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Fund size, liquidity and org chen hong


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Fund size, liquidity and org chen hong

  1. 1. Does Fund Size Erode Mutual Fund Performance? The Role of Liquidity and Organization By JOSEPH CHEN, HARRISON HONG, MING HUANG, AND JEEFREY D . KUBIK* We investigate the effect of scale on performance in the active money management industry. We first document that fund returns, both before and after fees and expenses, decline with lagged fund size, even after accounting for various perfor- mance benchmarks. We then explore a number of potential explanations for this relationship. This association is most pronounced among funds that have to invest in small and illiquid stocks, suggesting that these adverse scale effects are related to liquidity. Controlling for its size, a funds return does not deteriorate with the size of the family that it belongs to, indicating that scale need not be badfor performance depending on how the fund is organized. Finally, using data on whether funds are solo-managed or team-managed and the composition of fund investments, we explore the idea that scale erodes fund performance because of the interaction of liquidity and organizational diseconomies. {JEL G2, G20, G23, L2, L22) The mutual fund industry plays an increas- Stake of corporate equity and play a pivotal roleingly important role in the U.S. economy. Over in the determination of stock prices (see, e.g.,the past two decades, mutual funds have been Mark Grinblatt et al., 1995; Paul Gompers andamong the fastest growing institutions in this Andrew Metrick, 2001).country. At the end of 1980, they managed less In this paper, we tackle an issue that is fun-than $150 billion, but this figure had grown to damental to understanding the role of these mu-over $4 trillion by the end of 1997—a number tual funds in the economy—the economies oftbat exceeds aggregate bank deposits (Robert C. scale in the active money management industry.Pozen, 1998). Indeed, almost 50 percent of Namely, how does performance depend on thehouseholds today invest in mutual funds (In- size or asset base of the fund? A better under-vestment Company Institute, 2000). The most standing of this issue would naturally be usefulimportant and fastest-growing part of this in- for investors, especially in light of the massivedustry is funds that invest in stocks, particularly inflows that have increased the mean size ofactively managed ones. The explosion of news- funds in the recent past. At the same time, theletters, magazines, and such rating services as issue of the persistence of fund performanceMorningstar attest to the fact that investors depends crucially on the scale-ability of fundspend significant resources in identifying man- investments (see, e.g., Martin J. Gruber, 1996;agers with stock-picking ability. More impor- Jonathan Berk and Richard C. Green, 2002).tant, actively managed funds control a sizeable Moreover, the nature of the economies of scale in this industry may also have implications for the agency relationship between managers and * Chen: Marshall School of Business, University of investors and tbe optimal compensation con-Southern California, Hoffman Hall 701, Los Angeles, tract between them (see, e.g., Keith Brown etCA 90089 (e-mail:; Hong:Bendheim Center for Einance, Princeton University, al., 1996; Stan Becker and Greg Vaughn, 2001).26 Prospect Avenue, Princeton, NJ 08540 (e-mail: Therefore, understanding the effects of; Huang: Stanford Graduate School size on fund returns is an important first stepof Business and Cheong Kong Graduate School of Business, toward addressing such critical issues.Stanford University, Stanford, CA 94305 (; Kubik: Department of Economics, While the effect of scale on performance is anSyracuse University, 426 Eggers Hall, Syracuse, NY 13244 important question, it has received little re-(e-mail: search attention to date. Some practitioners 1276
  2. 2. VOL. 94 NO. 5 CHEN ETAL.: DOES FUND SIZE ERODE MUTUAL EUND PERFORMANCE? 1277 point out that there are advantages to scale, such nually). The corresponding figures for net fund as more resources for research and lower ex- retums (after fees and expenses are deducted) pense ratios. Others believe, however, that a are only slightly smaller. To put these magni- large asset base erodes fund performance be- tudes into some perspective, the funds in our cause of trading costs associated with liquidity sample on average underperform the market or price impact (see, e.g., Andre Perold and portfolio by about 96 basis points after fees and Robert S. Salomon, 1991; Roger Lowenstein, expenses. From this perspective, a 65- to 96- 1997). Whereas a small fund can easily put all basis-point annual spread in performance is not of its money in its best ideas, a lack of liquidity only statistically significant but also economi- forces a large fund to have to invest in its cally important. not-so-good ideas and take larger positions per Even after utilizing various performance stock than is optimal, thereby eroding perfor- benchmarks and controlling for other observ- mance. Using a small sample of funds from able fund characteristics, there are still a num- 1974 to 1984, Grinblatt and Sheridan Titman ber of potential explanations that might be (1989) find mixed evidence that fund retums consistent with the inverse relationship between decline with fund size. Needless to say, there is scale and fund retums. To further narrow the set no consensus on this issue. of explanations, we proceed to test a direct Using mutual fund data from 1962 to 1999, implication of the hypothesis that fund size we begin our investigation by using cross- erodes performance because of trading costs sectional variation to see whether performance associated with liquidity and price impact. If thedepends on lagged fund size. Since funds may "liquidity hypothesis" is true, then size ought tohave different styles, we adjust for such heter- erode performance much more for funds thatogeneity by utilizing various performance have to invest in small stocks, which tend to bebenchmarks that account for the possibility that illiquid. Consistent with this hypothesis, we findthey load differently on small cap stock, value that fund size matters much more for the retumsstock, and price momentum strategies. More- among such funds, identified as "small cap"over, fund size may be correlated with such funds in our database, than other funds.^ Indeed,other fund characteristics as fund age or turn- for other funds, size does not significantly affectover, and it may be these characteristics that are performance. This finding strongly indicatesdriving performance. Hence, we regress the var- that liquidity plays an important role in theious adjusted retums on lagged fund size (as documented diseconomies of scale.measured by the log of total net assets under We then delve deeper into the liquidity hy-management), and also include in the regres- pothesis by observing that liquidity means thatsions a host of other observable fund character- big funds need to find more stock ideas thanistics, including tumover, age, expense ratio, small funds do, but liquidity itself may nottotal load, past-year fund inflows, and past-year completely explain why they cannot go aboutretums. A number of studies wam that the re- doing this, i.e., why they cannot scale. Presum-ported retums of the smallest funds (those with ably, a large fund can afford to hire additionalless than $15 million in assets under manage- managers to cover more stocks. It can therebyment) might be upward biased. We exclude generate additional good ideas so that it can takethese funds from our baseline sample in esti-mating these regressions. The regressions indicate that a funds perfor- As we describe below, some theories suggest that themance is inversely correlated with its lagged smallest funds may have inferior performance to medium-assets under management. For instance, using sized ones because they are being run at a suboptimally small scale. Because it is difficult to make inferences re-monthly gross retums (before fees and expenses garding the performance of the smallest funds, we do notare deducted), a two-standard deviation shock attempt to measure such nonlinearities the log of a funds total assets under man- ^ Throughout the paper, we will sometimes refer to fundsagement this month yields anywhere from a 5.4- with few assets under management as "small funds" and funds that, by virtue of their fund style, have to invest into 7.7-basis-point movement in next months small stocks as "small cap funds." So small cap funds arefund retum, depending on the performance not necessarily small funds. Indeed, most are actually quitebenchmark (or about 65 to 96 basis points an- large in terms of assets under management.
