Mutual Fund Trading Costs and Diseconomies of Scale *

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1 Mutual Fund Trading Costs and Diseconomies of Scale * Jeffrey A. Busse Tarun Chordia Lei Jiang Yuehua Tang ** March 2015 ABSTRACT Larger mutual funds underperform smaller funds even though they have lower percentage transaction costs. Larger funds hold and trade a larger fraction of bigger, more liquid stocks, which leads to lower percentage transaction costs than smaller funds. Smaller funds outperform larger funds primarily when small cap stocks outperform large cap stocks. Overall, we find that it is not trading costs but fund holding characteristics, especially the market capitalization of stock holdings, that drive diseconomies of scale in the mutual fund industry. Keywords: Mutual funds, transaction costs, fund size, stock size, fund performance * We are grateful for comments from Viral Acharya, Vikas Agarwal, Gennaro Bernile, Lauren Cohen, Philip Dybvig, Fangjian Fu, Gary Gorton, Bruce Grundy, Jennifer Huang, Raymond Kan, Lubos Pastor, Gordon Phillips, Joshua Pollet, Michael Powers, Clemens Sialm, Jun Tu, Kumar Venkataraman, Youchang Wu, Hong Yan, Xuemin Yan, Huacheng Zhang, Xiaoyan Zhang, Guofu Zhou, and seminar participants at Cheung Kong GSB, University of Illinois, the 2014 China International Conference in Finance, the 2014 Singapore Management University Summer Institute of Finance Conference, and the 2014 Tsinghua Finance Workshop. We would like to thank Baozhong Yang for sharing the link table between the Abel Noser and Thomson Reuters Mutual Fund Holdings databases. Lei Jiang gratefully acknowledges support from AXA research fund and Tsinghua National Laboratory for Information Science and Technology. Jeffrey A. Busse, Goizueta Business School, Emory University, 1300 Clifton Road NE, Atlanta, GA 30322, USA; Tel: ; jbusse@emory.edu. Tarun Chordia, Goizueta Business School, Emory University, 1300 Clifton Road NE, Atlanta, GA 30322, USA; Tel: ; tarun.chordia@emory.edu. Lei Jiang, School of Economics and Management, Tsinghua University, Beijing, , China; Tel: ; jianglei@sem.tsinghua.edu.cn. ** Yuehua Tang, Lee Kong Chian School of Business, Singapore Management University, 50 Stamford Road #04-01, Singapore ; Tel ; yhtang@smu.edu.sg. 1

2 Fama s (1965) seminal work on market efficiency posits that market prices quickly incorporate information. Consistent with this idea, a vast literature on mutual fund performance, beginning with Jensen (1968), finds that fund managers do not consistently outperform benchmarks. While some evidence of short-term persistence in relative fund performance exists (see Bollen and Busse (2005)), there is little evidence to suggest that fund performance persists in the long run (see Carhart (1997)). Even so, Sirri and Tufano (1998) find that mutual fund investors chase past performance, a surprising finding given the evidence that fund managers do not add long-term value. Berk and Green s (2004) model of rational investors reconciles this puzzling behavior of performance chasing with the lack of superior mutual fund performance. They argue that fund managers have differential ability, which leads to the positive relation between past fund performance and cash inflows. One crucial assumption in the Berk and Green model is that mutual funds experience decreasing returns to scale. 1 Thus, in equilibrium, funds grow to the point where managers, even with differential ability, are unable to outperform benchmarks. The notion that mutual funds experience diseconomies of scale has received considerable attention. Many studies examine the relation between fund total net assets (TNA) and performance, and the general consensus from these studies is that, on average, larger funds underperform smaller funds. See, for instance, Chen et al. (2004), Edelen, Evans, and Kadlec (2007), Christoffersen, Keim, and Musto (2008), and Yan (2008). 2 More recently, Pastor and Stambaugh (2012) and Pastor, Stambaugh, and Taylor (2014) show that decreasing returns to scale also exist at the industry level. By contrast, Elton, Gruber, and Blake (2012), Reuter and 1 A number of papers assume diseconomies of scale in the mutual fund industry, e.g., Dangl, Wu, and Zechner (2008), Stoughton, Wu, and Zechner (2011), and Brown and Wu (2014). 2 One concern about these studies is an omitted variable bias in the relation between TNA and fund performance caused by omitting (the unknown) managerial skill, which is likely correlated with fund size as well as performance (see Pastor, Stambaugh, and Taylor (2014)). 1

