Momentum Loses Its Momentum: Implications for Market Efficiency

Transcription

1 Momentum Loses Its Momentum: Implications for Market Efficiency Debarati Bhattacharya, Raman Kumar, and Gokhan Sonaer ABSTRACT We evaluate the robustness of momentum returns in the US stock market over the period 1965 to We find that momentum profits have become insignificant since the late 1990s partially driven by pronounced increase in the volatility of momentum profits in the last 12 years. Past returns no longer explain the crosssectional variation in stock returns, not even following up markets. The patterns in the post holding period returns of momentum portfolios and risk adjusted identification period buy and hold returns of stocks in momentum supports improvement in market efficiency as a possible explanation for the declining momentum profits. Pamplin College of Business, Virginia Tech; Pamplin College of Business, Virginia Tech; and Palumbo-Donahue School of Business, Duquesne University; respectively. 0 Electronic copy available at:

2 Momentum in stock prices is one of the more persistent market anomalies. Jegadeesh and Titman (1993) were the first to document that a trading strategy that longs winner stocks and shorts loser stocks generates significant profits over a holding period of 3-12 months. They attribute the profits to delayed price reactions to firm-specific information, an indicator of market inefficiency. Subsequent literature labels such trading as the momentum strategy. Fama and French (1996) admit that their three-factor model cannot explain the continuation of short term returns of past winner and loser portfolios. Some advocates of market efficiency, however, suspected these observed regularities in returns arise because of data snooping. In a follow up study, Jegadeesh and Titman (2001) respond to such skepticisms by showing that momentum strategy continues to generate abnormal returns in the 1990s. They also interpret these findings from their out-of-sample tests as evidence that investors may not have learnt from the earlier return patterns. In a more recent working paper, Hwang and Rubesam (2008) build an inter-temporal model that explains momentum returns allowing for structural breaks over an extended sample period They document that momentum profits have slowly started declining in the last two decades of their sample period, a process that began in the early 90 s but delayed by the occurrence of high-technology stock bubble. Motivated by these findings, we examine the persistence of momentum profits in the more recent period. Using the data over the 1999 to 2010 sample period, we find that Jegadeesh and Titman (1993) momentum strategies fail to yield profits. This period is particularly interesting as it witnessed the dot-com bust after catching the 1 Electronic copy available at:

3 boom by its tail and also the financial crisis followed by the greatest stock market meltdown since the great depression. Some may argue that the recent turbulence in the economy with a series of high-loss episodes in the US stock market has rendered momentum strategy unprofitable. We counter this argument by showing that the rapid decline of momentum profits to insignificant levels in this 12-year period is not an outcome of a few unusual years. For instance, we use controls for the periods of unusual volatilities in the capital market, 2007 to 2009 in particular and yet fail to reject the hypothesis that momentum profits have not declined to insignificant levels. Excluding the last financial crisis, 2007 to 2009 serves the additional purpose of excluding spring of 2009 that witnessed the biggest momentum crash in the history of stock market since the summer of 1932 as alluded to by Daniel and Moskowitz (2011). We also investigate whether momentum profits resurface in this period following up markets as documented by Cooper, Gutirezz and Hameed (2004). Not only are these momentum profits insignificant on average following up markets, their distribution also reveal visible and statistical difference from those in the periods 1965 to 1989 and 1990 to 1998, indicating a deeper and more fundamental change in the underlying process of generation of momentum profits, beyond huge market crashes. The distribution of up market momentum profits in this period is extremely volatile interspersed with huge negative returns that suggest that momentum as a strategy has become riskier in the latest subperiod compared to the two earlier subperiods. We further examine whether cumulative past returns can explain the cross-sectional variation in stock returns. In the presence of return continuation, we expect past stock returns to be positively related to current stock returns, especially following up markets since momentum profits are 2 Electronic copy available at:

4 essentially up market phenomena. As expected in the periods 1965 to 1989 and 1990 to 1998, current stocks returns are positively related to past returns exclusively following up markets. However, in the current subperiod, with decline in momentum profits past returns fail to explain current returns following up markets and show a reliably negative relation following down market. We propose that the decline in momentum profits is a result of improved learning by investors and active trading strategies implemented by arbitrageurs of such profits, without making any distinction between information exploitation and information availability as explained by Friedman (1979). We predict such improvement in market efficiency conditions will result in intensified reaction to both winner and loser stocks in the identification period itself, which would result in either exhaustion or, at the least, a substantial reduction in return continuation in the holding period, and weakened return reversal (under the scenario of possible overreaction in the holding period perpetrated by behavioral biases) in the post holding period. Our predictions regarding improving market efficiency are supported by the evidence provided. Academic researchers have proposed possible rational and behavioral explanations for the source of momentum profits but even after a decade and half the debate is far from settled. Several authors, for example Conrad and Kaul (1998), Johnson (2002), and Chordia and Shivkumar (2002) propose risk-based explanations. They attribute momentum premium to crosssectional variation in expected returns, stochastic growth rates and time-variation of the sensitivities of the momentum strategies to various macroeconomic factors respectively. The 3

5 alternate view tries to explain the momentum premium using investors irrational behavior, overand under-reactions to new information in particular. Barberis, Shleifer, and Vishny (1998) and Daniel, Hirshleifer, and Subrahmanyam (1998) suggest that psychological biases in investors perceptions cause over- and under-reactions, which are responsible for momentum and long-term reversal. Hong and Stein (1999) introduce a model in which the slow diffusion of information creates short-term price under-reaction that allows momentum traders to profit. While Cooper, Gutirezz and Hameed (2004) support these findings, Zhang (2006) asserts that investors underreact more strongly to public information when there is more uncertainty. Brav and Heaton (2002) compare the behavioral theories of market anomalies that build on the irrationality of investors with the rational structural uncertainty theories of market anomalies that build on incomplete information, and suggest that their similar predictions make it empirically difficult to distinguish between them. Accordingly, our aim is not to distinguish between the behavioral and rational structural uncertainty explanations of the momentum profits, but to evaluate the persistence of momentum or lack thereof over nearly half a century, and to explore possible explanations for such a decline. We suggest two possible explanations for the declining momentum profits that both involve investor learning, and are not necessarily mutually exclusive. We begin the discussion of our explanations by defining three periods: (1) the identification (formation) period, during which the stocks are identified as winners and losers (2) the holding period during which the momentum traders long the past winners and short the past losers, and (3) the post-holding period during which we can examine the existence of reversals if any, to shed light on any possible overreaction as the cause of momentum profits in the holding 4

6 period. The first explanation proposes that momentum profits decline post 1998 because investors learn to value new information more accurately, specifically the information generated during the period the firms are identified as winners and losers (the identification or the formation period), thereby reducing mispricing in this period. The second explanation is that investors learn about the exploitable momentum profits and arbitrage them away. Both explanations predict intensified reaction to both winner and loser stocks in the identification period itself, which would result in either exhaustion or, at the least, a substantial reduction in return continuation in the holding period, and weakened return reversal (under the scenario of possible overreaction in the holding period perpetrated by behavioral biases) in the post holding period. We start our analyses by examining the monthly risk adjusted returns of the winner and loser portfolios over a 24-month post identification period (holding and post-holding periods). The post holding period returns show reversal in the pre-1999 period that is consistent with overreaction (Jegadeesh and Titman, 2001). Post 1998, neither the winner nor the loser portfolios earn returns that are reliably different from zero in the holding and the post-holding periods. We interpret the lack of return continuation and subsequent reversals in the holding and post-holding periods, respectively as evidence of improved market efficiency in the period 1999 to In addition, we employ a different buy and hold methodology for the new entrants to the winner and loser portfolios over the event time t - 5 to t + 24 months that allows us to test the empirical predictions of improved market efficiency better. Examination of the buy and hold 5

