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: ; [email protected]. Tarun Chordia, Goizueta Business School, Emory University, 1300 Clifton Road NE, Atlanta, GA 30322, USA; Tel: ; [email protected]. Lei Jiang, School of Economics and Management, Tsinghua University, Beijing, , China; Tel: ; [email protected]. ** Yuehua Tang, Lee Kong Chian School of Business, Singapore Management University, 50 Stamford Road #04-01, Singapore ; Tel ; [email protected]. 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

26 represents the set of fund-level control variables in month t 1, including the expense ratio, turnover, net flow, Log(fund age), and Log(family TNA). If transaction costs can fully explain the relation between fund size and performance, we expect the coefficient on,, to be negative and the coefficient on,, to be zero. By contrast, a significantly negative would be consistent with the existence of mutual fund diseconomies of scale after controlling for transaction costs. Table V reports time-series averages of the monthly coefficient estimates. Since persistence in fund performance could lead to serial correlation in the coefficient estimates, we use the Newey-West (1987) correction with three lags to adjust the Fama-MacBeth standard errors. We now discuss the results with execution shortfall as a measure of trading costs. Consistent with results in Table I, Panel B, we find little evidence that funds in the Abel Noser sample show statistically significant diminishing returns to scale in general. The coefficient on Log(TNA) is statistically insignificant in the univariate regressions, and it is negative but insignificant in the presence of fund level controls. [Insert Table V here] Similar to the evidence in prior studies (e.g., Chen et al. (2004), Yan (2008)), the coefficient estimate on Log(Family TNA) is positive and significant, suggesting that funds belonging to larger fund families earn higher returns, possibly because of superior trading expertise, but also because fund trades could be more easily internalized, leading to a reduction in trading costs. When lagged trading costs are introduced into the cross-sectional regressions in columns (3) and (7), the coefficient on Log(TNA) is unchanged, suggesting that trading costs do 20 We show in Table IA.IV of the Internet Appendix that the results are the same when using gross and net returns instead of the four-factor alpha as the dependent variable. 25

27 not impact diseconomies of scale. 21 Note also that trading costs do not impact fund returns after controlling for fund-level variables. Overall, our analysis of mutual fund trades does not support the idea that transaction costs drive the underperformance of large funds. Given that larger funds hold larger stocks and the empirical evidence that smaller stocks earn higher returns (i.e., the size effect), we now study the impact of fund holdings on fund returns by aggregating the monthly cross-sectional regression coefficients depending on whether the size effect in stock returns is present or not. Specifically, we first run monthly univariate cross-sectional regressions of excess stock returns on firm size using all common stocks in the CRSP database, and divide the months into two groups based on whether the coefficient on firm size (γ) is significantly negative at the five percent level (γ* < 0) or not. Note that we are not making any inference about γ. Rather, we only seek to divide the sample months into those that show evidence of the small firm effect and those that do not. In Table V, we aggregate the monthly coefficients of regression (6) for months when γ is significantly negative and for the other months. Of the 153 months in the Abel Noser sample, 64 months show a significantly negative γ. The coefficient on Log(TNA) when γ is significantly negative (γ* < 0) is 0.08 (t-statistic = 2.95) in column (8), while for months when γ is not significantly negative, the coefficient is 0.01 (t-statistic = 0.50) in column (9). The difference between the coefficients of Log(TNA) in the two subsamples reported in columns (6) and (10) is highly significant. This strongly suggests that mutual fund diseconomies of scale exist only in the presence of the stock size effect. In other words, large funds underperform their smaller counterparts only during months when small 21 We show in Table IA.V of the Internet Appendix that the results are similar if we use alternative trading cost measures calculated on a per TNA dollar basis: contemporaneous execution shortfall, lagged open price cost, and contemporaneous open price cost. Our results are also similar if we use trading cost measures calculated on a per trading dollar basis (results untabulated). 26

28 stocks significantly outperform large stocks. This is not surprising given that larger funds hold and trade larger stocks. Thus, it is not fund transaction costs but the market capitalization of fund portfolio holdings that account for diseconomies of scale in the mutual fund industry. E. Stock Size Premium and Mutual Fund Diseconomies of Scale Our evidence thus far indicates that transaction costs are not the reason larger funds underperform smaller funds. Furthermore, the Abel Noser sample analysis in Table V suggests that portfolio holding characteristics play an important role in explaining this relation. We now return to our larger Thomson S12 dataset to investigate more broadly whether portfolio holdings characteristics explain diseconomies of scale in the mutual fund industry. We estimate the regression in equation (6), but without the lagged trading costs, which are not available for the Thomson S12 sample. 22 Table VI reports the estimation results. [Insert Table VI here] Unlike Table V, the coefficient on Log(TNA) in the univariate regression is negative and significant. The coefficient estimate, in fact, becomes more negative in the presence of the fund level variables. Higher expense ratios reduce fund performance, while belonging to a larger fund family increases fund performance. There is some evidence that performance persists, as fund returns are positively auto-correlated. One concern is that the relation between Log (TNA) and fund returns could be biased because of a missing variable: the fund manager s skill. 23 The bias arises because the unknown managerial skill is likely to be positively related to both fund performance and TNA, thus 22 We show in Table IA.VI of the Internet Appendix that the results are the same when using gross and net returns instead of the four-factor alpha as the dependent variable. In addition, in Table IA.VII, we also control for investment objectives, and the results are essentially the same. 23 See Pastor, Stambaugh, and Taylor (2014) for a detailed discussion. 27

29 causing an upward bias in the coefficient estimate on Log(TNA). However, note that the coefficient estimate on Log(TNA) is significantly negative even though the bias causes it to be closer to zero. In other words, diseconomies of scale may be even stronger than that measured by the coefficient estimates on Log(TNA). More importantly, the coefficient on Log(TNA) is 0.07 (t-statistic = 4.19) when aggregated for months when γ is significantly negative (γ* < 0), and it is 0.01 (t-statistic = 1.43) for other months. The difference between the two coefficient estimates is highly significant, as shown in column (5). Overall, our evidence using the Thomson S12 sample suggests, once again, that the size effect plays an important role in the diseconomies of scale in the mutual fund industry. Next, we use a time-series portfolio approach to examine the impact of holding characteristics on diseconomies of scale. Specifically, we run time-series regressions of monthly mutual fund size quintile returns on the monthly Fama-French (1993) factors and a factor for momentum (Jegadeesh and Titman (1993)) as in Carhart (1997). We first sort all funds in the Thomson S12 sample into quintiles based on the previous month-end TNA and compute equalweighted monthly net returns in excess of the risk-free rate for each quintile. Table VII presents the coefficient estimates and alphas. [Insert Table VII here] The coefficient estimate on the excess market return, MKTRF, ranges from 0.85 to Given that we are regressing the returns of a portfolio of mutual funds on MKTRF, it is not surprising to find high t-statistics for the coefficient estimate on MKTRF. The coefficient estimates on SMB and HML suggest that small funds tilt towards small, value stocks, whereas larger funds are oriented more towards large, growth stocks. Alpha decreases from 0.01% for the 28

30 smallest fund quintile to 0.06% for the largest. 24 When the dependent variable is the difference in excess net returns between the smallest and the largest quintile of funds, the alpha is a significant 6.93 basis points per month, consistent with diseconomies of scale in the mutual fund industry. This magnitude is similar to that documented by Chen et al. (2004) and Yan (2008). Next we run the time-series regression using only months when the size effect is present, i.e., when γ is significantly negative (γ* < 0), and when it is not. 25 When regressing the difference in returns between the lowest and highest TNA quintile on the factors, the alpha is basis points with a t-statistic of 2.06 when γ is significantly negative. By contrast, when the size effect is not present, the mean performance of top TNA quintile funds is not statistically significantly worse than the performance of bottom TNA quintile funds. The difference between the two subsample alpha estimates is basis points per month, significant at the five percent level. These results bolster our previous evidence that it is the market capitalization of fund holdings that drives diseconomies of scale in the mutual fund industry. Larger funds underperform smaller funds because they hold larger stocks. These results allay the concern that window dressing drives our finding that large funds hold larger stocks. It could be the case that larger funds re-orient their portfolios towards larger stocks before they report their portfolios at quarter end. However, the result that larger funds underperform their smaller counterparts in the months when small stocks outperform large stocks suggests that large funds hold larger stocks throughout the quarter. 24 Differences in four-factor alphas across size quintiles suggest that the SMB factor does not fully control for return premia associated with small cap stocks. This finding is consistent with Brennan, Chordia, and Subrahmanyam (1998) and Chordia, Goyal, and Shanken (2015), who find return premia associated with stock characteristics even after controlling for risk factors such as SMB. 25 We show in Panels A and B of Table IA.VIII of the Internet Appendix that our results are similar if we control for other stock characteristics (i.e., the B/M ratio and momentum) when estimating the cross-sectional relation between stock return and market capitalization. These results hold for the Abel Noser sample as well (untabulated). 29

