Arbitrageurs identify and trade on

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1 Jieun Lee is an economist with the Financial and Monetary Studies Team, Economic Research Institute, Bank of Korea in Seoul, South Korea. Joseph P. Ogden is a professor of finance in the School of Management at SUNY-Buffalo in Buffalo, NY. joeogden@buffalo.edu Did the Profitability of Momentum and Reversal Strategies Decline with Arbitrage Costs After the Turn of the Millennium? Jieun Lee and Joseph P. Ogden Arbitrageurs identify and trade on mispriced securities, and their trades contribute to the eff i- ciency of security prices (Samuelson [1965], Fama [1970], Kyle [1985]). Arbitrage is costly, however, and these costs drive a wedge between actual market prices and efficient prices; i.e., pricing anomalies can exist even if all market participants are rational, though their size should be bounded by arbitrage costs (Fama [1991], Shleifer and Vishny [1997]). This article investigates the effect of arbitrage costs on the profitability of three well-known arbitrage strategies: momentum, long-term reversal, and short-term reversal. All three strategies involve the development of hedge portfolios based on past returns. The momentum strategy involves long and short positions, respectively, in stocks with the highest and lowest intermediate-term (three to twelve months) past returns; the long-term reversal strategy involves long and short positions, respectively, in stocks with lowest and highest long-term (three to five years) past returns; and the short-term reversal strategy involves long and short positions, respectively, in stocks with the lowest and highest one-month past returns. Jegadeesh and Titman [1993] were first to document evidence of the profitability of the momentum strategy, using data on NYSE and AMEX stocks for the years 1965 to In a follow-up study, Jegadeesh and Titman [2001] question whether (a) their original evidence could have been the result of data mining, or (b) investors learned from the earlier return patterns and thus arbitraged away momentum as a pricing anomaly. Instead, they find that momentum-strategy profitability in 1990 to 1998 is similar to that in the earlier period. Results from additional studies also attest to the robustness and persistence of momentum-strategy profitability (e.g., Figelman [2007]; Israel and Moskowitz [2013]). Fama and French [1996] find that the momentum strategy is profitable, as measured by both raw returns and abnormal returns generated using the Fama and French [1993] three-factor model. Furthermore, Lesmond et al. [2004] conduct cross-sectional tests of the relationship between momentum profit and transaction costs (estimated using the LOT model of Lesmond et al. [1999]), finding that profit increases with transaction costs and is negligible net of costs. (See also Korajczyk and Sadka [2004]; McLean [2010]; and Hong et al. [2000]). However, exceptions to the general profitability of the momentum strategy are noteworthy. In their original study, Jegadeesh and Titman [1993] also examine momentum-strategy returns over the years 1927 to 1940, a period marked by high stock-return IT IS ILLEGAL TO REPRODUCE THIS ARTICLE IN ANY FORMAT 70 Did the Profitability of Momentum and Reversal Strategies Decline with Arbitrage Costs? spring 2015 Copyright 2015

2 volatility and sharp market reversals. They find that the strategy performed very poorly during this period, and explain that this is because the strategy tends to select high- (low-) beta stocks following a market increase (decrease) and hence tends to perform poorly during market reversals. More recently, Chordia et al. [2014] examine momentum-strategy profitability using NYSE/ AMEX stocks, finding that momentum profits are significantly lower in the post-millennium period of 2001 to 2011 than in the pre-millennium period of 1976 to Consistent with our basic hypothesis (detailed subsequently), they argue that this reduction occurred because of the post-millennium reduction in arbitrage costs. However, their post-millennium period (as well as ours, 2001 to 2013) includes the period of the 2008 to 2009 financial crisis which, like the 1927 to 1940 period examined by Jegadeesh and Titman [1993], entailed high return volatility and a sharp market reversal. Thus, we will separately examine the effect of the financial crisis on momentum-strategy profitability. Our analysis of momentum strategy profitability also differs from that of Chordia et al. [2014] in terms of sample period, portfolio construction, and holding period, all defined later. We also examine cross-sectional effects. DeBondt and Thaler [1985, 1987] documented evidence of the profitability of the long-term reversal strategy. However, subsequent research on the reversal strategy has been limited, perhaps because Fama and French [1996] find that strategy profitability disappears in abnormal returns generated using the Fama-French [1993] three-factor model. However, further examination of the long-term reversal strategy is warranted because Fama and French [1996] use only NYSE stocks in their analysis, whereas the potential for mispricing may be greater for AMEX and NASDAQ stocks, which are often smaller and less liquid. Numerous studies (e.g., Jegadeesh [1990]; Lehmann [1990]; Lo and MacKinlay [1990]; Jegadeesh and Titman [1993]; Figelman [2007]; Novy-Marx [2012]; Chordia et al. [2014]) document evidence of a shortterm reversal effect for individual stocks. This effect has been attributed to the well-known, short-term bid-ask bounce phenomenon that induces negative first-order serial correlation in monthly returns. As such, strategy profitability should be directly related to arbitrage costs, both cross-sectionally and over time. Chordia et al. [2014] examine the profitability of this strategy using NYSE/AMEX stocks, finding that strategy profits are significantly lower in the postmillennium period of 2001 to 2011 than in the premillennium period of 1976 to Our analysis differs from Chordia et al. [2014] in terms of sample period and portfolio construction, defined later, and we also