The Revealed Preferences of Mutual Fund Managers
*Jeffrey A. Busse† Tarun Chordia‡ Lei Jiang§ Yuehua Tang**
February 2019
Abstract
This paper discerns two preferences of mutual fund managers. First, managers of larger funds trade less frequently and hold bigger stocks to actively avoid higher trading costs. Using a novel dataset of actual mutual fund trades, we find that larger funds realize lower percentage transaction costs than smaller funds. Gross returns of larger funds are lower than those of smaller funds due to the characteristics of their holdings. Our results highlight the tradeoffs between trading costs, portfolio characteristics, and fund performance. Second, fund managers emphasize net shareholder returns over the four-factor alpha, consistent with investor preferences.
*We are grateful for comments from Viral Acharya, Vikas Agarwal, Gennaro Bernile, Lauren Cohen, Philip Dybvig, Slava Fos, Fangjian Fu, Gary Gorton, Bruce Grundy, Jennifer Huang, Raymond Kan,Luboš Pástor, Gordon Phillips, Joshua Pollet, Michael Powers, Jon Reuter, Ronnie Sadka, Clemens Sialm, Jun Tu, Kumar Venkataraman, Chishen Wei, Jerry Warner, Youchang Wu, Hong Yan, Xuemin Yan, Huacheng Zhang, Xiaoyan Zhang, Guofu Zhou, and seminar participants at the University of Rochester. We would like to thank Baozhong Yang for sharing the link table between the Abel Noser and Thomson Reuters Mutual Fund Holdings databases, Luke Taylor for CRSP and Morningstar merged mutual fund data, and Richard Evans for data on fund ticker creation date. 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: +1 404- 727-0160; Email: jbusse@emory.edu.
‡ Tarun Chordia, Goizueta Business School, Emory University, 1300 Clifton Road NE, Atlanta, GA 30322, USA; Tel: +1 404-727- 1620; Email: tarun.chordia@emory.edu.
§ Lei Jiang, School of Economics and Management, Tsinghua University, Beijing, 100084, China; Tel: +86 10-62797084; Email:
jianglei@sem.tsinghua.edu.cn.
** Yuehua Tang, Warrington College of Business, University of Florida, 1454 Union Road, Gainesville, FL 32611, USA; Tel. +1 352-392-9985; Email: yuehua.tang@warrington.ufl.edu.
The Revealed Preferences of Mutual Fund Managers
Abstract
This paper discerns two preferences of mutual fund managers. First, managers of larger funds trade less frequently and hold bigger stocks to actively avoid higher trading costs. Using a novel dataset of actual mutual fund trades, we find that larger funds realize lower percentage transaction costs than smaller funds. Gross returns of larger funds are lower than those of smaller funds due to the characteristics of their holdings. Our results highlight the tradeoffs between trading costs, portfolio characteristics, and fund performance. Second, fund managers emphasize net shareholder returns over the four-factor alpha, consistent with investor preferences.
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The performance of mutual funds has been the focus of countless empirical studies dating back to Jensen (1968). The majority of this literature examines cross-sectional relations between performance and a particular variable, such as momentum (Carhart (1997)), transaction costs (Wermers (2000)), total net assets (TNA) (Chen, Hong, Huang, and Kubik (2004)), industry concentration (Kacperczyk, Sialm, and Zheng (2005)), or the return gap (Kacperczyk, Sialm, and Zheng (2008)), among many others. What may not be evident from these results, however, are important interdependencies between the relations, since the choices fund managers make based on one key relation can directly impact the relation we observe between other variables.
As an example of how a fund manager’s choices affect the observed relation between other variables, consider how a fund’s growth in TNA affects its performance. Pollett and Wilson (2008) show that funds tend to scale up their position sizes in direct proportion to increases in TNA, such that as funds grow, they would be expected to increase the mean size of their holdings and the size of their trades over time. An increase in trade size would be expected to lead to higher transaction costs, since Keim and Madhavan (1997) (henceforth, KM) and Novy-Marx and Velikov (2016) show that the transaction costs associated with trading a given stock increases with trade size.
However, KM also show that transaction costs decrease in stock liquidity. Consequently, whether or not transaction costs increase with TNA depends on the extent to which funds increase the liquidity of their holdings to offset expected increases in transaction costs associated with larger trades. Moreover, the empirical asset pricing literature documents a positive relation between stock returns and illiquidity (e.g., Amihud and Mendelson (1986) and Brennan, Chordia, and Subrahmanyam (1998)), which suggests that an increase in the liquidity of a fund’s stock holdings reduces the portfolio’s expected return.1 Taken together, these relations suggest substantial endogeneity in the portfolio choices fund managers make, and no clear ex ante relation between fund TNA and transaction costs or between fund TNA and performance.
1 Another downside is that, as funds increase their stock holdings liquidity, there are fewer opportunities to explore pricing inefficiencies (i.e., mispricing) among small and illiquid stocks.
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In this paper, we study the interdependencies between transaction costs, portfolio characteristics, and mutual fund performance. To do so, we merge mutual fund data from CRSP, Morningstar, and Thomson Reuters with trade data for a sample of 583 actively-managed U.S.
equity mutual funds from Abel Noser Solutions, a leading execution quality measurement service provider for institutional investors. We use the trade data to estimate fund realized transaction costs, which we relate to a wealth of cross sectional data from the other databases, including fund performance, estimated from CRSP mutual fund returns; portfolio holdings characteristics, based on holdings data from the Thomson Reuters mutual fund database; and fund investment style from Morningstar. Examining the interdependences of trading costs and fund characteristics (e.g., fund size) provides insights into fund managers’ preferences regarding portfolio strategies and how they vary as a function of fund TNA.
Conditional on trading the same stock, large funds have higher trading costs than smaller funds because large funds transact larger dollar amounts and trading costs increase in trade size due to price impact. However, the choice of fund holdings is endogenous: fund managers account for expected transaction costs when choosing the composition of their portfolios. We find that large funds hold and trade larger, more liquid stocks, and smaller funds hold and trade smaller, less liquid stocks. As a result, larger funds realize lower trading costs as a percentage of TNA than smaller funds. Moreover, we find that funds with higher cash inflows in a given month shift their portfolio holdings towards larger stocks over the subsequent months.
Large funds also alter their portfolios less often than small funds. Controlling for fund style, when sorting funds into quintiles based on TNA, funds in the top quintile have an average annual turnover ratio of 67%, while funds in the bottom quintile have an average turnover ratio of 115%.
