ALTERNATIVE MOMENTUM STRATEGIES. Faculdade de Economia da Universidade do Porto Rua Dr. Roberto Frias Porto Portugal

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1 FINANCIAL MARKETS ALTERNATIVE MOMENTUM STRATEGIES António de Melo da Costa Cerqueira, Faculdade de Economia da UP Elísio Fernando Moreira Brandão, Faculdade de Economia da UP Faculdade de Economia da Universidade do Porto Rua Dr. Roberto Frias Porto Portugal Tel: Fax:

2 2 FINANCIAL MARKETS ALTERNATIVE MOMENTUM STRATEGIES António Cerqueira, and Elísio Brandão ABSTRACT This paper investigates the profitability of alternative momentum trading strategies, using two variables to rank stocks in the formation period. We add to the significant literature that uses stock returns to sort stocks by providing evidence when adding accruals as a ranking variable. This procedure is based on prior strong evidence that the momentum and the accrual effects produce average abnormal stock returns not explained by standard risk factors. We find evidence that the new strategies generate portfolio returns significantly higher than standard momentum strategies. Moreover, our findings provide strong support for the explanations of momentum and accrual anomalies based on short selling costs. We also examine the persistence of the momentum strategy and we investigate whether its profitability varies between rising and falling stock markets, and whether it depends on the database used as a data source. Key Words: Financial Markets, Investment Strategies, Momentum Anomaly, Accrual Anomaly 1. INTRODUCTION This study examines opportunities of earning abnormal returns on the U.S. stock markets by using trading strategies that exploit the predictability of stock price movements. We analyse three alternative trading strategies based on the price continuation effect and the accrual effect, in order to investigate whether momentum and accruals represent independent anomalies that, in combination, reveal more extreme stock price mispricing. This study can be relevant because prior research found strong evidence that the momentum effect and the accrual effect produce average abnormal stock returns not explained by standard risk factors. Fama and French (2006) provide evidence that these anomalies are left unexplained by asset pricing models. Most of the investment strategies that exploit the predictability of stock price movements are based only on past returns. Investment strategies based on historical returns examined in the literature fall into two main categories: contrarian strategies and momentum strategies. Both contrarian and momentum strategies rank stocks based on their performance over some previous time horizon. Contrarian strategies are based on long-term negative autocorrelation in stock returns, and recommend buying past loser stocks and selling past winner stocks. Momentum strategies are based on medium-term positive autocorrelation in stock returns, and consist in selling past losers and taking a long position on past winners. This paper examines momentum strategies. Prior research has found strong evidence that equity markets exhibit medium-term return continuation and that momentum strategies yield significant profits. Jegadeesh and Titman (1993, 2001), using U.S. stock market data, document that strategies taking a long position in stocks with high returns over the previous 3 to 12 months and taking a short position in stocks with poor returns over the same period generate returns of about one percent per month for the following year. However, the momentum anomaly is not confined to the US. Rouwenhorst (1998) documents similar evidence in European stock markets, using data from 12 European countries. While most of previous evidence points to the profitability of momentum strategies, researchers do not agree regarding the explanations provided for the momentum effect. There has been many works analysing whether momentum reflects an improper response to information, data mining, market microstructure effect or improper control for risk factors. Jegadeesh and Titman (2001) find evidence supporting the behavioural hypothesis that the momentum effect arises because of a delayed overreaction to information. Because Jegadeesh and Titman

3 Alternative Momentum Strategies 3 (1993, 2001) provide the most well known studies on the momentum strategies, we are going to explore this explanation. In order to explore the overreaction based explanation, we propose alternative momentum strategies that analyse whether momentum has something to do with the finding of Sloan (1996) that investors fixate on reported earnings, so that stock prices fail to fully reflect information contained in the accrual and cash flow components of current earnings. He finds that investors tend to overreact to information contained in accruals, and that a trading strategy taking a long position in the stock of firms reporting relatively low levels of accruals and a short position in the stock of firms reporting relatively high levels of accruals generates positive abnormal stock returns for the following one and two years after portfolio formation. So we extend the analysis of Jegadeesh and Titman (2001) by examining a trading strategy based on past returns and accruals in addition to the JT price momentum strategies. It is important to emphasize that, unlike Sloan, that uses holding periods varying from one to three years, we use medium-term holding periods, because we are interested in analysing the medium-term overreaction effect and not the subsequent correction effect. Our sample uses adjusted monthly returns on NYSE, AMEX and NASDAQ stocks over the period from 1990 to We use this sample period to complement the Jegadeesh and Titman (2001) study that uses data on the same stocks for a period ending in There are two additional points in our tests that we consider to be relevant. Firstly, we investigate whether the results found in previous studies continue in falling markets. In