Robert Stambaugh Paper

Do Funds Make More When They Trade More?

ˇLuboˇs P´astor
Robert F. Stambaugh
Lucian A. Taylor *

February 9, 2015

Abstract

We find that active mutual funds perform better after trading more. This time-series relation between a fund’s turnover and its subsequent benchmarkadjusted return is especially strong for small, high-fee funds. These results are consistent with high-fee funds having greater skill to identify time-varying profit opportunities and with small funds being more able to exploit those opportunities. In addition to this novel evidence of managerial skill and fund-level decreasing returns to scale, we find evidence of industry-level decreasing returns: The positive turnover-performance relation weakens when funds act more in concert. We also identify a common component of fund trading that is correlated with mispricing proxies and helps predict fund returns.

*P´astor is at the University of Chicago Booth School of Business. Stambaugh and Taylor are at the Wharton School of the University of Pennsylvania. Email:lubos.pastor@chicagobooth.edu, stambaugh@ wharton.upenn.edu, luket@wharton.upenn.edu. We are grateful for comments from Jonathan Berk, Gene Fama, Vincent Glode, Todd Gormley, Christian Hansen, Marcin Kacperczyk, David Musto, Jonathan Reuter, Sergei Sarkissian, Clemens Sialm, and the audiences at the 2014 German Finance Association conference and the following universities and other institutions: Aalto, BI Oslo, Cass, Cheung Kong, Chicago, Copenhagen, Houston, Mannheim, McGill, NBIM, NHH Bergen, SAIF, Tsinghua PBCSF, Tsinghua SEM, and Wharton. We are also grateful to Yeguang Chi and Gerardo Manzo for superb research assistance.

1. Introduction

Mutual funds invest trillions of dollars on behalf of retail investors. The lion’s share of this money is actively managed, despite the growing popularity of passive investing.1 Whether skill guides the trades of actively managed funds has long been an important question, given active funds’ higher fees and trading costs. We take a fresh look at skill by analyzing time variation in active funds’ trading activity. We explore a simple idea: A fund trades more when it perceives greater profit opportunities. If the fund has the ability to identify and exploit those opportunities, then it should earn greater profit after trading more heavily.
We find that funds do earn more after trading more heavily. Specifically, a fund’s turnover positively predicts the fund’s subsequent benchmark-adjusted return. This new evidence of skill comes from our sample of 3,126 active U.S. equity mutual funds from 1979 through 2011. The result is significant not only statistically but also economically: a one-standarddeviation increase in turnover is associated with a 0.65% per year increase in performance for the typical fund. Funds seem to know when it’s a good time to trade.

The turnover-performance relation is stronger for funds that charge higher fees as well as funds that are smaller in size. These results further support the presence of skill and provide novel evidence of decreasing returns to scale at the individual-fund level. Because smaller funds trade smaller amounts, decreasing returns to scale associated with liquidity costs allow smaller funds to better exploit time-varying profit opportunities. Identifying those opportunities requires skill, and managers with greater skill should earn higher fees. Our results suggest that higher-fee funds are more skilled at identifying time-varying profit opportunities, and that smaller funds can better exploit those opportunities. Small, high-fee funds also have especially volatile turnover, consistent with their having greater abilities to identify and exploit time-varying opportunities.

Fund trading has a common component that appears to be related to mispricing in the stock market. Average turnover across funds-essentially the first principal component of turnover-is significantly related to three proxies for potential mispricing: investor sentiment, cross-sectional dispersion in individual stock returns, and aggregate stock market liquidity. Funds trade more when sentiment or dispersion is high or liquidity is low, suggesting that stocks are more mispriced when funds collectively perceive greater profit opportunities.

These perceptions seem justified, because average turnover positively predicts a fund’s

1As of 2013, mutual funds worldwide have about $30 trillion of assets under management, half of which is managed by U.S. funds. About 52% of U.S. mutual fund assets are held in equity funds, and 81.6% of the equity funds’ total net assets are managed actively (Investment Company Institute, 2014).

future return, even when we control for the fund’s own turnover. This predictive relation is highly significant: a one-standard-deviation increase in average turnover is associated with a 0.80% per year increase in fund performance. A fund’s performance can thus be predicted not only by its own turnover but also by other funds’ turnover. More trading by other funds appears to indicate greater profit opportunities in general. Any opportunity identified by a given fund is likely to be more profitable if there is generally more mispricing at that time, as indicated by other funds’ heavy trading.

The positive relation between average turnover and future fund returns is weaker in periods when funds act more in concert, as measured by the average correlation among the funds’ benchmark-adjusted returns. This evidence is consistent with decreasing returns to scale at the level of the active-management industry (see P´astor and Stambaugh, 2012, and P´astor, Stambaugh, and Taylor, 2014). When funds act in concert, pursuing the same profit opportunities, prices move and those opportunities become harder to find.

The relation between a fund’s return and lagged average turnover becomes even stronger when the average is calculated only across funds in the same size-fee category as the given fund. The turnover of other same-category funds thus seems to be a better signal of the fund’s profit opportunities than the turnover of different-category funds. This result suggests that funds in different size-fee categories pursue somewhat different opportunities.

We provide an investment perspective on the turnover-performance relation by applying a novel mapping between time-series regressions and investment strategies. We show that the estimated slope coefficient from our regression of a fund’s return on its lagged turnover is closely related to the average return of a strategy that dynamically allocates between the fund and its benchmark. The strategy invests more in the fund following higher turnover by the fund. When implemented for all funds and combined with a short position in the strategy’s static counterpart, this “timing” strategy produces an impressive annual Sharpe ratio of 0.79, which exceeds the Sharpe ratios of the market, size, value, and momentum factors over the same 1979–2011 period. This finding provides an additional perspective on the economic significance of the turnover-performance relation identified by our study.

Finally, we consider a cross-sectional investment strategy that captures an element of the time-series relation between turnover and performance. Every month, we sort funds into portfolios based on the ratio of a fund’s recent turnover to the trailing historical average of that fund’s turnover. We find that funds whose turnover is high based on this ratio tend to outperform funds whose turnover is low. Funds that have recently traded more than usual perform especially well when there are better profit opportunities in the market, as judged by high sentiment. This strategy’s performance is statistically significant, but it is weaker than the performance of the timing strategy, which is more directly motivated by our turnover-performance relation.

