Mutual Fund Performance in the Era of High-Frequency Trading

Transcription

1 Mutual Fund Performance in the Era of High-Frequency Trading Nan Qin 1 First draft: March 15, 2016 This version: August 27, 2016 Abstract This paper shows that intensity of high-frequency trading (HFT) in stocks held by mutual funds is negatively related to fund performance. This negative relation can largely be explained by the illiquidity premium: HFT-intensive stocks provide lower returns because the majority of these stocks are relatively liquid. Further analysis shows that this relation is not a self-selection bias, but indicates a causality: intensive HFT is a key reason for the existence of significant illiquidity premium, because high-frequency traders are very sensitive to illiquidity due to their very short investment horizon. However, there is no evidence to support the widespread concern that HFT raises trading costs of mutual funds. JEL classification: G12, G14, G23 Keywords: high-frequency trading, mutual fund performance, illiquidity premium, trading costs 1 Qin (nan.qin@cnu.edu; ) is from the Luter School of Business, Christopher Newport University, 106 Luter Hall, 1 Avenue of the Arts, Newport News, VA I thank Frank Hatheway from NASDAQ for providing the HFT data. NASDAQ makes the data freely available to academics providing a project description and signing a non-disclosure agreement. I thank Vijay Singal, Jonathan Brogaard, Ryan Riordan, and Gjergji Cici for comments and suggestions. All errors are my own. 1

2 Mutual Fund Performance in the Era of High-Frequency Trading Abstract This paper shows that intensity of high-frequency trading (HFT) in stocks held by mutual funds is negatively related to fund performance. This negative relation can largely be explained by the illiquidity premium: HFT-intensive stocks provide lower returns because the majority of these stocks are relatively liquid. Further analysis shows that this relation is not a self-selection bias, but indicates a causality: intensive HFT is a key reason for the existence of significant illiquidity premium, because high-frequency traders are very sensitive to illiquidity due to their very short investment horizon. However, there is no evidence to support the widespread concern that HFT raises trading costs of mutual funds. 1. Introduction High-frequency trading (HFT), typically defined as very large number of order submission, cancellation, and trades transacted by powerful computers at extremely high speed, has experienced rapid growth over the past two decades. It is commonly believed to account for more than 50% of the total trading volume of the U.S. stock markets. Practitioners and academic researchers generally believe that HFT provides liquidity, narrows bid-ask spreads, reduces liquidity risk, and improves market efficiency (Hendershott, Jones, and Menkveld, 2011; Hendershott and Riordan, 2013; Boehmer, Fong, and Wu, 2014; Conrad, Wahal, and Xiang, 2015; etc.). They argue that most market participants could benefit from the reduced trading costs and improved market efficiency. For example, Bill McNabb, CEO of the Vanguard Group, suggests that HFT has reduced trading costs for institutional investors. 2 However, not everyone is a proponent of HFT. There has been a widespread concern about HFT s potentially negative impact on the performance of traditional institutional investors, and some institutions have taken actions to protect themselves. Fidelity Investments and several other buy-side firms, for example, have been using alternative trading systems to execute block trades 2 Vanguard chief defends high-frequency trading firms. Financial Times. Apr. 25,

3 anonymously, so that they may reduce information leakage and forestall potentially predatory behaviors from high-frequency traders (HFTs). 3 THOR, an electronic trading platform developed by Royal Bank of Canada, is used by many institutional investors to dodge HFTs. Luminex, an alternative trading venue created in 2014 by Fidelity Investments and BlackRock Inc., specifically excludes HFTs to ensure relatively low costs for block trading from large institutional investors. 4 Investment firms concern about HFT is understandable. Although HFT could narrow bidask spreads and thus lower the explicit trading costs of other market participants, it may still raise the total trading costs of traditional institutional investors through higher price impact costs. Institutions which trade large blocks of shares usually split their orders across time. In this case, bid-ask spread does not fully reflect the trading cost because price impact costs usually play a more important role. If HFTs are able to predict order flows from large institutional investors and trade accordingly (in the so-called anticipatory trading), price impact costs of these institutional investors will be significantly higher and their performance will be negatively affected. Moreover, another possible channel through which HFT may negatively affect traditional institutional investors has long been ignored: HFT may increase illiquidity premium the cost of liquidity thus traditional institutional investors who have strong demand to liquid assets will be negatively affected. Amihud and Mendelson (1986), Chalmers and Kadlec (1998), among several other studies, document that investors require higher returns for holding illiquid assets compared to liquid assets, and this return premium of illiquidity is raised not only by the cost per trade, but also by traders trading frequencies. Compared to their low-frequency counterparts, traders with higher trading frequencies will accumulate larger amount of trading costs during each unit time. Therefore, they are more sensitive to trading costs, have stronger demand to liquid assets, and require higher returns from illiquid assets as compensation for trading costs. The implication in the context of HFT is that HFTs will prefer to trade liquid assets, and the presence of intensive HFT will amplify the magnitude of illiquidity premium by lowering the risk-adjusted returns of liquid assets and increasing those of illiquid assets. As the result, the majority of HFT-intensive stocks should be relatively liquid and deliver negative risk-adjusted returns, thus mutual funds holding such stocks will show significant underperformance. More importantly, for HFTs, the 3 "Fidelity explores new trading venue amid flash trade concerns". Reuters. Apr. 10, No high-frequency traders allowed at Luminex. The Wall Street Journal. Oct. 29,

4 lowered return of liquid assets is a reasonable compromise for substantial saving from low trading costs. However, for most traditional institutional investors who trade much less frequently, the gains from low trading costs of liquid assets can hardly offset the loss in the returns. Therefore, intensive HFT may cause the underperformance of traditional institutional investors who hold large amounts of liquid assets. So far the academia has not reached a consensus about HFT s impact on institutional investors. Tong (2013) studies HFT on 120 randomly-selected NASDAQ stocks (the so-called NASDAQ dataset ) and finds that HFT increases trading costs of traditional institutional investors. Hirschey (2013) finds that HFTs aggressive purchases and sales lead those of other investors and this can be best explained by the existence of an anticipatory trading channel through which HFTs may increase non-high-frequency traders (nhfts) trading costs. Malinova, Park, and Riordan (2013) investigate a change in regulatory fees in Canada and find that bid-ask spreads increased for institutional investors after a decline of HFT. Brogaard, Hendershott, Hunt, and Ysusi (2014) look at the technology upgrades that lower the latency of the London Stock Exchange and find that, following upgrades, the level of HFT increases but institutional traders costs remain unchanged. Therefore, they conclude that there is no clear evidence to support the criticism that HFT increases institutional execution costs. Overall, the existing literature gives mixed findings about the impact of HFT on the trading costs of traditional institutional investors, and none of them consider the possibility that HFT may affect the performance of traditional institutional investors through its impact on cross-sectional stock returns. The lack of consensus on this topic can be attributed to the limited availability of HFT data. The findings of Brogaard et al. (2014) and Malinova et al. (2013), for example, are based on U.K. and Canada data, respectively, while Hirschey (2013) and Tong (2013) focus only on 120 NASDAQ stocks in one or two years. My paper contributes to the literature by being the first to provide comprehensive evidence regarding HFT s impact on performance of institutional investors on the U.S. financial markets, the largest and the most mature financial markets in the world. Why is this topic so important? First, institutional investors, including all kinds of mutual funds, ETFs, pension funds, etc., are managing over $18 trillion collected from more than 90 4