7 returns of the winner stocks in the identification period, months t - 5 to t, shows that in the post 1998 period they reach substantially higher levels on average spiraling at a much faster rate compared to the pre 1999 period, and they eventually flatten out in the holding and post holding periods, months t + 1 to t An implication of these results is that an investor looking to profit from buying past winners in the post identification period could find that it is too late for her. Similar pattern is exhibited by the returns of loser stocks. However, front running the traditional momentum traders on the short end can be more difficult to implement. This is consistent with existing literature that associates higher asymmetry of information, transaction costs and other limits to arbitrage with stocks in the lowest performance decile. It is important to interpret these findings in the light of at least one of the dimensions of the colossal transformation that the capital market has undergone since the late 1990s, the exponential growth in trading volume reaching a level in 2010 that is eight times that of Much of this growth in the trading volume has been ascribed to the unprecedented rise in a new breed of traders, the high frequency and algorithmic traders (Hendershott, Jones, and Menkveld (2010)). Some academics, for example Chordia, Huh, and Subrahmanyam (2007) have labeled these traders as gray zone traders who might be considered to be somewhere in between the informed and uninformed traders. We accredit intense competition among these sophisticated traders alongside hedge funds and such-likes as one of the possible causes of intensified reaction to winner and loser stocks in the identification period and weakened return continuation in the holding period. We conclude that these findings point in the general direction of improved market efficiency with respect to momentum trading and profits since the late 1990s. 6

8 The rest of the paper is organized as follows: Section I describes the data and methodology and examines the robustness of momentum returns or lack thereof in the 1999 to 2010 period, Section II presents the analysis of post holding period returns in an effort to assess the extent to which the disappearance of momentum profits is caused by learning and overall improvement in market efficiency, and Section III concludes the paper. I. Decline of momentum profits to insignificant levels since 1999 In this section we examine whether momentum strategies continue to be profitable since the late 1990s. Jegadeesh and Titman (2001) document that their out of-sample tests designed to assess persistence of momentum profits in the 1990s performed at least as well as the ones conducted with the original sample in their earlier study in It has been a while since money managers and traders at large have acceded to the claims that momentum strategies generate substantial profits, and we have concurrently seen a phenomenal growth in the size of funds in their hands. Hedge funds managed about $1.64 trillion in 2011 up from $ 200 billion in 1998 and equity mutual funds managed about $11.8 trillion in 2010 up from $5.5 trillion in These developments raise a fairly obvious question. Has momentum survived this new era of the capital markets? Our analyses span over the period between 1965 and For this part of our analyses we divide the entire time period into three subperiods. The first subperiod corresponds to the Jegadeesh and Titman (1993) sample period, 1965 to 1989, the second subperiod covers the Jegadeesh and Titman (2001) out of sample period, 1990 to 1998, and the third subperiod 7

9 corresponds to the period 1999 to Our tests reveal strong evidence of momentum profits in the first, less strong evidence in the second consistent with the literature, and decline in momentum profits to insignificant levels in the third subperiod. A. Holding period returns: Evidence from subperiods Our sample is constructed from all common stocks traded on New York Stock Exchange (NYSE), American Stock Exchange (AMEX), and Nasdaq. We obtain the data related to the stock market from the Center for Research in Security Prices (CRSP) database, and accounting data from Standard and Poor s (S&P s) Compustat. We exclude all stocks priced below $5 at the beginning of the holding period and all stocks with market capitalizations smaller than that of the lowest NYSE size decile following Jegadeesh and Titman (2001). Following Jegadeesh and Titman (1993), we examine the profitability of 16 strategies that select stocks based on the their returns over the past 3,6,9,and 12 (J) months and hold them for either 3,6,9,or 12 (K) months in each of our three subperiods. At the end of each month (t), we sort stocks into 10 equally weighted portfolios based on their cumulative returns earned in the past J months (t J + 1 to t). We hold these portfolios for K months (t + 1 to t + K). As a result we have K overlapping portfolios each of which is assigned an equal weight in the portfolio. We also construct a momentum strategy portfolio that buys the winner portfolio (top past return decile) and sells the loser portfolio (bottom past return decile). However, unlike Jegadeesh and Titman (1993) we compute the portfolio returns using data from the CRSP monthly returns file. 8