  3. 3. 1278 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004small positions in lots of stocks as opposed to our fund size finding. For instance, it is notlarge positions in a few stocks. Indeed, the vast likely that this finding is due to large funds notmajority of stocks with small market capitaliza- caring about retums, since large families appar-tion are untouched by mutual funds (see, e.g.. ently do make sufficient investments to main-Hong, Lim, and Stein, 2000; Chen et al., 2002). tain performance.So there is clearly scope for even very large More important, these two findings makefunds to generate new ideas. Put another way, clear that liquidity and scale need not be bad forwhy cant two small funds (directed by two fund performance per se. In most families, ma-different managers) merge into one large fund jor decisions are decentralized in that the fundand still have the performance of the large one managers make stock picks without substantialbe equal to the sum of the two small ones? coordination with each other. So a family is an To see that assets under management need organization that credibly commits to lettingnot be bad for the performance of a fund orga- each of its fund managers run his or her ownnization, we consider the effect that the size of assets. Moreover, being part of a family maythe fund family has on fund performance. Many economize on certain fixed costs, as explainedfunds belong to fund families (e.g., the famous above. Thus, if a large fund is organized like aMagellan fund is part of the Fidelity family of fund family with different managers runningfunds), which allows us to measure separately small pots of money, then scale need not be badthe effect of fund size and the size of the rest of per se, just as family size does not appear to bethe family on fund performance. Controlling for bad for family size, we find that the assets under manage- Therefore, given that managers care a greatment of the other funds in the family that the deal about performance and that scale need notfund belongs to actually increase the funds be bad for performance per se, why does itperformance. A two-standard deviation shock to appear that scale erodes fund performance be-the size of the other funds in the family leads to cause of liquidity? Later in this paper, we ex-about a 4- to 6-basis-point movement in the plore some potential answers to this question.funds performance the following month (or Whereas a small fund can be mn by a singleabout 48- to 72-basis-points movement annu- manager, a large fund naturally needs moreally) depending on the performance measure managers, and so issues of how the decision-used. The effect is smaller than that of fund size making process is organized become important.on performance but is nonetheless statistically We conjecture that liquidity and scale affectand economically significant. As we explain in performance because of certain organizationaldetail below, the most plausible interpretation diseconomies. We pursue this perspective as aof this finding is that there are economies asso- means to motivate additional analysis involvingciated with trading commissions and lending fund stock holdings. We want to emphasize thatfees at the family level. Bigger families like our analysis is exploratory and that a number ofFidelity are able to get better concessions on altemative interpretations, which we describetrading commissions and eam higher lending below, are possible.fees for the stocks held by their funds. There are many types of organizational dis- These two findings—that fund performance economies that lead to different predictions ondeclines with the funds own size but increases why small organizations outperform largewith the size of the other funds in the family— ones.^ We conjecture that one type, known asare both interesting and intuitively appealing. hierarchy costs (see, e.g., Philippe Aghion andFirst, in our cross-sectional regressions, it is Jean Tiroie, 1997; Jeremy C. Stein, 2002), mayimportant to control for family size in order to be especially relevant for mutual funds and mo-find a sizeable impact of fund size on perfor- tivate our analysis by testing some predictions mance. The reason is that these two variables from Stein (2002). The basic premise is that in are positively correlated, and since family size is good for performance, it is important to con- ^ See Patrick Bolton and David S. Scharfstein (1998) and trol for it to identify the negative effect of fund Bengt Holmstrom and John Roberts (1998) for surveys on size. Second, the finding on family size also the boundaries of the firm that discuss such organizational rules out a number of altemative hypotheses for diseconomies.
  4. 4. VOL. 94 NO. 5 CHEN ETAL: DOES FUND SIZE ERODE MUTUAL FUND PERFORMANCE? 1279large organizations with hierarchies, the process involve the processing of soft information thanof agents fighting for (and potentially not hav- funds managed by many managers. Consistenting) their ideas implemented will affect agents with Stein (2002), we find that soto-managedex ante decisions of what ideas they want to funds are significantly more likely than co-work on. Stein (2002) argues that in the pres- managed funds to invest in local stocks andence of such hierarchy costs, small organiza- to do better than co-managed funds at pickingtions ought to outperform large ones at tasks local stocks. Finally, we find that controlling forthat involve the processing of soft information, fund size, solo-managed funds outperform co-(i.e., information that cannot be directly verified managed anyone other than the agent who produces Note that such hierarchy costs are not presentit). If the information is soft, then agents have a at the family level precisely because the familyharder time convincing others of their ideas and typically agrees not to reallocate resourcesit becomes more difficult to pass this informa- across funds. Indeed, different funds in a familytion up the organization. have their own boards that deal with such issues In the context of mutual funds, soft informa- as replacement of managers. So the manager intion most naturally corresponds to research or charge of a fund generally does not have toinvestment ideas related to local stocks (com- worry about the family taking away the fundspanies located near a fund headquarters) since resources and giving them to some other fund inanecdotal evidence indicates that investing in the family. More generally, the idea that agentssuch companies requires that the fund process incentives are weaker when they do not havesoft information, e.g., speaking with CEOs as control over asset allocation or investment de-opposed to simply looking at hard information cisions is in the work of Sanford J. Grossmanlike price-earnings ratios. This means that in and Oliver D. Hart (1986), Hart and John Moorelarge funds with hierarchies in which managers (1990), and Hart (1995).fight to have their ideas implemented, managers In sum, our paper makes a number of contri-may end up expending too much research effort butions. First, we carefully document that per-on quantitative measures of a company (i.e., formance dechnes with fund size. Second, wehard information) so as to convince others to establish the importance of liquidity in mediat-implement their ideas than they ideally would if ing this inverse relationship. Third, we point outthey controlled their own smaller funds. All else that the adverse effect of scale on performanceequal, targe funds may perform worse than need not be inevitable because we find thatsmall ones. family size actually improves fund perfor- Buitding on the work of Joshua D. Coval and mance. Finally, we provide some evidence thatTobias J. Moskowitz (1999, 2001), we find that, the reason fund size and liquidity do in factconsistent with Stein (2002), small funds, espe- erode performance may be due to organizationalcially those investing in small stocks, are diseconomies related to hierarchy costs. It issignificantly more likely than their larger coun- important to note, however, that our analysisterparts to invest in local stocks. Moreover, they into the nature of the organizational disecono-do much better at picking local stocks than large mies is exploratory and that there are otherfunds do.* interpretations, which we discuss below. Another implication of Stein (2002) is that Our paper proceeds as follows. In Section Icontrolling for fund size, funds that are man- we describe the data and in Section II the per-aged by one manager are better at tasks that formance benchmarks. In Section III we present our empirical findings. We explore alternative explanations in Section IV and conclude in " Steins analysis also suggests that large organizations * Section V.need not underperform small ones when it comes to pro-cessing hard information. In the context of the mutual fund I. Dataindustry, only passive index funds like Vanguard are likelyto rely solely on hard information. Most active mutual fundsrely to a significant degree on soft information. Interest- Our primary data on mutual funds come fromingly, anecdotal evidence indicates that scale is not as big an the Center for Research in Security Pricesissue for passive index funds as it is for active mutual funds. (CRSP) Mutual Fund Database, which spans the
  5. 5. 1280 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004years 1962 to 1999. Following many prior stud- 27,431 fund years in our analysis. In eachies, we restrict our analysis to diversified U.S. month, our sample includes on average 741equity mutual funds by excluding from our sam- funds. They have average total net assets (TNA)ple bond, intemational, and specialized sector of $282.5 million, with a standard deviation offunds.^ For a fund to be in our sample, it must $925.8 million. The interesting thing to notereport information on assets under management from the standard deviation figure is that there isand monthly retums. We require also that it a substantial spread in 7WA. Indeed, this be-have at least one year of reported retums. This comes transparent when we disaggregate theseadditional restriction is imposed because we need statistics by fund size quintiles. Those in theto form benchmark portfolios based on past fund smallest quintile have an average TNA of onlyperformance.^ Finally, a mutual fund may enter about $4.7 million, whereas the ones in the topthe database multiple times in the same month if it quintile have an average TNA of over $1.1 bil-has different share classes. We clean the data by lion. The funds in fund size quintiles twoeliminating such redundant observations. through five have a slightly higher mean of Table 1 reports summary statistics for our $352.3 million with a standard deviation of oversample. In panel (A), we report the means and $1 billion. For the usual reasons related tostandard deviations for the variables of interest scaling, the proxy of fund size that we will usefor each fund size quintile, for all funds, and for in our analysis is the log of a funds TNAfunds in fund size quintiles two (next to small- (LOGTNA). The statistics for this variable areest) to five (largest). Edwin J. Elton et al. (2001) reported in the row below that of TNA. Anotherwam that one has to be careful in making in- variable of interest is LOGFAMSIZE, which isferences regarding the performance of funds the log of one plus the cumulative TNA of thethat have less than $15 million in total net assets other funds in the funds family (i.e., the TNAunder management. They point out that there is of a funds family excluding its own TNA).a systematic upward bias in the reported retums In addition, the database reports a host ofamong these observations. This bias is poten- other fund characteristics that we utilize in ourtially problematic for our analysis since we are analysis. The first is fund tumover (TURN-interested in the relationship between scale and OVER), defined as the minimum of purchasesperformance. As we will see shortly, this cri- and sales over average TNA for the calendartique applies only to observations in fund size year. The average fund tumover is 54.2 percentquintile one (smallest), since the funds in the per year. The average fund age (AGE!) is aboutother quintiles typically have greater than $15 15.7 years. The funds in our sample have ex-million under management. Therefore, we focus pense ratios as a fraction of year-end TNA (EX-our analysis on the subsample of funds in fund PRATIO) that average about 97 basis points persize quintiles two through five. It tums out that year. They charge a total load (TOTLOAD) ofour results are robust whether or not we include about 4.36 percent (as a percentage of newthe smallest funds in our analysis. investments) on average. FLOW in month f is We utilize 3,439 distinct funds and a total defined as the funds TNA in month t minus the product of the funds TNA at month t - 12 with the net fund retum between months t - 12 and More specifically, we select mutual funds in the CRSP r, all divided by the funds TNA at month f - 12.Mutual Fund Database that have reported one of the fol-lowing investment objectives at any point. We first select The funds in the sample have an average fundmutual funds with the Investment Company Data, Inc. flow of 24.7 percent per year. These summary(ICDI) mutual fund objective of "aggressive growth," statistics are similar to those obtained for the"growth and income," or "long-term growth." We then add subsample of funds in fund size quintiles twoin mutual funds with the Strategic Insight mutual fundobjective of "aggressive growth," "flexible," "growth and through five.income," "growth," "income-growth," or "small companygrowth." Finally, we select mutual funds with the Wiesen-berger mutual fund objective code of "G," "G-I," "G-I-S," At the end of 1993, we have about 1,508 distinct funds"G-S," "GCI," "I-G," "I-S-G," "MCG," or "SCG." in our sample, very close to the number reported by previ- * We have also replicated our analysis without this re- ous studies that have used this database. Moreover, thestriction. The only difference is that the sample includes summary statistics below are similar to those reported inmore small funds, but the results are unchanged. these other studies as well.
