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1 College of Business Administration University of Rhode Island William A. Orme WORKING PAPER SERIES encouraging creative research Riding the Post Earning Announcement Drift: Evidence from Mutual Funds Ashiq Ali, Xuanjuan Chen, Tong Yao and Tong Yu 2006/2007 No. 14 This working paper series is intended to facilitate discussion and encourage the exchange of ideas. Inclusion here does not preclude publication elsewhere. It is the original work of the author(s) and subject to copyright regulations. Office of the Dean College of Business Administration Ballentine Hall 7 Lippitt Road Kingston, RI

2 Riding the Post Earnings Announcement Drift: Evidence from Mutual Funds Ashiq Ali*, Xuanjuan Chen**, Tong Yao***, Tong Yu**** January 2007 Preliminary Draft *University of Texas at Dallas; ** University of North Carolina at Wilmington; ***University of Arizona; ****University of Rhode Island. 1

3 Riding the Post Earnings Announcement Drift: Evidence from Mutual Funds Ashiq Ali, Xuanjuan Chen, Tong Yao, Tong Yu January 2007 Abstract This paper uses portfolio holdings and returns of mutual funds to study whether investors can profitably trade on the post earnings announcement drift (PEAD). We find that actively-managed US equity mutual funds on average trade on PEAD, even after controlling for different investment styles and momentum trading. Further, trading on PEAD is profitable: net of both transaction costs and fund expenses, the annual Carhart (1997) four-factor alpha of the top 10% of funds most actively following the PEAD strategy is 2.10% higher than that of a group of benchmark funds not actively using the strategy. However, across funds, more active trading on PEAD is associated with less portfolio diversification, higher volatility in fund returns and higher volatility in fund flows, representing adverse consequences of arbitrage risk. Finally, we document the temporal dynamics between fund trading and the profitability of the PEAD strategy: higher profitability attracts more intense trading by funds, which, in turn, leads to lower future profitability. 2

4 Riding the Post Earnings Announcement Drift: Evidence from Mutual Funds 1. Introduction Can investors profitably trade on the post earnings announcement drift (PEAD)? This question has recently attracted increased attention in the debate of market efficiency. PEAD, the pattern that stock prices drift in the direction of earnings surprise during months after earnings announcements, is dubbed by Fama (1998) as the granddaddy of all underreaction events. Initially reported by Ball and Brown (1968) and Jones and Litzenberg (1970), it is perhaps the first market anomaly rigorously scrutinized by academic studies. Yet, after almost four decades and having been well-publicized among investors, price drift after earnings announcements remains a significant phenomenon. To explain such persistence, some researchers conjecture that market frictions, in particular transaction costs, have prevented the anomaly from being arbitraged away; that is, PEAD may still be consistent with market efficiency under costly trading. 1 Several recent studies have attempted to quantify profits of trading strategies designed to exploit the PEAD anomaly using estimated transaction costs. However, due to their focus on different components of transaction costs as well as different data and methods employed, the results obtained by these studies are rather mixed. For example, Ke and Ramalingegowda (2005) find that active institutional investors generate net 1 Note that earning surprises typically predict stock returns for a relatively short horizon (below one year). This means that the PEAD trading strategy has high turnover and the impact of transaction cost for this strategy is potentially more significant relative to the impact on strategies exploiting return predictability at longer horizons, such as those based on accruals or value anomalies. It should also be pointed out that in addition to transaction cost explanation, there exist alternative explanations of the persistence of PEAD for example, omitted risk factor (e.g., Dyckman and Morse 1986; Ball 1992; Kothari 2001) and arbitrage risk (Mendenhall 2002). 3

5 arbitrage profits of 22% per year after trading costs; the empirical transaction cost model they consider is the one estimated by Keim and Madhavan (1997), using trades of large institutions during a three-year period from 1991 to Battalio and Mendenhall (2006) report a net trading profit of at least 14% per year if investors trade after earnings announcements in a timely fashion. Their trading cost estimates are the quoted bid-ask spreads. On the other hand, Chordia, Goyal, Sadka, Sadka and Shivakumar (2006) find that trading costs account for 66% to 100% of the paper profits for the PEAD strategy, where transaction costs are measured by price impact of trading based on trades and quotes data (TAQ). Similarly, Ng, Rusticus, and Verdi (2006) document insignificantly positive or even negative profits for the PEAD strategy after trading costs. They measure trading costs in the form of quoted spreads, effective spreads, as well as an indirect cost measure developed by Lesmond et al (1999). Apparently, the estimated profitability of the PEAD strategy is quite sensitive to transaction cost estimates. In this study, we provide an alternative approach for estimating the posttransaction-cost profitability of trading strategies exploiting market anomalies. We focus on the trading activities of a group of sophisticated investors actively managed US equity mutual funds. An important advantage of our approach is that we combine data on fund portfolio holdings with data on fund returns. Using data on fund holdings, we are able to quantify the intensity of a fund s trading on PEAD. Using fund return data, we can then examine whether funds actively following the strategy reap better performance relative to those who do not use the strategy. Our approach differs from existing studies in two main aspects. First, the trading strategies we examine are those actually implemented by mutual funds, rather than 4

6 hypothetical strategies. Hypothetical trading strategies analyzed in existing studies, such as the hedge portfolio that long in the top decile of stocks and short in the bottom decile of stocks sorted by earnings surprise, are designed to maximize paper trading profits without taking into account transaction costs or portfolio constraints. In reality, though, even sophisticated investors such as mutual funds face various portfolio constraints (e.g., no short-sale, maximum positions in particular stocks). Mutual funds may also optimize the PEAD strategy in the face of transaction costs. As a result, profits from hypothetical strategies may be quite different from the actual trading profits attained by sophisticated investors. Second, reported mutual fund returns are already net of actual transaction costs. Therefore, our approach does not rely on transaction cost estimates and can provide a more convincing conclusion on the profitability of the PEAD strategy. We measure how actively a fund trades on earnings surprises using the covariance between active portfolio weight changes and cross-sectionally standardized SUE (standardized unexpected earnings) of individual stocks in the fund portfolio. This measure, referred to SUE investing measure (SIM), is similar to the momentum investing measure of Grinblatt, Titman, and Wermers (1995). A high (low) value of SIM indicates that the fund actively buys high (low) SUE stocks and/or sells low (high) SUE stocks. We apply this measure to 2468 actively managed domestic equity funds that have portfolio holdings information from Thomson Financial and fund return information from CRSP over a 20-year sample period from 1984 to We find that on average these mutual funds have positive SUE investing measures. This suggests that as a whole, active mutual funds trade on the PEAD anomaly. The conclusion is robust after controlling for fund 5

7 investment styles along the dimensions of size and book-to-market ratio, as well as fund trading on momentum. To identify funds that actively trade on the anomaly rather than those having high SIMs by chance, in each quarter we average SIMs for a fund during the past four quarters and sort funds into deciles by the 4-quarter averaged SIM (SIM4). We find that the likelihood of funds in the decile of highest SIM4 to continue to stay in the top decile during the next four quarters is more than 30%, significantly higher than the likelihood due to random chance. That is, these funds intentionally and actively trade on the anomaly. We use net fund returns before fund expenses (i.e., fund management and administrative fees) to assess the profits, net of actual transaction costs, that mutual funds make from investing in the PEAD strategy. We find that the top 10% of funds most actively trading on the PEAD anomaly (those with highest SIM4) outperform funds who do not trade on PEAD (those with SIM4 close to zero) by 0.69% during the quarter after fund decile ranking (Q1) and 2.33% during the year after fund decile ranking (Q1 to Q4). When performance is measured by the Carhart (1997) four-factor model, the alphas of the top decile funds are higher than inactive funds by 0.66% during Q1 and higher by 2.28% during the four quarters from Q1 through Q4. These performance differences are all statistically and economically significant. Further, such performance differences cannot be explained by other factors potentially affecting fund performance, including fund size, fees, turnover, fund flow, investment style, and momentum trading. Finally, the top funds also slightly outperform inactive funds during the quarter of fund decile ranking (Q0) as well as during the four quarters prior to fund decile ranking (from Q(-3) to Q0), although 6

8 the performance difference is not statistically significant. Put together, the evidence suggests that the PEAD strategy leads to significant profits that outstrip the cost of trading. We also use the mutual fund data to examine the effect of arbitrage risk, which, according to Shleifer and Vishny (1997), is another form of market friction that may prevent sophisticated investors from arbitraging away market anomalies. We find that funds actively trading on PEAD tend to be smaller in size, hold less diversified portfolios as measured by the number of stocks and concentration of portfolio weights. More importantly, these funds have higher performance volatility and more volatile fund flows. This is evidence of negative effect of arbitrage risk that prevents mutual funds from aggressively chasing anomalies. The presence of arbitrage risk helps explain why mutual funds do not trade on PEAD more aggressively while such trading is still quite profitable. Finally, we examine whether mutual fund trading affects the profitability of the PEAD strategy over time. We find that when mutual funds trade more intensely on PEAD, the future profitability tends to be lower. On the other hand, higher profitability of the PEAD strategy leads to more intense mutual fund trading on the anomaly. This is consistent with the notion that mutual funds as a group of sophisticated investors actively engage in arbitrage activities that reduces market inefficiency. However, we do not find any visible time trend in the intensity of the use of the PEAD strategy. Overall, the evidence suggests a moderate role of mutual funds in arbitraging away the anomaly. The remainder of this paper is organized as the follows. Section 2 reviews the literature on the PEAD anomaly. Section 3 describes the data and methodology. Section 4 presents empirical results. Section 5 concludes. 7

9 2. Literature Review Post-earnings announcement drift (PEAD), also known as the SUE effect, is considered as one of the best-documented capital market anomalies (Brennan 1991; Fama; 1998). Ball and Brown (1968) and Jones and Litzenberger (1970) are the earliest studies documenting this anomaly. The PEAD effect refers to the phenomenon that stock returns continue to drift in the direction of earnings surprises for months after earnings are announced. Over the following decades, several papers use different sample and methods to confirm the drift, e.g., Foster, Olsen, and Shevlin (1984), Bernard and Thomas (1989, 1990), Ball and Bartov (1996), and Livnat and Mendenhall (2006). Further, studies report that PEAD persists over time. The literature generally attributes PEAD to investors underreaction to earnings information. Bernard and Thomas (1990) and Bartov (1992) show that investors act as if they form their earnings expectation based on a naïve seasonal random walk model and they are unaware that firms seasonally-differenced quarterly earnings are serially correlated. This naïve expectation results abnormal returns at earnings announcements to be predictable by past earnings. Ball and Bartov (1996) provide evidence that investors recognize the serial correlations among firms seasonally-differenced quarterly earnings but under estimate the extent of the serial correlations. Moreover, Bartov, Radhakrishnan and Krinsky (2000) present evidence that PEAD is strongest in firms with low institutional holdings; Bhattacharya (2001) shows that the volume of small trades but not large trades is associated with the magnitude of earnings surprises. 2 Further along this line, Barberis, Shleifer and Vishny (1998) show PEAD, and thus PEAD, arises when 2 Hirshleifer, Myers, Myers, and Teoh (2003), however, do not find evidence that individual investors drive PEAD. 8

