Trend-following Trading Strategies in U.S. Stocks: A Revisit. Andrew C. Szakmary* M. Carol Lancaster

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1 This article is forthcoming in The Financial Review. Trend-following Trading Strategies in U.S. Stocks: A Revisit Andrew C. Szakmary* University of Richmond M. Carol Lancaster University of Richmond Abstract We show that previous findings regarding the profitability of trend-following trading rules over intermediate horizons in futures markets also extend to individual U.S. stocks. Portfolios formed using technical indicators such as moving average or channel ratios, without employing cross-sectional rankings of any kind, tend to perform about as well as the more commonly examined momentum strategies. The profitability of these strategies appears significant, both statistically and economically, through 2007, but evidence of profitability vanishes after Market-state dependence, while clearly present, does not explain the post reduction in returns to these strategies. Keywords: trend-following; trading rules; momentum; stock market JEL classification: G11; G12; G14 * Corresponding Author: Robins School of Business, University of Richmond, Richmond, VA 23173; Phone: (804) ; fax: ; aszakmar@richmond.edu. We thank the editor, Robert A. Van Ness, two anonymous referees and meeting participants at the 2011 Eastern Finance Association conference for valuable comments and suggestions on earlier drafts of this paper. 0

2 1. Introduction A large number of studies, including Fama and Blume (1966), James (1968), and Jensen and Benington (1970), show simple trend-following trading strategies such as filter or dual moving average crossover rules generally fail to outperform buy-and-hold, even on a gross (before transactions costs) basis. 1 Although some later studies indicate that trend-following strategies outperform buy-and-hold on a gross basis, even these authors conclude that their strategies turn unprofitable in the presence of very modest transactions costs. For example, Sweeney (1988) argues that only floor traders would likely have been able to profitably use his 0.5% filter rule, and Corrado and Lee (1992) concede that one-way transactions costs of just 0.11% and 0.12%, respectively, would eliminate profits accruing to their 0.5% own-stock filter and 0.25% S&P 500 Index filter rules. Several recent studies of technical trading rules in individual stocks report even less promise in these strategies. For example, Szakmary, Davidson, and Schwarz (1999) show that own-stock filters or dual moving average crossover rules underperform buy-and-hold in Nasdaq stocks on a gross basis; and, Marshall, Young, and Rose (2006) report similar findings for candlestick strategies in Dow Jones Industrial Average stocks. 2 Based on the previous literature as a whole, it is fair to say that any evidence that trendfollowing technical trading rules can be used by investors to outperform buy-and-hold investing strategies in individual stocks appears underwhelming at best. 1 It is now generally accepted that other early studies that do report profitable trading strategies, e.g., Alexander (1961, 1964) and Levy (1967) suffer from various methodological problems (such as failure to include dividends, data-mining and the use of index data subject to non-synchronous trading) that render their conclusions suspect. 2 Many other well-known studies, e.g., Brock, Lakonishok, and LeBaron (1992), Sullivan, Timmermann, and White (1999), Moskowitz, Ooi, and Pedersen (2012), as well as many of the recent stock market studies discussed in the literature review by Park and Irwin (2007), examine the profitability of technical trading strategies in stock indices or futures and are therefore less directly relevant to our study, which focuses on individual stocks. 1

3 In contrast to these findings regarding pure trend-following rules, based on studies beginning with Jegadeesh and Titman (1993), there is overwhelming evidence that self-financing momentum strategies, which sort a large cross-section of stocks based on past returns, take long positions in stocks that have performed relatively well and short positions in those that have relatively poor past performance, earn very high returns. This divergence in findings regarding pure trend-following and momentum strategies in individual stocks is difficult to explain, and provides a key motivation for our study. Two recent studies examine trend-following strategies in a momentum framework in futures markets. Szakmary, Shen and Sharma (2010) examine pure trend-following and momentum trading strategies using the same long-term, monthly data set for 28 commodity futures. They show that all of these strategies produce weak evidence of abnormal returns in individual markets, but very powerful evidence of abnormal returns, both statistically and economically, when their results are aggregated across markets. In contrast to most previous studies, they show that the pure trend-following strategies they examine (e.g., dual moving average crossovers and channels) generally perform better than momentum strategies when evaluated in the same context. Moskowitz, Ooi and Pedersen (2012) evaluate a time-series momentum strategy that takes long (short) positions if excess returns relative to a risk-free asset are positive (negative) over some look-back period, for a broader array of futures markets that include equity indices, government bonds and currencies. They similarly find that the time-series momentum strategies perform at least as well as traditional cross-sectional momentum strategies. They further show that time-series momentum returns have small coefficients on standard risk factors, are highly correlated across asset classes and that noncommercial traders in futures 2