10 Table I presents the average monthly raw returns earned by the winner, loser and momentum (winner-loser) portfolios for all the 16 (J-month/K-month) strategies. Panels A, B, and C report returns and the corresponding p-values for the three subperiods as described above. Following Jegadeesh and Titman (2001) all our returns are calculated without skipping a month between the identification period and the holding period. [Table I around here] Table I reveals that over the periods 1965 to 1989 and 1990 to 1998, the returns for all the momentum strategies are positive and statistically significant confirming the results in Jegadeesh and Titman (1993) and Jegadeesh and Titman (2001). However, for the 1999 to 2010 period none of the 16 momentum strategies delivers any returns different from zero. Next, we compute the Fama-French three-factor alphas (Fama and French (1993)) earned by the winner, loser and momentum (winner-loser) portfolios for all the 16 (J-month/K-month) strategies. These alphas are reported in Table II. Panel A reports the alphas and the corresponding p-values for the period 1965 to 1989, panel B for the period 1990 to 1998, and panel C for the period 1999 to [Table II around here] The results of this analysis confirm the findings in Table I. Table II reveals that for all the 16 (J-month/K-month) strategies with a few exceptions the alphas of the loser portfolios are negative whereas the alphas of the winner portfolios are positive for the periods 1965 to

11 and 1990 to Momentum portfolios for all strategies earn statistically significant alphas for these two subperiods. In the period 1999 to 2010, none of the past return deciles earn alphas significantly different from zero and the alpha of momentum portfolio also disappears. Following Jegadeesh and Titman (1993) we now examine the six month formation/ six month holding strategy in more detail. 1 Table III presents the average monthly raw returns for the 10 past return portfolios. At the end of each month (t), we sort stocks into 10 equally weighted portfolios based on their cumulative returns earned in the past six months (t -5 to t). We hold these portfolios for the next six months (t +1 to t +6). This process presents us with six overlapping portfolios each of which is assigned an equal weight in the portfolio. We also construct a portfolio following momentum strategy that buys winner (top past return decile) and sells loser (bottom past return decile). [Table III around here] Table III shows that the average returns increase as we go from the lowest to the highest deciles for all the three subperiods. The momentum portfolio (P10-P1) on average earns a 1.1 % per month in the period 1965 to 1989 that continues in the period 1990 to Consistent with the findings of Jegadeesh and Titman (2001), the momentum portfolio in the second subperiod earns 1.37% a month. However, as noted earlier in Table I, the momentum returns decline to insignificant levels in the period 1999 to We repeat our tests in this section for all other strategies and this has no effect on inferences. 10

12 Table IV presents the alphas for the 10 past return portfolios. Past losers P1 earn negative alpha and past winners P10 earn positive alpha in the periods 1965 to 1989 and 1990 to The momentum portfolio (P10-P1) on average earns an alpha of 1.27% per month in the period 1965 to 1989 and 1.35% per month in the period 1990 to However, neither the past loser, or past winner or the momentum portfolios earn any alphas in the period 1999 to 2010 that are reliably different from zero. [Table IV around here] B. Seasonality and holding period returns In this subsection we examine whether the January effect on momentum profits reported by Jegadeesh and Titman (1993, 2001) have become pronounced in the period 1999 to 2010 so much so that the momentum profits in the non-january months are overshadowed. Table V presents average monthly returns earned by momentum portfolios in the January and non- January months. The momentum profits in January for our sample are no different from zero over the period The momentum profits for the non-january months are, however, positive and significant for the periods 1965 to 1989 and 1990 to 1988 but significantly in the period 1999 to The evidence indicates that there has not been any significant change in the absence of momentum profits in January for the period 1999 to 2010, and that combined with the declining momentum returns in non-january months explains the decline of momentum profits to insignificant levels for all months over this time period. [Table V around here] 11

