** 0.022**$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.197 0.219 0.123 0.066** 0.444 0.297 0.024** 0.017** 0.004*** 0.007*** Target date-by-year fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000 2,000 2,000 2000 2,000 2,000 2,000$$R^2$$76.96% 77.51% 58.40% 63.89% 49.59% 59.54% 32.20% 39.71% 26.58% 42.40% Panel B Dispersion in beta: U.S. equity U.S. debt Global equity Global debt Commodities Low market share$$\times$$1.935* 1.959** 2.165* 1.663 0.102*** 0.069** 0.055*** 0.054*** 0.103* 0.105*$$\quad$$Post-PPA family (0.988) (0.971) (1.300) (1.158) (0.033) (0.031) (0.019) (0.019) (0.062) (0.060) Low market share$$\times$$0.360* 0.432** 0.047 0.012 0.075** 0.054** 0.010 0.010 –0.014 –0.010$$\quad$$Pre-PPA family (0.204) (0.210) (0.291) (0.266) (0.031) (0.022) (0.008) (0.008) (0.014) (0.014) Medium market share 0.030 0.053 –0.114 –0.259 0.011 0.013 0.043 0.044 –0.016 –0.013 (0.169) (0.151) (0.342) (0.328) (0.013) (0.009) (0.027) (0.027) (0.016) (0.016) Index-fund-based TDF –0.178 –0.198 –0.162 –0.320 –0.004 –0.016 –0.028* –0.027 0.014 0.016 (0.147) (0.171) (0.362) (0.278) (0.025) (0.017) (0.016) (0.017) (0.015) (0.013) Average dispersion in demeaned 0.000 0.160 0.000 0.193*** 0.000 0.285*** 0.000 0.027 0.000 0.043$$\quad$$beta of family’s BFs (0.105) (0.018) (0.039) (0.040) (0.111)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.023** 0.016** 0.252 0.344 0.002*** 0.016** 0.006*** 0.005*** 0.116 0.209$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.127 0.127 0.103 0.145 0.511 0.634 0.031** 0.036** 0.058* 0.078* Target date-by-year fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000$$R^2$$6.55% 7.56% 6.75% 15.22% 11.99% 39.93% 7.21% 7.33% 7.48% 7.52% Panel A Beta: U.S. equity U.S. debt Global equity Global debt Commodities Low market share$$\times$$–0.046 –0.040 0.079** 0.071** –0.003 –0.006 0.020*** 0.019*** 0.010 0.013**$$\quad$$Post-PPA family (0.040) (0.038) (0.037) (0.028) (0.009) (0.008) (0.006) (0.006) (0.009) (0.006) Low market share$$\times$$0.000 0.002 0.024 0.021 0.005 0.004 0.006** 0.006** –0.006 –0.001$$\quad$$Pre-PPA family (0.029) (0.028) (0.022) (0.014) (0.005) (0.004) (0.003) (0.003) (0.007) (0.003) Medium market share 0.002 0.003 0.058** 0.056*** –0.008* –0.006 0.015*** 0.016*** –0.013 –0.008** (0.030) (0.030) (0.025) (0.018) (0.004) (0.004) (0.005) (0.005) (0.008) (0.004) Index-fund-based TDF –0.019 –0.016 0.056 0.029 –0.014** –0.012*** 0.010*** 0.010*** –0.004 –0.001 (0.016) (0.015) (0.036) (0.027) (0.006) (0.002) (0.003) (0.003) (0.005) (0.003) Average demeaned beta tilt 0.230 0.401*** 0.456*** 0.425*** 0.733***$$\quad$$of family’s BFs (0.186) (0.091) (0.105) (0.094) (0.112)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.413 0.456 0.088* 0.031** 0.580 0.510 0.001*** 0.003*** 0.011** 0.022**$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.197 0.219 0.123 0.066** 0.444 0.297 0.024** 0.017** 0.004*** 0.007*** Target date-by-year fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000 2,000 2,000 2000 2,000 2,000 2,000$$R^2$$76.96% 77.51% 58.40% 63.89% 49.59% 59.54% 32.20% 39.71% 26.58% 42.40% Panel B Dispersion in beta: U.S. equity U.S. debt Global equity Global debt Commodities Low market share$$\times$$1.935* 1.959** 2.165* 1.663 0.102*** 0.069** 0.055*** 0.054*** 0.103* 0.105*$$\quad$$Post-PPA family (0.988) (0.971) (1.300) (1.158) (0.033) (0.031) (0.019) (0.019) (0.062) (0.060) Low market share$$\times$$0.360* 0.432** 0.047 0.012 0.075** 0.054** 0.010 0.010 –0.014 –0.010$$\quad$$Pre-PPA family (0.204) (0.210) (0.291) (0.266) (0.031) (0.022) (0.008) (0.008) (0.014) (0.014) Medium market share 0.030 0.053 –0.114 –0.259 0.011 0.013 0.043 0.044 –0.016 –0.013 (0.169) (0.151) (0.342) (0.328) (0.013) (0.009) (0.027) (0.027) (0.016) (0.016) Index-fund-based TDF –0.178 –0.198 –0.162 –0.320 –0.004 –0.016 –0.028* –0.027 0.014 0.016 (0.147) (0.171) (0.362) (0.278) (0.025) (0.017) (0.016) (0.017) (0.015) (0.013) Average dispersion in demeaned 0.000 0.160 0.000 0.193*** 0.000 0.285*** 0.000 0.027 0.000 0.043$$\quad$$beta of family’s BFs (0.105) (0.018) (0.039) (0.040) (0.111)$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA = 0 0.023** 0.016** 0.252 0.344 0.002*** 0.016** 0.006*** 0.005*** 0.116 0.209$$H_0$$: Low$$\times$$Post-PPA$$\quad$$= Low$$\times$$Pre-PPA 0.127 0.127 0.103 0.145 0.511 0.634 0.031** 0.036** 0.058* 0.078* Target date-by-year fixed effects? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes$$N$$2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000$$R^2$$6.55% 7.56% 6.75% 15.22% 11.99% 39.93% 7.21% 7.33% 7.48% 7.52% The unit of observation is TDF$$i$$offered by family$$k$$in December of year$$t$$. In panel A, the dependent variable is the beta estimated for TDF$$i$$in a five-factor model using daily returns from year$$t$$. In panel B, the dependent variable is the squared deviation of each beta for TDF$$i$$in year$$t$$. The sample period covers 2001–2012. The set of independent variables matches Tables 4 and Table 5 except that we control for the average beta tilt of the family’s BFs in panel A and for the average squared deviation of the betas of the family’s BFs in panel B. Coefficients in panel B are multiplied by 100. Estimation performed via OLS. Standard errors are simultaneously clustered