4 markets exploit time series momentum to earn trading profits at the expense of commercial traders. The main purpose of our study is to determine whether some of the major findings of Szakmary, Shen, and Sharma (2010), and Moskowitz, Ooi, and Pedersen (2012), also extend to individual U.S. stocks over the period. Using the entire CRSP database of NYSE, Amex and Nasdaq stocks, we show they largely do. Portfolios formed using technical indicators such as moving average ratios, channels or past returns relative to a risk-free asset, without employing cross-sectional rankings of any kind, tend to perform about as well on average as momentum portfolios formed using cross-sectional ranks when the results are evaluated in a context that is typical of momentum studies (i.e., formation and holding periods of 6-12 months). We show that when applying price and size screening common in the momentum literature, both momentum and pure trend-following strategies were profitable in gross terms prior to 2007 and that returns earned by these strategies were probably in excess of transactions costs as well. However, we find no evidence that any of the strategies we examine are profitable post-2007, and show that the market state dependence of these strategies, while similar to that shown by Cooper, Gutierrez, and Hameed (2004) for momentum, does not fully explain their decline in profitability. Jegadeesh and Titman (1993) were the first to report momentum profits in the U.S. stock market. Using a different methodological approach, Conrad and Kaul (1998) nevertheless report similar findings. Conrad and Kaul, as well as Grundy and Martin (2001) show that the momentum strategies work in all subperiods they examine, being consistently profitable in the U.S. stock market since the 1920 s. Similarly, Jegadeesh and Titman (2001) find that in the period (which was not included in their original 1993 paper) momentum strategies 3

5 continue to be profitable to about the same degree as earlier; that is, the best strategies earn abnormal returns of approximately 1% per month in gross terms. Whether these returns are sufficiently high to overcome the transactions costs associated with the strategies is not totally clear. Korajczyk and Sadka (2004) find that momentum profits arising from long positions are robust to direct transactions costs such as brokerage commissions and bid-ask spreads, but not necessarily to price-impact costs associated with large-scale trading. Further, Lesmond, Schill, and Zhou (2004) assert that momentum profits are likely illusory because the transactions costs associated with momentum stocks are unusually high. Nevertheless, compared to the results reported for pure trend-following trading rules in the literature, the profitability of momentum strategies appears much more promising. 3 One potential explanation for why momentum strategies have been found to be more promising is that momentum strategies have both a cross-sectional and a time-series component, whereas pure trend-following strategies have only the latter. Conrad and Kaul (1998) argue that cross-sectional variation in the mean returns of individual securities plays an important role in momentum strategy profitability. However, later findings cast substantial doubt on the Conrad and Kaul hypothesis. 4 Furthermore, Chen and Hong (2002) and Jegadeesh and Titman (2002) 3 Two further points regarding momentum findings are worth briefly noting. First, there is considerable debate in the literature whether risk factors can explain momentum profits. On the one hand, Fama and French (1996) concede that their three-factor asset pricing model does not explain returns to momentum portfolios; Grundy and Martin (2001) confirm that the momentum strategy s average profitability cannot be explained as a reward for bearing the dynamic exposure to the three factors of the Fama and French model, nor by exposure to industry factors. Chui, Titman, and Wei (2010) argue that the profits to momentum strategies are too large, persistent and pervasive to be explained as a reward for bearing risk, and instead show strong evidence that, across countries, momentum profits are related to cultural differences associated with investor overconfidence. However, numerous other studies, e.g., Chordia and Shivakumar (2002), Johnson (2002) and Gu and Huang (2010), argue momentum profits can be at least partially explained in a rational model. Second, momentum strategies are profitable in a variety of markets, e.g., European stocks (Rouwenhorst, 1998), international stock market indices (Chan, Hameed, and Tong, 2000) and commodity futures (Shen, Szakmary, and Sharma, 2007; Miffre and Rallis, 2007), where trading costs have historically been much lower than in the U.S. stock market. 4 If momentum profits were due primarily to cross-sectional differences in mean returns, then past winners (losers) should continue to be superior (inferior) performers indefinitely into the future, but Jegadeesh and Titman (2001) 4

6 formally break down momentum profits, and argue that the profitability of momentum strategies is mostly due to time series dependence in realized returns rather than cross-sectional variation in expected returns. Other reasons that findings could differ between tests of momentum and pure trendfollowing strategies are related to trading horizon and aggregation of results across securities/markets. Most tests of filter, dual moving average crossover, and other technical trading strategies have used daily data and focused on very short trading horizons, whereas momentum studies typically use monthly data and focus on intermediate horizons (3-12 months). If trend-following predictability in stock returns exists mostly at intermediate horizons, it is more likely to be found by studies that focus on monthly rather than daily returns. Many studies of technical trading rules report results on a security-by-security basis, whereas momentum studies focus only on aggregate results across portfolios of securities, thereby reducing the idiosyncratic variation in returns and increasing the statistical power of their tests. Unlike most previous studies of pure trend-following rules, Szakmary, Shen, and Sharma (2010) and Moskowitz, Ooi, and Pedersen (2012), use monthly data and focus on aggregate results across markets. Behavioral theories explaining momentum have sought to reconcile momentum and many other forms of intermediate horizon (3-12 month) underreaction such as post-earnings announcement drift, underreaction to announcements of dividend initiations and omissions, underreaction to announcements of seasoned issues of common stock and changes in analyst recommendations, etc. (see Daniel, Hirshleifer, and Subrahmanyam, 1998, Appendix A for a more complete list) with seeming longer term (3-5 year horizon) overreactions as shown by De Bondt and Thaler (1985), Chopra, Lakonishok, and Ritter (1992) and numerous other studies. find that momentum portfolio (winners minus losers) returns are positive only during the first twelve months of portfolio formation; if anything, momentum returns beyond this 12-month horizon are negative. 5