examine cross-sectional effects and the effect of the recent financial crisis on strategy profitability. The basic hypothesis we test is that the confluence of three major developments in the U.S. stock markets, all of which occurred around the turn of the millennium, substantially reduced arbitrage costs and therefore the profitability of momentum, long-term reversal, and short-term reversal strategies. First is the transition, completed in early 2001, from one-eighth minimum tick sizes to decimal minimum tick sizes. Chakravarty et al. [2005] find that the switch resulted in a general decline in trading costs. Second is the nearly simultaneous introduction of SEC Rule 605 (regarding execution quality) and various trading mechanisms, including the SuperSOES (Small Order Execution System) and SuperMontage trading platforms. These mechanisms have resulted in lower trading costs and increased trading volume, and thus an environment that better facilitates arbitrage (e.g., Chung and Chuwonganant [2009]; Chordia et al. [2011]). Third, and perhaps most important, is the postmillennium proliferation of hedge funds. Although the emergence of hedge funds is part of a long-term trend of increasing institutional ownership of stocks in the U.S., hedge funds, as arbitrageurs, differ qualitatively from other institutional investors such as pension funds and mutual funds. The reasons: (a) hedge fund managerial contracts are more heavily laden with profit incentives (Goetzmann et al. [2003]); (b) hedge funds face fewer restrictions on short-selling (e.g., Fung and Hsieh [2011]); and (c) hedge funds are better structured to overcome limits of arbitrage (Hombert and Thesmar [2014]). Dichev and Yu [2011] report that hedge funds aggregate assets under management (AUM) doubled from $179.5 billion in 1999 to $386.7 billion in 2003, and doubled again to $718.8 billion in Moreover, Fung and Hsieh [2011] report that as of December 2008, roughly 40% of 8,558 hedge funds pursued a long/short investment style. (See also Zhou et al. [2010].) However, the financial crisis of 2008 to 2009 may be a confounding factor for our analysis. In addition to the potential effect of the crisis on momentumstrategy profitability discussed above, (a) transaction Spring 2015 The Journal of Portfolio Management 71

3 costs generally increased substantially during the crisis, though they abated thereafter (see our evidence later and Anand et al. [2013]); and (b) numerous hedge funds disappeared during and immediately after the crisis (including many that pursued long/short strategies), though their numbers increased thereafter (see Cao et al. [2014]). We separately investigate the effect of the financial crisis by examining the statistical significance of the various strategies for rolling time windows surrounding the crisis. For our empirical analysis we use data on NYSE, AMEX, and NASDAQ stocks for the years 1990 to We initially examine transaction costs, estimated using the LOT model of Lesmond et al. [1999], discussed in the next section. As expected, we find that transaction costs are substantially lower, on average, in the postmillennium subperiod of 2001 to 2013 versus the premillennium subperiod of 1990 to 2000, though they rose substantially during the financial crisis. We then examine the profitability of momentum, long-term, and shortterm reversal strategies in the two subperiods. We find that the profitability of the momentum strategy, on both raw and risk-adjusted bases, is significantly and substantially lower in the post- versus pre-millennium period. We obtain similar but statistically weaker results for both reversal strategies. Cross-sectionally, for all strategies we find that strategy profitability increases with transaction costs. Results of our time-windows analysis suggest that the financial crisis was associated with a decrease (increase) in the profitability of the momentum strategy (long- and short-term reversal strategies). However, for strictly post-crisis windows, profitability for all three strategies is at best marginally significant, suggesting that effects of the post-millennium developments discussed above are permanent. The article is organized as follows. The next section describes our data and methodology. The following two sections present results of our analyses of transaction costs and strategy profitability, respectively. The final section concludes. DATA AND METHODOLOGY Our data universe consists of stocks traded on the NYSE, AMEX, and NASDAQ exchanges from 1985 through 2013, obtained from the Center for Research in Security Prices (CRSP) daily and monthly databases. We retain only stocks with CRSP share code values of 10 or 11 (ordinary common stock of U.S. firms). We begin in 1985 so that we can calculate returns on all strategies for holding periods ending in January 1990 through December 2013 (288 months). A stock is included in a given strategy portfolio only if (a) sufficient past monthly returns are available on CRSP (with no missing returns) to calculate a return for the portfolio formation period, and (b) the stock price at the end of the portfolio formation period is at least $5 (imposed in order to avoid possible distortions of extremely illiquid stocks). We estimate transaction costs using the model of Lesmond et al. (LOT) [1999]. The LOT model is related to the basic market model given in Equation (1): R i,t = α i + β i R M,t + ε i,t (1) where R i,t and R M,t are the returns on a stock and the market portfolio, respectively, β i is the stock s beta, ε i,t is the firm s firm-specific return component, and α i is the expected return on the stock given that R M,t = 0. In the absence of costs, arbitrageurs will ensure that the return on the stock reflects new information represented by β i R M,t + ε i,t. However, transaction costs inhibit the incorporation of new information into the stock price. The LOT model allows for such frictions, as shown in Equation (2): R i,t = R i,t * - α i1 R i,t = 0 R i,t = R i,t * - α i2 if R i,t * < α i1 if α i1 R i,t α i2 if R i,t * > α i2 (2) where R i,t * = β i R M,t + ε i,t, and α i1 0 and α i2 0 are transaction cost parameters. An implicit assumption in the model is that arbitrageurs trade only if the value of new information (R i,t *) exceeds the cost of trading. The LOT transaction cost measure is α i2 - α i1 ; i.e., LOT is a measure of round-trip overall transaction costs. Empirically, LOT estimates have been found to be highly correlated with other measures of transaction costs (e.g., Lesmond et al. [1999]; Goyenko et al. [2009]; Hasbrouck [2009]), and have been used in asset pricing studies focusing on the pricing of illiquidity (e.g., Liu [2006]; Asparouhova et al. [2010]; Lynch and Tan [2010]; Kapadia and Pu [2012]). For each stockmonth we estimate Equation (2) by applying limited dependent variable regression (Maddala [1983]) to daily returns on the stock and the CRSP equally weighted 72 Did the Profitability of Momentum and Reversal Strategies Decline with Arbitrage Costs? spring 2015