order to get a separate period of falling markets, from 2000 to 2003, we construct three sub-samples: from 1991 to 1999, from 2000 to 2003, and from 2004 to Secondly, we have the opportunity to check if our results, which are based on data provided by Datastream, are consistent with prior results based on Compustat and CRSP data. Now we describe the main findings of this study in the case that uses past returns in portfolio formation. Our results show that the momentum trading strategy based on overlapping observations with a six-month formation period and a six-month holding period earns mean returns of about 0.98 % per month. This confirms the persistence of the momentum effect because it is very similar to the mean return of one percent per month reported by Jegadeesh and Titman (1993, 2001). The results of our tests are important because they contribute to the rejection of the hypothesis that the momentum effect is a product of data mining. In fact, we find evidence that momentum has continued after the period used by Jegadeesh and Titman (2001). Additionally, we have the opportunity to confirm that our findings, which are based on data provided by Datastream, are consistent with prior empirical tests for the same stock markets based on Compustat and CRSP. To check whether the results might be period specific, we perform an analysis of the momentum portfolio returns for three sub-periods ( ), ( ) and ( ). The results show that the momentum effect is not due to any particular period. However, the most unexpected finding is that even in the case of the falling stock market period from 2000 to 2003 the mean return for the strategy holds at the 1.24 % per month level. This opportunity of making such profits is really unexpected since during this four-year period the market as a whole earned a negative return of about - 51 % (- 10 %), as measured by the NASDAQ (DOW JONES) Index. In order to verify whether the profitability of the strategy is a compensation for risk, we measure the return for the strategy after controlling for firm size and specific risk. We find that momentum return is higher after controlling for risk, and this represents strong evidence that standard risk factors cannot explain the momentum effect. However, the most important finding is that the abnormal return for the strategy is mainly due to the return on the loser portfolio. This, in our opinion, is a major finding because it relates the momentum profitability with short selling. This finding points to a likely explanation for the momentum effect that attributes the abnormal return to short selling transaction costs. Our study examines another momentum strategy that uses abnormal returns to rank stocks in the formation period. This strategy generates higher returns after controlling for risk factors as compared with the standard momentum strategy. As in the first strategy the results of these tests suggest an explanation for the momentum anomaly related to short selling transaction costs. However, the aim of this paper is to propose trading strategies that use both information on past returns and accruals to rank stocks in the formation period. As we have mentioned previously, if these variables transmit independent information about future returns not included in current stock prices, then the use of a combination

4 4 of the two variables in portfolio formation should result in higher investment returns. The empirical tests show that this strategy generates a monthly mean return of 1.67 % that is significantly higher than the 0.98 % earned by the standard strategy. This clearly points to the accruals ability to reveal information on future stock returns not includes in past returns. The analysis of portfolio returns after controlling for firm size and systematic risk strongly supports the explanation for both momentum and accrual anomalies based on short selling costs. The remainder of this paper is organized as follows: Section I provides a short description of momentum and accrual anomalies, Section II describes the data and methodology, Section III provides evidence on the profitability of the momentum strategy based on past returns, Section IV investigates an alternative strategy based on abnormal past returns, Section V analyses trading strategies based on information on past returns and accruals, and Section V concludes the paper. 2. MOMENTUM AND ACCRUAL ANOMALIES Prior research provides evidence that trading strategies based on momentum generate average returns that standard asset pricing models cannot explain. Similar evidence is provided in the case of the accrual anomaly. Fama and French (2006) report evidence showing that both momentum and accrual anomalies cannot be explained by standard asset pricing models. The main goal of this work is to examine the profitability of trading strategies that combine information on past returns and accruals in portfolio formation. If the combination of these two variables in a strategy results in higher returns that in the case of only one of the variables, this imply that each of the variables adds new information and separate explanatory power for future firm performance. Momentum is the most well documented anomaly. Jegadeesh and Titman (1993, 2001) document that over medium-term horizons of three to twelve months, stocks with low past returns tend to have low future returns, and stocks with high past returns tend to exhibit high future returns. Investment strategies based on such momentum anomaly, by buying past winner portfolios and selling past loser portfolios, generate positive abnormal stock returns. Jegadeesh and Titman rank stocks based on their returns over formation periods ranging from three to twelve months. Using this ranking, they assign the stocks to ten equally weighted portfolio deciles. The zero net investment strategy consists in buying the stocks in the winner decile and selling those in the loser decile. Abnormal returns on the winner-loser portfolio are