5 million U.S. retail investors. 5 As their performance is closely related to the wealth of households and individuals, a negative impact of HFT on their performance, if exists, may imply a welfare loss of a large number of individuals and households. Second, institutional investors are significant contributors to market efficiency (Boehmer and Kelley, 2009). They typically conduct fundamental analysis and incorporate information into stock prices through trading. If they lose frequently when trading with HFTs and become hesitated in price discovery, market efficiency would be compromised. This paper provides empirical evidence of HFT s impact on the performance of institutional investors, based on a comprehensive sample of 2,688 U.S. actively-managed equity mutual funds during Specifically, I merge fund returns obtained from the CRSP U.S. Mutual Fund database with quarterly fund holdings reported by the S12 database of the Thomson Reuters. HFT intensity in each stock held or traded by the funds is proxied by quote updates proposed by Conrad et al. (2015). This setting establishes, for the first time, a direct link between monthly returns and HFT intensity in trade portfolios or holdings of the majority of U.S. equity mutual funds. The HFT proxy, quote updates, is defined as the number of any changes in the best bid or offer quote or size across all quote reporting venues in the U.S. The use of this proxy is justified by the fact that HFTs issue a lot more messages than nhfts. Compared to the measures used in other studies, quote updates has two major advantages. First, it captures one of essential features of HFT very large numbers of order submissions and cancellations. Second, it can be estimated by the NYSE TAQ database, which is publicly available for most U.S. stocks since Moreover, a comparison between quote updates and the NASDAQ dataset confirms its effectiveness quote updates indeed has very high correlations with actual HFT and significantly lower correlations with actual non-high-frequency-trading (nhft). 6 To control for the positive relation which arises naturally between firm size and quote updates, I extract the component of quote updates that is orthogonal to size and use it as the measure of HFT in this paper. I begin the empirical analysis by investigating the relation between HFT intensity in fund holdings (HFT H ) or trade portfolios (HFT T ) and their risk-adjusted returns. Specifically, for each 5 As of year-end of 2014; Investment Company Institute Factbook, Table A.1 in the Appendix. 5

6 month, I sort all funds into quintiles based on HFT H or HFT T during the previous calendar quarter. The equally-weighted or value-weighted return spread between the top and the bottom quintiles is then regressed on the Fama-French and Carhart four factors. A negative and significantly relation between HFT and fund performance is found: the top quintile underperforms the bottom quintile by 0.31% (0.28%) per month when funds are sorted by HFT H (HFT T ). A multivariate analysis in which monthly risk-adjusted fund returns are regressed on HFT intensity and fund characteristics confirms the above negative relation. Then, I examine possible explanations of this negative relation. First, two holding-based tests reject the hypothesis that HFT raises the trading costs of mutual funds. This negative relation between HFT intensity and fund performance exists even if the return of fund holdings, which is not affected by trading costs, is used to replace the NAV-based fund return in the quintile portfolio analysis. Moreover, cross-sectional regressions show that the fund return gap, the difference between fund return and return of holdings, is not affected by HFT intensity neither. This suggests that HFT is negatively related to fund performance through its impact on cross-sectional stocks returns, rather than through raised institutional trading costs. Next, I test the validity of the liquid-based explanation. Specifically, I add an illiquidity premium factor based on quoted spread to the Fama-French and Carhart four-factor model and redo the quintile portfolio analysis. The negative relation between HFT intensity and fund performance is narrowed by roughly a half once the illiquidity premium is controlled for, and is no longer statistically significant. This finding is consistent with the hypothesis that illiquidity premium amplified by HFT and HFTs preference toward liquid assets explain the negative relation between HFT intensity and fund performance. More importantly, I show that the illiquidity premium is significantly positive in stocks with intensive HFT, but is small and not statistically significant in the rest of the stocks. The implication is that the negative relation between HFT intensity and fund performance is not simply a manifestation of self-selection bias, but is a consequence of HFT without intensive HFT, there is no significant illiquidity premium in the first place. Finally, I investigate an alternative explanation. Several studies find that HFT increases volatility (Zhang 2010; Breckenfelder, 2013; Boehmer et al., 2014). Based on the finding of Ang, Hodrick, Xing, and Zhang (2006) that high idiosyncratic volatility (IVOL) is followed by low 6

7 stock return, it is possible that HFT affects fund performance through its impact on volatility. Adding a factor which captures the IVOL anomaly to the Fama-French and Carhart four-factor model, I find that the IVOL anomaly explains a limited fraction of the negative relation between HFT intensity and fund performance, though it does not substitute the effect of illiquidity premium. The findings of this paper ease the concern that HFT raises the trading costs of institutional investors, but reveal other challenges faced by managers of traditional investment companies. For the first time in the literature, this paper finds that intensive HFT may be detrimental to the performance of traditional institutional investors because it makes liquidity unnecessarily expensive to these investors. In addition, HFT could negatively affect performance of traditional institutional investors because it increases stock volatility, which is known to be related to low returns in future. In light of these findings, money managers should be cautious when buying or holding stocks experiencing intensive HFT. Finally, from a unique angle, this paper provides supporting evidence to the theoretical prediction of Amihud and Mendelson (1986) and Chalmers and Kadlec (1998) that, in addition to cost per trade, trading frequency is an important determinant of illiquidity premium. The rest of this paper is organized as follows. Section 2 describes the data sources, sample selection, proxies for HFT, and fund performance evaluation methods. Section 3 presents the relation between HFT and fund performance. Section 4 explores potential underlying mechanisms. Section 5 concludes. 2. Data and Methodology In this section, I first describe and summarize the sample of U.S. equity mutual funds and U.S. common stocks. Then, I discuss how the intensity of HFT is measured for an individual stock and for a mutual fund. Next, I introduce the factor models used to measure the risk-adjusted returns of mutual funds. 2.1 Sample of U.S. Equity Mutual Funds 7