By choosing stocks with greater liquidity and trading less often, larger funds experience lower annual trading costs per dollar of TNA. Controlling for style, funds in the top TNA quintile experience an annual performance drag due to trading costs that is less than half the trading cost of funds in the bottom TNA quintile.
In addition, the average annual expense ratio is 0.79% for top quintile TNA funds and 1.49%
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for bottom quintile TNA funds (controlling for style), likely due to economies of scale in management fees, back office support, etc. Together, lower trading costs and lower expense ratios provide large funds with a substantial cost advantage that amounts to approximately 1.35% per year. Despite these cost advantages, large funds do not outperform small funds on a net shareholder return basis, because small funds hold smaller, less liquid stocks. Presumably, if large funds emphasized in their portfolios the types of stocks held by smaller funds, the trading costs would subsume any potential gains from the illiquidity premium or from pricing inefficiencies in the space of small and illiquid stocks.2 After controlling for risk, we find that large funds and small funds have statistically indistinguishable Carhart (1997) four-factor alphas. Thus, small funds generate enough alpha by holding relatively illiquid stocks and/or exploiting pricing inefficiencies, so as to overcome their cost disadvantages relative to large funds.
The evidence that larger funds experience lower realized trading costs than smaller funds
“contradicts” a commonly posited explanation for diseconomies of scale among mutual funds. For instance, Berk and Green (2004) hypothesize that, “...large trades will be associated with a larger price impact and higher execution costs.” We find that, compared to smaller funds, larger funds trade less frequently and endogenously choose stocks of greater liquidity, allowing their relatively large trades to execute without suffering unusually high price concessions. Decreasing returns to scale requires that investment opportunities are limited. Ourresults suggest that potential trading costs constrain the investment opportunities of large funds and dissuade larger funds from holding the small and illiquid stocks that, on average, have higher returns. Thus, decreasing returns to scale could arise due to limited investment opportunities because of trading cost constraints, rather than realized trading costs. Our evidence suggests that the rationale for diseconomies of scale, while consistent with the model of Berk and Green (2004), is more subtle: large funds face constrained investment opportunities due to potential trading costs.
2 Given that anomalies are found mainly in small stocks, it is important to be cognizant of trading costs when executing anomaly- based trading strategies. Novy-Marx and Velikov (2016) show that profits from anomaly-based trading strategies are limited due to trading costs.
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Our last set of tests analyzes the impact of trading costs on fund performance. We find that mutual fund trading costs are negatively related to four-factor alpha, but insignificantly related to fund net returns. Smaller funds, which are less constrained by their size, choose strategies (such as holding smaller, more illiquid stocks) that emphasize positive effects on net shareholder returns even if those strategies, given their loadings on the Fama and French (1993) size factor SMB, negatively impact four-factor alpha. Consequently, our results are consistent with managers emphasizing net shareholder returns rather than four-factor alpha. Such an emphasis coincides with investor preferences for performance measures that do not control for factor-related returns, as shown by Barber, Huang, and Odean (2016), who find that investors treat returns attributable to size, value, and momentum factors as alpha.
Our paper contributes to the mutual fund literature in several ways. First, as far as we know, our study is the first to document a negative relation between fund size and realized transactions costs. We uncover this relation using a novel transaction-by-transaction dataset, which has clear advantages over prior studies that use only semi-annual or quarterly holding changes to estimate mutual fund trading costs (e.g., Wermers (2000), Kacperczyk, Sialm, and Zheng (2008)).3 Our evidence suggests that realized trading costs do not explain the well-known diseconomies of scale effect in mutual fund performance. Second, our study offers new evidence on the interdependencies between (i) transaction costs, (ii) portfolio characteristics, and (iii) mutual fund performance. We document that mutual funds hold bigger, more liquid stocks and trade less frequently to actively avoid incurring higher trading costs as they grow in size. This result suggests that decreasing returns to scale arises due to limited investment opportunities because of trading cost constraints, rather than realized trading costs.4
3 A few other studies use an indirect method to estimate fund trading costs by comparing daily returns between a fund and a benchmark (e.g., Bollen and Busse (2006) and Cici, Dahm, and Kempf (2015)). In addition, Anand et al. (2012) also utilize the Abel Noser database to analyze the trading costs of institutional investors. Since they could not identify specific institutions, they analyze the relation between trading costs and trading performance of institutional trading desk, both estimated from the Abel Noser data. Our research question is very different from theirs. We study the interdependences of trading costs and fund characteristics obtained from standard mutual fund data sources (e.g., fund size and portfolio characteristics) as we have the identities of the mutual funds in our sample.
4Our empirical evidence is consistent with the model in a contemporaneous working paper by Pástor, Stambaugh, and Taylor (2018). Their model predicts that, in equilibrium, larger funds should trade less and hold more liquid securities.
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Lastly, we document new evidence of fund managers’ emphasizing net shareholder returns rather than four-factor alphas, which aligns with prior evidence on the revealed preference of fund investors (e.g., Berk and van Binsbergen (2016) and Barber, Huang, and Odean (2016)). These two pieces of evidence together suggest that fund managers maximize the specific performance measures that investors emphasize when deciding where to invest.
I. Data, Variables, and Sample Overview A. Data Description
We construct our sample from multiple data sources. Fund names, returns, total net assets, 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. To ensure data accuracy, we only retain in our sample funds in the CRSP and Morningstar merged database.5 We obtain fund investment styles based on the three by three style box from Morningstar Direct.
Portfolio holdings are obtained from Thomson Reuters Mutual Fund Holdings (formerly CDA/Spectrum S12), 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. domestic equity mutual funds and exclude index funds.7 We exclude funds with fewer than 10 stocks to focus on diversified funds. Following Elton, Gruber, and Blake (2001), Chen et al. (2004) and Yan (2008), we exclude funds with less than $15
5 We use the merged sample used by Pástor, Stambaugh, and Taylor (2015), who find that discrepancies exist between the Morningstar and CRSP mutual fund databases. To correct for these discrepancies, they create a CRSP and Morningstar merged mutual fund dataset. The Data Appendix of their paper provides detailed matching and cleaning procedures:
http://faculty.chicagobooth.edu/lubos.pastor/research/Data_Appendix_Aug_2013_V3.pdf.
6 Prior to May 2004, mutual funds were required by the Securities Exchange Commission (SEC) to report their portfolio holdings at a semi-annual frequency, though many funds voluntarily disclosed their holdings at a quarterly frequency to Thomson Reuters.
