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 w