measured over holding periods of 3- to 12- months. Using overlapping observations, they replicate the strategy for every month of the sample period. The average return on the strategy is given by the average of all monthly replications. Using data on NYSE and AMEX stocks over the period from 1965 to 1989, Jegadeesh and Titman (1993) report average returns of about one percent per month on the winner-loser portfolio for the six-month strategy, and returns of about 1.5% for the 12 3 strategy. Jegadeesh and Titman (2001) report similar results using data on NYSE, AMEX and NASDAQ over the sample period from 1990 to However, the studies on the profitability of momentum strategies are not confined to the USA. Rouwenhorst (1998) reports similar momentum profitability in European stock markets. Griffin, Ji and Martin (2003) provide evidence that momentum profits in stock markets around the world are statistically significant. Several researchers have analysed whether momentum profits are a compensation for risk, by using standard asset pricing models. For example, Grundy and Martin (2001) found evidence that the profitability of momentum strategies cannot be explained by the three-factor model, or by cross-sectional variation in stock returns nor by industry factors. Some studies, for example Jegadeesh and Titman (2001), have analysed whether data mining can be the source of the momentum anomaly. However, given the geographically and temporarily distinct samples used in empirical studies, it is unlikely that the momentum anomaly would be a product of data mining. While there is widespread agreement about the profitability of momentum strategies, researchers disagree about the theoretical explanations for the anomaly. Daniel, Hirshleifer and Subrahmanyam (1998) propose a theoretical model based on investors behaviour, which explains price continuation in medium-term horizons and price reversals over long-term periods. Their model is based on investors overconfidence about the quality of their private information. If public information arriving later confirms private information this increases their overconfidence, but they attribute failure to noise. Hong and Stein (1999) propose a theoretical model based on the interaction between two distinct groups of investors that can explain underreaction in stock returns over

5 Alternative Momentum Strategies 5 medium-term periods. Jegadeesh and Titman (2001) found some evidence that overreaction in stock returns can explain part of the profitability of momentum strategies, and they document evidence that momentum profits cannot be attributed to data-mining. Lesmond, Schill and Zhou (2004) argue that momentum profits are a compensation for trading costs. However, despite the evidence on the profitability of momentum trading, there is no consensus on the source of the abnormal returns. In the case of the accrual anomaly, Sloan (1996) finds that firms with high levels of accruals tend to have low future returns, because stock prices do not fully reflect information contained in the accruals and cash flow components of current earning about future earnings. In fact, many studies have documented a positive contemporaneous association between stock returns and reported earnings. Also, cash flow from operations is an important measure of firm performance because it is less subject to discretionary decisions than is the operating income. This is so because the determination of the net income under the accrual system involves some level of subjectivity. Therefore, the accrual component of earnings exhibits lower persistence than the cash flow component of earnings. When investors do not anticipate that the accrual component of earnings mean reverts faster than the cash flow component of earnings, they tend to overestimate (underestimate) stocks with a relatively high (low) accrual component. According to Sloan (1996), investors fixate on earnings and make systematic errors in evaluating the impact of current earnings on future earnings, because they do not make full use of information contained in the accrual and cash flow components of current earnings. Sloan finds that high (low) levels of accruals are associated with negative (positive) future abnormal stock returns, and that the mispricing correction occurs around the date of future earnings announcements. More specifically Sloan provides evidence that a trading strategy taking a long position in a portfolio of firms reporting relatively low levels of accruals and a short position in the stock of firms reporting relatively high levels of accruals generates positive abnormal stock returns that are concentrated around future earning announcements. 3. DATA AND METHODOLOGY This section describes the data and methodology used to examine the profitability of momentum trading strategies based on past returns. The methodology applied in this part of the study is similar to that proposed by Jegadeesh and Titman (1993, 2001). Stocks are assigned to portfolio deciles according to a ranking based on their cumulative returns over the previous J month formation period. The strategy consists of buying the stocks in the winner decile and taking a short position in the loser decile, for the next K month holding period. Every month of the sample period, stocks are ranked based on their past performance over periods of 3, 6, 9, and 12 months, and their performance is measured for holding periods varying from 3 to 12 months. JT provide a more detailed analysis of the 6 6 strategy, which generates returns of about 1% per month. In order to ensure comparability between our results and those of JT we analyse the 6 6 strategy. Our sample uses adjusted monthly returns on NYSE, AMEX and NASDAQ stocks over the period from January 1990 to December We use this sample period to complement the Jegadeesh and Titman (2001) study that uses data provided by CRSP on the same Stock Exchanges for the period ending in However, because our tests use data