# Active Fundamental Performance

Active Fundamental Performance Abstract We propose a new measure, active fundamental performance (AFP), to identify skilled mutual fund managers. AFP evaluates fund investment skills conditioned on the release of firms’ fundamental information. For each fund, we examine the covariance between deviations of its portfolio weights from a benchmark portfolio and the underlying stock performance on days when firms publicize fundamental information. Because asset prices on these information days better reflect firm fundamentals, AFP can more effectively identify investment skills. From 1984 to 2014, funds in the top decile of high AFP subsequently outperformed those in the bottom decile by 2% to 3% per year. Received August 25, 2016; editorial decision December 17, 2017 by Editor Andrew Karolyi. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online. Despite a large body of literature examining performance evaluation, identifying skilled mutual fund managers remains challenging. Noise and random shocks to asset returns make it difficult to differentiate skills from luck. Because observed mutual fund alphas typically are small and noisy, an evaluator would need an unfeasibly long return series to identify a skilled manager reliably.1 Recent studies show that asset prices reflect fundamental information to a greater extent on news release days: the risk-return relationship tends to manifest more clearly, and stock-level mispricing tends to be corrected with the release of important fundamental information (e.g., Savor and Wilson 2013, 2014, 2016; Lucca and Moench 2015; Engelberg, McLean, and Pontiff 2015). Such findings have important implications for performance evaluation. When stock prices are more informative of their fundamental values, fund performance is more indicative of the manager’s investment skill. However, no existing performance measures have exploited this window of opportunity. With the current study, we intend to fill this gap. We propose a measure of fund investment skills conditioned on the release of firm fundamental information. We focus on price movements driven by fundamental information, and our measure uses available fund performance and stock return data more efficiently to increase the power of performance evaluation. Specifically, the proposed performance measure, which we refer to as “active fundamental performance” (AFP), captures the covariance between a fund’s portfolio weight deviation from a passive benchmark (or from previous holdings) and the stocks’ performance during a 3-day window surrounding subsequent earnings announcements. We choose this short window as a proxy for the release of fundamental information because earnings announcements, as major company information events, are associated with a substantial “correction” in stock prices. For instance, Sloan (1996) documents that approximately 40% of the profits from accrual strategies cluster in a 3-day earnings announcement window. La Porta et al. (1997) report that between 25% and 30% of the returns to various value strategies considered by Lakonishok, Shleifer, and Vishny (1994) are concentrated on the 3 days around earnings announcements. Jegadeesh and Titman (1993) estimate that approximately 25% of momentum profits are concentrated on the 3 days surrounding earnings announcements. More recently, Engelberg, McLean, and Pontiff (2015) investigate 97 stock return anomalies and find that anomaly returns are 7 times higher on earnings announcement days. This evidence suggests that the short window around earnings announcements is a period in which stock prices converge to fundamental values. Therefore, we posit that a fund’s underlying stock performance around earnings announcements can be particularly revealing in identifying active managers skilled in selecting mispriced securities and successfully predicting the correction in their prices. We analyze quarterly holdings data for 2,538 unique, actively managed U.S. equity funds over the period 1984–2014. For each fund in each quarter, we compute the index-based AFP (the covariance between a fund’s active weights, or portfolio weight deviations from its benchmark index, and the underlying stocks’ performance during subsequent earnings announcements) and the trade-based AFP (the covariance between changes in a fund’s portfolio weights and the underlying stocks’ performance during subsequent earnings announcements). We find that the index-based (trade-based) AFP measure is positive on average, with a cross-fund mean of 9.95 (5.40) basis points (bps) per 3-day window and a standard deviation of 32.46 (22.09) bps. These results suggest substantial cross-sectional heterogeneity in mutual funds’ performance; at least some managers exhibit skill. In addition, the measure shows a positive, albeit only moderate, correlation with other commonly used performance measures. For example, the index-based (trade-based) AFP has average cross-sectional correlations of 25%, 24%, 32%, and 17% (6%, 6%, 8%, and 23%) with raw fund returns, the four-factor alpha, Daniel et al.’s (1997) characteristic selectivity (CS) measure, and the Grinblatt and Titman (1993) measure, respectively. Thus, compared with other performance measures, AFP captures unique fund characteristics and substantial incremental information. We find that AFP strongly predicts subsequent fund performance. In univariate sorts by index-based (trade-based) AFP, mutual funds in the top decile with the highest AFP outperform those in the bottom decile with the lowest AFP by 2.76% (1.44%) per year. This outperformance cannot be accounted for by their different exposures to risk or style factors. For example, after adjusting for their differential loadings on the market, size, value, and momentum factors, mutual funds in the top decile with the highest index-based (trade-based) AFP continue to outperform those in the bottom decile by 2.40% (1.44%) per year. In other tests, we control for the effects of liquidity and post-earnings announcement drifts, and AFP remains a strong predictor of future fund performance. Note that our fund portfolio strategy is based on information about fund holdings lagged by at least 2 months. The U.S. Securities and Exchange Commission (SEC) requires mutual funds to disclose their portfolio composition within 2 months, making this strategy implementable for mutual fund investors or funds of mutual funds aiming to improve their selection performance. In double sorts, we find that the strong predictive power of AFP for future fund returns is incremental beyond that of various return- and holding-based performance measures, such as CS (Daniel et al. 1997), return gap (Kacperczyk, Sialm and Zheng 2008), reliance on public information (RPI; Kacperczyk and Seru 2007), and active share (Cremers and Petajisto 2009). We also find that mutual fund investors can further improve their returns if they combine the information contained in AFP with signals from return gap. For example, mutual funds in the top quartiles of the index-based AFP and return gap outperform those in the bottom quartiles by 3.36% per year based on the four-factor model. We also consider multiple regressions that jointly control for alternative measures of fund investment skill such as CS, return gap, RPI, and active share, together with other fund characteristics, including fund age, size, expense ratios, turnover, past flow, and past performance. We find that AFP remains statistically significant in predicting future fund performance in these regressions. In both the portfolio and the regression analyses, AFP significantly predicts future fund performance more consistently than the alternative performance measures. We conduct further analyses to shed light on the information sources for AFP. Using stock-level analyses, we find that both active weights and changes in portfolio weights can predict abnormal return around future earnings announcements and exhibit stronger predictability for companies with more information asymmetry (i.e., those with lower analyst coverage, higher idiosyncratic volatilities, and higher analyst disagreement). Moreover, high-AFP funds’ superior performance is more pronounced when financial analysts’ forecasts diverge. These results support the notion that the ability to form a superior estimate of firms’ fundamental values drives AFP and its performance forecasting power. The AFP measures also exhibit time-series persistence; for instance, mutual funds in the top decile with the highest index-based AFP continue to exhibit significantly higher AFP than those in the bottom decile in the subsequent 2 years. This persistence is largely due to the superior AFP of skilled funds in the top decile. The current study contributes to the broad literature on mutual fund performance and market efficiency by introducing a new performance measure as well as a new and more efficient way of using available data.2 We show that focusing on important data points (information days) and integrating information on the extent and quality of active management into a single measure yield substantially more power in identifying skilled managers. The AFP measure is related to Grinblatt and Titman’s (1993) benchmark-free performance measure and Daniel et al.’s (1997) characteristic-based performance measure, which are based on fund holdings and subsequent stock returns. Our innovation of conditioning on a fundamental information release goes further and exploits the high information-to-noise ratio during the time period in which prices tend to converge to their fundamental values. The conditional approach sharpens signals from subsequent stock performance and substantially improves the power to evaluate stock-picking skills. In unreported tests, we find that when we replace earnings announcement returns with stock returns in the entire subsequent quarter, AFP’s forecasting power for future fund performance disappears. Our study has implications for the growing literature that quantifies the level of activeness in a managed portfolio (e.g., Cremers and Petajisto 2009; Cremers et al. 2013; Petajisto 2013; Stambaugh 2014). We contribute to this literature stream by nesting the degree of activeness into a tight framework for performance evaluation. Our approach focuses on signed active portfolio weights (or changes in weights) and examines the covariance between the weights and the underlying stock returns on information days. Empirically, we show that the AFP measure helps separate skilled versus unskilled active funds with high active shares, which makes it particularly useful for mutual fund investors. Ali et al. (2004) and Baker et al. (2010) document evidence that trades by aggregate institutional investors and aggregate mutual funds forecast subsequent earnings surprises, respectively. Cohen, Frazzini, and Malloy (2008) track the shared educational network between mutual fund and corporate managers and find that connected stock holdings achieve high average returns, particularly during earnings announcements. In combination with studies documenting earnings announcements as the short period when stock prices quickly converge to the fundamental values, these papers provide a useful foundation for us to create a powerful fund-level performance measure that identifies skilled fund managers. Although the current study is closely related to Baker et al. (2010), it differs in several key aspects. First, whereas Baker et al. (2010) focus on whether mutual fund managers on average can pick stocks, we investigate how to identify individual managers who can select stocks. Second, in terms of empirical tests, Baker et al. (2010) focus on stock-level analyses, assessing earnings announcement returns of all fund trades or trades of a certain group of funds. In contrast, the current study focuses on fund-level analyses by proposing a new fund performance measure. Third, the emphasis in Baker et al. (2010) is on the ability of fund managers to forecast a firm’s future earnings number. An important contribution of our study is to introduce the notion of performance evaluation, conditional on the release of fundamental information. We use earnings announcements as a proxy and starting point, but our measure has broad implications and can include other fundamental information events. Another literature stream examines how investors use publicly available information and explores the potential performance implications. For instance, Kacperczyk and Seru (2007) examine mutual fund managers’ reliance on public information as reflected in analyst stock recommendations, and Fang, Peress, and Zheng (2014) investigate their reliance on mass media. Both studies show that relying on public information has negative consequences for mutual fund managers’ performance. In a different context, Engelberg, Reed, and Ringgenberg (2012) investigate the source of short sellers’ skills and show that short sellers have a superior ability to interpret and process publicly available information, which translates into investment skills. In contrast with these studies focusing on how fund managers make use of public information, which is backward looking, we evaluate fund performance conditional on the release of fundamental information with a forward-looking focus. The investment ability of fund managers includes but is not limited to their ability to process public information. The key to our identification is that the realization of superior fundamental performance tends to be catalyzed when important firm-level information such as earnings news is released to the public domain. 