31 F. Cash Flow and Change in Holding Stock Size In this section, we first examine the distribution of stocks by firm size in the mutual fund quintile portfolios. Specifically, we sort funds into quintiles based on their last month s TNA and also independently based on the firm size of their previous quarter s holdings using NYSE breakpoints. Panel A of Table VIII reports the time-series average of the proportion of fund holdings in each firm size quintile such that the holdings of each fund quintile add up to one. The results clearly show that, compared to small funds, large funds hold fewer small stocks and more large stocks in their portfolios. Small funds invest 7.18% (10.88%) of their assets in the smallest (second smallest) quintile of stocks, while the corresponding proportions for large funds are 1.91% (4.30%). Further, small (large) funds invest 49.71% (68.40%) of their assets in the largest quintile of stocks. The holding differences between large and small funds are statistically significant across all stock size quintiles. [Insert Table VIII here] Next, we focus on fund cash flows, the capital movements in and out of funds that cumulate over time into fund TNA. Examining flows provides insight into the time series dynamics that leads to diseconomies of scale. Given our analysis thus far, we anticipate that after a fund receives inflows, the average market capitalization of their portfolio stock holdings will increase. This expectation is based on the long-run relation between cash flows and TNA: cash inflows lead to TNA increases, and TNA is positively related to average portfolio holding market capitalization. Our analysis thus directly addresses Berk and Green s (2004) assumption that an increase in fund size due to capital inflows diminishes a fund manager s ability to generate higher returns. To analyze a fund s portfolio management response to fund flows, we first calculate the change in holding stock size due to active portfolio rebalancing as follows, 30

32 where is the natural logarithm of market capitalization of stock j as of time t 1; N is the number of stocks held by fund i; and and are the number of shares of stock j held by fund i at time t 1 and t, respectively; is the price of stock j at time t 1; is the weight of stock j in fund i s portfolio as of time t 1; is the imputed weight of stock j in fund i s portfolio at time t assuming stock prices do not change from time t 1 to time t. We use the imputed weight in order to abstract from stock size changes that occur solely due to price changes and not due to funds actively adjusting their portfolios. captures only the changes in holding stock size attributable to funds actively rebalancing their portfolios. If a fund does not rebalance its portfolio holdings from time t 1 to time t, the measure takes a value of zero. We calculate changes in portfolio holding stock size over a three-, six-, or twelve-month window (i.e., the period from time t 1 to time t spans three, six, or twelve months), rolling this window by one quarter at a time. We examine the relation between fund flows and the change in the average market capitalization of the portfolio holdings using the following cross sectional regressions, and 31

33 where, as defined in equation (7), represents the change in fund i s mean logged stock holding market capitalization from quarter t 1 to quarter t + k, (k = 0, 1, or 3), represents fund i s cumulative monthly dollar flow from quarter t 1 to t + k divided by fund TNA at t 1, is a dummy variable equal to 1 when, is a dummy variable equal to 1 when, and represents a set of fund-level control variables at quarter t 1, including fund return, expense ratio, turnover, net flow, Log(fund age), and Log(family TNA). Again, we calculate Fama-MacBeth (1973) t-statistics with Newey-West corrected standard errors with three lags. As before, we follow Sirri and Tufano (1998) in ensuring that our fund flow measure excludes any increase in fund size due to capital gains or dividends. This is important because we do not want to bias our results in favor of finding a relation between fund flows and changes in the market capitalization of holdings, which would mechanically occur as funds grow larger or smaller along with the stocks they hold. We break this mechanical link between fund flows and changes in the market capitalization of holdings by using pure inflows or outflows as independent variables in (8) and (9) and also by using with in equation (7) to focus only on active adjustments to the portfolios. Panel B of Table VIII presents the results. Lagged fund returns are negatively correlated with changes in the portfolios holding stock size, pointing to a relation between high lagged returns and a decrease in holding stock size. The negative correlation between and lagged turnover suggests that funds trade actively to reduce the market capitalization of their holdings. More important, cash flows are positively correlated with changes in the mean portfolio holding market capitalization at the three month horizon. The significant coefficient on inflows indicates that inflows lead to a contemporaneous increase in the mean portfolio holding 32

34 market capitalization. The converse, however, is not true for outflows, i.e., outflows do not lead to a decrease in portfolio holding market capitalization, as the coefficient on outflows is not distinguishable from zero. In economic terms, a one standard deviation increase in cumulative fund flow leads to an increase in the size of holdings by 3.0% over the next twelve months, based on our estimates in column (10). Our flow results complement our earlier results that fund stock holding characteristics, and market capitalization in particular, play a crucial role in the diseconomies of scale that characterizes the mutual fund industry. One concern is that fund managers may invest inflows first into larger, more liquid stocks before slowly deploying these inflows into smaller, less liquid stocks, which is why we also examine fund flows over longer horizons. The results are similar for the six-month time horizon regardless of whether or not we include fund-level control variables. At the twelve month horizon, although we continue to find a significant relation between holding market capitalization and net flows, the coefficient estimate on inflows is significant only in the presence of the fund-level variables. Results for changes in portfolio holdings over 24 months (untabulated) are similar to, albeit statistically weaker than, the results for 12 months. We also find that fund flows persist (the average autocorrelation coefficient is about 0.3), suggesting that fund managers can deploy the initial investments quickly into smaller stocks, since, on average, they can expect to meet any possible redemptions with additional inflows. Because it is unlikely that it takes six, twelve, or twenty-four months to deploy any inflows into smaller, less liquid stocks, we can safely conclude that funds actively tilt their portfolios towards larger stocks in response to inflows. 33

35 IV. Conclusion We find that large funds underperform small funds because of their stock holdings. A preference for stocks that generate relatively low return premiums likely stems from an overarching preference for stocks with sufficient liquidity (e.g., large market capitalization stocks). The relatively higher liquidity of the holdings of larger funds helps fund managers contain transaction costs. The finding that a fund s preference to hold a particular type of stock depends in part on the fund s size provides insight into the competitive equilibrium of the mutual fund industry. Although a few dominant management companies, such as Vanguard and Fidelity, control a significant fraction of industry assets, small fund companies and small funds do exist and, in many instances, prosper. A small fund enjoys the distinct advantage of access to a universe of stocks (i.e., with small cap and low liquidity) that big funds are less able to exploit. Whereas new, small funds are unable to compete with big funds on expenses, they more than make up for the expense disadvantage with an investment pool that offers higher average returns. By contrast, small companies in many other industries face built-in disadvantages. In the retail industry, for example, a firm s negotiating power with suppliers is often directly related to the size of its contract. Few retail firms can compete on price with Walmart or Amazon, for example, as their sales volume allows them to negotiate lower prices. In the mutual fund industry, transaction costs correlate positively with trade size. Ignoring skill, it is not surprising that big funds compete by charging low expenses whereas small funds have the opportunity to earn higher investment returns, the very dynamics that manifest themselves in the diseconomies of scale that we see across the fund industry. 34

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37 Brown David and Youchang Wu, 2014, Mutual Fund Flows and Cross-Fund Learning within Families, Journal of Finance, forthcoming. Busse, Jeffrey, T. Clifton Green, and Narasimhan Jegadeesh, 2012, Buy-Side Trades and Sell- Side Recommendations: Interactions and Information Content, Journal of Financial Markets 15, Busse, Jeffrey, and Qing Tong, 2012, Mutual Fund Industry Selection and Persistence, Review of Asset Pricing Studies 2, Carhart, Mark, 1997, On Persistence in Mutual Fund Performance, Journal of Finance 52, Chemmanur, Thomas, Shan He, and Gang Hu The Role of Institutional Investors in Seasoned Equity Offerings, Journal of Financial Economics 94: Chen, Joseph, Harrison Hong, Ming Huang, and Jeffrey Kubik, 2004, Does Fund Size Erode Mutual Fund Performance? The Role of Liquidity and Organization, American Economic Review 94, Chordia, Tarun, Amit Goyal, and Jay Shanken, 2015, Cross-sectional Asset Pricing with Individual Stocks: Betas versus Characteristics, Working Paper, Emory University. Christoffersen, Susan, Donald Keim, and David Musto, 2008, Valuable Information and Costly Liquidity: Evidence from Individual Mutual Fund Trades, Working Paper, University of Pennsylvania Dangl, Thomas, Youchang Wu, and Josef Zechner, 2008, Market Discipline and Internal Governance in the Mutual Fund Industry, Review of Financial Studies 21, Daniel, Kent, Mark Grinblatt, Sheridan Titman, and Russ Wermers, 1997, Measuring Mutual Fund Performance with Characteristic-Based Benchmarks, Journal of Finance 52, Daniel, Kent and Sheridan Titman, 1997, Evidence on the Characteristics of Cross Sectional Variation in Stock Returns, Journal of Finance 52, Edelen, Roger, Richard Evans, and Gregory Kadlec, 2007, Scale Effects in Mutual Fund Performance: The Role of Trading Costs, Working Paper, UC Davis and University of Virginia. Elton, Edwin, Martin Gruber, and Christopher Blake, 2001, A First Look at the Accuracy of the CRSP Mutual Database and a Comparison of the CRSP and Morningstar Mutual Fund Databases, Journal of Finance 56, Elton, Edwin, Martin Gruber, and Christopher Blake, 2012, Does Mutual Fund Size Matter? The Relationship Between Size and Performance, Review of Asset Pricing Studies 2,