8 The monthly sample of U.S. equity mutual funds is obtained from the Center for Research in Security Prices (CRSP) survivor-bias free US mutual fund database. The database contains information of net-of-expense returns, expense ratios, total net assets (TNA) and various other characteristics of both live and defunct funds. The main tests of this paper are based on a 13-year sample period from January 2003 to December 2015 during which time HFT was relatively intensive 7. Certain robustness tests are based on a sample period from January 1993 to December 2002 during which time HFT is generally thought to be less intensive or non-existing. Quarterly stock holdings of mutual funds are obtained from the S12 database of the Thomson Reuters. U.S. equity mutual funds are identified by their CRSP objective codes. 8 Fund records with TNA less than $10 million or age less than three years are removed to mitigate data biases, such as incubation bias (Evans, 2010), associated with small or young funds. I also exclude funds with less than 90% common stocks in their non-cash holdings because of their potentially different risk exposures 9. I aggregate all share classes (e.g., retail and institutional share classes) to the fund level and match fund returns and characteristics to their quarterly holdings. 10 Passively-managed funds, including both index funds and ETFs, are removed from the sample due to their passive nature. 11 The final sample includes 2,688 actively-managed domestic equity mutual funds. Panel A of Table 1 summarizes fund characteristics. The average (median) TNA is $1,645 ($316) million, suggesting that fund size is skewed by large funds. The average (median) fund age is (13.17) years. Expense ratio, as the ratio of a fund s operating expenses over total investment, averages at 1.23% per year. Fund turnover is measured by the minimum of aggregated sales or aggregated purchases of securities during a year divided by the fund s average TNA in the previous 12 months. The average turnover ratio is 82.44% per year for the overall sample. Monthly raw return, estimated as monthly net return plus 1/12 of annual expense ratio, averages 0.81%. Panel B of the table reports average characteristics of active fund in each year. Total number of 7 The New York Stock Exchange implemented automatic quote dissemination in 2003 to replace manual quote dissemination. The transition started in January and finished in May. As a result, high-frequency trading in U.S stocks increased significantly quote updates increased 150% compared to that in 2002, the highest annual growth rate during To be included into the sample, the CRSP objective code (CRSP_OBJ_CD) of a fund need to start with ED, which represents domestic equity funds. 9 The use of 80% or 70% as threshold does not significantly affect the results of this paper. 10 Combination of shares classes and matching of fund characteristics and holdings are based on the MFLink files obtained from the WRDS. 11 Passive funds are identified by the CRSP index fund indicator and ETF indicator. 8

9 funds in the sample increases from 1,301 in 2003 to 1,655 in 2011, and the declines to 1,305 in The average TNA of each fund increases from $862 million to about $2.7 billion over the sample period. Average expense ratio shows steady decline while average fund age shows steady growth. At the end of 2014, total size of this fund sample is around $3.50 trillion, representing 77% of the total market capitalization of all U.S. actively-managed domestic equity mutual funds 12. [Table 1] 2.2 Sample of U.S. Common Stocks The main stock sample includes 7,695 U.S. common stocks that are listed on the NYSE, AMEX and NASDAQ from January 2003 to December Monthly stock returns and characteristics are taken from the CRSP. Data on book value of equity are taken from Compustat. Intraday quote and trade data required in the estimation of HFT proxy and transaction costs are taken from NYSE TAQ. Number of analysts following and dispersion of analyst forecasts are obtained from the summary history file of the I/B/E/S. T-bill rates and risk factors, including the three Fama-French (1993) factors, the momentum factor of Carhart (1997), and the liquidity risk factor of Pastor-Stambaugh (2003), are obtained from WRDS at the University of Pennsylvania. Panel A of Table 2 reports the summary statistics of monthly stock characteristics based on a total of 610,532 stock-month observations. [Table 2] 2.3 Measures of HFT in Individual Stocks Quote updates as a proxy of HFT Following Conrad et al. (2015), I use quote updates, defined as number of any change in the best bid or offer quote or size across all quote reporting venues, as the proxy for HFT intensity in a stock over certain time interval. For each stock in each day over the sample period, quote updates are estimated based on the NYSE standard monthly TAQ data which is time-stamped to 12 Based on 2015 Investment Company Fact Book published by Investment Company Institute, the total size of all U.S. actively-managed domestic equity mutual funds at the end of 2014 is $4,559 billion. 9

10 the second. 13 Daily quote updates of a stock are then aggregated on a monthly or quarterly basis to measure the HFT intensity on this stock over that month or quarter. [Figure 1] Panel B of Table 2 illustrate monthly quote updates over the sample period. The average number of quote updates is 641 thousands per month, but the maximum is above 65 million. Consistent with Conrad et al. (2015), there is very noticeable difference in quote updates between small stocks and large stocks. The average quote updates of the smallest 20% stocks (measured by their market value at the end of the previous June) is 34 thousands per month, while that of the largest 20% stocks is 2.19 million. Moreover, Figure 1 illustrates that HFT grew rapidly through , but the rapid growth disappeared over the last four years of the sample period. This pattern is similar to the finding of Baron, Brogaard, and Kirilenko (2014) based on transactionlevel data and trader-identifiers Correlation between quote updates and actual HFT To validate the use of quote updates as an appropriate proxy for HFT, Table A.1 in the Appendix reports the Spearman and Pearson correlations between monthly quote updates and actual HFT activities on 120 randomly selected NASDAQ stocks in 2008 and Quote updates are highly correlated with actual HFT reported by NASDAQ, while the correlations between quote updates and nhft are much lower. In Panel A, when actual HFT intensity is measured as fraction of HFT volume in the total trading volume of a stock, the average Spearman (Pearson) correlation between quote updates and actual HFT intensity is 87.73% (67.45%), while that between quote updates and nhft intensity is % (-67.45%). In Panel B, when actual HFT intensity is measured as the ratio of HFT share volume to total shares outstanding, the average Spearman (Pearson) correlation between quote updates and actual HFT intensity is 67.27% (37.61%)), while that between quote updates and nhft intensity is 1.14% (-13.60%). The generally lower 13 The estimation of best bid and ask price is based on quotes reported by a total of 16 exchanges and trading venues (TAQ exchange code A, B, C, D, I, J, K, M, N, P, Q, T, W, X, Y and Z). To be included in the estimation process, a quote must have mode of 1, 2, 3, 6, 10 or 12. Any quote that has bid price larger than or equal to ask price, bid price less than or equal to $0.01, negative ask price, or non-positive bid or ask size will be removed. Quotes beyond regular trading hours are also removed. 10

11 magnitudes of Pearson correlations compared to Spearman correlations indicates non-linearity in the relation between quote updates and actual trading activities. In sum, quote updates is an effective proxy for HFT due to its high correlation with actual HFT and low correlations with actual nhft. Furthermore, a comparison between Panel A and B indicates that quote updates is closer to a relative measure of HFT, as its correlations with the fraction of HFT volume in total volume is much higher than its correlation with the share turnover ratio induced by HFT (87.74% versus 67.27% for Spearman correlation; 67.45% versus 37.61% for Pearson correlation). This difference is more pronounced in the largest 20% stocks (61.48% versus 12.42% for Spearman correlation; 59.10% versus 8.61% for Pearson correlation), on which HFT is generally more intensive. Therefore, in this paper I consider quote updates as a proxy for relative, rather than absolute, intensity of HFT Determinants of quote updates Examining the determinants of quote updates not only provides useful insights on the behavior and preference of HFTs, but may also preclude concerns on certain self-selection biases in the main tests. I examine the relation between quote updates and stock characteristics based on the following Fama-MacBeth (1973) cross-sectional regression:,,,, 1 where, is the natural log of quote updates of stock i in month t, and X is a vector of control variables including market value (MV) and book-to-market ratio (BM) estimated by the same approach of Fama and French (1992), stock return over the prior month (RET), share price at the beginning of the month (PRC), turnover ratio of the prior month (TO), time-weighted relative quoted spread (RQS) of the prior month, price impact cost of the prior month (PIC) estimated by the approach of Breen, Hodrick, and Korajczyk (2002), the Pastor and Stambaugh (2003) liquidity beta (LIQBeta), institutional ownership (IO), volatility of the prior month (VOL) estimated as the standard deviation of daily returns, number of analysts following (ANLY), analyst forecast dispersion (DISP) estimated as standard deviation of one-year earnings forecasts divided by the mean estimate, and the lagged dependent variable (DV). Most explanatory variables are lagged to 11