See Agarwal et al. (2015) for more details.
7 Note that funds in our final sample, on average, have 95% of their assets invested in common stocks. We follow Busse and Tong (2012) and Ferson and Lin (2014) and exclude 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, Exchange- Traded Fund, PowerShares, StreetTRACKS, 100, 400, 500, 600, 1000, 1500, 2000, 3000, 5000. We also remove funds with CRSP index fund flag “D” (pure index fund) or “E” (enhanced index fund).
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million in TNA. We also follow Evans (2010) and use the date the fund ticker was created to address incubation bias.8
We use mutual fund transactions data obtained from Abel Noser Solutions, a leading execution quality measurement service provider for institutional investors, to estimate fund transaction costs.9 Since Abel Noser analyzes fund transaction data, one concern is that the Abel Noser clientele is not representative of the broad universe of mutual funds typically analyzed in the literature. For instance, the clients of Abel Noser could be more cost conscience than the typical fund, such that their transaction costs are lower than average. Alternatively, funds with relatively high transaction costs or funds that trade more actively may be more likely to seek out the services of Abel Noser. To mitigate the effect that selection bias may have on transaction cost estimates based on the Abel Noser data, we focus on examining transaction cost differences between in- sample groups of funds (e.g., large funds vs. small funds) within the Abel Noser database. For instance, if Abel Noser data is comprised of funds with relatively low transaction costs, we mitigate this bias by examining the transaction cost differences between large and small in-sample funds.
Thus a cross-sectional relation between the transaction cost estimates and fund TNA is likely not impacted by the sample selection.10
Different from prior studies that use Abel Noser data, we are among the first to 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. Specifically, for each client manager X (as identified by “clientmgrcode”) in the Abel Noser dataset and for each reporting period between two adjacent portfolio report dates for a fund
8 We address incubation bias as follows. As in Evans (2010), we use the fund ticker creation date to identify funds that are incubated (i.e., when the difference between the earliest ticker creation date and the date of the first reported monthly return is greater than 12 months). If a fund is classified as incubated, we eliminate all data before the ticker creation date. The ticker creation date data cover all funds in existence at any point in time between January 1999 and January 2008. For a small set of funds that are not covered in the ticker creation date data (i.e., those that first appear after January 2008), we remove the first 3 years of return history as suggested by Evans (2010).
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, 2013), and Busse, Green, and Jegadeesh (2012), among many others.
10 Also note that the Abel Noser dataset has been used to study inference associated with the transaction costs of institutional investors (e.g., Anand et al. (2012)).
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M in the Thomson S12 data, we compute the change in holdings (i.e., across all trades with shares adjusted for splits and distributions) for client manager X in each stock during the reporting period.
We also compute split-adjusted changes in holdings by fund M for that reporting period. We then compare the change in holdings for fund 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 client manager name list (with the names for all
“clientmgrcode”) disclosed by Abel Noser in 2011.11
Our initial matched Abel Noser sample covers 1,079 unique funds in the merged Thomson S12–CRSP Mutual Fund database. Out of these funds, 583 are actively-managed U.S. equity funds based on the criteria specified above. Our final sample consists of trade-by-trade data for these 583 funds from January 1999 to September 2011. 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 2011. Consequently, we cannot match Abel Noser data to Thomson S12 data at the fund level after September 2011. The final sample has a monthly average of 198 funds over the sample period from January 1999 to September 2011. Although our sample is limited to funds in Abel Noser, it represents the only transaction-level dataset that can be used to provide inference based on actual mutual fund transactions.
B. Variable Description
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
11 It is important to note that our holdings and name matching procedures are performed at the fund level as identified by
“clientmgrcode” in the Abel Noser data, rather than at the institution/fund family level as identified by “managercode”. Multiple Abel Noser “clientmgrcode” may match to the same S12 fund for different periods. See the Appendix of Agarwal, Tang, and Yang (2012) for more details on the matching procedure: https://www.dropbox.com/s/ev9f8lxce9k8gjp/ATY_2012_Appendix.pdf?dl=0.
Also see the Appendix in Puckett and Yan (2011) for more details about the different identifiers in the Abel Noser data.
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months and the factor returns during that month.12 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.
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, book-to- market ratio, past six-month cumulative return, and the Amihud (2002) measure of illiquidity. We restrict our sample to stocks with CRSP share codes 10 or 11 (i.e., common stocks).13 We calculate monthly fund-level market capitalization, book-to-market ratio, momentum, and the Amihud illiquidity measure by weighting each firm-level stock characteristic according to its dollar weight in the most recent fund portfolio. We obtain monthly measures by assuming constant fund holdings between portfolio holding snapshots, which are typically available at a quarterly frequency.
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 market capitalization. We obtain book value from COMPUSTAT supplemented by book values from Ken French’s website.14 We winsorize the book-to-market ratio at the 0.5 and 99.5 percentile levels to eliminate outliers, although our results are not sensitive to this winsorization. Momentum is the six-month cumulative stock return over
12 Using the past 24 and 60 months for beta estimation yields similar results. Results for the five-factor alpha (i.e., adding a liquidity factor to the Carhart (1997) four-factor model) are also similar.
13 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.
14 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.
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the period from month t – 7 to t – 2. 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.15 Following Acharya and Pedersen (2005), we normalize the Amihud ratio and truncate it at 30 to eliminate the effect of outliers as follows:
𝐿𝑖,𝑡 = 1
𝐷𝑖,𝑡∑ |𝑟𝑖,𝑑,𝑡| 𝐷𝑉𝑂𝐿𝑖,𝑑,𝑡
𝐷𝑖,𝑡
𝑑=1
× 1,000,000 (1)
𝐴𝑚𝑖ℎ𝑢𝑑𝑖,𝑡 = 𝑚𝑖𝑛(0.25 + 0.3𝐿𝑖,𝑡× 𝑃𝑡−1𝑀 , 30), (2) where 𝑟𝑖,𝑑,𝑡 is the return on stock i on day d in month t, 𝐷𝑉𝑂𝐿𝑖,𝑑,𝑡 is the dollar trading volume, 𝐷𝑖,𝑡 represents the number of days in month t that stock i trades, and 𝑃𝑡−1𝑀 is the ratio of the capitalizations of the market portfolio at the end of month t – 1 and at the end of July 1962.
C. Sample Overview
Table I reports summary statistics of fund performance, fund characteristics, and portfolio holding characteristics for all sample funds grouped by TNA quintile controlling for investment style. We use Morningstar’s three by three style box, based on tercile groupings along market capitalization and growth/value dimensions, to group the fund sample into nine investment styles.