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39 Pollet, Joshua and Mungo Wilson, 2008, How Does Size Affect Mutual Fund Behavior? Journal of Finance 63, Puckett, Andy and Xuemin Yan, 2011, The Interim Trading Skills of Institutional Investors, Journal of Finance 66, Reuter, Jonathan and Eric Zitzewitz, 2013, How Much Does Size Erode Mutual Fund Performance? A Regression Discontinuity Approach, Working Paper, Boston College. Sirri, Erik and Peter Tufano, 1998, Costly Search and Mutual Fund Flows, Journal of Finance 53, Stoughton, Neal, Youchang Wu, and Josef Zechner, 2011, Intermediated Investment Management, Journal of Finance 66, Wermers, Russ, 2000, Mutual Fund Performance: An Empirical Decomposition into Stock- Picking Talent, Style, Transactions Costs, and Expenses, Journal of Finance 55, Yan, Xuemin, 2008, Liquidity, Investment Style, and the Relation between Fund Size and Fund Performance, Journal of Financial and Quantitative Analysis 43,

40 Figure 1: Time-Series of Mutual Fund Transaction Costs The figure plots the time-series of the 12-month moving average of the differences in mutual fund transaction cost per TNA dollar (unannualized) between the largest and smallest mutual fund size quintiles. We use execution shortfall in Panel A and open price cost in Panel B computed as in equations (1) and (2), respectively. We calculate both transaction cost measures using the Abel Noser institutional trading data from January of 1999 to September of Panel A: Execution Shortfall m1 2000m1 2001m1 2002m1 2003m1 2004m1 2005m1 2006m1 2007m1 2008m1 2009m1 2010m1 2011m1 Panel B: Open Price Cost m1 2000m1 2001m1 2002m1 2003m1 2004m1 2005m1 2006m1 2007m1 2008m1 2009m1 2010m1 2011m

41 Table I: Summary Statistics The table reports summary statistics of fund characteristics, holdings characteristics, and transaction cost measures. Panel A is based on the matched sample of the Thomson Reuters Mutual Fund Holdings database (Thomson S12 sample) and the CRSP Mutual Fund database, and Panel B is based on the matched sample of the Thomson Reuters Mutual Fund Holdings database, the CRSP Mutual Fund database, and the Abel Noser institutional trading data (Abel Noser sample). The sample period of the Thomson S12 sample is April 1980 through June 2012; the sample period of the Abel Noser sample is January 1999 through September In both panels, we first sort the funds each month by lagged total net assets (TNA) into quintile portfolios and then compute the time-series averages of the monthly cross-sectional means for the overall sample and for each mutual fund size quintile. Number of funds is the average number of funds each month in each portfolio. TNA is the sum of assets under management across all share classes of a fund. Fund age is the age of the oldest share class in the fund. We compute gross return by adding one-twelfth of the annual expense ratio to the monthly net fund returns. Four-factor alphas are estimated based on the Carhart (1997) model, calculated as the difference between the realized fund return in a given month and the sum of the product of the four-factor betas estimated over the previous 36-month and the factor returns during that month. Holding return is the value-weighted average return based on a fund s portfolio holdings from the Thomson S12 database. DGTW adjusted return and DGTW benchmark return are the Daniel et al. (1997, DGTW) benchmark-adjusted returns of a fund and its benchmark returns, respectively. We compute the Amihud (2002) illiquidity measure as the monthly average ratio of the absolute value of daily returns to the dollar trading volume. Momentum is the six-month cumulative stock returns over the period from month t 7 to month t 2. We compute stock turnover as the ratio of monthly trading volume to the previous month-end shares outstanding. Holding characteristics, including stock size, B/M ratio, momentum, stock turnover, and Amihud illiquidity are fund-level value-weighted averages of the corresponding variable computed based on a fund s most recent portfolio holdings. Fund flow is the average monthly net growth in fund assets beyond reinvested dividends and portfolio returns, summed over all share classes. Fund turnover and the expense ratio are the value weighted averages across all share classes. Family TNA is the sum of the total assets under management of all the funds in a fund family excluding the fund itself. In Panel B, we calculate execution shortfall and the open price cost measure from the Abel Noser institutional trading data using equations (1) and (2), respectively. We first compute these two measures for each trade, then multiply by the dollar value of each trade and sum over all trades in a month for a given fund. Then we divide by the average fund TNA of previous and current month-ends to obtain a monthly trading cost per TNA dollar. The number reported is annualized by multiplying the time-series average of the monthly cross-sectional mean fund-level trading cost per TNA dollar by twelve. We calculate commission, taxes, and fees on a per TNA dollar basis as in the case of the transaction cost measures. Total trading costs for execution shortfall and open price cost are sums of the respective cost and commissions, taxes, and fees. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. 40

42 Panel A: Thomson S12 Sample Mutual fund size quintile Variables All funds 1 (small) (large) Diff:1-5 t-stat. Number of funds TNA ($ million) ,350-3,313*** (-33.54) Fund Return Breakdown Gross return (%) *** (4.54) Net return (%) *** (3.59) Four-factor alpha (%) *** (2.84) Holding return (%) *** (3.41) DGTW benchmark return (%) ** (2.50) DGTW adjusted return (%) ** (2.49) Holdings Characteristics Stock size ($ billion) *** (-17.32) B/M ratio (1.36) Momentum (%) (0.49) Stock turnover (%) (-1.36) Amihud illiquidity *** (12.44) Other Fund Characteristics Expense ratio (%) *** (72.12) Fund age *** (-81.33) Fund flow (%) *** (10.98) Turnover (%) *** (22.18) Family TNA ($ billion) *** (-19.63) 41

43 Panel B: Abel Noser Sample Mutual Fund Size Quintile Variables All Funds 1 (Small) (Large) Diff:1-5 t-stat. Number of funds TNA ($ million) 2, ,573 11,596-11,531*** (-30.88) Fund Return Breakdown Gross return (%) * (1.84) Net return (%) (1.46) Four-factor alpha (%) (0.60) Holding return (%) * (1.82) DGTW benchmark return (%) ** (2.24) DGTW adjusted return (%) (0.79) Fund Transaction Costs per TNA Dollar Execution shortfall (%) *** (17.72) Open price cost (%) *** (13.02) Commission (%) *** (30.36) Tax and Fee (%) *** (8.22) Total, execution shortfall (%) *** (22.90) Total, open price cost (%) *** (17.21) Holdings Characteristics Stock size ($ billion) *** (-18.00) B/M ratio *** (14.45) Momentum (%) (-0.40) Stock turnover (%) (-1.13) Amihud illiquidity *** (5.93) Other Fund Characteristics Expense ratio (%) *** (77.34) Fund age *** (-83.50) Fund flow (%) *** (6.43) Turnover (%) *** (28.58) Family TNA ($ billion) *** (-19.60) 42