12 ensure that they are not predetermined. As reported by Table 3, quote updates increases by firm size, prior month return, turnover ratio, institutional ownership, and analyst following, and decreases by share price, direct trading cost (spread), price impact cost, and liquidity beta. This is consistent with the common understanding that HFTs prefer to trade large and liquid stocks, stocks with more institutional investors, low price stocks, and stocks with more available information. [Table 3] Controlling for size effect Large firms are naturally related to more intensive quoting activities due to their larger investor base, thus using quote updates directly to identify HFT-intensive stocks will lead to a bias towards large stocks. For example, without controlling for stock size, a comparison between stocks with more quote updates and those with fewer quote updates will largely be a comparison between large stocks and small stocks. To solve this problem, I follow a similar strategy of Karpoff and Lou (2010) to estimate a HFT intensity measure that is orthogonal to firm size. Specifically, for each month (quarter), I sort all stocks in the sample into deciles based on their market value at the end of the previous June, and then conduct the following monthly cross-sectional regression:,,,,, where, is the natural log of quote updates of stock i at month (quarter) t, and,, is a dummy variable that equals to 1 if firm i is within size decile k in month (quarter) t and 0 otherwise. Quote updates is log transformed because its relation with firm size is not linear. The regression residual,,, is denote as the HFT intensity measure for stock i in month (quarter) t,,. This approach largely controls the size effect on quoting activities so that HFT intensity of stocks with different size becomes comparable. In addition, monthly percentile ranking of quote updates within each size decile is used as an alternative HFT for robustness tests Results are not reported due to limited space, and are available upon request. The use of this alternative measure gives qualitatively and quantitatively similar results for most tests of this paper. 12

13 2.4 Average HFT Intensity of Fund Holdings and Trade Portfolios I focus on two channels through which HFT may put an impact on mutual fund performance. First, if HFT affects mutual fund performance through its impact on institutional trading costs, intensity of HFT in stocks of a fund s trade portfolio should be related to subsequent fund performance. Therefore, I estimate the weighted-average HFT intensity of a fund s trade portfolio (HFT T ) in a quarter as follows:,,,,,, 3 where, is the HFT intensity proxy for stock k in quarter t,, is number of stocks traded by fund i in quarter t,,, is the weight of stock k s dollar trading volume in the trade portfolio of fund i in quarter t:,,,,,. 4,,, Higher HFT T means the fund is facing more intensive HFT in stocks it has traded during quarter t. Since the S12 database contains only positions held, it is impossible to precisely estimate trading volumes of each stock in each quarter. Instead, trading volume of a stock and the total trading volume of a fund are estimated as the lower bonds of the actual values. Second, if HFT affects mutual fund performance through its potential impact on crosssectional stock returns, average intensity of HFT in a fund s current holdings should be more closely related to subsequent fund performance. I estimate the weighted-average HFT intensity of a fund s holdings (HFT H ) in a quarter as follows:,,,,,, 5 where,, is the weight of stock k in fund i at the end of quarter t, and, is the number of holdings of fund i in quarter t. In addition, to distinguish any potential difference between the impact of HFT on fund purchases and that on fund sales, I estimate weighted-average HFT intensity of a fund s purchases (HFT P ) and sales (HFT S ) in a quarter as follows: 13

14 , and,,,,, 6,,,,,, 7 where, and, are number of stocks purchased or sold by fund i in quarter t,,, is the weight of stock k s dollar trading volume in all purchases of fund i in quarter t: and,,,,,,,, 0,, 0,,,,,, is the weight of stock k s dollar trading volume in all sales of fund i in quarter t:,,,,,, 0,, 0.,,,,, Factor Models and Fund Performance Evaluation Fama-French and Carhart four-factor model In Section 3 when I investigate the impact of HFT on mutual fund performance, I mainly use Fama-French and Carhart four-factor model to measure the risk-adjusted returns of active mutual funds:,,,,,,,, 10 where,,,,,, and are the market excess return, risk-free return, smallminus-big factor, high-minus-low factor, and momentum factor in month t FF-Carhart four-factor model plus illiquidity premium factor and liquidity risk factor Amihud and Mendelson (1986), Amihud (2002) and Amihud, Hameed, Kang, and Zhang (2015), among many other studies, suggest that stocks with low liquidity level are associated with higher expected return. Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) argue that stocks with high liquidity risk (volatility in liquidity level) are associated with higher expected 14

15 return. To capture the potential impact of liquidity level and liquidity risk on stock and mutual fund performance, I add an illiquidity premium factor (IML, illiquid-minus-liquid), the Pastor and Stambaugh (2003) liquidity risk factor (PS), or both to the FF-Carhart four-factor model:,,,,,,,,. 11,,,,,,,. 12,,,,,,,,,. 13 I use relative quoted spread (RQS) as an inverse measure of liquidity, and follow a similar approach as in Amihud et al. (2015) to construct the IML factor 15. Specifically, at the beginning of each month t, stocks are sorted into terciles based on the volatilities of their daily returns in month t-3 to t-1 to control for the known volatility effect on cross-sectional stock returns. Within each volatility terciles, stocks are further sorted into deciles based on average RQS in month t-3 to t-1. Value-weighted returns are then estimated for each of these 30 (3 10) portfolios in month t+1, t+2 and t+3, while returns in month t are skipped to avoid potential short-term return reversals. The zero-investment illiquidity premium factor, IML, is constructed as differential returns between the three least liquid portfolios (across volatility terciles) and the three most liquid portfolios (across volatility terciles). During the sample period, the IML factor is significantly positive at 0.61% per month (t-value 3.23). The PS factor, on the other hand, is directly obtained from the website of Lubos Pastor Ferson-Schadt conditional model Ferson and Schadt (1996) argue that, due to confounding variation in mutual fund risks and risk premia, traditional factor models might be unreliable. Instead, they propose a performance evaluation model conditioned on public information variables. Following Kacperczyk et al. (2005), 15 Volume-weighted relative effective spread (RES) is also used to construct the IML factor in robustness tests. The use of RES gives qualitatively and quantitatively similar results in all the relevant tests. Results are not reported due to limited space, but are available upon request. 15