by family and year. *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. We find evidence in panel A that TDFs from post-PPA families with low market share have higher loadings on U.S. debt, global debt, and commodities than other TDFs. We also find that the beta tilts of TDFs are strongly positively correlated with the beta tilts of a family’s BFs. The effect is especially large for the exposure to the commodity factor, where a$$0.10$$increase in the commodity betas of a family’s BFs is associated with a$$0.07$$increase in the commodity betas of its TDFs. Of course, the typical investor is unlikely to know or care whether her TDF is offered by a family that has above-average allocations to global equity or commodities. The main finding in panel B is that TDFs from post-PPA families with low market share exhibit more diverse betas with respect to U.S. equity, global equity, global debt, and commodities. Overall, Table 6 suggests that the movement into riskier asset classes documented in Elton et al. (2015) is being driven by families entering the TDF market following the PPA. 4.6 Robustness We find that TDFs from post-PPA families with low market share engage in more risk-taking than TDFs from pre-PPA families with low market share which, in turn, engage in more risk-taking than other TDFs. This general pattern holds in alternative specifications and sample periods. For example, we find similar evidence of strategic risk-taking by TDFs from post-PPA families with low market share when, in Internet Appendix Table B.7, we reestimate our main specifications using family-level data. One potential concern is that, because our regression specifications do not allow the coefficient on the pre-PPA family with low market share dummy variable to change following the PPA, we are overstating the difference in risk-taking by TDFs from post-PPA versus pre-PPA families with low market share. This is not the case. Estimated magnitudes and statistical inferences with respect to differences in realized returns and ex ante risk are similar when, in Internet Appendix Tables B.8–B.10, we reestimate the specifications in Tables 4–6 using only data from 2007–2012. The estimated coefficients on the medium market share dummy variable are also similar. Many of our findings of strategic risk-taking also continue to hold, in Internet Appendix Tables B.11–B.13, when we further limit the sample period by excluding 2008 and 2009. Namely, we continue to find that post-PPA families with low market share exhibit the highest levels of cross-sectional dispersion in five-factor alphas and idiosyncratic risk and the lowest$$R^2$$s. However, fewer of the estimated coefficients on the low market share dummy variables are statistically significant in the regressions that focus on factor loadings, and we can no longer reject the hypothesis that the cross-sectional dispersion in net returns is greater for TDFs from post-PPA families with low market share than for comparable TDFs from pre-PPA families with low market share. Although our tests focus on a family’s share of the TDF market, the expected costs and benefits of increasing idiosyncratic risk may also depend on the family’s share of the overall mutual fund market or 401(k) market. Specifically, families with the lowest overall market shares may have the least to gain from pursuing an idiosyncratic return strategy, because consultants may still be reluctant to add them to retirement plan menus. Families with the highest overall market shares, on the other hand, may have the most to lose if abnormally low TDF returns damage their existing reputation with plan sponsors. We test these predictions in Internet Appendix Table B.14. One set of specifications includes dummy variables indicating low or medium market share in the overall mutual fund market (based on total assets under management in CRSP), rather than in the TDF market. Another set of specifications interacts the dummy variables indicating low, medium, and high market share in the TDF market with dummy variables indicating low, medium, and high market shares in the overall mutual fund market. While we find the strongest evidence of risk-taking by families with low market share in the TDF market and medium market share in the overall market, we also continue to find significantly higher levels of cross-sectional dispersion in net returns and five-factor alphas and higher levels of idiosyncratic risk among post-PPA families. In our final set of robustness tests, reported in Internet Appendix Table B.15, we focus only on each family’s year of entry, ignoring measures of market share. We find that TDFs from post-PPA families have higher levels of cross-sectional dispersion in net returns and five-factor alphas and higher levels of idiosyncratic risk than families that entered before 2003. We conclude that a significant fraction of the increased dispersion in realized returns and the increased levels of idiosyncratic risk following the PPA reflects strategic risk-taking. 5. Does TDF Heterogeneity Reflect Risk Matching? 