provided by Datastream, we have the opportunity to check if our results are consistent with prior results. One important point in our study is to investigate the momentum effect in falling markets. In order to get a separate period of falling markets (from 2000 to 2003) we construct three sub-samples: from January1990 to December 1999, from January 2000 to December 2003, and from January 2004 to December The number of firms with base date before January 2007 is 10453, including active and dead stocks. We do not exclude small firms because prior studies, for example Jegadeesh and Titman (2001) and Fama and French (2006), describe the momentum effect both for large and small stocks. In order to reduce survivorship bias we include in the sample stocks starting and delisting (privately held, merged, liquidated) during the sample period. Consequently, the number of stocks in each test period changes as companies enter and leave the exchange. Each test period includes a six-month ranking period followed by a six-month holding period. Because we use

6 6 overlapping observations we have a test period starting at the beginning of every month in the total sample. Because companies can delist during a test period we adopt the following procedure, we consider an eligible stock as the one that has at least seven months of return data at the beginning of each test period. If the data for the holding period is incomplete we adopt a zero return for the missing months. The application of this procedure results in a number of stocks across test periods varying from a minimum of 2343 stocks and a maximum of 6400 stocks, as reported in Table I. Table I Sample Construction This table reports the number of test periods and firms in the entire sample and in sub-samples. We use overlapping observations and each test period includes a six-month ranking period followed by a six-month holding period. Initial firms include active and dead stocks. The table reports the maximum and the minimum number of firms in test periods. Sub-samples 1990 / / / / 2006 Test Periods Initial Firms Max. Firms / Test Period Min. Firms / Test Period Every month in the sample period, individual stocks are ranked according to their cumulative monthly returns over the six-month formation period, and they are grouped into ten decile portfolios. Decile 1 is designated the loser portfolio and decile 10 the winner portfolio. A buy-and-hold return is calculated for each stock over the sixmonth holding period and the returns of the equally weighted portfolios are calculated. The return of the winnerloser portfolio is calculated, and the trading strategy is replicated in the next periods. The mean return for the strategy is given by the average of all the replications. 4. MOMENTUM STRATEGY BASED ON PAST RETURNS This section evaluates the profitability of momentum strategies based on past returns in the formation period. We concentrate on the strategy that uses a six-month formation period and a six-month holding period, following Jegadeesh and Titman (2001). At the end of each month, we rank all stocks in ascending order, based on their past six-month return. We then assign the stocks to one of the ten-decile portfolios (1- loser portfolio, 10- winner portfolio). These portfolios are equally weighted and held for the next six months. Table II presents the monthly mean return of the winner and loser portfolios. The winner (loser) portfolio earns 1.38 % (0.4 %) per month. The portfolio constructed by buying the past winner and selling the past loser earns 0.98 % per month (t =7.54), which is statistically significant. When we take into account the month of portfolio formation, the momentum strategy generates positive returns every month, except for January. However, the higher returns occur for portfolio formation in May, June and July. Table II Monthly returns of winner and loser portfolios Standard strategy At the end of each month, we rank stocks into ten decile portfolios based on their return over the six-month formation period. We use overlapping observations and each test period includes a six-month ranking period followed by a six-month holding period. The table reports the monthly returns of the winner, loser and winner-loser portfolios for the entire sample period. The table also reports the results specifying the month of portfolio formation. All Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Winner Loser Win-Los t statistic P

7 Alternative Momentum Strategies 7 In order to analyse whether the performance of the momentum strategy changes with the sub-period considered, we analyse in Table III the sub-samples from 1990 to 1999, the period of falling markets between 2000 and 2003, and the period from 2004 to Table III Mean return of winner and loser portfolio (sub-samples) Standard strategy At the end of each month, we rank stocks into ten decile portfolios based on their return over the six-month formation period. We use overlapping observations and each test period includes a six-month ranking period followed by a six-month holding period. The table reports the monthly mean return of the winner and loser portfolios for the entire sample period and sub-samples. Monthly return 1990/ / / /2006 Winner Loser Win-Los t statistic P The tests provide important results because they show that the momentum effect has continued after the period used by Jegadeesh and Titman (2001), therefore contributing to the rejection of the hypothesis of data mining. This outcome is even more relevant because our tests are based on data provided by Datastream, and we have got a monthly mean return for the strategy similar to JT, that reported a mean return of about 1 % per month. However, the most unexpected finding is the consistency of the mean return earned in all the sub-sample periods. Even in the case of the falling stock market period from 2000 to 2003 the mean return for the strategy holds at the 1.24 % per month level. This opportunity of making such profits