16 I use the following specification which includes interaction terms between several macroeconomic variables and market excess returns:,,,,,,,,,,,,,,,,,,,,, 14 where, is the demeaned value of 3-month T-bill rate, is the demeaned value of yield spread between the high-yield bond index and the investment-grade bond index, is the demeaned value of dividend yield of the S&P 500 index, is the demeaned value of yield spread between 1-year T-bills and 10-year T-notes. Treasury yields are obtained from the U.S. Department of the Treasury; dividend yield of the S&P 500 index is obtained from the WRDS; yields of the high-yield bond index and investment-grade bond index are obtained from Bank of America Merrill Lynch. The intercept of the model,, is the conditional risk-adjust performance of a mutual fund. 3. High-Frequency Trading and the Performance of Active Funds In this section, I investigate the relation between HFT and fund performance. I construct long-short portfolio by sorting funds based on HFT intensity in their trade portfolios or their holdings, and estimate its risk-adjust returns. Various factor models and specifications are used for robustness tests. Multivariate analysis is also conducted to provide additional evidence. 3.1 Quintile Portfolios At the beginning of each month, all funds in the sample are sorted into quintiles by the average HFT intensity in either their trade portfolios (HFT T ) or their holdings (HFT H ) during the previous calendar quarter. For example, HFT T and HFT H in the second quarter of 2013 are used to sort funds in July, August and September of The top quintile is considered to be more affected by HFT, and vice versa. Equally-weighted returns are then calculated for each quintile portfolio based on gross (pre-expense) or net (post-expense) fund returns, and portfolios are 16

17 rebalanced monthly. 16 The risk-adjusted returns are estimated by time-series regressions based on the Fama-French and Carhart four-factor model. Panel A of Table 4 reports the performance of quintile portfolios constructed by HFT T. The four-factor alphas decrease by HFT intensity for all the four specifications. For example, when gross returns and unconditional model are used, funds in the top quintile significantly underperform funds in the bottom quintile by a monthly alpha of 0.27% (t-value 2.26), or roughly 3.24% annually. The underperformance is of the same magnitude (0.27%, t-value 2.26) when conditional model is used. The use of gross-return or net return makes no noticeable difference. In Panel B, when quintile portfolios are constructed by HFT H, the pattern in the risk-adjusted returns are qualitatively similar but quantitatively stronger. For example, when gross returns and unconditional model are used, funds in the top quintile underperform funds in the bottom quintile by a monthly alpha of 0.31% (t-value 2.58), or roughly 3.72% per year. [Table 4] Panel C shows the 5 1 return spreads when quintile portfolios are constructed by the average HFT intensity on fund purchases (HFT P ) or sales (HFT S ) over the previous calendar quarter. Funds associated with more intensive HFT, again, underperform funds associated with less intensive HFT, and the magnitudes of this underperformance are similar in sorting by HFT P and sorting by HFT S. Finally, Panel D and E reports that the underperformance of funds associated with more intensive HFT is robust to various factor models and value weighting, and becomes stronger when the financial crisis period (01/ /2009) is removed, but does not exist over , during which period HFT is generally believed to be not intensive or non-existing. In addition, the results are robust to removing stocks below $5 (results are not reported). In sum, intensive HFT is related to significantly lower risk-adjusted returns of actively-managed mutual funds, and this negative relation is robust to different factor models, weighting methods, sorting methods, or the use of conditional models. 3.2 Evidence from Multivariate Analysis 16 The use of equal weighting is to prevent a few very large funds from dominating the test results. Value weighting is used in robustness tests and generates qualitatively and quantitatively similar results. 17

18 In addition to analysis based on quintile portfolios, the relation between HFT and fund performance are examined by performing Fama-MacBeth (1973) cross-sectional regressions of fund return or risk-adjusted return (alpha) on lagged HFT intensity:,,,,, 15 where, is the return or alpha of fund i in month t,, is the HFT intensity in trade portfolio (HFT T ) or holdings (HFT H ) of a fund, and X is a vector of control variables including fund size (TNA), turnover ratio (TO), age (Age), annual expense ratio (ExpRatio), average institutional ownership of fund holdings (IO), and lagged dependent variable (DV). Specifically, monthly alpha is estimated as the difference between fund excess return in that month and the return predicted by factor models, which is the product of fund factor loadings and the realizations of the factors in that month. Factor loadings are estimated based on time-series regression using gross returns in the previous 36 months. TO is defined as total dollar value of net purchases and sales by a fund in a quarter, estimated from holdings reported by the S12 database. All independent variables, except for Age and ExpRatio, are based on the previous calendar quarter to ensure they are not predetermined. [Table 5] Column [1]-[4] of Table 5 report the results based on HFT intensity in the trade portfolios of mutual funds (HFT ). Consistent with findings in Table 4, intensive HFT is negatively and significantly related to future fund performance. For example, when fund performance is measured by four-factor alpha, coefficient of HFT is (t-value -2.86). Results are qualitatively similar and quantitatively stronger when HFT intensity is measured based on fund holdings (HFT ), as reported by column [5]-[8]. In addition, lagged alpha or conditional alpha have positive and (marginally) significant coefficients, indicating short-term fund performance persistence to some extent. Average institutional ownership in fund holdings is negatively related to future fund performance, consistent with the finding of Sias, Starks, and Titman (2006) that institutional trading has direct impact on stock prices, and the finding of Nagel (2005) that higher institutional ownership relieves short-sale constraints. Fund size, turnover ratio, age and expense ratio, however, have no significant relation with fund risk-adjusted returns. In sum, results from panel regression confirm a significantly negative relation between HFT and future fund performance. 18

19 4. Potential Explanations In this section, I discuss potential explanations about the negative relation between HFT and performance of active funds found in Section 3. First, I investigate the possibility that HFT raises trading costs of mutual funds. Second, I examine whether HFT affects fund performance through its impact on illiquidity premium. Finally, I conduct robustness test on alternative explanations. 4.1 Institutional Trading Costs Total trading costs of investment institutions mainly include brokerage commissions, quoted spread, and price impact cost. If HFTs use anticipatory trading thus raise the price impact costs of mutual funds, total institutional trading costs will be increased and fund performance will be harmed. Due to the lacking of a comprehensive database on institutional trades and trading costs, I test the above hypothesis by two approaches based on fund holdings reported by the S12 database Quintile portfolios If the negative relation between HFT and fund performance is mainly a result of raised institutional trading costs, then this relation should largely disappear when trading costs are assumed to be zero. In other words, portfolios created by replicating the holdings of mutual funds and assuming zero trading cost should not be negatively affected by HFT. To test this hypothesis, I redo the quintile portfolio analysis using the return of holdings of funds instead of NAV-based returns. Specifically, the return of holdings of fund i in month t,,, is estimated as:,,,, 16, where,, is the weight of stock k in fund i at the end of month t-1, and, is the return of stock k in month t estimated from closing quote midpoint 17. As the S12 holdings data is on quarterly basis, I assume that the monthly share volume of a stock is 1/3 of the net share change 17 The use of returns calculated by closing quote mid-points gives very similar results. 19