The literature investigating the skill of active mutual funds is extensive. Average past performance delivers a seemingly negative verdict, since many studies show that active funds have underperformed passive benchmarks, net of fees.2 Yet active funds can have skill. Skilled funds might charge higher fees, and some funds might be more skilled than others. Moreover, with fund-level or industry-level decreasing returns to scale, skill does not equate to average performance, either gross or net of fees.3

Our investigation of skill adds a new dimension to the literature on the relation between mutual fund turnover and fund performance. The empirical evidence on this relation is mixed. For example, Elton, Gruber, Das, and Hlavka (1993) and Carhart (1997) find a negative turnover-performance relation, Wermers (2000) and Edelen, Evans, and Kadlec (2007) find no significant relation, and Dahlquist, Engstr¨om and S¨oderlind (2000) and Chen, Jagadeesh and Wermers (2001) find a positive relation. The main difference between these studies and ours is that all of these studies examine the cross-sectional relation between turnover and performance, whereas we focus on the time-series relation.4

We obtain our time-series results from panel regressions of fund returns on lagged fund turnover and various controls, including fund fixed effects. Fund fixed effects are crucial for finding a positive turnover-performance relation. With fund fixed effects, identification comes from within-fund time variation in turnover and performance, not from the crosssectional variation exploited in the prior studies mentioned above. If we drop fund fixed effects, the positive turnover-performance relation weakens to marginally significant. The relation wanes further if we replace fund fixed effects with month fixed effects, thereby isolating pure cross-sectional variation. These results underline the time-series nature of the turnover-performance relation. We do not find that higher-turnover funds perform better; we find that a given fund performs better when it trades more.

To help interpret our results from panel regressions with fixed effects, we present a formula for the slope coefficient from such regressions estimated in an unbalanced panel. The slope

2See, for example, Jensen (1968), Elton, Gruber, Das, and Hlavka (1993), Malkiel (1995), Gruber (1996), Carhart (1997),Wermers (2000), P´astor and Stambaugh (2002), and Fama and French (2010), among others. 3See Berk and Green (2004), P´astor and Stambaugh (2012), Berk and van Binsbergen (2014), P´astor, Stambaugh, and Taylor (2014), and Stambaugh (2014). 4The two studies that find a positive relation differ from our study in other ways as well. Dahlquist, Engstr¨om and S¨oderlind find this positive relation in a small sample of Swedish mutual funds (80 funds in 1993–1997); our sample of U.S. funds is much larger. Chen, Jagadeesh and Wermers find this relation based on the returns of the funds’ disclosed stock holdings, whereas we analyze the returns of the funds themselves.

from a panel regression with fund fixed effects is a weighted average of the slopes estimated fund by fund in pure time-series regressions of return on turnover. Greater weight is given to funds with longer samples and more volatile turnover. Analogously, with month fixed effects, the panel regression slope is a weighted average of the month-by-month estimates in pure cross-sectional regressions of return on turnover. More generally, our formula also clarifies the relation between a panel regression slope and the well-known estimator of Fama and MacBeth (1973). The Fama-MacBeth estimator emerges as a special case from a panel regression with month fixed effects if the panel is balanced and the cross-sectional variance of the independent variable is constant over time.

While we find that funds perform better after increasing their trading activity, others have related fund activity to performance in different ways. Kacperczyk, Sialm, and Zheng (2005) find that funds that are more active in the sense of having more concentrated portfolios perform better. Kacperczyk, Sialm, and Zheng (2008) find that a fund’s actions between portfolio disclosure dates, as summarized by the “return gap,” positively predict fund performance. Cremers and Petajisto (2009) find that funds that deviate more from their benchmarks, as measured by “active share,” perform better. Cremers, Ferreira, Matos, and Starks (2014) find similar results. In the same spirit, Amihud and Goyenko (2013) find better performance among funds having lower R-squareds from benchmark regressions. These studies are similar to ours in that they also find that more active funds perform better, but there are two important differences. First, all of these studies measure fund activity in ways different from ours. Second, all of them identify cross-sectional relations between activity and performance, whereas we establish a time-series relation.

Given this time-series perspective, our study is also related to the literature on time variation in mutual fund performance. Some authors, inspired by Ferson and Schadt (1996), model performance as a linear function of conditioning variables (e.g., Avramov and Wermers, 2006). Others relate fund performance to the business cycle (e.g., Moskowitz, 2000, Glode, 2011, Kosowski, 2011, and Kacperczyk, van Nieuwerburgh, and Veldkamp, 2013, 2014), to aggregate market returns (Glode, Hollifield, Kacperczyk, and Kogan, 2012), and to time variation in fund risk (e.g., Brown, Harlow, and Starks, 1996, and Huang, Sialm, and Zhang, 2011). None of these studies relate fund performance to fund turnover.

While we analyze funds’ ability to time their turnover, others have investigated the value of active fund management by examining different fund actions. Chen, Jegadeesh, and Wermers (2000) find that stocks recently bought by funds in aggregate outperform stocks recently sold, suggesting that funds have stock-picking skill. Baker, Litov, Wachter, and Wurgler (2010) find that much of this outperformance takes place around corporate earnings announcements, indicating one likely source of the funds’ skill. Cohen, Coval, and P´astor (2005) find that funds whose portfolio decisions are similar to those of other funds with strong track records perform better. Cohen, Frazzini, and Malloy (2008) find that fund managers perform better when they trade shares of firms they are connected to through their educational networks. Like us, all of these studies report that active management adds value, but they examine different dimensions of fund skill. Our finding that funds are able to successfully time their trading activity seems new in the literature.

Lastly, our analysis of the common variation in fund turnover is related to the literature on correlated trading behavior of mutual funds, or “herding.” Early studies include Nofsinger and Sias (1999) and Wermers (1999). More recently, Koch, Ruenzi, and Starks (2010) and Karolyi, Lee, and van Dijk (2012) argue that such correlated trading gives rise to commonality in liquidity among stocks. Commonality in individual stock turnover is analyzed by Lo and Wang (2000), Cremers and Mei (2007), and others. None of these studies examine fund turnover. Our analysis of the common component of fund turnover seems novel.

The rest of the paper is organized as follows. Section 2 documents the basic turnoverperformance relation. Section 3 examines this relation across categories of funds based on size and fees. Section 4 analyzes the common component of turnover and its predictive power for fund returns. Section 5 provides two investment perspectives on the turnover-performance relation. Section 6 concludes.