7 Daniel, Hirshleifer, and Subrahmanyam (1998) propose a theory based on investor overconfidence about the precision of private information, combined with biased self-attribution, that is consistent with these findings, and additionally predicts negative correlation between future momentum strategy returns and long-term past stock market performance. Another behavioral theory is that of Barberis, Shleifer, and Vishny (1998), who posit that conservatism (i.e., slowness to change beliefs in the face of new evidence) initially leads investors to underreact to new information while representativeness (Tversky and Kahneman, 1974) leads to eventual overreaction. Hong and Stein (1999) propose a model in which there are two types of traders, news watchers and momentum traders. Both intermediate horizon momentum and longterm reversals can be explained by interactions between these groups. Most crucially in the context of our study, as Jegadeesh and Titman (2001) note, all three of these behavioral theories predict that any intermediate horizon profits accrued by our trading strategies should partially reverse in the long run if positions are maintained beyond a 12-month horizon. 2. Data and research design 2.1. Data Our data are sourced from CRSP, and consist of daily and monthly observations on all stocks traded on the NYSE, Amex, and Nasdaq back to Data are reported through December 31, Because daily data prior to 1962 have only recently become available and most previous momentum studies use post-1962 data, the full period results reported in the paper are for January 1962 December Price and size screening Modern momentum studies typically screen out stocks with prices below $5 per share or those whose market capitalizations place them in the bottom 10% of NYSE stocks (see 6

8 Jegadeesh and Titman, 2001). We begin our study by downloading monthly return, stock price, and market capitalization data for all stocks in the monthly CRSP database. After deleting all stocks that did not have at least 12 consecutive months of return history and whose end-of-month prices never equaled or exceeded $5 per share, we were left with 22,489 stocks that remained as potential candidates for inclusion in our test portfolios. Most of these stocks do not trade for our entire January 1962 December 2013 sample period; furthermore, in computing returns to all test portfolios, as a rough equivalent of Jegadeesh and Titman s (2001) strategy of screening out the smallest 10% of stocks on the NYSE, at the end of each formation period we screen out all stocks in the bottom 20% of market capitalization across the NYSE, Amex and Nasdaq combined, and all stocks with prices under $5 per share. As will be detailed in Table 1, the average number of stocks available for inclusion in the various test portfolios over our entire sample period at any one time is 3, Formation and holding periods; calculation of holding period returns The formation period for all of our strategies is either 6 or 12 months in length and ends on the last trading day of each calendar month. The positions taken in each stock are determined from criteria applied to unit value (UV) indices. These UV indices are constructed from the monthly CRSP returns (including dividends), whereby the UV index is assigned a value of 1 for the month prior to the first monthly return reported in CRSP for a stock, and the UV index in each subsequent month equals UVt-1 x (1 + Rt), where Rt is the reported return in month t. Because the formation period UV indices are constructed from the monthly CRSP data, all of our trading strategies implicitly consider only end-of-month stock values for the purpose of generating trading signals. 7

9 The holding periods for portfolios formed using tested trading strategies are also 6 or 12 months long. However, the holding period returns are measured using a different data set constructed from the daily CRSP database. We download daily cumulative returns from CRSP for each of the 22,489 stocks that meet the initial criteria for inclusion in our study and add one to these figures to construct UV indices. We then sample the daily UV indices on the first trading day of each calendar month, and calculate 6 and 12-month holding period returns, respectively, as HPRt+6 = (UVt+6/UVt) -1 and HPRt+12 = (UVt+12/UVt) 1, where the time index t corresponds to the end of the previous calendar month, i.e., the end of the formation period. For example, if we wish to measure the 6-month holding period return on a stock selected based on criteria up to the last trading day of December 2006, we would calculate this as the UV index of the stock as of the first trading day of July 2007, divided by the UV index of the stock as of the first trading day of January 2007, minus one. 5 These procedures for calculating formation and holding period returns impose a one trading day lag between the generation of trading signals and the taking of positions based on the signals. We follow the procedures because we wish to avoid microstructure issues associated with bid-ask bounces, and because we believe it is unrealistic to assume that positions in stocks can be established instantaneously at the same closing prices that are used to generate the trading signals. 6 5 If a stock is delisted from CRSP during the holding period, we assume that the money invested in the stock earns the reported returns on the stock up to and including the delisting date, and the daily return on the CRSP valueweighted index after the delisting date, through the end of the scheduled holding period. We calculate a UV index based on these assumptions and measure the holding period return as described above. 6 Many previous momentum studies have estimated returns to strategies with even longer lags between the generation of trading signals and the taking of positions; for example, Jegadeesh and Titman (1993) used a oneweek lag, and Fama and French (1996), Korajczyk and Sadka (2004) and many other studies assume a 1-month lag, yet report similar findings. We use a 1-day lag to maximize the immediacy of information while still controlling for microstructure issues. 8