20 of that stock during that quarter. For example, if fund i holds 100 shares of stock x at the end of March 2013 and hold 130 shares of that stock at the end of June 2013, then I assume that the share volume of stock x purchased by fund i is 10 in each of April, May and June of 2013, and shares of x held by the fund at the end of April, May and June is 110, 120 and 130, respectively. In each month, I follow exactly the same approach of Table 4 to sort mutual funds into quintiles based on their HFT T or HFT H in the prior calendar quarter. The equally-weighted returns of each quintile as well as the 5 1 return spread are calculated based on and are then regressed on the Fama-French and Carhart four factors. Table 6 reports the four-factor-adjusted returns of quintile portfolios based on holdings. In column [1], funds are sorted by their lagged HFT T and trading costs are ignored. The 5 1 return spread is -0.24% per month (t-value -2.04), which is of similar magnitude as (but slightly smaller than) the one reported in Table 4 under the same specification. In column [3], funds are sorted by their lagged HFT H and trading costs are again ignored. The 5 1 return spread is -0.29% per month (t-value -2.27), which is, again, similar to the monthly return spread of -0.31% reported in Table 4 under the same specification. Clearly, trading costs is not likely to be a major explanation to the negative relation between HFT and fund performance. Funds associated with intensive HFT significantly underperform other funds even if trading costs are assumed to be zero. In addition, the above finding rules out the possibility that non-stock holdings interfere the test results. [Table 6] However, the above finding does not preclude the possibility that HFT may still affect fund performance to some extent through its impact on trading costs. To provide further evidence, I deduct trading costs, including both direct trading costs and price impact costs, from return of holdings to see if they make a noticeable difference. Specifically, I assume the direct cost to trade one share of a stock to be a half of its volume-weighted average effective spread in that month, thus trading q shares at price p with relative effective spread of k incurs a direct cost of. Following a similar approach as in Breen et al. (2002) and Korajczyk and Sadka (2004), I estimate price impact cost (PIC) as:,, 17 20

21 where, is the price impact cost function, is the prevailing market price of a share, and q is number of shares traded. Korajczyk and Sadka (2004) indicate that, under the assumptions that trade is divided into many infinitesimal trades and that no price reversion occurs over the trading period, the Breen et al. (2002) price impact cost function is, 1, where is the price impact coefficient and S is shares outstanding. Therefore, the total trading cost (TC) is the sum of the direct cost and the price impact cost:, 1. The estimation of the price impact coefficient,, is based on net trading volume and quotemidpoint return for each 5-minute trading interval. 18 First, all trades are classified as buyer initiated or seller initiated based on whether the transaction price is higher than or lower than the prevailing quote midpoint. Then, net turnover (NTO) for a 5-minute interval is defined as the ratio of net trading volume (buyer-initiated volume less seller-initiated volume times 1,000) to shares outstanding, and quote-midpoint return in each 5-minute interval is defined as the ratio of quotemidpoint (Q) change over the interval to quote-midpoint at the beginning of the interval. For stock i in month t, I run the following regression based on a total of 5-minute intervals to estimate the impact of its net trading volume on its midpoint return:,,,,. 19, Column [2] and [4] of Table 6 reports the four-factor-adjusted returns of quintile portfolios when estimated trading costs are deducted. When funds are sorted by HFT T, the 5 1 return spread is -0.23% per month (t-value -1.96), which is similar to the result reported in column [1] where trading costs are not deducted. When funds are sorted by HFT H, the 5 1 return spread is -0.28% per month (t-value -2.19), which is, again, very close to the corresponding result in column [3]. Overall, these findings imply that HFT s impact on institutional trading costs is negligible Multivariate analysis 18 The use of 30-minute interval gives very similar results. 21

22 The above quintile portfolio analysis may not provide very precise evidence regarding HFT s impact on institutional trading costs, because it is not based on individual fund level. To provide more reliable evidence, I conduct Fama-MacBeth (1973) cross-sectional regressions to examine the impact of HFT on the return gap of mutual funds. Following Kacperczyk, Sialm, and Zheng (2008), I define the return gap of fund i in month t,,, as:,,,,, 20 where, is the NAV-based return,, is the return of holdings, and, is the monthly expense ratio. The return gap is then regressed on HFT T or HFT H in the prior calendar quarter as well as other fund characteristics:,,,,, where, is the HFT intensity in trade portfolio (HFT T ) or holdings (HFT H ) of a fund, and X is a vector of control variables including fund size (TNA), turnover ratio (TO), age (Age), annual expense ratio (ExpRatio), average institutional ownership of fund holdings (IO), and lagged dependent variable (DV). [Table 7] As reported in column [1] and [2] of Table 7, neither HFT T nor HFT H is significantly related to fund return gap when trading costs are ignored. As reported in column [3] and [4], deducting trading costs based on the method described in the previous section does not change this result. Moreover, deducting fund expense ratio from the return gap does not change the results neither (not reported). Overall, both quantile portfolio analysis on return of holdings and multivariate analysis on fund return gap show no evidence that HFT increases the trading costs of mutual funds. This is consistent with the findings of Brogaard et al. (2014) that no increase in institutional trading costs has been found following technology upgrades that lower the latency of the London Stock Exchange. Moreover, it indicates that the underperformance of funds holding HFT-intensive stocks is actually caused by lower risk-adjusted returns of these stocks. Therefore, in the rest of this section I focus on HFT intensity in stocks held by the funds (HFT H ) rather than that in stocks traded by the funds (HFT T )

23 4.2 Illiquidity Premium Illiquid assets should deliver a return premium because investors require higher returns to compensate the higher trading costs of these assets, and the magnitude of this illiquidity premium could be increased by trading frequencies (Amihud and Mendelson, 1986; Barclay and Smith 1988; Chalmers and Kadlec 1998). Compared to their low-frequency counterparts, traders with higher trading frequencies will accumulate larger amount of trading costs during each unit time. Therefore, they are more sensitive to trading costs, have stronger demand to liquid assets, and require higher returns from illiquid assets as compensation for trading costs (Amihud and Mendelson, 1986). Specifically, investor i on stock j will generate a total trading cost of during each unit time, where is the trading frequency of investor i and is the spread of stock j. To compensate this trading cost, investor i will require an illiquidity premium of, which is an increasing function of the trading frequency of this investor. The implication in the context of HFT is that HFTs will prefer to trade liquid assets, 19 and the presence of intensive HFT will amplify the magnitude of illiquidity premium by lowering the risk-adjusted returns of liquid assets and increasing those of illiquid assets. As the result, the majority of HFT-intensive stocks are relatively liquid and deliver negative risk-adjusted returns, thus mutual funds holding such stocks will have significant underperformance Quintile portfolio analysis after controlling for illiquidity premium To validate the above liquidity-based explanation, I first compare the average relative quoted spreads (RQS) and relative effective spreads (RES) of holdings of funds associated with the most and the least intensive HFT. The average RQS in the holdings of the 20% funds with the most intensive HFT (measured by HFT H ) is 0.24%, while that of the 20% funds with the least intensive HFT is 0.56%. The same pattern can also be found in RES (0.15% versus 0.28%). Moreover, as reported in Table 3 and Figure 2.A, HFT intensity is negatively related to quoted 19 More precisely, liquidity-taking HFTs should prefer to trade liquid assets to save trading costs, while liquidityproviding HFTs may prefer to trade illiquid assets where more revenue can be collected. However, as reported in Baron et al. (2014), liquidity-taking HFTs contribute much more HFT volume than liquidity-providing HFTs. For example, in August 2012, 41% of all HFT volume on the E-mini S&P 500 futures market is generated by liquiditytaking HFTs, while 15% is generated by liquidity-providing HFTs. The rest HFT volume is generated by HFTs using both strategies. 23