2. The Turnover-Performance Relation

Active mutual funds pursue alpha-returns in excess of their benchmarks. The funds’ managers perceive opportunities for producing alpha and trade to exploit them. A manager trades more when he identifies more alpha-producing opportunities, so a skilled manager should perform better after he trades more. We look for such evidence of skill by estimating the relation between a fund’s turnover and its subsequent return. We specify this turnover-performance relation for a given fund i as the linear regression

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The skill we investigate is an ability to exploit opportunities in period t − 1 for which a nontrivial fraction of the payoff occurs in period t. A prime example is a purchase of an underpriced security in period t − 1 followed by the correction of the mispricing in period t. One can imagine other forms of skill that we would not detect. For example, a fund could have skill to identify short-horizon opportunities, such as liquidity provision, that deliver all of their profits in the same period in which the fund trades to exploit those opportunities. Such skill would impart no time-series relation between turnover in period t−1 and performance in period t. Similarly, the turnover-performance relation would be very weak, possibly undetectable, for a fund skilled only in identifying long-horizon opportunities that deliver most of their payoffs after the next period. Moreover, detecting skill using the turnover-performance relation requires variation over time in the extent to which profitable opportunities arise. In principle, a fund could be skilled at identifying opportunities that arise to the same extent every period. Such skill would impart no variation over time in trading and expected payoffs. Although the turnover-performance relation cannot detect all forms of skill, it nevertheless provides novel insights into the ability of funds to identify and exploit time-varying profit opportunities.

We explore the turnover-performance relation using the dataset constructed by P´astor, Stambaugh, and Taylor (2014), who combine CRSP and Morningstar data to obtain a sample of 3,126 actively managed U.S. domestic equity mutual funds covering the 1979–2011 period. To measure the dependent variable Ri,t, we follow the above study in using GrossRi,t, the fund’s net return minus the return on the benchmark index designated by Morningstar, plus the fund’s monthly expense ratio taken from CRSP. We use gross rather than net returns because our goal is to measure a fund’s ability to outperform a benchmark, not the value delivered to clients after fees. We estimate all regressions at a monthly frequency, but a fund’s turnover is reported only as the total for its fiscal year. Thus, we measure turnover, Xi,t−1, by the variable FundTurni,t−1, which is the fund’s turnover for the most recent 12- month period that ends before month t. This measure, reported by CRSP, is defined by the SEC as the lesser of the fund’s total purchases and sales, divided by the fund’s 12-month average total net asset value. By largely excluding turnover arising from flows to and from the fund, this measure reflects portfolio decisions to replace some holdings with others. We winsorize FundT urni,t−1 at the 1st and 99th percentiles.

To increase the power of our inferences in equation (1), we estimate a pooled time-series and cross-sectional regression that imposes the restriction

b1 = b2 = · · · = b ,               (2)

either across all funds or across funds within size-fee categories discussed later. We include fund fixed effects, so that b reflects only the contribution of within-fund time variation in turnover. The fund fixed effects correspond to the ai’s in equation (1) when the restriction in (2) is imposed across all funds. When later allowing b to differ across size-fee categories, we also include fixed effects for those categories, in which case a fund’s ai equals the sum of its fund and category fixed effects. The regression specification combining equations (1) and (2), which isolates the time-series contribution of turnover to performance, is our main specification. For comparison, we also consider other specifications, as we explain next.

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2.2. Robustness

The positive turnover-performance relation documented above, which is our main result, is robust to a variety of specification changes. We summarize the robustness results here and report them in detail in the online appendix, which is available on our websites. We have already shown that the turnover-performance relation obtains whether or not month fixed effects are included in the panel regression, which rules out all aggregate variables as the source of this relation. Furthermore, the relation obtains when we include benchmarkmonth fixed effects, ruling out any variables measured at the benchmark-month level.7 An example of such a variable is benchmark turnover, which can be reflected in a fund’s turnover to the extent that some of the fund’s trading passively responds to reconstitutions of the fund’s benchmark index. Adding benchmark-month fixed effects has a tiny effect on the estimated turnover-performance relation, strengthening our interpretation of this relation as being driven by skilled active trading. The relation also obtains, and is equally strong, when gross fund returns are replaced by net returns.

Importantly, the positive turnover-performance relation does not obtain in a placebo test in which we replace active funds by passive index funds, as identified by Morningstar. When we produce the counterpart of Table 1 for the universe of passive funds, we find no slope coefficient significantly different from zero. In fact, the estimated slope coefficients in the specifications with fund fixed effects are not even positive (the corresponding t-statistics in the bottom row of Table 1 are -0.51 and -1.07). This result is comforting because passive funds should not exhibit any skill in identifying time-varying profit opportunities. The fact that the turnover-performance relation emerges for active funds but not passive funds supports our skill-based interpretation of this relation.

Additional support for our interpretation comes from another placebo test, in which we replace our turnover measure, FundT urn, by flow-driven turnover. Funds often trade in response to inflows and outflows of capital. Such flow-driven trading is fairly mechanical in that its timing is determined mostly by the fund’s investors rather than the fund’s manager. Therefore, we expect flow-driven turnover to exhibit a weaker relation to fund performance compared to FundT urn, which largely excludes flow-driven trading, as noted earlier. To test this hypothesis, we construct two measures of flow-driven fund turnover. Both measures rely on monthly dollar flows, which we back out from the monthly series of fund size and fund returns, and both cover the same 12-month period as FundT urn. The first measure is

7Gormley and Matsa (2014), among others, advocate the use of a fixed-effects estimator as a way of controlling for unobserved group heterogeneity in finance applications.

the sum of the absolute values of the 12 monthly dollar flows, divided by the average fund size during the 12-month period. The second measure is the smaller of two sums, one of all positive dollar flows and one of all negative flows during the 12-month period, divided by average fund size. Consistent with our hypothesis, we find that neither measure of flowdriven turnover has any predictive power for fund returns, whether or not we include various controls such as FundT urn. Moreover, the inclusion of flow-driven turnover does not affect the significant predictive power of FundT urn for fund returns.