Then, each month, for each investment style, we divide funds into quintiles based on lag fund TNA, with the TNA quintile breakpoints determined by the funds associated with that investment style.
Lastly, we aggregate each quintile across the nine investment styles, such that the quintile statistics represent mean fund statistics controlling for investment style. We first compute the cross- sectional average each month across all of the funds in each quintile group and then take the time- series mean of the cross-sectional averages. We also report the simple time-series mean of the cross-sectional averages for all funds in the sample in the column labeled “All”.
[Insert Table I here]
15 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 Amihud illiquidity measure.
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Panel A of Table I shows no significant performance difference across funds sorted on the basis of TNA. The smallest fund quintile outperforms the largest fund quintile by an insignificant 0.07% in net shareholder return, but underperforms by an insignificant –0.03% when performance is measured by four-factor alpha. This evidence is consistent with Elton, Gruber, and Blake (2012), who also find no performance difference across fund size deciles after controlling for fund style.
Smaller funds have significantly higher mean expense ratios and significantly higher portfolio turnover than larger funds, where bottom (top) quintile funds show a mean expense and turnover ratio of 1.49% (0.79%) and 115% (67.1%), respectively. Given the cost advantages associated with both lower expense ratios and lower turnover (as turnover generates transaction costs), the finding of no statistically significant performance difference between small and large funds indicates that smaller funds offset these disadvantages elsewhere, possibly by realizing lower transaction costs per dollar traded, as hypothesized in the literature. We will shortly examine transaction cost differences between large and small funds.
Lastly, Table I reports the characteristics of fund portfolio holdings. The table shows that smaller funds hold smaller, less liquid stocks. For example, controlling for investment style, the mean market capitalization of the portfolio holdings of funds in the bottom TNA quintile is significantly less than the mean market capitalization of the portfolio holdings of funds in the top TNA quintile. Similarly, smaller funds have significantly higher mean estimates of the Amihud illiquidity measure. As liquidity impacts transaction costs, the statistics indicate fund managers combat the prospect of higher transaction costs as TNA and, by extension, trade size increases by transitioning toward stocks of greater liquidity.
In addition to holding less liquid stocks, smaller funds also hold stocks with higher book- to-market ratios (i.e., value stocks), with the bottom TNA quintile funds showing significantly higher book-to-market ratios than the top TNA quintile funds. Since it has been well documented that smaller, less liquid, and higher book-to-market stocks are characterized by greater average returns, it is apparent that, compared to larger funds, smaller funds focus on stocks that produce greater return premia, on average, and are arguably associated with higher investment
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opportunities due to lower price efficiency.16 The emphasis that small funds place on these types of stocks provides return premia that offsets the cost disadvantages stemming from the higher expense ratios and greater portfolio turnover noted above.
As a point of comparison between the Abel Noser-based mutual fund sample and a representative generic research sample during our 1999–2011 sample period, Panel B of Table I reports performance and fund characteristic statistics associated with the CRSP/Morningstar merged database, i.e., without narrowing the sample to funds that have trade data available from Abel Noser. The quintiles in Panel B are formed using the same procedure used in Panel A, where we control for investment style by first forming quintiles based on style and then aggregating the quintiles across styles. When we compare our Abel Noser sample to the CRSP/Morningstar merged sample along the dimensions of fund size, fund performance, and fund characteristics, we find that the Abel Noser sample is skewed toward larger TNA funds. For instance, the largest quintile of funds in the Abel Noser sample in Panel A shows mean TNA more than double that of the largest quintile of funds in the CRSP/Morningstar sample in Panel B. As a result, compared to the CRSP/Morningstar sample, the top TNA quintile funds in the Abel Noser sample have lower expense ratios. Similar to the Abel Noser sample, stocks held by the bottom TNA quintile funds in the CRSP/Morningstar sample show significantly greater Amihud illiquidity than stocks held by the top TNA quintile funds. Although we find significantly higher net shareholder returns for the smallest TNA quintile of funds compared to the largest TNA quintile of funds in the CRSP/Morningstar sample, there is no statistically significant difference in four-factor alpha across TNA quintiles, similar to the Abel Noser sample. Thus, both the Abel Noser sample and a more comprehensive CRSP/Morningstar sample provide no significant evidence of diseconomies of scale after controlling for style during the 1999–2011 time period, which, as noted above, is consistent with Elton, Gruber, and Blake (2012).
16 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).
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Owing to differences in the Abel Noser sample compared to a more comprehensive CRSP mutual fund sample, we base our inference on relations that should largely mitigate issues related to sample selection. For instance, regardless of the sample, we would expect a negative cross- sectional relation to exist between the expense ratio and net shareholder performance. As another example, although the transaction costs of funds in the Abel Noser sample may be biased relative to a more comprehensive sample, it seems unlikely that the bias would reverse the sign of the cross sectional correlation between transaction costs and fund TNA.
II. Empirical Analysis A. Trading Costs
A.1. Trading Cost Measure
We use Abel Noser transaction-level data to construct trading cost measures based on the difference between the trade execution price and a benchmark price:
𝑇𝑟𝑎𝑑𝑒 𝐶𝑜𝑠𝑡 = 𝐷 ∗𝑃𝑟𝑖𝑐𝑒 − 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑃𝑟𝑖𝑐𝑒
𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑃𝑟𝑖𝑐𝑒 , (3) where 𝑃𝑟𝑖𝑐𝑒 is the execution price of a trade, and 𝐷 denotes the trade direction, taking a value of 1 for a buy and –1 for a sell. Similar to KM, Anand et al. (2012), and Frazzini, Israel, and Moskowitz (2015), we use pre-ticket prices for 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑃𝑟𝑖𝑐𝑒, including (i) the price at the time the fund places the order ticket (i.e., execution shortfall, Anand et al. (2012)), (ii) the opening price on the day the first share in the order ticket trades (Anand et al. (2013) and Frazzini, Israel, and Moskowitz (2015)), and (iii) the closing price the day before the first share in the order ticket trades (KM and Frazzini, Israel, and Moskowitz (2015)). The transaction cost estimates capture implicit trading costs, including price impact and costs related to the bid-ask spread.
Abel Noser groups individual trades into trade tickets. Fund managers transmit orders to the trading desk in the form of tickets, which often encompass a number of individual trades.
