When Equity Mutual Fund Diversification Is Too Much Svetoslav Covachev * Abstract I study the marginal benefit of adding new stocks to the investment portfolios of active US equity mutual funds. Pollet and Wilson (2008) argue that equity mutual funds can improve performance in the face of liquidity constraints by diversifying their holdings. In doing so, mutual funds avoid executing very large trades, thus reducing their market price impact costs. I argue that if a fund is already diversified beyond a certain point, it will suffer from a depletion of new profitable investment ideas and hence further diversification may not improve performance. I propose a variable called fraction_new_stocks, which is the number of new stocks divided by the lagged number of total stocks held by a fund. I argue that its inverse is an empirical proxy for being too diversified to overcome liquidity constraints by diversifying further. I find evidence that funds with low values of fraction_new_stocks do not benefit from diversifying further, since their new stocks exhibit negative subsequent abnormal returns. My results are consistent with the rational framework of Berk and Green (2004), because they imply that managerial investment ability is a scarce resource and does not scale as the number of fund holdings increases. EFM Classification: 370 Keywords: Mutual funds, Equity, Diversification, New stocks * ESSEC Business School, Avenue Bernard Hirsch, 95021 Cergy-Pontoise Cedex, France; Email: svetoslav.covachev@essec.edu. 1
1. Introduction The topic of diversification in portfolio management has been extensively studied. In a classical Markowitz (1952) framework, diversification serves to eliminate idiosyncratic risk. It follows that there is a point, beyond which further diversification is of questionable benefit. Cohen, Polk, and Silli (2010) have shown that the top five stock picks of active managers, in terms of conviction, outperform the market on average. However, this is not the case for the remaining stocks in their portfolios. Therefore, the authors argue that there are incentives in the fund management industry to overdiversify and that investors would be better off, if portfolios were less diversified on average. There are arguments in favor of equity portfolio diversification beyond the elimination of idiosyncratic risk. Pollet and Wilson (2008) find evidence that liquidity constrained equity mutual funds benefit from diversification. The authors show that there is a positive association between fund diversification and subsequent risk-adjusted fund returns for these funds. Based on these results, Pollet and Wilson (2008) conclude that some liquidity constrained mutual funds may be underdiversified. However, the authors also argue that the typical equity fund prefers to scale up its existing stock holdings, as opposed to buying new stocks, to keep its portfolio concentrated in what it perceives to be the best stocks. This behavior is consistent with the implications on investors welfare of Cohen, Polk, and Silli s (2010) results. Funds are inclined to diversify their investment portfolios as they grow due to liquidity constraints. The consequence of not doing so is the buildup of large holdings, which leads to additional costs in the form of market price impact (Pollet and Wilson (2008)). On the other hand, funds that wish to diversify are faced with the challenge of identifying additional profitable investment opportunities. Some funds may be constrained in doing so, particularly the funds that 2
have already invested in many stocks. It is reasonable to expect that these funds find it much harder to invest in a given number of additional good stocks, as opposed to the funds that already hold few stocks, due to a smaller opportunity set. The former funds face a trade-off between deterioration in performance due to liquidity constraints and deterioration in performance due to investing outside of their areas of expertise. I study the limit of the capacity of funds to buy new stocks, to avoid the costs associated with liquidity constraints, without enduring additional costs. I introduce a variable called fraction_new_stocks, which I define as the number of new stocks added by a fund divided by the total number of stocks in the fund s portfolio as of its previous report date. I find evidence that funds with very low values of this measure in the current quarter have added new stocks with abnormally poor performance over the next quarter. Based on these results, I interpret fraction_new_stocks as an indicator of when diversification becomes costly and hence liquidity constraints become binding. Diversification constraints together with liquidity constraints explain why the returns to managerial skill do not scale with fund size as in the rational model of Berk and Green (2004). The rest of the paper is organized as follows. In Section 2, I form my hypotheses and design an empirical procedure to test them. In Section 3, I review the related literature. In Section 4, I introduce my data sources and provide summary statistics. Section 5 describes the methodology in detail. Section 6 contains the main empirical results of the paper. Section 7 provides additional empirical results. In Section 8, I conclude the paper. 3
2. Hypotheses Formation & Research Design If a fund invests in only a few new stocks in a given quarter, the marginal benefit of adding more new stocks to the portfolio is outweighed by the marginal cost of doing so. Specifically, the benefit is the reduction of price impact, relative to the purchase of more shares in the stocks already held by the fund. The cost is the dilution of performance, arising from adding new stocks that are inferior to the existing investments of the fund. Adding a few new stocks is an implicit signal of lack of conviction in their performance. Therefore, these new stocks picks are likely to be inferior on average to the new stocks selected by the funds that added many new stocks in the same quarter. It is reasonable to expect that adding 5 new stocks has a different economic significance for a fund that currently manages 30 stocks as opposed to another fund that already has 300 stocks in its portfolio. Furthermore, adding 5 high quality new stocks