  6. 6. VOL 94 NO. 5 CHENETAL.• DOES EUND SIZE ERODE MUTUAL FUND PERFORMANCE? 1281 TABLE 1—SUMMARY STATisncsPanel A: Time-series averages of cross-sectional averages and standard deviations Mutual fund size quintile 1 2 3 4 5 All funds Quintiles 2-5Number of funds 148.2 147.8 147,8 147.8 147,3 741,4 590,6TNA 4,7 22.2 60.6 165.4 1164,7 282.5 352,3 ($ million) [3.2] [7,2] [16.6] [54,8] [1797.1] [925.8] [1022.7]LOGTNA 1,09 2,94 3,96 4,94 6.45 3,87 4.57 ($ million) [1,01] [0.34] [0.27] [0.33] [0.75] [1,92] [1,38]LOGFAMSIZE 3,70 4,52 5,29 5.91 7.00 5,28 5.68 ($ million) [2,98] [2,89] [2,72] [2,56] [2,16] [2.92] [2.75]TURNOVER 42.07 55.68 59,09 61.20 52,17 54.17 57.07 (% per year) [83,03] [74.00] [68,60] [64.28] [54.56] [71.84] [67.21]AGE 8.17 11.90 14.82 18.43 25.16 15.67 17,57 (years) [8.54] [10.73] [12.85] [14,38] [15,06] [13,96] [14,33]EXPRATIO 1,29 1.08 0.94 0,85 0,68 0,97 0,89 (% per year) [1.11] [0.59] [0.46] [0.37] [0,31] [0.68] [0,48]TOTLOAD 3.41 4.19 4,32 4,57 5.28 4.36 4.59 (%) [3.32] [3,32] [3.34] [3.39] [2,88] [3.36] [3,32]FLOW 30.79 30,66 26,97 21.27 13.54 24,67 23.13 (% per year) [113,55] [113,36] [101,66] [84.08] [59.04] [102.64] [96.60]Panel B: Time-series averages of (monthly) correlations between fund characteristics (using alt funds) 77V-4 LOGTNA LOGFAMSIZE TURNOVER AGE EXPRATIO TOTLOAD FLOWTNA 1.00 0.56 0.24 -0,05 0.27 -0.19 0.10 -0.03LOGTNA 1.00 0.40 0.06 0.44 -0.31 0.19 -0.07LOGFAMSIZE 1.00 0.08 0.08 -0,19 0,25 -0.01TURNOVER 1.00 0.01 0.17 0.05 -0.01AGE 1.00 -0.13 0.19 -0.18EXPRATIO 1.00 -0,05 0,08TOTLOAD 1.00 -0.04FLOW 1.00Panel C: Time-series averages of (monthly) correlations between fund characteristicJ (excluding smallest 20 percent of funds) TNA LOGTNA LOGFAMSIZE TURNOVER AGE EXPRATIO TOTLOAD FLOWTNA 1,00 0,66 0.23 -0.08 0.24 -0.24 0.09 -0.03LOGTNA 1,00 0,35 -0.05 0,37 -0,36 0.13 -0.07LOGFAMSIZE 1.00 0.07 0.03 -0.17 0.22 -0,01TURNOVER 1.00 -0,04 0,26 0.03 0,01AGE 1,00 -0,18 0.17 -0,19EXPRATIO 1.00 0.01 0,10TOTLOAD 1,00 -0,05FLOW 1.00Panel D: Time-series averages of (monthly) cross-sectional averages of market-adjusted fiind retums Mutual fund size quintile 1 2 3 4 5 All funds Quintiles 2-5FUNDRET 0,09% 0,02% 0,03% -0,06% -0,06% 0,01% -0.02% (Gross) [3,04%] [2.64%] [2,61%] [2.46%] [2,00%] [2,62%] [2.48%]FUNDRET -0,02% -0,07% -0.05% -0,13% -0.12% -0.08% -0.09% (Net) [3,04%] [2,64%] [2.61%] [2,46%] [2.00%] [2.62%] [2,48%]Notes: This table reports summary statistics for the fiinds in our sample. "Number of funds" is the number of mutual funds that meet our selectioncriteria for being an active mutual fund in each month, TNA is the total net assets under management in millions of dollars, LOGTNA is the logarithmof TNA. LOGFAMSIZE is the logarithm of one plus the assets under management of the other funds in the family that the fund belongs to (excludingthe asset base of the fund itself). TURNOVER is fund tumover. defined as the minimum of aggregate purchases and sales of securities divided by theaverage TNA over the calendar year. AGE is the number of years since the establishment of the fund. EXPRATIO is the total annual management feesand expenses divided by year..end TNA. TOTLOAD is the total front-end, deferred, and rear-end charges as a percentage of new investments. FLOWis the percentage new fund flow into the mutual fund over the past year. TNA, LOGFAMSIZE, and FLOW are reported monthly. All other fundcharacteristics are reported once a year, EUNDRET is the monthly market-adjusted fund retum. These retums are calculated before (gross) and after(net) deducting fees and expenses. Panel (A) reports the time-series averages of monthly cross-sectional averages and monthly cross-sectional standarddeviations (shown in brackets) of fund characteristics. Panels (B) and (C) report the time-series averages of the cross-sectional correlations betweenfund characteristics. Panel (D) reports the time-series averages of monthly cross-sectional averages of market-adjusted fund retums. In panels (A) and(B), fund size quintile 1 (5) has the smallest (largest) funds. The sample is from January 1963 to December 1999.