44 Table II: Mutual Fund Trading Costs and Stock Characteristics This table reports summary statistics of fund trading dollar weighted trading costs and stock characteristics. Each month, we sort funds into quintiles based on lagged TNA. Panel A reports fund trading costs per trading dollar. For a given fund-month combination, we compute trading costs per trading dollar as the valueweighted average of the execution shortfall and the open price cost based on the dollar value of each trade by aggregating over all of a fund s trades in a given month. We then compute the time-series averages of monthly cross-sectional averages for the overall sample and each of the mutual fund size quintile. Commissions, taxes, and fees are also aggregated in a similar manner. In Panels B and C, we analyze funds trading behavior conditional on trading the same stock. For each stock-month combination, we compute total dollar trade value, total number of tickets (orders are submitted by the portfolio manager to the trade in the form of tickets), total number of trades, and average volume per ticket (Panel B), as well as trading dollar weighted trading cost measures (Panel C) for the overall sample and for each mutual fund size quintile. After that, we average across all stocks each month and then compute the time-series average across all sample months. Panel D reports fund trading dollar weighted stock characteristics. Similar to our calculation in Panel A, for a given fund-month combination, we compute trading dollar weighted stock characteristics (market capitalization, book-to-market ratio, momentum, turnover, and Amihud illiquidity measure) based on all of a fund s trades in a given month. We then compute the time-series average of monthly cross-sectional averages for the overall sample and each of the mutual fund size quintiles. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. The sample is the Abel Noser sample defined in Table I. Panel A: Fund Trading Costs per Trading Dollar Mutual Fund Size Quintile Variables All Funds 1 (Small) (Large) Diff:1-5 t-stat. Execution shortfall (%) *** (7.36) Open price cost (%) *** (5.84) Commission (%) *** (12.05) Tax and fee (%) *** (4.78) Total, execution shortfall (%) *** (9.45) Total, open price cost (%) *** (7.31) Panel B: Trade Statistics Conditional on Same Stock Mutual Fund Size Quintile Variables All Funds 1 (Small) (Large) Diff:1-5 t-stat. Trade dollars ($ million) *** (-26.18) Number of tickets *** (-31.71) Number of trades *** (-26.05) Volume per ticket (shares) 23,324 5,710 11,217 16,417 26,023 48,194-42,485*** (-47.79) 43

45 Panel C: Transaction Costs Conditional on Same Stock Mutual Fund Size Quintile Variables All Funds 1 (Small) (Large) Diff:1-5 t-stat. Execution shortfall (%) *** (-5.36) Open price cost (%) *** (-5.11) Commission (%) (1.21) Tax and Fee (%) *** (4.98) Total, execution shortfall (%) *** (-4.90) Total, open price cost (%) *** (-4.72) Panel D: Trading Stock Characteristics Mutual Fund Size Quintile Variables All funds 1 (Small) (Large) Diff:1-5 t-stat. Stock size ($ billion) *** (-16.79) B/M ratio *** (11.09) Momentum (%) * (-1.79) Stock turnover (%) *** (-2.19) Amihud illiquidity (0.66) 44

46 Table III: Determinants of Ticket Level Transaction Costs Panel A of this table reports the annual trading cost measures at the ticket level. The average of execution shortfall and total trading cost (i.e., execution shortfall + commissions + taxes and fees) are reported for all tickets, buys, and sells separately. Panel B reports Fama-MacBeth (1973) coefficient estimates from the regression of mutual fund transaction costs at the ticket level on the trade and fund level variables as shown in equation (5). Trade Size is the share volume of a ticket normalized by dividing by the average daily trading volume of the previous month. Price inverse is defined as one over the closing price of the trading day prior to the order placement date. Log(mktcap) is the logarithm of market capitalization of the traded stock at the previous month-end. Nasdaq is a dummy variable for stocks listed on Nasdaq stock exchange. All fund level independent variables are defined in Table I and lagged by one month. We first estimate cross-sectional regressions each month and then report the time-series average of the monthly coefficients. Fama-MacBeth (1973) t-statistics (in parenthesis) are corrected following Newey-West (1987) with three lags. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. The sample is the Abel Noser sample defined in Table I. Panel A: Ticket Level Transaction Costs by Year - Execution Shortfall All Buys Sells Tickets Implicit Total Tickets Implicit Total Tickets Implicit Total , , , , , , , , , , , , , , , , , , , , , , , , ,034, , , ,132, , , ,102, , , , , , , , , All 8,900, ,688, ,211,

47 Panel B: Determinants of Trade Level Transaction Costs - Execution Shortfall Implicit Total All Buy Sell All Buy Sell VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Trade size 0.009*** 0.009*** 0.008*** 0.008*** 0.010*** 0.010*** 0.011*** 0.011*** 0.010*** 0.009*** 0.011*** 0.012*** (6.55) (6.53) (6.42) (6.15) (6.11) (6.27) (7.13) (7.18) (7.30) (6.97) (6.49) (6.79) Price inverse 0.673*** 0.699*** * 0.786*** 0.816*** 2.228*** 2.269*** 1.965*** 2.059*** 2.301*** 2.351*** (4.67) (4.74) (1.54) (1.83) (5.22) (5.36) (12.74) (12.34) (13.71) (12.16) (12.76) (12.53) Log(mktcap) *** *** *** *** *** *** *** *** *** *** *** *** (-5.66) (-6.71) (-4.95) (-6.18) (-4.98) (-4.83) (-6.82) (-7.77) (-5.88) (-7.16) (-6.26) (-5.78) Nasdaq 0.035*** 0.026*** 0.024** *** 0.045*** * (4.33) (3.98) (2.55) (1.62) (2.78) (2.80) (1.22) (-0.11) (-0.31) (-0.93) (1.67) (1.46) Log(TNA) 0.007*** 0.009*** *** 0.010*** (2.64) (2.61) (1.20) (2.82) (2.92) (0.96) Expense ratio *** 0.047*** (1.50) (1.65) (0.07) (3.76) (3.12) (1.42) Fund turnover 0.037*** 0.030*** 0.033*** 0.034*** 0.030*** 0.028*** (4.31) (2.68) (4.22) (4.02) (2.63) (3.64) Fund flow *** *** *** *** (-4.22) (-3.36) (-1.58) (-4.61) (-3.39) (-1.50) Log(fund age) (-0.85) (-1.62) (0.17) (0.09) (-0.74) (0.98) Log(family TNA) ** *** *** (-0.58) (1.49) (-2.47) (-2.82) (-0.41) (-4.52) Lag fund return (-0.28) (0.24) (-0.64) (-0.42) (0.18) (-0.76) Constant 0.176*** 0.104* 0.193*** *** 0.264*** 0.277*** 0.265*** 0.255*** 0.137* 0.331*** 0.448*** (6.50) (1.67) (6.17) (0.35) (5.55) (2.87) (8.22) (3.86) (7.51) (1.89) (7.31) (4.51) Adj. R-squared Avg. month obs. 56,898 54,105 30,012 28,381 26,887 25,724 56,898 54,105 30,012 28,381 26,887 25,724 # of months

48 Table IV: Determinants of Fund Level Transaction Costs Panel A reports the number of observations and the summary statistics for execution shortfall and total trading cost (i.e., execution shortfall + commissions + taxes and fees) per trading dollar or per TNA dollar each year. Panels B and C report the Fama-MacBeth (1973) coefficient estimates from monthly cross-sectional regressions of the trading cost measures on fund attributes. The dependent variables are execution shortfall per trading dollar (in panel B) and execution shortfall per TNA Dollar (in panel C). Fund attributes (independent variables) are defined in Table I and lagged by one month. Fama-MacBeth (1973) t-statistics (in parenthesis) are corrected following Newey-West (1987) with three lags. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. The sample is the Abel Noser sample defined in Table I. Panel A: Fund Level Transaction Costs by Year - Execution Shortfall Costs per Trading Dollar Costs per TNA Dollar # Obs. Implicit Explicit Total Implicit Explicit Total , , , , , , , , , , , , All 27,

49 Panel B: Execution Shortfall per Trading Dollar Implicit Trading Costs Total Trading Costs VARIABLES (1) (2) (3) (4) (5) (6) Log(TNA) *** *** ** *** * * (-6.54) (-2.69) (-2.33) (-7.69) (-1.93) (-1.93) Lag trade cost *** *** (21.23) (19.33) Expense ratio *** *** *** *** (3.29) (2.81) (5.03) (4.00) Fund turnover *** *** *** *** (10.25) (10.04) (7.71) (9.12) Fund flow (-1.65) (-0.85) (0.90) (-1.13) Log(fund age) *** *** *** *** (4.21) (4.30) (4.64) (4.74) Log(family TNA) *** *** *** *** (-3.80) (-3.09) (-5.50) (-5.14) Lag fund return ** * *** ** (-2.22) (-1.92) (-2.88) (-2.44) Constant *** *** ** *** *** *** (11.02) (2.98) (2.01) (14.97) (5.20) (4.52) Observations 28,063 26,153 24,858 28,063 26,153 24,858 Adj. R-squared # of months