1. Methodology: AFP In this section, we develop our new measure of performance evaluation, AFP. The starting point is the covariance between portfolio weights and future asset returns, Cov($$w_{i,t}$$,$$R_{i,t})$$, as shown in Equation (1). As Grinblatt and Titman (1993) and Lo (2008) point out, aggregating the covariance over all investments is an intuitive way to examine managers’ skill to forecast asset returns. The portfolio weights reflect managers’ strategic decisions to buy, sell, or avoid an asset in anticipation of its future returns. A skilled manager whose percentage holdings of assets increase in future asset returns will on average exhibit a positive covariance. The covariance measure is theoretically appealing, in that it captures fund performance due to active portfolio management (Grinblatt and Titman 1993; Lo 2008):   \begin{align} &\underbrace {\sum\limits_{i=1}^N {Cov(w_{i,t} ,R_{i,t} )} }_{Active}=\sum\limits_{i=1}^N {E(w_{i,t} \times R_{i,t} )} -\sum\limits_{i=1}^N {E(w_{i,t} )\times E(R_{i,t} )}\notag \\ &\quad=\underbrace {E(R_{p,t} )}_{Total}-\underbrace {\sum\limits_{i=1}^N {E(w_{i,t} )\times E(R_{i,t} )} }_{Passive}, \end{align} (1) where $$w_{i,t}$$ is the weight of security $$i$$ in the fund’s portfolio at the beginning of period $$t$$, $$R_{i,t}$$ is security $$i$$’s return during period $$t$$, and $$N$$ is the number of securities in the fund’s portfolio. Equation (1) shows that the sum of the covariances across securities captures the difference between total portfolio returns $$R_{p,t}$$ and the passive return to the portfolio. We propose two innovations to the covariance measure. Motivated by recent studies on information releases and asset prices (see, e.g., Savor and Wilson 2013, 2014, 2016; Lucca and Moench 2015; Engelberg, McLean, and Pontiff 2015), we measure future asset returns within a short window during which price movements are driven by firm fundamental information. This approach helps mitigate the influence of noise in asset returns and increases the power of the covariance measure to identify investment skills. Specifically, we examine stock returns during 3-day windows around earnings announcements to focus on time periods during which stock prices tend to reflect this fundamental information. The advantage of focusing on earnings announcement returns lies in the high information-to-noise ratio on earnings announcement days and the large cross-section of earnings announcement events, both of which increase the power of performance evaluation. A disadvantage arises because firms release earnings numbers relatively infrequently, typically once per quarter. Although we choose a 3-day event window—a standard practice in event studies of earnings announcements—our results also are robust to using a 5-day event window. Our second innovation is to use benchmark-adjusted portfolio weights, instead of raw portfolio weights, to capture a manager’s active investment decisions. Cremers and Petajisto (2009) pioneered the idea of using benchmark-adjusted portfolio weights to measure a fund manager’s active investment decisions. We provide a theoretical illustration of this approach in Internet Appendix A. Because an actively managed mutual fund’s performance is typically benchmarked against a passive index, the passive index is a natural choice for the fund’s benchmark portfolio. Alternatively, we could use the fund’s own past holdings as a benchmark, thereby using changes in portfolio weights (i.e., fund trades) to compute AFP. Active weights, or deviations in portfolio weights from the benchmark, contain the fund manager’s information revealed through both recent and longer-term holdings. Changes in portfolio weights reflect recent portfolio adjustments and thus recent information about security returns. Ex ante, both active weights and changes in portfolio weights can be useful for assessing the manager’s skill, though the former may be more comprehensive in capturing the manager’s information set. Herein, we compute both index-based and trade-based AFP, and we report both sets of results. As Equation (2) indicates, our covariance measure reflects the expected abnormal fund returns during earnings announcements, attributable to the fund’s active portfolio decisions:   \begin{align} \textit{Cov}(w_{i,t} - w_{i,t}^b, \textit{CAR}_{i,t}) &= E[(w_{i,t} - w_t^b) \times \textit{CAR}_{i,t} ] - E(w_{i,t} - w_{i,t}^b) \times E(\textit{CAR}_{i,t})\notag\\ &= E[(w_{i,t} - w_{i,t}^b) \times \textit{CAR}_{i,t} ] - 0 \times E(\textit{CAR}_{i,t})\notag\\ &= E[(w_{i,t} - w_{i,t}^b) \times \textit{CAR}_{i,t} ]. \end{align} (2) We develop an empirical analog of the sum of this covariance measure across securities, termed AFP, in Equation (3):   \begin{align} \textit{AFP}_{j,t} = \sum\limits_{i=1}^{N_j} (w_{i,t}^j - w_{i,t}^{b_j})\textit{CAR}_{i,t}, \end{align} (3) where $$\textit{AFP}_{j,t}$$ is mutual fund $$j$$’s AFP based on its portfolio selection in quarter $$t$$, $${\boldsymbol{w}_{\boldsymbol{i,t}}^{\boldsymbol{j}}}$$ is the weight of stock $$i$$ in fund $$j$$’s portfolio at the start of quarter $$t$$, $${\boldsymbol{w}_{\boldsymbol{i,t}}^{\boldsymbol{b}_{\boldsymbol{j}}}}$$ is the weight of stock $$i$$ in fund $$j$$’s benchmark portfolio at the start of quarter $$t$$, $$\textit{CAR}_{i,t}$$ is stock $$i$$’s 3-day cumulative abnormal return surrounding its quarterly earnings announcement during quarter $$t$$, and $$N_{j}$$ is the number of stocks in fund $$j$$’s investment universe (i.e., the union of stocks held by the fund and those in the fund’s benchmark portfolio). The daily abnormal returns refer to the difference in daily returns between a stock and its size and book-to-market matched portfolio. We sum the daily abnormal returns from 1 day before to 1 day after earnings announcements to obtain the 3-day abnormal return. 2. Computing AFP 2.1 Sample construction We obtain the portfolio holdings for actively managed equity mutual funds from Thomson Reuters’s CDA/Spectrum Mutual Fund Holdings Database and returns for the individual mutual funds and other fund characteristics from the Center for Research in Security Prices (CRSP) Survivor-Bias-Free U.S. Mutual Fund Database. We then use the MFLINKS data set to merge the two databases, excluding balanced, bond, money market, international, index, and sector funds, as well as funds not invested primarily in equity securities. After applying this filter, the sample consists of 2,538 unique funds, ranging in time from the first quarter of 1984 to the second quarter of 2014. To select the benchmark index for fund managers, we follow Cremers and Petajisto’s (2009) procedure. The universe of benchmark indexes includes 19 widely used benchmark indexes: S&P 500, S&P 400, S&P 600, S&P 500/Barra Value, S&P 500/Barra Growth, Russell 1000, Russell 2000, Russell 3000, Russell Midcap, value and growth variants of the four Russell indexes, Wilshire 5000, and Wilshire 4500. For each fund in each quarter, we select an index that minimizes the average distance between the fund portfolio weights and the benchmark index weights. Data on the index holdings of the 12 Russell indexes since their inception come from the Frank Russell Company, and data on the S&P 500, S&P 400, and S&P 600 index holdings since December 1994 are provided by COMPUSTAT. For the remaining indexes and periods, we use the index funds holdings to approximate index holdings. The information on daily stock prices and returns for common stocks traded on the NYSE, AMEX, and NASDAQ comes from the CRSP daily stock files. We obtain firms’ announcement dates for quarterly earnings from COMPUSTAT and analysts’ consensus earnings forecasts from I/B/E/S. Panel A of Table 1 shows the summary statistics for mutual funds in our sample. An average fund in our sample manages $\$$1.39 billion of assets and is 15.70 years old. Their mutual fund investors achieve an average return of 2.39% per quarter. The net percentage fund flow is skewed to the right; the quarterly fund flow has a mean of 1.35% but a median of only$$-$$1.05%. On average, mutual funds in our sample incur an annual expense ratio of 1.23% and turn over their portfolios by 86.08% per year. These numbers are in line with the previous literature. Table 1 Descriptive statistics A. Summary statistics of fund characteristics Mean SD 25th pctl Median 75th pctl Total number of funds 2,538 TNA ( \$$ million) 1,391.33 5,391.59 72.30 246.08 883.23 Age (years) 15.70 14.55 6.00 11.00 19.00 Quarterly return (%) 2.39 10.24 –2.60 3.16 8.52 Flow (%) 1.35 13.79 –4.11 –1.05 3.37 Expense (%) 1.23 0.46 0.95 1.19 1.48 Turnover (%) 86.08 101.58 34.00 63.00 109.00 B. Average Spearman cross-sectional correlation coefficients TNA Age Quarterly return Flow Expense Age 0.29 Quarterly return 0.01 –0.01 Flow –0.01 –0.13 0.15 Expense –0.22 –0.21 –0.01 0.03 Turnover –0.09 –0.11 0.02 0.05 0.19 A. Summary statistics of fund characteristics Mean SD 25th pctl Median 75th pctl Total number of funds 2,538 TNA ($\$$million) 1,391.33 5,391.59 72.30 246.08 883.23 Age (years) 15.70 14.55 6.00 11.00 19.00 Quarterly return (%) 2.39 10.24 –2.60 3.16 8.52 Flow (%) 1.35 13.79 –4.11 –1.05 3.37 Expense (%) 1.23 0.46 0.95 1.19 1.48 Turnover (%) 86.08 101.58 34.00 63.00 109.00 B. Average Spearman cross-sectional correlation coefficients TNA Age Quarterly return Flow Expense Age 0.29 Quarterly return 0.01 –0.01 Flow –0.01 –0.13 0.15 Expense –0.22 –0.21 –0.01 0.03 Turnover –0.09 –0.11 0.02 0.05 0.19 This table presents descriptive statistics for our sample of mutual funds. The sample consists of 2,538 distinct mutual funds from 1984Q1 to 2014Q2. Panel A presents the summary statistics for fund characteristics. TNA is the quarter-end total net fund assets in millions of dollars; age is the fund age in years; quarterly return is the quarterly net fund return as a percentage; flow is the quarterly growth rate of assets under management as a percentage after adjusting for the appreciation of the fund’s assets; expense is the fund expense ratio as a percentage, and turnover is the turnover ratio of the fund as a percentage. Panel B shows the time-series average of the cross-sectional Spearman correlation coefficients for the variables of interest. Table 1 Descriptive statistics A. Summary statistics of fund characteristics Mean SD 25th pctl Median 75th pctl Total number of funds 2,538 TNA ( \$$ million)  1,391.33  5,391.59  72.30  246.08  883.23  Age (years)  15.70  14.55  6.00  11.00  19.00  Quarterly return (%)  2.39  10.24  –2.60  3.16  8.52  Flow (%)  1.35  13.79  –4.11  –1.05  3.37  