10 earnings follow a random walk but investors assume that earnings are mean-reverting, i.e., a stationary process. 3 There is less consensus on the cause of the persistent PEAD anomaly. One line of stories argues the presence of transaction costs deters arbitrage. Bhushan (1994) presents evidence indicating that the magnitude of the post-earnings announcement drift is inversely related to share price and annual dollar trading volume, the direct and indirect transaction costs. He argues that the drift exists only up to the level of transactions costs. Sadka (2005) and Chordia, Goyal, Sadka, Sadka and Shivakumar (2005) suggest that transaction costs inhibit the exploitation of the PEAD. Chordia et al (2005) shows that the estimated transaction costs account for 66% to 100% of the paper profits from long-short strategy designed to exploit the earning momentum anomaly. In the other extreme, Ball (1992) claim that the drift is too large to be bounded by transactions costs. Ke and Ramalingegowda (2005) show that transient institutional investors trade to exploit the post-earnings announcement drift. They show these investors could generate an abnormal return of 22% per year after transaction costs using Keim and Madhavan (1997) cost measures. Battalio and Mendenhall (2006) report investors earn an annual return of over 14% per year after transaction costs. The striking difference in PEAD profitability after transaction costs is because these studies estimate transaction costs with different model. Ke and Ramalingegowda (2005) apply a modified Keim and Madhavan s approach used in Wermers (2000) to estimate transaction cost. Ideally, a 3 A related but different theory is presented by Daniel, Hirshleifer, and Subrahmanyam (1998) that demonstrate underreaction arises when investors are overconfident -- they overweight their private information and underweight public earnings information. In this way, drift is positively associated with the degree of heterogeneous information among investors. Liang (2003), Garfinkel and Sokobin (200x), Francis, Lafond, Olsson, and Schipper (2003) present evidence on this premise. 9

11 measure the realized transaction costs helps us ascertain the actual effect of transaction costs. Another set of explanations for the persistence of the PEAD anomaly lies in arbitrage risks. Studies show high PEAD stocks share certain unfavorable characteristics, they are small in size (Bernard and Thomas, 1990), poorer in earning quality (Francis, Lafond, Olsson, and Schipper 2003), and greater in forecast dispersion (Liang 2003). Measuring arbitrage risks using a stock s idiosyncratic risk, Mendenhall (2004) shows firms with high levels of arbitrage risk experience drifts that, ceteris paribus, between 3 to 4 percentage points per quarter larger than firms with low levels of arbitrage risk. 3. Data and Empirical Methodology 3.1 Mutual Fund Sample Our mutual fund sample consists of actively-managed U.S. domestic equity funds. We obtain information on fund monthly returns and fund characteristics such as turnover and expense ratio from the CRSP Survivorship Bias Free Mutual Fund Database (hereafter the CRSP data ). In addition, we obtain information on fund stock holdings from the Thomson Financial CDA/Spectrum Database (hereafter the CDA data ). 4 During the past two decades, mutual funds were required to file with SEC their equity holdings on a semiannual basis, and many funds have voluntary disclosed their 4 Relative to the existing literature (e.g.,, Lev and Nissim 2004 and Ke and Ramalingegowda 2005) that examines the relationship between aggregate institutional ownership (from 13f filings) and accounting anomalies, our focus on mutual funds has several empirical advantages. For example, identifying activelymanaged equity mutual funds from the data is straightforward. On the other hand, the procedure to identify active institutional investors from passive ones is typically indirect, based on factors such as portfolio turnover, diversification, and momentum trading (see, e.g., Bushee 1998). Moreover, in the 13f data on institutional ownership, the active and passive portfolios of the same institution are not separately reported. For example, while the CDA data that we use contains information on equity holdings by Fidelity Magellan Fund, equity holdings information in the 13f data is only available for Fidelity Investments, the mutual fund company that manages a large number of active and passive funds. 10

12 holdings quarterly. 5 Thomson Financial collects information from both mandatory and voluntary reports and makes the data available commercially. This dataset has been used in a number of previous studies, such as Grinblatt and Titman (1989, 1993), Grinblatt, Titman, and Wermers (1995), Daniel, Grinblatt, Titman, and Wermers (1997), Wermers (2000, 2003), Cohen, Coval, and Pastor (2005), and Kacperczyk, Sialm, and Zheng (2005). In the CDA data, mutual funds are classified into nine categories according to their self-declared investment objectives: international, aggressive growth, growth, growth and income, municipal bonds, bond and preferred, balanced, metals, and unclassified. We focus on actively-managed U.S. domestic equity funds with the following three investment objectives: aggressive growth, growth, and growth and income. These three types of funds represent the majority of actively managed domestic equity funds in the U.S. and are the focus of previous studies; see, e.g., Wermers (2000). We further remove passive index funds and funds with apparently misreported investment objectives from the sample. The CDA data is then combined with the CRSP data to obtain complete information on fund holdings and fund returns. Before merging the two datasets, we first combine multiple share classes as a single fund in the CRSP data. These multiple share classes differ in sales charges and targeted investor clientele, but have the same portfolio composition. They have separate identification codes in the CRSP data but are treated as a single fund in the CDA data. We follow Wermers (2000) to merge the two datasets by matching fund names and ticker symbols. The details of the matching procedure can also 5 SEC mandated quarterly filing frequency for mutual funds before 1985, and switched to semiannual frequency afterwards. A recent SEC regulatory change makes the mandatory filing frequency quarterly again, starting from May

13 be found in Jiang, Yao, and Yu (2006). 6 To ensure data accuracy, among the matched funds we further exclude fund-quarter observations if the total net assets are below one million dollars or the total market value of reported holdings is less than 50 percent or more than 150 percent of the total net assets. We also require that, for a fund to be included in the analysis in quarter t, its latest lagged holdings are reported within 6 months of its current reporting. Our database eventually includes 2468 unique U.S. active equity funds that ever exist during 1984 to We report the summary statistics in the entire sample period in the first column of Table 1 followed by the snapshots of 1985, 1990, 1995, and Among the 2468 unique funds, 285 are aggressive growth funds; 1652 are growth funds; 531 are growth and income funds. There are 303 funds in year 1985 and 1253 funds in year This table reports the average fund characteristics first averaged across funds for each year and then averaged over the time series. The average total net assets (TNA) of funds in our sample is million, with an average annual return of 12.30%, an average annual turnover ratio of 85.03%, an average annualized load of 0.35%, and an average annual expense ratio of 1.27%. The average fund age, calculated as the time elapsed since the fund organization year in the CRSP data, is years. The mean number of stocks held in a fund is 97, whereas the median is 65. On average, 23.15% of funds report their holding semi-annually. This percentage goes low to 12.81% in 1985 but high in 1995 of a 57.91%. Fund sizes increase over time. It is $ million in As noted by previous studies (Daniel et al. 1997), both the CRSP and CDA data are free from the survivorship bias. However, the CDA dataset is slow in adding new funds. Therefore, some new funds already in the CRSP data may not be included in the CDA data; see, e.g., Wermers (2000). 7 There are only around 200 funds having matched return and holding information in the early 1980s. We begin our sample period from 1984 to ensure a large cross-section of funds. 12

14 and $ million in Fund expense ratios increase from 1.01% in 1985 to 1.39% in 2000, while load decrease from 0.53% in 1985 to 0.27% in Standardized Unexpected Earnings Following Bernard and Thomas (1990) and many other related studies, we measure standardized unexpected earnings (SUE) based on a model of seasonal random walk with a drift. Specifically, SUE of stock j reported in quarter t is defined as: SUE j, t = E j, t E σ j, t 4 j, t c j, t (1) where E j,t is quarterly earnings (COMPUSTAT quarterly data item 8) reported during quarter t, E j,t-4 is earnings reported four quarters ago. c j,t and σ j, t are the mean and standard deviation, respectively, of (E j,t E j,t-4 ) over the preceding 8 quarters, with a minimum of 4 quarters required for the observation to be valid. We use the financial statement reporting date in the COMPUSTAT dataset as the earnings announcement date. If the financial statement reporting date is missing, we assume earnings are announced two months after the fiscal quarter ends. 3.3 SUE Investing Measure We use the SUE investing measure (SIM) to quantify how actively a fund takes advantage of the post earnings announcement drift anomaly. Specifically, we identify all stocks with valid SUE observations reported within 3 months prior to the holding reporting date. A fund s SIM is the average of cross-sectionally standardized SUEs of 13

15 stocks weighted by the fund s active change in its portfolio holding since its prior holding reporting date: SIM i, t = N j= 1 ~ ( w wi, j, t k ) * ( SUE, i, j, t σ ( SUE t ) j t µ ( SUE t )) (k=1 or 2) (3) where SUE j,t is firm j s SUE reported within 3 months prior to holding reporting date; µ(sue t ) and σ(sue t ) are the cross-sectional mean and standard deviation of SUE j,t. w i, j, t is the portfolio weights on stock j held by fund i in quarter t and ~ w i, j, t k is the lagged portfolio weights after adjusting for price changes in buy-and-hold portfolios, k=1 for funds reporting holding quarterly and k=2 for funds reporting holding semi-annually. Denoting R j,t the quarterly return for stock j in quarter t, the lagged weight can be expressed as follows: ~ j, t k i= 0 w j, t k = k 1 j w w j, t k k 1 (1 + R i= 0 j, t i (1 + R ) j, t i ) (k=1 or 2) (4) When constructing SIM, we exclude stocks with price less than $1 at the end of quarter t. The reason for such exclusion is that some of our analyses involve measuring returns for stocks held by funds, and returns to penny stocks are inaccurately measured due to market microstructure issues. The SIM measure is in the spirit of the momentum investing measure of Grinblatt, Titman, and Wermers (1995). If the portfolio weight changes are uncorrelated with stock SUEs, i.e., for a randomly trade on the PEAD signal, SIM should on average be zero. A positive SIM, on the other hand, indicates that a fund trades toward high SUE stocks. 14

16 A criticism on the SIM measure is that a greater SIM may merely reflect a fund s more intensive PEAD trading in a quarter. This measure cannot effectively gauge a fund s persistent trading on the anomaly. To address this concern, we construct an alternative measure on fund PEAD trading, SIM4, which is the average of a fund s SIMs in the quarter of portfolio formation (Q0) and the prior 3 quarters. As noted in the data section, more than a quarter of our sample funds report their holding semi-annually. For these funds, SIM4 is the average of the SIMs reported in Q0 and 6 month ago. 3.4 Fund Performance Measures We consider four measures of fund performance. The first is after-expense fund net return. We compound monthly fund net returns from the CRSP data into quarterly net returns. The second measure is before-expense fund net return. Quarterly before-expense net return is the quarterly net return plus 1/4 of the annual expense ratio. The third and fourth performance measures are fund risk-adjusted returns, before and after expenses, based on the Carhart (1997) four-factor model. The estimation involves two steps. First, in each month t, we regress monthly excess returns of a fund in prior 12 months on the four factors of the corresponding months as the following: R it = α + b1 t RMRFt + b2t SMBt + b3t HMLt + b4tumdt + ε t (5) where R, is the monthly net return (before or after fund expenses) of fund i in month t in i t excess of the risk free rate (the yield on Treasury bills with one-month maturity, from CRSP). RMRF t is the monthly return on the CRSP value-weighted index in excess of the 15