Following KM and Anand et al. (2012), we evaluate costs on the basis of tickets rather than individual trades. As in Anand et al. (2012), we follow Abel Noser specifications to group trades
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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 as stated by Abel Noser. Computing costs at the ticket level, rather than at the individual trade level, directly impacts the price benchmark associated with a trade because all of the trades within a ticket utilize the same price benchmark. We compute ticket-level data as the value weighted average of the trade-level data using trading volume as the weight on each trade.
In our sample, each ticket includes an average of 1.26 trades.
Equation (3) captures the transaction cost associated with an individual ticket, and we refer to this as the ticket-level transaction cost. For a given fund month, we compute the value-weighted average ticket-level trading cost based on the dollar value of each ticket traded by the fund during the month. To obtain fund-level transaction costs for a given fund-month, we multiply the ticket- level cost measures in equation (3) by the dollar value of each ticket and then sum over all of the fund’s tickets in the month. We then divide by the average TNA of the previous and current month- ends. 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 by twelve to get an annual measure. The Abel Noser data provides two explicit trading cost measures, commission and tax plus fee, which we aggregate, as above, at the ticket or fund level. We obtain total trading costs by adding the corresponding commission and tax plus fee to the ticket- or fund-level trading cost measures.
By using actual mutual fund transaction data to estimate how mutual fund trading costs vary depending on cross-sectional fund and trade data, we differ from the standard approach in the mutual fund literature (e.g., Wermers (2000)and Kacperczyk, Sialm, and Zheng (2008)), where fund trading costs are estimated based on semi-annual or quarterly fund holding changes and KM’s analysis of the trades of 21 institutions from 1991–1993. We examine both implicit costs (i.e., price impact), based on equation (3), and total costs. Total costs represent the sum of implicit costs and explicit costs including commissions, taxes, and fees. Rather than focusing on the point estimates, we examine how trading costs vary in the cross-section.
14 A.2. How Do Transaction Costs Vary with Fund Size?
Given that larger funds are expected to have larger-size trades, and implicit trading costs positively correlate with trade size (as in KM), we might expect a positive relation to exist between fund-level transaction costs and fund TNA. This expectation is offset, however, by larger funds turning over their portfolios less frequently than smaller funds and larger funds holding more liquid stocks than smaller funds, as shown in Table I. Panel A of Table II reports fund-level annualized percentage transaction costs to show how transaction costs vary with fund size, controlling for investment style. The table indicates a strong negative relation between fund size and both implicit and total transaction costs. Based on execution shortfall, funds in the bottom TNA quintile show 0.41% (0.65%) significantly greater implicit (total) transaction costs than funds in the top TNA quintile. Results based on the open price cost and prior-day close cost are similar: bottom TNA quintile funds show an open price implicit (total) cost that is 0.51% (0.75%) greater than top TNA quintile funds, and bottom TNA quintile funds show a prior-day close implicit (total) cost that is 0.64% (0.89%) greater than top TNA quintile funds. Thus, large funds realize lower annual transaction costs than smaller funds. Beyond their statistical significance, the transaction cost difference between bottom TNA quintile funds and top TNA quintile funds are economically significant as well. The bottom TNA quintile fund transaction costs are often more than twice as large as the transaction costs of the top TNA quintile funds. Moreover, in untabulated results, we find that high TNA funds show lower transaction costs than low TNA funds even after controlling for family size in addition to fund style. This result suggests that our findings are not attributable to larger funds being affiliated with larger fund families with more skilled trading desks.
[Insert Table II here]
The negative relation between fund-level transaction costs and fund TNA could be driven by the negative relation between fund turnover and TNA. We can remove the impact associated with fund turnover by examining costs at the individual ticket level, expressed as a percentage of the dollar value of the trade. Panel B of Table II reports these ticket-level percentage costs, which are the ticket-dollar weighted averages of the ticket-level transaction cost estimates computed
15
using equation (3). Even after removing the effect associated with the lower turnover of larger funds, these ticket-level trading costs decrease with the size of the fund. Panel B of Table II shows that, controlling for investment style, all three implicit cost estimates decrease by approximately 10–20 basis points from funds in the smallest quintile to funds in the largest quintile. The decrease in total costs, which includes commissions, taxes, and fees, is larger, ranging from 12–22 basis points. The large difference in turnover between small TNA funds and large TNA funds combined with the small disadvantage in ticket-level trading costs for small TNA funds relative to large TNA funds results in the greater disadvantage in annualized fund-level transaction costs for smaller funds as shown in Panel A of Table II. That is, smaller funds incur the percentage costs reported in Panel B of Table II more often across time than larger funds because of their higher turnover.
A.3. Determinants of Ticket-Level Transaction Costs
To better understand what drives the negative cross-sectional relation between fund-level transaction costs and fund TNA, we first examine the cross sectional relation between transaction costs and trade characteristics at the ticket level. Our analysis relates to KM and Anand et al.
(2012), but with two important advantages. First, compared to KM, the Abel Noser sample of mutual fund transactions comprises a larger sample of institutions over a longer, more recent time period, the bulk of which is post-decimalization and thereby more representative of the current market microstructure. Second, by merging the Abel Noser trade data to the CRSP mutual fund database, our sample includes fund-level characteristics associated with the trade. Specific institutions are not identified in Anand et al.’s (2012) sample. Consequently, in addition to using trade characteristics, such as trade size, as independent variables, we also include fund characteristics, such as fund turnover. The fund-level variables become especially meaningful when we later examine the cross-sectional relation between fund-level transaction costs and fund characteristics.