24 spread and price impact cost, and HFT-intensive stocks tend to be liquid while most stocks with the least HFT intensity are illiquid. Thus HFT-intensive stocks are indeed more liquid. Next, I construct an illiquid-minus-liquid (IML) factor based on relative quoted spread to capture the illiquidity premium, and add this factor to the Fama-French and Carhart four-factor model to redo the quintile portfolio analysis of fund performance. As reported in Panel A of Table 8, after controlling for illiquidity premium, the 5 1 return spreads (based on fund raw returns) have been narrowed from -0.31% to -0.16% and is no long statistically significant (t-value 1.62). Loading of the IML factor is highly significantly at (t-value 3.81). Thus the illiquidity premium explains almost a half of the negative relation between HFT intensity and fund performance. Moreover, this result is robustness to many alternative specifications, such as valueweighted portfolios, removing stocks with share price below $5, IML factor constructed by effective spread. Removing the 01/ /2009 crisis period makes the result to be even stronger (results are not reported). [Table 8] Controlling for liquidity risk premium Recently studies generally find that HFT reduces liquidity risk. For example, Hendershott and Riordan (2013) find that algorithmic trading is likely to reduce liquidity risk by consuming liquidity when it is cheap and providing liquidity when it expensive. As stocks with high liquidity risk earn significant liquidity risk premium (Pastor and Stambaugh, 2003; Acharya and Pedersen, 2005), HFT may reduce expected stock returns by reducing liquidity risk, causing a negative impact on the performance of mutual funds which hold these stocks. To control for this liquidity risk premium effect, I add the Pastor and Stambaugh (2003) liquidity risk factor (PS) to the Fama- French and Carhart four-factor model and use this alternative five-factor model to evaluate the performance of quintile portfolios formed by HFT H. As reported in Panel B of Table 8, after controlling for liquidity risk premium, the 5 1 return spreads (based on fund raw returns) have been narrowed from -0.31% to -0.26% (t-value ), and the loading of the PS factor are significantly negative. Therefore, HFT is negatively related to fund performance partially because HFT-intensive stocks have lower liquidity risk. 24

25 However, potential self-selection bias cannot be precluded HFTs may prefer to trade stocks with low liquidity risk. Nevertheless, the 5 1 return spreads are still economically and statistically significant after controlling for liquidity risk premium. In Panel C, when the IML factor and the PS factor are both added to the four-factor model, the 5 1 return spreads (based on fund raw returns) is narrowed to -0.12% (t-value -1.34), and the loadings of both IML and PS factors are highly significant. Overall, these results suggest that the effect of illiquidity premium is not substituted by the liquid risk premium. Illiquidity premium explains roughly a half of the negative relation between HFT intensity and fund performance, while liquidity risk premium explains roughly onesixth of that negative relation Distinguish between self-selection bias and causality The above findings are consistent with the hypothesis that HFT negatively affects fund performance through its impact on illiquidity premium, but it does not necessarily represent a causality between intensive HFT and weaker fund performance: HFT-intensive stocks are likely to be liquid stocks, but the negative risk-adjusted returns of these stocks may not be caused by HFT. To preclude such a possibility, I examine whether HFT intensity is related to the magnitude of illiquidity premium by estimating the illiquidity premium conditional on HFT intensity in individual stocks. At the beginning of each month t, stocks are first sorted into terciles based on the average HFT intensity in month t-3 to t-1. Within each HFT tercile, stocks are sorted into terciles based on the volatilities of their daily returns in month t-3 to t-1 to control for the volatility effect. Within each volatility terciles, stocks are further sorted into deciles based on average RQS in month t-3 to t-1. For each HFT tercile, value-weight returns are estimated for each of the 30 (3 10) portfolios in month t+1, t+2 and t+3. The illiquidity premium is estimated as differential returns between the three least liquid portfolios (across volatility terciles) and the three most liquid portfolios (across volatility terciles). Moreover, as trading costs and HFT intensity are correlated, pre-sorting stocks on HFT intensity may reduce the cross-sectional dispersion of trading costs in each subsample, leading to underestimated illiquidity premium. To avoid this problem, an independent double sort is also used where stocks are sorted into 30 (3 10) subsamples based on their HFT intensity and RQS, independently. [Table 9] 25

26 As reported in Table 9, there is a strong illiquidity premium of 0.65% per month (t-value 2.75) in U.S. common stocks during the sample period of In addition, both conditional and independent sorts show that the illiquidity premium concentrates in HFT-intensive tercile of stocks but is small and not statistically significant in other two terciles. This finding is robust to the use of relative effective spread as alternative measures of liquidity (results are not reported). Overall, this finding is consistent with the hypothesis that the combination of cost per trade and trading frequency, not cost per trade alone, determines the illiquidity premium. More importantly, it clearly suggests a causality between intensive HFT and weaker fund performance: without the presence of intensive HFT, illiquidity premium will not exist in the first place. The above findings imply that the underperformance of mutual funds associated with intensive HFT is not a reasonable compromise to obtain more liquidity. For HFTs who hold and trade liquid assets, the lowered required returns of liquid assets can be offset by substantial savings from low trading costs. For most traditional institutional investors who trade much less frequently, however, the gains from low trading costs of liquid assets can hardly offset the loss in the expected returns. In this sense, intensive HFT causes the underperformance of traditional institutional investors who hold large amounts of liquid assets. 4.3 Robustness Tests for Alternative Explanations Idiosyncratic volatility anomaly HFT has been found to increases stock price volatility (Zhang 2010; Breckenfelder, 2013; Boehmer et al., 2014). As illustrated in Figure 2.B, HFT intensity is strongly correlated with volatility. Therefore, it is possible that the main findings of this paper is a result of the well-known idiosyncratic volatility (IVOL) anomaly HFT is negatively related to stock return and fund performance because it increases IVOL, which is known to be negatively related to stock return. To examine this possibility, I follow a similar methodology of Ang et al. (2006) to create a zero investment portfolio to capture the IVOL anomaly, and add the IVOL factor to the four-factor model to evaluate performance of portfolios sorted by HFT intensity. Specifically, IVOL of a stock in a month is estimated as the standard deviation of daily return residuals by the Fama-French three-factor model. Then, at the beginning of each month t, stocks are sorted into deciles by their IVOL over month t-3 to t-1. The IVOL factor is constructed as the difference between the value- 26