We estimate the turnover-performance relation at the monthly frequency. Even though funds report their turnover only annually, most of the variables used in our subsequent analysis, such as fund returns, fund size, industry size, sentiment, volatility, liquidity, correlation, and business-cycle indicators, are available on a monthly basis. Therefore, we choose the monthly frequency in an effort to utilize all available information. Nonetheless, when we reestimate the turnover-performance relation by using annual fund returns, we find a positive and highly significant time-series relation, just like in Table 1. In addition, we consider a specification that allows the slope coefficient from the monthly turnover-performance regression to depend on the number of months between the end of the 12-month period over which FundT urn is measured and the month in which the fund return is computed. Specifically, we add a term to the right-hand side of the regression that interacts the above number of months with FundT urn. We find that the interaction term does not enter significantly, suggesting that our constant-slope specification is appropriate.

Our turnover-performance relation captures the predictive power of FundT urn in a given fiscal year for fund performance in the following fiscal year (e.g., turnover in 2014 predicts returns in 2015). In principle, some fund trades could take longer to play out (e.g., a trade in 2014 could lead to profits in 2016).8 To test for such long-horizon effects, we add two more lags of FundT urn to the right-hand side of regression (7). We find that neither of those additional lags has any predictive power for returns after controlling for the most recent value of FundT urn, which retains its positive and significant coefficient. Therefore, we use only the most recent FundT urn in the rest of our analysis.
The positive turnover-performance relation emerges not only from the panel regression in Table 1, which imposes the restriction (2), but also from fund-by-fund regressions. For each fund i, we estimate the slope coefficient bi from the time-series regression in equation (1) in the full sample. We find that 61% of the OLS slope estimates bi are positive. Moreover, 9% (4%) of the bi‘s are significantly positive at the 5% (1%) confidence level. A weighted

8The relations between fund performance and funds’ investment horizons are analyzed by Yan and Zhang (2009), Cremers and Pareek (2014), and Lan and Wermers (2014), among others. average of these bi‘s appears in the bottom left cell of Table 1, as shown in equation (8).

Mutual funds sometimes benefit from receiving allocations of shares in initial public offerings (IPOs) at below-market prices. Lead underwriters tend to allocate more IPO shares to fund families from which they receive larger brokerage commissions (e.g., Reuter, 2006). To the extent that higher commissions are associated with higher turnover, this practice could potentially contribute to a positive turnover-performance relation. This contribution is unlikely to be substantial, though. Fund families tend to distribute IPO shares across funds based on criteria such as past returns and fees rather than turnover (Gaspar, Massa, and Matos, 2006). In addition, the high commissions that help families earn IPO allocations often reflect an elevated commission rate rather than high family turnover, and they are often paid around the time of the IPO rather than over the previous fiscal year.9 Moreover, the contribution of IPO allocations to fund performance seems modest. For each year between 1980 and 2013, we calculate the ratio of total money left on the table across all IPOs, obtained from Jay Ritter’s website, to total assets of active domestic equity mutual funds, obtained from the Investment Company Institute. This ratio, whose mean is 0.30%, exceeds the contribution of IPO allocations to fund performance because mutual funds receive only about 25% to 41% of IPO allocations, on average.10 IPOs thus boost average fund performance by only about 7.5 to 12 basis points per year. Furthermore, the IPO market has cooled significantly since year 2000. Money left on the table has decreased to only 0.10% of fund assets on average, so that IPOs have boosted average fund performance by only 2.5 to 4 basis points per year since January 2001. Yet the turnover-performance relation remains strong during this cold-IPO-market subperiod: the slope estimates in the bottom row of Table 1 remain positive and significant, with t-statistics in excess of 3.2.

We benchmark each fund’s performance against the index selected for each fund category by Morningstar. For example, for small-cap value funds, the benchmark is the Russell 2000 Value Index. Such an index-based adjustment is likely to adjust for fund style and risk more precisely than the commonly used loadings on the three Fama-French factors. The Fama-French factors are popular in mutual fund studies because their returns are freely available, unlike the Morningstar benchmark index data. Yet the Fama-French factors are not obvious benchmark choices because they are long-short portfolios whose returns cannot be costlessly achieved by mutual fund managers. Cremers, Petajisto, and Zitzewitz (2013) argue that the Fama-French model produces biased assessments of fund performance, and they recommend using index-based benchmarks instead. We follow this advice. But we find very similar results when we adjust fund returns by using the three Fama-French factors or

9See, for example, Nimalendran, Ritter, and Zhang (2007) and Goldstein, Irvine, and Puckett (2011). 10These estimates are from Reuter (2006), Ritter and Zhang (2007), and Field and Lowry (2009).

the four factors that also include momentum. In both cases, the slope coefficients in the top row of Table 1 remain insignificant while the slopes in the bottom row continue to be highly significant, with t-statistics ranging from 7.14 to 8.76.

We assess fund performance by subtracting the benchmark return from the fund’s return, effectively assuming that the fund’s benchmark beta is equal to one. This simple approach is popular in investment practice, and it circumvents the need to estimate the funds’ betas. When we estimate those betas using OLS, we find very similar results. To avoid using imprecise beta estimates for short-lived funds, we replace OLS betas of funds having track records shorter than 24 months by the average beta of funds in the same Morningstar category. Just as in Table 1, we find that the slope estimates in the top row are insignificant while the slopes in the bottom row are highly significant, with t-statistics of about 7.6.

The test described in the previous paragraph assumes that each fund’s beta is timeinvariant. In a separate test, we allow fund betas to vary over time. This test helps us assess whether the turnover-performance relation could be driven by time variation in systematic risk. If high turnover were associated with more risk, then the higher returns following high turnover could simply represent compensation for risk. However, it is not clear a priori why higher turnover should be followed by more as opposed to less systematic risk. Moreover, we do not fund any such relation in the data. When we model fund betas as a linear function of FundT urn, we find results very similar to those in Table 1.

We report all of our results based on the full sample period of 1979–2011. In addition, we verify the robustness of our results in the 2000–2011 subperiod, motivated by two potential structural changes in the data. The first change relates to the way CRSP reports turnover. Prior to September 1998, all funds’ fiscal years are reported as January–December, raising the possibility of inaccuracy, since after 1998 the timing of funds’ fiscal years varies across funds.11 The second change, identified by P´astor, Stambaugh, and Taylor (2014), relates to the reporting of fund size and expense ratios before 1993. Using the 2000–2011 subperiod provides a robustness check that is conservative in avoiding both potential structural changes. We find that all of our main conclusions are robust to using the 2000–2011 subperiod. For example, the time-series turnover-performance relation in Table 1 remains positive and significant, with t-statistics of 4.37 and 3.74 in the bottom row. In the online appendix, we report the counterparts of all of our tables estimated in the 2000–2011 subperiod.