50 Panel C: Execution Shortfall per TNA Dollar Implicit Trading Costs Total Trading Costs VARIABLES (1) (2) (3) (4) (5) (6) Log(TNA) *** *** *** *** *** *** (-12.76) (-5.43) (-4.60) (-15.89) (-7.48) (-5.66) Lag trade cost *** *** (24.31) (28.19) Expense ratio (0.57) (0.20) (0.51) (0.20) Fund turnover *** *** *** *** (12.41) (6.72) (12.99) (6.89) Fund flow (-0.87) (-1.19) (-0.82) (-1.63) Log(fund age) *** ** *** ** (2.68) (2.00) (3.36) (2.40) Log(family TNA) *** *** *** *** (-5.27) (-3.98) (-5.68) (-4.16) Lag fund return * (-1.79) (-0.63) (-1.38) (-0.99) Constant *** *** *** *** *** *** (16.32) (8.17) (6.01) (20.30) (9.97) (6.59) Observations 28,063 26,153 24,858 28,063 26,153 24,858 Adj. R-squared # of months

51 Table V: Transaction Costs, Fund Size, and Fund Performance: Cross-Sectional Regressions This table reports the Fama-MacBeth (1973) coefficients from monthly cross-sectional regressions of individual fund-level four-factor alphas on log(tna), lagged per TNA dollar execution shortfall or total trading costs, and other fund attributes. All independent variables are defined in Table I and lagged by one month. γ* < 0 represents the subsample period consisting of months with a significantly (at the five percent level) negative cross-sectional relation between a firm s market capitalization and its excess return based on all CRSP common stocks. Fama-MacBeth (1973) t-statistics (in parenthesis) are corrected following Newey-West (1987) with three lags. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. The sample is the Abel Noser sample defined in Table I. Implicit Trading Costs Total Trading Costs (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) VARIABLES All All All γ* < 0 Other Diff. All γ* < 0 Other Difference Log(TNA) *** ** *** ** (0.03) (-1.48) (-1.59) (-2.96) (0.45) (-2.53) (-1.54) (-2.95) (0.50) (-2.55) Lag trade cost (0.36) (-0.44) (0.79) (0.84) (0.03) (1.12) Lag fund return (0.64) (0.63) (1.35) (-0.41) (0.62) (1.35) (-0.42) Expense ratio (-0.67) (-0.19) (0.32) (-0.53) (-0.23) (0.26) (-0.54) Fund turnover * * (-1.02) (-1.13) (-1.73) (-0.04) (-1.20) (-1.78) (-0.08) Fund flow (-0.40) (-0.38) (1.30) (-1.50) (-0.39) (1.31) (-1.53) Log(fund age) (-0.56) (-0.02) (1.43) (-1.42) (-0.11) (1.39) (-1.48) Log(family TNA) *** *** *** *** *** (3.71) (3.47) (3.39) (1.29) (3.54) (3.47) (1.40) Constant (-0.50) (-0.48) (-0.21) (-0.49) (0.24) (-0.32) (-0.52) (0.14) Observations 27,859 26,455 25,157 10,230 14,927 25,157 10,230 14,927 Adj. R-squared # of months

52 Table VI: Stock Size Premium, Fund Size, and Fund Performance: Cross-Sectional Regressions This table reports the Fama-MacBeth (1973) coefficients from monthly cross-sectional regressions of individual fund-level four-factor alphas on log(tna) and other fund attributes. All independent variables are defined in Table I and lagged by one month. γ* < 0 represents the subsample period consisting of months with a significantly (at the five percent level) negative cross-sectional relation between a firm s market capitalization and its excess return based on all CRSP common stocks. Fama-MacBeth (1973) t-statistics (in parenthesis) are corrected following Newey-West (1987) with three lags. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. The sample is the Thomson S12 sample defined in Table I. (1) (2) (3) (4) (5) VARIABLES All All γ* < 0 Other Difference Log(TNA) *** *** *** *** (-2.60) (-3.28) (-4.19) (-1.43) (-3.03) Lag fund return ** ** (2.00) (1.99) (0.81) Expense ratio *** *** * (-3.20) (-3.15) (-1.69) Fund turnover (0.56) (-0.42) (1.03) Fund flow (1.33) (0.89) (1.08) Log(fund age) ** (-0.27) (1.64) (-1.97) Log(family TNA) *** ** *** (3.11) (2.28) (2.63) Constant * * (0.08) (1.95) (1.90) (1.11) Observations 339, , , ,050 Adj. R-squared # of Months

53 Table VII: Relation between Fund Size and Fund Performance: Time-Series Regressions This table examines the relation between fund size and fund performance using a time-series portfolio approach. All funds are sorted into quintiles each month based on their previous month-end TNA. Equally-weighted monthly net returns in excess of the risk-free rate are obtained for each quintile. The table presents the coefficient estimates and the alphas from the regression of the quintile portfolio excess returns on the Carhart (1997) factors. Also presented are the coefficient estimates and the alphas from the regression of the difference in returns between portfolios one and five. γ* < 0 represents the subsample period consisting of months with a significantly (at the five percent level) negative cross-sectional relation between a firm s market capitalization and its excess return based on all CRSP common stocks. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. The sample is the Thomson S12 sample defined in Table I. Mutual Fund Size Quintile Difference: 1-5 Model 1 (Small) (Large) All γ* < 0 Other Difference Alpha ** * ** ** ** (0.21) (-1.57) (-1.37) (-2.00) (-1.94) (2.09) (2.06) (-0.79) (2.19) MKTRF *** *** *** *** *** (94.78) (104.38) (104.62) (107.76) (118.96) (-1.56) SMB *** *** *** *** *** *** (13.76) (14.19) (14.35) (14.05) (10.70) (6.02) HML * *** *** *** (1.90) (2.88) (0.07) (-0.94) (-4.67) (6.67) UMD *** *** * (-0.87) (0.72) (2.71) (3.45) (0.86) (-1.84) Adj. R-squared # of Months

54 Table VIII: Fund Flows and Holding Stock Market Capitalization Panel A presents the distribution of stocks by firm size in the mutual fund quintile portfolios. Funds are sorted into quintiles based on their last month s TNA. Stock holdings are independently sorted into quintile portfolios based on their market capitalization (using NYSE breakpoints) from the previous quarter s holdings. Panel A reports the time-series average of the proportion of fund holdings in each firm size quintile. Note that the holdings of each fund quintile add up to one. The second to last column presents the difference in the fraction of holdings between the smallest and the largest fund size portfolios for a given firm size quintile. t-statistics in the last column are based on Newey-West corrected standard errors with twelve lags as the holdings are likely to be serially correlated. Panel B reports the Fama-MacBeth (1973) coefficient estimates from a regression of changes in the market capitalization of the fund-level holdings on cumulative fund flows and other fund-level control variables as shown in equations (8) and (9). PosFlow (NegFlow) is a dummy variable that takes a value of one for inflows (outflows) and is zero otherwise. The dependent variable (change in the market capitalization of the fund-level holdings) is computed over three-, six-, or twelve-month horizons, rolling by a quarter at a time and is designed to capture only the changes in holding stock size caused by funds actively rebalancing their portfolios and takes a value of zero if a fund does not actively rebalance its portfolio holdings. Fund flows are computed over the same period as the dependent variable (change in the market capitalization) and exclude any increase in fund size due to capital gains or dividends. The other independent variables are defined in Table I. Fama-MacBeth (1973) t-statistics (in parenthesis) are corrected following Newey-West (1987) with three lags. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. The sample is the Thomson S12 sample defined in Table I. Panel A. Mutual Fund Holding Behavior across Stock Size Mutual Fund Size Quintile Stock Market Cap Quintile 1 (Small) (Large) Difference: 1-5 t-stat. 1 (Small) *** (17.43) *** (24.77) *** (19.71) *** (2.72) 5 (Large) *** (-24.19) 53

55 Panel B. Fund Flows and Change in Fund Holding Stock Size Three Months Six Months Twelve Months (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Flow * *** *** *** *** *** (1.95) (3.02) (3.24) (3.85) (3.54) (3.88) PosFlow* Flow ** *** *** *** ** (2.31) (3.05) (2.96) (2.97) (1.50) (2.60) NegFlow * Flow (0.24) (0.47) (0.30) (0.13) (1.43) (1.33) Lag fund return *** *** *** *** (-3.78) (-3.86) (-2.93) (-2.74) (-0.68) (-0.61) Expense ratio (0.55) (0.54) (1.17) (1.30) (1.41) (1.53) Fund turnover *** *** *** *** *** *** (-3.91) (-3.86) (-4.51) (-4.37) (-3.41) (-3.28) Log(fund age) (-0.63) (-0.63) (-0.05) (0.00) (-1.11) (-1.48) Log(family TNA) (0.10) (0.05) (-0.15) (-0.12) (-0.79) (-0.71) Constant *** *** *** *** *** *** (-5.71) (0.19) (-5.56) (0.13) (-5.08) (0.12) (-4.79) (-0.21) (-4.01) (1.05) (-3.31) (1.34) Observations 94,174 84,509 94,174 84,509 92,246 82,445 92,246 82,445 88,081 78,575 88,081 78,575 Adj. R-squared # of Quarters