is likely to be far more challenging for the latter fund due to its smaller investment opportunity set. Therefore, I scale the number of new stocks of a fund by the total number of stocks that it held before the addition of the new stocks and refer to this measure as fraction_new_stocks. The inverse of this measure can be interpreted as a proxy for the severity of the constraints that the fund is facing in generating new profitable investment opportunities. I hypothesize that the new stocks of the funds with the lowest fraction_new_stocks subsequently underperform the new stocks of the funds with the highest fraction_new_stocks. The total number of stock holdings increases with fund size (as in Pollet and Wilson (2008)), thus decreasing the value of fraction_new_stocks for a given value of the number of new stocks. If my hypothesis holds, then managerial stock picking skill does not scale with the number of fund holdings. Therefore, my hypothesis is consistent with the rational model of Berk and Green (2004), according to which managerial skill does not scale with fund size. 4
There is also a reasonable counterargument. All other things equal, it is easier to pick a smaller number of high quality new stocks as opposed to a larger number due to a concentration of resources. The measure fraction_new_stocks is directly proportional to the number of new stocks selected, if the total number of old stocks is equal. Hence, low values of fraction_new_stocks may be associated with superior future performance of new stocks. To test the main hypothesis, I back test an active trading strategy consisting of two parts: I. sell the new stocks of the funds with the lowest fraction_new_stocks. II. Buy the new stocks of the funds with the highest fraction_new_stocks. My secondary hypothesis is that the underperformance conjectured in my primary hypothesis is even more pronounced in the sub-sample of funds with positive lagged net flows. The justification is as follows. Liquidity constraints are more immediate concerns for the subset of funds, which have recently received new money to invest. A fund with non-positive lagged net flows does not need to either scale up its existing holdings or purchase new stocks. Therefore, such funds do not face an immediate trade-off between price impact costs and the costs associated with overdiversification in the form of performance dilution. It follows that these funds are more likely to add new stocks to their portfolios for considerations unrelated to liquidity constraints. Therefore, the exclusion of funds with non-positive lagged net flows from the analysis is a cleaner approach to studying the trade-off, which should produce more pronounced results. 5
3. Related Literature In addition to contributing to the literature on diseconomies of scale, I also contribute to the literature on using the holdings of equity mutual funds to identify predictability in the cross-section of stock returns. Equity mutual funds herding is one of the known sources of stock return predictability. Stocks bought by herds of mutual funds subsequently outperform stocks sold by herds, according to Wermers (1999). Furthermore, the price impact of herding documented in that study is permanent. This implies that mutual funds herding provides informational content about the prospects of stocks that is gradually incorporated into stock prices. However, the author acknowledges that the strategy profiting from this behavior may no longer be profitable when transaction costs and shortselling constraints are taken into consideration. Not all herding by mutual funds is driven by information that is relevant to the economic values of stocks. Brown, Wei and Wermers (2014) show that mutual funds herd into stocks with positive analyst consensus recommendation updates and herd out of stocks with negative updates. However, the initial price impact is followed by a reversal. Therefore, while this herding behavior results in return predictability, mutual fund managers are either irrational or rationally incorporate career considerations into their decision making. There are studies that argue that mutual funds do possess superior stock picking skills, despite their well-known inability to outperform their benchmarks on average over long horizons after fees are taken into consideration. In the Berk and Green (2004) model, allocation of investors capital to highly skilled funds results in scaling effects that transfer the surplus from investors to fund managers. Dilution in the performance of skilled funds can also arise from limits to the 6
horizon over which the superior stock picking skill can be utilized. Chen, Jegadeesh and Wermers (2000) find evidence of short-term stock picking ability of mutual funds. In particular, the stocks which they buy have superior performance, over the next year, relative to those that they sell. However, the predictability horizon of one year is quite short and mutual funds tend to be infrequent traders. If fund managers are truly skillful, it raises the question of how the information contained within their reported holdings can be efficiently utilized to profit from that skill, without investing in the mutual funds and paying their fees. Wermers, Yao and Zhao (2012) address this issue. The authors develop a generalized inverse alpha (GIA) measure, which is constructed by efficiently aggregating mutual funds holdings and enables the prediction of future stock returns in the crosssection. Interestingly, this measure contains informational content that is distinct from publicly available quantitative information and its predictive power is interpreted by the authors as evidence for stock selection skill in the mutual fund industry. The short-selling constraints faced by equity mutual funds are another source of equity return predictability. Chen, Hong and Stein (2002) show that when a stock has a low breath of ownership among equity mutual funds, it has abnormally low future returns. The authors explain this phenomenon with the overpricing of stocks, which are held by only a few mutual funds. Institutional selling of these stocks in the face of bad news is limited due to the short-selling constraints faced by most equity mutual funds. Another way to forecast future stock returns is by using investor sentiment as a predictor. Frazzini and Lamont (2008) proxy investor sentiment for individual stocks with the flows coming into the mutual funds that hold those stocks. The authors find that mutual fund flows are the highest for the funds that hold the stocks with the lowest subsequent returns, a phenomenon they refer to 7