11In private communication, CRSP explained that this change in reporting is related to the change in its fund data provider from S&P to Lipper on August 31, 1998. CRSP has also explained the timing convention for turnover, which is the variable turn ratio in CRSP’s fund fees file. If the variable fiscal yearend is present in the file, turnover is measured over the 12-month period ending on the fiscal yearend date; otherwise turnover is measured over the 12-month period ending on the date marked by the variable begdt.

3. Fund Size and Fees Matter

Our evidence so far reveals that the typical fund performs better after it trades more. Next, we ask whether this turnover-performance relation differs across funds. We focus on two readily observed fund characteristics, a fund’s size and its expense ratio (or “fee,” for short). Both characteristics are related to fund performance. Fund size matters because larger funds tend to trade larger amounts. In the presence of decreasing returns to scale associated with liquidity costs, larger funds are less able to exploit alpha-producing opportunities (e.g., Perold and Salomon, 1991). Identifying those opportunities requires skill, and managers with greater skill should receive greater fee revenue in equilibrium (e.g., Berk and Green, 2004). Among funds of similar size, a manager with greater skill should thus have a higher expense ratio.

We explore the roles of fund size and fees in the turnover-performance relation. For each month t, we compute the terciles of FundSizei,t−1 and ExpenseRatioi,t−1, the most recent values of size and fees available from CRSP prior to month t. Each fund in the sample in month t is assigned to one of the resulting size and fee categories. We then estimate the turnover-performance relation, first separately within each of the size and fee categories and then within each of the nine size-fee categories for the 3 Ö 3 classification. To do so, we add fixed effects for the categories to the previous specification containing fund fixed effects. We estimate separate slopes on FundT urni,t−1 for each category, thereby imposing the restriction in equation (2) only within a category.

Table 2 reports the estimated slope coefficients on turnover. We see that both fund size and fees matter in the turnover-performance relation: the turnover coefficient is decreasing in fund size and increasing in expense ratio. The role of fund size is dramatic. In the one-way sort, small funds have a turnover coefficient of 0.00186 (t-statistic: 7.56), whereas mediumsized funds have a coefficient not even half as big, equal to 0.00086 (t = 3.74). The coefficient for large funds is lower by another half and insignificant-only 0.00043 (t = 1.46). Fees also play a strong role, even though the turnover-performance relation is significantly positive in all fee categories. In the one-way sort, the turnover coefficients increase monotonically in fees, producing a significant high-low difference (t = 4.06) and a high-fee coefficient three times higher than the low-fee value (0.00170 versus 0.00058).

The results in Table 2 for the 3 Ö 3 two-way sort are consistent with the effects of size and fees discussed above. For a given level of one characteristic, the other characteristic matters in the same direction as in the one-way sort results, judging by the signs of the small-large (size) and high-low (fee) differences. The joint roles of size and fees also imply a larger turnover coefficient for small, high-fee funds than for large, low-fee funds. That difference is indeed positive, with a t-statistic of 3.55. Small, high-fee funds have the largest t-statistic and the second largest slope coefficient among the nine fund categories.

The strong turnover-performance relation for small, high-fee funds has especially large economic significance because turnover is most volatile for those funds. Table 3 reports summary statistics for turnover within the size and fee categories. Panel B shows that FundT urni,t−1 for small, high-fee funds has a standard deviation of 0.547, as compared to 0.438 for all funds and only 0.379 for large, low-fee funds. In general, turnover volatility is increasing in fees and decreasing in fund size. Suppose we translate a one-standard-deviation difference in turnover to a difference in subsequent return. This measure of economic significance is especially large for small, high-fee funds, because their turnover has not only a large slope but also high volatility. Combining these values from Tables 2 and 3 implies that a one-standard-deviation increase in turnover for small, high-fee funds translates to an increase in expected return of 1.25% per year (= 0.00191 Ö 0.547 Ö 1200). This is a large effect, both relative to other funds and in absolute terms. Relative to other funds, the corresponding value for large, low-fee funds is only 0.21% (= 0.00046 Ö 0.379 Ö 1200), and the value for all funds, reported earlier, is 0.65%. In absolute terms, the 1.25% expected return increase is comparable to the average GrossRi,t of small, high-fee funds, which is 0.0938% per month, or 1.13% per year, as shown in Table 4. Interestingly, Table 4 also shows that smaller funds outperform larger funds, and high-fee funds outperform low-fee funds, in gross returns (though not in net returns). These patterns are similar to those in Table 2, suggesting that the turnover-performance relation might play a role in overall fund performance.

The importance of fund size in the turnover-performance relation in Table 2 presents novel evidence of decreasing returns to scale at the fund level. Prior studies of fund-level decreasing returns generally look for a direct negative relation between a fund’s return and its size.12 While point estimates from such approaches are often consistent with decreasing returns, statistical significance is elusive when applying methods that avoid econometric biases (see P´astor, Stambaugh, and Taylor, 2014). The disadvantage of a fund’s being large instead emerges here as a weaker relation, or even no relation, between the fund’s trading and its subsequent performance, in sharp contrast to the strong positive relation for small funds. Unlike the directly estimated relation between fund size and return, the role of fund size in the turnover-performance relation is highly significant, both economically and statistically.

More trading should produce higher returns the greater is the manager’s skill in identifying profitable opportunities. Managers with more skill should receive more fee revenue, as

12See, for example, Chen, Hong, Huang, and Kubik (2004), Yan (2008), and Reuter and Zitzewitz (2013).

noted earlier. Fee revenue is proportional to the expense ratio for a given fund size, implying a positive partial correlation between skill and expense ratio, conditional on size. Recall from the results of the two-way sort that within each size category, the turnover-performance relation is stronger for high-fee funds, consistent with such funds having greater skill. A one-way sort similarly reveals a stronger relation for high-fee funds, consistent with a positive simple correlation between skill and expense ratio. The latter correlation does not necessarily follow, as it depends on how size covaries with fees and skill in the cross-section, but it seems reasonable for managers with greater skill to charge higher fee rates.

