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1 College of Business Administration University of Rhode Island William A. Orme WORKING PAPER SERIES encouraging creative research Do Mutual Funds Profit From Accruals and NOA Anomalies? Ashiq Ali, Xuanjuan Chen, Tong Yao and Tong Yu 2005/2006 No. 3 This working paper series is intended to facilitate discussion and encourage the exchange of ideas. Inclusion here does not preclude publication elsewhere. It is the original work of the author(s) and subject to copyright regulations. Office of the Dean College of Business Administration Ballentine Hall 7 Lippitt Road Kingston, RI

2 (Preliminary, please do not quote without authors permission) Do Mutual Funds Profit from Accruals and NOA Anomalies? Ashiq Ali*, Xuanjuan Chen**, Tong Yao***, Tong Yu**** November 2005 Abstract: Using data on both fund stockholdings and fund returns, we show that mutual funds are able to make significant excess returns net of actual transaction costs from trading on accruals and net operating assets (NOA) anomalies. We find that the top 10% of mutual funds that are most aggressive in holding stocks consistent with the accruals (NOA) strategy have Fama-French 3-factor alphas of 3.33% (2.71%) per year. We also find that mutual funds more actively using the accruals (NOA) strategies exhibit higher volatility in both their net returns and fund flows. These factors likely represent the adverse consequences of arbitrage risk that funds face when they trade aggressively on these anomalies (Shleifer & Vishny 1997). *Department of Accounting and Information System, University of Texas, Dallas. ** Cameron School of Business, University of North Carolina, Wilmington ***Department of Finance, University of Arizona. ****College of Business Administration, University of Rhode Island. 1

3 Do Mutual Funds Profit from Accruals and NOA Anomalies? Abstract Using data on both fund stockholdings and fund returns, we show that mutual funds are able to make significant excess returns net of actual transaction costs from trading on accruals and net operating assets (NOA) anomalies. We find that the top 10% of mutual funds that are most aggressive in holding stocks consistent with the accruals (NOA) strategy have Fama-French 3-factor alphas of 3.33% (2.71%) per year. We also find that mutual funds more actively using the accruals (NOA) strategies exhibit higher volatility in both their net returns and fund flows. These factors likely represent the adverse consequences of arbitrage risk that funds face when they trade aggressively on these anomalies (Shleifer & Vishny 1997). 2

4 Do Mutual Funds Profit from Accruals and NOA Anomalies? Introduction Academic literature has identified various trading strategies to take advantage of accounting-based anomalies (Kothari 2001), and investors naïve response to information is believed to be the origin of many of these anomalies. An interesting question that follows is whether sophisticated investors can profitably implement such trading strategies. Several recent studies attempt to address this issue by comparing hypothetical returns from the trading strategies with estimates of trading costs that may be incurred on implementing the strategies. 1 The costs that are commonly considered are bid-ask spread, trading commission, price impact of block trades, and restrictions on short sales. However, these studies provide mixed evidence on whether the documented trading strategies can be profitably implemented. 2 The main reason for the difference in the conclusions across these studies is that in their analyses they consider either different sets of trading costs or estimate the magnitude of the costs using different approaches. 1 Empirical studies have associated substantial transaction costs with many trading strategies. They include the small-firm effect (Stoll and Whaley, 1983), the January effect (Reinganum, 1983; Bhardwaj and Brooks, 1992), the post-earnings announcement drift (Bhushan, 1994), closed-end fund discounts (Pontiff, 1996), expected price improvement from a switching strategy (Knez and Ready, 1996), under-reaction to analyst recommendations (Copeland and Mayers, 1982; Barber, Lehavy, McNichols, and Trueman, 2001), and momentum profits (Lesmond, Schill, and Zhou, 2004; Korajczyk and Sadka, 2002). In addition, Chen, Stanze, and Walanabe (2002) examine the effect of price pressures on the book-to-market, size, and momentum strategies. Bushee and Ready (2005) study the profitability of seven trading strategies in the presence of several types of market frictions including transaction costs. Hanna and Ready (2005) analyze the impact of transaction costs on trading strategies based on more than 50 measures of accounting information and past stock returns. 2 For example, for the momentum strategy, Lesmond et al. (2004) conclude that trading costs prevent profitable execution of the strategy. On the other hand, Bushee and Raedy (2005), Koraczyk and Sadka (2004), and Chen et al. (2002) conclude that trading on momentum strategy is likely to be profitable, though only for small fund sizes. 3

5 Our study addresses the above concern by considering returns to trading strategies net of actual rather than estimated transaction costs. We employ databases of mutual funds that provide for each of the funds not only the stockholding information but also information on returns net of actual transaction costs. The stockholding data allow us to determine which mutual funds actively pursue a given trading strategy. The net fund return data of those mutual funds then enable us to assess their profitability. We believe that ours is the first study that uses these two sets of information jointly to examine whether sophisticated investors can profitably implement trading strategies documented in the literature. 3 For our analysis, we consider two well-established and somewhat related accounting-based trading strategies, namely, the accruals anomaly (Sloan 1996) and the net operating assets (NOA) anomaly (Hirshleifer, Hou, Teoh, and Zhang 2004). The accruals anomaly refers to the negative relation between the current level of accounting accruals and future stocks returns. Sloan (1996) provides an explanation for the anomaly based on investors mis-reaction to information -- although the accrual component of earnings is less persistent than the cash flow component of earnings, naïve investors fail to recognize the difference in the persistence of accruals and cash flows. The NOA anomaly refers to the negative relation between NOA and future stock returns. Hirshlerfer et al. (2004) provide a similar explanation for the NOA anomaly. A firm s NOA is the accumulation over time of the difference between net operating income and 3 To our knowledge, the only type of anomaly-based trading strategy studied in the mutual fund literature is momentum. Grinblatt, Titman, and Wermers (1995), among others, study mutual fund trading on momentum using the stockholdings data but not the stock return data. Carhart (1997), among others, study momentum trading by funds using fund return data, but not the stockholdings data. 4

6 free cash flow. Naïve investors focus on accounting profitability and neglect information about cash profitability. Several studies have examined the factors that may prevent the well-publicized accruals anomaly from being arbitraged away. Desai, Krishnamurthy, and Venkataraman (2002), Richardson (2003), and Lev and Nissim (2004) show that stocks with extreme accruals typically have small size, low liquidity, and high risk. Mashruwala, Rajgopal and Shevlin (2004) find that idiosyncratic volatility of stocks in extreme accruals deciles is significantly greater than those of stocks in the median deciles. Constrained by data, none of the existing studies reports the actual consequence of these factors on the portfolio returns after transaction costs and return volatility of sophisticated investors who follow the accruals strategy. To quantify how aggressively a fund trades on these accounting-based anomalies, we construct accruals investing measures and NOA investing measures similar to the momentum investing measure of Grinblatt, Titman and Wermers (1995). These measures are a function of the magnitude of the accruals (NOA) of the stocks held by the fund and the portfolio weights of the stocks in the fund. Our analysis of these measures indicates that on average mutual funds actively follow the accruals strategy and the NOA strategy. Moreover, the accruals investing measures and the NOA investing measures are found to be persistent for a fund, suggesting the presence of a deliberate strategy by funds to trade on these anomalies. We use net fund returns before fund expenses to assess the profits, net of actual transaction costs, that funds make from investing in the accruals and the NOA strategies. We find that the top 10% funds that most aggressively follow the accruals strategy on 5

7 average have a significant 3-factor alpha of 3.33% per year. Moreover, this value is significantly higher than the 3-factor alpha of funds not actively using the strategy. This result suggests that mutual funds can and do make significant profits from the accruals strategy. Further, the top 10% funds that most aggressively follow the NOA strategy on average have a significant 3-factor alpha of 2.71% per year. This value is also significantly higher than the 3-factor alpha of funds not actively using the strategy. This result suggests that mutual funds also profit from the NOA strategy. In other words, transaction costs have not completely rendered these accounting-based trading strategies profitless. Finally, we document that the top 10% of funds that most aggressively follow the accruals and the NOA strategies exhibit significantly higher return volatility and fund flow volatility than that exhibited by other funds. These results seem to provide an explanation for why mutual funds do not pursue these arbitrage opportunities more aggressively in spite of the fact that transaction costs do not completely eliminate the profits from these trading strategies. Shleifer and Vishny (1997) argue that trading on mispricing is not completely riskless; in fact, it is often associated with substantial arbitrage risk. Because of asymmetric information, investors may withdraw money from delegated portfolio managers when intermediate fund performance suffers due to such arbitrage risks, even though arbitrage opportunities pursued by fund managers are ultimately profitable. Due to such adverse consequences of arbitrage risks, mutual funds trade on mispricing less aggressively, and these anomaly-based trading strategies remain profitable. 6

