Portfolio concentration and mutual fund performance. Jon A. Fulkerson

Transcription

1 Portfolio concentration and mutual fund performance Jon A. Fulkerson School of Business Administration University of Dayton Dayton, OH Timothy B. Riley * tbriley@uark.edu Sam M. Walton College of Business University of Arkansas Fayetteville, AR First Draft: August 2016 This Draft: September 2017 * Contact author.

2 Portfolio concentration and mutual fund performance Abstract Mutual fund managers should choose to increase the concentration of their portfolio when they possess information of great enough expected value to offset the risks of increased concentration. Consistent with that idea, we find that fund performance improves after concentration increases. Because the riskiness of increased concentration varies between funds and over time, the expected value of the information required by managers before choosing to increase concentration should also vary. Among other results, we show that the concentrationperformance relation is stronger for funds with less institutional ownership and when investor sentiment is low.

3 Portfolio concentration and mutual fund performance A rational mutual fund manager should only accept additional risk if there is sufficient expected compensation for that risk. Consider two portfolios that are equivalent in all aspects except that one portfolio contains one hundred equally weighted equities and the other contains ten equally weighted equities. The portfolio of one hundred equities should have significantly less idiosyncratic volatility than the portfolio of ten equities. Since classic financial theory states that idiosyncratic volatility is not priced, a mutual fund manager must believe he will be compensated through some nonsystematic means to be willing to hold the more volatile portfolio. Further, a portfolio of one hundred equities should be more liquid than a portfolio of ten equities, since the cost of selling a small amount of many different equities is less than the cost of selling a large amount of a few equities. While various aspects of liquidity may be priced, mutual funds are required to offer daily redeemability to investors, which limits the fund s capacity to effectively capture those premiums. Therefore, a fund manager must believe he will be compensated through some nonsystematic means to consider holding the less liquid portfolio. More generally, there must be an expected benefit when fund managers choose to hold a more concentrated portfolio to justify the costs of decreased diversification. We contend that mutual fund managers are compensated for holding more concentrated portfolios through a concentrated portfolio s ability to give disproportionate weight to a fund manager s most valuable information. If a fund manager has no information of significant value, then holding a fully diversified portfolio is preferable, since there would be no expected performance benefit from concentrating to offset the risks. Conversely, if the fund manager does have information of significant value, then concentrating the portfolio on those securities most

4 affected by that information should increase the expected performance of the fund and potentially justify the risks of increased concentration. Some fund managers could have means other than increased portfolio concentration to take advantage of valuable information. However, in our analysis, we focus on the investment behavior of common equity funds that rarely use shorting, leverage, or derivatives, so increasing portfolio concentration is typically the only available route to leverage information of value. Our argument is similar to the Treynor and Black (1973) model of active portfolio management. In their base case, a manager with no information will choose to hold a passive market portfolio with no idiosyncratic volatility. As the manager gains information about expected future returns, the manager uses those expectations to construct an active portfolio. That active portfolio is then paired with the passive market portfolio such that the weights maximize the full portfolio s expected information ratio (i.e., expected alpha divided by expected idiosyncratic volatility). In this setting, when managers have high quality information about expected future returns, they will pursue a more concentrated portfolio despite the increased idiosyncratic volatility. When they have low quality information about expected future returns, they will hold a less concentrated portfolio and closely track the market portfolio. If some mutual fund managers do possess valuable information at some points in time, then we would expect fund performance to improve when a fund manager chooses to increase portfolio concentration. Such an action signals that the fund manager believes his current information set is valuable enough to offset the concentration risks. Consistent with that idea, we find that funds that increase the concentration of their portfolios do realize higher subsequent risk-adjusted returns. On average, a fund that increases its concentration by one standard deviation experiences an annualized 40 basis point increase in risk-adjusted return. This result 2

5 suggests that some fund managers do possess information of significant value at some points in time and that such information meaningfully affects the returns of fund investors. The trade-off between the benefits and costs of a more concentrated portfolio should vary in the cross-section of mutual funds. For example, managers of funds with less institutional ownership could accept greater risk when increasing the concentration of their portfolios. Less sophisticated retail investors are more likely to misperceive and react adversely to the potential negative outcomes of increased concentration. As a result, the managers of funds with less institutional ownership should require greater expected compensation before choosing to increase the concentration of their portfolios. We show that there is significant cross-sectional variation in the relation between concentration and performance depending on institutional ownership. A fund with low institutional ownership that increases its concentration by one standard deviation has an average increase in its annualized risk-adjusted return of 52 basis points, compared to about zero for funds with high institutional ownership. We also find some evidence that funds with less liquid equities and funds with more difficult to value equities have a stronger relation between concentration and performance. In a similar fashion, the trade-off between the benefits and costs of a more concentrated portfolio should vary for all mutual funds depending on market conditions. For example, when aggregate liquidity is low, a fund manager choosing to increase concentration must accept greater risk. Increased concentration limits the fund manager s ability to spread liquiditymotivated trades across many different positions, which could lead to large forced trades. Those trades will be particularly expensive if aggregate liquidity is low. Therefore, when aggregate liquidity is low, fund managers as a group should require greater expected compensation before choosing to increase the concentration of their portfolios. We show that aggregate liquidity does 3