5.1 Risk-matching incentives Authors have shown that the properties of human capital returns have important implications for optimal portfolio choice and that ignoring them can lead to substantial utility costs (e.g., Davis and Willen 2000a; Davis and Willen 2000b; Davis and Willen 2002; Maurer et al. 2010; Fugazza et al. 2011; Guidolin and Hyde 2012; Bagliano et al. 2013). Of special interest is the heterogeneity in the properties of human capital returns across occupations and industries.29 Therefore, another explanation for the increased heterogeneity in TDF investment behavior is that it reflects an intentional differentiation of ex ante risk profiles to better match the heterogeneity in investor human capital and risk aversion across firms. As dispersion in glide paths is readily observable to plan sponsors and their consultants, one hypothesis is that firms whose employees have riskier human-capital endowments will pick safer TDFs for their 401(k) plans. For example, since firms in more competitive industries expose their employees to higher human-capital risk, they may choose to avoid TDFs with larger-than-average allocations to equity. This effect may be especially true when the plans feature automatic enrollment, since the TDFs in these plans are likely to be the default investment options. This form of risk matching, which we denote “human-capital risk matching,” implies a negative correlation between TDF risk and firm risk. Viceira (2009) highlights the potential benefits of human-capital risk matching: “Employees with volatile labor earnings or labor earnings that are highly correlated with equity returns should avoid investing in the current generation of life-cycle funds, which exhibit significant equity tilts. For these investors, their human wealth is less “bond-like” and more “equity-like.” Therefore they already have exposure to equities through their human wealth and should avoid excessive exposure, or any exposure at all, to equities in their portfolios. Since the correlation of labor earnings with stock returns is likely to be similar for employees within the same industry or company, these considerations suggest that there is a benefit to the creation of industry-specific or company-specific life-cycle funds.” On the other hand, if the risk attitudes of the representative employee vary across firms (Berk, Stanton, and Zechner 2010), and if different firms appeal to employees with different levels of risk aversion, then we should observe a positive, rather than negative correlation, between TDF risk profiles and firm risk profiles. We denote this “risk-preference matching.” Indeed, Viceira (2009) suggests that: “Mutual fund companies might want to consider offering life-cycle funds that exhibit different equity tilts. That is, they might want to offer “conservative,” “moderate,” and “aggressive” life-cycle funds. These funds will help capture investor heterogeneity in risk tolerance.” Interestingly, DOL (2013) emphasizes the need for plan fiduciaries to consider investor characteristics when choosing among TDF providers.30 While this memo highlights the benefits of a marketplace in which different TDFs offer different ex ante risk profiles, it also highlights the possibility that benefits from risk matching were not yet salient to the typical plan sponsor of mutual fund family. We do not take a stand on the form of the possible risk matching (human-capital risk matching vs. risk-preferences matching). In our main specifications, we simply test for nonzero correlations between firm risk and TDF risk using plan-level data and measures of systematic and idiosyncratic risk. Hence, we seek to characterize “average” patterns in risk matching, with the goal of determining whether risk-matching considerations help to explain the increased heterogeneity in TDF investment behavior in our sample following the PPA. However, as a robustness test, we also estimate specifications based on the absolute values of TDF risk and firm risk. These specifications are intended to capture situations in which some firms choose TDFs based on human-capital risk matching and other firms simultaneously choose TDFs based on risk-preference matching. 5.2 Testing for risk matching in plan-level data To test the risk-matching hypothesis, we analyze retirement plan-level data from BrightScope.31 The full database covers 16,766 distinct 401(k) and 403(b) plans, offered by 15,403 distinct firms, in 2010. There are more plans than firms because some firms offer multiple plans. For example, United Airlines offers separate retirement plans for its pilots and ground employees. Firm-level data include the firm’s name, primary address, and 6-digit North American Industry Classification System (NAICS) code. We are able to locate a ticker and estimate a CAPM beta for 1,740 of the firms in the BrightScope database.32 Plan-level data include assets under management, number of participants, whether the plan offers company stock, whether the plan has autoenrollment, whether the plan has a single recordkeeper (SRK), and the identity of the recordkeeper. Investment-level data include the name and type (mutual fund, collective trust, separate account, company stock, etc.) of each investment option offered by each plan, whether the investment option is a TDF, and the total dollars invested in the option. Table 7 presents the summary statistics for the BrightScope data set. Approximately 66% of the plans