3 Zitzewitz (2013), and Phillips, Pukthuanthong, and Rau (2014) find little evidence of diseconomies of scale at the individual fund level. 3 In this paper, we use a unique dataset of actual fund trades merged with fund portfolio holdings to first document evidence of diseconomies of scale and then to identify its underlying source. We find evidence of decreasing returns to scale, but for a reason that has not been uncovered in the literature thus far. In particular, it is the market capitalization of holdings, rather than trading costs, that drives diseconomies of scale in the mutual fund industry. Diseconomies of scale explanations typically follow two lines of reasoning. 4 First, for a given set of stock holdings, a fund faces increasingly large percentage transaction costs as its TNA increases, because altering a particular fraction of the portfolio requires transactions of larger dollar amounts, and larger dollar transactions would be expected to increase costs attributable to price impact. Alternatively, a fund could increase the number of stocks it holds as its size increases. Presumably, stocks added to the portfolio in response to new cash inflows would not reflect the fund manager s favorite stock picks, thereby reducing subsequent performance. However, since Pollet and Wilson (2008) find that funds do not increase the number of their holdings in proportion to increases in assets under management, transaction cost effects are the main remaining explanation in the literature for diseconomies of scale. Edelen, Evans, and Kadlec (2007) and Yan (2008) argue that increases in fund TNA adversely affect transaction costs. Edelen, Evans, and Kadlec infer fund trades from quarterly portfolio holdings, and they find that large changes in the holdings of larger funds increase 3 In subsets of funds grouped by investment objective, Elton, Gruber, and Blake (2012) find an insignificant relation between fund size and performance. Reuter and Zitzewitz (2013) analyze discrete changes in fund size associated with Morningstar rating changes using a regression discontinuity approach, while Phillips, Pukthuanthong, and Rau (2014) use instrumental variables to study the relation between fund size and performance. Both studies find little, if any, evidence of diseconomies of scale. 4 Berk and Green (2004) point to two sources of diseconomies of scale...with a sufficiently large fund, a manager will spread his information gathering activities too thin or that large trades will be associated with a larger price impact and higher execution costs. 2

4 transaction costs per dollar traded. Yan (2008) finds that diseconomies of scale are particularly evident among groups of funds that hold less liquid stocks. For funds that invest in relatively liquid stocks, Yan (2008) finds no evidence of diseconomies of scale. To precisely pin down whether larger funds underperform smaller funds due to higher trading costs, we analyze actual fund trades. We construct our sample by matching individual trades from the Abel Noser database of institutional trades to changes in portfolio holdings in the Thomson Reuters database of mutual fund portfolio holdings. We estimate trade-by-trade costs, including the price impact that has been suggested as the likely explanation for diseconomies of scale. We compute two transaction cost measures for funds in our Abel Noser sample: (i) execution shortfall (Anand et al. (2012)), which uses the stock price at the time of order placement as a benchmark, and (ii) open price cost, defined as the trade price relative to the stock s opening price on the day of the trade. Both measures capture implicit trading costs associated with a fund s actual trades, including price impact as well as costs related to the bidask spread. Given our transaction cost measures, one contribution of our paper is to provide an algorithm for estimating mutual fund trading costs at the trade level and also at the fund level. Prior studies (e.g., Wermers (2000)) typically estimate transaction costs based on Keim and Madhavan s (1997) analysis of the trades of 21 institutions from Anand et al. (2012) also provide trading cost estimates, but only for institutions in aggregate. Our matched sample of mutual funds from the Abel Noser database allows us to relate trading cost measures to fund characteristics. For instance, we find that transaction costs increase with fund turnover, age, and expense ratio, but they decrease with fund family TNA. Moreover, we use our matched Abel Noser data to precisely calculate trading costs as a percentage of TNA. Our estimates of the 3

5 annualized execution shortfall and open price cost as a fraction of TNA during the sample period are 0.55% and 0.73%, respectively. After accounting for commissions, taxes, and fees, the total average annualized execution shortfall and open price cost are 0.83% and 1.01%, respectively. These hidden trading costs, which funds typically do not report to investors, are comparable to the average annual expense ratio of 1.19%. More important for our purpose is the relation between fund size and transaction costs. Contrary to the notion that larger funds experience greater transaction costs than smaller funds, we find precisely the opposite result: larger funds experience lower percentage transaction costs than smaller funds, regardless of whether scaled by total dollar value traded or fund TNA. For instance, when sorted on TNA, the top quintile funds (i.e., the largest funds) experience an annual performance drag due to implicit and explicit trading costs of 0.35% based on execution shortfall as a fraction of TNA, whereas bottom quintile funds experience an annual performance drag of 1.07%. Fund-level transaction costs generally decrease with fund TNA. How can the transaction cost results be rationalized with diseconomies of scale? To answer this question, we examine the characteristics of stocks held by mutual funds, finding important differences related to fund size. Larger funds hold larger, more liquid stocks, and smaller funds hold smaller, less liquid stocks. Larger funds also trade larger and more liquid stocks. Although transaction costs do not explain performance differences, small funds outperform large funds by earning a premium from holding smaller, less liquid stocks. These premiums are more than enough to offset the greater percentage transaction costs that smaller funds incur. More importantly, we confirm that the negative relation between fund size and performance exists only during months when low market capitalization stocks outperform high 4

6 market capitalization stocks. Smaller funds outperform larger funds primarily when small stocks outperform large stocks. Portfolio holdings represent a conscious and strategic choice made by funds. Fund managers likely account for transaction costs when making portfolio decisions. Conditional on trading the same stock, we find that larger funds incur higher trading costs due to their larger trade sizes. Presumably, if large funds were to emphasize in their portfolios the types of stocks held by their smaller counterparts, the transaction costs incurred by larger funds would subsume the higher average returns of these stocks. Larger funds have lower transaction costs, probably because concerns about transaction costs cause these funds to hold larger, more liquid stocks. Our last test examines whether investor cash flows affect funds portfolio stock characteristics over time. We find that funds with higher cash inflows over three-, six-, and twelve-month horizons shift their portfolio holdings more towards larger stocks as compared to funds with lower cash inflows. This result provides insight into the time-series dynamics that leads to diseconomies of scale: higher fund inflows lead to larger increases in the average market capitalization of stock holdings. This finding is consistent with Berk and Green (2004), who argue that a fund s performance declines as its size increases. Our results point to a new mechanism behind mutual fund diseconomies of scale, shedding light on the specific forces underlying Berk and Green s (2004) model of active portfolio management. Whereas the results of Chen et al. (2004), Edelen, Evans, and Kadlec (2007), and Yan (2008) suggest that higher transaction costs lead to underperformance in relatively large funds, our results indicate that it is the portfolio composition of the large funds that leads to the underperformance. The choice of larger, more liquid stocks by larger funds likely reflect a deliberate response to transaction costs. Since it takes time for changes in fund 5