17 risk free rate; SMB t, HML t, and UMD t are the monthly returns on size, book-to-market, and momentum factors. 8 Then the four-factor adjusted return for fund i in month t is calculated as: Alpha ( ˆ ˆ ˆ ˆ i, t = Rit b1 RMRFt + b2smbt + b3 HMLt + b4umd) (6) where bˆ i s (i=1, 2, 3, 4) are the coefficients estimated from (5). Monthly factor-adjusted returns are compounded to quarterly returns. Finally, the fourth performance measure is the before-expense four-factor adjusted returns, which is the after-expense risk-adjusted returns plus amortized expense ratio. 4. Empirical Results 4.1 Post Earnings Announcement Drift We first confirm the stock-level post announcement drift documented in the prior literature. During the period from 1984 to 2003, at the end of each calendar quarter (Q0), we identify all stocks traded at major stock exchanges have information to estimate standardized unexpected earnings (SUE) from the COMPUSTAT database and with quarter-end stock price no less than $1 in the CRSP database. 9 We compute SUEs based on equation (1) for each stock reported during Q0. During the entire sample period, there are 393,287 stock-quarter observations in our sample. For convenience, we refer to this sample of stocks as the Stock Universe. Within the Stock Universe, we sort stocks 8 Data for SMB t, HML t, and UMD t are obtained from Ken French's website: We compound monthly factor returns into quarterly returns on each of the three factors. 9 The $1 minimum price restriction is imposed to avoid microstructure issues in measuring returns. It also alleviates the impact of transaction costs. 16

18 into equal-weighted decile portfolios based on their SUEs. D1 is the decile of stocks with the lowest SUEs and D10 is the decile of stocks with the highest SUEs. We evaluate returns to the decile portfolios during each of the five quarters starting from Q0, which are referred to as portfolio holding quarters from Q0 to Q4. To compute quarterly portfolio returns, we compound monthly stock returns from CRSP into quarterly returns. If a stock is delisted during a holding quarter, we assume that its return during the remaining period of the holding quarter is the delisting return reported in CRSP. If the CRSP delisting return is missing, we follow Shumway (1997) and assume that the delisting return is -33% if delisting is performance related, and zero otherwise. Naturally, a stock delisted during a holding quarter is not included in any decile portfolio for the subsequent holding quarters. Table 2 report time-series averages of quarterly portfolio returns in each decile portfolio during the five holding quarters (Q0 to Q4) for the stock universe. In Q0, the average return is -2.32% for D1 stocks and 11.20% for D10 stocks. This result is not surprising given the increasing SUE from D1 to D10 stocks in quarter 0. In Q1, the quarter immediately after portfolio formation, the average quarterly return to the D1 portfolio is 1.11%, and it is 5.14% for the D10 portfolio. The difference is 4.03% (t=10.12), significantly positive and consistent with the literature on the return predictability of PEAD. Note that the spreads between D10 and D1 portfolios remain significantly positive for Q2 and Q3, at 2.99% and 1.72% respectively, and turn into negative during Q4 at -0.50%. The decline in the profitability of the PEAD strategy from Q0 to Q3 and the negative profitability during Q4 are consistent with patterns reported by prior studies, e.g., Bernard and Thomas (1990). 17

19 In the last two rows of Table 2, we compute four-factor alphas for the quarterly spreads based on the Carhart (1997) four-factor model. Specifically, we perform the timeseries regression of the portfolio quarterly excess returns on the quarterly four-factor returns over the sample period and use the intercept term (alpha) as the abnormal return for each stock decile. The alpha spreads are 12.61% (t=28.84) in Q0, 3.02% (t=8.33) in Q1, 2.21% (t=5.85) in Q2, 1.24% (t=3.28) in Q3 and -0.63% (t=-1.50) in Q4. PEAD is robust against risk adjustment. We then look at the return predictability of the PEAD anomaly for stocks held by sample mutual funds. In each quarter, we identify all stocks from the stock universe that are held by at least one fund in our mutual fund sample. From 1984 to 2003, there are altogether 277,443 stock-quarter observations in this sample. We refer to the sample of stocks held by sample funds as stocks held by mutual funds. We use the decile ranking of SUE in the stock universe and estimate the equal-weighted portfolio returns on each decile for stocks held by mutual funds. Note that since stocks with price below $1 at the end of Q0 are excluded from the stock universe, they are also excluded from stocks held by mutual funds. 10 We report the result for stocks held by mutual funds in the last six columns of Table 2. The raw return spreads between D10 and D1 stocks from Q0 to Q4 are 12.82%, 3.38%, 2.60%, 1.75%, and -0.53%, respectively. This is analogous to the result for stock universe. The four-factor alpha spreads are consistent with those for stock universe as well. 10 We find that penny stocks account for a negligible proportion of stocks held by funds, although funds hold a fairly large number of stocks with price between $1 and $5. 18

20 Prior studies have documented that the return spreads generated by the PEAD anomaly declines over time (Johnson and Schartz, 2000; Brandt et all, 2006; Ryan and Zorwin, 2003; and Chordia et al., 2006). For example, Chordia et al. (2006) paper shows that the return spread based on PEAD anomaly decreases during 1990s, but increases again after To check if there is any time trend in the magnitude of PEAD, we plot the time-series of annual D10-D1 spreads for the holding period of Q1 in Figure 1. The spreads are plotted by calendar year, after aggregating quarterly spreads into annual observations. However, we do not see a clear time trend in PEAD profitability before and after 1990 as measured by the return difference in extreme decile portfolios sorted by SUEs. In our sample period, PEAD profitability peaks in early 1990s, low in mid and late 1990s and backs up after Do Mutual Funds On Average Follow the PEAD Strategy? Next, we examine whether mutual funds as a whole actively follow the PEAD strategy. As we mention in section 3.3, a positive SUE investing measure (SIM) indicates the use of the PEAD anomaly. As a result, we estimate the time-series average of the SIM measure for all sample funds. In each quarter from 1984 to 2003, we calculate the SIM for each of our sample mutual funds. We compute the following cross-sectional statistics for SIM across sample funds: 5, 25, 50, 75, 95 percentiles, mean, and standard deviation. The first two rows of Panel A of Table 3 report the time-series averages of these cross-sectional statistics. The time series average of the mean SIM for the full sample is 3.14% and the average of the 19

21 median SIM is 2.06%, both significant at the 1% level. This result support that on average, the sample mutual funds follow the PEAD strategy. Also reported in Table 3, we compute the average SIM4. The time-series average of the SIM4 for the full sample is 3.13% and the averaged median SIM4 is 2.17%, both significant at the 1% level. These magnitudes are almost identical to those of the SIM measure. However, SIM4 is less dispersed than SIM. SIM4 has a standard deviation of 7.78%, relative to 11.76% for SIM. To see whether mutual funds as a whole persistently trade on the PEAD anomaly, we plot the time-series distribution of the two fund PEAD trading intensity measures. The annual measures of SIM and SIM4 are the simple averages of the quarterly measures in a year. It clearly shows that both measures are positive in each year of our sample period. Further, to check the robustness and to control the possible impact of other trading strategies on the estimation of SIM measure, we perform the Fama-MacBeth regressions of aggregated fund trading on SUE and other stock characteristics: Tr t,j = β 0 + β 1 SUE t,j + β 2 SUE t-1,j + β 3 SUE t-2,j + β 4 SUE t-3,j + β 5 Size t,j + β 6 BM t,j + β 7 MOM t,j + β 8 Tr t-1,j +ε t,j (7) where Tr t,j is the difference of the fractions of a stock j s outstanding shares purchased by sample funds and the fraction of the shares sold by sample funds in quarter t. SUE t,j is standardized unexpected earnings of stock j reported in quarter t. LgSize t-1,j, LgBM t-1,j, and MOM t-1,j are the logarithm of stock j s market value and book-to-market ratio, and its momentum measured by stock return in the prior 12 months at the end of quarter prior to SUE measurement. Tr t-1,j is fund trading on stock j in quarter t-1. 20

22 Panel B of Table 3 reports the time-series average of the coefficients of the regressions. The coefficient on SUE is 0.42 (t=8.32), suggesting that funds tend to trade in stocks with high SUEs. The coefficients on lagged SUEs are insignificant, indicating funds shuffle their stock holding based on the most recent SUE information. The coefficients on LgSize, LgBM, and MOM are also significantly positive, indicating that funds tend to buy large stock, value stock, and momentum stock. This is consistent with prior studies (e.g., Carhart 1997; Grinblatt, Titman, and Wermers, 1995). However, after controlling for momentum trading, funds still respond actively to earnings momentum in their trading. In summary, the regression results suggest that the use of the PEAD strategy by mutual funds is not due to their investment styles or their trading on price momentum, and that mutual funds use fresh information contained in earnings surprises as it becomes available during Q0, rather than using information contained in earnings surprises during quarters before Q Persistence in the Use of the PEAD Strategy While the statistics in Table 3 suggest that mutual funds on average follow the PEAD strategy, the table also suggests that there is substantial difference across funds in using the strategy. For example, the 5% percentile fund has an average SIM of % while the 95% percentile fund has an average SIM of 22.60%. To further look at the cross-sectional difference, we compare the portfolio holdings of D10 funds with funds that do not actively trade on PEAD information. We define a group of inactive funds that do not actively use the strategy they are the 10% of funds with SIMs closest to, and symmetrically center around, zero. For each quarter, we 21

23 calculate the aggregate portfolio weight of a fund decile in each SUE decile of stocks. Portfolio weight is computed by first summing up the values of stocks in a SUE decile held by all the funds in a SIM decile, and then dividing the summed value by the aggregated value of equity holdings of the same funds. Figure 3 plots the time-series averages of these aggregate portfolio weights on stocks in each of the SUE decile of the D10 funds and the inactive funds. On average, D10 funds invest 5% of their money into D1 SUE stocks and about 17% of their money into D10 SUE stocks. In contract, the investment allocation into different SUE ranks by inactive funds is quite close to each other % in D1 SUE stocks and 10% in D10 stocks. Such cross-sectional difference may either reflect the difference in the ability and aggressiveness of using the strategy, or may simply reflect random chance. The issue is to separate intentional act from chance, which is quite similar to the problem of performance evaluation: high past fund returns could be due to either ability or luck on the part of fund managers; however, persistent good performance is less likely due to luck. This motivates an examination on the persistence in using of the PEAD strategy by funds. To do so, we sort all funds into deciles based on their SIM4, i.e., the average SIM from Q(-3) to Q0. D10 funds are those with the highest SIM4 and D1 funds are those with the lowest SIM4. We report the equal-weighted average SIM in each decile portfolio in Q0 and the subsequent 4 quarters. Due to the fact that some funds report semiannually, when computing SIM for Q1 (Q3), we only include funds reporting holdings for both Q0 and Q1 (Q3). 22