We estimate monthly cross-sectional regressions of ticket-level transaction costs on trade and fund-level variables as follows,
16 𝑇𝑟𝑎𝑑𝑒𝐶𝑜𝑠𝑡𝑖,𝑗,𝑘,𝑡 = 𝛼+𝛽1𝑇𝑖𝑐𝑘𝑒𝑡𝑆𝑖𝑧𝑒𝑖,𝑘,𝑡+ 𝛽2 1
𝑃𝑘+𝛽3𝐿𝑜𝑔𝑀𝑘𝑡𝐶𝑎𝑝𝑘,𝑡−1+𝛽4𝑁𝑎𝑠𝑑𝑎𝑞𝑘,𝑡+ 𝛽5𝐼𝑉𝑂𝐿𝑘,𝑡−1+ 𝛽6𝑠𝑖𝑑𝑒𝑖,𝑡∗ 𝑚𝑎𝑟𝑘𝑒𝑡𝑡+ 𝜆Ζ𝑗,𝑡−1+ 𝜁𝑖,𝑗,𝑘,𝑡, (4) where 𝑇𝑟𝑎𝑑𝑒𝐶𝑜𝑠𝑡𝑖,𝑗,𝑘,𝑡 is the ticket-level implicit or total cost per trade dollar for ticket i, stock k, and fund j at time t, 𝑇𝑖𝑐𝑘𝑒𝑡𝑆𝑖𝑧𝑒𝑖,𝑘,𝑡 is the trading volume of ticket i normalized by the average daily trading volume in the same stock in the previous calendar month,17 𝑃𝑘 is stock k’s closing price the day prior to the ticket’s first trade, 𝐿𝑜𝑔𝑀𝑘𝑡𝐶𝑎𝑝𝑘,𝑡−1 is the logarithm of stock k’s market capitalization (in millions of dollars) at the end of the month prior to the ticket’s first trade, 𝑁𝑎𝑠𝑑𝑎𝑞𝑘,𝑡 is a dummy variable that equals 1 if stock k is a Nasdaq listed stock, 𝐼𝑉𝑂𝐿𝑘,𝑡−1 is the idiosyncratic volatility calculated as the standard deviation of the residuals from a regression of daily returns on the CRSP value-weighted market return in a 12-month period ending with the last month end, 𝑠𝑖𝑑𝑒𝑖,𝑡 equals 1 if ticket i is a buy and –1 if it is a sell, 𝑚𝑎𝑟𝑘𝑒𝑡𝑡 is the CRSP value- weighted market return on the ticket’s execution date, and Ζ𝑗,𝑡−1 is a set of fund-level control variables at the end of the month prior to the ticket’s first trade, including investment style, expense ratio, turnover, net flow, Log(fund age), Log(TNA), Log(family TNA), and fund net return.
Table III reports the time series average of the monthly coefficient estimates as in Fama- MacBeth (1973) based on execution shortfall. The results for the other cost estimates, open price and prior-day close cost, are similar, and we include them in Table IA.I in the Internet Appendix.18 We analyze implicit and total transaction costs for buy transactions, sell transactions, and all (i.e., both buy and sell) transactions. Given that transaction costs persist, we adjust the Fama-MacBeth (1973) standard errors using the Newey-West (1987) correction.
[Insert Table III here]
17 Our ticket size variable in equation (4) differs slightly from the one used in KM. They calculate ticket size as shares traded divided by stock shares outstanding. We obtain similar results with their version of ticket size.
18 In the rest of the paper, unless otherwise noted, we present only the results for execution shortfall. Results associated with the open price and prior-day close costs are similar to those reported for execution shortfall.
17
Overall, we find a strong positive relation between ticket-level transaction costs and trade size, and a strong negative relation between ticket-level transaction costs and variables that capture the liquidity of the stock traded, consistent with KM. We also find that execution shortfall is strongly positively related to the stock market return. The strong relation between trade cost and ticket size is apparent for both buys and sells and for both implicit and total trade costs. The negative relation between trade cost and stock price is possibly a result of the higher proportional bid-ask spread among low price stocks, and, more generally, it is related to a strong positive relation between stock price and liquidity. This negative relation is especially evident in the total cost results in columns (4)–(6). 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. The positive coefficient on 𝐼𝑉𝑂𝐿 for sell transactions suggests that selling costs are higher for stocks with greater information uncertainty. Nasdaq stocks seem to have higher implicit trading costs but lower commissions and fees. Note also the strong significance of the side*market variable, which serves to remove the market’s effect on the cost estimate. Movements in the market impact the difference between a transacted price and its pre-ticket benchmark.19,20 For example, other things equal, a buy will transact at a higher (lower) price if the market moved up (down) between the pre-trade benchmark time and the time of execution.
To assess economic significance, we focus on column (4) for the total cost of all trades. A one standard deviation increase in ticket size increases total trading cost by about 6.3 basis points.
For stock characteristics, a one standard deviation increase in the price inverse (market capitalization) of the stock increases (decreases) total costs by 14.9 (2.6) basis points.
19Excluding the side*market variable does not change inference associated with the other regressors (see results in Table IA.II of the Internet Appendix)
20See Chiyachantana, Jain, Jiang, and Wood (2004).
18 A.4. Trade Characteristics of Funds with Different TNA
Given the cross-sectional regression results in Table III, we next examine differences in trade characteristics between different size funds to help understand why larger funds (presumably with larger trade sizes) exhibit lower ticket-level percentage trading costs, as indicated in Panel B of Table II. The main findings in Table III indicate that trade size and stock liquidity significantly impact the transaction cost of the trade. Table IV presents trade size data and characteristics of the stocks traded by funds as a function of fund TNA. In particular, in panel A, we sort funds into TNA quintiles, as before, controlling for fund style, and then report trade characteristics associated with each fund TNA quintile.
[Insert Table IV here]
Panel A1 of Table IV shows that the average ticket size of funds in the largest quintile ($2.0 million and 58,200 shares) is more than twice the average ticket size of funds in the smallest quintile ($888,000 and 28,100 shares). Although tickets are broken up into smaller size trades, the difference in the number of trades per ticket across the quintiles is small relative to the range of ticket sizes, such that the average trade size for large funds greatly exceeds the average trade size for small funds.
Consistent with the earlier Table I evidence regarding the characteristics of stocks that mutual funds hold in their portfolios, Panel A2 of Table IV suggests that larger funds realize lower ticket-level percentage trading costs than smaller funds because large funds trade larger, more liquid stocks. The average market capitalization of stocks traded by a quintile 5 fund ($34.4 billion) is significantly greater than the average market capitalization of stocks traded by a quintile 1 fund ($29.4 billion), as large funds proactively select stocks to avoid incurring prohibitively high transaction costs. Thus, the overall picture that we see thus far is that the small trades of small funds generate relatively low transaction costs. Consequently, smaller funds hold and trade less liquid stocks, as the less liquid stocks provide enough liquidity to accommodate smaller trades, while at the same time offering greater expected return compared to stocks of greater liquidity. By contrast, larger funds require larger-size trades that are susceptible to relatively large transaction
19
costs. To combat relatively high transaction costs, larger funds hold and trade relatively liquid stocks with relatively lower expected return.
To control for the endogeneity between realized trading costs and fund size, Panel B1 of Table IV compares trading costs across fund quintiles conditional on small funds and big funds trading the same stock in a given month. Specifically, we analyze trade tickets where the same stock is traded by at least one fund in both quintile 1 and quintile 5 in a given month, which is 63.7% (i.e., 5,852,590 trade tickets) of the full sample.21 For each stock-month combination, we compute the ticket value-weighted trading cost of each fund quintile. Then, we average across all stocks each month and finally compute the time-series average across all sample months.