4 index (representing the market) over the previous year. We establish portfolio formation periods for momentum and long-term reversal strategies as follows. As noted earlier, a momentum strategy involves long and short positions, respectively, in stocks with the highest and lowest intermediate-term past returns, while the long-term reversal strategy involves long and short positions, respectively, in stocks with the lowest and highest long-term past returns. However, across various studies uniformity is generally lacking regarding the precise duration and timing of the intermediate-term and long-term past returns for the respective strategies. An exception is that, in testing momentum, researchers consistently skip the final month prior to portfolio formation (month 1) in the calculation of intermediate-term past returns, in order to avoid the short-term reversal effect (e.g., Fama and French [1996]; Jegadeesh and Titman [2001]). We follow this rule. However, the formation-period timing issue is also clearly important in terms of distinguishing between intermediate-term momentum effects and long-term reversal effects, given that the two strategies suggest opposing relationships between past returns and holding-period returns. For instance, Fama and French [1996] sort NYSE stocks into deciles alternatively by cumulative past returns in months 48 to 2 and months 60 to 13. For the 48,2 specification they find a positive relationship between past returns and one-month holding period returns, suggesting that momentum dominates, while for the 60,13 specification they find a negative relationship, consistent with long-term return reversal (see their table VI). We use the following approach to address the portfolio formation timing issue for momentum versus long-term reversal strategies. First, we adopt a six-month holding period for both momentum and reversal strategies. We do so because, as a practical matter, transaction costs (which rise with portfolio turnover) would be lower for a six-month holding period than a one-month holding period. (See Korajczyk and Sadka [2004], Lesmond et al. [2004], and Figelman [2007] for discussion and analysis.) Second, we conduct a preliminary analysis of the profitability of various momentum strategies. Stocks are sorted monthly into quintiles based on cumulative returns for months T through 2 prior to portfolio formation, where T, varying from 3 to 48, defines a distinct momentum strategy in terms of the duration of the portfolio formation period. Third, for each momentum strategy and month we calculate the return (over the six-month holding period) on a portfolio that is long (short) on an equally weighted portfolio of stocks in the highest (lowest) quintile of past returns, and then calculate the mean return on the strategy over the full sample period of 1990 to Fourth, we identify the momentum strategy, T*, that provides the highest mean holding-period return, and define our momentum strategy using past returns for months T* to 2. Fifth and finally, we define our long-term reversal strategy using past returns for months 48 to T* + 1. Results of this approach (not tabulated) lead us to use past returns from months 7 to 2 (48 to 8) for the momentum (long-term reversal) strategy. (We obtain a similar value of T* using the single-month past return, single-month holding period return approach of Figelman [2007] and Novy-Marx [2012], and results are not highly sensitive to a marginal change in T). For the short-term reversal strategy, stocks are sorted monthly into quintiles based on returns in month 1 prior to portfolio formation, and the strategy return is the onemonth holding period return on a portfolio that is long (short) on an equally weighted portfolio of stocks in the lowest (highest) quintile of past returns. We use a onemonth holding period for this strategy due to the shortterm nature of the purported effect, though we note that this strategy would entail substantial transaction costs. Because we will be examining both raw and abnormal (i.e., risk-adjusted) strategy returns, we require a pricing model that adjusts for risk. For this purpose we use the Fama-French [1993] three-factor model. (We obtain similar results, untabulated, using the capital asset pricing model of Sharpe [1964] and Lintner [1965].) Denoting as R S,t the raw return on strategy S, abnormal returns via the Fama-French model are calculated using the time-series regression shown in Equation (3): R S,t r f,t = α S + b S (R m,t r f,t ) + s S SMB t + h S HML t + e S,t, (3) where r f,t is the risk-free rate, (R m,t r f,t ) is the excess return on a proxy for the market portfolio, and SMB t and HML t are size (small minus big) and book-tomarket (high minus low) factors. The abnormal return on strategy S is α S. We obtain monthly values of the Fama-French factors from the Wharton Research Data Services (WRDS) database. Spring 2015 The Journal of Portfolio Management 73