is really unexpected since during this fouryear period the market as a whole earned a negative return of about - 51 % (- 10 %), as measured by the NASDAQ (DOW JONES) Index. A. Empirical findings after controlling for firm size and systematic risk To examine whether the profitability of the momentum strategy is driven by firm size or systematic risk we use the model proposed by Collins and Hribar (2000). For each month in the sample we construct size portfolios by first ranking all the NYSE AMEX and NASDAQ stocks into ten size deciles, and we calculate the value weighted mean return on each decile. We measure firm size by the market value of equity. For each firm in the sample, we measure expected monthly returns by estimating the regression of their returns on the returns of the portfolio decile that the firm is a member. Table IV reports abnormal return statistics for the winner, loser and winner-loser portfolios. The winner portfolio return is 0.13 % per month, while the loser portfolio return is 1.67 % per month. The portfolio constructed by buying the past winner and selling the past loser earns 1.54 % per month (t =11.1), which is statistically significant, and higher than the 0.98 % per month generated before size and risk adjustments. Table IV Size and risk adjusted monthly returns of winner and loser portfolios Standard strategy At the end of each month, we rank stocks into ten decile portfolios based on their return over the six-month formation period. We use overlapping observations and each test period includes a six-month ranking period followed by a six-month holding period. The table reports the monthly returns of the winner, loser and winner-loser portfolios for the entire sample period, after controlling for firm size and systematic risk. The table also reports the results specifying the month of portfolio formation. All Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Winner Loser Win-Los t statistic P

8 8 These are important results because they show that the momentum effect is stronger after controlling for size and systematic risk. This outcome is even more relevant because the performance of the momentum strategy is mainly attributable to the negative abnormal return on the loser portfolio. In fact, the performance of the winner portfolio, after controlling for size and risk, is not statistically significant. Our results are consistent with the explanation of the momentum effect based on short selling transaction costs. The presence of significant transaction costs represents a limit to arbitrage, which would have corrected the stock mispricing. If investors use momentum strategies, the pressure of their trading would move stock prices and eliminate the momentum anomaly. 5. MOMENTUM STRATEGY BASED ON PAST ABNORMAL RETURNS This section examines the profitability of our second momentum strategy where stocks are attributed to decile portfolios based on their past abnormal returns. This strategy is likely to generate higher returns because it is based on the part of the stock performance that is not explained by standard asset pricing models. If the momentum effect is attributable to a biased reaction of investors to information, this should be captured by stock abnormal return. At the end of each month, we rank all stocks in ascending order, based on their past six-month abnormal return. We then assign the stocks to one of the ten-decile portfolios. These portfolios are equally weighted and held for the next six months. The Collins and Hribar (2000) model is used to measure abnormal stock returns. Table V presents the monthly mean return of the winner and loser portfolios. The winner (loser) portfolio earns 1.43 % (0.5 %) per month. The portfolio constructed by buying the past winner and selling the past loser earns 0.93 % per month (t =8.23), which is statistically significant. Table V Monthly returns of winner and loser portfolios Strategy based on abnormal stock returns At the end of each month, we rank stocks into ten decile portfolios based on their abnormal return over the six-month formation period. We use overlapping observations and each test period includes a six-month ranking period followed by a six-month holding period. The table reports the monthly returns of the winner, loser and winner-loser portfolios for the entire sample period. The table also reports the results specifying the month of portfolio formation. All Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Winner Loser Win-Los t statistic P The strategy that uses past abnormal stock returns to rank stocks generates a 0.93 % mean monthly return, while the standard strategy earns 0.98%. However the monthly mean returns are not statistically different, F = (P = 0.167). This suggests that abnormal stock return is not better than past stock return to rank stocks in portfolio formation period. However, we need to analyse it further by studying the performance of the strategy after adjusting for firm size and systematic risk. A. Empirical findings after controlling for firm size and systematic risk We need to analyse whether the profitability of the momentum strategy based on past abnormal returns is driven by firm size or systematic risk. We use the model proposed by Collins and Hribar (2000), described above. For each firm in the sample, we measure expected monthly returns by estimating the regression of their returns on the returns of the portfolio decile that the firm is a member. Table VI reports abnormal return statistics for the winner, loser and winner-loser portfolios. The winner portfolio return is 0.63 % per month, while the loser portfolio return is 2.78 % per month. The portfolio constructed by buying the past winner and selling the past loser earns 3.41 % per month (t =27.7), which is statistically significant, and higher than the 1.54 % per month generated by the standard momentum strategy after size and risk adjustments. However the difference is not statistically significant, F = (P = 0.14).