Expense (%)  1.23  0.46  0.95  1.19  1.48  Turnover (%)  86.08  101.58  34.00  63.00  109.00  B. Average Spearman cross-sectional correlation coefficients     TNA  Age  Quarterly return  Flow  Expense  Age  0.29              Quarterly return  0.01  –0.01           Flow  –0.01  –0.13  0.15        Expense  –0.22  –0.21  –0.01  0.03     Turnover  –0.09  –0.11  0.02  0.05  0.19  A. Summary statistics of fund characteristics     Mean  SD  25th pctl  Median  75th pctl  Total number of funds  2,538              TNA ( \$$million) 1,391.33 5,391.59 72.30 246.08 883.23 Age (years) 15.70 14.55 6.00 11.00 19.00 Quarterly return (%) 2.39 10.24 –2.60 3.16 8.52 Flow (%) 1.35 13.79 –4.11 –1.05 3.37 Expense (%) 1.23 0.46 0.95 1.19 1.48 Turnover (%) 86.08 101.58 34.00 63.00 109.00 B. Average Spearman cross-sectional correlation coefficients TNA Age Quarterly return Flow Expense Age 0.29 Quarterly return 0.01 –0.01 Flow –0.01 –0.13 0.15 Expense –0.22 –0.21 –0.01 0.03 Turnover –0.09 –0.11 0.02 0.05 0.19 This table presents descriptive statistics for our sample of mutual funds. The sample consists of 2,538 distinct mutual funds from 1984Q1 to 2014Q2. Panel A presents the summary statistics for fund characteristics. TNA is the quarter-end total net fund assets in millions of dollars; age is the fund age in years; quarterly return is the quarterly net fund return as a percentage; flow is the quarterly growth rate of assets under management as a percentage after adjusting for the appreciation of the fund’s assets; expense is the fund expense ratio as a percentage, and turnover is the turnover ratio of the fund as a percentage. Panel B shows the time-series average of the cross-sectional Spearman correlation coefficients for the variables of interest. Panel B of Table 1 shows the average Spearman cross-sectional correlation coefficients among fund characteristics. The results confirm our intuition: the average 29% correlation coefficient between fund size and age indicates that large funds tend to have a longer track record, and the correlation between fund size and expense ratio of$$-$$22% indicates that large funds tend to incur lower expense ratios. We also find a negative correlation of$$-$$13% between fund age and fund flow, consistent with the idea that established mutual funds with longer life spans tend to be stable, with a smaller percentage of inflows. In the next subsection, we analyze AFP. 2.2 Computing AFP For each fund in each quarter, we compute both index-based and trade-based AFP. For the trade-based AFP, we measure changes in portfolio weights and account for mechanical changes in portfolio weights due to stock price changes.3 Most earnings announcements (more than 89% in our sample) occur in the first 2 months after the quarter ends, so we use the time line in Figure 1: the active weights (changes in portfolio holdings) for fund$$j$$are measured at the end of month$$t$$(e.g., end of March), and the earnings announcements are observed in the first 2 months in the following quarter (e.g., April and May). We use Equation (3) to compute the AFP for fund$$j$$, or AFP$$_{j,t}$$. In the analysis of fund performance in the next section, we track the performance of fund$$j$$for the subsequent 3 months, including months$$t+$$3,$$t+$$4, and$$t+5 (e.g., June–August). Figure 1 View largeDownload slide Time line for AFP This figure illustrates the measurement of AFP. In this illustration, AFP is measured at the end of May. The portfolio compositions of mutual funds and their benchmarks (lagged portfolio weights adjusted for price changes for trade-based AFP) are measured in March and observable by the end of May. The earnings announcements arrive in April and in May. Mutual fund portfolios are formed using AFP (available in real time) at the beginning of June and held until the end of August. We then recompute AFP using new information; doing so initiates portfolio rebalancing. Figure 1 View largeDownload slide Time line for AFP This figure illustrates the measurement of AFP. In this illustration, AFP is measured at the end of May. The portfolio compositions of mutual funds and their benchmarks (lagged portfolio weights adjusted for price changes for trade-based AFP) are measured in March and observable by the end of May. The earnings announcements arrive in April and in May. Mutual fund portfolios are formed using AFP (available in real time) at the beginning of June and held until the end of August. We then recompute AFP using new information; doing so initiates portfolio rebalancing. We choose this time line to balance two key considerations. On the one hand, the closer earnings announcement dates are to the reported holdings dates, the more accurate are the AFP measures due to unobserved trades by mutual funds within the quarter. On the other hand, a longer time span between the announcement dates and the reported holdings dates allows us to include more firms in the analysis. Using the first 2 months of a quarter balances these two considerations: most firms report their quarterly performance in the first 2 months of a quarter, and the time span between the reported portfolio composition and earnings announcement performance is reasonably close. Moreover, from a practical perspective, because mutual funds are required to report their holdings within 2 months, the information required to compute AFP is available to investors in real time. Thus, the trading strategy is implementable. To provide further justification for our time line, in Figure 2 we plot the average AFP value for a median fund over the 13 weeks following a typical quarter end. It indicates that for an average fund, the value of AFP stabilizes during the eighth or ninth week after the quarter ends, when we observe the fund’s portfolio composition. Thus, we conclude that incorporating earnings events that occur after the first 2 months do not improve the information content of a fund’s AFP. Figure 2 View largeDownload slide Cumulative AFP over the weeks following quarter ends This figure plots the AFP for a median mutual fund in our sample, cumulative over the weeks following quarter ends, when the active fund weights or changes in portfolio weights are measured. Like in Equation (3), AFP is the sum of the product of the fund’s active portfolio weights (panel A) or changes in portfolio weights (panel B) and subsequent 3-day abnormal returns surrounding earnings announcements. The value of cumulative AFP at the end of week 13 is scaled to equal 1. Figure 2 View largeDownload slide Cumulative AFP over the weeks following quarter ends This figure plots the AFP for a median mutual fund in our sample, cumulative over the weeks following quarter ends, when the active fund weights or changes in portfolio weights are measured. Like in Equation (3), AFP is the sum of the product of the fund’s active portfolio weights (panel A) or changes in portfolio weights (panel B) and subsequent 3-day abnormal returns surrounding earnings announcements. The value of cumulative AFP at the end of week 13 is scaled to equal 1. For an average fund in a typical quarter, the index-based (trade-based) AFP is equal to 10.28 (5.30) bps, with a standard deviation of 84.72 (97.10) bps.4 A substantial proportion of the high variability of AFP comes from cross-fund dispersion. For each fund, we compute the average AFP over its entire life. The cross-fund standard deviation for index-based (trade-based) AFP is 32.46 (22.09) bps, which is 3.26 (4.09) times the cross-section mean of 9.95 (5.40) bps. This high cross-fund dispersion in AFP is the main focus of the current research. 3. Predicting Mutual Fund Performance by AFP 3.1 Portfolio sorts Using a portfolio-based analysis, we examine the profitability of a strategy that invests in mutual funds according to their AFP. Specifically, at the end of each May, August, November, and February, we sort mutual funds into ten portfolios by their AFP and rebalance them quarterly. We compute equally weighted returns for each decile portfolio over the following quarter, both after and before expenses. In addition, we estimate the risk-adjusted returns on the portfolios as intercepts from time-series regressions, according to the Capital Asset Pricing Model (CAPM); Fama and French’s (1993) three-factor model (market, size, and value); Carhart’s (1997) four-factor model, which augments the Fama-French factors with Jegadeesh and Titman’s (1993) momentum factor; and the five-factor model, which adds Pastor and Stambaugh’s (2003) liquidity risk factor to the four-factor model. For instance, the Carhart four-factor alpha is the intercept from the following time-series regression: \begin{align} R_{p,t} -R_{f,t}&= \alpha_p + \beta_m (R_{m,t}-R_{f,t}) + \beta_{\textit{smb}}\textit{SMB}_t +\beta_{\textit{hml}}\textit{HML}_t +\beta_{\textit{umd}}\textit{UMD}_t +\varepsilon_{p,t},\notag\\ \end{align} (4) whereR_{p,t}$$is the return in month$$t$$for fund portfolio$$p$$,$$R_{f,t}$$is the 1-month Treasury-bill rate in month$$t$$,$$R_{m,t}$$is the value-weighted stock market return in month$$t$$, SMB$$_{t}$$is the difference in returns between small and large capitalization stocks in month$$t$$, HML$$_{t}$$is the return difference between high and low book-to-market stocks in month$$t$$, and UMD$$_{t}$$is the return difference between stocks with high and low past returns in month$$t$$. Table 2 presents the portfolio results, which indicate that AFP predicts future fund performance. Panel A shows the net returns for portfolios of funds sorted by their AFP. In the quarter following portfolio formation, mutual funds with high index-based (trade-based) AFP in decile 10 outperform the funds with the lowest AFP in decile 1 by 23 (12) bps per month, or 2.76% (1.44%) per year. This superior performance cannot be attributed to their high propensity to take risks or different investment styles; the differences in the alphas obtained from the CAPM, Fama-French three-factor, Carhart four-factor, and Pastor-Stambaugh five-factor models are 21, 27, 20, and 22 (12, 15, 12, and 12) bps per month for index-based (trade-based) AFP, respectively, and all of these differences are statistically significant. Table 2 AFP and mutual fund returns: Decile portfolios A. Decile portfolios formed according to the index-based AFP Low 2 3 4 5 6 7 8 9 High High-low Net returns Average return 0.87 0.90 0.93 0.91 0.93 0.92 0.96 1.02 1.00 1.10 0.23*** (3.42) (3.74) (3.95) (3.89) (3.96) (3.90) (4.01) (4.18) (4.06) (4.16) (3.14) CAPM$$\alpha $$–0.18 –0.12 –0.08 –0.10 –0.08 –0.09 –0.06 –0.01 –0.03 0.03 0.21*** (–2.79) (–2.49) (–1.79) (–2.26) (–2.1) (–2.3) (–1.52) (–0.3) (–0.58) (0.37) (2.97) Fama-French$$\alpha$$–0.19 –0.14 –0.09 –0.11 –0.09 –0.11 –0.07 –0.01 –0.02 0.07 0.27*** (–3.52) (–3.28) (–2.52) (–3.27) (–2.87) (–3.28) (–2.13) (–0.26) (–0.39) (1.38) (3.59) Carhart$$\alpha $$–0.16 –0.12 –0.08 –0.10 –0.09 –0.11 –0.08 –0.03 –0.03 0.04 0.20*** (–2.95) (–2.84) (–2.29) (–2.8) (–2.39) (–3.16) (–2.24) (–0.72) (–0.76) (0.82) (3.23) Pastor-Stambaugh$$\alpha $$–0.17 –0.13 –0.09 –0.11 –0.09 –0.12 –0.08 –0.03 –0.03 0.05 0.22*** (–3.17) (–3.06) (–2.49) (–3.08) (–2.64) (–3.43) (–2.4) (–0.79) (–0.79) (0.93) (3.49) Gross returns Average return 0.97 1.00 1.03 1.00 1.02 1.01 1.05 1.11 1.10 1.20 0.23*** (3.83) (4.14) (4.35) (4.29) (4.35) (4.29) (4.41) (4.57) (4.46) (4.56) (3.14) CAPM$$\alpha $$–0.08 –0.02 0.02 0.00 0.01 0.00 0.03 0.08 0.07 0.13 0.21*** (–1.2) (–0.47) (0.38) (–0.03) (0.35) (0.02) (0.79) (1.74) (1.18) (1.74) (2.97) Fama-French$$\alpha $$–0.09 –0.04 0.00 –0.02 0.00 –0.01 0.02 0.09 0.08 0.18 0.27*** (–1.6) (–0.92) (0.11) (–0.57) (–0.04) (–0.42) (0.72) (2.44) (2.00) (3.33) (3.59) Carhart$$\alpha $$–0.05 –0.02 0.01 –0.01 0.01 –0.02 0.02 0.07 0.07 0.15 0.20*** (–0.98) (–0.54) (0.29) (–0.24) (0.23) (–0.47) (0.46) (1.88) (1.69) (2.84) (3.23) Pastor-Stambaugh$$\alpha $$–0.06 –0.03 0.00 –0.02 0.00 –0.02 0.01 0.07 0.07 0.15 0.22*** (–1.19) (–0.74) (0.05) (–0.51) (–0.01) (–0.7) (0.28) (1.79) (1.62) (2.89) (3.49) B. Decile portfolios formed according to the trade-based AFP Net returns Average return 0.87 0.92 0.92 0.90 0.93 0.88 0.88 