5 ANALYSIS OF TRANSACTION COSTS In this section we analyze LOT estimates of transaction costs both cross-sectionally and over time. Cross-sectionally we expect transaction costs to be inversely related to firm size, and inter-temporally we expect transaction costs generally to be lower in the post-millennium period (2001 to 2013) versus the premillennium period (1990 to 2000), though we expect a substantial increase during the financial crisis of 2008 to Results are displayed graphically and in tabular form in Exhibits 1 and 2, respectively. For both exhibits we initially calculate the mean LOT estimate for the given month and stock sample and then calculate the average (or median) of the means over time. Stocks of small (large) firms are defined monthly as firms with market equity values below (above) the median for all firms. Exhibit 1 shows quarterly averages of LOT estimates for 1990 to 2013, calculated alternatively using all firms, small firms, and large firms. Cross-sectionally, results are as expected: average LOT estimates are consistently and substantially higher for small firms than for large firms. Inter-temporal results are also as expected: for all firms, small firms, and large firms, average LOT estimates are generally lower in the post-millennium period, with the notable exception of late 2008 to early 2009, corresponding to the peak of the financial crisis, when average LOT estimates increased substantially for all stocks. Exhibit 2, panel A shows average LOT estimates for the full sample and indicated subsamples. The grand average (i.e., using all stocks for 1990 to 2013) is 4.39%. Cross-sectionally, as expected, the average is significantly higher for small firms than large firms. For the full period, the averages are 5.50% and 3.34%, respectively, for a difference of 2.16% (t-statistic of 12.20). Inter-temporally, as expected average estimates are significantly lower in the post-millennium period. Using all stocks, the average fell by 1.13% (t-statistic of -5.83) to 3.87% in the post-millennium period from 5.00% in the pre-millennium period, a relative change of 22.60%. However, the post-millennium reduction was greater for small firms (relative change of 26.86%) than for large firms (relative change of 16.21%), indicating that the liquidity-enhancing effects of the turn-of-the- E x h i b i t 1 Quarterly Averages of LOT Estimates of Transaction Costs for NYSE, AMEX, and NASDAQ Stocks, Note: LOT transaction cost estimates are obtained monthly for individual stocks using the model of Lesmond, Ogden, and Trzcinka [1999]. Small (large) firms are firms with market equity values that are below (above) than the contemporaneous median of all NYSE, AMEX, and NASDAQ stocks. Quarterly averages of monthly means are shown. 74 Did the Profitability of Momentum and Reversal Strategies Decline with Arbitrage Costs? spring 2015

6 E x h i b i t 2 LOT Estimates of Transaction Costs for the Full Period and Pre- and Post-Millennium Subperiods Note: LOT transaction cost estimates are obtained monthly for individual stocks using the model of Lesmond, Ogden, and Trzcinka [1999]. Small (large) firms are firms with market equity values that are less (greater) than the contemporaneous median of all NYSE, AMEX, and NASDAQ stocks. For each firm group and sample period, mean values are calculated for each month and then the average (panel A) or median (panel B) of the monthly means is calculated. millennium developments discussed earlier were greater for small firms. This conclusion is also borne out with results shown in the final portion of panel A, which shows average LOT estimates for stocks sorted monthly into terciles by LOT estimates. The post-millennium relative reductions in LOT estimates are, respectively, 16.82%, 23.28%, and 23.70% for stocks in the low-, medium-, and high-tercile subsamples. The post-millennium reduction in transaction costs reflected in averages in panel A may understate the general reduction due to the temporary effect of the 2008 to 2009 financial crisis, as illustrated in Exhibit 1. In panel B we adjust for this temporary effect by calculating medians, rather than averages, of monthly means, and compare medians in the pre- and post-millennium subperiods. The results are indeed more impressive, as the percentage changes in medians are 28.57%, 33.39%, and 21.74% for all firms, small firms, and large firms, respectively, and are 23.83%, 26.73%, and 30.88% for low-, medium-, and high-tercile stocks, respectively. Spring 2015 The Journal of Portfolio Management 75

7 In summary, the results in Exhibits 1 and 2 are consistent with our cross-sectional and inter-temporal predictions about the behavior of transaction costs. Thus, we maintain our corresponding prediction that the profitability of the various momentum and reversal strategies would be lower after the turn of the millennium. Further, the results prompt us to add an ancillary prediction: the post-millennium reduction in strategy profitability should be greater for stocks with higher transaction costs, because these stocks experienced the largest average decrease in transaction costs after the turn of the millennium. However, because both the spike and subsequent reduction in transaction costs and the stock market reversal associated with the financial crisis may have affected the profitability of one or more of the tested arbitrage strategies, a separate analysis of profitability around the crisis is necessary. ANALYSES OF STRATEGY PROFITABILITY This section conducts analyses of the profitability of the momentum, long-term reversal, and short-term reversal strategies defined earlier. Exhibit 3, panels A, B, and C show initial results for the respective strategies, using all stocks for the full period as well as the pre- and post-millennium subperiods. Each panel shows mean E x h i b i t 3 Mean Holding-Period Raw Returns on Momentum and Reversal Strategies for the Full Period and Pre- and Post-Millennium Subperiods Note: In panels A, B, and C, NYSE, AMEX, and NASDAQ stocks are sorted monthly into equally weighted portfolios by quintiles of cumulative return in months 7 to 2, months 48 to 8, and month 1, respectively, prior to portfolio formation. In panels A and B (panel C), each portfolio is then held for six months (one month). Shown in each panel and for indicated sample periods are mean holding-period raw returns on each quintile portfolio. Panel A also shows the mean holding-period return on a momentum strategy that is long in the past-return winner, or quintile 5 portfolio, and short in the pastreturn loser, or quintile 1 portfolio, while panels B and C also show the mean holding-period raw return on long-term and short-term reversal strategies, respectively, that are long in the past-return loser, or quintile 1 portfolio, and short in the past-return winner, or quintile 5 portfolio. T-statistics are adjusted for overlapping observations. 76 Did the Profitability of Momentum and Reversal Strategies Decline with Arbitrage Costs? spring 2015