as the dumb money effect. This result appears to contradict Berk and Green s (2004) model, because investors do not allocate their capital to the most skilled fund managers. If money flows to the funds that already hold the worst stocks going forward, then these funds would underperform subsequently, even without taking the impact of scaling into consideration. This implies that investors are not necessarily rewarding superior managerial skill. 4. Data The main source of data is The Center for Research in Security Prices (CRSP) Survivorship Bias Free Mutual Fund Database, from which I downloaded fund holdings and fund characteristics. Mutual fund share classes were aggregated to the fund level using crsp_portno as a unique fund identifier. The quantitative characteristics of each fund were calculated as weighted averages of the characteristics of the share classes belonging to the respective fund. The Total Net Asset (TNA) was used to weight the share classes of a fund. The qualitative characteristics of the share class with the highest TNA of each fund were used as the characteristics of the respective fund. Most fund characteristics are available on a monthly basis. However, the fund holdings of many funds are only available on a quarterly basis, particularly in the first half of the sample period. The sample consists of US domiciled equity mutual funds investing in US stocks, which I identified using the Kacperczyk, Sialm and Zheng (2008) filters. I then excluded the funds that are explicitly classified as index funds according to CRSP. The sample period is from January 2004 to December 2016. I downloaded stocks returns adjusted for dividends and splits from the CRSP database, accounting data from the Compustat North America database and summary statistics of the stock recommendations of financial analysts from the I/B/E/S database from Thomson Reuters. I 8
obtained equity IPO dates (as in Field and Karpoff (2002) and Loughran and Ritter (2004)) from the Field-Ritter dataset of company founding dates 1 and the Active Share measure (as in Petajisto (2013)) from the Antti Petajisto online data library 2. I retrieved the four factors of Fama and French (1993) and Carhart (1997) and the liquidity factors of Pástor and Stambaugh (2003) from the Wharton Research Data Services (WRDS) website 3, the five factors of Fama and French (2015) from the Kenneth French online data library 4 and the q-factors of Hou, Xue and Zhang (2015) by sending a formal request to Lu Zhang via the q-factor model website 5. In Table 1, I report summary statistics of the characteristics of the top (Panel A) and bottom (Panel B) decile funds, according to a one-way sort by fraction_new_stocks performed each quarter. The top decile funds have a mean value of fraction_new_stocks of 0.96, which means that on average they add 96 new stocks for every 100 old stocks in their portfolios. The bottom decile funds have a mean fraction_new_stocks of 0.01, which indicates that on average they add one new stock for every 100 old stocks that they hold. The bottom decile funds have a better mean monthly return, both before (1.16% versus 1.10%) and after fees (1.11% versus 1.01%), but a worse median monthly return. Therefore, it is not evident which group of funds provides superior returns to investors. The top decile funds are relatively small on average compared to the bottom decile funds. The former have a mean TNA of $782 million versus the $3,552 million mean TNA of the latter. The bottom decile funds have a lower mean expense ratio (0.84% versus 1.33%) and a lower mean turnover ratio (0.54 versus 1.30). The bottom decile funds are older by only about 2 years on average (15.43 versus 13.73). The bottom decile funds on average belong to larger fund families 1 https://site.warrington.ufl.edu/ritter/files/2016/09/foundingdates.pdf 2 http://www.petajisto.net/data.html 3 https://wrds-web.wharton.upenn.edu/wrds/ 4 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 5 https://sites.google.com/site/theqfactormodel/ 9
($120.25 billion versus $39.58 billion) with more numerous family members (36.04 versus 19.92). The bottom decile funds have slightly higher mean fractional flows (0.57% versus 0.29%). [Table 1 here] I report the summary statistics for fraction_new_stocks by year, for the 2004-2016 period, in Table 2. The median value decreases monotonically from 0.13 in 2004 to 0.03 in 2016. The mean values are influenced by large outliers. The largest mean value of 0.46 was reached during the peak of the financial crisis in 2008. During that year, both the standard deviation of fraction_new_stocks of 15.67 and the maximum value of 1660.00 were exceptionally high. However, very large values of fraction_new_stocks were relatively rare overall, since the annual 99 th percentile peaked at 4.00 in 2008 and was at or below 1.00 in seven out of the thirteen years of the sample period. Extreme outliers of fraction_new_stocks are arising from abnormally low denominators. There are cases where the denominator of the fraction is one, which signifies that the fund reported only a single stock on the previous report date. However, winsorizing fraction_new_stocks would not change the relative rankings of the funds and the strategy results. Furthermore, the strategy results are robust to excluding from the sample in each quarter the funds with fraction_new_stocks values below the 1 st percentile or above the 99 th percentile for that quarter. [Table 2 here] 10