0.93 0.95 0.99 0.12*** (3.23) (3.73) (3.80) (3.79) (3.88) (3.72) (3.67) (3.77) (3.82) (3.63) (2.98) CAPM$$\alpha $$–0.16 –0.06 –0.05 –0.05 –0.03 –0.07 –0.08 –0.05 –0.03 –0.04 0.12*** (–2.29) (–1.15) (–1.03) (–1.22) (–0.76) (–1.83) (–2.01) (–0.99) (–0.63) (–0.55) (2.94) Fama-French$$\alpha$$–0.14 –0.07 –0.08 –0.09 –0.05 –0.10 –0.11 –0.06 –0.03 0.01 0.15*** (–3.18) (–1.99) (–2.07) (–2.35) (–1.57) (–2.87) (–3.04) (–1.45) (–0.76) (0.11) (3.93) Carhart$$\alpha $$–0.15 –0.07 –0.07 –0.07 –0.04 –0.08 –0.10 –0.07 –0.04 –0.03 0.12*** (–3.28) (–1.63) (–1.89) (–1.92) (–1.15) (–2.32) (–2.62) (–1.85) (–0.96) (–0.7) (3.25) Pastor-Stambaugh$$\alpha $$–0.15 –0.07 –0.08 –0.08 –0.05 –0.09 –0.11 –0.08 –0.04 –0.03 0.12*** (–3.23) (–1.76) (–2.06) (–2.18) (–1.33) (–2.62) (–2.93) (–2.03) (–1.14) (–0.62) (3.34) Gross returns Average return 0.98 1.02 1.01 1.00 1.02 0.97 0.97 1.03 1.05 1.09 0.12*** (3.62) (4.13) (4.20) (4.18) (4.27) (4.12) (4.06) (4.16) (4.21) (4.03) (3.02) CAPM$$\alpha $$–0.05 0.04 0.05 0.04 0.06 0.02 0.01 0.05 0.07 0.06 0.12*** (–0.76) (0.85) (1.05) (0.93) (1.45) (0.52) (0.27) (1.00) (1.29) (0.84) (2.98) Fama-French$$\alpha $$–0.03 0.03 0.02 0.01 0.04 –0.01 –0.01 0.04 0.07 0.11 0.15*** (–0.79) (0.68) (0.54) (0.21) (1.14) (–0.15) (–0.36) (1.08) (1.92) (2.47) (3.98) Carhart$$\alpha $$–0.05 0.03 0.02 0.02 0.05 0.01 0.00 0.02 0.06 0.07 0.12*** (–1.03) (0.78) (0.57) (0.57) (1.37) (0.32) (–0.02) (0.63) (1.63) (1.53) (3.29) Pastor-Stambaugh$$\alpha $$–0.05 0.03 0.01 0.01 0.04 0.00 –0.01 0.02 0.06 0.08 0.12*** (–1.01) (0.62) (0.38) (0.29) (1.13) (0.01) (–0.33) (0.46) (1.47) (1.59) (3.39) A. Decile portfolios formed according to the index-based AFP Low 2 3 4 5 6 7 8 9 High High-low Net returns Average return 0.87 0.90 0.93 0.91 0.93 0.92 0.96 1.02 1.00 1.10 0.23*** (3.42) (3.74) (3.95) (3.89) (3.96) (3.90) (4.01) (4.18) (4.06) (4.16) (3.14) CAPM$$\alpha $$–0.18 –0.12 –0.08 –0.10 –0.08 –0.09 –0.06 –0.01 –0.03 0.03 0.21*** (–2.79) (–2.49) (–1.79) (–2.26) (–2.1) (–2.3) (–1.52) (–0.3) (–0.58) (0.37) (2.97) Fama-French$$\alpha$$–0.19 –0.14 –0.09 –0.11 –0.09 –0.11 –0.07 –0.01 –0.02 0.07 0.27*** (–3.52) (–3.28) (–2.52) (–3.27) (–2.87) (–3.28) (–2.13) (–0.26) (–0.39) (1.38) (3.59) Carhart$$\alpha $$–0.16 –0.12 –0.08 –0.10 –0.09 –0.11 –0.08 –0.03 –0.03 0.04 0.20*** (–2.95) (–2.84) (–2.29) (–2.8) (–2.39) (–3.16) (–2.24) (–0.72) (–0.76) (0.82) (3.23) Pastor-Stambaugh$$\alpha $$–0.17 –0.13 –0.09 –0.11 –0.09 –0.12 –0.08 –0.03 –0.03 0.05 0.22*** (–3.17) (–3.06) (–2.49) (–3.08) (–2.64) (–3.43) (–2.4) (–0.79) (–0.79) (0.93) (3.49) Gross returns Average return 0.97 1.00 1.03 1.00 1.02 1.01 1.05 1.11 1.10 1.20 0.23*** (3.83) (4.14) (4.35) (4.29) (4.35) (4.29) (4.41) (4.57) (4.46) (4.56) (3.14) CAPM$$\alpha $$–0.08 –0.02 0.02 0.00 0.01 0.00 0.03 0.08 0.07 0.13 0.21*** (–1.2) (–0.47) (0.38) (–0.03) (0.35) (0.02) (0.79) (1.74) (1.18) (1.74) (2.97) Fama-French$$\alpha $$–0.09 –0.04 0.00 –0.02 0.00 –0.01 0.02 0.09 0.08 0.18 0.27*** (–1.6) (–0.92) (0.11) (–0.57) (–0.04) (–0.42) (0.72) (2.44) (2.00) (3.33) (3.59) Carhart$$\alpha $$–0.05 –0.02 0.01 –0.01 0.01 –0.02 0.02 0.07 0.07 0.15 0.20*** (–0.98) (–0.54) (0.29) (–0.24) (0.23) (–0.47) (0.46) (1.88) (1.69) (2.84) (3.23) Pastor-Stambaugh$$\alpha $$–0.06 –0.03 0.00 –0.02 0.00 –0.02 0.01 0.07 0.07 0.15 0.22*** (–1.19) (–0.74) (0.05) (–0.51) (–0.01) (–0.7) (0.28) (1.79) (1.62) (2.89) (3.49) B. Decile portfolios formed according to the trade-based AFP Net returns Average return 0.87 0.92 0.92 0.90 0.93 0.88 0.88 0.93 0.95 0.99 0.12*** (3.23) (3.73) (3.80) (3.79) (3.88) (3.72) (3.67) (3.77) (3.82) (3.63) (2.98) CAPM$$\alpha $$–0.16 –0.06 –0.05 –0.05 –0.03 –0.07 –0.08 –0.05 –0.03 –0.04 0.12*** (–2.29) (–1.15) (–1.03) (–1.22) (–0.76) (–1.83) (–2.01) (–0.99) (–0.63) (–0.55) (2.94) Fama-French$$\alpha$$–0.14 –0.07 –0.08 –0.09 –0.05 –0.10 –0.11 –0.06 –0.03 0.01 0.15*** (–3.18) (–1.99) (–2.07) (–2.35) (–1.57) (–2.87) (–3.04) (–1.45) (–0.76) (0.11) (3.93) Carhart$$\alpha $$–0.15 –0.07 –0.07 –0.07 –0.04 –0.08 –0.10 –0.07 –0.04 –0.03 0.12*** (–3.28) (–1.63) (–1.89) (–1.92) (–1.15) (–2.32) (–2.62) (–1.85) (–0.96) (–0.7) (3.25) Pastor-Stambaugh$$\alpha $$–0.15 –0.07 –0.08 –0.08 –0.05 –0.09 –0.11 –0.08 –0.04 –0.03 0.12*** (–3.23) (–1.76) (–2.06) (–2.18) (–1.33) (–2.62) (–2.93) (–2.03) (–1.14) (–0.62) (3.34) Gross returns Average return 0.98 1.02 1.01 1.00 1.02 0.97 0.97 1.03 1.05 1.09 0.12*** (3.62) (4.13) (4.20) (4.18) (4.27) (4.12) (4.06) (4.16) (4.21) (4.03) (3.02) CAPM$$\alpha $$–0.05 0.04 0.05 0.04 0.06 0.02 0.01 0.05 0.07 0.06 0.12*** (–0.76) (0.85) (1.05) (0.93) (1.45) (0.52) (0.27) (1.00) (1.29) (0.84) (2.98) Fama-French$$\alpha $$–0.03 0.03 0.02 0.01 0.04 –0.01 –0.01 0.04 0.07 0.11 0.15*** (–0.79) (0.68) (0.54) (0.21) (1.14) (–0.15) (–0.36) (1.08) (1.92) (2.47) (3.98) Carhart$$\alpha $$–0.05 0.03 0.02 0.02 0.05 0.01 0.00 0.02 0.06 0.07 0.12*** (–1.03) (0.78) (0.57) (0.57) (1.37) (0.32) (–0.02) (0.63) (1.63) (1.53) (3.29) Pastor-Stambaugh$$\alpha $$–0.05 0.03 0.01 0.01 0.04 0.00 –0.01 0.02 0.06 0.08 0.12*** (–1.01) (0.62) (0.38) (0.29) (1.13) (0.01) (–0.33) (0.46) (1.47) (1.59) (3.39) This table presents the performance of decile fund portfolios formed according to their AFP. Like in Equation (3), AFP is the sum of the product of active portfolio weights (panel A) or changes in portfolio weights (panel B) and subsequent 3-day abnormal returns surrounding earnings announcements. We formed and rebalanced the decile portfolios at the end of 2 months after each quarter from 1984Q1 to 2014Q2 and the return series ranges from June 1984 to November 2014. Decile 10 is the portfolio of funds with the highest AFP value. We compute monthly equally weighted percentage net and gross (net plus expense ratio) returns on the portfolios, as well as risk-adjusted returns based on the CAPM, the Fama and French (1993) three-factor model, the Carhart (1997) four-factor model, and the Pastor and Stambaugh (2003) five-factor model. We report the alphas as a monthly percentage.$$t$$-statistics are shown in parentheses. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Table 2 AFP and mutual fund returns: Decile portfolios A. Decile portfolios formed according to the index-based AFP Low 2 3 4 5 6 7 8 9 High High-low Net returns Average return 0.87 0.90 0.93 0.91 0.93 0.92 0.96 1.02 1.00 1.10 0.23*** (3.42) (3.74) (3.95) (3.89) (3.96) (3.90) (4.01) (4.18) (4.06) (4.16) (3.14) CAPM$$\alpha $$–0.18 –0.12 –0.08 –0.10 –0.08 –0.09 –0.06 –0.01 –0.03 0.03 0.21*** (–2.79) (–2.49) (–1.79) (–2.26) (–2.1) (–2.3) (–1.52) (–0.3) (–0.58) (0.37) (2.97) Fama-French$$\alpha$$–0.19 –0.14 –0.09 –0.11 –0.09 –0.11 –0.07 –0.01 –0.02 0.07 0.27*** (–3.52) (–3.28) (–2.52) (–3.27) (–2.87) (–3.28) (–2.13) (–0.26) (–0.39) (1.38) (3.59) Carhart$$\alpha $$–0.16 –0.12 –0.08 –0.10 –0.09 –0.11 –0.08 –0.03 –0.03 0.04 0.20*** (–2.95) (–2.84) (–2.29) (–2.8) (–2.39) (–3.16) (–2.24) (–0.72) (–0.76) (0.82) (3.23) Pastor-Stambaugh$$\alpha $$–0.17 –0.13 –0.09 –0.11 –0.09 –0.12 –0.08 –0.03 –0.03 0.05 0.22*** (–3.17) (–3.06) (–2.49) (–3.08) (–2.64) (–3.43) (–2.4) (–0.79) (–0.79) (0.93) (3.49) Gross returns Average return 0.97 1.00 1.03 1.00 1.02 1.01 1.05 1.11 1.10 1.20 0.23*** (3.83) (4.14) (4.35) (4.29) (4.35) (4.29) (4.41) (4.57) (4.46) (4.56) (3.14) CAPM$$\alpha $$–0.08 –0.02 0.02 0.00 0.01 0.00 0.03 0.08 0.07 0.13 0.21*** (–1.2) (–0.47) (0.38) (–0.03) (0.35) (0.02) (0.79) (1.74) (1.18) (1.74) (2.97) Fama-French$$\alpha $$–0.09 –0.04 0.00 –0.02 0.00 –0.01 0.02 0.09 0.08 0.18 0.27*** (–1.6) (–0.92) (0.11) (–0.57) (–0.04) (–0.42) (0.72) (2.44) (2.00) (3.33) (3.59) Carhart$$\alpha $$–0.05 –0.02 0.01 –0.01 0.01 –0.02 0.02 0.07 0.07 0.15 0.20*** (–0.98) (–0.54) (0.29) (–0.24) (0.23) (–0.47) (0.46) (1.88) (1.69) (2.84) (3.23) Pastor-Stambaugh$$\alpha $$–0.06 –0.03 0.00 –0.02 0.00 –0.02 0.01 0.07 0.07 0.15 0.22*** (–1.19) (–0.74) (0.05) (–0.51) (–0.01) (–0.7) (0.28) (1.79) (1.62) (2.89) (3.49) B. Decile portfolios formed according to the trade-based AFP Net returns Average return 0.87 0.92 0.92 0.90 0.93 0.88 0.88 0.93 0.95 0.99 0.12*** (3.23) (3.73) (3.80) (3.79) (3.88) (3.72) (3.67) (3.77) (3.82) (3.63) (2.98) CAPM$$\alpha $$–0.16 –0.06 –0.05 –0.05 –0.03 –0.07 –0.08 –0.05 –0.03 –0.04 0.12*** (–2.29) (–1.15) (–1.03) (–1.22) (–0.76) (–1.83) (–2.01) (–0.99) (–0.63) (–0.55) (2.94) Fama-French$$\alpha$$–0.14 –0.07 –0.08 –0.09 –0.05 –0.10 –0.11 –0.06 –0.03 0.01 0.15*** (–3.18) (–1.99) (–2.07) (–2.35) (–1.57) (–2.87) (–3.04) (–1.45) (–0.76) (0.11) (3.93) Carhart$$\alpha $$–0.15 –0.07 –0.07 –0.07 –0.04 –0.08 –0.10 –0.07 –0.04 –0.03 0.12*** (–3.28) (–1.63) (–1.89) (–1.92) (–1.15) (–2.32) (–2.62) (–1.85) (–0.96) (–0.7) (3.25) Pastor-Stambaugh$$\alpha $$–0.15 –0.07 –0.08 –0.08 –0.05 –0.09 –0.11 –0.08 –0.04 –0.03 0.12*** (–3.23) (–1.76) (–2.06) (–2.18) (–1.33) (–2.62) (–2.93) (–2.03) (–1.14) (–0.62) (3.34) Gross returns Average return 0.98 1.02 1.01 1.00 1.02 0.97 0.97 1.03 1.05 1.09 0.12*** (3.62) (4.13) (4.20) (4.18) (4.27) (4.12) (4.06) (4.16) (4.21) (4.03) (3.02) CAPM$$\alpha $$–0.05 0.04 0.05 0.04 0.06 0.02 0.01 0.05 0.07 0.06 0.12*** (–0.76) (0.85) (1.05) (0.93) (1.45) (0.52) (0.27) (1.00) (1.29) (0.84) (2.98) Fama-French$$\alpha $$–0.03 0.03 0.02 0.01 0.04 –0.01 –0.01 0.04 0.07 0.11 0.15*** (–0.79) (0.68) (0.54) (0.21) (1.14) (–0.15) (–0.36) (1.08) (1.92) (2.47) (3.98) Carhart$$\alpha $$–0.05 0.03 0.02 0.02 0.05 0.01 0.00 0.02 0.06 0.07 0.12*** (–1.03) (0.78) (0.57) (0.57) (1.37) (0.32) (–0.02) (0.63) (1.63) (1.53) (3.29) Pastor-Stambaugh$$\alpha $$–0.05 0.03 0.01 0.01 0.04 0.00 –0.01 0.02 0.06 0.08 0.12*** (–1.01) (0.62) (0.38) (0.29) (1.13) (0.01) (–0.33) (0.46) (1.47) (1.59) (3.39) A. Decile portfolios formed according to the index-based AFP Low 2 3 4 5 6 7 8 9 High High-low Net returns Average return 0.87 0.90 0.93 0.91 0.93 0.92 0.96 1.02 1.00 1.10 0.23*** (3.42) (3.74) (3.95) (3.89) (3.96) (3.90) (4.01) (4.18) (4.06) (4.16) (3.14) CAPM$$\alpha $$–0.18 –0.12 –0.08 –0.10 –0.08 –0.09 –0.06 –0.01 –0.03 0.03 0.21*** (–2.79) (–2.49) (–1.79) (–2.26) (–2.1) (–2.3) (–1.52) (–0.3) (–0.58) (0.37) (2.97) Fama-French$$\alpha$$–0.19 –0.14 –0.09 –0.11 –0.09 –0.11 –0.07 –0.01 –0.02 0.07 0.27*** (–3.52) (–3.28) (–2.52) (–3.27) (–2.87) (–3.28) (–2.13) (–0.26) (–0.39) (1.38) (3.59) Carhart$$\alpha $$–0.16 –0.12 –0.08 –0.10 –0.09 –0.11 –0.08 –0.03 –0.03 0.04 0.20*** (–2.95) (–2.84) (–2.29) (–2.8) (–2.39) (–3.16) (–2.24) (–0.72) (–0.76) (0.82) (3.23) Pastor-Stambaugh$$\alpha $$–0.17 –0.13 –0.09 –0.11 –0.09 –0.12 –0.08 –0.03 –0.03 0.05 0.22*** (–3.17) (–3.06) (–2.49) (–3.08) (–2.64) (–3.43) (–2.4) (–0.79) (–0.79) (0.93) (3.49) Gross returns Average return 0.97 1.00 1.03 1.00 1.02 1.01 1.05 1.11 1.10 1.20 0.23*** (3.83) (4.14) (4.35) (4.29) (4.35) (4.29) (4.41) (4.57) (4.46) (4.56) (3.14) CAPM$$\alpha $$–0.08 –0.02 0.02 0.00 0.01 0.00 0.03 0.08 0.07 0.13 0.21*** (–1.2) (–0.47) (0.38) (–0.03) (0.35) (0.02) (0.79) (1.74) (1.18) (1.74) (2.97) Fama-French$$\alpha $$–0.09 –0.04 0.00 –0.02 0.00 –0.01 0.02 0.09 0.08 0.18 0.27*** (–1.6) (–0.92) (0.11) (–0.57) (–0.04) (–0.42) (0.72) (2.44) (2.00) (3.33) (3.59) Carhart$$\alpha $$–0.05 –0.02 0.01 –0.01 0.01 –0.02 0.02 0.07 0.07 0.15 0.20*** (–0.98) (–0.54) (0.29) (–0.24) (0.23) (–0.47) (0.46) (1.88) (1.69) (2.84) (3.23) Pastor-Stambaugh$$\alpha $$–0.06 –0.03 0.00 –0.02 0.00 –0.02 0.01 0.07 0.07 0.15 0.22*** (–1.19) (–0.74) (0.05) (–0.51) (–0.01) (–0.7) (0.28) (1.79) (1.62) (2.89) (3.49) B. Decile portfolios formed according to the trade-based AFP Net returns Average return 0.87 0.92 0.92 0.90 0.93 0.88 0.88 0.93 0.95 0.99 0.12*** (3.23) (3.73) (3.80) (3.79) (3.88) (3.72) (3.67) (3.77) (3.82) (3.63) (2.98) CAPM$$\alpha $$–0.16 –0.06 –0.05 –0.05 –0.03 –0.07 –0.08 –0.05 –0.03 –0.04 0.12*** (–2.29) (–1.15) (–1.03) (–1.22) (–0.76) (–1.83) (–2.01) (–0.99) (–0.63) (–0.55) (2.94) Fama-French$$\alpha$$–0.14 –0.07 –0.08 –0.09 –0.05 –0.10 –0.11 –0.06 –0.03 0.01 0.15*** (–3.18) (–1.99) (–2.07) (–2.35) (–1.57) (–2.87) (–3.04) (–1.45) (–0.76) (0.11) (3.93) Carhart$$\alpha $$–0.15 –0.07 –0.07 –0.07 –0.04 –0.08 –0.10 –0.07 –0.04 –0.03 0.12*** (–3.28) (–1.63) (–1.89) (–1.92) (–1.15) (–2.32) (–2.62) (–1.85) (–0.96) (–0.7) (3.25) Pastor-Stambaugh$$\alpha $$–0.15 –0.07 –0.08 –0.08 –0.05 –0.09 –0.11 –0.08 –0.04 –0.03 0.12*** (–3.23) (–1.76) (–2.06) (–2.18) (–1.33) (–2.62) (–2.93) (–2.03) (–1.14) (–0.62) (3.34) Gross returns Average return 0.98 1.02 1.01 1.00 1.02 0.97 0.97 1.03 1.05 1.09 0.12*** (3.62) (4.13) (4.20) (4.18) (4.27) (4.12) (4.06) (4.16) (4.21) (4.03) (3.02) CAPM$$\alpha $$–0.05 0.04 0.05 0.04 0.06 0.02 0.01 0.05 0.07 0.06 0.12*** (–0.76) (0.85) (1.05) (0.93) (1.45) (0.52) (0.27) (1.00) (1.29) (0.84) (2.98) Fama-French$$\alpha $$–0.03 0.03 0.02 0.01 0.04 –0.01 –0.01 0.04 0.07 0.11 0.15*** (–0.79) (0.68) (0.54) (0.21) (1.14) (–0.15) (–0.36) (1.08) (1.92) (2.47) (3.98) Carhart$$\alpha $$–0.05 0.03 0.02 0.02 0.05 0.01 0.00 0.02 0.06 0.07 0.12*** (–1.03) (0.78) (0.57) (0.57) (1.37) (0.32) (–0.02) (0.63) (1.63) (1.53) (3.29) Pastor-Stambaugh$$\alpha $$–0.05 0.03 0.01 0.01 0.04 0.00 –0.01 0.02 0.06 0.08 0.12*** (–1.01) (0.62) (0.38) (0.29) (1.13) (0.01) (–0.33) (0.46) (1.47) (1.59) (3.39) This table presents the performance of decile fund portfolios formed according to their AFP. Like in Equation (3), AFP is the sum of the product of active portfolio weights (panel A) or changes in portfolio weights (panel B) and subsequent 3-day abnormal returns surrounding earnings announcements. We formed and rebalanced the decile portfolios at the end of 2 months after each quarter from 1984Q1 to 2014Q2 and the return series ranges from June 1984 to November 2014. Decile 10 is the portfolio of funds with the highest AFP value. We compute monthly equally weighted percentage net and gross (net plus expense ratio) returns on the portfolios, as well as risk-adjusted returns based on the CAPM, the Fama and French (1993) three-factor model, the Carhart (1997) four-factor model, and the Pastor and Stambaugh (2003) five-factor model. We report the alphas as a monthly percentage.