8 Our study contributes to the literature in several ways. As mentioned before, several prior studies use estimates of transaction costs to address the question whether sophisticated investors can profitably implement anomaly-based trading strategy. They arrive at different conclusions because they consider different set of costs and use different methods for estimating the costs. By using data on mutual fund stockholdings and net fund returns, we provide more reliable evidence on this issue. We show that funds that aggressively follow the accruals and NOA trading strategies do make significant profits net of actual transactions costs. Second, ours is the first study that provides evidence on the Shleifer and Vishny (1997) thesis on the effect of arbitrage risk on fund flows due to the presence of performance-based arbitrage. They argue that investors cannot perfectly observe arbitrageurs abilities. Thus, investors update their beliefs about arbitrageurs talent based on past performance and allocate their capital accordingly. According to this argument, funds under the management of arbitrageurs would decline when intermediate fund performance suffers due to return volatility from arbitrage risks, even though arbitrage opportunities pursued by the fund managers may ultimately be profitable. We show that funds that more aggressively trade on accruals and NOA anomalies exhibit not only greater return volatility, but also greater volatility of fund flows, consistent with the prediction of Shleifer and Vishny (1997). Finally, our study contributes to the literature on the trading by sophisticated investors on accounting-based anomalies. Collins, Gong, and Hribar (2003) and Lev and Nissim (2004) show that institutional investors trade on the accruals strategy. We confirm 7

9 this result for actively managed mutual funds. 4 More importantly, for the newly documented NOA strategy, published in 2004, we are the first to show that sophisticated investors, represented by mutual funds, have been trading on this anomaly throughout our sample period, from 1984 to The remainder of this paper is organized in three sections. Section II describes the data and methodology. Section III presents empirical results. Section IV concludes. II. Data and Methodology A. Data We obtain financial statement data from the Compustat database and stock returns and prices from the CRSP monthly database. Information about mutual funds is from two sources. The first is the CRSP Survivorship Bias Free Mutual Fund Database (hereafter CRSP data ), which provides information on fund monthly returns and fund characteristics such as turnover and expense ratio. The second is the Thomson Financial CDA/Spectrum Database (hereafter CDA data ), which lists stock holdings of US mutual funds. During the past two decades, mutual funds were required to file with SEC their equity holdings on a semiannual basis, and over 80 percent of funds voluntary disclose their holdings quarterly (Kacperczyk, Sialm, and Zheng 2005). 5 Thomson Financial 4 Relative to the existing literature that examines institutional ownership and accounting anomalies, our focus on mutual funds has several empirical advantages. For example, identifying actively-managed equity mutual funds from the data is straightforward. On the other hand, the procedure to identify active institutional investors from passive ones is typically indirect, based factors such as portfolio turnover, diversification, and momentum trading (see, e.g, Bushee 1998). Moreover, in the institutional ownership data the active and passive portfolios of the same institution are not separately reported. 5 The mandatory filing frequency was quarterly before 1985, became semiannual afterwards, and switched back to quarterly after

10 collects information from both mandatory and voluntary reports and makes the data available commercially. This dataset has been used in a number of previous studies, such as Daniel, Grinblatt, Titman, and Wermers (1997), Grinblatt and Titman (1989, 1993), Grinblatt, Titman, and Wermers (1995), Wermers (2000, 2003), Cohen, Coval, and Pastor (2005), and Kacperczyk, Sialm, and Zheng (2005). 6 In the CDA data, funds are classified into nine categories according to their selfdeclared investment objectives: international, aggressive growth, growth, growth and income, municipal bonds, bond and preferred, balanced, metals, and unclassified. We focus on actively-managed U.S. domestic equity funds with the following three investment objectives: aggressive growth, growth, and growth and income. There are 3938 such funds in the CDA data during the sample period from 1984 to After removing passive index funds and funds with apparently misreported investment objectives, we obtain 3067 unique funds. 7 The CDA data is then combined with the CRSP data to obtain complete information on fund holdings and fund returns. Before merging the two datasets, we first combine multiple share classes as a single fund in the CRSP data. These multiple share classes differ in sales charges and targeted investor clientele, but have same portfolio compositions. They are treated as a single fund in the CDA data. We merge the two 6 As discussed before, there are several noted differences between the CDA data and the institutional holdings data based on the 13f filings (hereafter 13F data ). The 13F data, also available through Thomson Financial, reports equity holdings of various other types of institutional investors besides mutual funds, such as insurance firms, pensions, investment advisors, commercial banks, and investment banks. However, equity holdings in the 13F data are reported at the aggregated institution level, not at the fund level. For example, while the CDA data contains information on equity holdings by Fidelity Magellan Fund, equity holdings information in the 13F data is only available for Fidelity Investments, the mutual fund company that manages a large number of active and passive funds. 7 For example, some foreign-based funds, U.S.-based international funds, fixed-income funds, real estate funds, precious metal funds, balanced funds, and variable annuities sometimes misreport their investment objective as aggressive growth, growth, or growth and income. 9

11 datasets manually by matching fund names and ticker symbols. 8 The matching procedure follows Wermers (2000). We exclude fund-quarter observations if the total market value of reported holdings is less than 50 percent or more than 150 percent of the reported total net assets of the fund. The final matched database has 2,587 unique US active equity funds with qualified investment objectives. 9, 10 The details of the matching procedure can also be found in Jiang, Yao and Yu (2004). Table 1 reports the summary statistics for our mutual fund sample over the period of 1984 and Out of a total of 2587 funds, we have 1706 growth funds, 293 aggressive growth funds, and 588 growth and income funds -- these three types of funds represent the majority of actively managed domestic equity funds in US and are the focus of previous studies; see, e.g., Wermers (2000). We calculate the average fund characteristics by first averaging across funds in each year and then average over the time series. During our sample period from1984 to 2003, the average total net assets (TNA) of a typical fund in our sample is million, with an average annual return of percent, an average annual turnover ratio of 0.89, an average annualized load of 0.33 percent, and an average annual expense ratio of 1.25 percent. The average fund age, calculated as the time elapsed since the fund organization year in the CRSP data, is years. The mean number of stocks held in a fund is 86.85, whereas the median is Fund ticker symbols are generally not available in the CDA data before As noted by previous studies (Daniel et al. 1997), both the CRSP and CDA data are free from the survivorship bias. However, the CDA dataset is slow in adding new funds. Therefore, there are new funds already in the CRSP data but not in the CDA data yet; see, e.g., Wermers (2000). 10 The size of our merged mutual fund sample is comparable to those used in previous studies. For example, Wermers (2000) combines the CDA data with the CRSP dataset over the period between 1975 and His sample contains 1,788 equity funds. Kacperczyk, Sialm, and Zheng (2005) match the CRSP dataset with the CDA dataset over the period between 1984 and 1999 and report 1,971 unique active equity funds. Cohen, Coval, and Pastor (2005) also match the Thomson dataset with the CRSP dataset over the period between 1980 and 2002Q2. They report 235 matched funds at the end of 1980 and 1,526 matched funds in 2002Q2. 10