9 Alternative Momentum Strategies 9 Table VI Size and risk adjusted monthly returns of winner and loser portfolios Strategy based on abnormal stock returns At the end of each month, we rank stocks into ten decile portfolios based on their abnormal return over the six-month formation period. We use overlapping observations and each test period includes a six-month ranking period followed by a six-month holding period. The table reports the monthly returns of the winner, loser and winner-loser portfolios for the entire sample period, after controlling for firm size and systematic risk. The table also reports the results specifying the month of portfolio formation. All Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Winner Loser Win-Los t statistic P It is important to emphasize that the performance of this second strategy is also mainly due to the mean returns of the loser portfolio, and this suggests short selling transaction costs as the likely explanation for the momentum anomaly. 6. TRADING STRATEGY BASED ON PAST RETURNS AND ACCRUALS This section examines the profitability of a trading strategy where we use two ranking variables in portfolio formation. We have analysed previously the strategy that exploits price continuation and now we are going to describe the details related to the introduction of the accrual component of earnings as a ranking variable. In this section we introduce several changes in the trading strategy to take into account both the price continuation effect and the accrual effect. This study can be relevant because prior research found strong evidence that both the momentum effect and the accrual effect can produce average abnormal stock returns not explained by standard risk factors. Our empirical tests use data provided by Datastream on NYSE, AMEX and NASDAQ firms over the period from 1990 to 2006, to compute stock returns and accruals. We require firm observations to have monthly returns, as well as the necessary accounting information to calculate accruals, and we eliminate all financial firms because of the different nature of their accruals. As in the first part of our study we include in the sample stocks starting and delisting (privately held, merged, liquidated) during the sample period and we use overlapping observations. Consequently, the number of stocks in each test period changes as companies enter and leave the exchange. The results presented above show that the momentum trading strategy based on past stock returns with a sixmonth formation period and a six-month holding period earns mean monthly returns of about 0.98 % per month. Now we are going to introduce several changes in the momentum strategy based on the accrual component of earnings. The SFAS 95, November 1987, effective July 1988, requires the information necessary for computing the accrual component of earnings to be identified in the Statement of Cash Flows. Therefore, unlike Sloan (1996), that uses information from the balance sheet and income statement to compute accruals, we define accruals as the difference between the earnings and the cash flow measure. Besides, Hribar and Collins (2002) argue that the balance sheet method can lead to errors in accrual estimation in some cases, for example, mergers. Datastream provides information on variables that we can use to compute the accrual component of income from operating activities. We use the net income before extraordinary items deflated by the average of total assets as a measure of the earnings,

10 10 net income before extr. items EAR = average of total assets The average of total assets is measured from total assets at the beginning and at the end of the fiscal year. The cash flow is defined as the net cash flow from operating activities deflated by the average of total assets. net cash flow from oper. activ. CFO = average of total assets The accrual component of earnings is given by, ACC = EAR CFO In the study of Sloan (1996), the holding period begins four months after the end of the fiscal year because, by this time, almost all firm reports are publicly available. Unlike Sloan, that uses holding periods varying from one to three years, we use a six-month (twelve-month) holding period, because we are interested in analysing the medium-term overreaction effect and not the subsequent correction effect. Our strategy uses the finding of Sloan that investors do not anticipate the lower persistence of the accrual component of earnings, and that they tend to overprice (underprice) stocks with a relatively high (low) accrual component. If this holds true then a trading strategy can be designed to profit from such stock mispricing. We propose a trading strategy based both on the price continuation effect and on the accrual effect. The price continuation effect is expected to be stronger for stocks with relatively low levels of accruals, because the cash flow component of earnings exhibits more persistence than the accrual component of earnings. Therefore, firms with high past returns and low accruals must continue to perform well in the future. Empirical evidence has shown a negative association between high accruals and negative future abnormal returns, so firms with the lower past returns and high accruals must continue to perform poorly in the future. We investigate whether the mispricings related to the momentum and accrual effects are distinct. If these effects are independent, then the momentum effect is expected to be stronger after removing the mispricing associated with accrual overestimation. A trading strategy that exploits both effects is expected to generate abnormal returns in excess of those based only on price continuation. Sloan found that sorting firms on the