13 C. Extreme volatility and holding period returns since 1999 The post 1998 period, during which we document significant decline in momentum profits, experienced stretches of extreme stock market volatility as it witnessed the dot -com bust after catching the boom by its tail and also the financial crisis followed by the greatest stock market meltdown since the great depressions. We acknowledge the necessity of controlling for these periods of unusual volatilities. Table VI presents the monthly average returns for 10 portfolios formed on the basis of the past 6 months cumulative returns and held for another 6 months, earned in six separate time periods post The first two columns report the returns for the periods 1999 to 2004, and 2005 to The year 2004, besides dividing the post 1998 period into two halves, also roughly separates the tech bust and the subsequent recovery period. The first two columns of the table reveal that the momentum portfolios (P10-P1) earn no profit in the first as well as the second half of our last subperiod. The third column reports the returns for the period 1999 to 2010 excluding the last financial crisis, 2007 to 2009, a period that also include spring of 2009, the biggest momentum crash in the history of stock market since the summer of 1932 as alluded to by Daniel and Moskowitz (2011). The fourth column reports the returns for the period 2004 to 2010, excluding the tech boom and bust, 1999 to 2003 as well as the last financial crisis. Both the columns do not reveal any resurfacing of momentum profits, and it is especially interesting to find no momentum in the period 2004 to 2010 (excluding 2007 to 2009) since the market showed an upward trend in these years, a condition favorable for generating momentum profit. 12

14 [Table VI around here] D. Market cycles and holding period returns Cooper, Gutirezz, and Hameed (2004) document that momentum profits are significant following up market conditions. In this section we examine whether momentum profits reappear once controlled for the up and down market cycles. Following Cooper, Gutierrez, and Hameed (2004), we classify the months following a phase of 36 months of positive (negative) value weighted CRSP index returns as up (down) markets. Table VII presents the monthly average returns for 10 portfolios formed on the basis of the past 6 months cumulative returns and held for another 6 months earned following up and down market conditions. The results indicate that momentum portfolios (P10-P1) earn significant profits following up markets but they earn no profits reliably different from zero following down markets in the periods 1965 to 1989 and 1990 to 1998 confirming earlier findings. The period 1990 to 1998 experienced no down market conditions and this can partially explain, the larger momentum profit in this period recorded above compared to the period 1965 to However, in the period 1999 to 2010, momentum portfolios do not earn any profit reliably different from zero, regardless of market conditions. Not only are these momentum profits insignificant on average following up markets, their distribution also turns out of to be visibly and statistically very different from those in the first and the second subperiods indicating a deeper and more fundamental change in the underlying process of generation of momentum profits, beyond huge market crashes. [Table VII around here] 13

15 [Figure 1 around here] Figure 1 plots and compares the distribution of monthly returns of momentum portfolios (winners-losers), following up-markets. The solid line represents a fitted normal distribution and the dashed line represents fitted kernel density, estimated with bandwidth parameter of Panel A plots the distributions of monthly returns of these momentum portfolios in the periods 1965 to 1989 and 1999 to 2010 and Panel B plots the same for the periods 1990 to 1998 and 1999 to Momentum profits in the last subperiod show larger dispersion as compared to the two previous subperiods that explains the lack of statistical significance of the average momentum returns following up markets in this subperiod. Momentum as a strategy seems to have become riskier in the most recent subperiod. Kolmogorov-Smirnov (K-S) and Kuiper two sample tests that are used to assess the uniformity of a set of distributions show that these distributions are significantly different from each other. Panel C plots the distributions of monthly returns of momentum portfolios following up markets in the periods and The distributions look similar indicating comparable riskiness of the momentum strategy in the first two subperiods. The K-S and Kuiper tests confirm that these two distributions are not significantly different from one another. E. Holding period returns for small firms, large firms, low liquidity, and high liquidity firms It is quite possible that momentum strategy continues to be profitable among smaller and lower liquidity stocks for the simple reason that they are more expensive to trade. To address this possibility, in this subsection we separately examine the momentum returns generated by small 14