Besides fees, we consider two additional proxies for fund skill. First, we calculate gross alpha adjusted for both fund-level and industry-level returns to scale, following P´astor, Stambaugh, and Taylor (2014). Second, we take the unadjusted gross alpha over the fund’s lifetime. For both proxies, we find that high-skill funds exhibit a significantly stronger turnover-performance relation than low-skill funds. These results, which are consistent with those in Table 2 based on fees, are in the online appendix. The appendix also shows additional robustness results. For example, all the conclusions from Table 2 continue to hold if we replace benchmark-adjusted fund returns by returns adjusted for the three Fama-French factors or the four factors that also include momentum. The same is true if we allow the factor model betas to vary over time as a linear function of fund turnover. In addition, while the regressions in Table 2 exclude month fixed effects, including such fixed effects produces very similar results, and so does including benchmark-month fixed effects. Overall, our results suggest that high-fee funds have greater skill in identifying time-varying profit opportunities, and small funds are more able to exploit those opportunities.

Small funds also have higher average turnover than large funds. This result, shown in Panel A of Table 3, is consistent with a natural skill-based sorting of managers. Some managers are more skilled at identifying short-lived opportunities yielding profits over short horizons, while others are more adept at identifying opportunities with longer holding periods that allow patient trading. In a competitive market for managerial talent, one would expect the short-horizon managers to manage small funds: the liquidity constraints that bite when trades must be done quickly render their talents less useful in trading large amounts. In contrast, one would expect the long-horizon managers to manage large funds: their skills can be more profitably exploited by trading larger amounts, since their trades can be executed more patiently. Therefore, this sorting mechanism implies that smaller funds should hold their positions over shorter periods. This implication is supported by Panel A of Table 3, because the higher average turnover of smaller funds suggests those funds have shorter holding periods. The sorting mechanism also implies that larger funds should have more persistent turnover due to more patient trading. Indeed, Panel C of Table 3 shows that turnover of larger funds exhibits higher autocorrelation.

Our analysis focuses on two salient fund characteristics, size and fees. In addition, we ask whether the strength of the turnover-performance relation varies with fund style. Following the 3 Ö 3 Morningstar style box, we split funds into small-cap, mid-cap, and large-cap categories, and also separately into value, blend, and growth categories. For each style, we calculate a turnover-performance regression slope coefficient, producing a table analogous to Table 2. We report this table in the online appendix. The table shows that the turnoverperformance relation is positive and significant across all fund styles with the sole exception of mid-cap growth, for which the t-statistic is 1.60. The relation is about equally strong for value and growth funds, but it is significantly stronger for small-cap funds than for large-cap funds. This result is consistent with the common argument that mispricing is more likely to be found among small-cap stocks, which tend to exhibit lower institutional ownership and less analyst coverage compared to large-cap stocks. It makes sense for funds’ ability to spot and exploit trading opportunities to be stronger in stocks that are more mispriced.

4. What Other Funds Do Matters

We have shown that if Fund ABC trades more than usual this period, the fund typically performs better than usual next period. Suppose now that many other funds trade more than usual this period. Are there implications for the performance of Fund ABC? On the one hand, this heavier trading by other funds could be good news for Fund ABC. If there is more mispricing this period, as indicated by many funds trading more, then any opportunities identified by Fund ABC could be more profitable. On the other hand, if the other funds are identifying the same opportunities and thus acting in concert, their heavier trading could produce especially large price impacts, reducing mispricing that would otherwise benefit Fund ABC. This section considers both of these potential effects in exploring whether the turnover-performance relation depends on the trading activity of other funds. We begin by considering a mispricing-based explanation for common variation in fund turnover. We then investigate how that common variation impacts the turnover-performance relation.

4.1. Mispricing and Trading

When do funds, viewed collectively, trade more than usual? If alpha-producing opportunities arise from mispricing, then periods with more mispricing should be those when funds trade more. A simple measure of the common component in fund trading is the cross-sectional average of individual fund turnover. We let AvgTurnt denote average turnover contemporaneous with month t, that is, the average turnover across funds’ 12-month fiscal periods that contain month t. AvgTurnt, plotted in Panel A of Figure 1, fluctuates between 59% and 102% per year from 1979 to 2011.13 This series has a 95% correlation with the first principal component of individual fund turnover. We ask whether AvgTurnt is higher when mispricing is more likely. We use three proxies for the likelihood of mispricing: Sentimentt, V olatilityt, and Liquidityt. The three series are plotted in Panel B of Figure 1.

The first mispricing proxy, Sentimentt, is the value in month t of Baker and Wurgler’s (2006, 2007) investor-sentiment index. If sentiment-driven investors participate more heavily in the stock market during high-sentiment periods, the mispricing such investors create is more likely to occur during those periods (e.g., Stambaugh, Yu, and Yuan, 2012). We thus expect funds exploiting such mispricing to trade more when sentiment is high. Consistent with this prediction, a regression of AvgTurnt on Sentimentt produces a significantly positive coefficient (t = 3.17), as shown in the first column of Table 5. We include a time trend in the regression, given the positive trend in AvgTurnt evident in Figure 1. As reported in the last row, the R2 in the regression including Sentimentt exceeds the R2 when regressing on just the time trend by 0.171.

The second mispricing proxy, V olatilityt, is the cross-sectional standard deviation in month t of the returns on individual U.S. stocks.14
The rationale for this variable is that higher volatility corresponds to greater uncertainty about future values and thus greater potential for investors to err in assessing those values. As a result, periods of high volatility admit greater potential mispricing, and we expect funds exploiting such mispricing to trade more when volatility is high. Consistent with this prediction, a regression of AvgTurnt on V olatilityt produces a significantly positive coefficient (t = 7.23), as shown in column 2 of Table 5. The R2 in that regression, which again includes a time trend, exceeds the R2 in the trend-only regression by 0.189.

The third proxy, Liquidityt, is the value in month t of the stock-market liquidity measure of P´astor and Stambaugh (2003). Empirical evidence suggests that higher liquidity is accompanied by greater market efficiency (e.g., Chordia, Roll, and Subrahmanyam, 2008, 2011). In other words, periods of lower liquidity are more susceptible to mispricing. Therefore, we might expect funds to trade more when liquidity is lower. On the other hand, lower liquidity

13CRSP turnover data are missing in 1991 for unknown reasons. We therefore treat AvgTurn as missing in 1991 in our regressions. In Figure 1, though, we fill in average turnover in 1991 by using Morningstar data, for aesthetic purposes. We rely on CRSP turnover data in our analysis because Morningstar is ambiguous about the timing of funds’ fiscal years. 14We thank Bryan Kelly for providing this series.
also implies higher transaction costs, which could discourage funds from trading. Our evidence suggests that the former effect is stronger: Regressing AvgTurnt on Liquidityt yields a significantly negative coefficient (t = −4.14), reported in column 3 of Table 5. Including Liquidityt increases the R2 versus the trend-only regression by 0.024, a more modest increase than produced by the other two proxies.