6 have a significant effect on the relation between concentration and performance. A fund that increases its concentration by one standard deviation when aggregate liquidity is low has an average annualized increase in risk-adjusted return of 84 basis points, compared to about zero when aggregate liquidity is high. We likewise find that the relation between concentration and performance is stronger when expected volatility is high and investor sentiment is low. When considering these results, it is important to note that U.S. Securities and Exchange Commission (SEC) rules allow mutual funds to disclose their holdings with a 60-day delay. 1 As a result, there is a significant lag between when a concentration increase occurs and when investors observe that increase. That lag prevents investors from immediately responding to an increase in fund concentration by further diversifying their other holdings or selling the fund. The increased idiosyncratic volatility associated with a manager s choice to hold a more concentrated portfolio will unavoidably impact the overall risk of an investor s portfolio. That lag also prevents a trading strategy built around buying and selling funds in response to fund concentration changes from being profitable. Consistent with the value of a fund manager s information being time-varying and the costs of public disclosure, we find no empirical relation between concentration and risk-adjusted returns if we delay the use of our concentration measure until after it should be publically available. 2 Since investors cannot observe and profitably trade on changes in concentration, a Berk and Green (2004) style equilibrium in which investor flows respond to changes in concentration and prevent a relation between concentration and performance should not occur. 1 See Final Rule: Shareholder Reports and Quarterly Portfolio Disclosure of Registered Management Investment Companies 2 See Frank, Poterba, Shackelford, and Shoven (2004) for a full discussion of the potential costs of public disclosure of holdings by mutual funds. 4

7 Prior evidence on the relation between portfolio concentration and performance is mixed. On the one hand, Sapp and Yan (2008) find that more concentrated mutual funds underperform compared to less concentrated funds. On the other hand, Kacperczyk, Sialm, and Zheng (2005) find that funds concentrated within a small number of industries outperform less concentrated funds, and Ivkovic, Sialm, and Weisbenner (2008) show that households that hold more concentrated portfolios outperform households that hold less concentrated portfolios. However, these previous studies focus on cross-sectional differences in concentration. In our analysis, we consider the impact of the choice portfolio managers make to change the portfolio s concentration over time based on the time-varying value on their information set. That is, rather than test how funds with more concentrated portfolios perform compared to funds with less concentrated portfolios, we test whether individual funds perform better when their portfolios are more or less concentrated. Our model is similar in some respects to the model of Pastor, Stambaugh, and Taylor (2017). They show that mutual fund performance improves after turnover increases and contend that the relation occurs because fund managers choose to trade more when more profitable trading opportunities are available. The key difference between the models relates to costs. In their model, a fund should incur more costs when it trades more, but after the trading is complete the costs are sunk. In our model, funds could incur trading costs to increase concentration, but more importantly, increased concentration should create costs (e.g., increased volatility and decreased liquidity) which the fund must continue to pay and which are difficult to estimate in advance with precision. This difference in costs makes the fund manager s choice to increase concentration significantly different from the choice to increase the amount of trading. In an 5

8 expanded model, we show that controlling for turnover has little impact on the relation between concentration and performance. As a whole, our results have three key takeaways. First, we show that mutual fund managers choose to increase their portfolio concentration when there is sufficient expected compensation to offset the increased risk. Increasing concentration increases volatility and decreases liquidity, and fund managers demand compensation for accepting those risks. Second, our results suggest that some fund managers do possess valuable information at some points in time. If fund managers did not, then an increase in portfolio concentration should not be a positive predictor of a fund s risk-adjusted return. Third, we show that cross-sectional fund characteristics and time-varying market conditions have a significant impact on the costs of concentration. When fund characteristics or overall market conditions make increasing concentration a greater risk, fund managers require a greater expected compensation. We caution that our results do not imply that mutual funds as a group would benefit from increasing their portfolio concentration. The choice of an individual fund manager to increase concentration is a positive signal about the value of that manager s current information set relative to the current concentration risks. Other funds could be subject to greater concentration risks or have a less valuable information set. 1. Prior Work Kacperczyk, Sialm, and Zheng (2005) provide two potential reasons a mutual fund manager would increase portfolio concentration. First, the increase in idiosyncratic volatility that can be expected from increased concentration will benefit the fund manager if the costs of poor performance are small relative to the benefits from good performance. Chevalier and Ellison 6