offer some form of TDF, with 50% offering TDF mutual funds. When we count TDFs with different target retirement dates as a single investment option, TDFs represent 2.7% of the investment options and 9.7% ( \$$242 billion) of the $\$$2,495 billion in assets under management in our sample of plans in 2010.33 That TDFs managed almost 10% of DC assets in 2010 highlights the important role that TDFs have come to play in retirement wealth accumulation. Table 7 BrightScope sample: Summary statistics N Mean SD Min Max Plan characteristics in 2010$$\quad$$Assets (in millions) 16,766 134.62 708.67 0.01 36,741.60$$\quad$$Number of participants (in thousands) 16,766 2.00 8.08 0.00 306.61$$\quad$$Plan age in years 16,766 22.94 13.45 0.00 95.00$$\quad$$401(k) plan 16,766 0.91 0.29 0.00 1.00$$\quad$$Autoenrollment 16,766 0.23 0.42 0.00 1.00$$\quad$$Offers company stock 16,766 0.13 0.33 0.00 1.00$$\quad$$Offers any mutual funds 16,766 0.85 0.36 0.00 1.00$$\quad$$Offers any TDFs 16,766 0.66 0.47 0.00 1.00$$\quad$$Offers mutual fund TDFs 16,766 0.50 0.50 0.00 1.00$$\quad$$Single record keeper (SRK) 16,766 0.75 0.43 0.00 1.00$$\quad$$Fraction of TDFs managed by SRK 7,687 0.76 0.42 0.00 1.00$$\quad$$Fraction of non-TDFs managed by SRK? 7,687 0.39 0.28 0.00 1.00 Measures of firm risk in 2009$$\quad$$CAPM beta (firm-level) 1,740 1.37 0.91 –1.26 8.65$$\quad$$Standard deviation of total returns 1,740 0.17 0.10 0.04 1.27$$\quad$$Standard deviation of predicted returns 1,740 0.10 0.06 0.00 0.60$$\quad$$Standard deviation of residual returns 1,740 0.14 0.08 0.03 1.12$$\quad$$CAPM beta (3-digit industry-level) 16,301 1.21 0.48 0.14 2.57 Measures of mutual fund risk in 2009$$\quad$$CAPM beta of 2010 TDF 6,677 0.63 0.07 0.40 0.90$$\quad$$CAPM beta of 2020 TDF 7,581 0.78 0.06 0.63 1.00$$\quad$$CAPM beta of 2030 TDF 7,491 0.91 0.04 0.76 1.03$$\quad$$CAPM beta of 2040 TDF 7,641 0.96 0.04 0.85 1.04$$\quad$$CAPM beta of 2050 TDF 6,504 0.98 0.04 0.87 1.04$$\quad$$Average CAPM beta of mutual fund TDFs 8,277 0.79 0.06 0.32 1.02$$\quad$$Average CAPM beta of other mutual funds 14,064 0.83 0.15 –1.69 1.58 N Mean SD Min Max Plan characteristics in 2010$$\quad$$Assets (in millions) 16,766 134.62 708.67 0.01 36,741.60$$\quad$$Number of participants (in thousands) 16,766 2.00 8.08 0.00 306.61$$\quad$$Plan age in years 16,766 22.94 13.45 0.00 95.00$$\quad$$401(k) plan 16,766 0.91 0.29 0.00 1.00$$\quad$$Autoenrollment 16,766 0.23 0.42 0.00 1.00$$\quad$$Offers company stock 16,766 0.13 0.33 0.00 1.00$$\quad$$Offers any mutual funds 16,766 0.85 0.36 0.00 1.00$$\quad$$Offers any TDFs 16,766 0.66 0.47 0.00 1.00$$\quad$$Offers mutual fund TDFs 16,766 0.50 0.50 0.00 1.00$$\quad$$Single record keeper (SRK) 16,766 0.75 0.43 0.00 1.00$$\quad$$Fraction of TDFs managed by SRK 7,687 0.76 0.42 0.00 1.00$$\quad$$Fraction of non-TDFs managed by SRK? 7,687 0.39 0.28 0.00 1.00 Measures of firm risk in 2009$$\quad$$CAPM beta (firm-level) 1,740 1.37 0.91 –1.26 8.65$$\quad$$Standard deviation of total returns 1,740 0.17 0.10 0.04 1.27$$\quad$$Standard deviation of predicted returns 1,740 0.10 0.06 0.00 0.60$$\quad$$Standard deviation of residual returns 1,740 0.14 0.08 0.03 1.12$$\quad$$CAPM beta (3-digit industry-level) 16,301 1.21 0.48 0.14 2.57 Measures of mutual fund risk in 2009$$\quad$$CAPM beta of 2010 TDF 6,677 0.63 0.07 0.40 0.90$$\quad$$CAPM beta of 2020 TDF 7,581 0.78 0.06 0.63 1.00$$\quad$$CAPM beta of 2030 TDF 7,491 0.91 0.04 0.76 1.03$$\quad$$CAPM beta of 2040 TDF 7,641 0.96 0.04 0.85 1.04$$\quad$$CAPM beta of 2050 TDF 6,504 0.98 0.04 0.87 1.04$$\quad$$Average CAPM beta of mutual fund TDFs 8,277 0.79 0.06 0.32 1.02$$\quad$$Average CAPM beta of other mutual funds 14,064 0.83 0.15 –1.69 1.58 We obtained data on 16,766 investment menus from BrightScope, Inc. The unit of observation is retirement plan$$i$$offered by firm$$j$$in industry$$k$$in 2010. The sample is limited to single-employer 401(k) and 403(b) retirement plans. Plan-level characteristics include assets under management (across all investment options), the number of participants with positive account balances, the age of the plan in years, and dummy variables indicating whether the plan is a 401(k) plan; offers autoenrollment; offers company stock as an investment option; offers any mutual funds as investment options; offers any mutual funds, separate accounts, or collective trusts that behave like TDFs; offers mutual fund TDFs; and employs a single recordkeeper (SRK). For the subset of 7,687 plans that offer TDFs and have a single recordkeeper that is an asset management firm, we calculate the fraction of TDFs and non-TDFs that are managed by the SRK. We report several measures of firm risk. For those firms with publicly traded equity, we estimate a CAPM beta (using the 24 monthly stock returns through December 2009). In addition, we report the standard deviation of actual monthly returns (over the same 24 months), the standard deviation of systematic monthly returns (based on the CAPM beta and return on the market portfolio), and the standard deviation of alphas. To determine the industry-level CAPM beta, we assign each firm the median CAPM beta of the sample of publicly traded firms that share the same first 3 digits of the North American Industrial Classification