5. Methodology The variable fraction_new_stocksi,t is defined as the number of new stocks of fund i at time t, divided by the total number of stocks reported by fund i at time t-1. Time t for fund i is the fund s report date during the last month of the quarter. Time t-1 for fund i is the fund s latest report date prior to time t, which is typically either in the previous quarter or in the previous month, depending on the reporting frequency of the fund. A stock is defined as new for a fund, only if it is in the fund s quarter end reported holdings and is not in the reported holdings of the fund on any of the prior report dates. This criterion neglects false signals due to spurious gaps in the holdings data. Portfolios formation occurs at the end of each quarter (end of March, June, September and December) and consists of the following steps: I. Funds are sorted in each quarter end, according to fraction_new_stocks. II. III. Top and bottom decile funds are identified. Two lists are made one containing the new stocks of the top decile funds and the other containing the new stocks of the bottom decile funds. IV. Duplicate stocks are removed from the lists. V. Stocks that are in both lists are removed from both lists. VI. VII. The stocks on the list of new stocks of top decile funds are bought with equal weights. The stocks on the list of new stocks of bottom decile funds are sold short with equal weights. VIII. The portfolios are held for the entire next quarter. 11
The portfolios are non-overlapping and each has a holding period of exactly 3 months. There are exactly 52 different long-short portfolios over the entire sample period. To test the secondary hypothesis, I first split the sample into two sub-samples funds with positive lagged net flows and funds with non-positive lagged net flows. I then repeat steps I to VIII from above in both sub-samples separately. I use the fractional flow of Sirri and Tufano (1998), calculated on a quarterly basis, to measure net flows: TNA_FLOW it = n i,t n i,t 1 (1 + r i,t ) (1) where ni,t is the size of fund i at the end of quarter t, ni,t-1 is the fund size at the end of quarter t-1 and ri,t is the return of fund i for quarter t. I use a lag of one quarter, because equity mutual funds report their stock portfolio holdings on an at least quarterly basis. This lag size is sufficient to ensure that the mutual funds were aware of these flows before making the adjustments to their portfolios which are reported in the current quarter. 6. Main Empirical Results In this section, I present the empirical results for the risk-adjusted performance of the trading strategy described in Section 5. The tables in this section contain the outputs from time series regressions with the returns of the strategy portfolios as the dependent variables and combinations of common asset pricing factors as the independent variables. The observations are of monthly 12
frequency. I first document the results for the full sample and then proceed with the results for the sub-sample of funds with positive lagged net flows. 6.1 Full sample I report the alphas and the factor loadings of the portfolios formed by applying the strategy to the full sample, in Table 3. I summarize the results for the long-short portfolio in columns (1), (4) and (7). The estimated alpha of the strategy is between 0.32% per month and 0.48% per month, depending on which asset pricing model is used. The abnormal return is the highest according to the Carhart (1997) four-factor model in column (1) and lowest according to the variant of the Fama and French (2015) five factor model, which is augmented by the addition of Carhart s (1997) momentum factor, in column (4). The alpha estimate is statistically significant, at least at the 10% level, regardless of which asset pricing model is used. The strategy has a high and statistically significant at the 1% level positive loading on the profitability factor (RMW of Fama and French (2015) in column (4) and ROE of Hou, Xue and Zhang (2015) in column (7)). The strategy has a statistically significant negative loading on the momentum factor, only according to the variant of the q-factor model of Hou, Xue and Zhang (2015) with Carhart s (1997) momentum factor in column (7). There is weak evidence that the long-short portfolio has a positive exposure to the investment factor (CMA of Fama and French (2015) in column (4) and IA of Hou, Xue and Zhang (2015) in column (7)). However, the returns of the strategy do not appear to have an exposure to the returns of the other factors. [Table 3 here] 13
I present the results for the long and short portfolios separately in the column triples (2), (5), (8) and (3), (6), (9), respectively. This analysis shows that the abnormal profitability of the strategy is driven by the short portfolio, which has an alpha estimate of negative 52 basis points per month, significant at the 1% level, according to the Carhart (1997) four factor model in column (3). The short portfolio has a market beta, which is very close to one, according to all asset pricing models. It consists of small cap, low profitability and high investment stocks, according to the factor loadings. However, the short portfolio does not seem to have a strong tilt towards (away from) value and momentum stocks. 6.2 Sub-sample of funds with positive lagged net flows As discussed in the hypothesis formation and research design section, any overdiversification induced by liquidity constraints should be more pronounced in the sub-sample of funds that have recently received new money which they need to invest. Therefore, I examine the abnormal returns and factor exposures of the portfolios formed when the same strategy is applied to the sub-sample of funds with positive lagged net flows. I report the results in Table 4, where columns (1), (4) and (7) contain the output from the time series regressions with the return of the long-short portfolio as the dependent variable. The estimate of the monthly alpha of the strategy applied to the subsample ranges from 0.45% in column (4) to 0.65% in column (1). Therefore, the abnormal return is considerably higher relative to that of the strategy applied to the full sample. Furthermore, the alpha is statistically significant, at least at the 5% level, according to all asset pricing models used. The strategy has a strong and statistically significant negative loading on the profitability factor (columns (4) and (7)), as was the case in the full sample. The long-short portfolio has a negative loading on the momentum factor, implying that the strategy is contrarian. However, the strategy 14