9 (1997) and Sirri and Tufano (1998), among many others, find convexity in the relation between fund performance and flows. Funds with the best performance receive large inflows while funds with the worst performance receive relatively modest outflows. In this environment, idiosyncratic volatility can benefit the fund manager on average by increasing the likelihood of being one of the best performing funds. Brown, Harlow, and Starks (1996) show that fund managers with poor performance during the first half of the year will increase their volatility during the second half of the year, presumably in a gamble to rapidly improve their performance relative to other funds. Second, Kacperczyk, Sialm, and Zheng (2005) state that a mutual fund manager might increase portfolio concentration if his information set improves. In Treynor and Black s (1973) model of portfolio selection, a manager with no information should hold the market portfolio, but a manager with strong beliefs about particular securities should give those securities disproportionate weight by increasing portfolio concentration. Van Nieuwerburgh and Veldkamp (2010) consider the cost of information acquisition and find that a manager unwilling to undertake extensive search costs could also rationally hold a concentrated portfolio. Cohen, Polk, and Silli (2010) find that the largest positions in a fund s portfolio (i.e., the manager s best ideas ) significantly outperform, while Kacperczyk, Sialm, and Zheng (2005) find that fund managers that concentrate in a small number of industries outperform other fund managers. Both of those results imply that some funds benefit from portfolios concentrated in securities about which fund managers likely have their most valuable information. In our analysis, we focus on information-based motivations for increasing concentration rather than motivations driven by the shape of the flow-performance relation. The informationbased motivations should hold for portfolio management in general, not just for mutual funds 7

10 and their particular incentive structure. Furthermore, it is unclear whether mutual funds are actually subject to a convex flow-performance relation. Among U.S. equity funds, Spiegel and Zhang (2013) argue that the convex flow-performance relation is an artifact of a misspecified empirical model and show that such a relation does not exist if the model is properly specified; Clifford, Jordan, and Riley (2014) show that the convex relation is driven by a large number of very small funds and that the majority of assets in the industry are held by funds subject to a linear relation; and Kim (2013) finds the apparent convexity of the relation has diminished during the previous two decades. Among corporate bond funds, Chen and Qin (2017) find no evidence of a convex flow-performance relation, and Goldstein, Jiang, and Ng (2017) contend the relation is concave. The information-based motivations could initially appear inconsistent with the welldocumented underperformance of the average actively managed equity mutual fund. Jensen (1968), Ippolito (1989), and Gruber (1996) collectively study actively managed equity mutual funds from 1945 through 1994 using non-overlapping periods, and each finds a negative riskadjusted return after fees for the average fund in their sample. However, such results do not necessarily imply that fund managers do not ever possess valuable information. Chen, Jegadeesh, and Wermers (2000) find that the equities bought by funds significantly outperform the equities sold by funds, and Alexander, Cici, and Gibson (2007) show that purchases made by fund managers for purely valuation-motivated reasons outperform the market. Da, Gao, and Jagannathan (2011) identify a subset of funds that deliver persistent, positive risk-adjusted returns by trading heavily in equities affected by information events. Moreover, in the Berk and Green (2004) model, fund managers can consistently possess information of value but fail to consistently outperform the market due to decreasing returns to scale. Our analysis of the impact 8

11 of changes in concentration on fund performance provides a test of whether some fund managers do possess valuable information at some points in time. If fund managers information sets never have significant value, then concentrating a fund portfolio to give disproportionate weight to that information set should not have a positive effect on risk-adjusted performance. A mutual fund manager with valuable information must still balance the benefits of increased concentration against the costs. First, holding all else equal, total and idiosyncratic volatility will increase as portfolio concentration increases. Unless the fund manager s information set is valuable enough to offset that increased volatility, the fund could negatively impact common, simple evaluation metrics (e.g., the Sharpe ratio) by choosing to increase concentration. While the asset pricing literature has developed more sophisticated models for fund performance evaluation, Barber, Huang, and Odean (2016) and Berk and van Binsbergen (2016) both indicate that such relatively simple metrics still have a strong effect on fund flows. Second, choosing to increase concentration can also increase a fund s liquidity costs. Keim and Madhaven (1997) show that transaction costs for institutional traders increase with trade size. All else equal, a fund s trading costs should then increase as concentration increases since the fund will have to trade larger amounts of a smaller number of equities to generate the same amount of cash. Sapp and Yan (2008) find evidence that funds with concentrated portfolios do suffer liquidity problems, and Fulkerson and Riley (2016) show that highly concentrated funds experience per-dollar liquidity-motivated trading costs more than twice the size of less concentrated funds. 9