System (NAICS) code. To measure mutual fund risk, we estimate a CAPM beta (using the 24 monthly fund returns through December 2009). We report estimated betas separately for TDFs with target retirement dates of 2010, 2020, 2030, 2040, and 2050, for the full sample of TDFs, and for the sample of non-TDFs. The number of observations varies both because not all plans offer TDFs and because not all mutual funds could be matched to CRSP. Table 7 BrightScope sample: Summary statistics N Mean SD Min Max Plan characteristics in 2010$$\quad$$Assets (in millions) 16,766 134.62 708.67 0.01 36,741.60$$\quad$$Number of participants (in thousands) 16,766 2.00 8.08 0.00 306.61$$\quad$$Plan age in years 16,766 22.94 13.45 0.00 95.00$$\quad$$401(k) plan 16,766 0.91 0.29 0.00 1.00$$\quad$$Autoenrollment 16,766 0.23 0.42 0.00 1.00$$\quad$$Offers company stock 16,766 0.13 0.33 0.00 1.00$$\quad$$Offers any mutual funds 16,766 0.85 0.36 0.00 1.00$$\quad$$Offers any TDFs 16,766 0.66 0.47 0.00 1.00$$\quad$$Offers mutual fund TDFs 16,766 0.50 0.50 0.00 1.00$$\quad$$Single record keeper (SRK) 16,766 0.75 0.43 0.00 1.00$$\quad$$Fraction of TDFs managed by SRK 7,687 0.76 0.42 0.00 1.00$$\quad$$Fraction of non-TDFs managed by SRK? 7,687 0.39 0.28 0.00 1.00 Measures of firm risk in 2009$$\quad$$CAPM beta (firm-level) 1,740 1.37 0.91 –1.26 8.65$$\quad$$Standard deviation of total returns 1,740 0.17 0.10 0.04 1.27$$\quad$$Standard deviation of predicted returns 1,740 0.10 0.06 0.00 0.60$$\quad$$Standard deviation of residual returns 1,740 0.14 0.08 0.03 1.12$$\quad$$CAPM beta (3-digit industry-level) 16,301 1.21 0.48 0.14 2.57 Measures of mutual fund risk in 2009$$\quad$$CAPM beta of 2010 TDF 6,677 0.63 0.07 0.40 0.90$$\quad$$CAPM beta of 2020 TDF 7,581 0.78 0.06 0.63 1.00$$\quad$$CAPM beta of 2030 TDF 7,491 0.91 0.04 0.76 1.03$$\quad$$CAPM beta of 2040 TDF 7,641 0.96 0.04 0.85 1.04$$\quad$$CAPM beta of 2050 TDF 6,504 0.98 0.04 0.87 1.04$$\quad$$Average CAPM beta of mutual fund TDFs 8,277 0.79 0.06 0.32 1.02$$\quad$$Average CAPM beta of other mutual funds 14,064 0.83 0.15 –1.69 1.58 N Mean SD Min Max Plan characteristics in 2010$$\quad$$Assets (in millions) 16,766 134.62 708.67 0.01 36,741.60$$\quad$$Number of participants (in thousands) 16,766 2.00 8.08 0.00 306.61$$\quad$$Plan age in years 16,766 22.94 13.45 0.00 95.00$$\quad$$401(k) plan 16,766 0.91 0.29 0.00 1.00$$\quad$$Autoenrollment 16,766 0.23 0.42 0.00 1.00$$\quad$$Offers company stock 16,766 0.13 0.33 0.00 1.00$$\quad$$Offers any mutual funds 16,766 0.85 0.36 0.00 1.00$$\quad$$Offers any TDFs 16,766 0.66 0.47 0.00 1.00$$\quad$$Offers mutual fund TDFs 16,766 0.50 0.50 0.00 1.00$$\quad$$Single record keeper (SRK) 16,766 0.75 0.43 0.00 1.00$$\quad$$Fraction of TDFs managed by SRK 7,687 0.76 0.42 0.00 1.00$$\quad$$Fraction of non-TDFs managed by SRK? 7,687 0.39 0.28 0.00 1.00 Measures of firm risk in 2009$$\quad$$CAPM beta (firm-level) 1,740 1.37 0.91 –1.26 8.65$$\quad$$Standard deviation of total returns 1,740 0.17 0.10 0.04 1.27$$\quad$$Standard deviation of predicted returns 1,740 0.10 0.06 0.00 0.60$$\quad$$Standard deviation of residual returns 1,740 0.14 0.08 0.03 1.12$$\quad$$CAPM beta (3-digit industry-level) 16,301 1.21 0.48 0.14 2.57 Measures of mutual fund risk in 2009$$\quad$$CAPM beta of 2010 TDF 6,677 0.63 0.07 0.40 0.90$$\quad$$CAPM beta of 2020 TDF 7,581 0.78 0.06 0.63 1.00$$\quad$$CAPM beta of 2030 TDF 7,491 0.91 0.04 0.76 1.03$$\quad$$CAPM beta of 2040 TDF 7,641 0.96 0.04 0.85 1.04$$\quad$$CAPM beta of 2050 TDF 6,504 0.98 0.04 0.87 1.04$$\quad$$Average CAPM beta of mutual fund TDFs 8,277 0.79 0.06 0.32 1.02$$\quad$$Average CAPM beta of other mutual funds 14,064 0.83 0.15 –1.69 1.58 We obtained data on 16,766 investment menus from BrightScope, Inc. The unit of observation is retirement plan$$i$$offered by firm$$j$$in industry$$k$$in 2010. The sample is limited to single-employer 401(k) and 403(b) retirement plans. Plan-level characteristics include assets under management (across all investment options), the number of participants with positive account balances, the age of the plan in years, and dummy variables indicating whether the plan is a 401(k) plan; offers autoenrollment; offers company stock as an investment option; offers any mutual funds as investment options; offers any mutual funds, separate accounts, or collective trusts that behave like TDFs; offers mutual fund TDFs; and employs a single recordkeeper (SRK). For the subset of 7,687 plans that offer TDFs and have a single recordkeeper that is an asset management firm, we calculate the fraction of TDFs and non-TDFs that are managed by the SRK. We report several measures of firm risk. For those firms with publicly traded equity, we estimate a CAPM beta (using the 24 monthly stock returns through December 2009). In addition, we report the standard deviation of actual monthly returns (over the same 24 months), the standard deviation of systematic monthly returns (based on the CAPM beta and return on the market portfolio), and the standard deviation of alphas. To determine the industry-level CAPM beta, we assign each firm the median CAPM beta of the sample of publicly traded firms that share the same first 3 digits of the North American Industrial Classification System (NAICS) code. To