12 B. Methodology B.1 Measuring Accruals and Net Operating Assets Following Sloan (1996) and Chan, Chan, Jegadeesh, and Lakonishok (2004), we estimate individual stock accruals using the annual balance sheet and income statement information: Accruals = (ΔCA - ΔCASH) (ΔCL - ΔSTD - ΔTP) DEP = (ΔAR + ΔINV + ΔOCA) (ΔAP + ΔOCL) DEP (1) where ΔCA is the change in current assets (Compustat item 4); ΔCash is the change in cash/cash equivalents (item 1); ΔCL is the change in current liabilities (item 5); ΔSTD is the change in debt included in current liabilities (item 34); ΔTP is the change in income taxes payable (item 71); DEP is depreciation and amortization expense (item 14); ΔAR is the change in account receivable (item 2); ΔINV is the change in inventories (item 3); ΔOCA is the change in other current assets (item 4); ΔAP is the change in account payable (item 70); and ΔOCL is the change in other current liabilities (item 68). Consistent with prior studies, we scale accruals by the average of the beginning and ending total assets of the reporting year. To alleviate the influence of outliers, the top and bottom one percent accruals observations are winsorized in each year. Following Hirshleifer et al. (2004), net operating assets (NOA) are computed as: NOA = Operating Assets Operating Liabilities (2) where operating assets = total asset (item 6) cash and short term investment (item 1), operating liabilities = total asset STD LTD MI PS CE, STD = Debt included in current liabilities (item 34), LTD = Long Term Debt (item 9), MI = Minority Interests 11

13 (item 38), PS = Preferred Stocks (item 130), and CE = Common Equity (item 60). Following Hirshleifer et al. (2004), we treat the values of short-term debt, taxes payable, long-term debt, minority interest and preferred stock as zero if they are missing. Similar to accruals, we scale NOA by the average of the beginning and ending total assets of the reporting year and winsorize the top and bottom one percent NOA observations in each year. B.2 Characteristics-Adjusted Accruals and Characteristics-Adjusted NOA Based on the above raw accruals and NOA, we further construct characteristicsadjusted accruals and NOA. There are several reasons to control for stock characteristics in measuring anomaly-based trading by mutual funds. First, mutual funds often invest in different sub-universes of stocks (e.g., large cap growth, small cap value, etc.), which have different accruals and NOA characteristics. Mutual funds also employ other investment strategies, such as momentum trading, and we would like to control for their effect when measuring fund trading on the accruals and NOA anomalies. Second, it is well-documented that institutional investors have certain preferences for stocks (e.g., Del Guerico 1996; Gompers and Metrick 2001); such preferences may be uncorrelated to their stock selection ability, but related to the accruals or NOA of stocks. Finally, as noted by Xie (2001), the return-predictive power of accountings accruals primarily stems from the discretional component, not the non-discretional accruals. To control for these effects, in each year (referred to as accruals measurement year ) and within firms with the same two-digit SIC code, we perform the following cross-sectional regression to estimate characteristics-adjusted accruals: 12

14 Acc = α+β 1 LgSize + β 2 LgBM + β 3 PrRet+ β 4 InsHold+ β 5 (ΔREV/ATA) + β 6 (PPE/ATA) + ε (3) where LgSize is the logarithm of stock market value at the end of the accruals measurement year, LgBM is the logarithm of book-to-market ratio, measured as book value of equity (Compustat item 60) for the fiscal year ending within the accruals measurement year divided by market value of equity at the end of the accruals measurement year, and PrRet is a momentum variable, measured by the stock s return during the accrual measurement year. InsHold is the ratio of shares held by institutions divided by total shares outstanding of a stock at the end of the accruals measurement year. We use this variable to control for the general preference of institutional investors on stocks. 11 To compute InsHold, we aggregate the shares of a stock held by all institutions as reported in the 13F data at the end of accruals measurement year and divide it by the total shares outstanding of the stock. The control for nondiscretionary accruals and the industry effect follows Jones (1991) and Xie (2001). ΔREV/ATA is the difference of firms total revenue (Compustat item 12) during the accrual measurement year divided by the average total assets (Compustat item 6) at the end of the same year; PPE/ATA is the gross book value of property, plant and equipment (Compustat item 7) at the end of the accrual measurement year divided by the average total assets in the same year. We perform the regression in each year across firms with the same two-digit SIC code. The characteristics-adjusted accruals are the estimated residuals of the crosssectional regression (3). 11 Controlling for general institutional preference, although desirable, is not crucial to our results. We have performed analysis using characteristics-adjusted accruals without controlling for institutional holdings and have obtained similar results. The same is true for controlling for institutional holdings when computing characteristics-adjusted NOA. 13

15 The characteristics-adjusted NOA is constructed in a similar way. We perform the following regression in each year for all sample firms and take the estimated residuals as the characteristics-adjusted NOA: 12 NOA = α+β 1 LgSize + β 2 LgBM + β 3 PrRet + β 4 InsHold + ε (4) Again, LgSize, LgBM, PrRet, and InsHold are used to control for mutual fund investment styles, their other trading strategies, and the general preference of institutional investors. We compare the return-predictive power of the characteristics-adjusted variables and that of the raw variables. Following Sloan (1996) and Hirshleifer et al. (2004), in April of each year t we form equal-weighted decile portfolios of stocks ranked by raw accruals, characteristics-adjusted accruals, raw NOA, and characteristics-adjusted NOA. The portfolios are held from May of year t to April of year t+1. If a stock is delisted during the holding period, we assume that its return during the remaining holding period is the CRSP delisting return. Following Shumway (1997), when the delisting return is missing, it is replaced by -30 percent if the delisting is performance related and zero otherwise. The sample period is from 1980 to Table 2 shows that the return-predictive power of characteristics-adjusted variables is quite similar to that of the raw variables. On average, the bottom decile portfolio sorted by characteristics-adjusted accruals (NOA) outperform the top decile by 8.54 (10.98) percent per year. The return spreads are of the same magnitude as those reported by Sloan (1996) and Hirshleifer et al. (2004). 12 Unlike the accruals regression (3), which is run within each industry, the NOA regression (4) is run on all firms. We find that once controlling for the industry effect, the residual NOA has visibly lower power in predicting stock returns. A similar finding is reported by Zhang (2005). 14

16 In Figure 1, we plot the time series of the annual return spread between the top and bottom decile portfolios of stocks sorted on raw accruals and raw NOA, as well as those sorted on characteristics-adjusted accruals and characteristics-adjusted NOA. These spreads are positive in most years despite some fluctuations. The return spreads for portfolios formed on characteristics-adjusted variables closely track those for portfolios formed on raw variables. B.3 Accruals Investing Measures and NOA Investing Measures We construct accruals investing measures and NOA investing measures to quantify how aggressively a fund takes advantage of the accounting-based anomalies. These measures are in the spirit of the momentum investing measure of Grinblatt, Titman, and Wermers (1995). The first set of measures is based on stockholdings. The holding-based accrual investing measure is the negative of the weighted sum of characteristics-adjusted accruals for stocks held in the portfolio: n H, i t j= 1 AIM, = w i, j, t * AdjAcc j, t 1 (5) where is the portfolio weights on stock j held by fund i in June of year t. 13 w i, j, t AdjAcc j, t 1 is the characteristics-adjusted accruals during the fiscal year that ends in 13 Occasionally, some funds report their holdings for a month that is not at quarter-end. For all our analysis, we assume that the reported holdings are valid at the end of the reporting quarter. In addition, we do not include funds reporting their holdings semi-annually at the end of March and September. The impact is minimal because over 90 percent of funds in our sample report their holding in June of each year. 15

17 calendar year t n is the number of stocks held by a fund. We include a negative sign in the expression to make the measure positive for a fund that actively employs the accruals strategy. By construction, AdjAcc j, t 1 has zero cross-sectional mean. Hence for a randomly selected portfolio the expected value of AIMH,i,t is zero. A positive AIM H,i,t therefore indicates active use of the accruals strategy after controlling for other factors affecting the level of accruals for stocks held by the fund. The higher the AIM H,i,t, the more aggressive a fund is in exploiting the accruals anomaly. Similarly, we construct holding-based NOA investing measures to quantify the aggressiveness of the use of the NOA strategy: n NIM H, i, t = w i, j, t * AdjNOAj, t 1 (6) j= 1 where AdjNOA j, t 1 is a stock s characteristics-adjusted NOA during the fiscal year that ends in calendar year t-1. Similar to the holding-based AIM measures, a positive NIM indicates that a fund actively uses NOA strategy by tilting the portfolio weights towards low NOA stocks. Different from the holding-based AIM and NIM, the trading-based measures quantifies how funds change their portfolio weights based on accruals/noa information. The trading-based AIM is the negative of the sum of the product of the portfolio weight changes during a one-year period and characteristics-adjusted accruals for stocks held by the fund: H,i,t 14 To ensure that the accounting variables are known before the holding information, we match portfolio weight in June of year t with the accruals data for all fiscal year ends in calendar year t-1. Essentially, we are assuming here a reporting lag of at least 6 months for financial statements. 16