12 2. Data and methods In this section, we first discuss how we form our sample of U.S. equity mutual funds. We then discuss our methods of measuring concentration and performance. We leave the discussion of measures related to our sub-samples and robustness tests for the sections where those analyses are performed Mutual fund sample We build our sample of active U.S. equity mutual funds using the Center for Research in Security Prices (CRSP) Survivor-Bias-Free U.S. Mutual Fund database. We exclude any fund that CRSP identifies as an index fund, ETF, or variable annuity; use only funds which Lipper identifies as following a traditional long-only U.S. equity strategy; and require funds invest at least 80 percent of their assets in common equity. We also search fund names for key terms to further remove index funds and any funds not following a traditional long-only U.S. equity strategy. 3 To address the incubation bias identified by Evans (2010), we exclude a fund from the sample until it is at least two years old and has reached at least $20 million in assets. Once a fund enters our sample, it remains until it ceases operation or our sample period ends. We merge this sample of mutual funds with the Thomson Reuters Mutual Fund Holdings Database using MFLINKs to identify each fund s equity portfolio. Since 2004, funds have been required to report their holdings to the SEC on a quarterly basis. In previous years, funds were only required to report semiannually. However, in the Thomson Reuters data, many funds report on a quarterly basis prior to Schwarz and Potter (2016) find that those voluntary disclosures are likely driven by convenience rather than duplicity (pg. 3519) and show that the SEC data and Thomson Reuters data typically lead to similar empirical outcomes. The SEC 3 The list of key terms we use in the mutual fund name search is available upon request. 10

13 allows funds to report their holdings with a 60 day delay. We mark the date of the holdings based on when they applied to the fund, not when they should have been reported to the SEC. We collapse multiple share classes of a mutual fund into a single fund using the WFICN variable available in MFLINKs. Fund assets are the sum of the assets across all share classes of a fund. All other fund characteristics, including return, are an asset-weighted average of the share class values. Our final sample has 49,504 fund-quarter observations across 1,949 unique funds covering the period 1999 to Fund holdings are available starting in the 1980s, but our analysis begins in 1999 because that is the first full year in which CRSP has daily fund returns available, which allows us to effectively measure quarterly risk-adjusted fund returns Measuring concentration Our primary measure of concentration is the Herfindahl-Hirschman Index (HHI) of the percentage weights in a given mutual fund s equity portfolio. HHI measures concentration as the sum of the squared percentage weights and is bound between zero and 10,000. A fund with an infinitesimal weight on each of a large number of equities will have an HHI of near zero, and a fund with only one equity position will have an HHI of 10,000. We trim our sample at the 1st and 99th percentiles of HHI to eliminate outliers. In our final sample, the average HHI is 187, and the standard deviation is 85. For robustness, we consider whether our results hold using alternative and deconstructed measures of concentration in Section 5. Concentration is relatively stable over time for a given mutual fund. Table 1 sorts funds into deciles each quarter based on HHI and presents the percentage of fund-quarter observations that fall into each quarter t decile given the quarter t 4 decile. About 73 percent of funds in the lowest decile of HHI in quarter t 4 are also in the lowest decile in quarter t. Likewise, about 73 11

14 percent of funds in the highest decile of HHI in quarter t 4 are also in the highest decile in quarter t. A fund almost never moves from the lowest decile to the highest decile or vice versa, but there is still some variation. For instance, about 24.5 percent of funds which are in decile 5 in quarter t 4 fall outside of deciles 4, 5, and 6 in quarter t. Funds appear to have a concentration style (i.e., they are low, medium, or high concentration), but they do vary their concentration while staying within that style. [Table 1 about here] In our analysis, we adjust concentration to account for variation in the industry-wide concentration level. Figure 1 shows the median, 25th percentile, and 75th percentile of HHI for the mutual funds in our final sample each quarter from 1999 through There is a slight downward trend in the median concentration, but that trend is secondary to the quarter-to-quarter variation. In the first quarter of 1999 and second quarter of 2012, the median HHI is about 200. However, between those two dates, the median HHI drops below 180 on multiple occasions. We control for industry-wide changes in concentration by z-scoring (i.e., de-meaning and dividing by the standard deviation) HHI within each quarter. The adjusted measure captures how concentrated a fund is relative to other funds within a given quarter. [Figure 1 about here] 2.3. Measuring performance Since we have quarterly snapshots of mutual fund equity portfolios, we focus on measures of quarterly performance. We measure the risk-adjusted return of each fund each quarter using daily returns and a six-factor model: 6 r t rf t = α + β i f i,t + ε t (1) i=1 12