When all three mispricing proxies are included simultaneously as regressors, each enters with a coefficient and t-statistic very similar to when included just by itself. This allinclusive regression, reported in column 4 of Table 5, also adds two additional variables that control for potential effects of the business cycle and recent stock-market returns, but neither variable enters significantly. (The two variables are the Chicago Fed National Activity Index and the return on the CRSP value-weighted market index over the previous 12 months.) The combined ability of the three mispricing proxies to explain variance in AvgTurnt is substantial: the R2 exceeds that of the trend-only regression by 0.324.15 Overall, the results make sense: funds trade more when there is more mispricing.

What mispricing are funds exploiting? To see whether funds trade based on well-known market anomalies, we regress the returns of eleven such anomalies, as well as their composite return, on lagged average fund turnover. The eleven anomalies, whose returns we obtain from Stambaugh, Yu, and Yuan (2012), involve sorting stocks based on two measures of financial distress, two measures of stock issuance, accruals, net operating assets, momentum, gross profitability, asset growth, return on assets, and the investment-to-assets ratio. We find no significant slopes on average turnover. To the extent that funds trade more when there is more mispricing, they must be exploiting mispricing beyond these eleven anomalies.

Finally, we consider the role of stock market turnover in explaining AvgTurnt. We measure market turnover as total dollar volume over the previous 12 months divided by total market capitalization of ordinary common shares in CRSP. Market turnover reflects trading by all entities, includingmutual funds, so it could potentially be related to AvgTurnt. It could also be related to Sentimentt, which is constructed as the first principal component of six variables that include NYSE turnover. However, when we add market turnover to the all-inclusive specification in Table 5, it does not enter significantly, whereas the slope on Sentimentt remains positive and significant. The other two mispricing proxies also retain their signs and significance, and the remaining variables remain insignificant. In short,

15If we exclude the time trend from the regressions, we find results similar to those reported in Table 5. V olatility and Liquidity continue to enter significantly with the same signs as in Table 5, and the business cycle and market return remain insignificant. The only difference relates to Sentiment, whose coefficient retains the positive sign but loses statistical significance. This evidence suggests that Sentiment is better at capturing deviations of AvgTurn from its trend than in capturing the raw variation in AvgTurn.

adding market turnover does not affect any of our inferences in Table 5.

4.2. Other Funds: Evidence That They Matter

Next, we investigate how the trading of other funds enters the turnover-performance relation. We first ask whether average lagged fund turnover, which reflects commonality in fund trading, helps predict a given fund’s subsequent performance. We denote average lagged fund turnover, or the average of FundTurni,t−1 across i, by AvgTurnt−1.16 The first column of Table 6 reports the result of replacing FundTurni,t−1 by AvgTurnt−1 and then repeating the regression from the bottom left cell of Table 1, which includes fund fixed effects.17 We see a significantly positive coefficient on AvgTurnt−1 (t = 2.13), indicating that the common component of fund trading helps predict individual fund performance. The estimated slope coefficient, 0.00741, implies substantial economic significance. Given the time-series standard deviation of AvgTurnt−1, 0.090, a one-standard-deviation increase in the variable translates to an increase in expected return of 0.80% per year (= 0.00741 Ö 0.090 Ö 1200).

The information in AvgTurnt−1 about a fund’s subsequent performance is undiminished by conditioning on the fund’s own turnover. The results in column 2 of Table 6 reveal that the coefficient and t-statistic for AvgTurnt−1 are little changed by controlling for FundTurni,t−1. The importance of either variable is insensitive to whether the other is included, because the average correlation between FundTurni,t−1 and AvgTurnt−1 is a modest 0.131 (the “all-all” value in Panel A of Table 7). Both turnover variables remain significant also after controlling for additional variables described below (columns 3 through 7 of Table 6).

A simple story emerges from the joint abilities of FundTurni,t−1 and AvgTurnt−1 to predict fund performance. A given fund’s turnover, FundTurni,t−1, is higher-and its subsequent performance is better-when its own manager identifies more alpha-producing opportunities. When many managers identify such opportunities, AvgTurnt−1 is higher, and there is more mispricing in general. Even when a fund’s own manager does not identify

16Note that AvgTurnt−1 uses only information available before month t because it is the average of turnovers computed over 12-month periods that end before month t. It is thus reasonable to use AvgTurnt−1 to predict performance in month t. Also note that the notation for time subscripts is complicated by the fact that funds report turnover only annually. In Section 4.1, we use the notation AvgTurnt to denote average turnover across funds’ 12-month fiscal periods that contain month t. That notation is slightly inconsistent with the notation in this section because given our definition of FundTurni,t, the contemporaneous average turnover in Section 4.1 is the average of FundTurni,t+11 across i. We prefer to use the notation AvgTurnt (instead of AvgTurnt+11) in Section 4.1 to emphasize the contemporaneous nature of the analysis in that section. We hope the reader will pardon this slight abuse of notation. 17Month fixed effects must be omitted because a common time series is used as a regressor for each fund. Also, the regressions in Table 6 exclude a time trend, but the results are very similar if we include one.

unusually many opportunities in a given period, the opportunities he does identify are likely to be more profitable if there is generally more mispricing in that period.

Heavier trading by other funds is not necessarily all good news, however. Other funds are competitors whose trades can move prices. A stronger presence of active managers in the stock market produces greater price corrections and thus lowers the active managers’ alphas. That is the idea behind the concept of industry-level decreasing returns to scale, introduced by P´astor and Stambaugh (2012). In line with that concept, P´astor, Stambaugh, and Taylor (2014) find empirically that fund performance is negatively related to the size of the active management industry. Following that study, we define IndustrySizet−1 as the value in month t − 1 of the total assets managed by all funds in our sample, divided by the total market value of U.S. stocks. Our evidence, shown in column 3 of Table 6, confirms a significantly negative relation between fund performance and IndustrySizet−1.