7 size to significantly affect holding behavior, the mechanism we document can also explain why some studies fail to find evidence of diseconomies of scale in settings that only capture small changes in fund size (e.g., Reuter and Zitzewitz (2013) and Phillips, Pukthuanthong, and Rau (2014)). 5 The remainder of the paper proceeds as follows. Section I describes the data. Section II provides an overview of the sample and some preliminary analysis. Section III presents our main empirical analysis. Section IV concludes. I. Data A. Data Description Fund names, returns, total net assets (TNA), expense ratios, turnover ratios, and other fund characteristics are obtained from the Center for Research in Security Prices (CRSP) Survivorship Bias Free Mutual Fund Database. Mutual fund portfolio holdings and investment objectives are obtained from the Thomson Reuters Mutual Fund Holdings (formerly CDA/Spectrum S12) database, which provides portfolio holdings for all U.S. equity mutual funds, usually at a quarterly frequency. 6 We merge the CRSP Mutual Fund database and the Thomson Reuters Mutual Fund Holdings database using the MFLINKS table available on WRDS (see Wermers (2000)). We focus on actively-managed U.S. equity mutual funds and exclude balanced, bond, international, and index funds. 7 We exclude funds with the following investment objectives: 5 Also see McLemore (2014), who argues that in settings with small differences in fund size, tests may not have power to find support for diseconomies of scale. 6 Prior to May 2004, mutual funds are required by the Securities Exchange Commission (SEC) to report their portfolio holdings at a semi-annual frequency, though many funds voluntarily disclose their holdings at a quarterly frequency to Thomson Reuters. See Agarwal et al. (2014) for more details. 7 Following Busse and Tong (2012), we exclude from our sample funds whose names contain any of the following text strings: Index, Ind, Idx, Indx, Mkt,Market, Composite, S&P, SP, Russell, Nasdaq, DJ, Dow, Jones, Wilshire, NYSE, ishares, SPDR, HOLDRs, ETF, StreetTRACKS, 100, 400, 500, 600, 1000, 1500, 2000, 3000,

8 International, Municipal Bonds, Bond and Preferred, Balanced, and Metals. To be included in the sample, a fund s stock holdings must comprise at least 80% of all fund assets as reported by CRSP. We exclude funds with fewer than 10 stocks to focus on diversified funds. Following Elton et al. (2001), Chen et al. (2004), and Yan (2008), we also exclude funds with less than $15 million in TNA. The matched sample consists of 3,416 unique actively-managed U.S. equity mutual funds over the period from April 1980 to June 2012, corresponding to portfolio holdings availability in the Thomson S12 dataset. 8 Mutual fund transactions data are obtained from Abel Noser Solutions, a leading execution quality measurement service provider for institutional investors. 9 We merge the sample of actual fund trades with their portfolio holdings by matching money managers in the Abel Noser database with funds reporting portfolio holdings to the Thomson Reuters holdings database as follows. For each manager X in the Abel Noser dataset, and for each reporting period between two adjacent portfolio report dates for a manager M in the Thomson S12 data, we compute the change in holdings (i.e., total trades with shares adjusted for splits and distributions) for manager X in each stock during the reporting period. We also compute split-adjusted changes in holdings by manager M for that reporting period. We then compare the change in holdings for managers X and M for each stock to find a match. Lastly, we manually verify the matches identified above, using fund names from the Thomson S12 and CRSP Mutual Fund databases and a manager name list disclosed by Abel Noser in Our initial matched Abel Noser sample covers 1,079 unique funds in the merged Thomson S12-CRSP Mutual Fund database. Out of these funds, 660 are actively-managed U.S. 8 Our sample period begins in April 1980 because we need holdings from the first quarter of 1980 to calculate lagged fund portfolio holding characteristics. 9 Previous studies that use Abel Noser data include Goldstein et al. (2009), Chemmanur, He, and Hu (2009), Puckett and Yan (2011), Anand et al. (2012), and Busse, Green, and Jegadeesh (2012), among others. 10 See Agarwal, Tang, and Yang (2012) for more details on the matching procedure. 7