24 In Q0, SIM increases from -6.54% to 15.10% from D1 funds to D10 funds. The average SIM for inactive funds is 0.05, insignificantly different from 0. D10 funds exceed INACTIVE funds by 15.05% (t=33.71) in the average SIM while D1 funds trail INACTIVE funds by -6.59% (t=-12.42). In Q1, the average SIM for D1 funds is -1.54% while that of D10 funds is 9.24%. The SIM of D1 funds is 2.70% (t=3.86) below that of Inactive funds, but the SIM of D10 funds is 13.01% (t=9.45) above that of Inactive funds. The increasing pattern in SIM persists to Q4. A phenomenon worth noting is that in Q4 the difference of SIM between D10 and Inactive funds is 6.36% (t=14.53), still large in magnitude and statistically significant. However, such difference between D1 and Inactive funds is -0.49% (t=-1.27), which is no longer statistical significant. It appears that D10 funds persistently trade on the PEAD anomaly but D1 and Inactive funds do not actively invest in this anomaly. 11 Next, to further explore fund persistent trading in the PEAD anomaly, we calculate the transition probability that contains the empirical probability of being classified in decile j (j=1, 2,, and 10) sorted by SIM4 in Q4 conditional on being classified in decile k (k=1, 2,, and 10) sorted by SIM4 in Q0. To be specific, at the end of each quarter, we rank funds into deciles based on their average SIMs from Q(-3) to Q0. For funds in a given decile, we get the decile rank of all these funds based on their average SIMs in Q1 through Q4. This procedure gives us a 10 by 10 matrix of transition probabilities of SIM4 decile ranks from Q0 to Q4 in each quarter. We average each transition probabilities in this matrix across our sample period and plot these numbers in Figure Note that, to be able to keep a similar set of funds as those included in prior tables, we mix funds funds reporting their holding semi-annually and those with quarterly reporting. In unreported tests, we obtain similar results with a restricted sample that only include funds with quarterly reported holding data. 23

25 Prominently, the probabilities of a D10 fund continuing its D10 ranking during the subsequent four quarters are very high. 32% of D10 funds remain to be in D10 decile in Q4 while Only 5% D10 funds become D1 funds. Although not reported in the paper, Chi-square tests suggest that the conditional probability is significantly higher than 5%, the probability under the null of no persistence. By contrast, the persistence of D1 funds is much weaker: 19% of funds remain to be in D1 decile while 13% of funds switch their decile rank to D10 in Q4. The overall evidence in this section is consistent with the notion that funds in the top SIM4 decile intentionally and actively trade on the anomaly. 4.4 Do Mutual Funds Profit from the PEAD Strategy? We now turn to the central issue of this study: do mutual funds profit from the PEAD strategy? To address this question, we examine the cross-sectional relation between fund SIM measures and fund performance. We construct four fund performance measures: before-expense net return, afterexpense net return, before-expense four-factor adjusted returns, and after-expense fourfactor adjusted returns. Fund expenses are fees paid by fund investors to fund companies. As argued by Berk and Green (2004), due to competitive capital supply from fund investors, fund managers who are skilled may be able to extract all the rent from investors via charging high fees. Therefore the before-expense performance measure better reflects the skill of fund managers in taking advantage of market anomalies. The four-factor alpha measure is detailed in Section 3.4. In each quarter 0, we sort sample funds into deciles based on their 4-quarter average SIM (SIM4) from Q(-3) to Q0. We compute the performance of each fund in 24

26 four periods: Q(-3) to Q0, Q0, Q1, and Q1 to Q4. Fund returns from Q(-3) to Q0 are reported because we sort funds into deciles based on their 4-quarter average SIMs in the same period. Q0 is the quarter that funds implement the PEAD trading strategy. Q1 and Q1 through Q4 are the first quarter and year after fund PEAD trading. We calculate the averages of the performance measures across all funds in the same SIM4 decile. Table 5 reports the time series averages of the four performance measures for each fund decile. Our main focus here is the profitability of D10 funds, because they follow the PEAD strategy most actively. For comparison purpose we also report the performance of inactive funds, which by definition do not actively use the strategy. Panel A of Table 5 reports fund net returns before and after expense. Over Q(-3) to Q0, the average annual net return of D10 funds is 13.85% before expense and 12.83% after expenses. These numbers exceed the respective returns of inactive funds, by 0.39% and 0.38%, though they are insignificant different 0. In Q0, there is no significant different raw return between D10 and inactive funds, no matter the return is measured before or after fund expenses. These results suggest active fund trading do not bring an immediate benefit to mutual funds. However, trading on PEAD is profitable after Q0. In Q1, the average annual net return of D10 funds are 4.10% before fund expenses and 3.80% after fund expenses, significantly higher than 3.41% and 3.13% for inactive funds by 0.62% (t=2.04) and 0.69% (t=2.19). The same significant result holds for the subsequent one year after portfolio formation. For the period of Q1 to Q4, the difference between D10 and inactive funds is 2.33% (t=2.91) for the raw return before fund expenses and it is 1.99% (t=2.97) after fund expenses. This suggests that D10 funds, by taking advantage of the post 25

27 earnings announcement drift, do generate superior performance that benefits fund investors. As reported in Panel B of Table 5, performance based on four-factor risk adjusted returns exhibits similar patterns. For example, before-expense adjusted return differences between D10 funds and INACTIVE funds are 0.31% (t=0.52), 0.24% (t=1.41), 0.66% (t=2.20), and 2.28% (t=2.83) for the periods of Q(-3) to Q0, Q0, Q1 and Q1 to Q4. Further, while after-expense adjusted returns for D10 funds have been insignificantly positive, they are significantly higher than those for inactive funds. Funds aggressively exploring the PEAD anomaly have a better return after risk adjustment. To examine the time series pattern of the profitability of funds that most actively trade on the PEAD anomaly, we plot the four-factor adjusted return of D10 funds in each of the sample year in Figure 5. Except for 1985 and 1991, before-expense adjusted returns in other years over our sample period are positive. Several concerns arise in concluding that better returns after portfolio formation period are actually attributable to fund use of the PEAD anomaly. As discussed in Section 4.2 (?), other trading strategies may be correlated with the PEAD anomaly. In addition, prior studies suggest that fund characteristics may affect fund performance. For example, Chan et al suggest fund size negatively affect fund performance while fund family size positively affects fund performance. In Table 6, we perform regressions of fund performance on SIM4 and a number of control variables. It takes the following form: R i,t =β 0,t + β 1,t SIM4 i,t + β 2,t SIZESCORE4 i,t + β 3, tbmscore i,t + β 4,t MOMSCORE i,t + β 5,t FEE i,t + β 6,t TURNOVER i,t + β 7,t SIZE i,t + β 8,t FAMSIZE i,t + β 9,t AGE i,t 26

28 + β 10,t FLOW i,t + β 11,t STDEV i,t + ε i,t (7) where R i,t is either measured by fund net return or four-factor adjusted return in Q1 or Q1 to Q4. SIM4 is the average SIM over Q(-3) to Q0. SIZESCORE4, BMSCORE4, and MOMSCORE4 are the averages of cross-sectionally standardized size, B/M, and momentum of stocks held by a fund weighted by the fund trading over Q(-3) to Q0. 12 Fee is the quarterly fund expense. TURNOVER is quarterly fund turnover. SIZE is the logarithm of fund total net assets (TNA). FAMSIZE is the logarithm of fund family TNA. LOGAGE is the logarithm of fund age. FLOW is the growth rate of TNA of a fund after adjusting for the appreciation of the TNA. STDEV is the standard deviation of fund net return in the previous year. To control for serial correlations, we consider the Newey- West adjusted t-statistics in an order of lag 8. The first two columns report the results when we use net returns or the four-factor adjusted returns in Q1 on SIM4, three score measures and various fund characteristics. We find the coefficient on SIM4 are 0.53 (t=2.16) in the net return regression and it is 0.61 (t=2.04) in 4-factor adjusted return regression. In Columns (3) and (4), we measure fund performance using returns from Q1 to Q4. We find similar results. The coefficient on SIM4 are 0.57 (t=2.65) in the net return regression and it is 0.65 (t=2.73) in 4-factor adjusted return regression. The results suggest that funds performance in Q1 and Q1 through Q4 is positively associated with PEAD trading after controlling potential trading on other anomalies and alternative fund characteristics. 4.5 A Closer Look at Transaction Cost and Interim Trading 12 Similar to the SIM measure, when constructing these score measures, we require the stock prices to be greater than $1 at the end of each quarter. 27

29 The results above suggest that funds actively following the PEAD strategy are not profitable in Q0 but significantly profitable in Q1. That is, transaction costs have not eliminated the profitability of the strategy. This finding appears to be consistent with Ke and Ramalingegowda (2005) suggest transient institutional investors arbitrage generates an abnormal return, however, inconsistent with Chordia et al (2005) s assertion that transaction costs inhibit the exploitation of the PEAD. In this section, we provide further evidence on transaction costs to reconcile our evidence with prior studies. The reason why prior studies on whether trading on PEAD is profitable have reached mixed conclusions is that they differ in the measure of transaction costs and the timing of the arbitrage activity. For example, Ke and Ramalingegowda (2005) assume that investors can trade on the anomaly within the earnings announcement month, and they use the empirical transaction cost function originally estimated by Keim and Madhavan (1997) to estimate the transaction cost in the next 3, 6, and 9 holding period. Chordia et al. (2006), in each month, sort sample firms into deciles based on the most recent SUE and follow Jegadeesh and Titman (1993) in forming decile portfolios to estimate a six month holding period return after transaction costs. They consider the transaction cost measure of Keim and Madhavan (1997) as well as the price impact measures estimated by Korajczyk and Sadka (2004), and by Chen, Stanzl, and Watanabe (2004), where the latter two measures are based on the trades and quotes (TAQ) data provided by NYSE. 13 Due to these differences, Ke and 13 Battalio and Mendenhall (2006) assume that investors can trade on PEAD during the intraday period immediately after earnings announcements, or at the first market closing after earnings announcements. The transaction cost measure they consider is mainly the quoted bid-ask spread. Ng, Rusticus, and Verdi (2006) assume trading at the end of the calendar quarter after announcements. They consider transaction costs in the form of quoted spreads, effective spreads, as well as LDV, an indirect cost measure developed by Lesmond et al (1999), which implicitly reflects the effects of various transaction cost components commissions, bid-ask spreads, and price impact. 28