Industry size is one way of measuring the degree of competition among funds. Another way, which we introduce here, is to gauge the extent to which funds act in concert. We use a simple return-based measure, AvgCorrt−1, which is the average pairwise correlation between all individual funds’ benchmark-adjusted gross returns in the 12 months ending in month t− 1. AvgCorrt−1 fluctuates between 0.01 and 0.26 from 1979 to 2011. We interpret higher values of AvgCorrt−1 as indicating more concerted active trading by funds. We find that AvgCorrt−1 is negatively related to fund performance (t = −2.42; see column 4 of Table 6). This result is consistent with the interpretation that when funds trade more in concert, prices are impacted and profit opportunities are reduced.

The price impact of funds’ concerted trading should be stronger when those funds trade more heavily. Therefore, when AvgTurnt−1 is higher, the effect of AvgCorrt−1 on performance should be less favorable. Similarly, the more funds act in concert (i.e., the higher AvgCorrt−1), the less favorable should be their heavier trading (AvgTurnt−1). Either way, we expect fund performance to be negatively related to the interaction term AvgTurnt−1 Ö AvgCorrt−1. This is indeed the case, as shown in column 5 of Table 6 (t = −2.69). At the same time, the slope on AvgTurnt−1 remains positive and significant. We thus see simultaneous support for both the positive and negative aspects of heavier trading by other funds. This evidence suggests that the benefit of the greater mispricing reflected in other funds’ heavier trading is countered by greater price correction when those funds act more in concert.

This opposing effect of funds acting in concert is consistent with the previously discussed concept of industry-level decreasing returns to scale. The underlying mechanism behind that concept is that a larger industry implies more money chasing the same alpha-producing opportunities, thereby moving prices more and reducing each active fund’s alpha. Our measure of AvgTurnt−1 Ö AvgCorrt−1 directly addresses this effect of more money acting in concert. The significantly negative relation between this term and performance provides additional and novel evidence of industry-level decreasing returns to scale.

Interestingly, adding the interaction term in column 5 of Table 6 changes the sign of the slope on AvgCorrt−1 from negative to positive (t = 2.55). This result highlights a positive aspect of concerted fund trading, as measured by AvgCorrt−1. If funds choose to make similar trades at the same time, they must perceive those trades as attractive. If those funds are skilled, their perceptions are correct and their concerted trading thus indicates more mispricing, with favorable implications for performance. This positive effect of concerted trading is opposed by the negative effect discussed earlier. Which effect prevails depends on the amount of other funds’ trading. The estimates in column 5 indicate that when fund trading is light (i.e., AvgTurnt−1 is low), the positive effect prevails and AvgCorrt−1 is positively related to performance. When trading is heavy, though, the negative effect prevails. The negative effect also prevails on average, as shown in column 4. We thus see that the benefit of the greater mispricing signaled by other funds’ concerted trading is more than offset by the cost of greater price correction when those funds trade more heavily.

To explore the robustness of our inferences about how performance relates to what other funds do, we add the three mispricing proxies to the regression in Table 6 (column 6). We also allow FundTurni,t−1 to enter differently across the nine size-fee categories, as in Section 3 (column 7). In both specifications, the statistical significance of AvgTurnt−1, AvgCorrt−1, and their interaction is unaffected by the inclusion of the mispricing proxies, and the corresponding slope coefficients are close to those reported earlier. The three mispricing proxies enter with the same signs in predicting performance (Table 6) as they do in explaining the variation in AvgTurnt−1 (Table 5), though in Table 6 only Sentimentt−1 is significant (t = 3.42). This result suggests that turnover, with both its common and fund-specific dimensions, largely subsumes performance-relevant mispricing information in the other two mispricing proxies, V olatilityt−1 and Liquidityt−1. In contrast, Sentimentt−1 contains additional information about future fund performance.

So far we have treated other funds as being all other funds, for simplicity. For a given fund, “other” funds can also be defined more narrowly as those sharing the fund’s characteristics. Motivation for this alternative definition arises from Table 7. Panel A reports the correlation between FundTurni,t−1 and AvgTurnt−1, with the correlation averaged across all funds as well as across just the funds within a size and fee category. Panel B repeats the same calculations while replacing AvgTurnt−1 with OwnCellAvgTurnt−1, the average lagged turnover calculated across only those funds belonging to the same size and fee tercile as fund i in month t. When comparing Panels A and B, we see that FundTurni,t−1 has a lower average correlation with AvgTurnt−1 than it has with OwnCellAvgTurnt−1. This inequality holds for every one of the six one-way and nine two-way size and fee categories. These results reveal greater common variation in turnover among funds with similar sizes and fees than among all funds taken together.

If trading by other funds signals the presence of greater mispricing, then heavier trading by funds similar to one’s own could signal greater mispricing that is especially relevant. In other words, heavier trading by less similar funds could be less relevant to one’s own fund. This possibility is consistent with the above evidence that the turnover of one’s own fund typically comoves more with the turnover of funds that have similar size and fees. It is also consistent with the natural sorting mechanism discussed at the end of Section 3.

Since there is more commonality in turnover among similar funds, it is natural to ask whether similar funds’ trading helps explain performance. We run regressions similar to those in Table 6 but replace AvgTurnt−1 with OwnCellAvgTurnt−1. The results are in Table 8. We also add AvgTurnt−1 as an independent variable, allowing a horse race between it and its own-cell counterpart. The latter wins, consistent with the greater relevance of what other similar funds do. The t-statistics for OwnCellAvgTurnt−1, which range from 3.11 to 7.02, are uniformly higher than the corresponding t-statistics for AvgTurnt−1 in Table 6. Moreover, AvgTurnt−1 becomes insignificant, driven out by OwnCellAvgTurnt−1. Finally, AvgCorrt−1 plays a similar role as before: the interaction term OwnCellAvgTurnt−1 Ö AvgCorrt−1 enters significantly negatively (t = −2.90).

Overall, our results show that a fund’s performance is related not only to its own turnover but also to that of other funds, especially other similar funds. Heavier trading by other funds signals greater mispricing and is positively related to performance, but there is also an opposing negative relation to the extent that funds act in concert.

5. Investment Perspectives

In this section, we take an investment perspective to assess the economic significance of our regression results. We examine the performance of two investment strategies designed to exploit the turnover-performance relation.

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