portfolio appears to be insensitive to the other factors used (including the Pástor and Stambaugh (2003) liquidity factors, which were used in untabulated tests). [Table 4 here] I summarize the long portfolio results in columns (2), (5) and (8). Unlike the long portfolio of the full sample, the long portfolio in the sub-sample has a statistically significant (at the 1% level) alpha estimate of 18 basis points per month, according to the variant of the q-factor model with momentum in column (8). The short portfolio results are in columns (3), (6) and (9). The short portfolio has a statistically significant positive momentum factor loading, regardless of which asset pricing model is used, unlike the short portfolio of the full sample. The exposure of the short portfolio of the sub-sample to the other factors is similar to that of the short portfolio of the full sample. From the results discussed so far, it is evident that the strategy has superior risk-adjusted performance in the sub-sample of funds with positive lagged net flows. For a complete comparison, it may be of interest to examine the performance of the strategy in the sub-sample of funds with non-positive lagged net flows. Although, the untabulated alpha estimates have positive signs, they are not statistically significant at the conventional levels. 15
7. Supplementary Empirical Results 7.1 Initial Public Offering (IPO) stocks The strategy portfolios are formed at least a couple of days after the funds bought the new stocks. This is so, because mutual funds report snapshots of their holdings at regular intervals, but do not report the exact date on which they added a given stock. Therefore, new stocks holdings can only be inferred from the reported holdings with a time lag, which has an upper bound equal to the time interval between two consecutive report dates. It follows that the portfolio returns are not necessarily indicative of the returns that the funds obtain when buying and holding the new stocks. It is plausible that the bottom decile funds achieve non-negative abnormal returns from buying new stocks, which appear to be negative when the first few days or weeks of the holding period are excluded. This effect is likely to be particularly large in the case of IPO stocks, which tend to have large positive abnormal returns on the first day of trading (Loughran and Ritter (2004)). Therefore, it is meaningful to examine how the percentage of stocks that went public in the quarter prior to portfolio formation differs between the long and short portfolios. On average, 0.62% of the stocks of the long portfolio are recent IPO stocks. However, 6.01% of the stocks of the short portfolio had their IPOs in the previous quarter, on average. Furthermore, the difference between the two percentages is statistically significant at the 1% level. Therefore, it appears that the bottom decile funds put a greater emphasis on obtaining IPO allocations. Given these funds are larger and come from larger fund families, they may have better access to IPO allocations. To address this issue, I test the same strategy as before, but only include in the long and short portfolios the new stocks with IPOs that occurred within the three months prior to portfolio formation. The resulting long portfolio has a statistically insignificant alpha, according to all of the asset pricing models used in the main analysis. The short portfolio also has a statistically 16
insignificant alpha estimate according to the Carhart (1997) and Fama and French (2015) models. However, it has a marginally statistically significant q-factor model alpha estimate of 1.73% per month (t-stat 1.93). Furthermore, the return of the short portfolio is likely to be lower than the average return that the bottom decile funds earned by holding these recent IPO stocks. This is so, because the strategy excludes the first few days or weeks of post-ipo returns, which are abnormally high on average (Loughran and Ritter (2004)). Therefore, the bottom decile funds are unlikely to suffer from a deterioration of performance, when they add recent IPO stocks to their portfolios. Motivated by the results above, I remove the recent IPO stocks from both portfolios of the main strategy of Section 6.1 to improve its performance. Another justification for removing IPO stocks is that they may be difficult to short sell. I report the results in Table 5. The enhanced strategy earns a q-factor model alpha of 0.42% per month (column (7)), which is statistically significant at the 5% level. The improvement in the performance of the strategy arises mainly from a deterioration in the performance of the short portfolio, as can be seen by comparing columns (3), (6) and (9) of Table 5 with the respective columns of Table 3. The short portfolio consists of the new stocks of the mutual funds with the lowest fraction_new_stocks values, which I deem to be facing diminishing returns to scale. These funds have a depletion of possibilities for new investments, since they have already invested in a very large number of stocks. However, they still add a few new stocks to avoid building up very large positions in their existing stocks holdings. This explains why their new stocks are underperforming and why they focus on IPO stocks, where this underperformance is not observed. [Table 5 here] 17
7.2 Financial analyst coverage and recommendation updates Coverage of stocks by financial analysts is an important consideration. Mutual funds can obtain information about stocks in a faster and less costly manner when coverage is high. However, a lot of that information may already be reflected in the share price and hence there may be less opportunity for generating alpha. It is therefore unclear whether a wider financial analyst coverage helps mutual funds in making profitable additions to their investment portfolios. In addition, the recommendation updates of financial analysts can cause herding behavior of mutual funds due to career concerns as in Brown, Wei and Wermers (2014). The authors show that such herding leads to price impact and subsequent return reversal and is thus attributable to noise. To obtain additional insight, I briefly explore the differences in measures that summarize analyst coverage and recommendations between the new stocks of the top decile funds (long