9 equity funds based on the criteria specified above. Our final sample consists of trade-by-trade data for these 660 funds from January 1999 to September The January 1999 starting point for the trade data corresponds to the beginning of the period we can identify matches from the Abel Noser database. Abel Noser stopped providing the fund-level identifier in the institutional trading data after September Consequently, we cannot match Abel Noser data to Thomson S12 data at the fund level after September Thus, we analyze two distinct samples: (i) the Thomson S12 sample with a monthly average of 878 funds over the sample period from April 1980 to June 2012, and (ii) the Abel Noser sample with a monthly average of 182 funds over the sample period from January 1999 to September We conduct tests over both samples, but for tests that utilize transaction cost measures, we present results only for the Abel Noser sample. B. Variable Construction B.1. Trading Cost Measures We use the Abel Noser data to construct two trading cost measures for our mutual fund sample: (i) execution shortfall (e.g., Anand et al. (2012)), and (ii) open price cost. The former uses the price at the time of order placement (i.e., the volume-weighted execution price in the market during the minute the order is placed) as a benchmark, and the latter uses the opening price on the day of the trade as a benchmark: where is the execution price of a trade, and denotes the trade direction, taking a value of 1 for a buy and 1 for a sell. Equations (1) and (2) provide transaction cost estimates for each 8

10 trade. Fund managers submit order tickets, and each ticket can correspond to multiple trades. Later we provide trading cost estimates at the ticket level as in Keim and Madhavan (1997) and Anand et al. (2012). Both measures capture implicit trading costs, including price impact as well as costs related to the bid-ask spread. We aggregate the above per trade costs to obtain two trading cost measures at the fund month level: (i) trading costs per trading dollar, and (ii) trading costs per TNA dollar. For a given fund month, we compute trading costs per trading dollar as the value-weighted average of the execution shortfall or open price cost based on the dollar value of each trade by aggregating over all of a fund s trades in a given month. To obtain trading cost per TNA dollar, we multiply the execution shortfall and open price cost by the dollar value of each trade and then sum over all trades in a month for a given fund. We then divide by the average TNA of the previous and current month-ends to obtain a monthly trading cost per TNA dollar. In order to make this cost measure comparable to the fund expense ratio, we multiply the time series average of the monthly fund-level trading cost per TNA by twelve to get an annual measure. We also use the Abel Noser data to calculate two explicit trading cost measures (commission and tax plus fee), aggregated, as above, on a per trading dollar basis or on a per TNA dollar basis. We add the corresponding commission and tax plus fee to the trading cost per trading dollar or the trading cost per TNA dollar to obtain total trading costs. B.2. Fund Characteristics To measure performance, we compute alphas using the Carhart (1997) four-factor model. Specifically, the four-factor alpha is calculated as the difference between a fund s net return in a given month and the sum of the product of the four-factor betas estimated over the previous 36-9

11 months and the factor returns during that month. 11 The four-factor model includes the CRSP value-weighted excess market return (Mktrf), size (SMB), book-to-market (HML), and momentum (UMD) factors. We require a minimum of 12 monthly observations when estimating the betas. Other fund characteristics are constructed as follows. Since the CRSP mutual fund database lists multiple share classes separately, we aggregate share-class level data to fund-level data. We compute fund TNA by summing TNA across all share classes. Fund age is the age of the oldest share class in the fund. We calculate value-weighted averages of the expense ratio and fund turnover across all share classes. Family TNA is the aggregate TNA across all funds in a family, excluding the fund itself. Fund flows are measured as the average monthly net growth in fund assets beyond capital gains and reinvested dividends (e.g., Sirri and Tufano (1998)) and are value-weighted across all share classes to obtain the total net flow across all share classes. B.3. Portfolio Holding Characteristics For each stock in a fund s portfolio, we calculate stock-level characteristics using data from CRSP and COMPUSTAT. The stock level characteristics are market capitalization, bookto-market ratio, past six-month cumulative return, turnover ratio, and the Amihud (2002) measure of illiquidity. We restrict our sample to stocks with CRSP share codes 10 or 11 (i.e., common stocks). 12 We calculate monthly fund-level market capitalization, book-to-market ratio, momentum, turnover ratio, and the Amihud illiquidity measure by weighting each firm-level stock characteristic according to its dollar weight in the most recent fund portfolio. Since fund 11 We have also experimented with using the past 24 and 60 months for beta estimation and obtain similar results. Our results for the CAPM alpha, the Fama-French (1993) three-factor alpha, and the five-factor alpha (adding the Pastor and Stambaugh (2003) liquidity factor to the Carhart (1997) four-factor model) are also similar. 12 We base our reported results on all mutual fund stock holdings regardless of share price. Our results are unchanged if we eliminate stocks with share price below $5 at the previous month-end. 10

12 holdings are available mostly at a quarterly frequency, we obtain monthly measures by assuming constant fund holdings between quarters. Book-to-market ratio is calculated as the book value of equity (assumed to be available six months after the fiscal year end) divided by the previous month s market capitalization. We obtain book value from COMPUSTAT supplemented by book values from Ken French s website. 13 We winsorize the book-to-market ratio at the 0.5 and 99.5 percent levels to eliminate outliers, although our results are not sensitive to this winsorization. Momentum is the six-month cumulative stock return over the period from month t 7 to t 2, and stock turnover is the monthly trading volume as a fraction of the previous month-end shares outstanding. 14 For a given stock, the Amihud (2002) illiquidity measure is the average ratio of the daily absolute return to its dollar trading volume over all the trading dates in a given month. Following Acharya and Pedersen (2005), we normalize the Amihud ratio to adjust for inflation and truncate it at 30 to eliminate the effect of outliers as follows: where is the return on stock i on day d in month t, is the dollar trading volume, represents the number of days in month t that stock i trades, and is the ratio of the capitalizations of the market portfolio at the end of month t 1 and at the end of July Having described the filtering of the data and the construction of the cost measures, we are now ready to study the data. 13 See 14 Given that trading volume was overstated on Nasdaq due to inter-dealer trades, we follow Gao and Ritter (2010) to adjust NASDAQ trading volume when computing the turnover ratio and the Amihud illiquidity measure. 11