30 Ramalingegowda (2005) and Battalio and Mendenhall (2006) find that the PEAD strategy is highly profitable, whereas Chordia et al. (2006) and Ng, Rusticus, and Verdi (2006) report that the strategy either generates insignificantly positive profit or even loses money after transaction costs. While Table 5 shows that trading on the PEAD anomaly is not profitable in Q0 but profitable in Q1, it is unclear of the role of transaction costs and the effect of the timing of trading in Q0 and Q1. Here, we decompose fund net returns in Q0 and Q1 to provide further evidence. Consider the before-expense fund net return for Q0. It can be decomposed into three components: 1) the return generated by holding stocks passively from beginning to the end of the quarter (passive effect), 2) return generated by fund trading during Q0, possibly in response to earnings announcements (interim trading effect), and 3) transaction costs incurred during Q0. The passive effect can be measured directly using buy-and-holding returns in Q0 on stocks held by funds at the beginning of Q0. We follow Kacperczyk et al. (2006) and measure the joint effect of interim trading and transaction costs by return gap, which is the difference between before-expense net return and the buy-and-hold passive return. Finally, we consider two direct transaction cost measures used in the above studies: transaction costs estimated by Keim and Madhavan (1997) and Wermers (2000) (hereafter KMCOST) and the price impact measure by Korajczyk and Sadka (2004) (hereafter KSCOST). We provide the details in estimating these transaction costs in the Appendix. We report the Q0 net return decomposition in Panel A of Table 7. The first column, we report before-expense fund net return sorted by the average SIM measure from Q(-3) to Q0 (SIM4 in Q0). The return difference between D10 and inactive funds of 29

31 0.30% is insignificant different zero, suggesting trading on the PEAD anomaly is not profitable in Q0. We then decompose fund net returns into gross returns weighted by portfolio holding at the beginning of quarter 0 and return gap (GAP). D10 gross return exceeds that of inactive funds by 0.37% (t=1.36). The difference for GAP is -0.07%. Our results on GAP indicate that the net benefit of interim trading and transaction costs in Q0 is not statistically significant. We then look at the two direct transaction costs measures to see if the insignificant GAP spread is due to transaction costs. The equal-weighted averages of KMCOST and KSCOST occurred in Q0 in each of the SIM4 sorted deciles are reported in the last two columns in Panel A, Table 7. We observe a U-shape of both transaction cost measures across the SIM4 deciles. More importantly, the average KMCOST for D10 funds is 0.82% per quarter, significantly higher than the 0.45% of INACTIVE funds. The average KSCOST for D10 funds is 1.05%, also significantly higher than the 0.61% of INACTIVE funds. 14 Taken together, our evidence suggests that because the passing holding at the beginning of Q0 does not provide higher returns, and the interim trading benefit during Q0 is tradeoff by the transaction cost during Q0, funds trade on the PEAD anomaly do not generate higher before-expense fund net return. However, Table 5 shows that funds trade on the PEAD more aggressively have higher return in Q1. We decompose before-expense fund net return in Q1 to explore the reason. The decomposition is similar to that of Q0, except that we further decompose gross return based on stock holding as the beginning of Q1 into two parts: (i) passive returns given fund holding at the beginning of Q0 and (2) passive return given fund 14 This result is consistent with Chordia et al (2005) that point out KMCOST may underestimate transaction costs. 30

32 trading during Q0. Panel B of Table 5 reports the return decomposition in Q1 and direct transaction costs sorted by SIM4 in Q0. Note that the sorting variable is SIM4 in Q0, which is the same as the sorting variable in Panel A. The reason is that we want to know the impact of trading in Q0 on the return in Q1. The first column shows that, in Q1, D10 funds significantly outperform INACTIVE funds by 0.69% (t=2.18). Among this margin of 0.69%, 0.26% (t=1.53) comes from passive return from holding starting at the beginning of Q0, 0.45% (t=3.92) comes from the passive return by trading in Q0, and % (t=-0.08) comes from GAP in Q1. Finally, we perform regression of return gap on SIM4 and different transaction costs, all measured in quarter 0, to test if the net benefit of interim trading in Q0 is positively related to trading on the PEAD strategy (SIM4) after controlling for transaction costs. The full regression is as the follows: GAP i,t =β 0 + β 1 SIM4i,t + β 2 COSTi,t +β 3 INTENSITY i,t + β 4 EXETREME i,t + β 5 IPO i,t + β 6 FEE i,t-1 + β 7 TURNOVER i,t-1 +Β 8 SIZEi,t-1 + β 9 FAMSIZE i,t- + β 10 AGE i,t-1 + β 11 FLOW i,t-1 + β 12 STDEV i,t-1 + β 13 SIZESCORE4 i,t-1 +β 14 BMSCORE4 i,t-1 + β 15 MOMSCORE4 i,t-1 +ε i,t (8) where SIM4 measures the use of the PEAD anomaly. KMCOST and KSCOST are the direct transaction costs measures; INTENSITY is the sum of the product of absolute value of fund weight changes and absolute value of cross-sectionally standardized SUEs; EXTREME is the aggregate absolute value of weight changes in the two extreme SUE deciles. All these four measures are used to capture the effect of transaction costs in trading on the PEAD anomaly. We follow Kacperczyk, Sialm, and Zheng (2006) to control fund characteristics in the regressions. IPO is the percentage of IPO holding in a 31

33 fund. As IPOs are typically underpriced, fund investment in IPOs is a measure of interim trading benefit beyond trading on the PEAD anomaly. FEE is the quarterly fund expense. TURNOVER is quarterly fund turnover. SIZE is the logarithm of fund total net assets (TNA). FAMSIZE is the logarithm of sum of TNA of funds belonging to the same fund family. AGE is the logarithm of fund age, measured as the number of years since fund organization. FLOW is the growth rate of TNA of a fund after adjusting for the appreciation of the TNA. STDEV is the standard deviation of fund net return in the previous year. SIZESCORE4, VALUESCORE4, and MOMSCORE4 are also included. The results are reported in Table 8. The first column shows that without controlling for transaction costs, the coefficient on SIM4 is insignificantly positive. This is consistent with our result in Panel A of Table 7: no obvious pattern of return gap across SIM4 rankings. Yet, column 2 shows that after considering transaction costs, the coefficient on SIM4 is 0.26 (t=2.05), significant at the 5% level. We obtain similar result when using KSCOST as the direct transaction cost measure in column 3. It appears that trading on PEAD does generate instant benefit for mutual funds in Q0, but the benefit is eroded by the high transaction cost during the trading. 4.6 The Effect of Arbitrage Risk The results thus far suggest that investing on the PEAD is profitable after transaction cost. This is puzzling because the PEAD anomaly exists even though mutual funds appear to profit from it. Why mutual funds do not exploit the abnormal returns from investing the PEAD strategy to the point of totally eliminating the profitability? 32

34 Based on our evidence, transaction cost alone does not explain why investing on the PEAD anomaly remains profitable. We examine an explanation based on arbitrage risk (Shleifer and Vishny 1997). For arbitrage risk to serve as an impediment to the implementation of the PEAD strategy by mutual funds, there are three necessary conditions. First, idiosyncratic returns to stocks with extreme SUE funds must be highly volatile. Mendenhall (2004) shows firms with high levels of arbitrage risk experience drifts that, ceteris paribus, between 3 to 4 percentage points per quarter larger than firms with low levels of arbitrage risk. Here, we provide evidence on the second and third conditions. That is, funds aggressively following the strategy cannot effectively diversify and should exhibit high performance fluctuation; investors money flow in and out of these funds should also be highly volatile. We first examine several characteristics of mutual funds in each SIM4 decile, including (i) total net assets (TNAs), (ii) the percentage of assets invested in stocks, (iii) the percentage of assets in cash, (iv) the number of stocks held by a fund, and (v) fund portfolio concentration, as measured by the Herfindahl index of portfolio weights. We measure the first three characteristics at the end of each year and obtain the data from the CRSP mutual fund database. The number of stocks held by a fund and the Herfindahl index are measured at the end of each quarter and the data are from the CDA mutual fund holding data. The Herfindahl index is calculated as the sum of the squared portfolio weights (w i,j,t ) of stocks held by a fund: N 2, t = i, j, t ) j= 1 H i ( w (9) A higher Herfindahl index indicates a less diversified portfolio. 33

35 The first 5 columns in Table 9 reports the averages of these fund characteristics in each fund decile (sorted by fund SIM4) as well as for the INACTIVE fund group. Several patterns are worth noting. First, funds actively pursuing the PEAD strategy, D10 funds, are smaller in terms of total net assets. The average TNA of D10 funds is $ million and that of the INACTIVE funds is $ million; the difference is significant at the 1% level (t = -2.63). Smaller funds can be more active in using the PEAD strategy possibly because they are nimbler to implement aggressive investment strategies. It is also more costly for smaller funds to hold many stocks for diversification purpose. Second, D10 funds appear to be less diversified than INACTIVE funds. The average number of stocks held by D10 funds is 93, and by the INACTIVE funds is 109; the difference is significant (t = -5.71). The average Herfindahl index for D10 funds is 3.12% and that for INACTIVE funds is 2.79%; the difference is significant (t = 5.34). These results are consistent with the notion that funds aggressively following the PEAD strategy may not be able to effectively diversify away idiosyncratic risks. Next, we examine the impact of the PEAD strategy on fund return volatility. We sort funds into deciles by SIM4 at the end of each quarter t, and get monthly return of each decile in the following year. A fund s total risk is its standard deviation of monthly net returns in the subsequent year and its idiosyncratic risk is the standard deviation of residuals from the 4-factor models in the subsequent year. We first average the return volatility in each fund decile in each quarter and then calculate their time-series average. The results are reported in Table 9. The average annualized net return volatility is 18.77% for D10 funds and 14.55% for INACTIVE funds; the difference is 4.22% and significant at the 1% level (t=2.87). The difference between D10 and INACTIVE funds in 34

36 the volatilities of the 4-factor residual returns of 2.33% is also significant at 5% level (t=2.30). These results suggest that funds more actively following the PEAD strategy exhibit significantly greater performance volatility. In the last two columns in Table 9, we examine the fund flow volatility of mutual funds that aggressively follow the PEAD strategy. Following Sirri and Tufano (1998), we calculate monthly fund flow as TNA TNA i, τ i, τ 1 * (1 + i, τ ) FLOW i, τ = (10) TNA i, τ 1 R where TNA i,τ is the total net assets of fund i at the end of month τ and R i, τ is fund monthly return. To ensure the consistency of the flow measure, we exclude monthly fund flow observations from our analysis if a fund experiences merger during the month. Similar to return volatility, we sort funds into deciles by SIM4 at the end of each quarter t, and get monthly equal-weighted fund flows of each decile in the following year. Fund flow volatility is the standard deviation of monthly flows in the subsequent year (FlowVol). The residual fund flow volatility is the residual term from annual crosssectional regressions of fund flow volatility: FlowVol i,t =β 0,t +β 1,t Size i,t-1 +β 2,t Exp i,t-1 +β 3,t Load i,t-1 +β 4,t Age i,t-1 +β 5,t R i,t-1 +ε i,t (11) where the logarithm of fund size (Size), expense ratio (Exp), fund load dummy (Load), fund age (Age), and average fund annual monthly return (R) are measured at the end of previous year. We first average the return volatility and flow volatility across fund deciles in each quarter and then calculate their time-series average. The choice of these control variables is based on prior literature, e.g., Sirri and Tufano (1998). The annualized flow volatility is 15.86% for D10 funds and 10.46% for INACTIVE funds; the difference is significant (t=4.16). The corresponding values for the 35