Similar to the pattern within the broader sample in Panel A of Table IV, large funds trade considerably larger tickets and also larger trades within tickets compared to small funds after conditioning on trading the same stock. In Panel B2 of Table IV, large funds average $1.7 million and 51,000 shares per ticket, while small funds average $124,000 and 4,300 shares per ticket. The large difference in ticket size leads to a big difference in trading cost estimates between small and large funds when trading the same stock. Conditional on the stock traded, top TNA quintile funds realize a value-weighted execution shortfall, open price cost, and price-day close cost of 0.17%, 0.25%, and 0.31%, respectively, which is significantly higher than the 0.12%, 0.18%, and 0.20%
costs for bottom quintile funds. The difference between the top and bottom quintiles in all three implicit cost estimates is approximately 5–11 basis points, and all differences are statistically significant. The transaction cost disadvantage for large funds when conditioning on the stock traded and the preference for trading larger, more liquid stocks as in Panel A1 of Table IV suggest that fund managers account for expected trading costs when deciding which stocks to include in their portfolios.
In sum, large funds incur higher ticket-level trading costs when conditioning on the underlying stock that is traded. However, across all of the stocks that they trade, large funds realize
21 We obtain qualitatively similar results if we compare trading costs across TNA quintiles conditional on funds in all five quintiles (i.e., at least one fund) trading the same stock in a given month.
20
lower fund-level trading costs than small funds because they turn over their portfolios less frequently, and they trade stocks with low price impact, i.e., the larger and more liquid stocks.
A.5. Determinants of Fund-Level Transaction Costs
Having examined the determinants of ticket-level trading costs, we now examine cross sectional determinants of fund-level transaction costs. Fund-level transaction costs comprise an aggregation of the ticket-level transaction costs associated with all the trades a fund makes over time, and represent the total transaction cost drag on performance reflected in net shareholder returns. This analysis augments the univariate fund-level transaction cost analysis in Table II.
We examine the relation between fund-level transaction costs and several fund-level attributes in monthly Fama-MacBeth (1973) cross-sectional regressions similar to equation (4), but after excluding the ticket- and stock-level variables. We again follow Newey-West (1987) to adjust the Fama-MacBeth (1973) standard errors. Table V reports the results using execution shortfall; Table IA.III in the Internet Appendix shows results based on open price cost and prior- day close cost.
[Insert Table V here]
Table V shows a very strong negative relation between implicit or total fund-level trading costs and log(TNA) regardless of whether we include other fund-level controls. The clear message is that, compared to smaller funds, larger funds have lower total transaction costs as a percentage of fund TNA. The finding that larger funds realize significantly lower total percentage transaction costs is consistent with our earlier evidence in Panel A of Table II.22 The table also reports a significant positive relation between fund-level transaction costs and fund turnover. The dependent variable represents the aggregate of all fund transaction costs across all fund trades within the month, expressed as a percentage of fund TNA. Other things equal, higher turnover generates higher total percentage trading costs, consistent with the positive coefficient in Table V.
22 It could be argued that there is a mechanical relation between log(TNA) and fund-level percentage trading cost. However, TNA also impacts the numerator of fund-level percentage trading costs because it is related to the type of stocks traded and to fund turnover. Note that Panel B of Table IV suggests that if large funds traded the same stocks as smaller funds and had the same turnover, then the fund-level percentage trading costs would be higher for larger funds.
21
There is a significant negative relation between fund-level trading costs and family TNA, possibly because large families hire more skilled traders or negotiate lower commissions. The negative relation between fund-level trading costs and expense ratio could relate to soft dollar arrangements between funds and brokers. In these arrangements, brokers charge funds relatively high commissions, but then rebate a portion of the commission to the fund, which then uses the rebate to pay other non-commission related expenses. The practice can lead to relatively high percentage commission fees that are offset within the fund by a relatively lower expense ratio, as the commission rebate subsidizes fund expenses. The other fund specific characteristics, including flow, age, and lag fund return, show no consistent significant relation to fund-level transaction costs. Fund-level trading costs are highly persistent, as evidenced by the large, significant, positive coefficients on the lagged trading cost. Note also that the average R2 in the panels is substantially higher when lagged trading cost is included as a regressor.
B. Fund Flows and the Change in Holding Stock Size
Although the analysis thus far has examined cross-sectional relations between fund TNA, transaction costs, and the liquidity of fund holdings, the results have strong implications for how funds respond to investor flows across time. In particular, as a fund grows its asset base across time, we should see a transition in its portfolio from stocks of lower liquidity and higher return premium to stocks of higher liquidity and lower return premium, as funds actively manage their transaction costs. We analyze these dynamics in this section by examining the impact of fund flows on the types of stocks that funds hold in their portfolios. Our analysis relates to Pollet and Wilson (2008), who examine how funds increase the number of unique stock positions in their portfolio as they grow. We analyze how funds manage transaction costs via the liquidity of the stocks that they trade and hold. Our hypothesis is that as funds grow, they tilt their portfolios towards larger stocks in order to manage their trading costs.
Since we do not need transactions cost data in this analysis, we utilize the Thomson S12 dataset, which begins about two decades before the Abel Noser data. Panel A of Table VI reports
22
summary statistics for the Thomson S12 database after controlling for the investment style as before. The Thomson S12 sample averages 926 funds each month, with an average of about 185 funds in each fund size quintile over the sample period from April 1980 to June 2012. The Thomson S12 sample is considerably larger than the Abel Noser sample, mainly because Abel Noser has a limited number of clients. Consistent with our earlier comparison to standard data samples in this literature, the Thomson S12 sample includes smaller funds than the Abel Noser sample. 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 $71 million and $13.0 billion, respectively. Similar to the Abel Noser sample, the Thomson S12 sample shows that, on average, smaller funds hold smaller, less liquid stocks and have a higher expense ratio than larger funds.
[Insert Table VI here]
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 (controlling for fund investment style) and also independently based on the firm size of their previous quarter’s holdings using NYSE breakpoints. Panel B of Table VI 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 6.44% (9.85%) of their assets in the smallest (second smallest) quintile of stocks, while the corresponding proportions for large funds are 2.16% (4.58%). Furthermore, small (large) funds invest 52.90% (67.77%) 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.