56 Internet Appendix for Mutual Fund Trading Costs and Diseconomies of Scale This Internet Appendix tabulates additional results for some of the empirical tests that are mentioned in the paper. 55

57 Table IA.I Summary Statistics: Subsample Results The table reports summary statistics of Table I for two subsamples separately: months with significant stock size effect (γ* < 0) and other months. Panel A is based on the Thomson S12 sample, and Panel B is based on the Abel Noser sample. In both panels, we first sort the funds each month by lagged total net assets (TNA) into quintile portfolios and then compute the time-series averages of the monthly cross-sectional means for each of the subsample and for each mutual fund size quintile. Panel A: Thomson S12 Sample Mutual fund size quintile Variables All funds 1 (small) (large) Diff:1-5 t-stat. A1. Months with γ*<0 Gross return (%) *** (7.12) Net return (%) *** (6.53) Four-factor alpha (%) ** (2.45) A2. Other Months Gross return (%) (0.05) Net return (%) (-0.75) Four-factor alpha (%) (1.63) Panel B: Abel Noser Sample Mutual Fund Size Quintile Variables All Funds 1 (Small) (Large) Diff:1-5 t-stat. B1. Months with γ*<0 Gross return (%) *** (3.05) Net return (%) *** (2.82) Four-factor alpha (%) * (1.70) B2. Other Months Gross return (%) (-0.41) Net return (%) (-0.73) Four-factor alpha (%) (-0.84) 56

58 Table IA.II Determinants of Ticket Level Transaction Costs: Open Price Cost We repeat the analyses in Table III using the open price cost measure, rather than the execution shortfall measure. We use the Abel Noser sample from 1999m1 to 2011m9 in the analyses. Panel A reports summary statistics of trading cost measures at the ticket level. We report the averages of the open price cost and total trading cost (i.e., open price cost + commissions + taxes and fees) of all tickets, buys, and sells separately. Panel B reports Fama-MacBeth (1973) estimation results on the determinants of mutual fund transaction costs at the ticket level. All independent variables are defined in Tables I and III. We first estimate crosssectional regressions each month and then report the time-series average of the monthly coefficients. We calculate Fama-MacBeth (1973) t-statistics with Newey-West correction for serial correlation of three lags. We indicate statistical significance of one, five, and ten percent by ***, **, and * respectively. t- statistics are reported in parenthesis. Panel A. Ticket Level Transaction Costs by Year - Open Price Cost All Buys Sells Tickets Implicit Total Tickets Implicit Total Tickets Implicit Total , , , , , , , , , , , , , , , , , , , , , , , , ,034, , , ,132, , , ,102, , , , , , , , , All 8,900, ,688, ,211,

59 Panel B: Determinants of Trade Level Transaction Costs - Open Price Cost Implicit Total All Buy Sell All Buy Sell VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Trade size 0.008*** 0.006*** 0.004*** 0.003*** 0.011*** 0.009*** 0.010*** 0.008*** 0.005*** 0.004*** 0.013*** 0.011*** (5.39) (6.17) (3.68) (3.27) (5.21) (5.74) (6.15) (7.17) (5.31) (5.20) (5.62) (6.38) Price inverse 1.004*** 1.039*** 0.510** 0.592*** 1.123*** 1.156*** 2.557*** 2.606*** 2.293*** 2.388*** 2.634*** 2.687*** (5.94) (5.77) (2.60) (2.63) (6.51) (6.36) (12.97) (12.15) (11.07) (10.08) (13.13) (12.44) Log(mktcap) 0.008** * *** 0.019*** 0.010* ** ** *** 0.012** (2.02) (-0.58) (-1.76) (-3.35) (3.47) (1.79) (0.25) (-2.00) (-2.48) (-3.99) (2.11) (0.70) Nasdaq 0.063*** 0.047*** 0.040** ** 0.076** 0.036*** 0.020* ** (4.65) (3.67) (2.01) (1.58) (2.53) (2.17) (3.07) (1.75) (0.51) (0.07) (2.05) (1.59) Log(TNA) 0.019*** 0.016** 0.024*** 0.019*** 0.016*** 0.023*** (3.09) (2.57) (3.16) (3.23) (2.82) (3.14) Expense ratio * (-1.49) (-1.85) (-1.32) (-0.45) (-0.97) (-0.33) Fund turnover 0.088*** 0.079*** 0.086*** 0.086*** 0.079*** 0.081*** (8.18) (5.65) (8.86) (8.16) (5.84) (8.21) Fund flow *** * *** * (-3.12) (-1.70) (-1.47) (-3.27) (-1.78) (-1.44) Log(fund age) (-0.54) (-1.15) (-0.47) (-0.04) (-0.56) (-0.11) Log(family TNA) 0.014** 0.014** 0.013* (2.16) (2.24) (1.96) (0.78) (0.94) (0.58) Lag fund return ** ** (-1.49) (-0.09) (-2.11) (-1.60) (-0.14) (-2.16) Constant * 0.103** ** 0.115** *** (0.36) (-1.92) (2.00) (-0.74) (-0.28) (-2.09) (2.55) (-0.47) (3.04) (0.09) (1.45) (-0.61) Adj. R-squared Avg. month obs. 57,609 54,772 30,380 28,723 27,229 26,049 57,609 54,772 30,380 28,723 27,229 26,049 # of months

60 Table IA.III Determinants of Fund Level Transaction Costs - Open Price Cost We repeat the analyses in Table IV using the open price cost measure, rather than the execution shortfall measure. In panel A, we report the number of observations and summary statistics for the open price cost and total trading cost (i.e., open price cost + commissions + taxes and fees) per Trading dollar or per TNA dollar each year. Panels B and C report Fama-MacBeth (1973) estimation results on the determinants of mutual fund transaction costs. We first estimate cross-sectional regressions each month and then report the time-series average of the monthly coefficients. We use the Abel Noser sample from 1999m1 to 2011m9 in the analyses. The dependent variables are the open price cost per trading dollar (in panel B) and the open price cost per TNA dollar (in panel C), both calculated from the Abel Noser institutional trading data. We calculate Fama-MacBeth (1973) t-statistics with Newey-West correction for serial correlation of three lags. We define all independent variables in Table I and we lag them by one month. We indicate statistical significance of one, five, and ten percent by ***, **, and * respectively. t-statistics are reported in parenthesis. Panel A: Fund Level Transaction Costs by Year - Open Price Cost Costs per Trading Dollar Costs per TNA Dollar # Obs. Implicit Explicit Total Implicit Explicit Total , , , , , , , , , , , , All 27,

61 Panel B: Open Price Cost Per Trading Dollar Implicit Trading Costs Total Trading Costs VARIABLES (1) (2) (3) (4) (5) (6) Log(TNA) *** *** *** *** *** *** (-5.24) (-4.99) (-4.16) (-6.37) (-3.97) (-3.98) Lag trade cost *** *** (23.03) (20.81) Expense ratio (-0.58) (-0.38) (1.26) (0.46) Fund turnover *** *** *** *** (11.14) (10.17) (9.31) (9.96) Fund flow * (-1.77) (-0.99) (0.58) (-1.23) Log(fund age) *** *** *** *** (4.91) (4.67) (5.09) (4.76) Log(family TNA) * *** ** (-1.97) (-1.17) (-3.43) (-2.59) Lag fund return *** ** *** ** (-3.12) (-2.20) (-3.49) (-2.56) Constant *** ** * *** *** *** (11.19) (2.20) (1.84) (15.43) (3.62) (3.71) Observations 28,375 26,453 25,458 28,375 26,453 25,458 Adj. R-squared # of months

62 Panel C: Open Price Cost Per TNA Dollar Implicit Trading Costs Total Trading Costs VARIABLES (1) (2) (3) (4) (5) (6) Log(TNA) *** *** *** *** *** *** (-9.34) (-5.47) (-4.56) (-12.24) (-7.18) (-5.64) Lag trade cost *** *** (33.36) (36.04) Expense ratio ** * ** * (-2.18) (-1.94) (-2.12) (-1.68) Fund turnover *** *** *** *** (9.66) (7.94) (10.52) (8.01) Fund flow (-0.42) (-1.13) (-0.41) (-1.25) Log(fund age) *** ** *** *** (3.37) (2.39) (3.78) (2.66) Log(family TNA) *** ** *** *** (-3.63) (-2.46) (-4.30) (-2.93) Lag fund return *** ** (-2.64) (-1.02) (-2.36) (-0.97) Constant *** *** *** *** *** *** (14.15) (7.66) (5.92) (18.09) (9.74) (6.90) Observations 28,375 26,453 25,458 28,375 26,453 25,458 Adj. R-squared # of months