13 II. Sample Overview and Preliminary Analyses Table I reports summary statistics of fund characteristics, holdings characteristics, and transaction cost measures. Each month, we divide sample funds into five portfolios based on lagged TNA and report descriptive statistics for each fund size quintile. Panel A reports summary statistics for the Thomson S12 sample, and Panel B reports summary statistics for the Abel Noser sample. For fund-level variables, we first compute the cross-sectional average across all of the funds in each fund size quintile and then take the time-series mean of the crosssectional averages. We also report the time-series average of the number of funds in each portfolio each month. [Insert Table I here] The Thomson S12 sample averages 878 funds monthly, with an average of 176 funds in each fund size quintile over the sample period. Given that Abel Noser has a limited number of clients as well as the difficulty in linking the data to Thomson Reuters and CRSP Mutual Fund data, the Abel Noser sample is much smaller, with an average of 182 funds per month. The average TNA is $838 million in the Thomson S12 sample and about $2.8 billion for the Abel Noser sample. In both samples, large variations in fund TNA exist. The average fund TNA is $37 million for quintile 1 and $3.4 billion for quintile 5 in the Thomson S12 sample. Corresponding averages in the Abel Noser sample are $65 million and $11.6 billion, respectively. Panel A of Table I shows that funds with larger TNA show both lower net monthly returns and lower gross monthly returns (computed by adding 1/12 of the expense ratio to net returns). The monthly average gross return (net return) declines from 1.15% (1.04%) for the smallest TNA quintile to 1.00% (0.92%) for the largest TNA quintile. Holding return, which we compute using quarter-end fund holdings assuming no change in holdings over the quarter, also declines from an average of 1.18% for the smallest fund quintile to 1.06% per month for the 12

14 largest fund quintile. The return differential between the low and high TNA funds is consistent with diseconomies of scale in the mutual fund industry. Further, the four-factor alpha decreases across fund TNA quintiles from 0.02% for the smallest quintile to 0.09% per month for the largest quintile. Note that the difference in the average gross (net) return between the smallest and the largest fund quintile is 0.15% (0.12%) per month, while the corresponding difference in the four-factor alpha is 0.06% per month. Thus, differences in factor loadings of the four-factor model capture about half of the gross or net return difference between small and large funds. Later, we examine time-series regressions of returns on the four factors to document differences in factor loadings. We also compute each portfolio s Daniel et al. (DGTW, 1997) characteristic-adjusted return. We form 125 portfolios in June of each year based on a three-way quintile sorting along the size (using the NYSE size quintile), B/M, and momentum dimensions. The abnormal performance of a stock is its return in excess of its DGTW benchmark portfolio, and the DGTWadjusted return for each fund aggregates over all the component stocks using the most recent portfolio dollar value weighting. The DGTW benchmark portfolios capture more than half the difference in net returns between small and large funds. In the Thompson S12 sample in Panel A, the DGTW-adjusted return difference between the smallest and largest quintile is 0.05% per month, as compared to 0.15% and 0.12% in gross and net returns, respectively. This suggests that the characteristics of stocks held by funds may be an important driver of diseconomies of scale. Overall, the pattern of return differences between small and large mutual funds in the Thomson S12 sample confirms results in the prior literature that show diseconomies of scale in the mutual fund industry (e.g., Chen et al. (2004) and Yan (2008)). 13

15 The net and gross return differences between small and large funds are even larger in Panel B for the Abel Noser sample. For instance, the return differentials in net and gross returns are 0.18% and 0.23%, respectively, though only the latter is significant at the 10% level. The DGTW adjusted return differential is 0.05%, while the four-factor alpha differential is 0.04%, both insignificant at conventional levels. Our later analysis in Section III uncovers that the negative relation between fund size and performance exists only during months when low market capitalization stocks outperform high market capitalization stocks. When we calculate the summary statistics of fund returns for two subsamples separately: (i) months when small size stocks significantly outperform large size stocks, and (ii) other months (see Table IA.I of the Internet Appendix), we find that, for both the Thomson S12 and Abel Noser samples, smaller funds outperform larger funds primarily when small stocks outperform large stocks. On average, larger funds are older, belong to larger fund families, and have lower expense and turnover ratios. The average expense ratio (i.e., annual fund operating expenses as a percentage of TNA, including management fee, administrative fee, 12b-1 fee, etc.) for the Thomson S12 (Abel Noser) sample ranges from 1.34% (1.46%) for the smallest funds to 0.93% (0.84%) for the largest funds. The fact that larger funds have lower expenses indicates that expenses do not explain the lower performance of larger funds. Thus, the driving force behind diseconomies of scale is important enough to override the expense advantage of large TNA funds. For both the Thomson S12 and Abel Noser samples, we find that larger funds hold larger market capitalization and more liquid stocks. In addition, in the Abel Noser sample, larger funds tend to hold stocks with lower book-to-market ratios (i.e., growth stocks). Since it has been well documented that larger, more liquid, and lower book-to-market stocks are characterized by lower 14