15 where r t is the net return for a given fund in a given quarter on day t, rf t is the risk-free rate on day t, and α is the risk-adjusted net daily return. In all of our subsequent analysis, we convert alpha to a quarterly value by multiplying the daily value by 62.5 (= 250/4). We use net returns to capture the experience of actual fund investors, but our conclusions are unchanged if we use gross returns. f i,t is the return on pricing factor i on day t. Our set of factors include the market (beta), the size (SMB), and value (HML) factors from Fama and French (1993), the momentum factor (UMD) from Carhart (1997), and the profitability (RMW) and investment (CMA) factors from Fama and French (2015). The Fama-French four-factor model, which does not include RMW and CMA, is commonly used in mutual fund research, but Jordan and Riley (2015) show that inclusion of RMW and CMA is important to correct for a significant bias related to the low volatility anomaly. 4 Fama and French (2016) also show that those factors help explain many other apparent equity pricing anomalies (e.g., share repurchases). Nonetheless, for robustness, we test and discuss how the choice of factor models impacts our results in Section 6.2. In all of our analyses, we use both alpha and the t-statistic associated with alpha to measure a fund s risk-adjusted performance. While alpha is easier to interpret economically, the alpha t-statistic has better statistical properties because it controls for differences in residual volatility within a mutual fund over time and between funds. 5 Controlling for those differences is particularly important in our analysis because the level of residual volatility in a fund s returns should have a positive relation to concentration. All else equal, a more concentrated portfolio is less diversified and will therefore have greater residual volatility. In our sample, the correlation 4 Among many other papers, see Ang, Hodrick, Xing, and Zhang (2006), Baker, Bradley, and Wurgler (2011), Frazzini and Pedersen (2014), and Hou and Loh (2016) for a discussion of the low volatility anomaly. 5 Kosowski, Timmermann, Wermers, and White (2006) provide a full discussion of the relative properties of alpha and the alpha t-statistic. 13

16 between a fund s idiosyncratic volatility calculated from the six-factor model during quarter t and a fund s HHI at the beginning of quarter t is Furthermore, an increase in the alpha t- statistic represents an increase in the information ratio, which indicates an increase in the quality of a fund manager s information set. The information ratio is also what managers in the Treynor and Black (1973) model seek to maximize. After trimming alpha at the 1st and 99th percentiles to eliminate outliers, the average alpha in our sample is 0.24 percent per quarter, with a standard deviation of 2.48 percent. This underperformance of about 1 percent per year for the average mutual fund is consistent with prior work (e.g., French s (2008) estimate of 0.67 percent per year and Gruber s (1996) estimate of 0.65 percent per year). The average alpha t-statistic is 0.14, with a standard deviation of The relation between concentration and performance We test the relation between concentration and performance using the following model: Perf i,t+1 = α + β Con i,t + Fund FE + Time FE + ε i,t+1 (2) where Perf i,t+1 is the performance of mutual fund i in quarter t + 1 measured using either sixfactor alpha or the alpha t-statistic. Con i,t is the concentration of fund i's equity portfolio at the end of quarter t measured using HHI. Since HHI is z-scored, β can be interpreted as the impact on performance of a one standard deviation increase in concentration. Fund FE and Time FE are fund and time fixed effects. We test specifications that include and exclude both groups of fixed effects. When the model excludes fund fixed effects, it examines how differences in concentration between funds impact performance. When the model includes fund fixed effects, it examines how differences in concentration within a fund impact performance. We do not include 6 In untabulated tests, we find that a within-fund one standard deviation increase in HHI predicts that annualized idiosyncratic volatility will increase by about 0.62 percentage points (t-stat = 18.12) in the subsequent quarter. 14

17 any control variables in our base model, but we discuss that decision and expand the model in Section 6.1. Table 2 shows results from various estimations of this model. Panel A shows results using alpha as the measure of performance, and Panel B shows results using the alpha t-statistic as the measure of performance. Regardless of the measure of performance, we find no evidence that differences in concentration between mutual funds impact performance. With fund fixed effects excluded from the model, changes in HHI have no economically or statistically significant relation to performance. Funds with relatively high and low concentration perform about the same on average, which is consistent with some of the results of Sapp and Yan (2008). [Table 2 about here] In contrast, we find that differences in concentration within a mutual fund do impact performance. With fund fixed effects included in the model, a one standard deviation increase in HHI predicts that alpha will be about 0.10 percent greater in the subsequent quarter. That effect is modest, about 0.40 percent per year, but statistically strong using both alpha and the alpha t- statistic. Therefore, consistent with our hypothesis that a fund manager will choose to increase portfolio concentration when he believes that his current information set is valuable enough to offset the concentration risks, a fund s performance is better in quarters in which a fund s equity portfolio is more concentrated. 7 7 In untabulated tests, we find (1) our conclusions hold regardless of whether a mutual fund s long-run average HHI is above or below the mean, (2) no evidence that our results are driven by very large changes in HHI, and (3) a one standard deviation increase in the publically available measure of HHI predicts that alpha will be about 0.05 percent greater (t-stat = 1.22) in the subsequent quarter. 15