16 and large stocks, and also by high and low liquidity stocks. Following Jegadeesh and Titman (2001), the Small Cap group (Large Cap) comprises of stocks that are smaller (larger) than the median NYSE stock by market capitalization at the beginning of the holding period. 2 Illiquidity is estimated as ratio of absolute one day return to dollar volume in that particular day, a measure proposed by Amihud (2002). Low (High) Liquidity stocks have higher (lower) average illiquidity than the median illiquidity stock in the month preceding the identification period (t - 6). We use the liquidity measure as of the sixth month before the holding period to make liquidity sorting process independent from the past return sorting process. [Table VIII around here] The results in Table VIII indicate that the momentum effect that was prevalent in all size and liquidity categories till 1998, decline uniformly across all these groups of stocks in the period 1999 to F. Cross-sectional variation in returns explained by past returns In the subsections above, we have provided evidence that momentum strategies no longer earn significant returns since 1999, and that these results are robust to various controls for seasonality, extreme volatilities and cycles in the capital market. However, financial market anomalies are patterns in security returns not only in time series but also in the cross-section that are not predicted by the central theory of asset pricing. We suspect that with declining return 2 We repeat our analysis with size subsamples formed on the basis of the market capitalization at the beginning of the identification period to make the size sorting process more independent from the past return sorting process and this has no effect on inferences. 15

17 continuation to relative strength portfolios, the past returns can no longer explain cross-sectional variation in stock returns. To investigate whether past returns explain stock returns in the cross section, we adopt the methodology employed by Fama and French (1992). We carry out Fama- MacBeth regressions of monthly returns of individual stocks on its past cumulative returns (t -12 to t -2) controlling for post ranking beta, size, asset -to-market equity and asset -to-book equity. The only accounting ratio used in the regressions is the natural logarithm of book-to-market ln(be/me). BE is the book value of common equity plus balance-sheet deferred taxes, and ME is the market equity. BE is obtained for each firm's latest fiscal year ending in calendar year t 1 and BE/ME is computed using market equity (ME) in December of year t - 1. However, firm size, the natural logarithm of market equity ln(me) is measured in June of year t. The explanatory variables for individual stocks are matched with CRSP returns for the months from July of year t to June of year t + 1. The gap between the accounting data and the returns ensures that the accounting data are available prior to the return. Following Fama and French (1996), the cumulative past returns for each stock, each month are computed by cumulating their returns from t -12 to t -2 months. Individual stocks are assigned post-ranking β of the size-β portfolio that they are in at the end of June of year t. We compute the post-ranking βs as in Fama and French (1992). Each June all NYSE stocks are sorted based on market equity to determine NYSE size decile cut -off points. Then, all NYSE, AMEX and NASDAQ stocks that have data both on CRSP and COMPUSTAT are assigned to these size deciles based on NYSE cut -off points. We sort stocks in each size decile, based on their pre-ranking βs. The pre-ranking βs are estimated using t - 24 to t - 60 monthly stock returns. The equal weighted average monthly returns of the 16

18 100 size-β portfolios are computed over 12 months following June of each year and the postranking βs for these 100 size-β portfolios are estimated for the full period. We use Fowler and Rorke (1983) correction in estimating the βs. [Table IX around here] Table IX presents the results of these Fama-MacBeth regressions. 3 These results clearly demonstrate that a positive relation between current and past stocks returns exists for the periods 1965 to 1989 and 1990 to 1998, but is no longer significant in the period 1990 to This confirms our postulate that as momentum returns decline to insignificant levels, past returns can no more explain cross-sectional variation in stock returns. The regressions also show that market β does not help explain average stock returns for the entire sample period confirming the results of Fama and French (1992). The small firm effect prevails through the first two subperiods, though relatively weaker in the post 1989 period. However, it is subsumed by the book-tomarket. The value stocks on the other hand continue to outperform growth stocks over the entire sample period. The results are consistent with the existing literature on widely known stock market anomalies. Momentum profits have been linked to market states in the literature. We earlier presented evidence that momentum profits are insignificant on average following 3-year up markets in the 1999 to 2010 period, in contrast to the two previous subperiods. Now, we examine 3 We also include natural logarithm of asset-to-market and asset-to-book ratios as explanatory variables in the regressions and this does not have bearing on our inferences. 17