16 average return cross-sectionally, it is not surprising to find the diseconomies of scale result. 15 Note that in the Thomson S12 sample, the differential between small and large funds in terms of the market capitalization of firms they hold is $4.7 billion. While this difference may seem small, our later analysis in Section III.F shows that there is a large difference in the proportion of fund holdings in each firm size quintile between large and small TNA funds. Also note that a large fraction of the increase in stock size occurs between quintiles 4 and 5, which coincides with a large fraction of the difference in returns. The difference in net returns between quintiles 1 and 4 is 0.057% while that between quintiles 4 and 5 is 0.064%. In Panel B, in the Abel Noser sample, the market capitalization differential is over $16 billion, and changes in the B/M ratio and illiquidity are non-monotonic, leading to a more nuanced return pattern across the mutual fund quintiles. We now examine how trading costs vary with fund size. First, we find that our two implicit trading cost measures, execution shortfall and open price cost, decrease with fund size. Panel B of Table I shows that for the Abel Noser sample, funds in quintiles 1 to 5 incur annualized average transaction costs as measured by execution shortfall per TNA dollar of 69, 85, 52, 47, and 22 basis points, respectively. Similarly, the open price cost for funds in quintiles 1 to 5 are 99, 105, 67, 56, and 40 basis points, respectively. Figure 1 plots a twelve month moving average of the differences between the bottom and top fund size quintiles in per TNA dollar transaction cost measures (unannualized). For the most part, larger funds have lower transaction costs than smaller funds. Thus, contrary to the idea that larger funds experience larger price impact in their trades, we find the opposite result: larger funds experience lower transaction costs. Second, when examining explicit trading cost measures, we find that commissions, taxes, and 15 See Banz (1981), Fama and French (1992), Daniel and Titman (1997), Amihud and Mendelson (1986), Brennan, Chordia, Subrahmanyam (1998), and Avramov and Chordia (2006a, 2006b). 15

17 fees per TNA dollar are also lower for larger funds. Therefore, neither implicit nor explicit trading costs can explain diseconomies of scale in the mutual fund industry. [Insert Figure 1 here] One contribution of this paper is that we are the first to provide precise estimates of mutual fund transaction costs using actual mutual fund trade data. Prior studies (e.g., Wermers (2000)) typically estimate transaction costs based on Keim and Madhavan s (1997) analysis of the trades of 21 institutions from As an example of how our analysis captures differences in the evolution of transaction costs over time, Wermers (2000) reports a mean annual transaction cost estimate of 80 basis points for his sample of equity funds over For our transaction cost sample period, our estimates of annualized execution shortfall and open price cost as a fraction of TNA dollars are 0.55% and 0.73%, respectively. After accounting for commissions, taxes, and fees, the total average annualized execution shortfall and open price cost amount to 0.83% and 1.01% respectively. These hidden trading costs, which typically are not reported to investors, are comparable to the average expense ratio of 1.19% per annum. There are two important caveats to the interpretation of the transaction cost analysis. First, our data provides transaction cost estimates only for trades that were consummated. It could be the case that a fraction of the desired trades were not executed due to high trading costs. Given that our data consists of actual trades, we cannot estimate the cost of forgone trades. Second, fund managers account for expected transaction costs when forming their portfolios. All things equal, managers prefer stocks with greater liquidity, since these stocks can be traded at lower cost. The preference for more liquid stocks is likely stronger for larger funds because their larger portfolio positions requires larger trades on average. Consequently, our findings that large funds 16

18 have lower transaction costs is endogenous to the fund managers decision to hold stocks that generate lower transaction costs, and this endogeneity likely relates to fund size. We return to this issue later. III. Results In this section, we first use the Abel Noser data to more comprehensively analyze the determinants of fund transaction costs. We examine the effects of trade, stock, and fund characteristics on transaction costs at the trade level and at the fund level. We then examine whether transaction costs drive diseconomies of scale. Next, we examine how portfolio holding market capitalization relates to the tendency for small funds to outperform large funds. Lastly, we analyze how fund flows affect changes in the average market capitalization of fund portfolio holdings over time. A. Transaction Costs Per Trading Dollar We first analyze monthly fund trading costs scaled by dollar value traded (unannualized). Recall that these costs are the fund-month trading-dollar-weighted averages of the execution shortfall and open price cost computed using equations (1) and (2). We refer to these costs as trading costs per trading dollar. As in the case of trading costs per TNA dollar, these per trading dollar costs also decline with the size of the fund. Panel A of Table II shows that the execution shortfall (open price cost) decreases from 19 (26) basis points for funds in the smallest quintile to 10 (16) basis points for funds in the largest quintile. The decline in total trading costs, which includes commissions, taxes, and fees, is even larger. Once again, the results suggest that trading costs are not driving diseconomies of scale in the mutual fund industry. [Insert Table II here] 17