measure mutual fund risk, we estimate a CAPM beta (using the 24 monthly fund returns through December 2009). We report estimated betas separately for TDFs with target retirement dates of 2010, 2020, 2030, 2040, and 2050, for the full sample of TDFs, and for the sample of non-TDFs. The number of observations varies both because not all plans offer TDFs and because not all mutual funds could be matched to CRSP. The advantage of using plan data from 2010 to test for risk matching is that plan sponsors were able to choose from the full range of TDFs introduced following the PPA. Table 7 reveals considerable dispersion in firm risk, whether measured by the CAPM beta or the standard deviation of residual returns. Consistent with our earlier analysis, it also reveals significant dispersion in the CAPM betas of the TDFs offered within the plans. For example, the estimated CAPM betas of 2020 TDFs range from 0.63 to 1.00. Within our sample, there are 7,687 retirement plans that offer TDFs and employ an SRK that is also an asset management firm. When we distinguish investment options managed by SRKs from investment options managed by other asset management firms, we find that 76% of TDFs are managed by SRKs versus 39% of non-TDF investments. That plan sponsors disproportionately offer the TDFs of their recordkeepers is suggestive evidence against risk matching, but only if plan sponsors are not choosing recordkeepers based on the TDFs that they offer.34 To formally test for a correlation between the riskiness of a firm and the riskiness of the TDF that the firm offers to its employees, we estimate the following cross-sectional model: \begin{eqnarray} \mbox{TDF risk}_{ijk} = a + b\ \mbox{firm risk}_{j} + c^\top X_{i} + e_{ijk}, \end{eqnarray} (3) where$$\mbox{TDF risk}_{ijk}$$measures of the risk of the TDF(s) offered in plan$$i$$sponsored by firm$$j$$in industry$$k$$, and$$\mbox{firm risk}_{j}$$measures the risk of the plan sponsor. For each target date, we subtract the average CAPM beta (or idiosyncratic volatility) of TDFs with the same target date and then average the target date-level tilts across all target dates. The resultant plan-level tilt is the dependent variable. If there is any form of risk matching, the estimated coefficient on$$\mbox{firm risk}_{j}$$will be nonzero. The$$X_{i}$$vector includes several plan-level (i.e., demand-side) controls. Because plan sponsors may focus more on TDF risk when plans feature autoenrollment, we include a dummy indicating if the plan features autoenrollment and, in some specifications, an interaction between the measure of firm risk and the dummy indicating if the plan has autoenrollment. Our measure of plan-level risk is the average risk of the non-TDF mutual fund options. We also include the natural logarithm of plan assets, the natural logarithm of plan participants, a dummy indicating if the plan offers company stock. The$$X_{i}$$vector also includes several family-level (i.e., supply-side) controls. Because we find that plans are more likely to offer the TDFs of their recordkeepers, we include either a dummy equal to one if plan$$i$$has an SRK, or the market share of the SRK’s investment options in the BrightScope sample. The prediction, based on our earlier findings, is that TDFs offered by families with a higher share of the 401(k) market will exhibit lower levels of risk-taking.35 We also include dummy variables indicating whether the TDF is offered by a pre-PPA family with low market share or a post-PPA family with low market share. These variables allow us to explore whether we continue to observe higher levels of risk-taking by low market share families that appear on at least one investment menu. In some specifications, we include a separate fixed effect for each industry (defined using the first 3 digits of the NAICS code), to control for average differences in firm risk across industries. Standard errors are clustered by industry. We include in the analysis plans that offer at least one TDF that BrightScope classifies as a mutual fund regardless of the target date, for a total of 7,983 retirement plans, 968 of which are offered by a publicly traded firm. We report the regression results in Table 8. Within the sample of publicly traded firms, the estimated regression coefficients on firm risk are negative, but they are neither statistically nor economically distinguishable from zero. While the adjusted$$R^2$$in the first specification is 11.57%, most of the explanatory power is coming from the supply-side variables. When we exclude the SRK and low market share dummy variables, the adjusted$$R^2$$is only 2.18%. Moreover, the modest increase in adjusted$$R^2$$(from 11.57% to 14.21%) when we introduce industry fixed effects, suggests limited matching of TDF risk to average industry risk. Among the demand-side variables, we find that TDF risk decreases with plan assets and increases with the number of plan participants, but neither effect is economically large. Table 8 Testing for risk matching in plan-level data Panel A Dependent variable: Average CAPM beta tilt of TDFs in plan$$i$$CAPM beta of firm$$j$$–0.002 –0.001 –0.003 (0.002) (0.003) (0.003) Median CAPM beta within 0.005** 0.004 0.006 0.006$$\quad$$industry of