  7. 7. 1282 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004 Panel (B) of Table 1 reports the time-series funds in quintile five underperform the marketaverages of the cross-sectional correlations be- by 6 basis points. The difference of 8 basistween the various fund characteristics. A num- points per month, or 96 basis points a year, is anber of patterns emerge. First, LOGTNA is economically interesting number. Net fund re-strongly correlated with LOGFAMSIZE (0.40). tums also appear to be negatively correlatedSecond, EXPRATIO varies inversely with LOG- with fund size, though the spread is somewhatTNA (-0.31), while TOTLOAD and AGE vary smaller than using gross retums. We do notpositively with LOGTNA (0.19 and 0.44, re- want to overinterpret these results since we havespectively). Panel (C) reports the analogous not controlled for heterogeneity in fund stylesnumbers for the funds in fund size quintiles two nor calculated any type of statistical signifi-through five. The results are similar to those in cance in this table.panel (B). It is apparent from panels (B) and (C) In addition to the CRSP Mutual Fund Data-that we need to control for these fund charac- base, we also utilize the CDA Spectmm Data-teristics in estimating the cross-sectional rela- base to analyze the effect of fund size on thetionship between fund size and performance. composition of fund stock holdings and the Finally, we report in panel (D) the means and performance of these holdings. The reason westandard deviations for the monthly fund re- need to augment our analysis with this databasetums, FUNDRET, where we measure these re- is that the CRSP Mutual Fund Database doesturns in a couple of different ways. We first not contain information on fund positions inreport summary statistics for gross fund retums individual stocks. The CDA Spectrum Databaseadjusted by the retum of the market portfolio reports a funds stock positions on a quarterly(simple market-adjusted retums). Monthly basis but it is not available until the early 1980sgross fund retums are calculated by adding back and does not report a funds cash positions.the expenses to net fund retums by taking the Russ Wermers (2000) compared the funds inyear-end expense ratio, dividing it by 12, and these two databases and found that the activeadding it to the monthly returns during the year. funds represented in the two databases are com-For the whole sample, the average monthly per- parable. So while the CDA Spectmm Databaseformance is 1 basis point with a standard devi- is less effective than the CRSP Mutual Fundation of 2.62 percent. The funds in fund size Database in measuring performance, it is ade-quintiles two through five do slightly worse, quate for analyzing the effects of fund size onwith a mean of - 2 basis points and a standard stock positions. We will provide a more detaileddeviation of 2.48 percent. We also report these discussion of this database in Section III.summary statistics using net fund retums. Thefunds in our sample underperform the market by II. Methodology8 basis points per month, or 96 basis points peryear, after fees and expenses are deducted. Our empirical strategy udli2£s cross-sectional These figures are almost identical to those variation to see how fund performance variesdocumented in other studies. These studies find with lagged fund size. We could have adopted athat fund managers do have the ability to beat or fixed-effects approach by looking at whetherstay even with the market before management changes in a funds performance are related tofees (see, e.g., Grinblatt and Titman, 1989; changes in its size. Such an approach is subject,Grinblatt et al., 1995; Kent Daniel et al., 1997). however, to a regression-to-the-mean bias. AHowever, mutual fund investors are apparently fund with a year or two of lucky performancewilling to pay a lot in fees for limited stock- will experience an increase in fund size. Butpicking ability, which results in their risk- performance will regress to the mean, leading toadjusted fund retums being significantly a spurious conclusion that an increase in fundnegative (see, e.g., Michael C. Jensen, 1968; size is associated with a decrease in fund re-Burton G. Malkiel, 1995; Gmber, 1996). tums. Measuring the effect of fund size on Moreover, notice that smaller funds appear to performance using cross-sectional regressionsoutperform their larger counterparts. For in- is less subject to such bias. Indeed, it may evenstance, funds in quintile two have an average be conservative given our goal, since largermonthly gross retum of 2 basis points, while funds are likely to be better funds or they would
  8. 8. VOL. 94 NO. 5 CHEN ETAL: DOES FUND SIZE ERODE MUTUAL FUND PERFORMANCE? 1283not have become large in the first place. We are stock index net of the one-month Treasurylikely to be biased toward finding any disecono- rate (VWRF), the returns to the Fama andmies of scale using cross-sectional variation. French (1993) SMB (small stocks minus large There are two major worries that arise, how- stocks) and HML (high book-to-market stocksever, when using cross-sectional variation. The minus low book-to-market stocks) portfolios,first is that funds of different sizes may be in and the retums-to-price momentum portfoliodifferent styles. For instance, small funds might MOM 12 (a portfolio that is long stocks that arebe more likely than large funds to pursue small past-12-month winners and short stocks that arestock, value stock, and price momentum strate- past-12-month losers and hold for one month).gies, which have been documented to generate The summary statistics for these portfolio re-abnormal retums. While it is not clear that one tums are similar to those reported in other mu-necessarily wants to adjust for such heterogene- tual fund studies.ity, it would be more interesting if we found that Since we are interested in the relationshippast fund size influences future performance between fund size and performance, we sorteven after accounting for variations in fund mutual funds at the beginning of each monthstyles. The second worry is that fund size might based on the quintile rankings of their previous-be correlated with other fund characteristics month TNA.^ We then track these five portfoliossuch as fund age or tumover, and it may be for one month and use the entire time series ofthese characteristics that are driving perfor- their monthly net retums to calculate the load-mance. For instance, fund size may be measur- ings to the various factors (VWRF, SMB, HML,ing whether a fund is active or passive (which MOM 12) for each of these five portfolios. Formay be captured by fund tumover). While we each month, each mutual fund inherits the load-have tried our best to mle out passive funds in ings of the one of these five portfolios that itour sample constmction, it is possible that some belongs to. In other words, if a mutual fundfunds may just be indexers. And if it tums out stays in the same-size quintile throughout itsthat indexers happen to be large funds because life, its loadings remain the same. But if itmore investors put their money in such funds, moves from one size quintile to another duringthen size may be picking up differences in the a certain month, it inherits a new set of load-degree of activity among funds. ings with which we adjust its next months performance. A. Fund Performance Benchmarks Panel (B) reports the loadings of the five fund-size (TNA) sorted mutual fund portfolios A very conservative way to deal with the first using the CAPMworry about heterogeneity in fund styles is toadjust for fund performance by various bench-marks. In this paper, we consider, in addition to (1)simple market-adjusted retums, retums adjusted R,,, = a, + ^,. VWRF, + £,.,, f = 1,..., rby the Capital Asset Pricing Model (CAPM) ofWilliam F. Sharpe (1964). We also considerretums adjusted using the Eugene F. Fama where R;, is the (net fund) retum on one of ourand Kenneth R. French (1993) three-factor five fund-size-sorted mutual fund portfolios inmodel, and this model augmented with the month t in excess of the one-month T-bill re-momentum factor of Narasimhan Jegadeesh and tum, a, is the excess retum of that portfolio, j3,-Titman (1993), which has been shown in is the loading on the market portfolio, and s,.,various contexts to provide explanatory power stands for a generic error term that is uncorre-for the observed cross-sectional variation in lated with all other independent variables. Asfund performance (see, e.g., Mark M. Carhart,1997). Panel (A) of Table 2 reports the summary We also sort mutual funds by their past-12-month re-statistics for the various portfolios that make up tums to form benchmark portfolios. Our results are un-our performance benchmarks. Among these changed when using these benchmark portfolios. We omitare the returns on the CRSP value-weighted these results for brevity.