8 percent holding-period return on each of the individual quintile portfolios as well as on the strategy, which in panel A is the mean difference between holding-period returns on the quintile 5 (past winner) and quintile 1 (past loser) portfolios, and in panels B and C is the mean difference between holding-period returns on the quintile 1 (past loser) and quintile 5 (past winner) portfolios. Regarding momentum, for the full period mean holding-period returns increase monotonically with past returns, from 3.82% for quintile 1 to 8.48% for quintile 5. The difference, the mean holding-period return on the strategy, is 4.66% (t-statistic of 6.81). Thus, the momentum strategy is reliably profitable for the full sample period. Moreover, the results appear to be consistent with arguments by Fama [1991] and Shleifer and Vishny [1997] and Lesmond et al. [2004] evidence that momentum profit is negligible after transaction costs, as the mean strategy return, 4.66%, is very close to the average (median) value of LOT estimates for the full sample, 4.39% (4.50%), as shown in Exhibit 2, panel A (panel B). Results differ markedly, though, for the pre- versus post-millennium periods, as shown in the second and third columns of panel A, respectively. For the pre-millennium period, mean holding-period returns increase monotonically with past returns, and the mean strategy return, 8.10%, is large and highly significant (t-statistic of 8.49). In contrast, for the post-millennium sub period, mean holding-period returns increase monotonically with past returns only through quintile 4 and falter slightly for quintile 5. The mean strategy return is only 1.75% and is only marginally significant (t-statistic of 1.92). The change in mean strategy return, 6.35%, is highly significant (t-statistic of 4.81). These results are consistent with our basic prediction that momentum profitability would be lower after the turn of the millennium. However, we also note that the change in momentum-strategy profitability, 6.35%, is far larger than the post-millennium reduction in average (median) LOT estimates, 1.13% ( 1.36%), as shown in Exhibit 2, panel A (panel B). Thus, the results appear to be inconsistent with the argument that strategy profitability would be bounded by transaction costs. There are several possible explanations for this discrepancy. One possibility is that the post-millennium influx of hedge funds (as marginal investors) may have reduced effective transaction costs beyond that reflected in LOT estimates. Another possibility, which we investigate later, is that momentum-strategy profitability was dealt a severe blow during the financial crisis as stock market returns sharply reversed. Regarding the long-term reversal strategy, panel B shows that for the full sample period, mean holding-period returns decrease monotonically with past returns, from 8.02% for quintile 1 to 5.68% for quintile 5, as expected. The difference, the mean holdingperiod strategy return, is 2.33% and is highly significant (t-statistic of 5.12). Thus, the reversal strategy is reliably profitable for the full sample period. For the subperiods, the mean strategy return is lower in the post-millennium subperiod (1.90% with a t-statistic of 2.80) than in the pre-millennium subperiod (2.84% with a t-statistic of 4.86), qualitatively consistent with our hypothesis. However, the change, 0.94%, is insignificant (t-statistic of 1.04). Finally, for the short-term reversal strategy, panel C shows that for the full sample period, mean holdingperiod returns generally decrease (though not monotonically) with past returns, as expected. Mean strategy profitability is positive and highly significant for the full sample period (1.28% with a t-statistic of 4.68) as well as both the pre-millennium period (1.45% with a t-statistic of 3.01) and the post-millennium period (1.14% with a t-statistic of 3.83). The post- versus premillennium change in mean strategy profitability is negative, as expected, but is insignificant ( 0.31% with a t-statistic of 0.58). Thus, for both the long- and shortterm reversal strategies, results are weak with respect to our prediction that strategy profitability would fall in the post-millennium period. Later we investigate the possible inf luence of the financial crisis on the postmillennium performance of both of these strategies. Next we focus more closely on cross-sectional and inter-temporal variation in the profitability of the tested strategies. In the process we examine (a) strategy returns for subsamples of stocks sorted monthly into terciles by LOT estimates, and (b) both raw and abnormal returns. Results for the momentum, long-term reversal, and short-term reversal strategies are displayed in Exhibits 4, 5, and 6, respectively. Exhibit 4, panels A and B show mean raw and abnormal returns, respectively, on the momentum strategy for the full sample and indicated cross-sectional (rows) and inter-temporal (columns) subsamples. Spring 2015 The Journal of Portfolio Management 77