firm$$j$$(0.002) (0.003) (0.004) (0.004) Median CAPM beta –0.007** –0.007**$$\quad\times$$Autoenrollment (0.003) (0.003) Single record keeper (SRK)? –0.020*** –0.018*** –0.007*** (0.004) (0.005) (0.002) Market share of SRK –0.138*** –0.103*** –0.104*** –0.107***$$\quad$$within BrightScope (0.024) (0.012) (0.011) (0.012) TDF from Pre-PPA family –0.010*** –0.009** –0.018*** –0.008*** –0.010*** –0.009*** –0.009***$$\quad$$with Low market share (0.004) (0.004) (0.006) (0.002) (0.003) (0.003) (0.003) TDF from Post-PPA family 0.091*** 0.089*** 0.077*** 0.096*** 0.102*** 0.102*** 0.101***$$\quad$$with Low market share (0.017) (0.019) (0.016) (0.006) (0.006) (0.006) (0.006) ln(plan assets) –0.007*** –0.007*** –0.006* –0.008*** –0.006*** –0.006*** –0.006*** (0.002) (0.003) (0.003) (0.001) (0.001) (0.001) (0.001) ln(number of participants) 0.005** 0.006** 0.005 0.004*** 0.003** 0.003** 0.003** (0.002) (0.003) (0.003) (0.001) (0.001) (0.001) (0.001) Autoenrollment 0.001 0.001 –0.001 0.001 0.000 0.008** 0.008** (0.002) (0.002) (0.002) (0.001) (0.001) (0.004) (0.004) Offer company stock? 0.000 –0.002 –0.007** 0.005** 0.002 0.002 0.002 (0.003) (0.003) (0.003) (0.002) (0.002) (0.002) (0.002) Average risk of non-TDFs 0.045**$$\quad$$offered by plan$$j$$(0.022)$$H_0$$: Low$$\times$$Pre-PPA$$\qquad$$= Low$$\times$$Post-PPA 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** Industry fixed effects? — Yes Yes — — — —$$N$$968 968 758 7,983 5,504 5,504 5,504 Adj.$$R^2$$(excl. supply-side) 2.18% 5.73% 5.73% 3.39% 3.39% 3.44% 3.45% Adj.$$R^2$$11.57% 14.21% 19.25% 14.86% 19.41% 19.50% 19.61% Panel B Dependent variable: Standard deviation of idiosyncratic returns tilt of TDFs in plan$$i$$Idiosyncratic risk of firm$$j$$–0.002 0.004 0.004 (0.040) (0.047) (0.054) Median idiosyncratic risk within –0.069 –0.116* –0.159** –0.179**$$\quad$$industry of firm$$j$$(0.050) (0.062) (0.073) (0.072) Median idiosyncratic risk 0.164 0.168$$\quad\times$$Autoenrollment (0.109) (0.108) Single record keeper (SRK)? –0.007 –0.006 0.016** (0.012) (0.013) (0.006) Market share of SRK –0.346*** –0.306*** –0.307*** –0.289***$$\quad$$within BrightScope (0.082) (0.071) (0.071) (0.070) TDF from Pre-PPA family 0.133*** 0.128*** 0.087** 0.097*** 0.081*** 0.080*** 0.086***$$\quad$$with Low market share (0.033) (0.035) (0.041) (0.009) (0.019) (0.019) (0.018) TDF from Post-PPA family 0.176*** 0.159** 0.023 0.216*** 0.167*** 0.167*** 0.167***$$\quad$$with Low market share (0.060) (0.066) (0.031) (0.017) (0.025) (0.025) (0.026) ln(plan assets) –0.031*** –0.032*** –0.038*** –0.035*** –0.038*** –0.038*** –0.038*** (0.007) (0.009) (0.007) (0.003) (0.004) (0.004) (0.004) ln(number of participants) 0.019*** 0.022** 0.028*** 0.021*** 0.023*** 0.023*** 0.022*** (0.007) (0.010) (0.009) (0.002) (0.003) (0.003) (0.003) Autoenrollment –0.010 –0.011 –0.014* 0.005 0.006 –0.014 –0.014 (0.008) (0.008) (0.008) (0.004) (0.006) (0.014) (0.014) Offer company stock? –0.012 –0.002 –0.003 –0.007 –0.005 –0.005 –0.001 (0.009) (0.011) (0.012) (0.007) (0.008) (0.008) (0.008) Average risk of non-TDFs 1.627*$$\quad$$offered by plan$$j$$(0.851)$$H_0$$: Low$$\times$$Pre-PPA$$\qquad$$= Low$$\times$$Post-PPA 0.517 0.687 0.172 0.000*** 0.000*** 0.000*** 0.000*** Industry fixed effects? — Yes Yes — — — —$$N$$968 968 758 7,983 5,504 5,504 5,504 Adj.$$R^2$$(excl. supply-side) 5.50% 8.60% 8.60% 5.84% 5.84% 5.85% 6.64% Adj.$$R^2$$11.58% 13.86% 20.57% 14.23% 19.54% 19.56% 20.66% Panel A Dependent variable: Average CAPM beta tilt of TDFs in plan$$i$$CAPM beta of firm$$j$$–0.002 –0.001 –0.003 (0.002) (0.003) (0.003) Median CAPM beta within 0.005** 0.004 0.006 0.006$$\quad$$industry of firm$$j$$(0.002) (0.003) (0.004) (0.004) Median CAPM beta –0.007** –0.007**$$\quad\times$$Autoenrollment (0.003) (0.003) Single record keeper (SRK)? –0.020*** –0.018*** –0.007*** (0.004) (0.005) (0.002) Market share of SRK –0.138*** –0.103*** –0.104*** –0.107***$$\quad$$within BrightScope (0.024) (0.012) (0.011) (0.012) TDF from Pre-PPA family –0.010*** –0.009** –0.018*** –0.008*** –0.010*** –0.009*** –0.009***$$\quad$$with Low market share (0.004) (0.004) (0.006) (0.002) (0.003) (0.003) (0.003) TDF from Post-PPA family 0.091*** 0.089*** 0.077*** 0.096*** 0.102*** 0.102*** 0.101***$$\quad$$with Low market share (0.017) (0.019) (0.016) (0.006) (0.006) (0.006) (0.006) ln(plan assets) –0.007*** –0.007*** –0.006* –0.008*** –0.006*** –0.006*** –0.006*** (0.002) (0.003) (0.003) (0.001) (0.001) (0.001) (0.001) ln(number of participants) 0.005** 0.006** 0.005 0.004*** 0.003** 0.003** 0.003** (0.002) (0.003) (0.003) (0.001) (0.001) (0.001) (0.001) Autoenrollment 0.001 0.001 –0.001 0.001 0.000 0.008** 0.008** (0.002) (0.002) (0.002) (0.001) (0.001) (0.004) (0.004) Offer company stock? 0.000 –0.002 –0.007** 0.005** 0.002 0.002 0.002 (0.003) (0.003) (0.003) (0.002) (0.002) (0.002) (0.002) Average risk of non-TDFs 0.045**$$\quad$$offered by plan$$j$$(0.022)$$H_0$$: Low$$\times$$Pre-PPA$$\qquad$$= Low$$\times$$Post-PPA 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** Industry fixed effects? — Yes Yes — — — —$$N$$968 968 758 7,983 5,504 5,504 5,504 Adj.$$R^2$$(excl. supply-side) 2.18% 5.73% 5.73% 3.39% 3.39% 3.44% 3.45% Adj.