19 Note that trading costs as measured by the open price cost are higher than those measured using execution shortfall. The difference between the two costs is about four basis points on average. This suggests that there is some slippage in price between the opening price on the day when the order is placed and the time when the order is placed, possibly because (i) fund managers condition on returns and chase prices, or (ii) other traders anticipate fund managers trading intentions and front-run them. Without knowing the exact time when portfolio managers send the trading order to the trading desk, it is difficult to distinguish between these two explanations. However, instead of using the opening price as a benchmark, we also use the previous day close as a benchmark. We find that there is more slippage from the previous day s closing price (results untabulated), which suggests fund managers chase returns, possibly following information shocks. Larger funds likely have lower transaction costs because they trade larger stocks. We now examine trading costs when large and small funds trade the same stock. Panel B of Table II provides trade statistics and Panel C presents trading costs conditional on trading the same stock. The monthly dollar trading volume in the largest (smallest) quintile funds averages $25.83 ($0.61) million, divided among (5.63) trade tickets, with a trade size of 48,194 (5,710) shares per ticket. In our sample, 100% of the tickets execute on the day they are submitted, but this could be because large trades are broken into several tickets. Conditional on the stock being traded, larger funds trade larger quantities and likely face higher trading costs. As discussed earlier, the trading requirements faced by large funds likely affect their portfolio decisions and thus impact the overall transaction cost estimates in Table I and in Panel A of Table II, which show an inverse relation between fund TNA and transaction costs. To control for the endogeneity between realized transaction costs and fund size, Panel C of Table II 18

20 compares transaction costs by fund quintile after conditioning on trading the same stock. As expected, conditional on trading the same stock, a positive relation between fund size and transaction costs exists, as larger trades have a higher price impact. For instance, conditioning on the stock traded, top TNA quintile funds experience a value-weighted execution shortfall (open price cost) of 0.25% (0.34%), which is significantly greater than the 0.18% (0.23%) for bottom quintile funds. Thus, large TNA funds realize lower transaction costs than smaller TNA funds, but only because they hold and trade stocks that are cheaper to trade. The contrasting transaction cost results when conditioning on the stock traded suggest that fund managers account for expected trading costs when deciding which stocks to include in their portfolios. Table I shows that larger funds hold larger stocks. But do they also trade larger stocks? For each fund TNA quintile, Panel D of Table II reports the trade dollar value-weighted averages of characteristics of stocks traded by funds. Consistent with an effort to contain transaction costs, it is indeed the case that large funds trade stocks of greater market capitalization and greater stock turnover. Also apparent is a preference of large TNA funds for stocks with lower B/M ratio, possibly because of their preference for high market capitalization stocks. B. Determinants of Trade-Level Transaction Costs We next examine how trade-level transaction costs relate to trade characteristics such as trade size and stock characteristics including market capitalization and share price. This exercise is similar to that conducted by Keim and Madhavan (1997) and Anand et al. (2012) for all institutions. We focus on mutual funds during the period Given our unique matched data set, we are able to use fund level variables as well. We further conduct a fund level analysis of trading costs. The idea is to provide an algorithm for computing mutual fund transaction costs either at the trade level or at the fund level. 19

21 To provide an indication of how transaction costs change over time, we first report estimates of execution shortfall and total costs (which include commissions, taxes, and fees) by year in Panel A of Table III. Our results for the open price cost are similar. 16 We compute execution shortfall at the ticket level by taking an equally weighted average of the cost per ticket across all tickets in a year. The ticket level data is obtained as the value weighted average of the trade level data using trading volume as the weight on each trade. Following Anand et al. (2012), we group trades by the same fund manager and the same broker on the same stock into tickets by matching on the price at the time of order submission and ensuring that the sum of the trade share volumes equals the ticket volume. We find a 99.6% match of trades to tickets and discard the remaining 0.4%. The overall average execution shortfall for all trades amounts to 12.4 basis points, and for buys (sells) it is 9.3 (15.9) basis points. After accounting for commissions, taxes, and fees, the average total trading cost is 23.9 basis points, about twice the magnitude of implicit trading cost. These measures differ from those in Panel A of Table II because we take an equal weighted average across all tickets in a year, rather than value weighting by the dollar trading volume for each fund-month. Trading costs generally decline over time. The big decrease in trading costs for sells from 2000 to 2011 is probably attributable to a decline in bid-ask spreads following decimalization. However, there is an increase in 2008 probably due to market dislocations during the financial crisis. In general, the trading cost associated with buying shares is lower than that associated with selling. 17 Note in particular the substantial increase in the cost to sell as liquidity dries up in For the rest of the paper, we do not present results for tests using the open price cost, as they are similar to those reported with execution shortfall. We report the open price cost results in Tables IA.II, IA.III, and IA.V in our Internet Appendix. 17 See also Brennan et al. (2012). 20

22 To examine determinants of transaction costs, we estimate monthly cross-sectional regressions of ticket-level transaction costs on several trade and fund level variables as follows, (5) where is the execution shortfall or total cost (which includes commissions, taxes, and fees) per trading dollar for stock i at time t, is the share volume of a ticket normalized by dividing by the average daily trading volume of the previous month, 18 is stock i s closing price the day prior to the trade, market capitalization at the end of the month prior to the trade, is the logarithm of stock i s is a dummy variable that equals 1 if stock i is a Nasdaq stock, and is a set of fund-level control variables at the end of the month prior to the trade, including expense ratio, turnover, net flow, Log(fund age), Log(TNA), Log(family TNA), and fund net return. We run the cross-sectional regression in (5) every month, and Panel B of Table III reports the time series average of the monthly coefficient estimates as in Fama-MacBeth (1973). Given that transaction costs persist, we adjust the Fama- MacBeth standard errors using the Newey-West (1987) correction with three lags. [Insert Table III here] Focusing first on the transaction level variables, we find that execution shortfall is related positively to trade size, Nasdaq dummy, and the inverse of price and is negatively related to firm size. Larger trades have a greater price impact, on average. The strong relation between trade cost and trade size is apparent in all of the alternative specifications for both buys and sells. The negative relation between trade cost and stock price is especially evident in the total cost results 18 Our trade size variable in equation (5) is slightly different from the one used in Keim and Madhavan (1997). They calculate trade size as shares traded divided by stock shares outstanding. We obtain similar results with their version of trade size. 21