9 E x h i b i t 4 Mean Holding-Period Raw and Abnormal Returns on the Momentum Strategy by Transaction Cost Terciles and for Pre- and Post-Millennium Subperiods Note: Momentum-strategy portfolios are formed monthly, involve a long (short) position in an equally weighted portfolio of NYSE, AMEX, and NASDAQ stocks in the highest (lowest) quintile of cumulative return in months 7 to 2 prior to portfolio formation, and are held for six months. Panel A shows mean holding-period raw returns on the momentum strategy for indicated sample periods, calculated using either all NYSE, AMEX, and NASDAQ stocks or subsamples, defined monthly, involving only stocks in the low, medium, or high tercile of LOT estimates of transaction costs. Panel B shows corresponding mean holding-period abnormal returns calculated using the Fama-French [1993] three-factor model. T-statistics are adjusted for overlapping observations. Results in the first row of panel A are the same as those reported in Exhibit 3, panel A, and are repeated here for convenience. The second, third, and fourth rows show results for subsamples of stocks in the low, medium, and high terciles of LOT estimates of transaction costs, respectively. For the full period the mean raw strategy return is reliably positive for all three terciles and, as expected, increases monotonically with transaction costs, from 1.10% (t-statistic of 3.72) for the low tercile to 5.46% (t-statistic of 7.66) for the high tercile. The difference of mean raw strategy returns for the high- versus low-tercile subsamples is reliably positive (4.36% with a t-statistic of 6.98). However, the cross-sectional results are stronger for the pre-millennium subperiod. Specifically, while the mean raw strategy return is reliably positive for all three LOT terciles in the pre-millennium period, in the post-millennium period the mean is reliably positive only for the high-tercile subsample. In addition, the difference of mean raw strategy returns for the high- versus low-tercile subsamples is larger and more reliable in the pre-millennium period (7.47% with a t-statistic of 7.53) than in the post-millennium period (1.72% with a t-statistic of 2.36). These results occur because the post- versus pre-millennium change in mean raw strategy return increases in size with transaction costs. The changes are 1.81% (t-statistic of 3.13), 5.16% (t-statistic of 5.94), and 7.56% (t-statistic of 5.49) for the low, medium, and high transaction cost terciles, respectively. These results are consistent with our ancillary hypothesis that the post-millennium decrease in momentum-strategy return would be greater for stocks with high transaction costs because, as shown in Exhibit 2, transaction costs fell more after the turn of the millennium for high-cost stocks. Results for abnormal returns shown in panel B are similar to those in panel A. We note initially that mean abnormal momentum-strategy returns are positive for every subsample and period, and most are reliable, consistent with Fama and French s [1996] finding that momentum-strategy profitability is robust to risk adjustment via the Fama-French three-factor model. However, results are also consistent with our predictions, as mean abnormal returns (a) reliably increase with transaction costs, (b) are reliably lower after the turn of the millennium, and (c) decrease more, post-millennium, for high-cost stocks. Mean raw and abnormal returns on the long-term reversal strategy are shown in Exhibit 5, panels A and B, respectively. Results in the first row of panel A are the same as those reported in Exhibit 3, panel B, and are 78 Did the Profitability of Momentum and Reversal Strategies Decline with Arbitrage Costs? spring 2015

10 E x h i b i t 5 Mean Holding-Period Raw and Abnormal Returns on the Long-Term Reversal Strategy by Transaction Cost Terciles and for Pre- and Post- Millennium Subperiods Note: Long-term reversal strategy portfolios are formed monthly, involve a long (short) position in an equally weighted portfolio of NYSE, AMEX, and NASDAQ stocks in the lowest (highest) quintile of cumulative return in months 48 to 8 prior to portfolio formation, and are held for six months. Panel A shows mean holding-period raw returns on the long-term reversal strategy for indicated sample periods, calculated using either all NYSE, AMEX, and NASDAQ stocks or subsamples, defined monthly, involving only stocks in the low, medium, or high tercile of LOT estimates of transaction costs. Panel B shows corresponding mean holding-period abnormal returns calculated using the Fama and French [1993] three-factor model. T-statistics are adjusted for overlapping observations. repeated here for convenience. The second, third, and fourth rows show results for subsamples of firms in the low, medium, and high LOT terciles, respectively. For the full sample period, as expected, (a) the mean raw strategy return increases monotonically with transaction costs, though it is reliably positive only for the medium and high terciles, and (b) the difference of mean raw strategy returns for the high- versus low-tercile subsamples is reliably positive (3.93% with a t-statistic of 5.51). However, inter-temporal results are mixed. On one hand, the difference of mean raw strategy returns for the high- versus low-tercile subsamples is larger and more reliable in the pre-millennium period (6.45% with a t-statistic of 6.33) than in the post-millennium period (1.80% with a t-statistic of 1.86), as expected. On the other hand, while mean raw strategy return falls reliably after the turn of the millennium for high-cost tercile stocks, it actually increases reliably for low-cost tercile stocks. Regarding results for abnormal returns shown in panel B, note initially that for the full sample the mean abnormal strategy return is reliably positive (1.69% with a t-statistic of 4.45), inconsistent with Fama and French s [1996] f inding that longterm reversal strategy profitability disappears after adjusting for the Fama-French factors. However, for low-tercile stocks that may be more representative of the NYSE stocks analyzed by Fama and French [1996], the mean abnormal return is reliably negative, though small in size ( 0.39% with a t-statistic of 2.13), while the mean return is large and highly reliable for high-tercile stocks (2.77% with a t-statistic of 3.54). Inter-temporally, results using all stocks are consistent with our basic prediction because the post- versus pre-millennium change in the mean abnormal return, 4.99%, is large and reliable (t-statistic of 6.05), though this result appears to be driven primarily by high-tercile stocks, for which the corresponding change is 7.10% (t-statistic of 3.73). Mean raw and abnormal returns on the short-term reversal strategy are shown in Exhibit 6, panels A and B, respectively. Results for raw returns are generally consistent with our cross-sectional and inter-temporal predictions, because the mean raw return (a) increases monotonically with transaction costs for the full sample period as well as the pre- and post-millennium periods, and (b) falls post-millennium versus pre-millennium for all stocks, as well as for the low-, medium-, and hightercile subsamples. However, while the cross-sectional results are significant, the inter-temporal results are insignificant. The results for abnormal returns shown in panel B are very similar. Spring 2015 The Journal of Portfolio Management 79