relative magnitude of the accrual component of earnings is equivalent to sort on the absolute magnitude of accruals, because accruals and cash flows are negatively correlated. Therefore, in our tests we use the absolute magnitude of accruals to rank firms. At the end of each month, individual firms are ranked according to the accrual component of earnings in prior year s reported accruals. We begin by ranking firms according to the cumulative monthly return on past six months, and stocks are grouped into ten decile portfolios according to their ranking. Decile 1 is designated the loser portfolio and decile 10 winner portfolio. Within the winner portfolio we consider only firms with the 20% lower accruals, and within the loser portfolio we consider only firms with the 20% higher accruals. A buy-andhold return is calculated for each stock over the holding period and the returns of the equally weighted decile portfolios are calculated. The return of the winner-loser portfolio is calculated for the holding period, and the trading strategy is replicated in the next periods. We calculate the mean return for the strategy as the average of all the replications. This section evaluates the profitability of a momentum strategy based on information on past returns and accruals in the formation period. Table VII presents the monthly mean return of the winner and loser portfolios. The winner (loser) portfolio earns 1.63 % (-0.04 %) per month. The portfolio constructed by buying the past winner and selling the past loser earns 1.67 % per month (t =10.4), which is statistically significant, and significantly higher than 0.98 % earned by the standard strategy, F = (P = 0.008). The strategy generates significant returns all the months, except for November, December and January. The higher returns occur in May and June, and this confirms the approach proposed in previous studies that use these months for portfolio formation, because they argue that by this time of the year all accounting reports are publicly known.

11 Alternative Momentum Strategies 11 Table VII Monthly returns of winner and loser portfolios Strategy based on past returns and accruals At the end of each month, we rank stocks into ten decile portfolios based on their return over the six-month formation period. Decile 1 is designated the loser portfolio and decile 10 winner portfolio. Within the winner portfolio we consider only firms with the 20% lower accruals, and within the loser portfolio we consider only firms with the 20% higher accruals. We use overlapping observations and each test period includes a six-month ranking period followed by a six-month holding period. The table reports the monthly returns of the winner, loser and winner-loser portfolios for the entire sample period. The table also reports the results specifying the month of portfolio formation. All Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Winner Loser Win-Los t statistic p A. Empirical findings after controlling for firm size and systematic risk We need to analyse whether the profitability of momentum strategy based both on past returns and accruals is driven by firm size or systematic risk. We use the model proposed by Collins and Hribar (2000), described above. For each firm in the sample, we measure expected monthly returns by estimating the regression of their returns on the returns of the portfolio decile that the firm is a member. Table VIII Size and risk adjusted monthly returns of winner and loser portfolios Strategy based on past returns and accruals At the end of each month, we rank stocks into ten decile portfolios based on their return over the six-month formation period. Within the winner portfolio we consider only firms with the 20% lower accruals, and within the loser portfolio we consider only firms with the 20% higher accruals. We use overlapping observations and each test period includes a six-month ranking period followed by a six-month holding period. The table reports the monthly returns of the winner, loser and winner-loser portfolios for the entire sample period, after controlling for firm size and systematic risk. The table also reports the results specifying the month of portfolio formation. All Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Winner Loser Win-Los t statistic P Table VIII reports abnormal return statistics for the winner, loser and winner-loser portfolios. The winner portfolio return is 0.05 % per month, while the loser portfolio return is 2.46 % per month. The portfolio constructed by buying the past winner and selling the past loser earns 2.51 % per month (t =14.6). It is important to emphasize that the performance of this strategy after controlling for firm size and systematic risk is also mainly due to the mean return on the loser portfolio, and this suggests short selling transaction costs as the likely explanation for the profitability of the strategy. If transaction costs were absent, investors would have learned how to profit from these statistical patterns in stock returns, and their trading would have corrected the stock mispricing. 7. CONCLUSIONS This section describes the main conclusions of our study. The study examines the average monthly returns of three trading strategies based either on past stock returns or on both past stock returns and accounting accruals. We begin by studying the standard momentum strategy proposed by Jegadeesh and Titman (1993), we analyse a momentum strategy that uses abnormal past returns to rank stocks in the formation period, and we propose a new strategy that uses both past stock returns and accounting accruals for portfolio formation. The empirical tests use data provided by Datastream on NYSE, AMEX and NASDAQ stocks.