It could be argued that, due to their size, larger funds are likely to hold portfolios that mimic market weights. In the last column of Panel B of Table VI, we list the market capitalization weight of the different quintile portfolios of the overall market based on NYSE breakpoints. The market capitalization weight of stocks in the largest quintile amounts to 71.9%, which is considerably
23
larger than the weight in these stocks of the smallest funds. In fact, it is also larger than that of the largest funds, suggesting that the largest funds also hold a lower proportion of the largest stocks to take advantage of higher returns and possible mispricing in smaller stocks. Further, larger funds also hold a lower proportion of the smallest stocks than the market capitalization weight of the smallest stocks, possibly to avoid the higher transaction costs associated with these stocks for large-size trades.
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 affect the characteristics of fund holdings. 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 tests whether an increase in fund size due to capital inflows leads to an increase in the market capitalization of the stocks in the fund portfolio.
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,
∆𝑆𝑡𝑜𝑐𝑘𝑆𝑖𝑧𝑒𝑖,𝑡−1,𝑡 = ∑(𝜔̂𝑖,𝑗,𝑡− 𝜔𝑖,𝑗,𝑡−1)
𝑁
𝑗=1
𝑀𝑘𝑡𝐶𝑎𝑝𝑗,𝑡−1,
𝜔𝑖,𝑗,𝑡−1 = 𝑆𝑖,𝑗,𝑡−1𝑃𝑗,𝑡−1
∑𝑁𝑘=1𝑆𝑖,𝑘,𝑡−1𝑃𝑘,𝑡−1, 𝜔̂𝑖,𝑗,𝑡 = 𝑆𝑖,𝑗,𝑡𝑃𝑗,𝑡−1
∑𝑁𝑘=1𝑆𝑖,𝑘,𝑡𝑃𝑘,𝑡−1, (5) where 𝑀𝑘𝑡𝐶𝑎𝑝𝑗,𝑡−1 is the natural logarithm of market capitalization (in millions of dollars) of stock j as of time t – 1; N is the number of stocks held by fund i; and 𝑆𝑖,𝑗,𝑡−1 and 𝑆𝑖,𝑗,𝑡 are the number of shares of stock j held by fund i at time t – 1 and t, respectively; 𝑃𝑗,𝑡−1 is the price of stock j at time t – 1; 𝜔𝑖,𝑗,𝑡−1 is the weight of stock j in fund i’s portfolio as of time t – 1; 𝜔̂𝑖,𝑗,𝑡 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.
24
∆𝑆𝑡𝑜𝑐𝑘𝑆𝑖𝑧𝑒𝑖,𝑡−1,𝑡 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 3-, 6-, 12-, or 24-month window (i.e., the period from time t – 1 to time t spans 3, 6, 12, or 24 months), rolling this window by one quarter at a time.
We examine the relation between fund flows and the subsequent change in the average market capitalization of the portfolio holdings using the following cross sectional regressions,
∆𝑆𝑡𝑜𝑐𝑘𝑆𝑖𝑧𝑒𝑖,𝑡,𝑡+𝑘 = 𝛼 + 𝛽1 𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡 + 𝜆Χ𝑖,𝑡 + 𝜖𝑖,𝑡,𝑡+𝑘, (6)
∆𝑆𝑡𝑜𝑐𝑘𝑆𝑖𝑧𝑒𝑖,𝑡,𝑡+𝑘 = 𝛼 + 𝛽1 𝑃𝑜𝑠𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡∗ 𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡
+𝛽2 𝑁𝑒𝑔𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡∗ 𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡+ 𝜆Χ𝑖,𝑡 + 𝜖𝑖,𝑡,𝑡+𝑘, (7) where ∆𝑆𝑡𝑜𝑐𝑘𝑆𝑖𝑧𝑒𝑖,𝑡,𝑡+𝑘, as defined in equation (5), represents the change in fund i’s mean logged stock holding market capitalization from quarter end t to quarter end t + k, (k = 1, 2, 4, or 8), 𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡 represents fund i’s cumulative monthly dollar flow from quarter end t – 1 to quarter end t divided by fund TNA at t – 1, 𝑃𝑜𝑠𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡 is a dummy variable equal to 1 when 𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡 > 0, 𝑁𝑒𝑔𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡 is a dummy variable equal to 1 when 𝐹𝑙𝑜𝑤𝑖,𝑡−1,𝑡< 0, and 𝛸𝑖,𝑡 represents a set of fund-level control variables at quarter end t, including fund return, expense ratio, turnover, Log(fund age), Log(family TNA), and fund style fixed effects. Again, we calculate Fama-MacBeth (1973) t-statistics with Newey-West corrected standard errors.
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 size changes and changes in the market capitalization of holdings that 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 (6) and (7) and also by using 𝑃𝑗,𝑡−1 with 𝜔̂𝑖,𝑗,𝑡 in equation (6) to focus only on active adjustments to the portfolios.
25
Panel C of Table VI presents the results. We reject the null of no relation between fund flows and the change in holdings. Fund flows positively correlate with subsequent changes in the mean portfolio holding market capitalization. The positive coefficient on inflows indicates that inflows lead to an increase in the mean portfolio holding market capitalization for up to two years.
The converse is true for outflows, i.e., outflows lead to a decrease in portfolio holding market capitalization. Our flow results provide evidence that the relation between fund stock holding characteristics and TNA is not solely attributable to fund style, since a positive relation exists between the liquidity of a fund’s stock holdings and its TNA in the time series. It also indicates that in order to manage their trading costs when facing high cash inflows, funds tend to buy larger stocks.
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 changes in holding stock size over longer horizons. The results are similar for the 6-, 12-, and 24-month time horizons, with the magnitude of the fund flow coefficients being larger compared to the one for the 3-month horizon. In economic terms, based on our estimates in columns (5) and (7), a one standard deviation increase in cumulative fund flow leads to an increase in the size of holdings by 2.2% (4.1%) over the next 12 (24) months. We also find that fund flows persist (the average autocorrelation is about 0.52), suggesting that fund managers can deploy initial investments quickly into smaller stocks, because, on average, they can expect to meet any possible future redemptions with additional inflows. Since it is unlikely that it takes 6, 12, or 24 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 an increase in size due to inflows.
C. Trading Costs, Fund Holdings Liquidity, and Fund Performance
The main effects that we document—an inverse relation between TNA and transaction costs or holdings illiquidity—directly impact fund net shareholder returns. The mutual fund literature examines performance from numerous perspectives, including, for example, raw