37 residual flow volatility are 3.88% and -0.98%; the difference is once again significant (t = 3.27). These results suggest that funds more actively following the PEAD strategy exhibit greater fund flow volatility than funds inactive with respect to the PEAD strategy. 4.7 Mutual Fund PEAD Investment and SUE Profitability In this section, we explore the intertemporal dynamics of mutual fund trading intensity in the PEAD anomaly and PEAD trading profitability. We hypothesize that, On the one hand, profitability of PEAD trading positively affects mutual fund investment in the anomaly. On the other hand, mutual fund PEAD trading negatively affects the PEAD return predictability. That is, more intensive PEAD related trading mutual funds lowers the profitability of PEAD trading. Our analysis is partly motivated by the observation that stock returns become less sensitive to earnings-related information (e.g., Lev and Zarowin 1999 and Ryan and Zarowin 2003). Johson and Schwartz (2000) show that the hedged portfolio four-quarter abnormal return for the period is about twothirds of the magnitude during Brandt et al. (2006) present similar evidence on declining SUE profitability declines over time. For example, the one-quarter ahead average abnormal return from the SUE strategy decreases by 0.40%, from 1.21% in the period to 0.81% in the period. If the declining PEAD profitability is attributable to the investment behavior of savvy investors, the investment practice of mutual funds, a group of active-trading and sophisticated investors, would have a substantial impact on the profit of this trading anomaly. To test the above hypotheses, we perform the following regression: SIM4 t+3 =β 0 +β 1 SIM4 t-1 +β 2 PROF t-1 + β 3 DEF t-1 +β 4 DP t-1 +β 5 TBILL t-1 +β 6 TERM t-1 + β 7 SENTI t-1 +v t (12) 36

38 PROF t = γ 0 + γ 1 SIM4 t-1 + γ 2 PROF t-1 + γ 3 DEF t-1 + γ 4 DP t-1 + γ 5 TBILL t-1 +γ 6 TERM t-1 + γ 7 SENTI t-1 +v t (13) Equation (12) examines if profitability of PEAD trading positively affects mutual fund investment in the anomaly and (13) looks at if mutual fund PEAD trading negatively affects the PEAD return predictability. The dependent variable in equation (12), SIM4, is the equal-weighted mean of the average SIM from the quarter of portfolio formation (Q0) to the 3rd quarter afterward (Q3). It is used as the average trading intensity in the PEAD anomaly performed by mutual funds. The dependent variable in equation (13), PEAD trading profitability (PROF), is measured by the coefficient on SUE from the crosssectional regressions of the returns on stock SUEs in each quarter. Both raw return and four-factor adjusted returns are used in the estimation. In both equations, lagged SIM4 and PROF are included as explanatory variables. In addition, a set of macro variables are included. DEF is the default premium. DP is the dividend/price ratio. TBILL is risk free rate of return. TERM is the term premium. SENTI is the investor sentiment index. Young and Simon (2003) find that, these macro variables, except for SENTI, can explain a significant portion of variation in time-series profitability of PEAD trading. We use the GMM procedure to estimate these equations where a Bart Kernel is used to estimate the density function. We ues the Newey-West test with an order of 8-quarter lags for the t-statistics. In the first column of Table 10, we report the coefficients in the regression of future PEAD trading intensity (SIM4) on past profitability of PEAD. The coefficient on lagged PROF is (t=2.99), consistent with the hypothesis that higher PEAD profitability leads to more intensive PEAD trading. In addition, the coefficient on lagged SIM4 is 0.79(t=2.58), indicating strongly persistent in PEAD trading by mutual funds. 37

39 The second column reports the results of the regression of PROF on lagged SIM4. Here PROF is estimated based on raw return. The coefficient on SIM4 is (t=-2.33). In words, a more intensive trading in PEAD reduces the future profitability of the PEAD anomaly. The coefficient on lagged PROF is insignificantly positive. Further, PEAD profitability is inversely related to default premium, positively related to the risk free rate of return and the term premium. These are consistent with the results reported in Young and Simon (2002). In Columns (3) and (4), we report the results when estimating PEAD profitability using the four-factor adjusted returns. The results are generally consistent with those reported in the first two columns. Taken together, our evidence in this section support the hypotheses that (i) greater (less) PEAD profitability results in more (less) intensive trading in arbitraging the predictive return of the PEAD anomaly, and (ii) greater PEAD trading dissipates PEAD profitability. 5. Conclusion This paper provides evidence that mutual funds that actively follow the PEAD strategy make profits, net of actual transaction costs. The 10 percent of the funds that most actively follow this strategy make a profit of 2.68% as measured by the Carhart 4- factor alpha before fund expenses in the year subsequent to earnings announcement, which are both statistically and economically significant. These funds outperform funds inactively trading on the PEAD anomaly by a margin of 2.28% in term of their fourfactor adjusted alpha. 38

40 Profitable implementation of an anomaly-based trading strategy has been the subject of several prior studies. However, these studies rely on estimated values of transaction costs. Different from these studies, we examine this issue by considering actual transaction costs. We employ databases of mutual funds that provide for each of the funds not only the stockholding information but also information on returns net of actual transaction costs. The stockholding data allow us to determine which mutual funds actively pursue a given trading strategy. The net fund return data then enable us to assess their profitability. Our results show that funds more actively using the PEAD strategy exhibit higher volatility in both fund returns and fund flows. These factors represent the adverse consequences of arbitrage risks that funds face when they trade aggressively on a market anomaly (Shleifer and Vishny 1997). These results seem to provide an explanation for why mutual funds do not more aggressively pursue the PEAD strategy until the abnormal returns after transaction costs from pursuing the strategy are completely eliminated. Finally we explore the intertemporal dynamics of fund PEAD trading intensity and PEAD profitability. We find, on the one hand, that greater PEAD trading dissipates PEAD profitability, and, on the other hand, that greater (less) PEAD profitability results in more (less) intensive trading in arbitraging the predictive return of the PEAD anomaly. 39

41 Appendix Our first transaction costs measure, named as KMCOST, follows Keim and Madhavan (1997) and Wermers (2000). We use the following fitted regressions in Wermers (2000) without the year factor to estimate the total cost of purchasing or selling stock j during quarter t, as a percentage of the total value of the trade: B Nasdaq 1 C j, t = D j, t Trsize j, t 0.084Log( mcap j, t ) ( P S Nasdaq 1 C j, t = D j, t Trsize j, t 0.059Log( mcap j, t ) ( P j, t j, t ) ) Where C, is the transaction cost for buying stock j and B j t C, is the transaction cost for S j t selling stock j. D, is a dummy variable that equals one if the trade occurs on Nasdaq Nasdaq j t and zero otherwise, Trsize j,t is the ratio of the dollar value of the purchase to the market vapitalization of the stock, Log (mcap j,t ) is the natural log of the market capitalization of the stock (expressed in $thousands), and P j,t is the stock price at the time of the trade. The KMCOST of a fund in a quarter is the sum of the cost of all trades during that quarter divided by the total value of the stock holding of the fund at the beginning of that quarter. The second transaction cost measure, named as KSCOST, follows Korajczyk and Sadka (2004). The total price impact of a trade of q j,t shares is calculated through q 0 f ( p, x) dx 0 q p BKHK λ j, τ p q BHK x mcap j, t j, t λ j τ j, t mcap ji, t j, t ( e 1) dx = ( e 1) BHK λ j, τ, p j, t q j, t 40

42 BHK Where λ j, τ is estimated using coefficients reported in Table 2 of Korajczyk and Sadka (2004) and stock characteristics at the end of quarter t-1. Specifically, for stock listed in NYSE/AMEX and Nasdaq, BHK λ j, τ (*10 5 ) is estimated, respectively, as below: λ, = X X X X X X X X X 9 BHK j τ λ, = X X X X X X X X 9 BHK j τ where X1 = Market cap at the end of last month divided by the average market cap of CRSP, minus one; X2 = Total volume during the last three months divided by the average firm volume on NYSE, minus one; X3 = Stock price at the end of last month divided by the price six month prior, minus one; X4 = Absolute value of X3; X5 = Dummy variable equal to unity if the firm is included in the S&P 500 index; X6 = Dividend yield; X7 = R2 of returns regressed on NYSE index, (monthly returns over the last 36 months); X8 = Dummy variable equal to unity if the firm is traded on NYSE; X9 = Inverse of stock price of the previous month. The KSCOST of a fund in a quarter is the sum of the price impact of all trades during that quarter divided by the total value of the stock holding of the fund at the beginning of that quarter. 41

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46 Shleifer, A. and R. Vishny, 1997, The Limits of Arbitrage. Journal of Finance 52 (1997): Wermers, R. 2000, Mutual Fund Performance: An Empirical Decomposition into Stock- Picking Talent, Style, Transactions Costs, and Expenses. Journal of Finance 55 (2000):

47 Table 1: Summary Statistics for Mutual Funds Number of distinct funds 2, ,253 AG funds GRO funds 1, G&I funds Number of fund-quarter observations 58, ,639 2,562 4,696 Total Net Assets ($ Millions) Net Return (%/year) Turnover (%/year) Load (%/year) Expense Ratio (%/year) Age (year) # of stocks held Mean # of stocks held Median % semiannual reporting funds This table reports summary statistics for the sample of actively managed US equity mutual funds with Thomson Financial CDA portfolio holdings data and CRSP fund returns data. To be included in the analysis, the reporting period of a fund between the current and the lagged quarter should be no greater than six months. Fund total net assets, annual return, turnover, annual load, expense ratio, and fund age are obtained from CRSP. Fund annual load is the total load divided by 7, and fund age is the number of years since fund organization. Information on the average and median numbers of stocks held by funds is from Thomson Financial. Percentage of funds with semiannual reporting is the number of funds with semiannual reporting divided by the total number of funds in each quarter. We average these fund characteristics across funds in each year and then report their time series means. The sample period is from 1984 to

48 Table 2: Stock Returns of Decile Portfolios Sorted by SUEs SUE # of stocks Stock Universe Q0 Q1 Q2 Q3 Q4 # of stocks Stocks Held by Sample Funds Q0 Q1 Q2 Q3 Q4 A. Raw Returns D D D10-D (t-stat) (32.06) (10.12) (8.20) (4.69) (-1.37) (32.47) (8.49) (7.07) (4.70) (-1.39) B. 4-factor Alphas D10-D (t-stat) (28.84) (8.33) (5.85) (3.28) (-1.50) (30.12) (7.02) (4.53) (2.62) (-1.69) This table compares the characteristics of the CRSP/COMPUSTAT stock universe with stocks held by sample mutual funds. Stock universe refers to all stocks in the CRSP database with price greater than $1 and with standardized unexpected earnings (SUE) information from COMPUSTAT database. Fund-held stocks additionally require that a stock is held by at least one of our sample funds at the end of a quarter. In each quarter t, we sort stock into deciles based on SUE reported within quarter t. We report the time series average of equal-weighted SUE, stock returns in quarter t and the subsequent four quarters, and number of observations in each SUE decile. Raw returns are obtained directly from CRSP dataset after adjusting delisting returns, and the four-factor alpha in each decile is the intercept term of the time-series regression of decile portfolio return on the four-factor loadings in each quarter. The statistics of the return differences between D10 and D1 stocks are reported in the parentheses. The sample period is from 1984 to