  9. 9. 1284 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004 TABLE 2—SUMMARY STATISTICS FOR PERFORMANCE BENCHMARKSPanel A: Summary statistics of the factors Cross-correlations Mean SD ofFactor retum retum VWRF SMB HML MOM 12VWRF 0,58% 4,37% 1,00 0,32 -0,39 -0,02SMB 0,17% 2,90% 1,00 -0,16 -0,30HML 0,34% 2,63% 1,00 -0,15MOM 12 0,96% 1,00Panel B: Loadings calculated using the CAPM CAPMPortfolio Alpha VWRF1 (small) 0,04% 0,872 -0,02% 0,913 -0,01% 0,934 -0,09% 0,925 (large) -0,07% 0,91Panel C: Loadings calculated using the 3-Factor model and the 4-Factor model 3-Factor model 4-Factor modelPortfolio Alpha VWRF SMB HML Alpha VWRF SMB HML MOM 121 (small) 0,01% 0,82 0,29 0,03 -0,02% 0,82 0,30 0,04 0,032 -0,03% 0,84 0,27 -0,01 -0,09% 0,85 0,30 0,00 0,053 0,01% 0,87 0,22 -0,05 -0,06% 0,87 0,25 -0,03 0,064 -0,06% 0,87 0,18 -0,05 -0,13% 0,87 0,20 -0,04 0,065 (large) -0,05% 0,88 0,08 -0,06 -0,10% 0,88 0,10 -0,05 0,05Notes: This table reports the loadings of the five (equal-weighted) TWA-sorted fund portfolios on various factors. Panel (A)reports the summary statistics for the factors, VWRF is the retum on the CRSP value-weighted stock index in excess of theone-month Treasury rate, SMB is the retum on a portfolio of small stocks minus large stocks, HML is the retum on a portfoliolong high book-to-market stocks and short low book-to-market stocks, MOM 12 is the retum on a portfolio long stocks thatare past-12-month winners and short those that are past-12-month losers. Panel (B) reports the loadings calculated using theCAPM, Panel (C) reports the loadings calculated using the Fama-French (1993) 3-Factor model and this model augmentedwith the momentum factor (4-Factor model). The sample period is from January 1963 to December 1999,Other papers have found, the average mutual (3) R,,, = a,. + ft,, VWRF, + jS,,^ SMB,fund has a beta of around 0.91, reflecting thefact that mutual funds hold some cash or bonds + i3,,3 HML, + j3,,4 MOM 12, + s,,.in their portfolios. Notice that there is only aslight variation in the market beta (j8,s) fromthe smallest to the largest fund size portfolio:the smallest portfolio has a somewhat smaller where R,-, is the (net fund) retum on one of ourbeta, but not by much. five size-sorted mutual fund portfolios in month Panel (C) reports the loadings for two addi- t in excess of the one-month T-bill retum, a,- istional performance models, the Fama-French the excess retum, j3,s are loadings on the var-three-factor model and this three-factor model ious portfolios, and e,,, stands for a generic erroraugmented by a momentum factor term that is uncorrelated with all other indepen- dent variables. We see that small funds tend to(2) R,, = a, + p,, VWRF, + jB..^ SMB, have higher loadings on SMB and HML, but large funds tend to load a bit more on momen- + )3,,3 HML, + e,, t=,...,T tum. For instance, the loading on SMB for the
  10. 10. VOL. 94 NO. 5 CHEN ETAL: DOES FUND SIZE ERODE MUTUAL FUND PERFORMANCE? 1285 three-factor model for funds in quintile one is stands for a generic error term that is uncorre- 0.29 while the corresponding loading for funds lated with all other independent variables. The in quintile five is 0.08. And whereas large funds coefficient of interest is ({), which captures the load negatively on HML (-0.06 for the largest relationship between fund size and fund perfor-funds), the smallest funds load positively on mance, controlling for other fund characteris-HML (0.03). (Eric G. Falkenstein [1996] also tics. 7 is the vector of loadings on the controlfinds some evidence that larger funds tend to variables. We then take the estimates from theseplay large and glamour stocks by looking at monthly regressions and follow Fama and Mac-fund holdings.) Beth (1973) in taking their time series means We have also redone all of our analysis by and standard deviations to form our overall es-calculating these loadings using gross fund re- timates of the effects of fund characteristics ontums instead of net fund retums. As the results performance.are very similar to using net fund retums, for We will also utilize an additional regressionbrevity we will use the loadings summarized in specification given by the following:Table 2 to adjust fund performance below(whether it be gross or net retums). Using the (5) FUNDRET,, = fjL + i, -1entire time series of a particular fund (we re-quire at least 36 months of data), we also cal-culate the loadings separately for each mutualfund using equations (1) to (3). This techniqueis not as good in the sense that we have a muchmore selective requirement on selection and the where the dummy indicator Ind,styie) (thatestimated loadings tend to be very noisy. In any equals one if a fund belongs to a certain stylecase, our results are unchanged, so we omit category and zero otherwise) and the remainingthese results for brevity. variables are the same as in equation (3). The coefficient of interest is <^2, > which measures the B. Regression Specifications differential effect of fund size on retums across different fund styles. It is important to note that To deal with the second concem related to the we do not attempt to measure whether the rela-correlation of fund size with other fund charac- tionship between fund performance and fundteristics, we analyze the effect of past fund size size may be nonlinear. While some theorieson performance in the regression framework might suggest that very small funds may haveproposed by Fama and James D. MacBeth. inferior performance to medium-sized ones be-(1973), where we can control for the effects of cause they are being operated at a suboptimallyother fund characteristics on perfonnance. Spe- small scale, we are unable to get at this issuecifically, the regression specification that we because inference regarding the performance ofutilize is the smallest funds is problematic for the reasons articulated in Section 11.(4) FUNDRET,, = /i, III. Results A. Relationship between Fund Size andwhere FUNDRETi, is the retum (either gross or Performancenet) of fund / in month t adjusted by variousperformance benchmarks, /a is a constant, LOG- In Table 3, we report the estimation resultsTNAi,_, is the measure of fund size, and X,,,_, for the baseline regression specification given inis a set of control variables (in month t - ) that equation (4). We begin by reporting the resultsincludes LOGFAMSIZEi,_,, TURNOVERi,_,, for gross fund retums. The sample consists ofAGEi,^ „ EXPRATIOi,^^, TOTLOADi,_ j , and funds from fund size quintiles two through five.FLOWj,^^. In addition, we include in tifie right- Notice that the coefficient in front of LOGTNAhand side LAGFUNDRETi,_^, which is the is negative and statistically significant acrosspast-year retum of the fund. Here, e,, again the four perfonnance measures. The coefficients
  11. 11. 1286 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004 TABLE 3—REGRESSION1 OF FUND PERFORMANCE ON LAGGED FUND SIZE Gross fund retums Net fund retums Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorINTERCEPT 0,056 0,087 0,080 0,019 0,026 0,056 0,049 -0,011 (0,96) (1,63) (1,28) (0,30) (0,44) (1,05) (0,79) (0,18)LOGTNA,,., -0,028 -0,028 -0,023 -0,020 -0,025 -0,025 -0,020 -0,018 (3,02) (3,04) (2,42) (2,15) (2,75) (2,76) (2,16) (1,89)LOGFAMSIZE,,., 0,007 0,007 0,007 0,007 0,007 0,007 0,007 0,007 (2,26) (2,27) (2,22) (2,21) (2,33) (2,34) (2,29) (2,28)TURNOVER,,., 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0.000 (0,85) (0,86) (0,85) (0,83) (0,77) (0,78) (0,77) (0,75)AGE,,., -0,001 -0,001 -0,001 -0,001 0,000 0,000 -0,001 -0,001 (0,62) (0,62) (0,64) (0,63) (0,52) (0,53) (0,55) (0,54)EXPRATIO,,., -0,004 -0,004 -0,007 -0,007 -0,039 -0,038 -0,041 -0,041 (0,11) (0,09) (0,18) (0,18) (0,97) (0,95) (1,04) (1,05)TOTLOAD,,., 0,003 0,003 0,003 0,003 0,003 0,003 0,003 0,003 (1,26) (1,25) (1,26) (1,29) (1,21) (1,20) (1,21) (1.25)FLOW,,., 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 (0,50) (0,50) (0,51) (0,49) (0,47) (0,47) (0,48) (0,46)LAGFUNDRET,,., 0,029 0,028 0,028 0,029 0,029 0,029 0,029 0,029 (6,00) (5,98) (6,00) (5,99) (6,03) (6,01) (6.03) (6,02)No, of months 444 444 444 444 444 444 444 444Notes: This table shows the Fama-MacBeth (1973) estimates of monthly fund retums regressed on fund characteristics laggedone month. The sample includes only funds that fall within fund size quintiles two to five. Fund retums are calculated before(gross) and after (net) deducting fees and expenses. These retums are adjusted using the market model, the CAPM, theFama-French (1993) 3-Factor model, and the 4-Factor model. The dependent variable is FUNDRET. LOGTNA is the naturallogarithm of TNA. LOGFAMSIZE is the natural logarithm of one plus the size of the family that the fund belongs to,TURNOVER is fund tumover and AGE is the number of years since the organization of the mutual fund. EXPRATIO is thetotal annual management fees and expenses divided by TNA. TOTLOAD is the total front-end, deferred, and rear-end chargesas a percentage of new investments, FLOW is the percentage new fund flow into the mutual fund over the past one year,LAGFUNDRET is the cumulative (buy-hold) fund retum over the past 12 months. The sample is from January 1963 toDecember 1999, The f-statistics are adjusted for serial correlation using Newey-West (1987) lags of order three and are shownin parentheses.obtained using either market-adjusted or standard deviation shock in fund size yields aCAPM-adjusted retums are around -0.028 movement in next years fund retum that iswith r-statistics of around three. Since one stan- approximately 10 percent of the annual volatil-dard deviation of LOGTNA is 1.38, a two-stan- ity of mutual funds (96 basis points divided bydard deviation shock to fund size means that 10 percent). Another way to think about theseperformance changes by -0.028 times 2.8, or 8 magnitudes is that the typical fund has a grossbasis points per month (96 basis points per fund perfonnance net of the market retum thatyear). For the other two performance bench- is basically near zero. As a result, a spread inmarks, the 3-factor and 4-factor adjusted re- fund performance of anywhere from 70 to 96tums, the coefficients are slightly smaller at basis points a yeiir is quite economically-0.02, but both are still statistically significant significant.with r-statistics of between 2.1 and 2.5. For Table 3 also reveals a number of other inter-these coefficients, a two-standard deviation esting findings. The only other variables besideshock to fund size means that performance fund size that are statistically significant arechanges by around 70 basis points annually. LOGFAMSIZE and LAGFUNDRET. Interest- To put these magnitudes into some perspec- ingly, LOGFAMSIZE predicts better fund per-tive, observe that a standard deviation of mutual formance. We will have much more to sayfund retums is around 10 percent annually, with about the coefficient in front of LOGFAMSIZEslight variations around this figure depending later. It should be emphasized at this point thaton the performance measure. Hence, a two- it is important to control for family size in order