10 Although our holding periods are 6 and 12 months long, our data are monthly. To provide consistency with most previous momentum studies, we report monthly returns throughout our study (except in Table 6 where we compute net returns after likely transactions costs). We obtain the monthly return to a trading strategy by averaging the holding period returns across all stocks in the portfolio (i.e., we implicitly assume all portfolios are equally-weighted), then calculate the monthly return as MHPRt+i = (1 + Average HPR) 1/i 1, where i = 6 or 12 depending on the holding period length. Due to the overlapping nature of our reported results (i.e., holding period length exceeds frequency of observations) all of our standard errors and t-statistics are based on Newey and West (1987) consistent covariance matrices, with the number of lags set to equal 6 and 12, respectively, depending on the length of the holding period Trading strategies Momentum As in previous studies, all stocks as of the end of each calendar month that meet price and market capitalization screening criteria are ranked cross-sectionally based on their past returns. We evaluate returns to four specific parameterizations of the momentum strategy: 1) rank stocks based on 6-month formation period return, take long positions in the top 10% and short positions in the bottom 10%; 2) use a 6-month formation period but take long (short) position in the top (bottom) 30% based on past returns; 3) use a 12-month formation period and take long (short) positions in the top (bottom) 10%; and, 4) use a 12-month formation period and take long (short) positions in the top (bottom) 30%. While most previous momentum studies focus on top and bottom decile returns, some studies (e.g., Park, 2010) examine top/bottom 30% momentum strategies. The latter, holding three times as many stocks on average, could be more directly comparable in this respect to some of the alternative trend-following rules. 9

11 Channel Conceptually, channel strategies are similar to the filter rules used in many early studies. They have been applied in a variety of contexts, e.g., currencies (Taylor, 1994) and commodity futures (Lukac and Brorsen, 1990; Szakmary, Shen, and Sharma, 2010). In a channel strategy, a long position is taken in a stock if the latest end-of-month unit value exceeds the maximum of the end-of-month unit values over the previous L months multiplied by (1+X%), and a short position if the latest unit value is less than the minimum of the end-of month unit values over the previous L months multiplied by (1-X%). If the latest unit value is between these values, no position is taken. The four specific channel rules we investigate are 1) 6-month channel, no band, i.e., L = 6 and X = 0; 2) 6-month channel, 5% band, (L = 6 and X = 5); 3) 12-month channel, no band (L = 12 and X = 0); and, 4) 12-month channel, 5% band (L = 12 and X = 5) Dual moving average crossover Dual moving average crossover (DMAC) strategies have been investigated in currencies (Szakmary and Mathur 1997), commodity futures (Park and Irwin, 2005; Szakmary, Shen, and Sharma, 2010), stock indices (Brock, Lakonishok, and LeBaron, 1992; Sullivan, Timmerman, and White 1999), and, using a very different procedure from ours, by Park (2010) in individual stocks. In a DMAC strategy, a long position is taken in a stock if the short-term moving average unit value (STMA) exceeds the long-term moving average unit value (LTMA) by B percent, i.e., if STMA > LTMA*(1+B), and a short position is taken if STMA < LTMA*(1-B). No position is taken when STMA is within the band, i.e., when LTMA*(1-B) < STMA < LTMA*(1+B). Only month-end unit values are used in the above calculations. The four specific strategies we consider are 1) 6-month DMAC with 5% band (STMA=1, LTMA=6, B=0.05); 2) 6-month DMAC with 10% band (STMA=1, LTMA=6, B=0.10); 3) 12-month DMAC with 10% band 10

12 (STMA=1, LTMA=12, B=0.10); and, 4) 12-month DMAC with 20% band (STMA=1, LTMA=12, B=0.20) Time-series momentum The time-series momentum strategy developed by Moskowitz, Ooi, and Pedersen (2012) compares the formation period returns on each stock to the returns on a risk-free asset over the same time period. It then takes a long position in each stock that had a total return over the previous L months that is greater than or equal to the return on the risk-free asset, and a short position in each stock with an L-month return that is less than the risk-free return. We use the one-month T-bill returns reported by Ibbotson and Associates (2014) as a proxy for the return on the risk-free asset and evaluate two specific strategies: 1) L=6 months and 2) L=12 months Practical differences between momentum and other trend-following strategies By virtue of its cross-sectional rankings, the momentum strategy (as implemented in previous studies and described above) takes an approximately equal number of long and short positions in each calendar month. However, the other strategies we examine do not have this property. As criteria for inclusion in portfolios are generally absolute, the relative proportions of stocks that meet criteria for inclusion in long and short portfolios can vary greatly over time depending on stock market performance during the formation period. 7 Consider the 12-month DMAC strategy with a 20% band. Because the U.S. stock market in general performed poorly over a formation period extending from October 2001 September 2002, for a holding period beginning October 1, 2002, the strategy would have held long positions in only 147 stocks and 7 In this respect, our research design differs crucially from Park (2010), who ranks stocks based on a moving average ratio during some formation period and takes long and short positions, respectively, in the top and bottom 10% (or 30%) of stocks based on their moving average ratios. Thus, like the momentum strategy, Park s research design retains a cross-sectional aspect in the selection of stocks, whereas our trend-following rules do not. George and Hwang (2004), who examine future stock performance based on the nearness of a stock s price to its past 52-week high, also employ cross-sectional rankings based on this indicator. 11