23 in columns (7)-(12), where trading costs reflect a combination of implicit costs, including price impact and costs associated with the bid-ask spread, and explicit costs, including commissions, fees, and taxes. Institutions typically pay brokers a fixed commission fee per traded share (e.g., $0.01 per share), such that a trade s commission expense expressed as a percentage of the total dollar value of the trade increases as share price decreases. The strong inverse relation between trading costs and the market capitalization of the traded stock is consistent with the positive relation between a stock s market capitalization and its liquidity. Nasdaq stocks, in general, have higher trading costs as measured by execution shortfall, but not when commissions, taxes, and fees are also considered, possibly because commissions, taxes, and fees are the same across all stocks, and this dilutes the impact of the Nasdaq dummy. With fund level variables, we find that ticket level trading costs are higher for larger size funds. Costs are higher for funds with higher outflows and higher expense ratios. Selling costs are lower for funds that belong to larger fund families. The positive correlation between trading costs and the expense ratio is probably symptomatic of funds not being careful about costs. The negative coefficient on fund flows is consistent with the result that selling costs are higher than buying costs, and with more outflows, funds may be forced to sell stocks. A larger fund family should have lower transactions costs since it more likely has trading expertise, and it seems that this expertise is manifested when selling shares, as shown in columns (6) and (12). To assess economic significance, we focus on regression (8) for the total cost of all trades. A one standard deviation increase in trade size (price inverse) increases total trading cost by about 8.4 (22.4) basis points, while a one standard deviation increase in the market capitalization of the stock decreases total costs by 3.9 basis points. For the fund level variables, a one standard deviation increase in Log(TNA) (expense ratio) increases total trading costs by 1.3 (1.7) basis 22

24 points, respectively, while a one standard deviation increase in family TNA (fund flows) decreases the cost by 2.3 (1.3) basis points. These numbers are significant in relation to the average total cost of 23.9 basis points (from Panel A of Table III). C. Determinants of Fund-Level Transaction Costs In Table III, we examine trading costs at the level of each ticket. We now examine trading costs at the fund-month level, looking beyond the univariate fund size relation in Panel B of Table I and Panel A of Table II. Panel A of Table IV presents trading costs by year. The execution shortfall and total costs per trading dollar and per TNA dollar (unannualized) for each fund-month are computed as before and presented by year. The trading cost pattern is similar to that in Panel A of Table III. Costs generally decrease over time, with a large decrease from 2000 to 2011 and an increase in 2008 during the financial crisis. [Insert Table IV here] We now examine the relation between fund size and transaction costs after controlling for a number of fund level attributes in monthly Fama-MacBeth (1973) cross-sectional regressions as in equation (5), but after excluding the trade and stock level variables. Once again, we follow Newey-West (1987) to adjust the Fama-MacBeth (1973) standard errors. Consistent with the results in Panel B of Table I and Panel A of Table II, we find that larger funds have smaller transaction costs than smaller funds, as measured by either execution shortfall per trading dollar in Panel B or execution shortfall per TNA dollar in Panel C of Table IV. In all eight specifications of Panels B and C, the coefficient on fund TNA is negative and significant at the 23

25 10% level or better. 19 Thus, our results again run counter to arguments in the prior literature that larger funds experience higher transaction costs than smaller funds. Moreover, fund transaction costs also relate to other fund characteristics, such as turnover ratio, family size, and age. The greater the turnover ratio of a fund, the greater its transaction costs, and the larger the fund s family size, the lower its transaction costs. Interestingly, conditional on the other variables included in the regression, older funds tend to experience larger transaction costs. The expense ratio is also positively correlated with execution shortfall per trading dollar but not with execution shortfall per TNA dollar, possibly because of the negative correlation between TNA and the expense ratio. Transaction costs highly persist, as evidenced by the significant coefficient estimate on lagged trading cost and the increase in average adjusted-r 2 in the presence of lagged trading cost. While the coefficient estimate on log(tna) decreases in the presence of lagged trading cost, the inference does not change. Overall, our results in Tables III and IV provide an algorithm to estimate mutual fund trading costs at the transaction level and also at the fund-month level. D. Transaction Costs and Fund Performance In this section, we study the impact of transaction costs on fund performance. We run monthly cross-sectional regressions of fund returns on trading costs while controlling for fundlevel variables as follows, Χ (6) where denotes the four-factor alpha of fund i in month t, 20 is the logarithm of fund i s TNA in month t 1, is defined as in equation (5), and 19 It could be argued that there is a mechanical relation between log(tna) and trading cost per TNA dollar. However, TNA also impacts the numerator of trading costs per TNA dollar because it is related to the type of stocks a fund trades and to trading volume. Also note that the coefficient estimates on log(tna) are actually smaller in Panel B than in Panel A of Table IV. 24