18 AIM n T, j, t = wi, j, t wi, j, t 1 ) * j= 1 ( AdjAcc (7) where and are portfolio weights in June of year t and t-1 and the accruals w i, j, t w i, j, t 1 information is for the fiscal year that ends in the calendar year t-1. Note that portfolio weights can change due to either active trading or the passive effect of stock price change. To control for the later, following Grinblatt, Titman, and Wermers (1995), we compute the portfolio weights and using the average month-end stock prices w i, j, t w i, j, t 1 for June of year t and June of year t-1. Similarly, we construct the following trading-based NOA investing measures: j, t 1 NIM n T, i, t = ( wi, j, t wi, j, t 1 ) * j= 1 AdjNOA j, t 1 (8) We expect a positive trading-based AIM (NIM) when a fund manager trades towards low accruals (NOA) stocks and against high accruals (NOA) stocks. Jointly, we refer to AIM H, AIM T, NIM H, and NIM T as anomaly investing measures. B.4 Fund Performance Measures We use two sets of fund performance measures. The first set is the quarterly fund gross return following Grinblatt and Titman (1989), Daniel et al. (1997) and Wermers (2000). It is the buy-and-hold return on the beginning-of-quarter portfolio holdings: GR n n i, t = wi, j, t R j, t + 1 wi, j, t ) j= 1 j= 1 ( RF (9) where is the portfolio weight of fund i on stock j at the beginning of quarter t, is w i, j, t R j, t the buy-and-hold return of stock j in quarter t, and RF t is the risk-free return in quarter t. If a fund reports portfolio holdings semiannually, we estimate their holding at the t 17

19 beginnings of the interim quarter by assuming that they complete half of the portfolio changes in each quarter. We exclude observations from the analysis if the two reporting dates are more than six months apart. The fund performance calculated from equation (9) is the gross return before deducting fund expenses and transaction costs. The second set of fund performance measures are based on the CRSP fund net returns. Net returns are monthly fund returns after expense ratios and net of actual transaction costs. Expense ratios are funds management and administrative fees. Thus, a better measure of the benefit of investing on market anomalies is the fund return before deducting fund expenses. We include fund net returns before and after expense ratio in our analysis. To compute before-expense return, we add 1/12 of fund annual expense ratio to fund monthly net returns. In addition, to control for risk exposure, we also use the following Fama-French (1993) three-factor model and Carhart (1997) four-factor model to estimate risk-adjusted alphas. ER it = α + b RMRF + s SMB + h HML + ε, (10) i i t i t i t t ER i, t = α i + bi RMRFt + sismbt + hi HMLt + piumdt + ε t, (11) where ER i, t is the monthly net return (before or after fund expenses) of fund i in month t in excess of the risk free rate (the yield on Treasury bills with one-month maturity, from CRSP). RMRF t is the monthly return on the CRSP value-weighted index in excess of the risk free rate; SMBt, HML t, and UMD t are the monthly returns on size, book-to-market, and momentum factors. 15 The regressions are performed in each year for each fund. 15 Data for SMB t, HML t, and UMD t are obtained from Ken French's website: 18

20 To facilitate comparison, we annualize all the performance measures when reporting empirical results. III. Empirical Results A. Anomaly-based Investing by Mutual Funds A.1 Holding-based and Trading-based Measures We examine the holdings-based AIM (AIM H ) and NIM (NIM H ) to see if mutual funds hold more low-accruals/noa stocks after controlling other factors that may affect mutual fund stock selection. The specific procedure is as follows. In each year, we first calculate the equal-weighted averages of AIM H and AIM T across all funds. Then, we compute their time series means and time series t-statistics. Reported in Table 3, the mean AIM H and NIM H for all sample funds are 5.78 and 3.63 respectively, both significantly positive at the 1 percent level. The results suggest that on average mutual fund portfolio holdings tilt toward stocks with lower characteristics-adjusted accruals and NOA. When we break down funds by their investment objectives, we find similar results, except for the insignificant NIM H value for the growth and income category. 16 Table 3 also reports the results for the trading-based measures. The trading-based measures quantify the portfolio weight changes in response to accruals/noa information. The time series mean of AIM T is positive at the 1 percent significance level for the full sample and for the subsamples of aggressive growth and growth funds. The time series mean of NIM T is also positive, but only significant at the 10 percent level for the full 16 While the accruals anomaly has been well published since the work of Sloan (1996), the NOA anomaly is only recently documented by academic studies. Therefore, the finding that mutual funds on average invest in stocks with low NOA is interesting. Quite likely, although mutual fund managers may not be directly aware of this anomaly, the fundamental analysis they perform generates stock-picking information that is correlated with the NOA signal. 19

21 sample. 17 This, however, does not necessarily suggest that mutual funds use the NOA strategy less aggressively. As noted by Hirshleifer et al. (2004), the level of NOA is fairly persistent over time. Therefore the NOA strategy requires low trading intensity. To be specific, if a firm has low NOA in year t, it is likely to have low NOA in year t+1. An optimal way to take advantage of the NOA-related mispricing is simply to buy the stock and hold the position for both year t and t+1, without trading within the two years. While on average mutual funds use the accruals and NOA strategies, there are substantial differences across funds. To illustrate this, we rank funds on their AIM H and NIM H values in each year. D10 is the decile of funds with the highest AIM H or NIM H (those most actively using the accruals/noa strategies), whereas D1 is the decile of funds with the lowest AIM H or NIM H (those using the strategies in the opposite direction). Figure 2 displays the difference in stock holdings between D1 and D10 funds, in terms of the characteristics-adjusted accruals/noa. We follow four steps to generate this figure. First, in each year we sort stocks into deciles based on the characteristics-adjusted accruals/noa. Second, we aggregate the portfolio weights of a given fund in each stock decile. Third, we average these portfolio weights in each stock decile for the D1 and D10 funds respectively. Finally, we plot the time-series means of the average portfolio weights for D10 and D1 fund deciles, as well as the difference between the two fund deciles. The cross-fund difference in the intensity of anomaly-based investing is evident. For AIM H -sorted D10 funds, the average portfolio weight in the lowest stock accruals decile is percent and that in the highest stock accruals decile is 2.58 percent. In 17 In unreported tests, we also compute value-weighted average AIM and NIM. The results lead to the same conclusions. 20

22 other words, D10 funds invest more in low accruals/noa stocks and less in high accruals/noa stocks. Interestingly, even for D10 funds, their most concentrated portfolio holdings are not in the stock decile with the lowest characteristics-adjusted accruals/noa, but rather in the second and third lowest accruals deciles or in the second lowest NOA decile. Similarly, Figure 3 illustrates the trading of D1 and D10 funds on stocks in different accruals/noa deciles. Here D1 and D10 funds are ranked by their trading-based AIM/NIM, and we plot the time series means of the average portfolio weight changes in each stock decile, instead of average portfolio weights as in Figure 2. For AIM T -sorted D10 funds, the average portfolio weight change in the lowest stock accruals decile is 4.6 percent while that in the highest stock accruals decile is -3.1 percent. In other words, funds most actively trading on the accruals strategy are net buyers of low-accruals stocks and net sellers of high-accruals stocks. The plot of portfolio weight changes for the NIM H -sorted D10 and D1 funds reveals a similar pattern, though to a less magnitude. Overall, there is a significant cross-sectional difference in fund trading in response to accruals/noa signals. A.2 Regression-based Analysis The results in Table 3 suggest active use of the accruals/noa strategies by mutual funds. As a robustness check of our fund-level evidence, we perform stock-level Fama-MacBeth regression analysis that is similar to the approach of Lev and Nissim (2004). Specifically, in each year t, we perform the following cross-sectional regression across all stocks: 21