13 short positions in 842. Conversely, for a holding period beginning September 1, 2003, the strategy would have held long positions in 1482 stocks and short positions in just 14 stocks. Throughout the paper, we assume long and short portfolios are equally-weighted; for long-short portfolios, we assume equal dollar amounts are invested in long positions and short positions in each calendar month. For example, for the holding period beginning September 1, 2003 for the DMAC strategy above, the long-short return we would report in the paper would be the average monthly return on the 1482 stocks held long minus the average monthly return on the 14 stocks with short positions Major Results As a substitute for a table of summary statistics, which we cannot feasibly provide given the number of stocks in the CRSP database, Table 1 shows buy-and-hold returns to portfolios which hold equally-weighted long positions each month in all stocks that meet our screening criteria, for our entire January 1962 December 2013 sample and five subperiods. The portfolio formation demarcation points between subperiods reflect the elimination of fixed commissions on the NYSE on May 1, 1975, the October 19, 1987 stock market crash, the completion of the switch to decimal pricing of stocks on the NASDAQ (the last major U.S. exchange to do so) on April 9, 2001, and July 2, We assume every stock meeting our previously stated screening criteria at the end of each calendar month t is purchased at the closing price on the first trading day of month t+1 and held for 6 months. Because stocks are held for 6 months but portfolios are formed monthly, our returns data are overlapping, and we use Newey and West (1987) standard 8 In those relatively few instances where a trading strategy picks no stocks to hold long (take short positions in), we assume a zero return on long (short) positions over the subsequent scheduled holding period. 9 Portfolios formed after July 2007 would have been affected by the great recession of and subsequent events. Additionally, an earlier version of this paper, and tests conducted by Szakmary, Shen, and Sharma (2010) who s trading rules most closely resemble ours, used data through December Thus our last subperiod can also be interpreted as an out-of-sample test of the profitability of most of the strategies examined. 12

14 errors (with 6 lags in this case) to calculate the reported t-statistics. We also provide the annualized Sharpe ratio, computed as: ann. Sharpe ratio = [1+mean(MHPR t+6 MRFR t+6 )] 12 1 NWSD 12, where MHPRt+6 is the monthly holding period return on an equally-weighted portfolio held for 6 months, MRFRt+6 is the monthly holding period return on 1 month T-bills over the same horizon, and NWSD is the Newey and West standard deviation of monthly excess returns, adjusted for 6 months of overlap. Finally, we provide the average number of stocks held, which reflects the total universe of stocks in the database that meet screening criteria in a typical month. < INSERT TABLE 1 HERE > Our results indicate that stocks meeting standard screening criteria earned a mean monthly return of 0.94% over our entire sample period. This compares to 0.88% per month on both the CRSP value-weighted index and on the S&P 500 index (as reported in Ibbotson and Associates, 2014) over a similar period. Our subperiod results show that stocks earned relatively low returns in the first period (portfolios formed prior to May 1, 1975), relatively high returns in the second period (portfolios formed May 1, 1975 through October 16, 1987), close to average returns in the third and fourth periods, and well below average returns since July Table 2 shows the returns to the trading strategies described in section 2, implemented with stocks meeting standard screening criteria for our full sample period. We report mean monthly returns on equally-weighted portfolios of stocks for which each strategy suggests a long position, similar mean monthly returns on short positions, and returns to a self-financing strategy (labeled L-S) in which an equal dollar amount of stocks is purchased and sold short one day after the end of each formation period. The t-statistics use Newey and West (1987) standard errors to account for the overlapping data. We report results for both 6 and 12-month holding periods. 13

15 < INSERT TABLE 2 HERE > Our results show that while some trading strategies perform better than others, all of the strategies perform well. In every case, for the 6-month holding periods, the mean return to a long position is greater (and the mean return to a short position is less) than the buy and hold return in Table For both 6 and 12-month holding periods, the returns to self-financing portfolios are significantly positive for every one of the trading strategies examined, even though we would expect these returns to equal zero if the trading strategies had no predictive power for future returns. We do not find marked differences in profitability between momentum and other, pure trend-following strategies. If we judge primarily based on the long short returns, the best performing momentum strategy appears to use a 6-month formation period and take long (short) positions in the top (bottom) 10% of stocks based on past returns. For 6-month holding periods, based on the mean return, this strategy is outperformed by two of the non-momentum strategies (12-month channel with 5% band, 12-month DMAC with 20% band); based on Sharpe ratios, an additional five pure trend-following strategies outperform it. For 12-month holding periods, the best momentum strategy is outperformed by four non-momentum strategies based on mean returns and nine based on Sharpe ratios. Looking at the average results across four momentum and ten other strategies, Table 2 shows the long-short returns are about equal, on average, for the momentum and other strategies for 6-month holding periods. For 12-month holding periods, the other strategies earn returns that are 0.19% per month higher; a formal statistical test that takes the overlapping observations into account reveals that this difference is significant at the 5% level (t-statistic = 2.36). For 6-month holding periods, the momentum rules on average appear to 10 Later, in Table 4, we report formal statistical tests of whether the returns to long positions equal buy-and-hold returns, and for the entire sample we find that this equality is rejected at the 1% level for every rule examined. We conducted (albeit do not report) statistical tests for the short positions and found similar results. 14