27 weighted returns of the top and the bottom deciles in month t+1, t+2 and t+3. During the sample period, the IVOL factor is significantly positive at -0.89% per month (t-value -2.47). [Table 10] As reported in Panel A of Table 10, after controlling for IVOL, the risk-adjusted return spread between the top and bottom quintiles of funds sorted by HFT intensity is narrowed from % to -0.24% (t-value -2.35), while the loading of the IVOL factor is significantly positive (tvalue 2.50). Therefore, the IVOL anomaly does explain a limited fraction of the negative relation between HFT intensity and fund performance. As reported in Panel B of Table 10, the 5 1 return spreads (by gross return) is -0.08% (t-value -1.02) when illiquidity premium, liquidity risk premium, and IVOL anomaly are all controlled for, and loadings of the three factors are significantly positive. Therefore, all the three effects contribute to the negative relation between HFT intensity and fund performance, but the impact of illiquidity premium is far greater than other two effects. The above finding is not likely to be caused by a self-selection bias. The common belief is that, instead of trading high volatility stocks and bear a high risk, HFTs prefer to trade low volatility stocks to earn small but certain profits. Consistent with this belief, as reported in Table 3, quote updates is negatively related to lagged volatility once lagged quoted updates is controlled for. Therefore, the positive relation between HFT intensity and volatility is more likely to represent a causality suggested by Zhang (2010), Breckenfelder (2013) and Boehmer et al. (2014). Though the exact reason for the IVOL anomaly is still not clear, a reasonable explanation is that IVOL increases the probability of margin call of short positions thus exacerbates short sale constraint, leading to temporary overpricing (Stambaugh, Yu, and Yuan, 2015). If this is the case, then findings of this section imply an additional channel through which HFT can cause underperformance of mutual fund: HFT intensifies short-sale constraint by raising volatility, thus contributes to temporary overpricing of HFT-intensive stocks and worse future performance of funds that hold these stocks Temporary overpricing 27

28 HFTs clearly select which stocks to trade. If HFTs prefer to trade overpriced stocks, then the negative relation between HFT intensity and fund performance merely comes from a selfselection. However, this possibility is not likely to explain the main finding of this paper, for the following reasons. First, there is no reason to believe that HFTs have a particular interest in overpriced stocks. The literature generally finds that HFT increases intraday price efficiency by trading in the direction of permanent price changes and in the opposite direction of transitory pricing errors (Brogaard et al. 2014), and that intensive HFT is associated with intraday price series that is closer to random walk (Conrad et al, 2015). Thus it is reasonable to believe that HFTs are interested in mispriced stocks, and are actively involved in price discovery by buying underpriced stocks and selling overpriced ones. However, as nhfts, HFTs face short sale constraints it is easier to buy than to sell. Therefore, there is more reason to believe that HFTs prefer underpriced stocks instead of overpriced ones, if HFTs have a preference towards mispricing at all. Second, the 2008 short sale ban could provide insights about the preference of HFTs towards overpricing. Autore et al. (2011) find that short-banned stocks experienced overpricing after the ban initiated. However, as reported by Brogaard et al. (2015), non-short HFT volume declined, rather than increased, for short-banned stocks. 20 This is, again, contradicting to the possibility that HFTs prefer to trade overpriced stocks. To further preclude this possibility, I use short interest ratio (SIR) as a proxy for temporary overpricing to construct a factor to capture the future price correction of temporarily overpriced stocks. Many empirical studies, such as Asquith, Pathak, and Ritter (2005), consider SIR as a proxy of short demand, which reflect investors perception about overpricing. Specifically, SIR of a stock in a month is estimated as the ratio of shares held in short positions to total shares outstanding. Then, at the beginning of each month t, stocks are sorted into deciles by their average SIR in month t-3 to t-1. The SIR factor is then constructed as the difference between the value-weighted returns of the top and the bottom deciles, and is significantly negative over the sample period (-0.70% per month with t-value of -3.25). As reported in Panel C of Table 10, after controlling for SIR, the risk-adjusted return spread between the top and bottom quintiles of funds sorted by HFT intensity is still highly significant at -0.30% (t-value 2.58), while the loading of the SIR factor is not 20 As reported by Brogaard et al. (2015), the average relative HFT volume declined from 23.91% (of the total volume) to 15.53% for short-banned stocks, while average HFT short volume declined only by 5.63% (of the total volume). Therefore, average non-short HFT volume declined by 2.75% (of the total volume). 28

29 statistically significant (t-value 1.47). This is, again, contradicting to the possibility that the negative relation between HFT intensity and fund performance is a manifestation of HFTs preference towards temporarily overpriced stocks. 5. Conclusion High-frequency trading (HFT) has experienced rapid growth over the past decade, yet our understanding to its impacts on the financial markets and on other market participants is still very limited. Though several studies suggest that HFT reduces trading costs and improves market efficiency, there are still widespread concerns regarding its potentially negative impact on the performance of traditional institutional investors. Among these concerns, most attentions have been given to HFT s predatory trading which may increase trading costs of other institutional investors, but little has been discussed regarding HFT s potential impact on the cross-sectional stock returns. Moreover, limited availability of HFT data restricts comprehensive studies on HFT, leading to mixed and inclusive empirical findings. This paper contributes to the literature by being the first to provide comprehensive evidence regarding HFT s impact on performance of actively-managed U.S. equity mutual funds. The HFT proxy used in this paper, quote updates, ensures the full coverage over U.S. common stocks while maintaining high correlations with the actual HFT. Return and characteristics of U.S. equity mutual funds are merged with quarterly fund holdings, so that the fund returns are directly linked to HFT intensity in fund holdings or trade portfolios. Based on this sitting, this paper finds that intensive HFT in stocks traded or held by the funds is related to significantly lower risk-adjusted fund returns in future. Monthly four-factor-adjusted return spread between the top quintile and the bottom quintile of funds sorted by HFT intensity in their holdings is -0.31%. Further analyses show that nearly a half of this negative abnormal return could be explained by illiquidity premium amplified by high-frequency traders (HFTs), while a limited fraction of it is attributable to liquidity risk premium and HFT-induced volatility. However, contradicting to the general impression, holdings-based performance analyses do not support the argument that HFT increases trading costs of traditional institutional investors. 29

30 The findings of this paper ease the concern about HFT s negative impact on the trading costs of other institutional investors, but reveal other challenges faced by managers of traditional investment companies. For the first time in the literature, this paper finds that intensive HFT may be detrimental to the performance of traditional institutional investors because it makes liquidity to be unnecessarily expensive to these investors. In addition, HFT could negatively affect performance of traditional institutional investors because it increases stock volatility, which is associated to lower stock returns in future. In light of these findings, money managers should be cautious when buying or holding stocks experiencing intensive HFT. 30

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34 Figure 1: Daily Quote Updates Over This figure shows average monthly quote updates ( 10 3 ) of 7,695 U.S. common stocks that were traded in NYSE, AMEX and NASDAQ over Stocks are categorized into five quintiles based on their market capitalization

35 Figure 2: Number of Stocks Across HFT and Characteristics Quintiles This figure shows the number of stocks within each independently-sorted HFT and liquidity or volatility quintile. The sample includes 7,695 U.S. common stocks that were traded in NYSE, AMEX and NASDAQ over In each month, stocks are sorted into quintiles by their HFT intensity (estimated by formula (2)) and by their timeweighted relative quoted spread (Panel A) or by their volatility estimated from daily returns (Panel B), respectively, to obtain 25 (5 5) subsamples with potentially unequal number of stocks in each. Number of stocks in each subsample is then averaged across the whole sample period and is plotted in the figure High HFT 2 Low HFT Panel A: Number of stocks across HFT and liquidity quintiles High HFT 2 Low HFT Panel B: Number of stocks across HFT and volatility quintiles 35