$$R^2$$11.57% 14.21% 19.25% 14.86% 19.41% 19.50% 19.61% Panel B Dependent variable: Standard deviation of idiosyncratic returns tilt of TDFs in plan$$i$$Idiosyncratic risk of firm$$j$$–0.002 0.004 0.004 (0.040) (0.047) (0.054) Median idiosyncratic risk within –0.069 –0.116* –0.159** –0.179**$$\quad$$industry of firm$$j$$(0.050) (0.062) (0.073) (0.072) Median idiosyncratic risk 0.164 0.168$$\quad\times$$Autoenrollment (0.109) (0.108) Single record keeper (SRK)? –0.007 –0.006 0.016** (0.012) (0.013) (0.006) Market share of SRK –0.346*** –0.306*** –0.307*** –0.289***$$\quad$$within BrightScope (0.082) (0.071) (0.071) (0.070) TDF from Pre-PPA family 0.133*** 0.128*** 0.087** 0.097*** 0.081*** 0.080*** 0.086***$$\quad$$with Low market share (0.033) (0.035) (0.041) (0.009) (0.019) (0.019) (0.018) TDF from Post-PPA family 0.176*** 0.159** 0.023 0.216*** 0.167*** 0.167*** 0.167***$$\quad$$with Low market share (0.060) (0.066) (0.031) (0.017) (0.025) (0.025) (0.026) ln(plan assets) –0.031*** –0.032*** –0.038*** –0.035*** –0.038*** –0.038*** –0.038*** (0.007) (0.009) (0.007) (0.003) (0.004) (0.004) (0.004) ln(number of participants) 0.019*** 0.022** 0.028*** 0.021*** 0.023*** 0.023*** 0.022*** (0.007) (0.010) (0.009) (0.002) (0.003) (0.003) (0.003) Autoenrollment –0.010 –0.011 –0.014* 0.005 0.006 –0.014 –0.014 (0.008) (0.008) (0.008) (0.004) (0.006) (0.014) (0.014) Offer company stock? –0.012 –0.002 –0.003 –0.007 –0.005 –0.005 –0.001 (0.009) (0.011) (0.012) (0.007) (0.008) (0.008) (0.008) Average risk of non-TDFs 1.627*$$\quad$$offered by plan$$j$$(0.851)$$H_0$$: Low$$\times$$Pre-PPA$$\qquad$$= Low$$\times$$Post-PPA 0.517 0.687 0.172 0.000*** 0.000*** 0.000*** 0.000*** Industry fixed effects? — Yes Yes — — — —$$N$$968 968 758 7,983 5,504 5,504 5,504 Adj.$$R^2$$(excl. supply-side) 5.50% 8.60% 8.60% 5.84% 5.84% 5.85% 6.64% Adj.$$R^2$$11.58% 13.86% 20.57% 14.23% 19.54% 19.56% 20.66% The unit of observation is the single-employer DC retirement plan$$i$$offered by firm$$j$$in industry$$k$$in 2010. The dependent variable measures the risk of the TDFs offered by plan$$i$$. In panel A, our measure of risk is the average target-date adjusted tilt in CAPM beta. In panel B, it is the average target-date adjusted standard deviation of idiosyncratic monthly returns. The sample is limited to the 95.8% of plans that offer TDFs from a single family. The independent variables of interest are analogous measures of firm-level or industry-level risk. Plan-level (i.e., demand-side) independent variables include the natural logarithm of retirement plan$$i$$assets in 2010; the natural logarithm of the number of plan$$i$$participants in 2010; a dummy equal to one if plan$$i$$has autoenrollment; a dummy equal to one if plan$$i$$offers company stock; the average risk of non-TDF mutual funds in plan$$i$$; and an interaction between the measure of firm risk and the dummy indicating if the plan has autoenrollment. Family-level (i.e., supply-side) independent variables include a dummy equal to one if plan$$i$$has a single recordkeeper (SRK); the market share of the SRK’s investments in BrightScope in 2010; a dummy equal to one if TDFs are offered by a Pre-PPA family with Low market share in 2009; and a dummy equal to one if TDFs are offered by a Post-PPA family with Low market share in 2009. Some specifications include a separate fixed effect for each of the 70 industries (defined by the first 3 digits of the NAICS code). Estimation performed via OLS. Standard errors are clustered by industry. *, **, and *** denote statistical significance at the 10% level, 5% level, and 1% level, respectively. Adjusted$$R^2$$fall significantly when we exclude the supply-side variables. Table 8 Testing for risk matching in plan-level data Panel A Dependent variable: Average CAPM beta tilt of TDFs in plan$$i$$CAPM beta of firm$$j$$–0.002 –0.001 –0.003 (0.002) (0.003) (0.003) Median CAPM beta within 0.005** 0.004 0.006 0.006$$\quad$$industry of firm$$j$$(0.002) (0.003) (0.004) (0.004) Median CAPM beta –0.007** –0.007**$$\quad\times$$Autoenrollment (0.003) (0.003) Single record keeper (SRK)? –0.020*** –0.018*** –0.007*** (0.004) (0.005) (0.002) Market share of SRK –0.138*** –0.103*** –0.104*** –0.107***$$\quad$$within BrightScope (0.024) (0.012) (0.011) (0.012) TDF from Pre-PPA family –0.010*** –0.009** –0.018*** –0.008*** –0.010*** –0.009*** –0.009***$$\quad$$with Low market share (0.004) (0.004) (0.006) (0.002) (0.003) (0.003) (0.003) TDF from Post-PPA family 0.091*** 0.089*** 0.077*** 0.096*** 0.102*** 0.102*** 0.101***$$\quad$$with Low market share (0.017) (0.019) (0.016) (0.006) (0.006) (0.006) (0.006) ln(plan assets) –0.007*** –0.007*** –0.006* –0.008*** –0.006*** –0.006*** –0.006*** (0.002) (0.003) (0.003) (0.001) (0.001) (0.001) (0.001) ln(number of participants) 0.005** 0.006** 0.005 0.004*** 0.003** 0.003** 0.003** (0.002) (0.003) (0.003) (0.001) (0.001) (0.001) (0.001) Autoenrollment 0.001 0.001 –0.001 0.001 0.000 0.008** 0.008** (0.002) (0.002) (0.002) (0.001) (0.001) (0.004) (0.004) Offer company stock? 0.000 –0.002 –0.007** 0.005** 0.002 0.002 0.002 (0.003) (0.003) (0.003) (0.002) (0.002) (0.002) (0.002) Average risk of non-TDFs 0.045**$$\quad$$offered by plan$$j$$(0.022)$$H_0$$: Low$$\times$$Pre-PPA$$\qquad$$= Low$$\times$\$Post-PPA  0.000***  0.000***  0.000***  0.000***  0.000***  0.000***  0.000***  Industry fixed e