16 earn slightly higher returns on long positions, but the other strategies appear to pick stocks to short that earn somewhat lower future returns; however, none of these differences are statistically significant. For 12-month holding periods, long position returns are almost exactly equal between momentum and other strategies, but the other strategies pick stocks to short that earn significantly lower future returns at the 5% level (t-statistic = -2.10). Based on the full sample results, we find that pure trend-following strategies that avoid cross-sectional comparisons across stocks in taking positions appear to perform about as well as momentum strategies. 11 Because all strategies (at least before transactions costs) appear to perform best using 6-month holding periods, and because comparisons between momentum and other strategies are not markedly affected by the holding period, we focus on 6-month holding periods for the balance of the paper to conserve space. < INSERT TABLE 3 HERE > Table 3 shows results for long-short returns by subperiod for 6-month holding periods. The subperiod results are of interest for several reasons. First, as has been frequently pointed out in the literature, there is inevitably a large element of data-mining in any study of trading rules, so it is important to check whether the performance of the rules is consistent across various periods, particularly those that have not been examined in previous work. Second, several studies, e.g., Korajczyk and Sadka (2004), Lesmond, Schill, and Zhou (2004), have questioned whether momentum strategies are profitable after taking transactions costs into account. It is interesting to examine to what degree the momentum and other strategies remain profitable in the post-april 9, 2001 decimal pricing period when bid-ask spreads on U.S. stocks are much lower 11 The time series momentum strategies do earn lower returns than the other strategies. However, because they typically take positions in a much larger number of stocks, their t-statistics and Sharpe ratios are still high, and they compare well with the top/bottom 30% momentum strategies that also take relatively large numbers of positions. 15

17 than previously. Finally, Daniel and Moskowitz (2013) report that momentum strategies suffered a huge crash in profitability as the stock market recovered from the financial crash, further indicating that an examination of the post-2007 period is warranted. The most remarkable aspect of the results in Table 3 is the difference in the recent performance of all of the strategies versus what prevailed in earlier time periods. For the first three subperiods, extending through portfolios formed up to 4/6/2001, the mean long-short return for every strategy is consistently positive and statistically significant at the 1% level or better. During the fourth (4/9/2001-7/1/2007) subperiod, which follows the introduction of decimal pricing, but precedes the recession, mean returns are generally lower, but remain statistically significant for 11 of the 14 strategies examined. While the other strategies appear to hold up better than the momentum strategies during this period, the 0.35% difference in mean monthly return is not statistically significant (t-statistic = 1.24). The most striking result is the absence of any evidence of profitability for portfolios formed after 7/1/2007. The momentum and time-series momentum strategies actually earn negative mean returns during this most recent subperiod, and while the channel and DMAC strategies do have positive mean returns, they are nowhere near statistically significant. The difference in mean returns between the other strategies (0.17%) and the momentum strategies (-0.20%) is also not statistically significant (t-statistic = 0.81). In a later test, we will examine if the absence of post-2007 profitability can be explained by the market state-dependence of momentum strategies that has been shown by Cooper, Gutierrez, and Hameed (2004). < INSERT TABLE 4 HERE > In the presence of short-sale constraints, traditional self-financing strategies could be difficult for investors to implement. In Table 4, we report full sample and subperiod results for 16

18 long-only strategies, relative to a buy-and-hold strategy that takes long positions in all stocks meeting standard price and size screens. For the full sample, the difference between mean trading strategy and buy-and-hold return (TS-BH) is positive and statistically significant at the 1% level in every case, and there is no statistically significant difference in mean TS-BH return between momentum and other strategies (t-statistic = -1.64). The subperiod results for TS-BH long returns tell a similar story to the long-short returns reported in Table 3: during the first three subperiods, a large majority of the strategies experience significantly positive mean TS-BH returns. To a substantial extent, this profitability appears to continue during the 4/9/2001-7/1/2007 period, as all of the strategies earn positive mean TS-BH returns with 10 strategies exhibiting significantly positive returns. However, the diminishment in post-2007 profitability is once again striking, as 13 of the strategies earn negative (albeit not statistically significant) mean TS-BH returns during this final subperiod. 4. Additional Tests Because there is likely to be some overlap in the stocks selected by the various strategies, one question raised by the results in the previous section is the incremental contribution of each set of strategies (i.e., momentum, channel, dual moving average crossover, and time-series momentum) to overall profitability during our full sample period. To shed further light on this question, similar to George and Hwang (2004) and Park (2010), we implement a cross-sectional regression approach pioneered by Fama and MacBeth (1973). These results are reported in Table 5. < INSERT TABLE 5 HERE > We focus on four strategies, each of which are the best-performing strategies within their class (based on their Sharpe ratios) over the full sample: 6-month formation period momentum 17