18 4. Variation in the relation between concentration and performance We expect that the strength of the relation between concentration and performance will vary depending on the characteristics of the mutual fund and market conditions. Some circumstances should create greater concentration risk for a fund. In those circumstances, a fund manager should only increase concentration if the expected compensation is sufficiently greater. In this section, we first consider how cross-sectional variation in fund characteristics affects the relation between concentration and performance. We then consider how time-series variation in market conditions affects the same relation Cross-sectional variation A one standard deviation increase in concentration improves performance by 0.10 percent in the subsequent quarter on average, but the strength of that relation should vary between mutual funds depending on fund characteristics that affect concentration risk. In this section, we consider three fund characteristics related to the risks of holding a more concentrated portfolio. The first characteristic we consider is the average liquidity of the equities held by the fund. Keim and Madhaven (1997) show that transaction costs for institutional traders increase with trade size, so a fund with a more concentrated portfolio should incur greater costs if forced to sell assets (e.g., to meet a large, unexpected redemption request) because the fund will have fewer equities over which to spread its liquidity-motivated trades. Those costs will be amplified for funds that invest in relatively illiquid equities. To compensate for the risk of more expensive potential forced transactions, fund managers who hold relatively illiquid equities should require greater expected compensation before choosing to increase concentration. We measure liquidity for a fund as the asset-weighted average Amihud (2002) liquidity of its equity holdings. 16

19 The second characteristic we consider is how difficult it is to value the equities held by a mutual fund. As concentration increases, greater weight is put on a smaller number of equities, which decreases the opportunity for a fund manager to diversify his valuation errors. For example, the performance of a portfolio consisting of a single equity is dependent on the accuracy of a single valuation, while the performance of a portfolio consisting of 100 equities depends on the valuations being correct on average. Holding all else equal, a fund manager that primarily invests in equities with less certain intrinsic values should have lower confidence in the precision of his estimates, which increases the risk of reducing the diversification of the valuation errors. Therefore, fund managers should require greater expected compensation before choosing to increase concentration if their valuation certainty is lower. We measure valuation certainty as the sum of the asset-weighted average profitability (RMW) and investment (CMA) exposures of a mutual fund s equity holdings. Equities issued by firms that are less profitable and making large investments are typically more difficult to evaluate through traditional means (e.g., discounted cash flow models), which should make fund managers less certain of their intrinsic value. A fund with a combined exposure to RMW and CMA which is large and negative invests heavily in equities with returns correlated with the returns on those difficult to value equities and is likely to face greater risk if the diversification of valuation errors is reduced. The final characteristic we consider is the proportion of the mutual fund held by institutional investors. There are significant differences between retail and institutional investors. Del Guercio and Tkac (2002) and Salganik (2013) show that institutional investors use more complex methods of evaluating their investments compared to retail investors. Barber, Huang, and Odean (2016) likewise show that, in general, more sophisticated investors use more 17

20 sophisticated models. Further, our discussions with fund companies suggest that institutional investors have greater access to fund management. Given the due diligence process of most institutions, there is often a direct relationship developed between institutional investors and the fund or fund family. Retail investors are more likely to treat fund managers like money doctors as described by Gennaioli, Shleifer, and Vishny (2015) because they lack the knowledge, tools, and access to properly evaluate fund managers. As a result of the differences between retail and institutional investors, the managers of mutual funds that primarily have institutional investors can expect their investors to better understand their investment choices and their potential consequences. For example, if tracking error increases as a result of increased concentration, institutional investors could investigate the cause of the increased tracking error themselves or speak directly with management about the cause before making any decisions. Having less sophistication and access, retail investors could instead opt to quickly exit the fund after seeing increased tracking error because the increase lessened their trust in the fund manager and gave them the perception that the manager is gambling with their money. Since having more informed investors makes it less risky to increase concentration, managers of funds that primarily have institutional investors should require less expected compensation before choosing to increase concentration. 8 To measure institutional ownership, we calculate the percentage of fund assets held in share classes which are designated by CRSP as for institutional investors only. We test how these three characteristics affect the strength of the relation between concentration and performance by dividing the sample into groups at the beginning of each 8 Managers of mutual funds that primarily have institutional investors may also have lower liquidity concerns with respect to increased concentration. Our conversations with fund managers suggest that institutional investors are unlikely to make large, unexpected redemption requests, and most funds have the right to use in-kind redemptions for requests greater than $250,000 (e.g., Clients Pull Cash From Valeant Investor, Get Stock Instead, The Wall Street Journal, April 8, 2016). 18