11 E x h i b i t 6 Mean Holding-Period Raw and Abnormal Returns on the Short-Term Reversal Strategy by Transaction Cost Terciles and for Pre- and Post- Millennium Subperiods Note: Short-term reversal strategy portfolios are formed monthly, involve a long (short) position in an equally weighted portfolio of NYSE, AMEX, and NASDAQ stocks in the lowest (highest) quintile of cumulative return in month 1 prior to portfolio formation, and are held for one month. Panel A shows mean holding-period raw returns on the short-term reversal strategy for indicated sample periods, calculated using either all NYSE, AMEX, and NASDAQ stocks or subsamples, defined monthly, involving only stocks in the low, medium, or high tercile of LOT estimates of transaction costs. Panel B shows corresponding mean holding-period abnormal returns calculated using the Fama and French [1993] three-factor model. T-statistics are adjusted for overlapping observations. For our final analysis, we attempt to assess the effect of the 2008 to 2009 financial crisis on the profitability of each strategy. We do so by calculating t-statistics for mean raw and abnormal returns on each strategy for rolling three-year (36-month) windows running across the full sample period. Results are displayed in Exhibit 7, panels A and B for raw and abnormal returns, respectively. In each panel results for momentum, long-term reversal, and short-term reversal are labeled MOM, L.T. Rev., and S.T. Rev., respectively. Focusing initially on results for momentum (MOM) we find, as expected, that the t-values are generally higher in the pre- versus post-millennium period, occasionally exceeding 10.0 in the former. However, in the post-millennium period and prior to the onset of the financial crisis, t-values also consistently exceed 2.0, and sometimes exceed 6.0. The financial crisis, though, had a devastating effect on strategy profitability, indicated by negative t-values starting in mid-2009, which follow and ref lect the sharp market return reversal that occurred in early This evidence suggests that the post-millennium decrease in strategy profitability is due in part to temporary effects of the financial crisis. On the other hand, t-values for 36-month windows ending in any of the months of 2013 involve strategy returns that are realized well after the end of the financial crisis, and these t-values indicate only marginal significance (i.e., they fluctuate around 2.0). Thus, we tentatively conclude that the profit-reducing effects of the turnof-the-millennium developments discussed earlier are permanent. Results associated with abnormal returns on the momentum strategy, displayed in panel B, are similar, so for brevity we do not discuss them. Results for the long-term reversal strategy (L.T. Rev.) differ markedly and in several respects from those for momentum. First, with respect to both raw and abnormal returns, t-values indicate that this strategy is much less reliable than the momentum strategy, with negative t-values occurring in both the pre- and post-millennium periods. Second, t-values fall over the post-millennium, pre-crises period and then rise during and immediately after the crisis, suggesting some influence of the crisis. Nevertheless, we tentatively conclude that the profitreducing effects of the turn-of-the-millennium developments discussed earlier are permanent because, for both raw and abnormal returns, t-values do not exceed 2.0 for any 36-month window ending after January 2005, including those ending in Finally, we discuss results for the short-term reversal strategy (S.T. Rev.). T-values for this strategy are less volatile than for the momentum or long-term reversal 80 Did the Profitability of Momentum and Reversal Strategies Decline with Arbitrage Costs? spring 2015

12 E x h i b i t 7 T-statistics for Holding-Period Raw (Panel A) and Abnormal (Panel B) Returns on Momentum, Long-Term Reversal, and Short-Term Reversal Strategies Over Time Using Rolling 36-Month Windows Note: Panel A (Panel B) shows t-statistics for holding-period raw (abnormal) returns on previously defined momentum (MOM), long-term reversal (L.T. Rev.) and short-term reversal (S.T. Rev.) strategies for rolling 36-month windows ending in December 1992 through December strategies. For raw strategy returns (panel A), the t-values are consistently greater than 2.0 through December 1999 and fluctuate around 2.0 thereafter. T-values fall (rise) prior to (shortly after) the financial crisis, indicating that the crisis had some effect on strategy profitability. Nevertheless, we tentatively conclude that the profitreducing effects of the turn-of-the-millennium developments discussed earlier are permanent because none of the t-values are greater than 2.0 after April 2012, i.e., for windows that do not encompass the financial crisis. Similar results obtain using abnormal strategy returns, as shown in panel B. SUMMARY This article tests the hypothesis that a confluence of developments in the U.S. equity markets around the turn of the millennium, including the switch to decimal minimum tick sizes, the introduction of SEC Rule 605 and the SuperSOES and SuperMontage trading platforms, and the proliferation of hedge funds, would have reduced arbitrage costs and therefore the profitability of arbitrage strategies, including momentum, longterm reversal, and short-term reversal. Empirically, we examine transaction costs and strategy profitability Spring 2015 The Journal of Portfolio Management 81