$$t$$-statistics are shown in parentheses. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. We conjecture that the relatively weaker results using trade-based measure may be due to confounding empirical factors, such as the fact that fund flows often induce substantial trading activities by mutual funds (e.g., Lou 2012; Vayanos and Woolley 2013). Moreover, active weights capture a broader information set of fund managers revealed through both recent and longer-term holdings, whereas changes in portfolio weights are driven by their recent portfolio adjustments and thus reflect only their recent information. Panel B shows the results based on gross fund returns by adding back expenses, which potentially provide a clearer picture of the value in terms of the alpha created by fund managers. These results indicate that fund managers with high index-based (trade-based) AFP produce a monthly gross Carhart four-factor alpha of 15 (7) bps, with a$$t$$-statistic of 2.84 (1.53), whereas managers with low AFP produce a monthly gross four-factor alpha of$$-$$5 ($$-5) bps that is statistically indistinguishable from 0, before expenses. This finding lends further support to the notion that fund managers with high AFP tend to be skilled. 3.1.1 Accounting for the post-earnings announcement drift Researchers have documented the post-earnings announcement drift (PEAD), a tendency for stock prices to drift in the direction of earnings surprises in the weeks following earnings announcements (e.g., Ball and Brown 1968; Bernard and Thomas 1989). Although we could also view exploiting PEAD as an indicator of investment skill, we aim to distinguish between a fund manager’s ability to forecast firms’ fundamental values and his or her ability to trade on released earnings news. To examine whether the forecasting power of AFP is driven by PEAD, we form hedge portfolios that replicate the payoffs of strategies exploiting PEADs. Specifically, we follow Livnat and Mendenhall (2006) and compute the standardized earnings surprise (SUE) for each stock in each quarter: \begin{align} SUE_{i,t}=\frac{X_{i,t}-E(X_{i,t})}{P_{i,t}}, \end{align} (5) whereX_{i,t}$$is earnings per share for stock$$i $$in quarter$$t$$, E($$X_{i,t})$$is expected earnings per share for stock$$i $$in quarter$$t$$, and$$P_{i,t}$$is the price for stock$$i $$at the end of quarter$$t$$. We use the forecasts of a seasonal random walk model and consensus analyst earnings forecasts as proxies for expected earnings per share. Our primary measure of quarterly earnings is based on the primary earnings per share before extraordinary items. As a robustness check, we also consider the earnings surprises after excluding special items. We label the SUE based on the seasonal random walk model as SUE1, the SUE after excluding special items as SUE2, and the SUE based on consensus analyst forecasts as SUE3. At the end of each month, we form decile portfolios based on the SUE in the previous month. We then compute the equally weighted returns on a strategy that buys stocks in the top three deciles (high SUE) and short sells stocks in the bottom three deciles (low SUE). In turn, PEAD1, PEAD2, and PEAD3 refer to the returns on the three strategies based on alternative calculations of SUE. The results in Table 3 show that, even after we control for the effect of PEAD, the superior performance of high AFP funds remains economically and statistically significant. This finding suggests that the superior performance of high AFP funds cannot be explained by a strategy to exploit PEAD.5 Table 3 AFP and mutual fund returns: Controlling for the influence of the post-earnings announcement drift A. Decile portfolios formed according to the index-based AFP Low 2 3 4 5 6 7 8 9 High High-low Net return Six-factor: PEAD1 –0.30 –0.26 –0.20 –0.22 –0.20 –0.21 –0.18 –0.10 –0.11 –0.01 0.29*** (–4.14) (–4.86) (–4.66) (–4.75) (–4.37) (–4.68) (–3.75) (–2) (–1.74) (–0.09) (3.42) Six-factor: PEAD2 –0.32 –0.29 –0.22 –0.24 –0.22 –0.22 –0.19 –0.11 –0.11 –0.02 0.30*** (–4.46) (–5.32) (–5.16) (–5.23) (–4.83) (–5.13) (–4.09) (–2.22) (–1.84) (–0.21) (3.43) Six-factor: PEAD3 –0.23 –0.17 –0.13 –0.15 –0.12 –0.16 –0.12 –0.06 –0.08 0.01 0.24*** (–4.38) (–3.93) (–3.6) (–4.16) (–3.42) (–4.54) (–3.57) (–1.58) (–1.9) (0.20) (3.79) Gross return Six-factor: PEAD1 –0.19 –0.17 –0.11 –0.13 –0.11 –0.11 –0.09 –0.01 –0.01 0.10 0.29*** (–2.69) (–3.07) (–2.51) (–2.76) (–2.36) (–2.58) (–1.81) (–0.14) (–0.15) (1.23) (3.43) Six-factor: PEAD2 –0.22 –0.19 –0.13 –0.15 –0.12 –0.13 –0.10 –0.02 –0.01 0.09 0.30*** (–3.01) (–3.51) (–2.96) (–3.2) (–2.77) (–2.98) (–2.09) (–0.33) (–0.23) (1.11) (3.43) Six-factor: PEAD3 –0.13 –0.07 –0.04 –0.06 –0.03 –0.06 –0.03 0.04 0.02 0.12 0.24*** (–2.4) (–1.62) (–1) (–1.61) (–0.86) (–1.83) (–0.89) (1.02) (0.49) (2.06) (3.79) Net return Six-factor: PEAD1 –0.24 –0.17 –0.19 –0.20 –0.15 –0.19 –0.21 –0.17 –0.14 –0.08 0.16*** (–3.56) (–2.97) (–4.02) (–4.46) (–2.84) (–4.28) (–4.91) (–3.12) (–3) (–1.11) (4.08) Six-factor: PEAD2 –0.26 –0.19 –0.21 –0.21 –0.16 –0.20 –0.22 –0.18 –0.15 –0.09 0.17*** (–3.86) (–3.33) (–4.48) (–4.93) (–3.24) (–4.66) (–5.37) (–3.35) (–3.32) (–1.25) (4.19) Six-factor: PEAD3 –0.22 –0.13 –0.12 –0.13 –0.09 –0.13 –0.15 –0.12 –0.09 –0.07 0.14*** (–4.53) (–3.17) (–3.11) (–3.43) (–2.29) (–3.79) (–4.22) (–3.01) (–2.33) (–1.52) (3.50) Gross return Six-factor: PEAD1 –0.13 –0.07 –0.10 –0.10 –0.05 –0.09 –0.12 –0.07 –0.04 0.03 0.16*** (–1.99) (–1.27) (–2.01) (–2.34) (–1.04) (–2.15) (–2.71) (–1.34) (–0.86) (0.39) (4.12) Six-factor: PEAD2 –0.15 –0.09 –0.11 –0.12 –0.07 –0.11 –0.13 –0.08 –0.05 0.02 0.17*** (–2.27) (–1.6) (–2.44) (–2.76) (–1.38) (–2.48) (–3.12) (–1.54) (–1.12) (0.25) (4.23) Six-factor: PEAD3 –0.11 –0.03 –0.02 –0.04 0.01 –0.04 –0.05 –0.02 0.01 0.03 0.15*** (–2.35) (–0.74) (–0.64) (–0.99) (0.15) (–1.07) (–1.55) (–0.59) (0.23) (0.67) (3.54) A. Decile portfolios formed according to the index-based AFP Low 2 3 4 5 6 7 8 9 High High-low Net return Six-factor: PEAD1 –0.30 –0.26 –0.20 –0.22 –0.20 –0.21 –0.18 –0.10 –0.11 –0.01 0.29*** (–4.14) (–4.86) (–4.66) (–4.75) (–4.37) (–4.68) (–3.75) (–2) (–1.74) (–0.09) (3.42) Six-factor: PEAD2 –0.32 –0.29 –0.22 –0.24 –0.22 –0.22 –0.19 –0.11 –0.11 –0.02 0.30*** (–4.46) (–5.32) (–5.16) (–5.23) (–4.83) (–5.13) (–4.09) (–2.22) (–1.84) (–0.21) (3.43) Six-factor: PEAD3 –0.23 –0.17 –0.13 –0.15 –0.12 –0.16 –0.12 –0.06 –0.08 0.01 0.24*** (–4.38) (–3.93) (–3.6) (–4.16) (–3.42) (–4.54) (–3.57) (–1.58) (–1.9) (0.20) (3.79) Gross return Six-factor: PEAD1 –0.19 –0.17 –0.11 –0.13 –0.11 –0.11 –0.09 –0.01 –0.01 0.10 0.29*** (–2.69) (–3.07) (–2.51) (–2.76) (–2.36) (–2.58) (–1.81) (–0.14) (–0.15) (1.23) (3.43) Six-factor: PEAD2 –0.22 –0.19 –0.13 –0.15 –0.12 –0.13 –0.10 –0.02 –0.01 0.09 0.30*** (–3.01) (–3.51) (–2.96) (–3.2) (–2.77) (–2.98) (–2.09) (–0.33) (–0.23) (1.11) (3.43) Six-factor: PEAD3 –0.13 –0.07 –0.04 –0.06 –0.03 –0.06 –0.03 0.04 0.02 0.12 0.24*** (–2.4) (–1.62) (–1) (–1.61) (–0.86) (–1.83) (–0.89) (1.02) (0.49) (2.06) (3.79) Net return Six-factor: PEAD1 –0.24 –0.17 –0.19 –0.20 –0.15 –0.19 –0.21 –0.17 –0.14 –0.08 0.16*** (–3.56) (–2.97) (–4.02) (–4.46) (–2.84) (–4.28) (–4.91) (–3.12) (–3) (–1.11) (4.08) Six-factor: PEAD2 –0.26 –0.19 –0.21 –0.21 –0.16 –0.20 –0.22 –0.18 –0.15 –0.09 0.17*** (–3.86) (–3.33) (–4.48) (–4.93) (–3.24) (–4.66) (–5.37) (–3.35) (–3.32) (–1.25) (4.19) Six-factor: PEAD3 –0.22 –0.13 –0.12 –0.13 –0.09 –0.13 –0.15 –0.12 –0.09 –0.07 0.14*** (–4.53) (–3.17) (–3.11) (–3.43) (–2.29) (–3.79) (–4.22) (–3.01) (–2.33) (–1.52) (3.50) Gross return Six-factor: PEAD1 –0.13 –0.07 –0.10 –0.10 –0.05 –0.09 –0.12 –0.07 –0.04 0.03 0.16*** (–1.99) (–1.27) (–2.01) (–2.34) (–1.04) (–2.15) (–2.71) (–1.34) (–0.86) (0.39) (4.12) Six-factor: PEAD2 –0.15 –0.09 –0.11 –0.12 –0.07 –0.11 –0.13 –0.08 –0.05 0.02 0.17*** (–2.27) (–1.6) (–2.44) (–2.76) (–1.38) (–2.48) (–3.12) (–1.54) (–1.12) (0.25) (4.23) Six-factor: PEAD3 –0.11 –0.03 –0.02 –0.04 0.01 –0.04 –0.05 –0.02 0.01 0.03 0.15*** (–2.35) (–0.74) (–0.64) (–0.99) (0.15) (–1.07) (–1.55) (–0.59) (0.23) (0.67) (3.54) This table presents the performance of decile fund portfolios formed according to their AFP, controlling for the influence of PEAD. Specifically, we construct hedge portfolios that seek to replicate the payoffs of strategies exploiting the post-earnings announcement drift. We follow Livnat and Mendenhall (2006) and compute the SUE for each stock in each quarter: we use the seasonal random walk model and consensus analyst earnings forecast to proxy for expected earnings per share. We use the primary earnings per share before extraordinary items as our primary measure of quarterly earnings, and we consider the earnings surprise after the exclusion of special items. We label the SUE according to the seasonal random walk model as SUE1, the SUE after the exclusion of special items as SUE2, and the SUE based on consensus analyst forecasts as SUE3. At the end of each month, we form decile portfolios based on the SUE in the previous month and compute the equally weighted returns on a strategy that buys stocks in the top three deciles with high SUE and shorts stocks in the bottom three deciles with low SUE. The returns on the three strategies based on three SUEs are called returns to PEAD1, PEAD2, and PEAD3. We report the alphas as a monthly percentage using three versions of the six-factor models that augment the five-factor model in Table 3 ($$\alpha )$$with the return to a strategy that exploits PEAD. The$$t$$-statistics are shown in parentheses. *, **, and *** denote statistical significance at the 10%, 5%, and 1% levels, respectively. Table 3 AFP and mutual fund returns: Controlling for the influence of the post-earnings announcement drift A. Decile portfolios formed according to the index-based AFP Low 2 3 4 5 6 7 8 9 High High-low Net return Six-factor: PEAD1 –0.30 –0.26 –0.20 –0.22 –0.20 –0.21 –0.18 –0.10 –0.11 –0.01 0.29*** (–4.14) (–4.86) (–4.66) (–4.75) (–4.37) (–4.68) (–3.75) (–2) (–1.74) (–0.09) (3.42) Six-factor: PEAD2 –0.32 –0.29 –0.22 –0.24 –0.22 –0.22 –0.19 –0.11 –0.11 –0.02 0.30*** (–4.46) (–5.32) (–5.16) (–5.23) (–4.83) (–5.13) (–4.09) (–2.22) (–1.84) (–0.21) (3.43) Six-factor: PEAD3 –0.23 –0.17 –0.13 –0.15 –0.12 –0.16 –0.12 –0.06 –0.08 0.01 0.24*** (–4.38) (–3.93) (–3.6) (–4.16) (–3.42) (–4.54) (–3.57) (–1.58) (–1.9) (0.20) (3.79) Gross return Six-factor: PEAD1 –0.19 –0.17 –0.11 –0.13 –0.11 –0.11 –0.09 –0.01 –0.01 0.10 0.29*** (–2.69) (–3.07) (–2.51) (–2.76) (–2.36) (–2.58) (–1.81) (–0.14) (–0.15) (1.23) (3.43) Six-factor: PEAD2 –0.22 –0.19 –0.13 –0.15 –0.12 –0.13 –0.10 –0.02 –0.01 0.09 0.30*** (–3.01) (–3.51) (–2.96) (–3.2) (–2.77) (–2.98) (–2.09) (–0.33) (–0.23) (1.11) (3.43) Six-factor: PEAD3 –0.13 –0.07 –0.04 –0.06 –0.03 –0.06 –0.03 0.04 0.02 0.12 0.24*** (–2.4) (–1.62) (–1) (–1.61) (–0.86) (–1.83) (–0.89) (1.02) (0.49) (2.06) (3.79) Net return Six-factor: PEAD1 –0.24 –0.17 –0.19 –0.20 –0.15 –0.19 –0.21 –0.17 –0.14 –0.08 0.16*** (–3.56) (–2.97) (–4.02) (–4.46) (–2.84) (–4.28) (–4.91) (–3.12) (–3) (–1.11) (4.08) Six-factor: PEAD2 –0.26 –0.19 –0.21 –0.21 –0.16 –0.20 –0.22 –0.18 –0.15 –0.09 0.17*** (–3.86) (–3.33) (–4.48) (–4.93) (–3.24) (–4.66) (–5.37) (–3.35) (–3.32) (–1.25) (4.19) Six-factor: PEAD3 –0.22 –0.13 –0.12 –0.13 –0.09 –0.13 –0.15 –0.12 –0.09 –0.07 0.14*** (–4.53) (–3.17) (–3.11) (–3.43) (–2.29) (–3.79) (–4.22) (–3.01) (–2.33) (–1.52) (3.50) Gross return Six-factor: PEAD1 –0.13 –0.07 –0.10 –0.10 –0.05 –0.09 –0.12 –0.07 –0.04 0.03 0.16*** (–1.99) (–1.27) (–2.01) (–2.34) (–1.04) (–2.15) (–2.71) (–1.34) (–0.86) (0.39) (4.12) Six-factor: PEAD2 –0.15 –0.09 –0.11 –0.12 –0.07 –0.11 –0.13 –0.08 –0.05 0.02 0.17*** (–2.27) (–1.6) (–2.44) (–2.76) (–1.38) (–2.48) (–3.12) (–1.54) (–1.12) (0.25) (4.23) Six-factor: PEAD3 –0.11 –0.03 –0.02 –0.04 0.01 –0.04 –0.05 –0.02 0.01 0.03 0.15*** (–2.35) (–0.74) (–0.64) (–0.99) (0.15) (–1.07) (–1.55) (–0.59) (0.23) (0.67) (3.54) A. Decile portfolios formed according to the index-based AFP Low 2 3 4 5 6 7 8 9 High High-low Net return Six-factor: PEAD1 –0.30 –0.26 –0.20 –0.22 –0.20 –0.21 –0.18 –0.10 –0.11 –0.01 0.29*** (–4.14) (–4.86) (–4.66) (–4.75) (–4.37) (–4.68) (–3.75) (–2) (–1.74) (–0.09) (3.42) Six-factor: PEAD2 –0.32 –0.29 –0.22 –0.24 –0.22 –0.22 –0.19 –0.11 –0.11 –0.02 0.30*** (–4.46) (–5.32) (–5.16) (–5.23) (–4.83) (–5.13) (–4.09) (–2.22) (–1.84) (–0.21) (3.43) Six-factor: PEAD3 –0.23 –0.17 –0.13 –0.15 –0.12 –0.16 –0.12 –0.06 –0.08 0.01 0.24*** (–4.38) (–3.93) (–3.6) (–4.16) (–3.42) (–4.54) (–3.57) (–1.58) (–1.9) (0.20) (3.79) Gross return Six-factor: PEAD1 –0.19 –0.17 –0.11 –0.13 –0.11 –0.11 –0.09 –0.01 –0.01 0.10 0.29*** (–2.69) (–3.07) (–2.51) (–2.76) (–2.36) (–2.58) (–1.81) (–0.14) (–0.15) (1.23) (3.43) Six-factor: PEAD2 –0.22 –0.19 –0.13 –0.15 –0.12 –0.13 –0.10 –0.02 –0.01 0.09 0.30*** (–3.01) (–3.51) (–2.96) (–3.2) (–2.77) (–2.98) (–2.09) (–0.33) (–0.23) (1.11) (3.43) Six-factor: PEAD3 –0.13 –0.07 –0.04 –0.06 –0.03 –0.06 –0.03 0.04 0.02 0.12 0.24*** (–2.4) (–1.62) (–1) (–1.61) (–0.86) (–1.83) (–0.89) (1.02) (0.49) (2.06) (3.79) Net return Six-factor: PEAD1 –0.24 –0.17 –0.19 –0.20 –0.15 –0.19 –0.21 –0.17 –0.14 –0.08 0.16*** (–3.56) (–2.97) (–4.02) (–4.46) (–2.84) (–4.28) (–4.91) (–3.12) (–3) (–1.11) (4.08) Six-factor: PEAD2 –0.26 –0.19 –0.21 –0.21 –0.16 –0.20 –0.22 –0.18 –0.15 –0.09 0.17*** (–3.86) (–3.33) (–4.48) (–4.93) (–3.24) (–4.66) (–5.37) (–3.35) (–3.32) (–1.25) (4.19) Six-factor: PEAD3 –0.22 –0.13 –0.12 –0.13 –0.09 –0.13 –0.15 –0.12 –0.09 –0.07 0.14*** (–4.53) (–3.17) (–3.11) (–3.43) (–2.29) (–3.79) (–4.22) (–3.01) (–2.33) (–1.52) (3.50) Gross return Six-factor: PEAD1 –0.13 –0.07 –0.10 –0.10 –0.05 –0.09 –0.12 –0.07 –0.04 0.03 0.16*** (–1.99) (–1.27) (–2.01) (–2.34) (–1.04) (–2.15) (–2.71) (–1.34) (–0.86) (0.39) (4.12) Six-factor: PEAD2 –0.15 –0.09 –0.11 –0.12 –0.07 –0.11 –0.13 –0.08 –0.05 0.02 0.17*** (–2.27) (–1.6) (–2.44) (–2.76) (–1.38) (–2.48) (–3.12) (–1.54) (–1.12) (0.25) (4.23) Six-factor: PEAD3 –0.11 –0.03 –0.02 –0.04 0.01 –0.04 –0.05 –0.02 0.01 0.03 0.15*** (–2.35) (–0.74) (–0.64) (–0.99) (0.15) (–1.07) (–1.55) (–0.59) (0.23) (0.67) (3.54) This table presents the performance of decile fund portfolios formed according to their AFP, controlling for the influence of PEAD. Specifically, we construct hedge portfolios that seek to replicate the payoffs of strategies exploiting the post-earnings announcement drift. We follow Livnat and Mendenhall (2006) and compute the SUE for each stock in each quarter: we use the seasonal random walk model and consensus analyst earnings forecast to proxy for expected earnings per share. We use the primary earnings per share before extraordinary items as our primary measure of quarterly earnings, and we consider the earnings surprise after the exclusion of special items. We label the SUE according to the seasonal random walk model as SUE1, the SUE after the exclusion of special items as SUE2, and the SUE based on consensus analyst forecasts as SUE3. At the end of each month, we form decile portfolios based on the SUE in the previous month and compute the equally weighted returns on a strategy that buys stocks in the top three deciles with high SUE and shorts stocks in the bottom three deciles with low SUE. The returns on the three strategies based on three SUEs are called returns to PEAD1, PEAD2, and PEAD3. We report the alphas as a monthly percentage using three versions of the six-factor models that augment the five-factor model in Table 3 ($$\alpha )$$with the return to a strategy that exploits PEAD. The$$t$$-statistics are shown in parentheses. *, **, and *** denote statistical significance at the 10%, 5%, and 1% levels, respectively. 3.2 Double sorts In this subsection, we evaluate the robustness of the performance predictive power of AFP using double sorts, for two main reasons. First, researchers have reported a number of fund characteristics that are related to fund skill; it is therefore important to assess in detail the incremental forecasting power of AFP for fund performance relative to these characteristics. Second, if different proxies of fund skill contain complementary information, it is possible to find potential interactions between AFP and these fund characteristics. We examine CS (Daniel et al. 1997), the return gap (Kacperczyk, Sialm and Zheng 2008), RPI (Kacperczyk and Seru 2007), and active shares (Cremers and Petajisto 2009).6 The CS measure is the characteristic-adjusted return on a fund’s stock holdings. The characteristic benchmarks are formed on the basis of size, industry-adjusted book-to-market, and momentum, following Daniel et al. (1997). The return gap (Kacperczyk, Sialm and Zheng 2008) reflects the difference between a fund’s realized return and the hypothetical fund return implied by the fund’s stock holdings. It captures the value created by the fund manager due to unobserved actions, such as interim trades. A fund’s reliance on public information (Kacperczyk and Seru 2007) measures the extent to which a fund’s trades can be explained by analyst stock recommendations. The active share variable (Cremers and Petajisto 2009) measures the extent to which a fund manager’s portfolio holdings deviate from those of the benchmark index. We provide detailed descriptions of these measures in Internet Appendix B. The results in Table 4 indicate that AFP has substantial incremental forecasting power for future fund performance. Among the five variables we consider, AFP and return gap significantly predict future fund performance.7 AFP also shows strong performance forecasting power after we control for alternative measures of skill. For instance, Table 4, panel A.1, provides results using double sorts on AFP and the CS measure. The findings indicate that AFP predicts future fund performance, after controlling for CS. The return spread between funds with high and low AFP is large and statistically significant among funds in the top three quartiles. Table 4 Performance predictive power of AFP: Double sorts A. Double sorts on index-based AFP and fund characteristics AFP All Low 2 3 High High-low A.1. CS All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low CS –0.02 –0.05 –0.05 –0.01 0.00 0.04 (–0.34) (–0.68) (–0.82) (–0.25) (–0.04) (0.83) 2 –0.06 –0.10 –0.05 –0.08 –0.01 0.10** (–1.59) (–2.26) (–1.23) (–2.01) (–0.12) (2.28) 3 –0.10 –0.13 –0.15 –0.08 0.01 0.13*** (–3.08) (–3.12) (–3.83) (–2.2) (0.16) (2.87) High CS –0.13 –0.19 –0.14 –0.13 –0.02 0.18*** (–2.31) (–3.3) (–2.18) (–2.56) (–0.29) (3.05) High-low –0.10 –0.15* –0.09 –0.12 –0.02 0.13* (–1.21) (–1.72) (–0.88) (–1.43) (–0.17) (1.82) A.2 Return gap All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low return gap –0.14 –0.20 –0.14 –0.12 –0.08 0.12** (–3.38) (–4.16) (–2.82) (–2.83) (–1.62) (2.47) 2 –0.08 –0.11 –0.11 –0.10 0.01 0.13** (–2.5) (–2.48) (–3.01) (–2.71) (0.26) (2.27) 3 –0.07 –0.08 –0.09 –0.05 –0.02 0.06 (–1.71) (–1.62) (–2.15) (–1.22) (–0.41) (1.35) High return gap –0.03 –0.09 –0.09 –0.08 0.08 0.17*** (–0.78) (–1.63) (–1.8) (–1.61) (1.58) (3.44) High-low 0.11*** 0.11** 0.06 0.04 0.17*** 0.06 (2.71) (2.22) (1.06) (0.67) (3.56) (1.09) A.3 RPI All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low RPI –0.06 –0.09 –0.09 –0.10 0.01 0.10 (–1.08) (–1.28) (–1.35) (–1.8) (0.08) (1.31) 2 –0.10 –0.19 –0.14 –0.12 0.03 0.21** (–1.78) (–2.33) (–2.6) (–2.1) (0.32) (2.36) 3 –0.10 –0.17 –0.08 –0.13 –0.01 0.16** (–1.76) (–2.31) (–1.31) (–2.18) (–0.1) (2.14) High RPI –0.06 –0.12 –0.10 –0.05 0.00 0.13* (–1.02) (–1.69) (–1.52) (–0.66) (0.06) (1.68) High-low 0.00 –0.03 –0.01 0.05 0.00 0.03 (–0.05) (–0.68) (–0.17) (0.97) (–0.02) (0.56) A.4 Active share All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Inactive –0.07 –0.01 –0.05 –0.07 –0.07 –0.06 (–2.91) (–0.35) (–2.01) (–2.24) (–1.43) (–0.85) 2 –0.08 –0.09 –0.14 –0.10 –0.03 0.07 (–2.27) (–1.72) (–2.88) (–2.48) (–0.6) (0.96) 3 –0.08 –0.21 –0.10 –0.12 0.03 0.24*** (–1.55) (–3.02) (–1.59) (–1.89) (0.40) (3.09) Active –0.03 –0.10 –0.18 –0.09 0.06 0.16** (–0.5) (–1.24) (–1.89) (–1.21) (0.78) (2.28) Active-inactive 0.04 –0.08 –0.13 –0.03 0.13 0.22** (0.55) (–1.01) (–1.35) (–0.36) (1.46) (2.25) B. Double sorts on trade-based AFP and fund characteristics B.1 CS All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low CS –0.02 –0.05 0.03 –0.02 –0.04 0.01 (–0.34) (–0.72) (0.44) (–0.3) (–0.59) (0.22) 2 –0.06 –0.05 –0.08 –0.09 –0.04 0.02 (–1.59) (–1.29) (–1.9) (–2.21) (–0.8) (0.55) 3 –0.10 –0.13 –0.12 –0.10 –0.05 0.08* (–3.08) (–3.22) (–3.19) (–2.88) (–1.2) (1.96) High CS –0.13 –0.14 –0.12 –0.14 –0.07 0.08** (–2.31) (–2.24) (–2.21) (–2.74) (–1.13) (2.05) High-low –0.10 –0.09 –0.15 –0.13 –0.03 0.07 (–1.21) (–1.06) (–1.63) (–1.61) (–0.3) (1.30) B.2 Return gap All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low return gap –0.14 –0.09 –0.15 –0.16 –0.14 –0.05 (–3.38) (–1.86) (–3.15) (–4.25) (–2.76) (–1.2) 2 –0.08 –0.12 –0.08 –0.09 –0.04 0.08** (–2.5) (–3.11) (–2.12) (–2.08) (–0.99) (2.12) 3 –0.07 –0.10 –0.05 –0.07 –0.06 0.04 (–1.71) (–2.24) (–1.15) (–1.73) (–1.38) (1.00) High return gap –0.03 –0.10 –0.04 –0.04 0.02 0.12** (–0.78) (–1.74) (–0.88) (–0.75) (0.42) (2.58) High-low 0.11*** 0.00 0.11* 0.12** 0.16*** 0.16*** (2.71) (–0.04) (1.81) (2.45) (3.70) (3.08) B.3 RPI All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low RPI –0.06 –0.07 –0.05 –0.08 –0.05 0.02 (–1.08) (–1.06) (–0.79) (–1.33) (–0.81) (0.47) 2 –0.10 –0.11 –0.10 –0.09 –0.07 0.04 (–1.78) (–1.49) (–1.77) (–1.42) (–0.89) (0.66) 3 –0.10 –0.09 –0.14 –0.07 –0.13 –0.03 (–1.76) (–1.26) (–2.25) (–1.16) (–1.7) (–0.5) High RPI –0.06 –0.13 –0.07 –0.06 0.00 0.13** (–1.02) (–1.64) (–1.06) (–0.95) (0.01) (1.99) High-low 0.00 –0.05 –0.02 0.02 0.05 0.10** (–0.05) (–1.01) (–0.48) (0.46) (1.17) (1.98) B.4 Active share All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Inactive –0.07 –0.06 –0.06 –0.07 –0.01 0.06 (–2.91) (–1.83) (–2) (–2.87) (–0.2) (1.47) 2 –0.08 –0.09 –0.09 –0.14 –0.07 0.02 (–2.27) (–1.68) (–1.55) (–3.24) (–1.69) (0.38) 3 –0.08 –0.07 –0.12 –0.10 –0.05 0.02 (–1.55) (–0.94) (–1.88) (–1.73) (–0.78) (0.40) Active –0.03 –0.11 –0.10 –0.04 –0.03 0.08 (–0.5) (–1.43) (–1.13) (–0.46) (–0.41) (1.62) Active-inactive 0.04 –0.04 –0.04 0.03 –0.02 0.02 (0.55) (–0.6) (–0.45) (0.43) (–0.28) (0.42) A. Double sorts on index-based AFP and fund characteristics AFP All Low 2 3 High High-low A.1. CS All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low CS –0.02 –0.05 –0.05 –0.01 0.00 0.04 (–0.34) (–0.68) (–0.82) (–0.25) (–0.04) (0.83) 2 –0.06 –0.10 –0.05 –0.08 –0.01 0.10** (–1.59) (–2.26) (–1.23) (–2.01) (–0.12) (2.28) 