63 Table IA.IV Transaction Costs, Fund Size, and Fund Performance: Gross and Net Returns We repeat the analyses in Table V using gross fund return (in Panel A) and net fund return (in Panel B), rather than individual fund alpha. The table reports Fama-MacBeth (1973) estimation results of monthly fund performance regressed on fund TNA, execution shortfall per TNA dollar, and other control variables. We first estimate cross-sectional regressions each month and then report the time-series average of the monthly coefficients. We use the Abel Noser sample from 1999m1 to 2011m9 in the analyses. We calculate execution shortfall per TNA dollar using Abel Noser institutional trading data. We calculate Fama-MacBeth (1973) t-statistics with Newey-West correction for serial correlation of three lags. γ* < 0 (other) represents the subsample period consisting of months with a significantly (at the five percent level) negative cross-sectional relation between a firm s market capitalization and its excess return based on all CRSP common stocks. We indicate statistical significance of one, five, and ten percent by ***, **, and * respectively. t-statistics are reported in parenthesis. Panel A: Gross Fund Return and Execution Shortfall Implicit Trading Costs Total Trading Costs (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) VARIABLES All All All γ* < 0 Other Diff. All γ* < 0 Other Diff. Log(TNA) *** ** *** ** (-1.42) (-1.27) (-1.32) (-2.84) (0.23) (-2.18) (-1.29) (-2.84) (0.27) (-2.21) Lag trade cost (0.73) (0.04) (0.86) (1.31) (0.39) (1.34) Lag fund return ** ** * ** * (2.45) (2.30) (1.01) (1.99) (2.29) (1.01) (1.98) Expense ratio (0.68) (1.09) (0.58) (0.63) (1.04) (0.50) (0.66) Fund turnover ** ** (-0.07) (-0.22) (-2.01) (1.08) (-0.29) (-2.06) (1.00) Fund flow * * *** * *** (1.91) (1.91) (2.73) (-0.04) (1.87) (2.74) (-0.09) Log(fund age) (-0.04) (0.22) (0.75) (-0.24) (0.13) (0.71) (-0.32) Log(family TNA) (0.58) (0.57) (0.05) (0.59) (0.71) (0.12) (0.70) Constant *** ** (1.58) (1.30) (1.35) (-0.89) (2.65) (1.29) (-0.90) (2.59) Observations 28,377 26,455 25,157 10,230 14,927 25,157 10,230 14,927 Adj. R-squared Num groups

64 Panel B: Net Fund Return and Execution Shortfall Implicit Trading Costs Total Trading Costs (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) VARIABLES All All All γ* < 0 Other Diff. All γ* < 0 Other Diff. Log(TNA) *** ** *** ** (-1.08) (-1.26) (-1.31) (-2.83) (0.24) (-2.18) (-1.27) (-2.83) (0.28) (-2.21) Lag trade cost (0.73) (0.03) (0.86) (1.30) (0.38) (1.34) Lag fund return ** ** * ** * (2.44) (2.30) (1.01) (1.98) (2.29) (1.01) (1.98) Expense ratio (-0.77) (-0.43) (-0.13) (-0.34) (-0.48) (-0.21) (-0.32) Fund turnover ** ** (-0.06) (-0.22) (-2.00) (1.08) (-0.28) (-2.05) (1.01) Fund flow * * *** * *** (1.93) (1.93) (2.75) (-0.03) (1.90) (2.76) (-0.08) Log(fund age) (-0.04) (0.22) (0.77) (-0.25) (0.12) (0.72) (-0.33) Log(family TNA) (0.62) (0.61) (0.08) (0.61) (0.75) (0.15) (0.72) Constant ** ** (1.24) (1.24) (1.29) (-0.92) (2.61) (1.23) (-0.94) (2.54) Observations 28,377 26,455 25,157 10,230 14,927 25,157 10,230 14,927 Adj. R-squared Num groups

65 Table IA.V Transaction Costs, Fund Size, and Fund Performance: Alternative Trading Cost Measures We repeat the analyses in Table V using alternative per TNA dollar trading cost measures: contemporaneous execution shortfall measures (Panel A), lagged open price cost measures (Panel B), and contemporaneous open price cost measures (Panel C). The table reports Fama-MacBeth (1973) estimation results of monthly individual fund alphas regressed on fund TNA, per TNA dollar trading cost measures, and other control variables. We first estimate cross-sectional regressions each month and then report the time-series average of the monthly coefficients. We use the Abel Noser sample from 1999m1 to 2011m9 in the analyses. We calculate per TNA dollar trading cost measures using Abel Noser institutional trading data. We calculate Fama-MacBeth (1973) t-statistics with Newey-West correction for serial correlation of three lags. γ* < 0 (other) represents the subsample period consisting of months with (without) a significantly (at the five percent level) negative cross-sectional relation between a firm s market capitalization and its excess return based on all CRSP common stocks. We indicate statistical significance of one, five, and ten percent by ***, **, and * respectively. t-statistics are reported in parenthesis. Panel A: Contemporaneous Execution Shortfall Measure Implicit Trading Costs Total Trading Costs (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) VARIABLES All All All γ* < 0 Other Diff. All γ* < 0 Other Diff. Log(TNA) *** ** *** ** (0.03) (-1.48) (-1.48) (-2.80) (0.45) (-2.38) (-1.51) (-2.82) (0.43) (-2.38) Current trade cost * (-1.77) (-0.87) (-1.15) (-1.24) (-0.42) (-0.88) Lag fund return (0.64) (0.66) (1.44) (-0.47) (0.68) (1.45) (-0.45) Expense ratio (-0.67) (-0.50) (-0.37) (-0.28) (-0.55) (-0.42) (-0.30) Fund turnover (-1.02) (-0.82) (-1.60) (0.23) (-0.86) (-1.62) (0.21) Fund flow (-0.40) (-0.26) (1.20) (-1.25) (-0.30) (1.20) (-1.31) Log(fund age) (-0.56) (-0.37) (0.93) (-1.45) (-0.41) (0.89) (-1.46) Log(family TNA) *** *** *** * *** *** * (3.71) (3.35) (3.35) (1.70) (3.42) (3.41) (1.78) Constant (-0.50) (-0.48) (-0.36) (-0.28) (-0.18) (-0.39) (-0.30) (-0.21) Observations 27,859 26,455 26,153 10,736 15,417 26,153 10,736 15,417 Adj. R-squared Num groups

66 Panel B: Lagged Open Price Cost Measure Implicit Trading Costs Total Trading Costs (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) VARIABLES All All All γ* < 0 Other Diff. All γ* < 0 Other Diff. Log(TNA) *** ** *** ** (0.03) (-1.48) (-1.48) (-3.00) (0.52) (-2.54) (-1.48) (-3.02) (0.52) (-2.55) Lag trade cost * * (-1.33) (-1.83) (-0.32) (-1.04) (-1.70) (-0.10) Lag fund return (0.64) (0.64) (1.30) (-0.39) (0.65) (1.31) (-0.39) Expense ratio (-0.67) (-0.14) (0.25) (-0.40) (-0.15) (0.23) (-0.40) Fund turnover (-1.02) (-0.99) (-1.50) (-0.03) (-1.06) (-1.54) (-0.08) Fund flow (-0.40) (-0.18) (1.25) (-1.25) (-0.23) (1.26) (-1.32) Log(fund age) (-0.56) (-0.10) (1.30) (-1.39) (-0.14) (1.29) (-1.44) Log(family TNA) *** *** *** *** *** (3.71) (3.49) (3.31) (1.36) (3.52) (3.34) (1.39) Constant (-0.50) (-0.48) (-0.28) (-0.35) (0.04) (-0.27) (-0.35) (0.04) Observations 27,859 26,455 25,460 10,303 15,157 25,460 10,303 15,157 Adj. R-squared Num groups