23 1 2 3 h α + β AdjAcc + γ ROA + γ 1/ PRICE + γ VOL + ε (12) i, j, t = i, t i. t j, t 1 i, t j, t 1 i, t ( ) t 1 i, t t Δh = α + β AdjAcc + γ ROA + γ 1/ PRICE + γ VOL + ε (13) t, j, t i, t i. t j, t 1 i, t j, t 1 i, t ( ) t 1 i, t t 1 Equation (12) is to analyze determinants of fund holdings, where the dependent variable, h i, j, t, is the percentage of all outstanding shares of stock j held by the sample funds in June of year t. Equation (13) is to analyze the determinants of fund trading, where the dependent variable, Δ h i, j, t, is the change in the percentage of all outstanding shares of a stock held by mutual funds from June of year t-1 to June of year t. Independent variables in both regressions include characteristics-adjusted accruals and several control variables -- returns on assets (ROA) as a measure of operating performance, the inverse of stock price (1/PRICE) as a proxy for transaction costs, and the average monthly trading volume of a stock divided by its total shares outstanding (VOL) as a measure of liquidity. Similar to Lev and Nissim (2004), we use these variables to control for institutional preference in stock holdings. 18 For example, existing empirical evidence suggests that institutional investors tend to prefer stocks with good operating performance (Del Guercio 1996; Bushee 2001), and have an aversion toward stocks with high transaction costs and low liquidity (Falkenstein 1996; Gompers and Metrick 2001). Similar regressions are performed with characteristics-adjusted NOA as an explanatory variable instead of characteristics-adjusted accruals. After obtaining estimated coefficients for the cross-sectional regressions in each period, we compute the time-series means of the estimated coefficients as well as their time-series t-statistics. The results are reported in Table 4. Consistent with prior studies 18 Lev and Nissim (2004) consider a battery of control variables. The control variables we use here are a subset of theirs. A few other variables are implicitly controlled for when we compute the characteristicsadjusted accruals. 22

24 on institutional investors preference, we find that funds tend to invest in stocks with high ROA, high price, and high trading volume. More importantly, the coefficients on characteristics-adjusted accruals and NOA in all the regressions are significantly negative, indicating that mutual funds as a whole actively hold and trade stocks consistent with the accruals and NOA strategies. A.3 Determinants of Intensity of Anomaly-based Investing Next, we investigate whether the intensity of anomaly-based investing is related to certain fund characteristics and whether the anomaly-based investing by mutual funds is persistent. For this purpose, we perform the following Fama-MacBeth regressions: AIM γ AIM + γ LgAge + γ LgTNA + γ TURN + γ EXP + ε (14) H, t = 0 H, t 1 1 t 1 2 t 1 3 t 1 4 t 1 AIM γ AIM + γ LgAge + γ LgTNA + γ TURN + γ EXP + ε (15) T, = t 0 T, t 1 1 t 1 2 t 1 3 t 1 4 t 1 where LgAge is the logarithm of fund age, LgTNA is the logarithm of total net assets, TURN is the fund turnover ratio; EXP is fund expense ratio. All these variables are measured for year t-1. Previous studies have shown that the above fund characteristics affect fund performance and flows (see, e.g., Carhart 1997; Sirri and Tufano 1998; Chen, Hong, Huang, and Kubik 2005). We are interested in whether they also affect the intensity of anomaly-based investing. In addition, the lagged AIM variables AIM H,t-1 and AIM T,t-1 are used to measure the persistence of anomaly based investing. The regression is performed in each year and we compute the time series means of the estimated coefficients and their time-series t-statistics. Similar regressions are performed with NIM H and NIM T as dependent variables and lagged NIM H and NIM T as explanatory variables. 23

25 The results are reported in Table 5. We find that fund size and fund turnover have some consistent explanatory power on the intensity of anomaly-based investing. Larger funds and higher turnover funds seem to use both the accruals and NOA strategies more intensely. Moreover, fund use of the accruals and NOA strategies is persistent. The average coefficients on lagged AIM H, AIM T, NIM H and NIM T are all significantly positive. The evidence on the persistence of these measures is important. It suggests that the crosssectional difference in anomaly-based trading is not completely by chance; it is at least partially due to active fund strategy. B. Profitability of Anomaly-based Investing B.1 Fund Performance and Holding-based Anomaly Investing Measures We now address the next question: do mutual funds more actively using the accruals and NOA strategies have better performance? We first examine fund performance as measured by gross returns. In June of each year t, we rank mutual funds into deciles according to their holdings-based AIM H or NIM H. As defined before, funds in the D1 decile are those with the lowest AIM H or NIM H, and funds in the D10 decile are those with the highest AIM H or NIM H. For comparison purpose, we additionally define a group of inactive funds. These are the 10 percent of funds with AIM H or NIM H closest to, and centered around, zero. In other words, the inactive funds include 5 percent of funds with the lowest but positive AIM H or NIM H and the 5 percent of funds with the highest but negative AIM H or NIM H. By definition, these funds do not actively use the accruals or NOA strategy, and their average AIM H or NIM H is close to zero. We compute the average gross returns during the next year (July of year t to June of year t+1) for each fund decile 24

26 and additionally for the inactive fund group. The time series means of these average gross returns, as well as their time series t-statistics, are reported in Panel A of Table 6. We also report the difference in gross returns between D10 and D1 funds and the difference between D10 funds and the inactive funds. The results show that D10 funds significantly outperform D1 funds as well as the inactive funds. In Panel B of Table 6, we compare fund net returns (before and after expenses), as well as their corresponding 3-factor alphas and 4-factor alphas, across fund deciles. Again, funds are ranked into deciles by holding-based AIM H and NIM H. We find that the D10 funds, i.e., those most actively using the accruals (NOA) strategy, significantly outperform the D1 funds (those using the strategy in the opposite direction) and inactive funds (those not significantly using the strategy). For example, the difference in average net returns between D10 and inactive funds is 2.63 percent before expense and 2.46 percent after expense. The differences in 3-factor alphas and 4-factor alphas are even higher. For NIM H, the before- and after-expense net return spreads between the D10 and inactive funds are 2.10 and 2.15 percent respectively. The differences in 3-factor and 4- factor alphas are slightly lower, but remain statistically significant at the ten percent level. It is worth noting that before-expense net returns are typically lower than beforeexpense gross returns. A main component of this spread is transaction costs. Indeed, a number of studies, such as Grinblatt and Titman (1989) and Wermers (2000), have used this spread as a measure of transaction costs (albeit a noisy one). Using AIM H as an example, the spreads are 1.19 percent (17.14%-15.95%) for D10 funds and 0.63 percent (13.95%-13.32%) for the inactive funds. The difference between these two spreads,

27 percent, can be viewed as the additional transaction costs due to trading on the accruals strategy. This result confirms the premise of Lev and Nissim (2004) that transaction costs are an important impediment to the accruals strategy. However, most importantly, the evidence on the fund net returns shows that profits from following the accruals and NOA strategies remain statistically and economically significant after transaction costs. In Figure 4, we plot the spreads in net returns and in the 3-factor alphas, both before expense, between the D10 and D1 funds for each sample year. Fund deciles are formed based on AIM H and NIM H. The spreads are positive in most years, similar to the spreads between top and bottom deciles of stocks sorted by their accruals and NOA, as plotted in figure 1. It should be noted that we do not attribute all the performance difference between D10 and D1 funds to the active and deliberate use of the accruals or NOA strategy. Perhaps most funds in the D1 decile have low AIM or NIM just by chance; and similarly, some funds in the D10 decile have high AIM or NIM by chance. Rather, the evidence presented in this section should be interpreted as that whether funds trade on these anomalies deliberately or not, transaction costs have not eliminated all the abnormal profits. B.2 Fund Performance and Trading-based Anomaly Investing Measures We further examine performance difference across funds ranked by trading-based anomaly-investing measures. In each year, we rank funds into deciles on AIM T / NIM T, and then compute the average gross returns for each fund decile in the subsequent year. Panel A of Table 7 shows that trading on both the accruals anomaly and the NOA 26