  12. 12. VOL 94 NO. 5 CHEN ETAL: DOES FUND SIZE ERODE MUTUAL FUND PERFORMANCE? 1287 to find a sizeable impact of fund size on perfor- bottom fund size quintile is biased upward, so mance. This is because fund and family size are we should not draw too much from this analysis positively correlated, and since family size is other than that our results are unchanged by good for performance, it is important to control including them in the sample. For brevity, we for it to identify the negative effect of fund size. report only the coefficients in front of LOGTNA This is a major reason why other studies that and LOGFAMSIZE. Using gross fund retums, have had fund size as a control variable in the coefficient in front of LOGTNA ranges from explaining fund retums do not find any signifi- -0.019 to -0.026 depending on the perfor- cant effect. As a result, these studies mention mance measure. For net fund retums, it ranges fund size only in passing and do not provide any from -0.015 to -0.022. All the coefficients are analysis whatsoever. statistically significant at the 5-percent level, The fact that the coefficient in front of with the exception of the coefficient obtained LAGFUNDRET is significant suggests that using 3-factor adjusted net fund retums. The there is some persistence in fund retums. As for coefficient in this instance is significant only at the rest of the variables, some come in with the 10-percent level of significance. The mag- expected signs, though none is statistically sig- nitudes are somewhat smaller using the full nificant. The coefficient in front of EXPRATIO sample than the sample that excludes the small- is negative, consistent with industry observa- est quintile. This difference, however, is not tions that larger funds have lower expense ra- large. Moreover, the coefficients in front of tios. The coefficients in front of TOTLOAD and LOGFAMSIZE are similar in magnitude to TURNOVER are positive, as these two variables those obtained in Table 3. As such, we conclude are thought to be proxies for whether a fund is that our key findings in Table 3 are robust to active or passive. Fund fiow has a negligible including all funds in the sample. ability to predict fund retums, and the age of the In panel (B), we attempt to predict a fundsfund comes in with a negative sign but is sta- cumulative retum next year rather than its retumtistically insignificant. next month. Not surprisingly, we find similar We next report the results of the baseline results to those in Table 3. The coefficient inregression using net fund retums. The coeffi- front of LOGTNA is negative and statisticallycient in front of LOGTNA is still negative and significant across all performance benchmarks.statistically significant across all performance Indeed, the economic magnitudes implied bybenchmarks. Indeed, the coefficient in front of these estimates are similar to those obtained inLOGTNA is only slightly smaller using net fund Table 3. These statements apply equally toretums than using gross fund retums. The ob- LOGFAMSIZE.servations regarding the economic significance In panels (C) and (D), we split our bench-of fund size made earlier continue to hold. If mark sample in half to see whether our esti-anything, they are even more relevant in this mates on LOGTNA and LOGFAMSIZE dependcontext since the typical fund tends to under- on particular subperiods 1963 to 1980 and 1981perform the market by about 96 basis points to 1999. It appears that LOGTNA has a strongannually. The coefficients in front of the other negative effect on performance regardless of thevariables have similar signs to those obtained subperiods, since the economic magnitudes areusing gross fund retums. Importantly, keep in very similar to those obtained in Table 3. Wemind that the coefficient in front of LOGFAM- would not be surprised if the coefficients wereSIZE is just as statistically and economically not statistically significant since we havesignificant using net fund retums as gross fund smaller sample sizes in panels (C) and (D). Butretums. even with only half the sample size, LOGTNA In Table 4, we present various permutations comes in significantly for a number of the per-involving the regression specification in equa- formance measures. In contrast, it appears thattion (4) to see if the results in Table 3 are robust. the effect of LOGFAMSIZE on perfonnance isIn panel (A), we present the results using all the much more pronounced in the latter half of thefunds in our sample, including those in the sample.smallest fund size quintile. As we mentioned The analyses in Tables 3 and 4 strongly in-earlier, the performance of the funds in the dicate that fund size is negatively related to
  13. 13. 1288 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004 TABLE 4—REGRESSION OF FUND RETURNS ON LAGGED FUND SIZE, ROBUSTNESS CHECKSPanel A: Sample includes all funds Gross fund retums Net fund retums Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorLOGTNA,, , -0,023 -0,026 -0,019 -0,021 -0,020 -0,022 -0,015 -0,017 (2,59) (2.94) (2,22) (2,48) (2,16) (2,49) (1,76) (2,02)LOGFAMSIZE,, , 0,006 0,006 0,006 0,006 0,006 0,006 0,006 0,006 (1,99) (2,03) (1,99) (2,05) (2,10) (2,15) (2,11) (2,17)No, of months 444 444 444 444 ^AA 444 444 444Panel B: Dependent variable is 12-month (non-overlapping) fund retums Gross fund retums Net fund retums Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorLOGTNA,, , -0,436 -0,440 -0,345 -0,312 -0,402 -0,406 -0,312 -0,280 (3,26) (3,27) (2,40) (2,19) (3,07) (3,07) (2,20) (1,99)LOGFAMSIZE,,., 0,088 0,089 0,088 0,088 0,090 0,091 0,090 0,090 (2,05) (2,06) (2,05) (2,07) (2,10) (2,12) (2,11) (2,12)No, of years 37 37 37 37 37 37 37 37Panel C: Sample period is from 1963 to 1980 Gross fund retums Net fund retums Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorLOGTNA,,., -0,035 -0,034 -0,021 -0,019 -0,032 -0,032 -0,019 -0,016 (2,41) (2,42) (1,51) (1,33) (2,22) (2,23) (1,32) (1.15)LOGFAMSIZE,,., 0,002 0,002 0,002 0,002 0,002 0,002 0,002 0,002 (0,49) (0,50) (0,45) (0,44) (0,56) (0,58) (0,53) (0,52)No, of months 216 216 216 216 216 216 216 216Panel D: Sample period is from 1981 to 1999 Gross fund retums Net fund retums Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorLOGTNA,, , -0,021 -0,022 -0.024 -0,022 -0,019 -0,019 -0,022 -0,019 (1,84) (1,86) (1,93) (1,71) (1,64) (1,65) (1,74) (1,53)LOGFAMSIZE,,., 0,012 0,012 0,012 0,012 0,012 0,012 0,012 0,012 (2,53) (2,53) (2,50) (2,50) (2,55) (2,55) (2,52) (2.52)No, of months 228 228 228 228 228 228 228 228Notes: This table presents robustness checks of the regression specification in Table 3, In panel (A), the sample includes allfunds. In panel (B), the dependent variable is 12-month fund retums and the regressions are non-overlapping. In panel (C),the sample consists only of observations from 1963 to 1980, In panel (D), the sample consists only of observations from 1981to 1999. LOGTNA is the natural logarithm of TNA. LOGFAMSIZE is the natural logarithm of one plus the size of the familythat the fund belongs to. Estimates of the intercept and other independent variables are omitted for brevity. The otherindependent variables include TURNOVER, AGE, EXPRATIO, TOTLOAD, FLOW, and LAGFUNDRET. The f-statistics areadjusted for serial correlation using Newey-West (1987) lags of order three and are shown in parentheses.future fund perfonnance. Moreover, we are able number of potential explanations for thisto rule out that this relationship is driven by relationship.differences in fund styles or mechanical corre- Three explanations come to mind. First, thelations of fund size with other observable fund lagged fund size and performance relationshipcharacteristics. However, there still remain a is due to transaction costs associated with li-