portfolio) and the new stocks of the bottom decile funds (short portfolio). I present the averages of these measures for the two groups of new stocks in Table 6. Column (1) contains the averages for the new stocks of the long portfolio, column (2) consists of the averages for the new stocks of the short portfolio and column (3) shows the differences in the averages between the two groups. The stocks of the long portfolio are followed by 10.41 financial analysts on average, whereas the stocks of the short portfolio are followed by 7.64 financial analysts on average. The difference is statistically significant at the 1% level. Furthermore, the stocks of the long (short) portfolio were recently upgraded by 1.52% (1.12%) of the analysts following the stocks on average. The difference between the averages of the two groups of stocks is statistically significant at the 1% level. In addition, the stocks of the long (short) portfolio were recently downgraded by 1.55% (1.64%) of the analysts following the stocks on average. However, this difference is not statistically significant. The new stocks of the top decile funds had worse average 18
recommendations in the quarter prior to portfolio formation as opposed to the new stocks of the bottom decile funds (2.28 versus 2.22, where 1 is the best possible recommendation). This difference is statistically significant at the 1% level. Considering these results, it seems that the bottom decile funds struggle due to investing in less covered stocks with better average analysts recommendations, but lower percentage of recent recommendation upgrades. This evidence is consistent with the funds with the lowest fraction_new_stocks values, adding stocks that they are less informed about when diversifying their portfolios. [Table 6 here] 7.3 Active Share measure The variable fraction_new_stocks is high for funds that add many new stocks. The constituents of a major stock market index change slowly over time. Cremers and Petajisto s (2009) Active Share measures how much the holdings of a fund deviate from the constituents of its benchmark index. Therefore, it is reasonable to expect that a fund with a high fraction_new_stocks will also have a high Active Share and that the two variables might be closely related. The top decile funds have a higher average Active Share relative to the bottom decile funds (0.84 versus 0.54) and a higher average tracking error (0.07 versus 0.04), as expected. However, the sample Pearson correlation coefficient between the two measures is only 0.02 from 2004 to 2009. Although the linear correlation between fraction_new_stocks and Active Share is very weakly positive, it is worth checking if the latter is driving the main results. For this purpose, I implement the same trading strategy as in Section 6.1 over the 2004 to 2009 period, with Active Share instead of fraction_new_stocks as the variable, according to which the funds are sorted. All 19
portfolios of new stocks formed in this way have statistically and economically insignificant alphas, regardless of which asset pricing model is used. Therefore, I conclude that the two measures are distinct, despite their similarities. 7.4 Additional tests There are a number of fund level variables that are likely to be correlated with fraction_new_stocks, including size and turnover, as well as the numerator and the denominator of the fraction. However, I find that replacing fraction_new_stocks with any of these variables, in the main trading strategy of Section 6.1, produces results which are neither similar, nor meaningful. Thus, I believe that fraction_new_stocks is a superior empirical proxy for diminishing returns to scale arising from overdiversification induced by liquidity constraints. 8. Conclusion I study diminishing returns to scale in the mutual fund industry, by focusing on the marginal impact of adding new stocks on the performance of active US equity mutual funds. I propose a measure called fraction_new_stocks, which is defined as the number of new stocks added by an active equity mutual fund divided by the total number of stocks held by that fund on the previous reporting date. I use this measure as an indicator of when funds are too diversified to overcome liquidity constraints, in the form of the market impact of scaling existing holdings, by purchasing new stocks. I argue that low values of the measure are associated with overdiversification and binding liquidity constraints. I find evidence that supports my primary hypothesis that the equity mutual funds with the lowest values of fraction_new_stocks add new stocks with worse future 20
performance relative to the funds with the highest values of the variable. This evidence is consistent with equity mutual funds facing diseconomies of scale as their number of total stock holdings grows as in the Berk and Green (2004) model. I argue that liquidity constraints are more imminent for mutual funds with positive lagged net flows. The empirical evidence supports my secondary hypothesis that the magnitude of the effect studied is even larger in this sub-sample. This result is consistent with the funds with the lowest fraction_new_stocks, among the funds having recently received new money from investors, being the most overdiversified. I also explore how the variable fraction_new_stocks is related to other fund level variables. The funds with the lowest values of fraction_new_stocks tend to be larger, older, belong to larger fund families, charge lower fees and have lower turnover ratios. These findings are consistent with the diminishing returns to scale argument. Finally, I emphasize that I am studying only marginal effects. The funds which I deem to be overdiversified may not be underperforming the rest of the funds overall. Their investors are likely to benefit from their lean fees and superior IPO allocations. 21