28 anomaly is significantly profitable in terms of gross returns. D10 funds ranked by AIM T and NIM T respectively outperform the corresponding inactive funds by 2.99 and 2.24 percent. Panel B of Table 7 reports the profitability of anomaly-based trading in terms of the net return based measures. The cross-sectional patterns are similar to those in Panel A. Comparing results in Panel A with those in Panel B, we can see that transaction costs continue to play an important role in reducing the profitability of these trading strategies. For AIM T, the spreads between gross returns and before-expense net returns for D10 funds and the inactive funds are 1.30 percent (17.24% 15.94%) and 0.51 percent (14.25% 13.74%). Figure 5 plots the spreads in before-expense net returns and in the before-expense 3-factor alphas for each sample year between the D10 and D1 funds ranked by AIM / NIM. The return spreads are mostly positive under AIMT ranking and to a less T T extent so under NIM T ranking. Again, not all the funds in D10 and D1 deciles are there by deliberate trading. Rather, we interpret the results as that transaction costs have not completely eliminated the profitability of the accruals- and NOA-based trading. The results in Table 6 and 7 have several important implications. First, transaction costs do have a significant impact on the profitability of the accruals and NOA strategies. Second, despite transaction costs, investing on the accruals and NOA anomalies remains profitable. The importance of the second implication can be better understood from the perspective of a financial market with perfectly elastic supply of arbitrage capital. In such a financial market, investors will send their money to fund managers as long as funds are 27

29 profitable, and fund managers will aggressively trade on an anomaly until such trading becomes unprofitable. In the presence of transaction costs, mispricing could not be completely eliminated, but the profit of anomaly-based investing would be completely eliminated due to perfect capital supply. Comparing this ideal scenario with the empirical evidence reported here, we conclude that transaction costs alone cannot completely explain why investing on these anomalies remains profitable. Of course, transaction cost is not the only type of market frictions that erode the profitability of anomaly-based investing. Another important type of friction is short-sale constraints. For various reasons, mutual funds are self-constrained not to take short positions in stocks (see, e.g., Almazan, Brown, Carlson, and Chapman, 2004). The effect of short-sale constraints on fund performance, however, should be similar to that of transaction costs. In a market with short-sale constraints but perfect supply of arbitrage capital, mutual funds would take aggressive long positions in undervalued stocks until profits from such investments are driven to zero. B.3 The Effect of Arbitrage Risk If transaction costs and short-sale constraints cannot explain the significant profitability of anomaly-based investing, what other market frictions can? We conjecture that the co-existence of continued profitability of anomaly-based trading and the continued presence of anomalies is mainly due to arbitrage risk. The mechanism for arbitrage risk to prevent market anomalies being completely arbitraged away is explained in Shleifer and Vishny (1997). They point out that trading on mispricing is seldom riskless; in fact, it is often associated with substantial arbitrage risk, which in their 28

30 definition is the idiosyncratic risk of returns to investing in mispriced securities. Such risk may not be fully diversified away in an arbitrage portfolio because arbitrageurs tend to hold only a limited number of stocks in their portfolios. As a result, higher arbitrage risk translates into higher volatility in portfolio performance. Further, because of asymmetric information inherent in delegated portfolio management, investors may withdraw money from a fund when intermediate fund performance suffers due to such arbitrage risk, even though the arbitrage opportunities pursued by the fund should be ultimately profitable. As a consequence, funds would trade on mispricing less aggressively, and such trading remains profitable. At fund level, two types of effects are key to the role of arbitrage risk, as suggested by Shleifer and Vishny (1997). First, arbitrage risk increases return volatility for funds actively trading on market anomalies. Second, arbitrage risk also makes flows to such funds highly volatile. We empirically analyze these two effects. We first examine the effect of arbitrage risk on fund return volatility. In each year (July of year t to June of year t+1) we compute both the average standard deviation of net returns and the average standard deviation of the idiosyncratic component of net returns for each fund, where the idiosyncratic component of fund returns are the residuals from the 3-factor and 4-factor models. We then rank funds into deciles based on holding- and trading-based AIM and NIM in June of year t. Again, we define the inactive funds as the 10 percent of funds with AIM H or NIM H closest to zero. For each fund decile as well as for the group of inactive funds, we calculate the averages of standard deviations of net returns and idiosyncratic returns. Their time-series means and time-series t-statistics are 29

31 reported in Table 8. Panel A is for funds ranked by holding-based measures and Panel B is for funds ranked by trading-based measures. Results in both panels confirm the positive relation between arbitrage risk and fund return volatility. For funds sorted by holding- and trading-based AIM, those in the extreme deciles have significantly higher net return volatility and idiosyncratic return volatility relative to the inactive funds. For example, when funds are sorted by AIM H, the net return volatility and 3-factor idiosyncratic volatility of D10 funds are significantly higher than those for the inactive funds by 1.37% and 0.66% respectively. There is evidence that stocks with extreme accruals tend to have higher idiosyncratic risks (e.g., Lev and Nissim, 2005; Mashruwala Rajgopal, and Shevlin, 2004). Also recall from Table 1 that the median number of stocks held by a mutual fund is below 60. The evidence suggests that mutual funds have not effectively diversified away the idiosyncratic risks inherent in pursuing the accruals strategy. A similar pattern is found for funds ranked by NOA investing measures -- funds ranked in the extreme deciles of NIM also have substantially higher return volatilities relative to the inactive funds. Next, we examine the effect of arbitrage risk on fund flow volatility to see whether investors are sensitive to interim performance of funds that aggressively use accruals and NOA strategies. According to Shleifer and Vishny (1997), investors rely on interim fund performance to infer managers ability. If fund performance suffers temporarily, investors may withdraw money, thereby undermining fund managers arbitrage positions. This suggests that flows to funds engaging in arbitrage trading are also volatile. Following Sirri and Tufano (1998), we calculate monthly fund flow as 30

32 FLOW i, t = TNA i, t TNA TNA i, t 1 * (1 + i, t 1 R i, t ) where TNA i,t is the total net assets of fund i at the end of month t and R i, t is fund monthly return. Fund flow volatility is the standard deviation of monthly flows from July of year t to June of year t+1, i.e., during the 12 months after fund ranking. To control for other factors that are unrelated to arbitrage risk but may also affect fund flows, we additionally compute the residual flow volatility, which is the estimated residual from annual cross-sectional regression of fund flow volatility in year t onto the logarithm of fund size, expense ratio, load dummy, and fund age measured at the end of year t-1, as well as fund annual net return for year t-1. The load dummy takes the value of one if the fund is a load fund, and zero otherwise. We calculate the averages of flow volatility and residual flow volatility for each fund decile ranked by anomaly-investing measures, and report their time series means and time series t-statistics in Table 9. Panel A is for funds sorted by holding-based measures and Panel B is for funds sorted by trading-based measures. The results in both panels show that the volatility of flows is substantially higher for funds ranked in the extreme deciles relative to the inactive funds. This confirms that indeed investor response is more volatile when arbitrage risk increases the variability of interim fund performance. Such volatile investor response limits the ability of mutual funds to fully pursue arbitrage opportunities. IV. Conclusion 31

33 In this paper, we provide evidence that mutual funds actively trade on and profit from two accounting-based anomalies: the well-publicized accruals anomaly and the recently documented net operating assets anomaly. We also find that transaction costs have not completely prevented mutual funds from profiting on these anomalies, while at the same time mutual funds have not traded aggressive enough in exploiting the mispricing. Further analysis shows that funds more aggressively using the accruals and NOA strategies exhibit higher volatility in both fund returns and fund flows. This is consistent with the effect of arbitrage risk (Shleifer and Vishny 1997). 32

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38 Table 1 Summary Statistics for Mutual Funds Table I reports summary statistics of the mutual fund sample. We first compute the averages for total net assets, annual returns, turnovers, annual loads, expense ratios, and numbers of stocks held across funds in each year, and then report their time series averages. Annual load is the total load divided by 7. Age is the number of years from the fund organization year in the CRSP data. AGG, GRO, and G&I refer to fund subsamples with different investment objectives -- aggressive growth, growth funds, and growth and income. All Funds AGG GRO G&I Number of funds Total Net Assets ($ Millions) Annual Return (%/year) Turnover (%/year) Annual Load (%/year) Expense Ratio (%/year) Age (year) Average number of stocks held Median number of stocks held