  14. 14. VOL. 94 NO. 5 CHEN ETAL: DOES FUND SIZE ERODE MUTUAL EUND PERFORMANCE? 1289 quidity or price impact. We call this the "liquid- reason is that small stocks are notoriously illiq- ity hypothesis." Second, perhaps investors in uid. As a result, funds that have to invest in large funds are less discriminating about returns small stocks are more likely to need new stock than investors in small funds. One reason why ideas with asset base growth, whereas large this might be the case is that such large funds as funds can simply increase their existing posi-Magellan are better at marketing and are able tions without being hurt too much by price to attract investors through advertising. In impact.contrast, small funds without such marketing Importantly, this test of the liquidity hypoth-operations may need to rely more on perfor- esis also allows us to discriminate between themance to attract and maintain investors. We other two hypotheses. First, existing researchcall this the "clientele hypothesis." Third, finds that there is little variation in incentivesfund size is inversely related to performance between "small cap" funds (i.e., funds that havebecause of fund incentives to lock in assets to invest in small stocks) and other funds (see,under management after a long string of good e.g., Andres Almazan et al., 2001). Hence, thispast performances.^ When a fund is small and prediction ought to help us discriminate be-has a limited reputation, the manager goes tween our hypothesis and the alternativeabout the business of stock picking. But as the "agency-risk-taking" story involving fund in-fund gets large because of good past perfor- centives. Moreover, since funds that have tomance, the manager may for various reasons invest in small stocks tend to do better thanlock in his fund size by being passive (or other funds, it is not likely that our results arebeing a "closet indexer" as practitioners put due to the clientele of these funds being moreit). We call this the "agency-risk-taking hy- irrational than those investing in other funds.pothesis." The general theme behind the sec- This allows us to distinguish the liquidity storyond and third hypotheses is that after funds from the chentele story.reach a certain size, they no longer care about In the CRSP Mutual Fund Database, we aremaximizing returns. fortunate that each fund self-reports its style, and so we looked for style descriptions contain- B. The Role of Liquidity: Fund Size, Fund ing the words "small cap." It turns out that one Styles, and the Number of Stocks in a Funds style, "Small Cap Growth," fits this criterion. Portfolio Funds in this category are likely to have to invest in small stocks by virtue of their style In order to narrow the list of potential expla- designation. Thus, we identify a fund in ournations, we design a test of the liquidity hypoth- sample as either Small Cap Growth if it has everesis. To the extent that liquidity is driving our reported itself as such or "Not Small Capfindings above, we would expect to see that Growth." (Funds rarely change their self-fund size matters much more for performance reported style.) Unfortunately, funds with thisamong funds that have to invest in small stocks designation are not prevalent until the early(i.e., stocks with small market capitalization) 1980s. Therefore, throughout the analysis inthan funds that get to invest in large stocks. The this section, we limit our sample to the 1981- 1999 period. During this period, there are on average 165 such funds each year. The corre- More generally, it may be that after many years of good sponding number for the overall sample duringperformance, bad performance follows for whatever reason. this period is about 1,000. Therefore, Small CapWe are offering here a plausible economic mechanism for Growth represents a small but healthy slice ofwhy this might come about. The ex ante plausibility of thisalternative story is, however, somewhat mixed. On the one the overall population. Also, the average TNA ofhand, the burgeoning empirical literature on career concerns these funds is $212.9 million with a standardsuggests that fund managers ought to be bolder with past deviation of $566.7 million. The average TNAsuccess (see, e.g., Judith A. Chevalier and Glenn D. Ellison, of a fund in the overall sample during this latter1999 and Hong, Kubik, and Solomon, 2000). On the otherhand, the fee structure means that funds may want to lock in period is $431.5 million with a standard devia-assets under management because investors are typically tion of $1.58 billion. Thus, Small Cap Growthslow to pull their money out of funds (Brown et al., 1996; funds are smaller than the typical fund. But theyChevalier and Ellison, 1997). are still quite big and there is a healthy fund size
  15. 15. 1290 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004distribution among them, so that we can mea- Cap fund and zero otherwise) and an addi-sure the effect of fund size on performance. tional interaction term involving LOGTNA and Table 5, panel (A), reports what happens to IndjLC) as in equation (5). We first report thethe results in Table 3 when we augment the results for gross fund returns. The coefficient inregression specifications by including a front of LOGTNA is about -0.03 (across thedummy indicator Ind(no, SCG} (which equals four performance benchmarks). Importantly,one if a fund is not Small Cap Growth and the coefficient in front of the interaction term iszero otherwise) and an additional interaction positive and statistically significant (about 0.03term involving LOGTNA and Indjno, SCQ) as across the four performance benchmarks). Thisin equation (5). We first report the results for is the sign predicted by the liquidity hypothesisgross fund returns. The coefficient in front of since it says that for Large Cap funds, there isLOGTNA is about -0.06 (across the four no effect of fund size on performance. Theperformance benchmarks). Importantly, the results using net fund returns reported arecoefficient in front of the interaction term is similar.positive and statistically significant (about These findings suggest that liquidity plays an0.04 across the four performance bench- important role in eroding performance. More-marks). This is the sign predicted by the li- over, as many practitioners have pointed out,quidity hypothesis since it says that for Not since managers of funds get compensated onSmall Cap Growth funds, there is a smaller assets under management, they are not likelyeffect of fund size on performance. The effect voluntarily to keep their funds small just be-is economically interesting as well. Since the cause it hurts the returns of their investors, whotwo coefficients, -0.06 and 0.04, are similar may not be aware of the downside of scale (seein magnitude, a sizeable fraction of the effect Becker and Vaughn, 2001, and Section IV forof fund size on performance comes from further discussion). small cap funds. The results using net fund As we pointed out in the beginning of thereturns reported are similar. paper, however, liquidity means that large In panel (A) of Table 5, we compared Small funds need to find more stock ideas than small Cap Growth funds to all other funds. In panel funds, but it does not therefore follow that (B) of Table 5, we delve a bit deeper into the they cannot. Indeed, large funds can hire "liquidity hypothesis" by looking at how fund more managers to follow more stocks. To see performance varies with fund size depending that this is possible, we calculate some basic on whether a fund is a Large Cap fund, one summary statistics on fund holdings by fund that is supposed to invest in large-cap stocks." size quintiles. Since the CRSP Mutual Fund We augment the regression specification of Database does not have this information, we Table 3 by introducing a dummy variable turn to the CDA Spectrum Database. We take (whieh equals one if a fund is a Large data from the end of September 1997 and calculate the number of stocks held by each fund. The median fund in the smallest fund " We merged the CRSP Mutual Fund Database and the size quintile has about 16 stocks in its port-CDA Spectrum Database so that we have information on the folio, while the median fund in the largeststocks held by the funds in our sample. We have verified fund size quintile has about 66 stocks in itsthat mutual funds with the self-reported fund style of SmallCap Growth do indeed invest in stocks with a much lower porffolio, even though the large funds aremarket capitalization than held by funds of other styles. In many times bigger than their smaller counter-contrast, mutual funds whose self-reported fund style is parts. These numbers make clear that large"Growth and Income" invest in much larger stocks when funds do not significantly scale up the numbercompared to funds with other styles. As a result, we char- of stocks that they hold or cover relative toacterize these funds as Large Cap funds in our analysisabove. Moreover, we have also verified that Small Cap their smaller counterparts. Yet, there is plentyfunds hold stocks that are more illiquid in the sense that thestocks in their portfolios tend to have much larger Kylelambdas and bid-ask spreads than the stocks held byfunds of other styles. And Large Cap funds hold stocks Related literature finds that mutual fund investors arethat are much more liquid than those held by funds of susceptible to marketing (see, e.g., Gruber, 1996; Eric R.other styles. Sirri and Peter Tufano, 1998; Lu Zheng, 1999).