19 top-bottom 10% (MOM), 12-month channel with 5% band (CH), 12-month DMAC with 20% band (DMAC), and 6-month formation period time series momentum (TSM). Panel A contains time series averages of cross-sectional regression coefficients and t-statistics (in parentheses). Following Park (2010), the basic functional form of the regression equation is: MHPRit+6 = b1t Rit + b2t ln(sizeit) + b3t MWit + b4t MLit + b5t CWit + b6t CLit + b7t DWit + b8t DLit + B9t TWit + b10t TLit + eit, where MHPRit+6 is the monthly holding period return on stock i for a subsequent 6-month holding period beginning on the first trading day after the end of month t, Rit is the return on stock i during month t, sizeit is the market capitalization of stock i at the end of month t, MWit is a dummy variable equaling 1 if stock i is identified as a winner according to the MOM strategy in month t and 0 otherwise, and MLit is a is a dummy variable equaling 1 if stock i is identified as a loser according to the MOM strategy in month t and 0 otherwise. The remaining independent variables are similarly defined dummy variables for the CH strategy (CWit and CLit), the DMAC strategy (DWit and DLit) and the TSM strategy (TWit and TLit). The model is estimated using dummy variables for each of the four trading strategies separately, and for all of the trading strategies combined. Unlike Park (2010), we do not include a constant term in the regressions to avoid perfect multicolinearity issues: as previously discussed, for some strategies, in some months, there could be no identified winner or loser stocks. Without a constant term, the estimated coefficients on ln(sizeit) partly proxy for historical mean stock returns and, therefore are difficult to interpret. We do not report these coefficients and those on Rit (which are almost uniformly insignificant) to conserve space. When the cross-sectional regressions are estimated for each trading strategy separately, the results for winner loser dummies in Table 5, Panel A are mostly consistent with the longshort returns reported for the same strategies in Table 2, although one notable difference is that 18

20 the t-statistics in Table 5 are lower. Nevertheless, the t-statistics appear to remain significantly positive for all but the Channel strategy, which is borderline significant at 5%. When the model is estimated for all four trading strategies combined, the only significant (negative) coefficient is the one on the DMAC loser dummy. The winner loser dummies for all four strategies in the combined regressions are positive on average but none are statistically significant at the 5% level the DMAC strategy, which is the best-performing of the strategies in Table 2 for 6-month holding periods, comes closest, with a t-statistic of The results do not provide a clearindication that any of the strategies is dominant. One reason for this could be provided by the results in Panel B of Table 5, wherein we report pairwise correlations across the winner and loser dummies between the various strategies. These correlations range between about 0.2 and 0.5, indicating that there is a moderate degree of overlap in the stocks selected by the four strategies. For both winner and loser dummies, the correlations appear to be higher with respect to the DMAC strategy than the other three. < INSERT TABLE 6 HERE > Another interesting question is whether the sizable pre-2007 gross returns reported for our long-short trading strategies in Table 2 were robust to likely transactions costs. Table 6 presents some evidence regarding this question for our third and fourth subperiods (portfolios formed 10/19/1987 4/6/2001 and 4/9/2001 7/1/2007, respectively). One measure of direct transactions costs used by Lesmond, Schill, and Zhou (2004) is the sum of the effective bid-ask spread and quoted commission, in percentage terms. The mean direct effective spread and mean quoted commission estimates, for the 10/19/1987 4/6/2001 period in Panel A of Table 6, which form the basis for the transactions costs estimates in Panel C for all strategies, are assumed to equal those provided for the Jegadeesh and Titman (2001) momentum strategy by Lesmond, 19

21 Schill and Zhou (2004, Table 2) for the period. Based on annual estimates of mean effective spreads for NYSE stocks computed from the TAQ data by Chung and Zhang (2014, Table 2), we assume spreads in the 4/9/2001 7/1/2007 period equal times those in the earlier period. The commissions assumed for the 4/9/2001 7/1/2007 period, given the ascendancy of online trading by this time, reflect an assumed average transaction size of $10,000 and a round-turn commission charge of $20 (which is typical of online discount brokerages). 12 In Panel B of Table 6, similar to Lesmond, Schill, and Zhou (2004, Table 1), we report likely transaction cost-related characteristics of stocks held by selected trading strategies (same trading strategies as in Table 5). These results show that the DMAC strategy picks stocks that are very similar in terms of median stock price and median market capitalization to a momentum strategy similar to one also examined by Lesmond, Schill, and Zhou (2004). There is, however, some indication that the channel strategy and particularly the time-series momentum strategy (especially for losers/short positions) tend to hold stocks that have higher prices and market capitalizations, and thus lower trading costs. We will assume that the stocks held by the various strategies have equal transactions costs, except for one adjustment. The position repeated row in Panel B reflects the percent of the time when a position in a stock taken 6 months earlier is carried over for the following 6 months. This does differ substantially across strategies. Because exploiting a long-short trading strategy requires both buying and selling stocks associated with long positions, and shorting and clearing stocks associated with short positions unless a position carries over (see Lesmond, Schill, and Zhou, 2004), for each strategy and subperiod, the estimated transaction costs in Panel C are calculated as: (mean effective direct spread, losers + mean quoted commission, losers) x (1 position repeated, losers) + (mean 12 For example, Charles Schwab, one of the largest discount brokerages, charges a flat $8.95 commission for online trades regardless of trade size. This cost would, of course, be incurred twice if a stock is bought and later sold. 20