21 quarter. For liquidity and valuation certainty, we divide the sample into terciles. For institutional ownership, we divide the sample into low (< 10%), medium (>10% & <75%), and high (>75%) groups using manual cut-offs because a large number of mutual funds which have almost no institutional ownership or almost complete institutional ownership. 9 We then estimate Eq. (2) with fund and time fixed effects included using the observations within each of the groups. Funds do not often switch between groups over time because the characteristics we consider are relatively time invariant. For instance, the proportion of institutional ownership in month t and month t 12 has a correlation of As a result of this time invariance, it is difficult to estimate the differences between the low and high groups in a single estimation because a fund fixed effects model requires within-fund changes for identification. Table 3 presents results from these sub-samples. Looking first at Panel A, mutual funds that invest in relatively illiquid equities have a stronger relation between concentration and performance as measured by alpha. Within the low tercile of equity liquidity, a one standard deviation increase in HHI predicts an increase in alpha of 0.15 percent in the next quarter. In the other two terciles, the increase is only 0.08 percent and is not statistically different from zero at conventional levels. However, if the alpha t-statistic is used to measure performance, the low and high terciles of equity liquidity have a similar relation between concentration and performance. Hence, while some of our results suggest that funds that invest in less liquid equities do have a stronger relation between concentration and performance, that conclusion is not supported using our most rigorous test. The variation in the strength of the relation between concentration and performance depending on fund liquidity may be limited in our sample because all of the tested funds invest in a highly liquid market and generally avoid the least liquid portion of that market 9 Our results are not sensitive to the precise cut-offs used. 19

22 (i.e., micro-cap equities). Put more simply, there is very limited variation in liquidity between the funds in our sample. [Table 3 about here] Looking next at Panel B, mutual funds that primarily invest in more difficult to value equities have a stronger relation between concentration and performance. Among funds in the low tercile of valuation certainty, a one standard deviation increase in HHI predicts alpha will be 0.12 percent greater in the next quarter. Among funds in the high tercile, the effect of concentration on performance is economically small and not statistically distinguishable from zero. Using the alpha t-statistic to measure performance, there is only a small economic difference in effect between the low and high terciles, but the effect is not statistically significant at conventional levels in the high tercile. Finally, looking at Panel C, funds with less institutional ownership have a stronger relation between concentration and performance. Within the low tercile of institutional ownership, a one standard deviation increase in HHI predicts that alpha will be 0.13 percent greater in the next quarter. In comparison, there is no economically meaningful or statistically significant relation between concentration and performance in the high tercile. Our conclusions are the same if the alpha t-statistic is used to measure performance. While the results in Panel A are mixed, the results in Panels B and C are both consistent with fund managers requiring greater expected compensation when the risks associated with increased concentration are greater Time-series variation If market conditions make increased concentration riskier, mutual fund managers should require greater expected compensation before choosing to increase their portfolio concentration. 20

23 Therefore, we would expect a stronger relation between concentration and performance when market conditions make holding a more concentrated portfolio riskier. In this section, we consider three market conditions that we expect will influence the riskiness of increased concentration. The first is the expected market volatility. When expected market volatility is high, the riskiness of increasing concentrated portfolio increases because, all else equal, more concentrated portfolios will have greater total and idiosyncratic volatility. Campbell (1993, 1996) and Chen (2002) show that investors prefer to hedge against increases in market volatility because such increases represent a deterioration in the investment opportunity set. Increasing portfolio concentration when expected volatility is high is therefore riskier because it increases the expected volatility of the mutual fund at a time when investors prefer to be hedged against volatility. Since concentration risk is greater when the expected market volatility is high, a fund manager in that state of the world should require greater expected compensation before choosing to increase concentration. We measure expected volatility using the CBOE Volatility Index (i.e., the VIX), which capture the market s expectation of near-term volatility using S&P 500 option prices. The second measure we consider is the aggregate level of market liquidity. As discussed before, a mutual fund with a more concentrated portfolio is likely to incur greater costs if forced to make liquidity-motivated trades because the fund will have fewer equities over which to spread trading. When aggregate liquidity is low those costs will be further amplified. Consequently, when market conditions make forced transactions more expensive than normal, a fund manager should require greater expected compensation before choosing to increase 21

24 concentration. We measure the level of aggregate liquidity in the U.S. equity market following Pastor and Stambaugh (2003). 10 The final measure we consider is investor sentiment. When investor sentiment is low, the risks associated with increasing portfolio concentration increase because investors have a preference against speculative investing. That is, a mutual fund manager who increases their portfolio s concentration when sentiment is low is increasing idiosyncratic volatility at a time when investors prefer the opposite. There are significant risks in moving against investor preferences (e.g., large redemptions could occur), so fund managers should require greater expected compensation before choosing to increase concentration when investor sentiment is low. We measure investor sentiment following Baker and Wurgler (2006). 11 While it is possible that our three measures of market conditions are proxies for the same underlying trends, the correlations between the measures suggest that each captures unique information. Investor sentiment has a correlation of 0.02 with the VIX and a correlation of 0.04 with aggregate liquidity. The VIX and aggregate liquidity have a correlation To test the relation between concentration and performance in different market conditions, we first sort the monthly time-series of each measure into terciles. We then estimate Eq. (2) with the fund and time fixed effects included using the observations within each tercile. 12 The market condition (low, medium, or high) in month t is matched to the end of quarter t holdings dates, so the mutual fund manager s concentration choice is made using 10 We thank Lubos Pastor for making the aggregate liquidity measure available on his website We thank Jeffrey Wurgler for making the investor sentiment measure available on his website For consistency with the cross-sectional results, we continue to report results using separate groups even though the time invariance problem is no longer present. However, in untabulated tests, we respecified the models using dummy variables and found statistically significant differences between the groups in the expected directions. 22