3 –0.10 –0.13 –0.15 –0.08 0.01 0.13*** (–3.08) (–3.12) (–3.83) (–2.2) (0.16) (2.87) High CS –0.13 –0.19 –0.14 –0.13 –0.02 0.18*** (–2.31) (–3.3) (–2.18) (–2.56) (–0.29) (3.05) High-low –0.10 –0.15* –0.09 –0.12 –0.02 0.13* (–1.21) (–1.72) (–0.88) (–1.43) (–0.17) (1.82) A.2 Return gap All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low return gap –0.14 –0.20 –0.14 –0.12 –0.08 0.12** (–3.38) (–4.16) (–2.82) (–2.83) (–1.62) (2.47) 2 –0.08 –0.11 –0.11 –0.10 0.01 0.13** (–2.5) (–2.48) (–3.01) (–2.71) (0.26) (2.27) 3 –0.07 –0.08 –0.09 –0.05 –0.02 0.06 (–1.71) (–1.62) (–2.15) (–1.22) (–0.41) (1.35) High return gap –0.03 –0.09 –0.09 –0.08 0.08 0.17*** (–0.78) (–1.63) (–1.8) (–1.61) (1.58) (3.44) High-low 0.11*** 0.11** 0.06 0.04 0.17*** 0.06 (2.71) (2.22) (1.06) (0.67) (3.56) (1.09) A.3 RPI All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low RPI –0.06 –0.09 –0.09 –0.10 0.01 0.10 (–1.08) (–1.28) (–1.35) (–1.8) (0.08) (1.31) 2 –0.10 –0.19 –0.14 –0.12 0.03 0.21** (–1.78) (–2.33) (–2.6) (–2.1) (0.32) (2.36) 3 –0.10 –0.17 –0.08 –0.13 –0.01 0.16** (–1.76) (–2.31) (–1.31) (–2.18) (–0.1) (2.14) High RPI –0.06 –0.12 –0.10 –0.05 0.00 0.13* (–1.02) (–1.69) (–1.52) (–0.66) (0.06) (1.68) High-low 0.00 –0.03 –0.01 0.05 0.00 0.03 (–0.05) (–0.68) (–0.17) (0.97) (–0.02) (0.56) A.4 Active share All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Inactive –0.07 –0.01 –0.05 –0.07 –0.07 –0.06 (–2.91) (–0.35) (–2.01) (–2.24) (–1.43) (–0.85) 2 –0.08 –0.09 –0.14 –0.10 –0.03 0.07 (–2.27) (–1.72) (–2.88) (–2.48) (–0.6) (0.96) 3 –0.08 –0.21 –0.10 –0.12 0.03 0.24*** (–1.55) (–3.02) (–1.59) (–1.89) (0.40) (3.09) Active –0.03 –0.10 –0.18 –0.09 0.06 0.16** (–0.5) (–1.24) (–1.89) (–1.21) (0.78) (2.28) Active-inactive 0.04 –0.08 –0.13 –0.03 0.13 0.22** (0.55) (–1.01) (–1.35) (–0.36) (1.46) (2.25) B. Double sorts on trade-based AFP and fund characteristics B.1 CS All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low CS –0.02 –0.05 0.03 –0.02 –0.04 0.01 (–0.34) (–0.72) (0.44) (–0.3) (–0.59) (0.22) 2 –0.06 –0.05 –0.08 –0.09 –0.04 0.02 (–1.59) (–1.29) (–1.9) (–2.21) (–0.8) (0.55) 3 –0.10 –0.13 –0.12 –0.10 –0.05 0.08* (–3.08) (–3.22) (–3.19) (–2.88) (–1.2) (1.96) High CS –0.13 –0.14 –0.12 –0.14 –0.07 0.08** (–2.31) (–2.24) (–2.21) (–2.74) (–1.13) (2.05) High-low –0.10 –0.09 –0.15 –0.13 –0.03 0.07 (–1.21) (–1.06) (–1.63) (–1.61) (–0.3) (1.30) B.2 Return gap All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low return gap –0.14 –0.09 –0.15 –0.16 –0.14 –0.05 (–3.38) (–1.86) (–3.15) (–4.25) (–2.76) (–1.2) 2 –0.08 –0.12 –0.08 –0.09 –0.04 0.08** (–2.5) (–3.11) (–2.12) (–2.08) (–0.99) (2.12) 3 –0.07 –0.10 –0.05 –0.07 –0.06 0.04 (–1.71) (–2.24) (–1.15) (–1.73) (–1.38) (1.00) High return gap –0.03 –0.10 –0.04 –0.04 0.02 0.12** (–0.78) (–1.74) (–0.88) (–0.75) (0.42) (2.58) High-low 0.11*** 0.00 0.11* 0.12** 0.16*** 0.16*** (2.71) (–0.04) (1.81) (2.45) (3.70) (3.08) B.3 RPI All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low RPI –0.06 –0.07 –0.05 –0.08 –0.05 0.02 (–1.08) (–1.06) (–0.79) (–1.33) (–0.81) (0.47) 2 –0.10 –0.11 –0.10 –0.09 –0.07 0.04 (–1.78) (–1.49) (–1.77) (–1.42) (–0.89) (0.66) 3 –0.10 –0.09 –0.14 –0.07 –0.13 –0.03 (–1.76) (–1.26) (–2.25) (–1.16) (–1.7) (–0.5) High RPI –0.06 –0.13 –0.07 –0.06 0.00 0.13** (–1.02) (–1.64) (–1.06) (–0.95) (0.01) (1.99) High-low 0.00 –0.05 –0.02 0.02 0.05 0.10** (–0.05) (–1.01) (–0.48) (0.46) (1.17) (1.98) B.4 Active share All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Inactive –0.07 –0.06 –0.06 –0.07 –0.01 0.06 (–2.91) (–1.83) (–2) (–2.87) (–0.2) (1.47) 2 –0.08 –0.09 –0.09 –0.14 –0.07 0.02 (–2.27) (–1.68) (–1.55) (–3.24) (–1.69) (0.38) 3 –0.08 –0.07 –0.12 –0.10 –0.05 0.02 (–1.55) (–0.94) (–1.88) (–1.73) (–0.78) (0.40) Active –0.03 –0.11 –0.10 –0.04 –0.03 0.08 (–0.5) (–1.43) (–1.13) (–0.46) (–0.41) (1.62) Active-inactive 0.04 –0.04 –0.04 0.03 –0.02 0.02 (0.55) (–0.6) (–0.45) (0.43) (–0.28) (0.42) This table presents the performance of portfolios formed using the AFP and fund characteristics that relate to fund skill. We sort funds independently into four groups based on AFP and into four groups based on the following fund characteristics: DGTW characteristic selectivity (CS, subpanel 1), return gap (subpanel 2), reliance on public information (subpanel 3), and active share (subpanel 4). The “All” row and “All” column represent portfolios based on a univariate sort of AFP and an alternative fund characteristic, respectively. We report the Carhart (1997) four-factor$$\alpha $$as a monthly percentage, based on net returns for each of the 16 portfolios.$$t$$-statistics are shown in parentheses. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Table 4 Performance predictive power of AFP: Double sorts A. Double sorts on index-based AFP and fund characteristics AFP All Low 2 3 High High-low A.1. CS All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low CS –0.02 –0.05 –0.05 –0.01 0.00 0.04 (–0.34) (–0.68) (–0.82) (–0.25) (–0.04) (0.83) 2 –0.06 –0.10 –0.05 –0.08 –0.01 0.10** (–1.59) (–2.26) (–1.23) (–2.01) (–0.12) (2.28) 3 –0.10 –0.13 –0.15 –0.08 0.01 0.13*** (–3.08) (–3.12) (–3.83) (–2.2) (0.16) (2.87) High CS –0.13 –0.19 –0.14 –0.13 –0.02 0.18*** (–2.31) (–3.3) (–2.18) (–2.56) (–0.29) (3.05) High-low –0.10 –0.15* –0.09 –0.12 –0.02 0.13* (–1.21) (–1.72) (–0.88) (–1.43) (–0.17) (1.82) A.2 Return gap All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low return gap –0.14 –0.20 –0.14 –0.12 –0.08 0.12** (–3.38) (–4.16) (–2.82) (–2.83) (–1.62) (2.47) 2 –0.08 –0.11 –0.11 –0.10 0.01 0.13** (–2.5) (–2.48) (–3.01) (–2.71) (0.26) (2.27) 3 –0.07 –0.08 –0.09 –0.05 –0.02 0.06 (–1.71) (–1.62) (–2.15) (–1.22) (–0.41) (1.35) High return gap –0.03 –0.09 –0.09 –0.08 0.08 0.17*** (–0.78) (–1.63) (–1.8) (–1.61) (1.58) (3.44) High-low 0.11*** 0.11** 0.06 0.04 0.17*** 0.06 (2.71) (2.22) (1.06) (0.67) (3.56) (1.09) A.3 RPI All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low RPI –0.06 –0.09 –0.09 –0.10 0.01 0.10 (–1.08) (–1.28) (–1.35) (–1.8) (0.08) (1.31) 2 –0.10 –0.19 –0.14 –0.12 0.03 0.21** (–1.78) (–2.33) (–2.6) (–2.1) (0.32) (2.36) 3 –0.10 –0.17 –0.08 –0.13 –0.01 0.16** (–1.76) (–2.31) (–1.31) (–2.18) (–0.1) (2.14) High RPI –0.06 –0.12 –0.10 –0.05 0.00 0.13* (–1.02) (–1.69) (–1.52) (–0.66) (0.06) (1.68) High-low 0.00 –0.03 –0.01 0.05 0.00 0.03 (–0.05) (–0.68) (–0.17) (0.97) (–0.02) (0.56) A.4 Active share All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Inactive –0.07 –0.01 –0.05 –0.07 –0.07 –0.06 (–2.91) (–0.35) (–2.01) (–2.24) (–1.43) (–0.85) 2 –0.08 –0.09 –0.14 –0.10 –0.03 0.07 (–2.27) (–1.72) (–2.88) (–2.48) (–0.6) (0.96) 3 –0.08 –0.21 –0.10 –0.12 0.03 0.24*** (–1.55) (–3.02) (–1.59) (–1.89) (0.40) (3.09) Active –0.03 –0.10 –0.18 –0.09 0.06 0.16** (–0.5) (–1.24) (–1.89) (–1.21) (0.78) (2.28) Active-inactive 0.04 –0.08 –0.13 –0.03 0.13 0.22** (0.55) (–1.01) (–1.35) (–0.36) (1.46) (2.25) B. Double sorts on trade-based AFP and fund characteristics B.1 CS All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low CS –0.02 –0.05 0.03 –0.02 –0.04 0.01 (–0.34) (–0.72) (0.44) (–0.3) (–0.59) (0.22) 2 –0.06 –0.05 –0.08 –0.09 –0.04 0.02 (–1.59) (–1.29) (–1.9) (–2.21) (–0.8) (0.55) 3 –0.10 –0.13 –0.12 –0.10 –0.05 0.08* (–3.08) (–3.22) (–3.19) (–2.88) (–1.2) (1.96) High CS –0.13 –0.14 –0.12 –0.14 –0.07 0.08** (–2.31) (–2.24) (–2.21) (–2.74) (–1.13) (2.05) High-low –0.10 –0.09 –0.15 –0.13 –0.03 0.07 (–1.21) (–1.06) (–1.63) (–1.61) (–0.3) (1.30) B.2 Return gap All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low return gap –0.14 –0.09 –0.15 –0.16 –0.14 –0.05 (–3.38) (–1.86) (–3.15) (–4.25) (–2.76) (–1.2) 2 –0.08 –0.12 –0.08 –0.09 –0.04 0.08** (–2.5) (–3.11) (–2.12) (–2.08) (–0.99) (2.12) 3 –0.07 –0.10 –0.05 –0.07 –0.06 0.04 (–1.71) (–2.24) (–1.15) (–1.73) (–1.38) (1.00) High return gap –0.03 –0.10 –0.04 –0.04 0.02 0.12** (–0.78) (–1.74) (–0.88) (–0.75) (0.42) (2.58) High-low 0.11*** 0.00 0.11* 0.12** 0.16*** 0.16*** (2.71) (–0.04) (1.81) (2.45) (3.70) (3.08) B.3 RPI All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low RPI –0.06 –0.07 –0.05 –0.08 –0.05 0.02 (–1.08) (–1.06) (–0.79) (–1.33) (–0.81) (0.47) 2 –0.10 –0.11 –0.10 –0.09 –0.07 0.04 (–1.78) (–1.49) (–1.77) (–1.42) (–0.89) (0.66) 3 –0.10 –0.09 –0.14 –0.07 –0.13 –0.03 (–1.76) (–1.26) (–2.25) (–1.16) (–1.7) (–0.5) High RPI –0.06 –0.13 –0.07 –0.06 0.00 0.13** (–1.02) (–1.64) (–1.06) (–0.95) (0.01) (1.99) High-low 0.00 –0.05 –0.02 0.02 0.05 0.10** (–0.05) (–1.01) (–0.48) (0.46) (1.17) (1.98) B.4 Active share All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Inactive –0.07 –0.06 –0.06 –0.07 –0.01 0.06 (–2.91) (–1.83) (–2) (–2.87) (–0.2) (1.47) 2 –0.08 –0.09 –0.09 –0.14 –0.07 0.02 (–2.27) (–1.68) (–1.55) (–3.24) (–1.69) (0.38) 3 –0.08 –0.07 –0.12 –0.10 –0.05 0.02 (–1.55) (–0.94) (–1.88) (–1.73) (–0.78) (0.40) Active –0.03 –0.11 –0.10 –0.04 –0.03 0.08 (–0.5) (–1.43) (–1.13) (–0.46) (–0.41) (1.62) Active-inactive 0.04 –0.04 –0.04 0.03 –0.02 0.02 (0.55) (–0.6) (–0.45) (0.43) (–0.28) (0.42) A. Double sorts on index-based AFP and fund characteristics AFP All Low 2 3 High High-low A.1. CS All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low CS –0.02 –0.05 –0.05 –0.01 0.00 0.04 (–0.34) (–0.68) (–0.82) (–0.25) (–0.04) (0.83) 2 –0.06 –0.10 –0.05 –0.08 –0.01 0.10** (–1.59) (–2.26) (–1.23) (–2.01) (–0.12) (2.28) 3 –0.10 –0.13 –0.15 –0.08 0.01 0.13*** (–3.08) (–3.12) (–3.83) (–2.2) (0.16) (2.87) High CS –0.13 –0.19 –0.14 –0.13 –0.02 0.18*** (–2.31) (–3.3) (–2.18) (–2.56) (–0.29) (3.05) High-low –0.10 –0.15* –0.09 –0.12 –0.02 0.13* (–1.21) (–1.72) (–0.88) (–1.43) (–0.17) (1.82) A.2 Return gap All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low return gap –0.14 –0.20 –0.14 –0.12 –0.08 0.12** (–3.38) (–4.16) (–2.82) (–2.83) (–1.62) (2.47) 2 –0.08 –0.11 –0.11 –0.10 0.01 0.13** (–2.5) (–2.48) (–3.01) (–2.71) (0.26) (2.27) 3 –0.07 –0.08 –0.09 –0.05 –0.02 0.06 (–1.71) (–1.62) (–2.15) (–1.22) (–0.41) (1.35) High return gap –0.03 –0.09 –0.09 –0.08 0.08 0.17*** (–0.78) (–1.63) (–1.8) (–1.61) (1.58) (3.44) High-low 0.11*** 0.11** 0.06 0.04 0.17*** 0.06 (2.71) (2.22) (1.06) (0.67) (3.56) (1.09) A.3 RPI All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Low RPI –0.06 –0.09 –0.09 –0.10 0.01 0.10 (–1.08) (–1.28) (–1.35) (–1.8) (0.08) (1.31) 2 –0.10 –0.19 –0.14 –0.12 0.03 0.21** (–1.78) (–2.33) (–2.6) (–2.1) (0.32) (2.36) 3 –0.10 –0.17 –0.08 –0.13 –0.01 0.16** (–1.76) (–2.31) (–1.31) (–2.18) (–0.1) (2.14) High RPI –0.06 –0.12 –0.10 –0.05 0.00 0.13* (–1.02) (–1.69) (–1.52) (–0.66) (0.06) (1.68) High-low 0.00 –0.03 –0.01 0.05 0.00 0.03 (–0.05) (–0.68) (–0.17) (0.97) (–0.02) (0.56) A.4 Active share All –0.12 –0.10 –0.08 0.00 0.12*** (–2.89) (–2.82) (–2.47) (–0.02) (2.90) Inactive –0.07 –0.01 –0.05 –0.07 –0.07 –0.06 (–2.91) (–0.35) (–2.01) (–2.24) (–1.43) (–0.85) 2 –0.08 –0.09 –0.14 –0.10 –0.03 0.07 (–2.27) (–1.72) (–2.88) (–2.48) (–0.6) (0.96) 3 –0.08 –0.21 –0.10 –0.12 0.03 0.24*** (–1.55) (–3.02) (–1.59) (–1.89) (0.40) (3.09) Active –0.03 –0.10 –0.18 –0.09 0.06 0.16** (–0.5) (–1.24) (–1.89) (–1.21) (0.78) (2.28) Active-inactive 0.04 –0.08 –0.13 –0.03 0.13 0.22** (0.55) (–1.01) (–1.35) (–0.36) (1.46) (2.25) B. Double sorts on trade-based AFP and fund characteristics B.1 CS All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low CS –0.02 –0.05 0.03 –0.02 –0.04 0.01 (–0.34) (–0.72) (0.44) (–0.3) (–0.59) (0.22) 2 –0.06 –0.05 –0.08 –0.09 –0.04 0.02 (–1.59) (–1.29) (–1.9) (–2.21) (–0.8) (0.55) 3 –0.10 –0.13 –0.12 –0.10 –0.05 0.08* (–3.08) (–3.22) (–3.19) (–2.88) (–1.2) (1.96) High CS –0.13 –0.14 –0.12 –0.14 –0.07 0.08** (–2.31) (–2.24) (–2.21) (–2.74) (–1.13) (2.05) High-low –0.10 –0.09 –0.15 –0.13 –0.03 0.07 (–1.21) (–1.06) (–1.63) (–1.61) (–0.3) (1.30) B.2 Return gap All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low return gap –0.14 –0.09 –0.15 –0.16 –0.14 –0.05 (–3.38) (–1.86) (–3.15) (–4.25) (–2.76) (–1.2) 2 –0.08 –0.12 –0.08 –0.09 –0.04 0.08** (–2.5) (–3.11) (–2.12) (–2.08) (–0.99) (2.12) 3 –0.07 –0.10 –0.05 –0.07 –0.06 0.04 (–1.71) (–2.24) (–1.15) (–1.73) (–1.38) (1.00) High return gap –0.03 –0.10 –0.04 –0.04 0.02 0.12** (–0.78) (–1.74) (–0.88) (–0.75) (0.42) (2.58) High-low 0.11*** 0.00 0.11* 0.12** 0.16*** 0.16*** (2.71) (–0.04) (1.81) (2.45) (3.70) (3.08) B.3 RPI All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Low RPI –0.06 –0.07 –0.05 –0.08 –0.05 0.02 (–1.08) (–1.06) (–0.79) (–1.33) (–0.81) (0.47) 2 –0.10 –0.11 –0.10 –0.09 –0.07 0.04 (–1.78) (–1.49) (–1.77) (–1.42) (–0.89) (0.66) 3 –0.10 –0.09 –0.14 –0.07 –0.13 –0.03 (–1.76) (–1.26) (–2.25) (–1.16) (–1.7) (–0.5) High RPI –0.06 –0.13 –0.07 –0.06 0.00 0.13** (–1.02) (–1.64) (–1.06) (–0.95) (0.01) (1.99) High-low 0.00 –0.05 –0.02 0.02 0.05 0.10** (–0.05) (–1.01) (–0.48) (0.46) (1.17) (1.98) B.4 Active share All –0.10 –0.07 –0.08 –0.05 0.05** (–2.57) (–2.05) (–2.51) (–1.34) (2.01) Inactive –0.07 –0.06 –0.06 –0.07 –0.01 0.06 (–2.91) (–1.83) (–2) (–2.87) (–0.2) (1.47) 2 –0.08 –0.09 –0.09 –0.14 –0.07 0.02 (–2.27) (–1.68) (–1.55) (–3.24) (–1.69) (0.38) 3 –0.08 –0.07 –0.12 –0.10 –0.05 0.02 (–1.55) (–0.94) (–1.88) (–1.73) (–0.78) (0.40) Active –0.03 –0.11 –0.10 –0.04 –0.03 0.08 (–0.5) (–1.43) (–1.13) (–0.46) (–0.41) (1.62) Active-inactive 0.04 –0.04 –0.04 0.03 –0.02 0.02 (0.55) (–0.6) (–0.45) (0.43) (–0.28) (0.42) This table presents the performance of portfolios formed using the AFP and fund characteristics that relate to fund skill. We sort funds independently into four groups based on AFP and into four groups based on the following fund characteristics: DGTW characteristic selectivity (CS, subpanel 1), return gap (subpanel 2), reliance on public information (subpanel 3), and active share (subpanel 4). The “All” row and “All” column represent portfolios based on a univariate sort of AFP and an alternative fund characteristic, respectively. We report the Carhart (1997) four-factor$$\alpha $$as a monthly percentage, based on net returns for each of the 16 portfolios.