49 Table 3: Fund Trading in PEAD Anomaly Panel A: SUE Investing Measures (%) 5% 25% Mean Median 75% 95% Std SIM (t-stat) (-44.26) (-16.73) (19.78) (16.30) (40.10) (51.43) (57.59) SIM (t-stat) (-40.62) (-12.23) (32.44) (29.91) (52.10) (47.28) (49.87) Panel B: Stock Level Regressions of Fund Trading on SUE SUE t SUE t-1 SUE t-2 SUE t-3 LgSize t-1 LgBM t-1 MOM t-1 Tr t-1 Adj R 2 Coeff (t-stat) (8.32) (0.23) (-0.15) (-0.17) (5.31) (2.38) (8.65) (1.94) Panel A reports the summary statistics of the SUE Investing Measure (in percent) for all sample funds. To be included in the analysis, the reporting period of a fund between the current and the lagged quarter should be no greater than 6 months. In each quarter t, the following SUE investing measure is computed: N ~ SUE j, t µ ( SUEt ) SIM, i, t = ( wi, j, t wi, j, t k ) * ( ) (k=1 or 2), where w i, j, t is the portfolio weights on stock j j = 1 σ ( SUEt ) held by fund i reported within quarter t; wi, j, t k is the lagged portfolio weights on stock j held by fund i after adjusting for price changes in buy-and-hold portfolios. SUE j, is the standardized unexpected earnings t reported in quarter t for firm j. µ (SUE) and σ the cross-sectional mean and standard deviation of SUEs for all stocks in the CRSP universe in quarter t. SIM4 is the average SIM of a fund from quarter t-3 to quarter t. We calculate the summary statistics of SIM across funds in each quarter and then computed their time-series average. Panel B reports the coefficients of the Fama-MacBeth regressions of aggregated fund trading on SUE and other stock characteristics: Tr t, j = SUEt, j + SUEt 1, j + SUEt 2, j + SUEt 3, j + LgSizet, j + LgBMt, j + MOMt, j + Trt 1, j + ε. Tr t, j t,j is the difference of the fractions of a stock j s outstanding shares purchased by sample funds and the fraction of the shares sold by sample funds in quarter t. SUE t,j is standardized unexpected earnings of stock j reported in quarter t. LgSize t-1,j, LgBM t-1,j, and MOM t-1,j are the logarithm of stock j s market value and book-to-market ratio, and its momentum measured by stock return in the prior 12 months at the end of quarter prior to SUE measurement. Tr t-1,j is fund trading on stock j in quarter t-1. We perform the cross-sectional regression each quarter and report the time-series average of the coefficients and their t-statistics. In both panels, the timeseries t-statistics are in the parentheses. The sample period is from 1984 to

50 Table 4: Persistence of SIM Measures SIM4 0 Rank SIM 0 (%) SIM 1 (%) SIM 2 (%) SIM 3 (%) SIM 4 (%) D (-24.37) (-5.32) (1.12) (2.84) (3.41) (-14.66) (-1.92) (3.31) (4.12) (5.92) (-5.92) (3.98) (4.80) (5.54) (6.03) (3.18) (6.09) (5.99) (7.78) (6.76) (9.47) (8.58) (8.62) (10.35) (9.11) (16.28) (8.69) (8.29) (12.22) (11.02) (22.13) (9.83) (10.78) (15.24) (12.25) (25.70) (11.16) (12.79) (14.32) (12.64) (29.81) (13.17) (13.94) (17.58) (16.76) D (34.28) (21.27) (19.94) (17.40) (16.70) INACTIVE (t-stat) (0.36) (5.97) (5.25) (7.77) (6.95) D1-INACTIVE (t-stat) (-12.42) (-3.86) (-1.93) (-1.84) (-1.27) D10-INACTIVE (t-stat) (33.71) (9.45) (15.58) (11.33) (14.53) This table reports the equally-weighted averaged SIMs (in percent) in the quarter of portfolio formation (Q0) and the subsequent four quarters (Q1 through Q4) in each decile portfolio. The sorting variable is the 4-quarter average SIM (SIM4) in Q0, measured as the average of SIM measures from quarters -3 to 0. D10 funds have the highest SIM4 0 and D1 funds have the lowest SIM4 0. INACTIVE funds are the 10% of funds with the 4-quarter average trading SIM closest to, and centered around, zero in Q0. The time-series t- statistics are in the parentheses. The sample period is from 1984 to

51 Table 5: Fund Returns across SUE Investing Measures Panel A: Fund Net Returns across SIM4 Deciles (%) Before Expense After Expense SIM4 0 Rank Q(-3)-Q0 Q0 Q1 Q1-Q4 Q(-3)-Q0 Q0 Q1 Q1-Q4 D D INACTIVE D10 INACTIVE (t-stat) (0.58) (1.23) (2.18) (2.91) (0.22) (0.82) (2.29) (2.97) Panel B: Four-factor Adjusted Returns across Fund Deciles sorted by SIM4 Deciles (%) Before Expense After Expense SIM4 0 Rank Q(-3)-Q0 Q0 Q1 Q1-Q4 Q(-3)-Q0 Q0 Q1 Q1-Q4 D (2.59) (0.85) (1.87) (2.72) (-0.27) (-0.98) (-1.10) (-2.15) (2.42) (1.32) (0.45) (0.73) (0.09) (-0.98) (-1.93) (-2.17) (2.85) (1.27) (1.01) (1.02) (0.08) (-0.61) (-1.06) (-2.06) (2.80) (1.41) (1.39) (2.40) (-0.27) (-0.55) (-0.59) (-0.40) (1.73) (1.47) (1.07) (1.62) (-1.20) (-0.55) (-1.05) (-1.85) (1.10) (0.97) (1.21) (1.84) (-1.70) (-0.93) (-0.85) (-1.48) (0.74) (0.58) (0.88) (2.42) (-1.59) (-1.11) (-0.92) (-0.12) (1.08) (1.52) (0.51) (2.32) (-1.43) (0.30) (-0.95) (-0.03) (0.53) (0.46) (1.59) (2.67) (-1.56) (0.59) (0.07) (0.78) D (2.08) (1.82) (2.37) (3.61) (0.28) (0.75) (1.01) (2.14) INACTIVE (1.65) (1.84) (0.90) (1.52) (-0.27) (-0.09) (-0.91) (-1.35) D10 INACTIVE (t-stat) (0.52) (1.41) (2.20) (2.83) (0.74) (1.19) (1.97) (2.75) This table reports the equal-weighted averaged fund returns before and after expenses around Q0 across fund deciles sorted by the 4-quarter average SIM (SIM4) in Q0. D10 funds have the highest SIM4 0 and D1 funds have the lowest SIM4 0. INACTIVE funds are the 10% of funds with SIM4 closest to, and centered around, zero. The average fund performance for decile portfolios, the INACTIVE funds, and the differences between D10 and INACTIVE funds are reported. Panel A measures fund performance using net returns and Panel B measures fund performance using four-factor adjusted returns. The Newey-West tests in an order of lag 8 are performed for the performance analyses of Q(-3) to Q0 and Q1 to Q4. The t-statistics are reported in the parentheses. The sample period is from 1984 to

52 Table 6: Regression of Fund Returns on SUE Investing Measures Q1 Q1 to Q4 Net Returns 4-factor Adjusted 4-factor Adjusted Net Returns Returns Returns INTERCEPT (3.53) (1.47) (6.51) (1.28) SIM4 t (2.16) (2.04) (2.65) (2.73) SIZESCORE4 t (2.47) (1.80) (2.45) (1.96) BMSCORE4 t (0.34) (0.49) (-1.05) (-0.60) MOMSCORE4 t (1.38) (1.49) (1.51) (1.71) FEE t (-0.45) (-1.39) (-0.80) (-0.76) TURNOVER t (1.08) (1.20) (1.98) (2.25) SIZE t (-1.24) (-1.39) (-1.35) (-1.65) FAMSIZE t (2.48) (1.80) (1.88) (1.93) AGE t (-0.73) (-0.05) (0.61) (-0.12) FLOW t (1.41) (1.83) (0.26) (1.45) STDEV t (1.59) (1.75) (2.90) (1.32) ADJ R This table reports the time-series average of coefficients of the Fama-MacBeth regressions of quarterly fund returns (in percent) on SIM4 (in percent), investment intensity on other strategies and fund characteristics. Fund returns are measured either as fund net return or risk-adjusted returns. SIZESCORE4, BMSCORE4, and MOMSCORE4 are the averages of cross-sectionally standardized size, B/M, and momentum of stocks held by a fund weighted by the fund trading over Q(-3) to Q0. Fee is the quarterly fund expense. TURNOVER is quarterly fund turnover. SIZE is the logarithm of fund total net assets (TNA). FAMSIZE is the logarithm of fund family TNA. AGE is the logarithm of fund age. FLOW is the growth rate of TNA of a fund after adjusting for the appreciation of the TNA. STDEV is the standard deviation of fund net return in the previous year. The Newey-West adjusted t-statistics in an order of lag 8 are in parentheses. The sample period is from 1984 to

53 Table 7: Fund Returns Decomposition Panel A: Q0 Net Return Decomposition (1) (2) (3) (4) (5) SIM4 0 Ranking Net (%) Gross GAP KMCost KSCost Before Exp (%) (%) (%) (%) D D INACTIVE D10 INACTIVE (t-stat) (1.23) (1.36) (-0.89) (2.18) (3.44) Panel B: Q1 Net Return Decomposition (1) (2) (3) (4) (5) (6) SIM4 0 Ranking Net Ret (%) Grossh (%) Grosst (%) GAP KMCost KSCost Before Exp (Q0 Beg hold) (Q0 Trade) (%) (%) (%) D D INACTIVE D10 INACTIVE (t-stat) (2.18) (1.53) (3.92) (-0.08) (1.97) (3.71) Panel A reports fund before-expense net returns, gross returns, the gap in before-expense net returns and gross returns (GAP), and two transaction cost measures in the quarter of portfolio formation (Q0). Funds are sorted into deciles based on SIM4 in Q0. D10 funds have the highest SIM4 0 and D1 funds have the lowest SIM4 0. INACTIVE funds are the 10% of funds with SIM4 closest to, and centered around, zero. Net return before expense is a fund s net return plus ¼ of its annual expense. Gross return is a fund s hypothetical return weighted by its holding at the beginning of a quarter. KMCost is a fund s transaction cost following Keim and Madhavan (1997) and KSCost is the estimated transaction cost following Korajczyk and Sadka (2004). In Panel B, all funds are sorted into deciles based on their SIM4 in Q0. The similar items are reported expect that in Q1 and we further decompose fund holding at the beginning of Q1 into portfolio holding at the beginning of Q0 and the holding change in Q0. The differences of these measures between D10 and INACTIVE funds are reported. The time-series t-statistics for the performance differences between D10 and inactive funds are reported in the parentheses. The sample period is from 1984 to