22 effective direct spread, winners + mean quoted commission, winners) x (1 position repeated, winners). Unlike in earlier tables, both the gross and net returns in Panel C are total holding period returns over 6-month periods. The results in Panel C indicate that while transactions costs for all of the trading strategies are sizable, the strategies generally were still significantly profitable prior to 2007 net of assumed transactions costs. Despite very high trading costs, all of the strategies earned significantly positive mean net returns over the 10/19/1987 4/6/2001 period, and all but the momentum strategy continued to earn significantly positive mean net returns over the 4/9/2001 7/1/2007 period. These findings, however, should be interpreted with caution for two reasons. First, the four strategies examined in Table 6 are the best-performing strategies over the entire sample period, so data-mining could be a factor in our results. 13 Second, our transactions costs estimates, along with other estimates used in Lesmond, Schill, and Zhou (2004), do not factor in indirect effects such as price impact costs. Some alternative, indirect evidence of the robustness of pre-2007 returns to transactions costs can also be gleaned from the results of a more stringent stock screen. In an earlier version of this paper, we reported average returns to all of the trading rules when they are applied to a much smaller universe of stocks, wherein we screened out stocks with share prices less than $20 or whose market capitalization placed them in the bottom 80% of NYSE/AMEX/NASDAQ stocks as of the end of the formation period. These results, which are not reported in a table in this version to conserve space, show that the more stringent screen resulted in an average monthly return reduction across the long-short strategies examined of 0.38% over the This concern is mitigated somewhat by the fact that in the preceding 5/1/ /16/1987 period, the four strategies we examine were also the top performing ones in each class based on their Sharpe ratios, as indicated by the results in Table 3. 21

23 period, but mean returns remained highly significant when the strategies were implemented with these relatively low trading-cost stocks. One remaining question that begs examination is why the strategies cease to be profitable post One possible reason is that returns to momentum strategies have been shown to be market-state dependent (Cooper, Gutierrez, and Hameed, 2004) and, given the huge bear market of , the average market state differs in the post-2007 period from what prevailed prior to that time. As defined by Cooper, Gutierrez, and Hameed, the market-state is determined by the 36-month total return to the CRSP value-weighted index ending in the portfolio formation month. Within the context of our study, their regression model is as follows: MHPRj,t+6 = b1j UPMKTt + b2j DNMKTt + ejt, where MHPRj,t+6 denotes the monthly holding period return on trading strategy j for a subsequent 6-month holding period beginning on the first trading day after the end of month t, and UPMKTt (DNMKTt) are 0,1 dummy variables equaling one if the CRSP value-weighted index experienced a nonnegative (negative) cumulative total return over a 36-month period ending in month t. In previous work examining only momentum strategies, Cooper, Gutierrez, and Hameed show that the coefficient on UPMKTt is highly positive and significant, while the coefficient on DNMKTt is insignificant, indicating that momentum profits accrue only after UPMKT states. We note that for portfolio formation months between July 2007 and June 2013, based on this definition, the DNMKT state has prevailed 37.5% of the time (versus only 11.5% of the time prior to July 2007). < INSERT TABLE 7 HERE > Evidence regarding the sensitivity of returns on selected trading strategies to market states, and whether this sensitivity can explain the post-2007 profitability decline, is provided in Table 7. In Panel A, we estimate the model (Cooper, Gutierrez, and Hameed, 2004) for the four 22

24 trading strategies in Tables 5 and 6. These results confirm the findings of Cooper, Gutierrez, and Hameed, that momentum profits are highly state-dependent, and show that to a large degree they carry over to the pure trend-following trading strategies as well, as the coefficients on UPMKT are uniformly positive and significant, and the coefficients on DNMKT uniformly insignificant. These findings are supportive of the behavioral model of Daniel, Hirshleifer, and Subrahmanyam (1998), which predicts negative correlation between future momentum strategy returns and longterm past stock market performance. In Panel B of Table 7, we attempt to answer whether the drop in post-2007 profitability is statistically significant by regressing trading strategy returns on a constant and a POST2007 dummy, which is defined to be 1 if month t is July 2007 or later. We find that for all but the channel strategy, the null hypothesis that there is no difference in profitability can be rejected in favor of the alternative that profitability has declined, at the 5% level. Finally, in Panel C, we estimate a regression model that includes both market state and post-2007 dummies, i.e., MHPRj,t+6 = b1j UPMKTt + b2j DNMKTt + b3j POST2007t + ejt. Comparing these results to those in Panel B reveals that while accounting for market states does make the coefficients on the post-2007 dummy less negative, for two of the strategies (DMAC and time-series momentum) we still find that the coefficient on POST2007 is significantly negative while for the remaining two strategies the t-statistics on POST2007 are and Thus, we find that exposure to differing market states can explain only a small part of the post profitability decline. In an earlier version of this paper that used data through 2007, we conducted some additional tests related to long-term reversals and risk factors. While we do not report these results here to conserve space, some discussion is warranted insofar as these results provide evidence on the behavioral and risk-based theories discussed in the introduction. In the reversal 23