References Berk, J. B., & Green, R. C. (2004). Mutual fund flows and performance in rational markets. Journal of Political Economy, 112(6), 1269-1295. Brown, N., Wei, K., & Wermers, R. (2014). Analyst Recommendations, Mutual Fund Herding, and Overreaction in Stock Prices. Management Science, 60(1), 1-20. Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57-82. Chen, J., Hong, H., & Stein, J. C. (2002). Breadth of ownership and stock returns. Journal of Financial Economics, 66(2), 171-205. Chen, H. L., Jegadeesh, N., & Wermers, R. (2000). The value of active mutual fund management: An examination of the stockholdings and trades of fund managers. Journal of Financial and Quantitative Analysis, 35(3), 343-368. Cohen, R. B., Polk, C., & Silli, B. (2010). Best ideas. Working paper, London School of Economics. Cremers, K. M., & Petajisto, A. (2009). How active is your fund manager? A new measure that predicts performance. The Review of Financial Studies, 22(9), 3329-3365. Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56. Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22. Field, L. C., & Karpoff, J. M. (2002). Takeover defenses of IPO firms. The Journal of Finance, 57(5), 1857-1889. Frazzini, A., & Lamont, O. A. (2008). Dumb money: Mutual fund flows and the cross-section of stock returns. Journal of Financial Economics, 88(2), 299-322. Hou, K., Xue, C. & Zhang, L. (2015). Digesting Anomalies: An Investment Approach. Review of Financial Studies, 28(3), 650-705. Kacperczyk, M., Sialm, C., & Zheng, L. (2008). Unobserved actions of mutual funds. The Review of Financial Studies, 21(6), 2379-2416. Loughran, T., & Ritter, J. R. (2004). Why has IPO underpricing changed over time?. Financial Management, 33(3), 5-37. Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. Pástor, Ľ., & Stambaugh, R. F. (2003). Liquidity risk and expected stock returns. Journal of Political Economy, 111(3), 642-685. 22
Petajisto, A. (2013). Active share and mutual fund performance. Financial Analysts Journal, 69(4), 73-93. Pollet, J. M., & Wilson, M. (2008). How does size affect mutual fund behavior?. The Journal of Finance, 63(6), 2941-2969. Sirri, E. R., & Tufano, P. (1998). Costly search and mutual fund flows. The Journal of Finance, 53(5), 1589-1622. Wermers, R. (1999). Mutual fund herding and the impact on stock prices. The Journal of Finance, 54(2), 581-622. Wermers, R., Yao, T., & Zhao, J. (2012). Forecasting stock returns through an efficient aggregation of mutual fund holdings. The Review of Financial Studies, 25(12), 3490-3529. 23
Table 1: Summary Statistics I report summary statistics for the top and bottom decile funds in a ranking by fraction_new_stocks performed every quarter. The sample period is from January 2004 to December 2016. The variable fraction_new_stocks is the number of new stocks reported by a fund in the final month of the quarter divided by the total number of stocks reported by the fund on its previous reporting date. Raw Monthly Return is the before fees return of a fund in the final month of the quarter. Net Monthly Return is the after fees return of a fund in the final month of the quarter. Total Net Assets (TNA) is the size of a fund as of the quarter end. Net Expense ratio is the annual fee as a percentage of TNA that a fund charged its investors to cover its operating expenses. Fund Turnover Ratio is the minimum of the annual aggregated sales and the annual aggregated purchases of securities by a fund divided by the fund s 12-month average TNA. Age of Fund is the number of years since the inception date of a fund. Number of Funds in the Family is the total number of funds in the mutual fund family that a fund belongs to. Family Total Size is the sum of the TNA of the funds in the mutual fund family that a fund belongs to, including the fund itself. Family Size is the sum of the TNA of the funds in the mutual fund family that a fund belongs to, excluding the fund itself. Fractional Flow is the net flow of a fund in the last month of the quarter as a percentage of its TNA as of the beginning of the month. Panel A: Top decile funds Variable Mean Median Std Dev 1st Pctl 99th Pctl fraction_new_stocks 0.96 0.33 5.69 0.14 12.50 Raw Monthly Return (%) 1.10 1.21 4.64-12.62 12.32 Net Monthly Return (%) 1.01 1.11 4.64-12.73 12.17 Total Net Assets ($ million) 782 153 4290 11 8402 Net Expense Ratio (% per year) 1.33 1.30 0.49 0.20 2.81 Fund Turnover Ratio 1.30 0.95 1.48 0.08 6.84 Age of Fund 13.73 11.99 10.49 0.63 55.24 Number of Funds in the Family 19.92 14.00 22.78 1.00 154.00 Family Total Size ($ million) 39579 6227 131647 14 741609 Family Size ($ million) 38798 5849 130634 0 726822 Fractional Flow (% of TNA) 0.29-0.68 15.06-19.81 28.33 Panel B: Bottom decile funds Variable Mean Median Std Dev 1st Pctl 99th Pctl fraction_new_stocks 0.01 0.01 0.01 0.00 0.03 Raw Monthly Return (%) 1.16 1.13 4.28-11.21 11.34 Net Monthly Return (%) 1.11 1.07 4.28-11.25 11.30 Total Net Assets ($ million) 3552 502 16595 14 61655 Net Expense Ratio (% per year) 0.84 0.87 0.50 0.04 1.97 Fund Turnover Ratio 0.54 0.27 1.07 0.02 5.30 Age of Fund 15.43 13.31 11.31 1.06 65.47 Number of Funds in the Family 36.04 26.00 38.18 1.00 176.00 Family Total Size ($ million) 120253 21491 253523 47 1216444 Family Size ($ million) 116701 19830 246944 0 1188007 Fractional Flow (% of TNA) 0.57-0.42 25.14-19.57 22.93 24
Table 2: Time-trend of fraction_new_stocks I report summary statistics for the variable fraction_new_stocks by year from 2004 to 2016. I define fraction_new_stocks as the number of new stocks reported by a fund as of the quarter end divided by the total number of stock holdings reported by the fund on its preceding reporting date. Year Mean Median Std Dev Min 1st Pctl 99th Pctl Max 2004 0.22 0.13 0.56 0.00 0.00 1.13 20.00 2005 0.25 0.12 1.06 0.00 0.01 2.00 60.00 2006 0.23 0.10 1.17 0.00 0.01 1.92 63.33 2007 0.18 0.10 1.31 0.00 0.00 1.00 110.70 2008 0.46 0.08 15.67 0.00 0.00 4.00 1660.00 2009 0.28 0.07 2.64 0.00 0.00 2.00 110.00 2010 0.11 0.05 0.43 0.00 0.00 0.92 23.00 2011 0.08 0.05 0.19 0.00 0.00 0.53 11.46 2012 0.08 0.04 0.80 0.00 0.00 0.50 105.00 2013 0.22 0.04 2.64 0.00 0.00 3.00 206.00 2014 0.07 0.04 0.47 0.00 0.00 0.50 57.00 2015 0.08 0.03 1.51 0.00 0.00 0.50 164.00 2016 0.07 0.03 0.18 0.00 0.00 0.56 13.13 25