67 Panel C: Contemporaneous Open Price Cost Measure Implicit Trading Costs Total Trading Costs (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) VARIABLES All All All γ* < 0 Other Diff. All γ* < 0 Other Diff. Log(TNA) *** ** *** ** (0.03) (-1.48) (-1.60) (-2.86) (0.32) (-2.32) (-1.63) (-2.88) (0.30) (-2.33) Current trade cost ** * (-2.21) (-1.53) (-1.35) (-1.97) (-1.23) (-1.27) Lag fund return (0.64) (0.60) (1.39) (-0.50) (0.63) (1.41) (-0.49) Expense ratio (-0.67) (-0.66) (-0.41) (-0.44) (-0.67) (-0.44) (-0.43) Fund turnover (-1.02) (-0.62) (-1.58) (0.43) (-0.63) (-1.57) (0.42) Fund flow (-0.40) (-0.27) (1.18) (-1.23) (-0.30) (1.18) (-1.27) Log(fund age) (-0.56) (-0.37) (0.88) (-1.39) (-0.37) (0.88) (-1.39) Log(family TNA) *** *** *** *** *** (3.71) (3.46) (3.52) (1.64) (3.47) (3.51) (1.65) Constant (-0.50) (-0.48) (-0.32) (-0.37) (-0.05) (-0.29) (-0.35) (-0.03) Observations 27,859 26,455 26,453 10,808 15,645 26,453 10,808 15,645 Adj. R-squared Num groups

68 Table IA.VI Stock Size Premium, Fund Size, and Fund Performance: Gross and Net Returns We repeat the analyses in Table VI using gross fund return (in Panel A) and net fund return (in Panel B), rather than individual fund alpha. The table reports Fama-MacBeth (1973) estimation results of monthly fund returns regressed on fund TNA and other control variables. We first estimate cross-sectional regression each month and then report the time-series average of the monthly coefficients. We use the Thomson S12 sample from 1980m4 to 2012m6 in the analyses. We lag all independent variables by one month. We define other variables in Table I. We calculate Fama-MacBeth (1973) t-statistics with Newey-West correction for serial correlation of three lags. γ* < 0 (other) represents the subsample period consisting of months with (without) a significantly (at the five percent level) negative cross-sectional relation between a firm s market capitalization and its excess return based on all CRSP common stocks. We indicate statistical significance of one, five, and ten percent by ***, **, and * respectively. t- statistics are reported in parenthesis. Panel A: Gross Fund Return (1) (2) (3) (4) (5) VARIABLES All All γ* < 0 Other Diff. Log(TNA) *** *** *** *** (-3.87) (-3.61) (-5.06) (-1.52) (-3.16) Lag fund return *** *** *** (4.86) (2.78) (3.83) Expense ratio ** (0.13) (1.99) (-1.34) Fund turnover ** ** (2.07) (0.76) (2.06) Fund flow ** ** (2.00) (2.00) (1.01) Log(fund age) *** *** (0.70) (-2.77) (3.60) Log(family TNA) *** *** (3.28) (0.20) (4.08) Constant *** *** *** (4.76) (4.71) (1.18) (5.32) Observations 348, , , ,050 Adj. R-squared # of Months

69 Panel B: Net Fund Return (1) (2) (3) (4) (5) VARIABLES All All γ* < 0 Other Diff. Log(TNA) *** *** *** *** (-3.03) (-3.43) (-4.92) (-1.33) (-3.18) Lag fund return *** *** *** (4.86) (2.78) (3.83) Expense ratio * *** (-1.87) (0.50) (-3.01) Fund turnover ** ** (1.99) (0.71) (2.00) Fund flow ** ** (1.98) (1.99) (0.99) Log(fund age) *** *** (0.74) (-2.77) (3.66) Log(family TNA) *** *** (3.29) (0.22) (4.09) Constant *** *** *** (4.26) (4.57) (1.09) (5.19) Observations 348, , , ,050 Adj. R-squared # of Months

70 Table IA.VII Stock Size Premium, Fund Size, and Fund Performance: Controlling Fund Investment Objectives We repeat the analyses in Table VI using gross fund return (in Panel A), net fund return (in Panel B), and individual fund alpha (in Panel C), controlling for the investment objective of each fund (defined in Thomson S12). The table reports Fama-MacBeth (1973) estimation results of monthly fund performance regressed on fund TNA and other control variables. We first estimate cross-sectional regression each month and then report the time-series average of the monthly coefficients. We use the Thomson S12 sample from 1980m4 to 2012m6 in the analyses. We lag all independent variables by one month. We define other variables in Table I. We calculate Fama-MacBeth (1973) t- statistics with Newey-West correction for serial correlation of three lags. γ* < 0 (other) represents the subsample period consisting of months with (without) a significantly (at the five percent level) negative cross-sectional relation between a firm s market capitalization and its excess return based on all CRSP common stocks. We indicate statistical significance of one, five, and ten percent by ***, **, and * respectively. t-statistics are reported in parenthesis. Panel A: Gross Fund Return (1) (2) (3) (4) (5) VARIABLES All All γ* < 0 Other Diff. Log(TNA) *** *** *** *** (-3.37) (-3.43) (-4.80) (-1.43) (-3.05) Lag fund return *** ** *** (4.93) (2.56) (4.14) Expense ratio * (0.09) (1.88) (-1.30) Fund turnover ** *** (2.33) (0.38) (2.75) Fund flow ** *** (2.56) (2.63) (1.19) Log(fund age) *** *** (0.10) (-2.72) (2.75) Log(family TNA) *** *** (2.82) (-0.37) (3.94) Constant *** *** *** (4.46) (4.48) (1.38) (4.70) Inv. obj. dummies Yes Yes Yes Yes Observations 345, , , ,738 Adj. R-squared # of Months

71 Panel B: Net Fund Return (1) (2) (3) (4) (5) VARIABLES All All γ* < 0 Other Diff. Log(TNA) ** *** *** *** (-2.55) (-3.23) (-4.66) (-1.22) (-3.07) Lag fund return *** ** *** (4.93) (2.56) (4.14) Expense ratio ** *** (-2.24) (0.21) (-3.16) Fund turnover ** *** (2.25) (0.33) (2.68) Fund flow ** *** (2.54) (2.62) (1.17) Log(fund age) *** *** (0.15) (-2.72) (2.81) Log(family TNA) *** *** (2.83) (-0.36) (3.95) Constant *** *** *** (3.97) (4.34) (1.30) (4.59) Inv. obj. dummies Yes Yes Yes Yes Observations 345, , , ,738 Adj. R-squared # of Months Panel C: Four-Factor Alpha (1) (2) (3) (4) (5) VARIABLES All All γ* < 0 Other Diff. Log(TNA) ** *** *** *** (-2.53) (-3.23) (-4.12) (-1.36) (-3.09) Lag fund return ** ** (2.52) (2.25) (1.21) Expense ratio *** *** * (-3.34) (-2.96) (-1.96) Fund turnover (0.47) (-0.50) (0.98) Fund flow (1.03) (0.79) (0.78) Log(fund age) * ** (-0.15) (1.79) (-2.13) Log(family TNA) *** ** ** (2.77) (2.37) (2.20) Constant ** * (0.05) (2.22) (1.84) (1.39) Inv. obj. dummies Yes Yes Yes Yes Observations 336, , , ,738 Adj. R-squared # of Months

72 Table IA.VIII Subsample Analysis: Alternative Measure of Stock Size Effect We repeat the subsample analyses in Tables VI and Table VII using an alternative measure of stock size effect. In particular, we include other stock characteristics (i.e., the B/M ratio and momentum) when estimating the crosssectional relation between stock return and market capitalization. γ* < 0 represents the subsample period consisting of months with a significantly (at the five percent level) negative cross-sectional relation between a firm s market capitalization and its excess return based on all CRSP common stocks after controlling for other stock characteristics. In Panel A, we report the cross-sectional regression results corresponding to Table VI. In Panel B, we report the time-series regression results corresponding to Table VII. Statistical significance of one, five, and ten percent are indicated by ***, **, and * respectively. The sample is the Thomson S12 sample defined in Table I. Panel A. Cross-Sectional Regressions (1) (2) (3) (4) VARIABLES All months γ* < 0 Other Difference Log(TNA) *** *** ** ** (-3.28) (-3.71) (-2.00) (-2.38) Lag fund return ** * (2.00) (1.75) (1.03) Expense ratio *** *** * (-3.20) (-3.09) (-1.78) Fund turnover (0.56) (0.52) (0.31) Fund flow (1.33) (0.58) (1.32) Log(fund age) (-0.27) (1.32) (-1.52) Log(family TNA) *** * *** (3.11) (1.96) (2.88) Constant * * (1.95) (1.93) (1.12) Observations 308, , ,028 Adj. R-squared # of Months

73 Panel B. Time-Series Regressions Difference: 1-5 Model All months γ* < 0 Other Difference Alpha ** *** *** (2.09) (3.54) (-0.49) (3.08) MKTRF (-1.56) SMB *** (6.02) HML *** (6.67) UMD * (-1.84) Adj. R-squared # of Months