39 Table 2 Returns to Decile Portfolios of Stocks Sorted by Accruals and Net Operating Assets At the end of April of each year t we form equal-weighted portfolios of stocks based on accruals, net operating assets (NOA), as well as characteristics-adjusted accruals and NOA. The portfolios are held from May of year t to April of year t+1. We report the average returns of the decile portfolios during the period from 1984 to The time-series t-statistics are in the parentheses. Decile Portfolios Stocks Sorted by Accruals (%/year) Stocks Sorted by NOA (%/year) Raw Characteristicsadjusted Raw Characteristicsadjusted D1 (lowest) D10 (highest) D1-D (5.07) (5.96) (4.28) (5.38) 38

40 Table 3 Holding-based and Trading-based Anomaly Investing Measures We first compute the accruals investing measures (AIM) and NOA investing measures (NIM), both holdingbased and trading-based, for each fund in June of each year, and then report their time-series averages. The time-series t-statistics are in the parentheses. The sample period is from 1984 to AIM H *10 3 NIM H *10 3 AIM T *10 3 NIM T *10 3 All Funds (11.00) (5.21) (3.81) (1.85) AGG (8.90) (2.48) (3.84) (2.75) GRO (10.47) (2.39) (3.74) (2.22) G&I (7.59) (0.62) (1.20) (1.38) 39

41 Table 4 Regressions of Aggregate Fund Holding and Trading on Accruals and NOA We report the time series averages of estimated coefficients from annual stock-level cross-sectional regressions. The dependent variables are aggregate portfolio weight, defined the percentage of a stocks outstanding shares held by sample funds in June of year t, and aggregate portfolio weight change, defined as the change in the percentage of a stock s outstanding shares held by sample funds from June of year t-1 to June of year t. The explanatory variables include characteristics-adjusted accruals and NOA, as well as control variables including returns on assets (ROA), the inverse of stock price (1/Price), and the average monthly stock trading volume divided by the total shares outstanding (VOL). Adjusted R 2 is the time-series average of the adjusted R-squares for the cross-sectional regressions. The time-series t-statistics of the average coefficients are in the parentheses. (1) (2) (3) (4) Dependent Variable Portfolio weights Weight changes Portfolio weights Weight changes Intercept 5.94 (7.14) 1.08 (1.47) 5.61 (7.57)) 1.01 (1.48) Characteristics-adjusted Accruals (-2.73) (-2.05) Characteristics-adjusted NOA (-1.83) (-1.67) ROA t (6.94) 0.30 (1.26) 3.47 (7.48) 0.34 (1.29) 1/PRICE t (-6.93) (-2.47) (-7.20) (-2.74) VOL t (3.75) (-0.34) (3.81) (-0.35) Adjusted R

42 Table 5 Determinants and Persistence of Anomaly Investing Measures We report the time-series averages of estimated coefficients from annual cross-sectional regressions. The dependent variables are holding-based and trading-based AIM and NIM for year t. The explanatory variables include AIM and NIM for year t-1, as well as several fund characteristics. LogAge is the logarithm of fund age, LogTNA is the logarithm of fund total net assets, Turnover is annual fund turnover, and expense is the expense ratio. All fund characteristics are measured at the end of year t-1. Adjusted R 2 is the time-series average of the adjusted R-squares for the cross-sectional regressions. The time-series t- statistics are in the parentheses. (1) (2) (3) (4) Dependent Variable AIM H *10 3 AIM T *10 3 NIM H *10 3 NIM T *10 3 Intercept (-0.35) (-0.21) 6.25 (1.50) (0.56) Lagged AIM H * (12.75) Lagged AIM T * (1.92) Lagged NIM H * (38.96) Lagged NIM T * (2.09) LogAge t (1.30) (-0.52) 1.01 (1.94) (-0.21) LogTNA t (2.37) 1.21 (1.85) 1.68 (2.48) 2.10 (2.04) Turnover t (3.19) 0.64 (1.69) 1.67 (1.43) 2.19 (2.84) Expense t (-0.47) (0.68) (-0.63) (-1.54) Adjusted R

43 Table 6 Fund Performance across Holding-based Anomaly Investing Measures In Panel A, we first compute in each year the average annual gross return for funds in each decile sorted by either AIM H or NIM H, and then report their time-series averages. In Panel B, we first compute in each year the averages of annual net returns and 3-factor and 4-factor alphas for funds in each decile sorted by either AIM H or NIM H, and then report their timeseries averages. Net returns and alphas are evaluated both before and after adjusting for fund expense ratios. INACTIVE refers to the 10 percent of funds with AIM H or NIM H closest to zero. The time-series t-statistics are in the parentheses. Panel A: Gross Returns Funds Sorted by AIM H Funds Sorted by NIM H D (2.83) (2.72) (3.34) (3.43) (3.47) (3.77) (3.59) (3.28) (3.57) (3.16) (3.65) (3.42) (3.61) (2.75) (3.62) (3.12) (3.55) (3.47) D (3.33) (3.32) INACTIVE (3.71) (3.36) D10 INACTIVE (2.60) (2.53) D10 D (3.07) (3.15) 42

44 Panel B: Net Returns Funds Sorted by AIM H Funds Sorted by NIM H Net Return 3-factor Alpha 4-factor Alpha Net Return 3-factor Alpha 4-factor Alpha before expense after expense before expense after expense before expense after expense before expense after expense before expense after expense before expense after expense D (2.75) (2.68) (0.29) (-0.68) (0.53) (-0.73) (3.44) (3.13) (0.33) (-0.69) (0.53) (-0.72) (2.90) (2.65) (0.86) (-0.93) (0.58) (-1.10) (3.45) (3.28) (0.29) (-0.94) (0.64) (-0.41) (3.71) (3.44) (0.72) (-0.81) (0.54) (-0.79) (3.17) (2.83) (0.37) (-0.70) (0.60) (-0.99) (3.72) (3.48) (0.64) (-1.09) (0.95) (-0.76) (2.94) (3.51) (0.52) (-0.36) (0.47) (-0.52) (3.63) (3.39) (1.11) (-0.46) (0.90) (-0.55) (3.48) (3.45) (0.65) (-0.24) (0.68) (-0.23) (3.82) (3.59) (1.27) (0.11) (1.21) (-0.95) (3.52) (3.62) (0.98) (-0.20) (0.72) (-0.27) (3.66) (3.44) (1.43) (0.92) (1.26) (0.76) (3.48) (2.72) (1.59) (0.87) (1.09) (0.56) (3.68) (3.47) (1.29) (1.15) (1.81) (1.30) (3.76) (3.01) (1.34) (0.93) (1.11) (0.63) (3.31) (3.10) (2.67) (1.97) (2.41) (1.56) (3.53) (3.82) (1.96) (1.17) (1.73) (0.39) D (2.99) (2.78) (2.86) (2.83) (4.22) (2.82) (3.16) (3.05) (2.34) (1.57) (1.63) (0.74) INACTIVE (3.68) (3.72) (1.14) (-0.46) (0.69) (-0.53) (3.46) (3.12) (0.31) (-0.20) (0.47) (-0.31) D10 INACTIVE (2.31) (2.06) (3.98) (3.92) (3.43) (2.82) (2.08) (1.96) (2.04) (2.09) (1.76) (1.82) D10 D (2.57) (2.23) (3.12) (2.80) (2.81) (3.10) (2.49) (2.35) (2.36) (2.15) (2.14) (1.99) 43

45 Table 7 Fund Performance across Trading-based Anomaly Investing Measures In Panel A, we first compute in each year the average annual gross return for funds in each decile sorted by either AIM T or NIM T, and then report their time-series averages. In Panel B, we first compute in each year the averages of annual net returns and 3-factor and 4-factor alphas for funds in each decile sorted by either AIM T or NIM T, and then report their timeseries averages. Net returns and alphas are evaluated both before and after adjusting for fund expense ratios.. INACTIVE refers to the 10 percent of funds with AIM T or NIM T closest to zero. The time-series t-statistics are in the parentheses. Panel A: Gross Returns Funds Sorted by AIM T Funds Sorted by NIM T D (3.02) (3.19) (3.55) (3.14) (3.64) (3.52) (3.85) (3.43) (3.70) (3.57) (3.60) (3.02) (3.49) (3.55) (3.72) (3.14) (3.20) (3.25) D (3.09) (3.07) INACTIVE (3.80) (3.56) D10 INACTIVE (2.60) (2.15) D10 D (2.76) (2.03) 44