25 contemporaneous information about market conditions. Not all quarters in the sample have the same number of funds, so the number of fund-quarter observations in each tercile is unequal. [Table 4 about here] Table 4 presents results from these sub-samples. Regardless of how performance is measured, the patterns across the terciles are consistent with mutual fund managers requiring greater expected compensation when market conditions have made the risks associated with increased concentration greater. Looking first at Panel A, the impact of concentration on performance is large within the high tercile of expected market volatility. A one standard deviation increase in concentration predicts alpha will be 0.22 percent greater in the next quarter. There is no economically or statistically significant relation between concentration and performance within the low tercile. Looking next at Panels B and C, the impact of concentration on performance is large within the low terciles of aggregate liquidity and investor sentiment. A one standard deviation increase in concentration in those terciles predicts alpha will be about 0.20 percent greater in the next quarter. There is no relation between concentration and performance within the high tercile of either measure. 5. Alternative and deconstructed measures of concentration Using the Herfindahl-Hirschman Index as our primary measure of concentration is somewhat arbitrary. It is well-known and is commonly used to measure concentration in other contexts (e.g., within industries), but there is no theoretical reason to expect the particular construction of HHI to be ideal for the measurement of mutual fund concentration. In this section, we first consider whether the relation between concentration and performance holds if alternative measures of concentration are used. We then deconstruct concentration into two 23

26 components and consider whether the relation between concentration and performance is driven by one, both, or the combination of the two components Alternative measures of concentration We test four alternative measures of concentration. The first two measures, HHI 3 and HHI 1.5, are modifications of the traditional HHI. Rather than sum the squared percentage weights, HHI 3 sums the cubed percentage weights, and HHI 1.5 sums the weights after they have been raised to the power of 1.5. Compared to the original HHI measure, HHI 3 places greater emphasis on the largest weights, and HHI 1.5 places less emphasis on the largest weights. The other two measures, Min 25 and Min 50, reflect the minimum number of equity positions necessary to capture a given percentage of equity portfolio assets. Min 25 is the minimum number of positions needed to capture 25 percent of portfolio assets, and Min 50 is the minimum number of positions needed to capture 50 percent of portfolio assets. When Min 25 and Min 50 increase, concentration decreases. As with HHI, we z-score our alternative measures of concentration within each quarter. [Table 5 about here] Table 5 shows results from Eq. (2) with the fund and time fixed effects included using these alternative measures of concentration. Panel A uses alpha as the measure of performance, and Panel B uses the alpha t-statistic as the measure of performance. Regardless of which measures of concentration and performance are used, there is a significant relation between concentration and performance. The impact on alpha of a one standard deviation increase in concentration varies between 0.07 percent and 0.11 percent per quarter and is statistically significant at conventional levels in all specifications. Consequently, it appears that our original 24

27 finding of a positive relation between concentration and performance and our resulting conclusions are not driven by the particular construction of the Herfindahl-Hirschman Index but instead hold more generally Deconstructed measures of concentration A mutual fund manager has two routes to change portfolio concentration. She can change the number of positions in the portfolio, or she can change the weights on the current portfolio positions. For example, imagine a fund that holds 100 equally-weighted positions. That fund would have an HHI of 100. The manager of that fund could increase the fund s HHI to 200 by (1) selling 50 of those positions and continuing to equally-weight the remaining 50 positions or (2) keeping all 100 positions while giving one of the positions a weight of about 10.9 percent and equally-weighting the other positions. Both choices produce the same change in HHI, but they are considerably different decisions by the fund manager. We test the relation between those two different concentration choices and performance by deconstructing our original concentration into two measures. The first measure, Number of Holdings, is a count of the number of equity positions held by the mutual fund. It captures changes in concentration related to changes in the number of positions. The second measure, Squared Deviations, is the sum of the squared differences between the equity position weights and the inverse of the number of equity positions. It captures changes in concentration related to changes in the position weights by measuring how far a portfolio is from being equallyweighted. As Number of Holdings decreases and Squared Deviations increases, concentration increases. Like prior measures of concentration, we z-score both measures within each quarter. 25