  16. 16. VOL. 94 NO. 5 CHEN ETAL: DOES FUND SIZE ERODE MUTUAL FUND PERFORMANCE? 1291 TABLE 5—EFFECT OF FUND SIZE ON P E R F O R M A N C E B Y F U N D STYLEPanel A: Small Cap Growth funds Gross fund ireturns Net fund returns Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorINTERCEPT 0,205 0,257 0,320 0.263 0,175 0,226 0,289 0,231 (1.27) (1.53) (2,44) (1.98) (1,08) (1,34) (2,20) (1.75)IND|„„, scoi -0,250 -0.252 -0,260 -0.262 -0,249 -0,251 -0.259 -0.261 (1,54) (1,55) (1.62) (1,63) (1.53) (1.54) (1.61) (1,62)LOGTNAi,_, -0,058 -0.058 -0.063 -0,061 -0,055 -0,056 -0.060 -0,058 (3,15) (3.17) (3,40) (3,29) (3.03) (3,05) (3,28) (3,17)LOGTNAij_, * 0,040 0.041 0.043 0,044 0,040 0.041 0,043 0,044 ND|n,,scG| (2,36) (2.39) (2.53) (2,56) (2,35) (2,37) (2.52) (2,55)LOGFAMSIZEi , _ , 0,012 0,012 0,011 0,011 0,012 0,012 0,012 0,012 (2,57) (2,57) (2,54) (2,54) (2,59) (2,59) (2,57) (2,56)TURNOVERi,^ , 0,000 0.000 0.000 0,000 0,000 0,000 0.000 0,000 (1.62) (1.61) (1,62) (1.61) (1,57) (1,56) (1,57) (1,57)AGEij^i -0.001 -0,001 -0.001 -0,001 -0,001 -0.001 -0,001 -0,001 (0,98) (0,97) (0.98) (0.97) (0,87) (0,87) (0,88) (0,87)EXPRATIOij_, -0,018 -0.018 -0.019 -0,019 -0,062 -0,062 -0,064 -0.063 (0.44) (0,43) (0.46) (0,44) (1.49) (1.48) (1.52) (1.51)TOTLOADi,_, 0.001 0,001 O.OOI 0.001 0,001 0,001 0.001 0,001 (0.54) (0,54) (0.52) (0.52) (0.48) (0.47) (0,46) (0.46)FLOWi,^ I 0.000 0,000 0.000 0,000 0,000 0.000 0.000 0.000 (0,96) (0,95) (0.90) (0,92) (1.02) (1,02) (0,96) (0,99)FUNDRETi,_, 0,022 0,022 0,021 0,021 0.022 0,022 0,022 0,022 (3,45) (3,45) (3.43) (3,42) (3,48) (3,48) (3.45) (3,45)No, of months 228 228 228 228 228 228 228 228Panel B: Large Cap funds Gross fund returns Net fund returns Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorINTERCEPT 0,016 0,068 0,128 0.068 -0,017 0,035 0.095 0,034- (0.19) (0,84) (1.72) (0.92) (0.20) (0,43) (1.27) (0,47)IND|LC} -0,119 -0,121 -0,119 -0.120 -0,112 -0,114 -0.112 -0,113 (1,31) (1.33) (1.33) (1.34) (1,23) (1.25) (1.24) (1.26)LOGTOA,,,., -0,029 -0,029 -0,032 -0,029 -0,027 -0.027 -0,029 -0.027 (2,22) (2,24) (2,45) (2,25) (2.02) (2,05) (2.26) (2,05)LOGTNAij _ 1 • 0.031 0,031 0.031 0,031 0,030 0,030 0.030 0,030 (2,29) (2,32) (2.34) (2,36) (2,23) (2.26) (2.28) (2,30)LOGFAMSIZEij ,_, 0,011 0,011 0.011 0,011 0,011 0,011 0.011 0,011 (2,54) (2,54) (2,51) (2.51) (2,58) (2,58) (2,55) (2.55)TVRNOVERi,_ , 0,000 0,000 0,000 0.000 0,000 0,000 0,000 0.000 (1,80) (1,79) (1,80) (1.79) (1.75) (1.75) (1.76) (1,75)A(Eij_i -0,001 -0,001 -0,001 -0.001 -0,001 -0,001 -0,001 -0,001 (1,26) (1,25) (1.26) (1.25) (1,17) (1.17) (1,17) (1.16)EXPRATIOi,_, -0.020 -0,019 -0,021 -0,020 -0,065 -0.065 -0.066 -0.065 (0,49) (0,48) (0,52) (0.50) (1.63) (1,62) (1,66) (1.64)TOTLOADi,^, 0,001 0.001 0,001 0,001 0.001 0,001 0,001 0,001 (0,35) (0,35) (0,34) (0,35) (0,30) (0,30) (0,29) (0,29)FLOWij_, 0,000 0,000 0,000 0,000 0.000 0,000 0,000 0,000 (0,84) (0.82) (0,77) (0,79) (0.89) (0,88) (0,83) (0.85)FUNDRETi,^ 1 0,020 0,020 0,020 0,020 0.021 0,020 0,020 0.020 (3,10) (3,09) (3,07) (3,07) (3,13) (3,12) (3,10) (3,09)No, of months 228 228 228 228 228 228 228 228Noles: This table reports the Fama-MacBeth (1973) estimates of monthly fund returns regressed on fund characteristics lagged one month. Thesample includes only funds that fall within fund size quintiles two to five. Fund returns are calculated before (gross) and after (net) deductingfees and expenses. These fund returns are adjusted using the market model, the CAPM, the Fama-French (1993) 3-Factor model, and the4-Factor model. In panel (A), the regression specification is the one in Table 3 but augmented with lND|no,scG|. which is a dummy variablethat equals one if the self-reported fund style is not Small Cap Growth and zero otherwise and this indicator variable interacted with LOGTNA.In panel (B), instead of IND,no, scc). " ^ augment the regression with IND|LCI, which is a dummy variable that equals one if the fund styleis identified as a Large Cap fund. The sample is from January 1981 to December 1999, The r-statistics are adjusted for serial correlation usingNewey-West (1987) lags of order three and are shown in parentheses.
  17. 17. 1292 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004 TABLE 6—EFFECT OF FAMILY SIZE ON PERFORMANCE BY FUND STYLEPanel A: Fund size quintiles two to five Gross fund :returns Net fund returns Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorLOGTNAi, , -0,051 -0,052 -0.056 -0,054 -0,048 -0,049 -0,053 -0,051 (2,83) (2,86) (3,13) (3,02) (2,70) (2,72) (3,01) (2,89)LOGTNAi, , * 0,033 0,034 0,036 0.037 0,033 0,033 0,036 0,036 IND (not SCG) (1,94) (1,98) (2,12) (2,15) (1,93) (1,96) (2,10) (2,14)LOGFAMSIZEi, i 0,007 0,007 0,007 0,007 0,007 0,007 0,007 0.007 (0,70) (0,70) (0,69) (0,70) (0,70) (0,70) (0,69) (0,70)LOGFAMSIZEi,.^ * 0,004 0,004 0,004 0,004 0.004 0,004 0,004 0,004 IND, (0,41) (0,41) (0,41) (0,40) (0,42) (0,42) (0,42) (0,41)No, of months 228 228 228 228 228 228 228 228Panel B: All fitnd size quintiles one to five Gross fund returns Net fund returns Market-Adj Beta-Adj 3-Factor 4-Factor Market-Adj Beta-Adj 3-Factor 4-FactorLOGTNAi, , -0,067 -0,070 -0,071 -0,072 -0,064 -0,067 -0,068 -0,069 (3,67) (3,83) (3,87) (3,91) (3,51) (3,67) (3,71) (3,76)LOGTNAi, , * 0,065 0,065 0,067 0,066 0,065 0,065 0,067 0,066 (3,52) (3,52) (3,61) (3,56) (3,53) (3,53) (3,62) (3,57)LOGFAMSIZEi, , 0,012 0,012 0,012 0,012 0,012 0,012 0,012 0.012 (1,13) (1,13) (1,11) (1,11) (1,15) (1,15) (1.13) (1,13)LOGFAMSIZEi,.^ * -0,003 -0,002 -0,002 -0,002 -0,002 -0,002 -0,002 -0,002 INDjnot SCG} (0,23) (0,21) (0,23) (0,21) (0,23) (0,21) (0,22) (0,21)No, of months 228 228 228 228 228 228 228 228Notes: This table reports the Fama-MacBeth (1973) estimates of monthly fund returns regressed on fund characteristics laggedone month. Fund returns are calculated before (gross) and after (net) deducting fees and expenses. These returns are adjustedusing the market model, the CAPM, the Fama-French (1993) 3-Factor model, and the 4-Factor model. The regressionspecification is the one in Table 5 but augmented with Ind|no,scG) which is a dummy variable which equals one if theself-reported fund style is Not Small Cap Growth and zero otherwise, interacted with LOGFAMSIZE. Estimates of theintercept and the other independent variables are omitted for brevity. The other independent variables include TURNOVER,AGE, EXPRATIO, TOTLOAD, FLOW, and LAGFUNDRET. The sample is from January 1981 to December 1999, The(-statistics are adjusted for serial correlations using Newey-West (1987) and are shown in parentheses.of scope for them to do so given the thousands to about a 3.85-basis-point movement in theof stocks available. funds performance the following month (or about a 46-basis-point movement annually) de- C. The Role of Organization: The Effect of pending on the performance measure used. The Family Size on Performance effect is smaller than that of fund size on returns but is nonetheless statistically and economically To see that assets under management need significant. In other words, assets under man-not be bad for the performance of a fund orga- agement are not bad for a fund organizationsnization, recall from Table 3 that controlling for performance per size, assets under management of the other In Table 6, we extend our analysis of thefunds in the family that the fund belongs to effect of family size on fund returns by seeingactually increase the funds performance. The whether this effect varies across fund styles.coefficient in front of LOGFAMSIZE is roughly Our hope is that family size is just as important0.007 regardless of the performance benchmark for Small Cap Growth funds as for other funds.used. One standard deviation of this variable is After all, it is these funds that are most affected2.75, so a two-standard deviation shock in the by scale. For us to claim that scale is not bad persize of the family that the fund belongs to leads se, even accounting for liquidity, we would like