13 using data on NYSE, AMEX, and NASDAQ stocks for the years 1990 to 2013, with foci on the pre- and post-millennium periods of 1990 to 2000 and 2001 to 2013, respectively, as well as the 2008 to 2009 financial crisis. Evidence is generally consistent with predictions, though effects of the financial crisis of 2008 to 2009 are also evident, especially for momentum. ENDNOTE The authors thank Kenneth Kim, Sahn-Wook Huh, Ajay Bhootra, Qing Ma, Kiyoung Park, colleagues at SUNY at Buffalo, the University of New Orleans, the Bank of Korea, session participants at the 2011 FMA conference, the 2012 Korean Economic Association conference, the 2013 Korean Money and Finance Conference, the 2013 World Finance Conference, and an anonymous Journal of Portfolio Management referee for valuable comments. REFERENCES Anand, A., P. Irvine, A. Puckett, and K. Venkataraman. Institutional Trading and Stock Resiliency: Evidence From the Financial Crisis. Journal of Financial Economics, 108 (2013), pp Asparouhova, E., H. Bessembinder, and I. Kalcheva. Liquidity Biases in Asset Pricing Tests. Journal of Financial Economics, 96 (2010), pp Cao, C., B. Liang, A. Lo., and L. Petrasek. Hedge Fund Holdings and Stock Market Efficiency. Working paper, May Chakravarty, S., V. Panchapagesan, and R Wood. Did Decimalization Hurt Institutional Investors? Journal of Financial Markets, 8 (2005), pp Chordia, T., R. Roll, and A. Subrahmanyam. Recent Trends in Trading Activity and Market Quality, Journal of Financial Economics, 101 (2011), pp Chordia, T., A. Subrahmanyam. and Q. Tong. Have Capital Market Anomalies Attenuated in the Recent Era of High Liquidity and Trading Activity? Journal of Accounting Economics, 58 (2014), pp Chung, K., and C. Chuwonganant. Transparency and Market Quality: Evidence from SuperMontage. Journal of Financial Intermediation, 18 (2009), pp Debondt, W., and R. Thaler. Does the Stock-Market Overreact? Journal of Finance, 40 (1985), pp Further Evidence of Investor Overreaction and Stock Market Seasonality. Journal of Finance, 42 (1987), pp Dichev, I., and G. Yu. Higher Risk, Lower Returns: What Hedge Fund Investors Really Earn. Journal of Financial Economics, 100 (2011), pp Fama, E. Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance, 25 (1970), pp Efficient Capital Markets: II. Journal of Finance, 46 (1991), pp Fama, E. and K. French. Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 33 (1993), pp Multifactor Explanations of Asset Pricing Anomalies. Journal of Finance, 51 (1996), pp Figelman, I. Stock Return Momentum and Reversal. The Journal of Portfolio Management, 34 (2007), pp Fung, W., and D.A. Hsieh. The Risk in Hedge Fund Strategies: Theory and Evidence from Long/Short Equity Hedge Funds. Journal of Empirical Finance, 18 (2011), pp Goetzmann, W., J. Ingersoll, Jr. and S. Ross. High Water Marks and Hedge Fund Management Contracts. Journal of Finance, 43 (2003), pp Goyenko, R., C. Holden, and C. Trzcinka. Do Liquidity Measures Measure Liquidity? Journal of Financial Economics, 92 (2009), pp Hasbrouck, J. Trading Costs and Returns for U.S. Equities: Estimating Effective Costs from Daily Data. Journal of Finance, 64 (2009), pp Hombert, J., and D. Thesmar. Overcoming Limits of Arbitrage: Theory and Evidence. Journal of Financial Economics, 111 (2014), pp Hong, H., T. Lim, and J. Stein. Bad News Travels Slowly: Size, Analyst Coverage, and the Profitability of Momentum Strategies. Journal of Finance, 55 (2000), pp Did the Profitability of Momentum and Reversal Strategies Decline with Arbitrage Costs? spring 2015

14 Israel, R., and T. Moskowitz. The Role of Shorting, Firm Size, and Time on Market Anomalies. Journal of Financial Economics, 108 (2013), pp Jegadeesh, N. Evidence of Predictable Behavior of Security Returns. Journal of Finance, 45 (1990), pp Jegadeesh, N., and S. Titman. Returns to Buying Winners and Selling Losers Implications for Stock-Market Efficiency, Journal of Finance, 48 (1993), pp Profitability of Momentum Strategies: An Evaluation of Alternative Explanations. Journal of Finance, 56 (2001), pp Kapadia, N., and X. Pu. Limited Arbitrage between Equity and Credit Markets. Journal of Financial Economics, 105, (2012), pp Korajczyk, R., and R. Sadka. Are Momentum Profits Robust to Trading Costs? Journal of Finance, 59 (2004), pp Kyle, A.S. Continuous Auctions and Insider Trading. Econometrica, 53 (1985), pp Lesmond, D., J. Ogden, and C. Trzcinka. A New Estimate of Transaction Costs. Review of Financial Studies, 12 (1999), p Lesmond, D., M. Schill, and C. Zhou. The Illusory Nature of Momentum Profits. Journal of Financial Economics, 71 (2004), pp Lintner, J. The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics, 47 (1965), pp Lynch, A., and S. Tan. Multiple Risky Assets, Transaction Costs, and Return Predictability: Allocation Rules and Implications for U.S. Investors. Journal of Financial and Quantitative Analysis, 45 (2010), pp Maddala, G. Limited Dependent and Qualitative Variables in Econometrics. Cambridge, U.K.: Cambridge University Press, McLean, R. Idiosyncratic Risk, Long-Term Reversal, and Momentum. Journal of Financial and Quantitative Analysis, 45 (2010), pp Novy-Marx, R. Is Momentum Really Momentum? Journal of Financial Economics, 103 (2012), pp Samuelson, P. Proof that Properly Anticipated Prices Fluctuate Randomly. Industrial Management Review, 6 (1965), pp Sharpe, W.F. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19 (1964), pp Shleifer, A., and R. Vishny. The Limits of Arbitrage. Journal of Finance, 52 (1997), pp Zhou, X., A. Litke, and M. McLaughlin. A Style-Based Market Risk Model for Hedge Fund Portfolios. The Journal of Portfolio Management, 36 (2010), pp To order reprints of this article, please contact Dewey Palmieri at dpalmieri@ iijournals.com or Liu, W. A Liquidity-Augmented Capital Asset Pricing Model. Journal of Financial Economics, 82 (2006), pp Spring 2015 The Journal of Portfolio Management 83