12 12 We document that the average monthly returns of the standard momentum strategy for the period from 1990 to 2006 are very similar to those found by Jegadeesh and Titman (2001) for the period ending in Our findings contribute to the rejection of data mining as a source of the momentum effect. These results are even more relevant because we use data provided by Datastream in contrast with prior studies that use Compustat and CRSP data. The sample period includes the years between 2000 and 2003 of falling stock markets that we use to analyse the momentum profits when market returns are negative. We find that the returns on the loser and winner portfolios decreased, but that the returns on the winner-loser portfolio were not significantly different from the average returns on the total sample period. This paper also examines trading strategies that use both information on past returns and accruals to rank stocks in the formation period. If these variables transmit independent information about future returns not included in current stock prices, then the use of a combination of the two variables in portfolio formation should result in higher investment returns. The empirical tests show that this strategy generates a monthly mean return that is significantly higher than the mean return earned by the standard strategy. This clearly points to the accruals ability to reveal information on future stock returns not includes in past returns. In order to investigate whether the profits on the strategies are a compensation for risk we measure the mean returns after controlling for size and systematic risk. We find evidence that the mean returns of the winner-loser portfolio are even higher after controlling for risk factors. Another important finding is that the abnormal return for the strategy is mainly due to the return on the loser portfolio. This, in our opinion, is a major finding because it relates the momentum profitability with short selling. This finding points to a likely explanation for the momentum effect that attributes the abnormal return to short selling transaction costs. However, more work has to be done to test this potential explanation for the momentum and accrual anomalies based on short selling transaction costs. 8. REFERENCES Collins, Daniel W., Paul Hribar, (2000), Earnings-based and accrual-based market anomalies: one effect or two?, Journal of Accounting and Economics, vol. 29, nº1, pp Daniel, Kent, David Hirshleifer, and Avanidhar Subrahmanyam, (1998), Investor psychology and security market under- and overreactions, Journal of Finance, vol. 53, nº6, pp Fama, Eugene F., and Kenneth R. French, (2006), Dissecting anomalies, Working paper, George, Thomas J., and Chuan-Yang Hwang, (2004), The 52-week high and momentum investing, Journal of Finance, vol. 59, nº5, pp Griffin, John M., Xiuqing Ji, and J. Spencer Martin, (2003), Momentum investing and business cycle risk: evidence from pole to pole, Journal of Finance, vol. 58, nº6, pp Grundy, Bruce D., and J. Spencer Martin, (2001), Understanding the nature of the risks and the source of the rewards to momentum investing, Review of Financial Studies, vol. 14, nº1, pp Hong, Harrison, and Jeremy C. Stein, (1999), A unified theory of underreaction, momentum trading, and overreaction in asset markets, Journal of Finance, vol. 54, nº6, pp Hribar, Paul, and Daniel W. Collins, (2002), Errors in estimating accruals: implications for empirical research, Journal of Accounting Research, vol. 40, nº1, pp Huang, Dayong, (2006), Market states and international momentum strategies, Quarterly Review of Economics and Finance, vol. 46, nº3, pp Jegadeesh, Narasimhan, and Sheridan Titman, (1993), Returns to buying winners and selling losers: implications for stock market efficiency, Journal of Finance, vol. 48, nº1, pp Jegadeesh, Narasimhan, and Sheridan Titman, (2001), Profitability of momentum strategies: an evaluation of alternative explanations, Journal of Finance, vol. 56, nº2, pp

13 Alternative Momentum Strategies 13 Jones, Jennifer J., (1991), Earnings management during import relief investigations, Journal of Accounting Research, vol. 29, nº2, pp Korajczyk, Robert A., and Ronnie Sadka, (2004), Are momentum profits robust to trading costs?, Journal of Finance, vol. 59, nº3, pp Lesmond, David A., Michael J. Schill, Chunsheng Zhou, (2004), The illusory nature of momentum profits, Journal of Financial Economics, vol. 71, nº2, pp Rouwenhorst, K. Geert, (1998), International momentum strategies, Journal of Finance, vol. 53, nº1, pp Safieddine, Assem, and Ramana Sonti, (2007), Momentum and industry growth, Review of Financial Economics,vol. 16, nº2, pp Sloan, Richard G., (1996), Do stock prices fully reflect information in accruals and cash flows about future earnings, Accounting Review, vol. 71, nº3, pp