Table 3: Risk-adjusted returns of trading strategy portfolios I form each quarter end a long portfolio of the new stocks of the funds that rank in the top decile and a short portfolio of the new stocks of the funds that rank in the bottom decile, in a ranking of active equity mutual funds based on fraction_new_stocks. Duplicate stocks are removed so that a stock can only appear once in either the long portfolio or the short portfolio, but not in both. All portfolios are equal-weighted. There is a total of 52 distinct non-overlapping long-short portfolios, held for 3 months after their respective formation dates. This results in 156 monthly observations of portfolio returns from January 2004 to December 2016. I run a time-series regression of the portfolio returns against risk factors. The intercept and slope coefficient estimates for the long portfolio are in columns (2), (5) and (8), whereas columns (3), (6) and (9) contain the estimates for the short portfolio. The results for the long-short portfolio are presented in columns (1), (4) and (7). The factors in columns (1)-(3) are the four factors of Carhart (1997), the factors in columns (4)-(6) are the Fama and French (2015) factors plus momentum and the factors in columns (7)-(9) are the Hou, Xue and Zhang (2015) factors plus momentum. The t-stats are reported in parentheses. (1) Long- Alpha 0.48 (2.92) Rm-Rf 0.00 (0.09) SMB -0.05 (-0.69) HML 0.06 (0.79) (2) Long (3) (4) Long- 0.32 (1.93) (5) Long (6) (7) Long- 0.36 (2.22) (8) Long (9) -0.03 (-0.58) -0.52 (-2.87) 0.01 (0.27) -0.30 (-1.76) 0.05 (1.40) -0.31 (-1.91) 1.08 1.07 (66.81) (21.28) 0.66 0.71 (24.07) (8.33) 0.07 0.01 (2.63) (0.12) Rm-Rf_5 0.07 1.05 0.97 (1.54) (66.25) (19.45) SMB_5 0.01 0.63 0.63 (0.08) (25.08) (7.85) HML_5 0.00 0.01 0.01 (0.03) (0.49) (0.13) RMW_5 0.41-0.14-0.55 (3.61) (-3.87) (-4.68) CMA_5 0.22-0.12-0.35 (1.72) (-2.83) (-2.54) MKT_Q 0.06 1.02 0.96 (1.22) (91.31) (20.59) ME_Q 0.01 0.60 0.59 (0.11) (33.87) (7.98) IA_Q 0.19-0.01-0.20 (1.66) (-0.46) (-1.78) ROE_Q 0.37-0.21-0.59 (3.41) (-8.27) (-5.41) UMD -0.03-0.11-0.08-0.04-0.10-0.06-0.14-0.03 0.11 (-0.78) (-8.11) (-1.87) (-1.08) (-7.99) (-1.49) (-2.95) (-2.75) (2.32) Observations 156 156 156 156 156 156 156 156 156 R 2 0.02 0.98 0.86 0.11 0.99 0.88 0.09 0.99 0.89 26
Table 4: Risk-adjusted returns of trading strategy portfolios in the sub-sample of mutual funds with positive lagged net flows I exclude in each quarter funds with non-positive flows in the previous quarter. I measure flows using the fractional flow of Sirri and Tufano (1998), which is equal to (fund sizei,t / fund sizei,t-1)- (1+returni,t). I form each quarter end a long portfolio of the new stocks of the funds that rank in the top decile and a short portfolio of the new stocks of the funds that rank in the bottom decile, in a ranking of active equity mutual funds based on fraction_new_stocks. Duplicate stocks are removed so that a stock can only appear once in either the long portfolio or the short portfolio. All portfolios are equal-weighted. There is a total of 50 distinct non-overlapping long-short portfolios, each held for 3 months. This results in 150 monthly observations of portfolio returns from January 2004 to December 2016. I run a time-series regression of the portfolio returns against risk factors. The factors in columns (1)-(3) are the four factors of Carhart (1997), the factors in columns (4)- (6) are the Fama and French (2015) factors plus momentum and the factors in columns (7)-(9) are the Hou, Xue and Zhang (2015) factors plus momentum. The t-stats are reported in parentheses. (1) Long- Alpha 0.65 (3.32) Rm-Rf -0.07 (-1.21) SMB -0.08 (-0.86) HML -0.02 (-0.22) (2) Long (3) (4) Long- 0.45 (2.32) (5) Long (6) (7) Long- 0.56 (2.86) (8) Long (9) 0.07 (0.99) -0.58 (-2.92) 0.11 (1.51) -0.34 (-1.80) 0.18 (3.11) -0.39 (-2.07) 1.04 1.10 (48.82) (20.04) 0.69 0.77 (19.12) (8.23) 0.04 0.06 (1.34) (0.74) Rm-Rf_5 0.01 1.01 0.99 (0.21) (46.82) (18.17) SMB_5 0.01 0.67 0.66 (0.11) (19.41) (7.52) HML_5-0.06-0.00 0.05 (-0.63) (-0.12) (0.60) RMW_5 0.51-0.13-0.64 (3.71) (-2.43) (-4.79) CMA_5 0.15-0.15-0.31 (0.96) (-2.53) (-1.99) MKT_Q -0.02 0.97 0.99 (-0.29) (58.28) (18.39) ME_Q -0.07 0.62 0.70 (-0.82) (23.37) (8.12) IA_Q 0.21-0.05-0.26 (1.52) (-1.12) (-1.96) ROE_Q 0.24-0.27-0.50 (1.76) (-6.79) (-3.97) UMD -0.23-0.14 0.09-0.24-0.13 0.11-0.29-0.04 0.25 (-4.93) (-7.80) (1.89) (-5.37) (-7.61) (2.57) (-4.90) (-2.40) (4.45) Observations 150 150 150 150 150 150 150 150 150 R 2 0.16 0.97 0.84 0.24 0.98 0.87 0.19 0.99 0.87 27
Table 5: Risk-adjusted returns of trading strategy portfolios excluding recent IPO stocks I form each quarter end a long portfolio of the new stocks of the funds that rank in the top decile and a short portfolio of the new stocks of the funds that rank in the bottom decile, in a ranking of active equity mutual funds based on fraction_new_stocks. I remove stocks, whose Initial Public Offering (IPO) occurred in the portfolio formation quarter. Duplicate stocks are removed so that a stock can only appear once in either the long portfolio or the short portfolio, but not in both. All portfolios are equal-weighted. There is a total of 52 distinct non-overlapping long-short portfolios, held for 3 months after their respective formation dates. This results in 156 monthly observations of portfolio returns from January 2004 to December 2016. I run a time-series regression of the portfolio returns against risk factors. The factors in columns (1)-(3) are the four factors of Carhart (1997), the factors in columns (4)-(6) are the Fama and French (2015) factors plus momentum and the factors in columns (7)-(9) are the Hou, Xue and Zhang (2015) factors plus momentum. The t- stats are reported in parentheses. (1) Long- Alpha 0.53 (3.22) Rm-Rf 0.00 (0.07) SMB -0.04 (-0.53) HML 0.04 (0.52) (2) Long (3) (4) Long- 0.36 (2.22) (5) Long (6) (7) Long- 0.42 (2.58) (8) Long (9) -0.03 (-0.56) -0.56 (-3.16) 0.01 (0.25) -0.35 (-2.05) 0.05 (1.43) -0.36 (-2.28) 1.08 1.08 (67.66) (21.72) 0.65 0.69 (24.16) (8.27) 0.07 0.03 (2.74) (0.40) Rm-Rf_5 0.07 1.05 0.98 (1.51) (66.94) (19.85) SMB_5 0.02 0.63 0.61 (0.30) (25.13) (7.71) HML_5-0.01 0.01 0.02 (-0.13) (0.54) (0.30) RMW_5 0.41-0.14-0.55 (3.68) (-3.75) (-4.73) CMA_5 0.19-0.12-0.31 (1.51) (-2.74) (-2.32) MKT_Q 0.05 1.02 0.97 (1.08) (92.89) (21.05) ME_Q 0.01 0.59 0.59 (0.12) (34.16) (8.02) IA_Q 0.15-0.01-0.15 (1.29) (-0.24) (-1.37) ROE_Q 0.34-0.21-0.55 (3.08) (-8.25) (-5.10) UMD -0.03-0.11-0.09-0.04-0.10-0.06-0.12-0.03 0.09 (-0.70) (-8.18) (-1.99) (-0.97) (-8.05) (-1.63) (-2.62) (-2.88) (1.98) Observations 156 156 156 156 156 156 156 156 156 R 2 0.01 0.98 0.86 0.10 0.99 0.89 0.07 0.99 0.89 28