54 Table 8: Determinants of Return Gap (1) (2) (3) INTERCEPT 1.74 (3.58) 1.52 (2.41) 1.46 (2.69) SIM (0.69) 0.26 (2.05) 0.32 (2.91) KMCOST (-3.87) KSCOST (-4.21) INTENSITY (-2.36) 1.07 (2.19) EXTREME (-2.70) (-2.61) IPO 0.16 (0.59) 0.39 (1.12) 1.21 (1.81) FEE 0.25 (6.60) 0.25 (6.84) 0.08 (2.57) TURNOVER 0.29 (2.69) 0.25 (3.36) 0.23 (2.55) SIZE (-2.83) (-2.67) (-2.36) FAMSIZE 0.01 (2.06) 0.01 (2.38) 0.01 (2.16) AGE 0.12 (3.51) 0.04 (1.61) FLOW (-5.93) (-5.52) (-3.71) STDEV 0.17 (2.33) 0.20 (2.71) 0.19 (2.43) SIZERANK 0.22 (2.00) 0.15 (1.67) 0.23 (1.60) BMRANK (-2.57) (-2.88) (-2.65) MOMRANK 0.28 (6.19) 0.27 (5.88) 0.80 (9.96) Adj R This table reports the coefficients of Fama-MacBeth quarterly regression of fund return gap on fund characteristics. The dependent variable (GAP, in percent) is calculated as the difference between its quarterly net returns and quarterly gross return using beginning-quarter fund holding in the SUE measurement quarter. INTENSITY, trading intensity, is the sum of the product of absolute value of fund weight changes and absolute value of cross-sectionally standardized SUEs. EXTREME is the aggregate absolute value of weight changes in the two extreme deciles. KMCOST is the estimated transaction cost of a fund following Keim and Madhavan (1997). KSCOST is the estimated transaction cost of a fund following Korajczyk and Sadka (2004). IPO is the percentage of a fund s holding in IPO stocks. Fee is the quarterly fund expense. TURNOVER is fund turnover. SIZE is the logarithm of fund total net assets (TNA). FAMSIZE is the logarithm of fund family TNA. AGE is the logarithm of fund age. FLOW is the growth rate of TNA of a fund after adjusting for the appreciation of the TNA. STDEV is the standard deviation of fund net return in the previous year. SIZESCORE, BMSCORE, and MOMSCORE are calculated as the averages of cross-sectionally standardized size, B/M, and momentum of stocks held by a fund weighted by the fund trading in Q0. Return gaps, KMCost, KSCost, FLOW, and STDEV are expressed in percent per quarter. The Newey-West adjusted t-statistics in an order of lag 8 are in parentheses. 53

55 Table 9: Fund Characteristics, Return and Flow Volatilities across SIM Deciles SIM4 0-Sorted Fund Deciles TNA ($ Mil) Pct in Stocks (%) Pct in Cash (%) Num. of Stocks HIndex (%) Total Return Risk Idiosyncra tic Return Risk Flow Volatility Residual Flow Volatility D D INACTIVE D10 INACTIVE % (-2.63) (1.15) (0.53) (-5.71) (5.34) (2.87) (2.30) (4.16) (3.27) This table reports time-series means of fund characteristics, fund return volatility and fund flow volatility for each 4-quarter average SIM-sorted fund decile. Total net assets, the percentage of assets invested in stocks, and the percentage of assets held as cash, are obtained from the CRSP mutual fund database and are measures as of the end of each year. The number of stocks held at the end of each quarter is from the CDA database. The Herfindahl index is calculated as the sum of the squared percentages of assets invested in each stock to the total assets invested in all stock by a fund. A fund s total risk is its standard deviation of monthly net returns in the subsequent year. Idiosyncratic risk is the standard deviation of residuals from the 4-factor models in the subsequent year: R i, t RF t = α i + b i RMRF t + s i SMB t + h i HML t + p iumd t + ε i, t where R i,t -RF t is the monthly net return after fund expenses of fund i in month t in excess of the risk free rate (the yield on Treasury bills with one-month maturity in CRSP). RMRF t is the monthly return on the CRSP value-weighted index in excess of the risk free rate; SMB t, HML t, and UMD t are the monthly returns on size, book-to-market, and momentum factors. Fund flow volatility is the standard deviation of monthly flows in the subsequent year (FlowVol). The residual fund flow volatility is the estimated residual from annual cross-sectional regressions of fund flow volatility: FlowVol i, t = γ 0, i + γ 1, i Size i, t 1 + γ 2, i Exp i, t 1 + γ 3, i Load i, t 1 + γ 4, i Age t 1 + γ 5, i R i, t 1 + ε i, t Where the logarithm of fund size (Size), expense ratio (Exp), fund load dummy (Load), fund age (Age), and average fund annual monthly return (R) are measured at the end of previous year. We first average the return volatility and flow volatility across fund deciles in each quarter and then calculate their time-series average. The difference in fund volatility between D10 and INACTIVE funds are also reported. The Newey-West adjusted time-series t-statistics are in parentheses. The sample period is from 1984 to

56 Table 10: Fund Trading Intensity on PEAD Profitability Raw Returns Four-factor Adj. Returns SIM4 t+3 PROF t SIM4 t+3 PROF t Intercept (3.01) (-0.02) (2.79) (0.12) SIM4 t (2.58) (-2.23) (2.44) (-1.89) PROF t (2.99) (1.62) (2.28) (0.67) DEF t (-1.19) (-1.62) (-1.22) (-0.12) DP t (-0.22) (-1.57) (-10.25) (-0.14) TBILL t (1.21) (2.06) (1.51) (0.72) TERM t (0.83) (1.95) (1.27) (0.22) SENTI t (-0.93) (-1.24) (-1.00) (0.51) Adj. R This table reports the results of the intertemporal regressions of PEAD profitability (PROF) and mutual fund trading intensity as follows: SIM4 t+3 =β 0 + β 1 SIM4 t-1 + β 2 PROF t-1 + β 3 DEF t-1 + β 4 DP t-1 + β 5 TBILL t-1 + β 6 TERM t-1 + β 7 SENTI t-1 +v t PROF t = γ 0 + γ 1 SIM4 t-1 + γ 2 PROF t-1 + γ 3 DEF t-1 + γ 4 DP t-1 + γ 5 TBILL t-1 + γ 6 TERM t-1 + γ 7 SENTI t-1 +v t SIM4 is the equal-weighted mean of the average SIM from the quarter of portfolio formation (Q0) to the 3rd quarter afterward (Q3). PROF is the PEAD trading profit, measured as the coefficient on SUE from the cross-sectional regression of stock returns on SUEs in each quarter. Both raw returns and four-factor adjusted returns are used in the regressions. Mutual fund PEAD trading intensity is measured by SIM4. DEF is the default premium. DP is the dividend/price ratio. TBILL is risk free rate of return. TERM is the term premium. SENTI is the investor sentiment index. The GMM estimation with Bart Kernel and the Newey-West test with a lag of order 8 are used. The t-statistics are reported in the parentheses. 55

57 Figure 1 Return Difference between D10 and D1 Portfolios Sorted by Stock SUEs 0.4 (A) Difference in Raw Returns between D10 and D1 Stocks (B) Difference in Four-factor Adj. Returns between D10 and D1 Stocks This figure plots the return difference between D10 and D1 portfolios sorted by stock SUEs. At the end of each quarter, we form equal-weighted decile portfolios of all Compustat-CRSP stocks based on their standardized unexpected earnings (SUEs) reported during that quarter. We compute the quarterly raw stock return and four-factor adjusted return for each stock decile based on SUE at the beginning of quarter t. The four-factor risk adjusted return of a stock is computed using the difference between the quarterly compounded stock returns and the returns based on factor loadings estimated from the four factor model with stock returns in the prior 12 months. Quarterly returns are compounded into annual returns. Panel A plots the time series of the raw return spreads between the top and bottom decile portfolios. Panel B plots the time series of the four-factor adjusted return spreads between the top and bottom decile portfolios. 56

58 Figure 2 SUE Investing Measure across Time 0.06 SIM SIM This figure plots equal-weighted average SUE investing measure (SIM) and 4-quarter averaged SIM (SIM4) of the sample funds from 1984 to

59 Figure 3 Portfolio Weights in Stock Deciles Sorted by SUEs INACTIVE Funds D10 Funds Fractional Holding SUE Decile This figure illustrates the distributions of portfolio holding across SUE deciles for D10 and inactive funds. From 1984 to 2003, at the end of each quarter t stocks are sorted into deciles based on their standardized unexpected earnings (SUEs). The fractions of portfolio holding across the SUE deciles are evaluated for D10 funds and inactive funds, where D10 funds are those with the highest SIM and INACTIVE funds are the 10% of funds with SIM4 closest to, and centered around, zero. The time series means of the average fractional holding in each stock decile are plotted for D1 and D10 funds, 58

60 Figure 4 Persistence of SUE Investing Measures This figure plots the probability distribution of the average SIM decile ranks in quarters t+1 through t+4 (SIM4 t+4 ) conditional on initial average SIM ranks in quarters t-3 through t (SIM4 t ). In each quarter t, funds are sorted into deciles based on their SIM4. For funds in each decile rank, we compute the probability distribution across the SIM4 decile distributions in quarter t+4. 59

61 Figure 5 Performance of Top Fund Deciles Sorted by SIM4 4-factor Adjusted returns of D10 Funds From 1984 to 2003, in each quarter t, we sort funds into deciles based on their SIM4 at the beginning of the quarter and compute the four-factor adjusted return before expenses for D10 funds in quarter t. Quarterly returns are compounded into annual returns and plotted. 60

62 Founded in 1892, the University of Rhode Island is one of eight land, urban, and sea grant universities in the United States. The 1,200-acre rural campus is less than ten miles from Narragansett Bay and highlights its traditions of natural resource, marine and urban related research. There are over 14,000 undergraduate and graduate students enrolled in seven degreegranting colleges representing 48 states and the District of Columbia. More than 500 international students represent 59 different countries. Eighteen percent of the freshman class graduated in the top ten percent of their high school classes. The teaching and research faculty numbers over 600 and the University offers 101 undergraduate programs and 86 advanced degree programs. URI students have received Rhodes, Fulbright, Truman, Goldwater, and Udall scholarships. There are over 80,000 active alumnae. The University of Rhode Island started to offer undergraduate business administration courses in In 1962, the MBA program was introduced and the PhD program began in the mid 1980s. The College of Business Administration is accredited by The AACSB International - The Association to Advance Collegiate Schools of Business in The College of Business enrolls over 1400 undergraduate students and more than 300 graduate students. Mission Our responsibility is to provide strong academic programs that instill excellence, confidence and strong leadership skills in our graduates. Our aim is to (1) promote critical and independent thinking, (2) foster personal responsibility and (3) develop students whose performance and commitment mark them as leaders contributing to the business community and society. The College will serve as a center for business scholarship, creative research and outreach activities to the citizens and institutions of the State of Rhode Island as well as the regional, national and international communities. The creation of this working paper series has been funded by an endowment established by William A. Orme, URI College of Business Administration, Class of 1949 and former head of the General Electric Foundation. This working paper series is intended to permit faculty members to obtain feedback on research activities before the research is submitted to academic and professional journals and professional associations for presentations. An award is presented annually for the most outstanding paper submitted. Ballentine Hall Quadrangle Univ. of Rhode Island Kingston, Rhode Island