46 B: Net Returns Funds Sorted by AIM T Funds Sorted by NIM T Net Return 3-factor Alpha 4-factor Alpha Net Return 3-factor Alpha 4-factor Alpha after before after before after before after before after before expense expense expense expense expense expense expens expense expense expense before expense after expense e D (3.07) (2.82) (0.36) (-1.31) (0.25) (-1.23) (3.26) (2.46) (0.39) (-0.95) (0.52) (-0.92) (3.24) (2.99) (0.25) (-0.86) (0.52) (-0.95) (3.35) (2.49) (0.23) (-0.75) (0.94) (-0.81) (3.51) (3.26) (0.59) (-0.97) (0.53) (-0.86) (3.60) (2.53) (0.28) (0.81) (0.67) (-0.71) (3.82) (3.57) (0.85) (-0.76) (0.75) (-0.71) (3.67) (2.68) (0.69) (-0.83) (0.68) (-0.65) (3.67) (3.53) (0.92) (-0.62) (0.86) (-0.46) (3.52) (2.76) (0.78) (-0.72) (0.79) (-0.46) (3.66) (3.45) (0.86) (-0.38) (0.95) (-0.46) (3.54) (2.73) (0.65) (-0.86) (0.76) (-0.83) (3.52) (3.30) (0.73) (-0.11) (10.2) (-0.19) (3.62) (2.65) (0.86) (-0.20) (0.96) (-0.76) (3.54) (3.31) (1.32) (0.65) (1.26) (0.56) (3.42) (2.53) (0.84) (0.26) (0.94) (-0.39) (3.06) (2.84) (1.74) (1.53) (1.96) (1.45) (3.21) (2.41) (1.06) (0.53) (1.06) (0.51) D (2.90) (2.68) (3.45) (2.06) (2.67) (2.13) (3.05) (2.80) (1.76) (1.08) (1.47) (0.84) INACTIVE (3.64) (3.55) (0.45) (-0.98) (0.74) (-0.62) (3.54) (2.72) (0.37) (-0.50) (0.96) (-0.75) D10 INACTIVE (2.06) (1.83) (2.76) (2.89) (2.29) (2.41) (1.92) (1.75) (1.57) (1.72) (1.53) (1.78) D10 D (2.16) (2.45) (3.06) (3.11) (2.59) (3.12) (2.22) (2.01) (1.73) (1.65) (1.86) (1.93) 45

47 Table 8 Fund Return Volatility across Anomaly Investing Measures We first compute in each year the averages of standard deviations of monthly net returns and monthly idiosyncratic returns for funds within each decile sorted by an anomaly investing measure, and then report their time-series averages. The idiosyncratic returns are estimated residuals from the 3-factor and 4-factor models. Panel A is for funds sorted by holding-based measures. Panel B is for funds sorted by tradingbased measures. INACTIVE refers to the 10 percent of funds with AIM or NIM closest to zero. The timeseries t-statistics are in the parentheses. Panel A: Holding-based Measures Funds Sorted by AIM H (%/year) Total Risk 3-factor Idiosyncratic Risk 4-factor Idiosyncra tic Risk Funds Sorted by NIM H (%/year) Total Risk 3-factor Idiosyncratic Risk 4-factor Idiosyncrati c Risk D D INACTIVE D10 INACTIVE (5.20) (7.36) (6.54) (2.35) (3.48) (4.09) Panel B: Trading-based Measures Funds Sorted by AIM T (%/year) Total Risk 3-factor Idiosyncratic Risk 4-factor Idiosyncra tic Risk Funds Sorted by NIM T (%/year) Total Risk 3-factor Idiosyncratic Risk 4-factor Idiosyncratic Risk D D INACTIVE D10 INACTIVE (9.15) (7.85) (7.63) (7.15)) (4.20) (4.15) 46

48 Table 9 Fund Flow Volatility across Anomaly Investing Measures We first compute in each year the averages of the volatility and residual volatility of monthly flows for funds within each decile sorted by an anomaly investing measure, and then report their time-series averages. The residual flow volatility is the estimated residual from cross-sectional regression of fund flow volatility onto the logarithm of fund size, total fees, lagged fund returns. Panel A is for funds sorted by holding-based measures. Panel B is for funds sorted by trading-based measures.. INACTIVE refers to the 10 percent of funds with AIM or NIM closest to zero. The time-series t-statistics are in the parentheses. Panel A: Holding-based Measures Funds Sorted by AIM H (%/year) Funds Sorted by NIM H (%/year) Flow Volatility Residual Flow Volatility Flow Volatility Residual Flow Volatility D D INACTIVE D10 INACTIVE (5.09) (6.66) (4.16) (6.63) Panel B: Trading-based Measures Funds Sorted by AIM T (%/year) Funds Sorted by NIM T (%/year) Flow Volatility Residual Flow Volatility Flow Volatility Residual Flow Volatility D D INACTIVE D10 INACTIVE (5.39) (7.72) (4.54) (7.14) 47

49 Figure 1 Hedged Portfolio Returns for Accruals and NOA Strategies Figure 1 plots the average annual return spreads between the bottom and top deciles of stocks ranked on accruals and NOA, as well as characteristics-adjusted accruals and NOA. Return Difference between Top and Bottom Deciles Sorted by Accruals Return Difference between Top and Bottom Deciles Sorted by NOA Return Difference between Top and Bottom Deciles Sorted by Characteristics-adjusted Accruals Return Difference between Top and Bottom Deciles Sorted by Characteristics-adjusted NOA

50 Figure 2 Average Portfolio Weights across Characteristics-adjusted Accruals and NOA Figure 2 plots the average portfolio weights in each stock decile for top and bottom fund deciles, as well as the differences of portfolio weights between the top and bottom fund deciles. Stocks are sorted into deciles by characteristics-adjusted accruals and NOA. Funds are sorted into deciles by AIM H and NIM H. 0.2 Portfolio Weight D10-D1 D1 Funds D10 Funds Characteristics-adjusted Accruals Decile 0.2 Portfolio Weight D10-D1 D1 Funds D10 Funds Characteristics-adjusted NOA Decile 49

51 Figure 3 Portfolio Weight Changes across Characteristics-adjusted Accruals and NOA Figure 2 plots the average portfolio weight changes in each stock decile for top and bottom fund deciles, as well as the differences of portfolio weights between the top and bottom fund deciles. Stocks are sorted into deciles by characteristics-adjusted accruals and NOA. Funds are sorted into deciles by AIM T and NIM T respectively. 0.1 Portfolio Weight Change D10-D1 D10 Funds D1 Funds Characteristics-adjusted Accruals Decile 0.1 Portfolio Weight Change D10-D1 D1 Funds D10 Funds Characteristics-adjusted NOA Decile 50

52 Figure 4 Performance Differences between Top and Bottom Fund Deciles Sorted by Holding-based Anomaly Investing Measures Figure 4 plots the time series of the differences in before-expense annual net returns and the corresponding 3-factor alphas between the top and bottom fund deciles ranked by AIM H and NIM H Difference in Net Returns between Top and Bottom Fund Deciles Sorted by AIM H Difference in 3-factor Alphas between Top and Bottom Fund Deciles Sorted by AIM H Difference in Net Returns between Top and Bottom Fund Deciles Sorted by NIM H Difference in 3-factor Alphas between Top and Bottom Fund Decile Sorted by NIM H

53 Figure 5 Performance Differences between Top and Bottom Funds Sorted by Trading-based Anomaly Investing Measures Figure 5 plots the time series of the differences in before-expense annual net returns and the corresponding 3-factor alphas between the top and bottom fund deciles ranked by AIM T and NIM T Difference in Net Returns between Top and Bottom Fund Deciles Sorted by AIM T Difference in 3-factor Alphas between Top and Bottom Fund Deciles Sorted by AIM T Difference in Net Returns between Top and Bottom Fund Deciles Sorted by NIM T Difference in 3-factor Alphas between Top and Bottom Fund Deciles Sorted by NIM T

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