$$t$$-statistics are shown in parentheses. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. In these double sorts, the return gap stands out as a strong predictor of future fund performance. For instance, in Table 4, panel A.2, funds with a high return gap outperform their peers with a low return gap for two quartiles of funds sorted by AFP. Despite this strong performance, AFP predicts future fund performance among three quartiles of funds sorted by return gap, even though AFP is limited to quarterly reporting and does not capture intraquarter trades, whereas return gaps do. Therefore, it is useful to combine the information signals from both the return gap and AFP for fund manager selection. As Table 4, panel A.2, shows, mutual funds in the top quartiles of the AFP and return gap yield a net four-factor alpha of 0.96% per year, whereas funds in the bottom quartiles of the AFP and return gap generate a net four-factor alpha of$$-$$2.40% per year. Mutual funds investors who switch from the unskilled funds to the skilled funds in our sample period would have achieved an increase in the four-factor alpha of 3.36% per year. 3.3 Predictive panel regressions We also use multivariate regressions to examine the incremental predictive power of AFP for mutual fund performance after we control for other performance predictors and fund characteristics. Our measure of mutual fund performance is the four-factor alpha measured as the difference between the realized fund return in excess of the expected return from a four-factor model, which includes the market, size, value, and momentum factors. To estimate the factor loadings, we use rolling-window time-series regressions of fund returns in the previous 3 years. In addition to CS, return gap, RPI, and active share, the fund characteristics we consider include fund size, measured as the natural log of fund assets under management, the natural log of fund age in years, the expense ratio, fund turnover, percentage flows in the past quarter, and fund alpha estimated in the past 3 years. Table 5 presents the results from the predictive panel regressions. We start with a univariate regression with each of the skill measure, and then run a multivariate regression controlling for fund characteristics. Finally, we specify a regression which includes all the measures of skill and fund characteristics. To control for aggregate movements in fund returns over time, we include time fixed effects in all the regressions. Furthermore, because the residuals might correlate within funds, we cluster standard errors by fund (Petersen 2009).8 Table 5 AFP and mutual fund returns: Predictive panel regressions A. Index-based AFP (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) AFP_Index 2.955*** 2.467*** 3.063*** (4.38) (3.58) (3.46) CS 0.420** –0.186 –0.185 (1.98) (–0.89) (–0.73) Return gap 10.68*** 7.077** 3.661 (3.99) (2.52) (0.94) RPI –0.230* –0.245** –0.306** (–1.95) (–2.04) (–2.42) Active share 0.141*** 0.185*** 0.174*** (3.75) (4.93) (4.45) log(TNA) –0.00759*** –0.00758*** –0.00680*** –0.0123*** –0.00700** –0.00894** (–2.93) (–2.92) (–2.61) (–3.45) (–2.05) (–2.45) log(Age) –0.00376 –0.00364 –0.00448 0.00129 –0.00285 0.00143 (–0.65) (–0.62) (–0.76) (0.17) (–0.42) (0.19) Expense –8.630*** –8.589*** –8.763*** –7.488*** –8.835*** –8.815*** (–7.23) (–7.17) (–7.17) (–4.81) (–6.33) (–5.70) Turnover –0.0206*** –0.0206*** –0.0197*** –0.0155** –0.0248*** –0.0171** (–3.16) (–3.15) (–3.03) (–2.18) (–2.83) (–2.16) Past flow 0.107*** 0.110*** 0.103*** 0.107** 0.130*** 0.124** (2.73) (2.82) (2.63) (2.13) (2.72) (2.47) Past alpha 6.020*** 6.225*** 6.432*** 2.468 3.952** 3.586** (4.08) (4.14) (4.35) (1.42) (2.27) (1.96) Adj. R$$^{\mathrm{2}}$$0.0928 0.0911 0.0927 0.0910 0.0925 0.0912 0.101 0.0984 0.0962 0.0944 0.0990 N 239,966 222,398 239,919 222,354 230,597 214,372 150,351 138,771 167,343 153,011 123,731 B. Trade-based AFP AFP_Trade 1.472** 1.242* 2.067** (2.33) (1.90) (2.40) CS 0.420** –0.186 –0.177 (1.98) (–0.89) (–0.70) Return gap 10.68*** 7.077** 3.696 (3.99) (2.52) (0.95) RPI –0.230* –0.245** –0.308** (–1.95) (–2.04) (–2.43) Active share 0.141*** 0.185*** 0.173*** (3.75) (4.93) (4.44) log(TNA) –0.00748*** –0.00758*** –0.00680*** –0.0123*** –0.00700** –0.00880** (–2.88) (–2.92) (–2.61) (–3.45) (–2.05) (–2.41) log(Age) –0.00374 –0.00364 –0.00448 0.00129 –0.00285 0.00175 (–0.64) (–0.62) (–0.76) (0.17) (–0.42) (0.24) Expense –8.615*** –8.589*** –8.763*** –7.488*** –8.835*** –8.795*** (–7.20) (–7.17) (–7.17) (–4.81) (–6.33) (–5.68) Turnover –0.0207*** –0.0206*** –0.0197*** –0.0155** –0.0248*** –0.0173** (–3.17) (–3.15) (–3.03) (–2.18) (–2.83) (–2.19) Past flow 0.107*** 0.110*** 0.103*** 0.107** 0.130*** 0.124** (2.72) (2.82) (2.63) (2.13) (2.72) (2.46) Past alpha 6.001*** 6.225*** 6.432*** 2.468 3.952** 3.538* (4.05) (4.14) (4.35) (1.42) (2.27) (1.94) Adj. R$$^{\mathrm{2}}$$0.0927 0.0911 0.0927 0.0910 0.0925 0.0912 0.101 0.0984 0.0962 0.0944 0.0989 N 239,966 222,398 239,919 222,354 230,597 214,372 150,351 138,771 167,343 153,011 123,731 A. Index-based AFP (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) AFP_Index 2.955*** 2.467*** 3.063*** (4.38) (3.58) (3.46) CS 0.420** –0.186 –0.185 (1.98) (–0.89) (–0.73) Return gap 10.68*** 7.077** 3.661 (3.99) (2.52) (0.94) RPI –0.230* –0.245** –0.306** (–1.95) (–2.04) (–2.42) Active share 0.141*** 0.185*** 0.174*** (3.75) (4.93) (4.45) log(TNA) –0.00759*** –0.00758*** –0.00680*** –0.0123*** –0.00700** –0.00894** (–2.93) (–2.92) (–2.61) (–3.45) (–2.05) (–2.45) log(Age) –0.00376 –0.00364 –0.00448 0.00129 –0.00285 0.00143 (–0.65) (–0.62) (–0.76) (0.17) (–0.42) (0.19) Expense –8.630*** –8.589*** –8.763*** –7.488*** –8.835*** –8.815*** (–7.23) (–7.17) (–7.17) (–4.81) (–6.33) (–5.70) Turnover –0.0206*** –0.0206*** –0.0197*** –0.0155** –0.0248*** –0.0171** (–3.16) (–3.15) (–3.03) (–2.18) (–2.83) (–2.16) Past flow 0.107*** 0.110*** 0.103*** 0.107** 0.130*** 0.124** (2.73) (2.82) (2.63) (2.13) (2.72) (2.47) Past alpha 6.020*** 6.225*** 6.432*** 2.468 3.952** 3.586** (4.08) (4.14) (4.35) (1.42) (2.27) (1.96) Adj. R$$^{\mathrm{2}}$$0.0928 0.0911 0.0927 0.0910 0.0925 0.0912 0.101 0.0984 0.0962 0.0944 0.0990 N 239,966 222,398 239,919 222,354 230,597 214,372 150,351 138,771 167,343 153,011 123,731 B. Trade-based AFP AFP_Trade 1.472** 1.242* 2.067** (2.33) (1.90) (2.40) CS 0.420** –0.186 –0.177 (1.98) (–0.89) (–0.70) Return gap 10.68*** 7.077** 3.696 (3.99) (2.52) (0.95) RPI –0.230* –0.245** –0.308** (–1.95) (–2.04) (–2.43) Active share 0.141*** 0.185*** 0.173*** (3.75) (4.93) (4.44) log(TNA) –0.00748*** –0.00758*** –0.00680*** –0.0123*** –0.00700** –0.00880** (–2.88) (–2.92) (–2.61) (–3.45) (–2.05) (–2.41) log(Age) –0.00374 –0.00364 –0.00448 0.00129 –0.00285 0.00175 (–0.64) (–0.62) (–0.76) (0.17) (–0.42) (0.24) Expense –8.615*** –8.589*** –8.763*** –7.488*** –8.835*** –8.795*** (–7.20) (–7.17) (–7.17) (–4.81) (–6.33) (–5.68) Turnover –0.0207*** –0.0206*** –0.0197*** –0.0155** –0.0248*** –0.0173** (–3.17) (–3.15) (–3.03) (–2.18) (–2.83) (–2.19) Past flow 0.107*** 0.110*** 0.103*** 0.107** 0.130*** 0.124** (2.72) (2.82) (2.63) (2.13) (2.72) (2.46) Past alpha 6.001*** 6.225*** 6.432*** 2.468 3.952** 3.538* (4.05) (4.14) (4.35) (1.42) (2.27) (1.94) Adj. R$$^{\mathrm{2}}$$0.0927 0.0911 0.0927 0.0910 0.0925 0.0912 0.101 0.0984 0.0962 0.0944 0.0989 N 239,966 222,398 239,919 222,354 230,597 214,372 150,351 138,771 167,343 153,011 123,731 This table presents coefficient estimates from predictive panel regressions estimating the association between the AFP and future fund performance. Like in Equation (3), AFP is the sum of the product of active portfolio weights (changes in portfolio weights) and subsequent 3-day abnormal returns surrounding earnings announcements for the index-based (trade-based) measure. We also include other holdings-based measures of skill such as CS, return gap, RPI, and active share. All measures of skill are winsorized at the top and the bottom 5%. We measure future mutual fund performance using Carhart’s (1997) four-factor alpha (as a percentage), where fund betas are estimated using rolling-window regressions in the past 3 years. The panel regressions control for fund size, fund age, expense ratio, fund turnover, fund percentage flow in the past quarter, and fund alpha in the past 3 years. The regressions include time fixed effects, and the standard errors are clustered by fund.$$t$$-statistics are presented in parentheses. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Table 5 AFP and mutual fund returns: Predictive panel regressions A. Index-based AFP (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) AFP_Index 2.955*** 2.467*** 3.063*** (4.38) (3.58) (3.46) CS 0.420** –0.186 –0.185 (1.98) (–0.89) (–0.73) Return gap 10.68*** 7.077** 3.661 (3.99) (2.52) (0.94) RPI –0.230* –0.245** –0.306** (–1.95) (–2.04) (–2.42) Active share 0.141*** 0.185*** 0.174*** (3.75) (4.93) (4.45) log(TNA) –0.00759*** –0.00758*** –0.00680*** –0.0123*** –0.00700** –0.00894** (–2.93) (–2.92) (–2.61) (–3.45) (–2.05) (–2.45) log(Age) –0.00376 –0.00364 –0.00448 0.00129 –0.00285 0.00143 (–0.65) (–0.62) (–0.76) (0.17) (–0.42) (0.19) Expense –8.630*** –8.589*** –8.763*** –7.488*** –8.835*** –8.815*** (–7.23) (–7.17) (–7.17) (–4.81) (–6.33) (–5.70) Turnover –0.0206*** –0.0206*** –0.0197*** –0.0155** –0.0248*** –0.0171** (–3.16) (–3.15) (–3.03) (–2.18) (–2.83) (–2.16) Past flow 0.107*** 0.110*** 0.103*** 0.107** 0.130*** 0.124** (2.73) (2.82) (2.63) (2.13) (2.72) (2.47) Past alpha 6.020*** 6.225*** 6.432*** 2.468 3.952** 3.586** (4.08) (4.14) (4.35) (1.42) (2.27) (1.96) Adj. R$$^{\mathrm{2}}\$  0.0928  0.0911  0.0927  0.0910  0.0925  0.0912  0.101  0.0984  0.0962  0.0944  0.0990  N  239,966  222,398  239,919  222,354  230,597  214,372  150,351  138,771  167,343  153,011  123,731  B. Trade-based AFP  AFP_Trade  1.472**  1.242*                          2.067**     (2.33)  (1.90)                          (2.40)  CS        0.420**  –0.186                    –0.177           (1.98)  (–0.89)                    (–0.70)  Return gap              10.68***  7.077**              3.696                 (3.99)  (2.52)              (0.95)  RPI                    –0.230*  –0.245**        –0.308**                       (–1.95)  (–2.04)        (–2.43)  Active share                          0.141***  0.185***  0.173***                             (3.75)  (4.93)  (4.44)  log(TNA)     –0.0