19 whether past returns explain stock returns in the cross-section after controlling for market states. We carry out Fama-MacBeth regressions of monthly returns of individual stocks as in Table IX, splitting the subperiods into up and down market states this time. [Table X around here] Table X confirms all our previous findings. In the periods 1965 to 1989 and 1990 to 1998, past stocks return is positively related to current stocks returns exclusively following up markets. However, in the current subperiod, past returns fail to explain current returns following up markets and show a reliably negative relation following down market. So with decline in momentum profits, past returns do not show the expected positive relation with current stock returns. II. Possible explanations for the declining momentum profits since 1999 In this section, we discuss two possible explanations for the post 1998 decline in momentum profits. The first explanation proposes that momentum profits decline post 1998 as investors learn to value new information more accurately, specifically the information generated during the identification period, thereby reducing mispricing in this period. To the extent the momentum profits were a result of under-reaction to new information in the identification period, such learning would decrease the extent of under-reaction, thereby increasing (decreasing) the returns of the winners (losers) in the identification period, and decreasing the momentum profits in the holding period. Such improved learning would also reduce the extent of any delayed over- 18

20 reaction to the new information in the holding period, and thus we should not observe price reversals in the post holding period. The second explanation proposes that investors simply recognize that momentum strategy is profitable and trade in ways that arbitrage away such profits partially consistent with Schwert (2003) that documents two primary reasons for the disappearance of an anomaly in the behavior of asset prices, first, sample selection bias, and second, uncovering of anomaly by investors who trade in the assets to arbitrage it away. Competition amongst arbitrageurs to buy the winners and short the losers would induce them to try to identify the winners and losers earlier and earlier. Earlier identification and execution of the momentum strategy in the latter part of the identification period itself would reduce, and eventually eliminate the abnormal returns in the holding period. Moreover, the incentive and the competition amongst the arbitrageurs to unwind the long and short trades before any losses due to any possible over-reaction in the holding period would eventually eliminate any systematic over-reaction and subsequent reversals. Both the explanations predict intensified reaction to winner and loser stocks in the identification period itself, exhaustion or, at the least, a substantial reduction in return continuation in the holding period, and weakened return reversal (under possible overreaction in the holding period perpetrated by behavioral biases) in the post holding period. We are not able to distinguish between the two proposed explanations, because of the similarities in their empirical predictions. Instead, our empirical design aims at simply discerning 19

21 the role of improving market efficiency, a consequence of both of these explanations that build on investor learning in the decline of momentum profits of late. A. Post Holding Period Return Reversal for Winner and Loser Portfolios Table XI presents the risk adjusted returns and the corresponding statistical significance earned by the winner and loser portfolios constructed on the basis of the past six months returns over a 24-month post identification period. Figure 2 plots the monthly three-factor alphas reported in Table XI. In the pre 1999 period, the winners show a dramatic reversal of returns in the second year and the losers show substantial reduction in return continuation beyond the first year. The evidence is consistent with overreaction and subsequent price correction hypothesis. We interpret these results as evidence of market inefficiency, but we are cautious in not implicating investor irrationality as the cause. Following Friedman (1979), we argue that it is quite possible that a completely rational agent may not have complete knowledge of the fundamental structure of the economy that induces him to behave in a way that is indistinguishable from that of an irrational agent. Limits to arbitrage can explain the larger changes/faster decline of return continuation in the winner portfolios. The profit making opportunities from trading past losers will be eliminated more slowly than those from trading past winners, because of transaction costs, short sale restrictions and other trading constraints. [Table XI around here] [Figure 2 around here] 20

22 Post 1998, neither of the winner or the loser portfolios earn returns that are reliably different from zero in the post identification period. We interpret the lack of return continuation and subsequent reversal in the post identification period as evidence of improvement of market efficiency in the period 1999 to The markets could have become more efficient either because information gets impounded into prices faster in this period, or because investors learn about the profitability of momentum strategies, or both. As explained earlier, we do not distinguish between these two explanations. B. Identification Period Buy and Hold Returns for Winner and Loser Stocks Improving market efficiency predicts intensified market reaction to both past winner and loser stocks in the identification period, exhaustion or at the least a substantial reduction of profitable outcomes by either investing in past winner or divesting in past losers in the holding period, and weakened return reversal in the post holding period. To test these implications of improved market efficiency, we compute the buy and hold abnormal returns of new winner and loser stocks during the identification period and in the following 24 months. New winners (losers) are the stocks that enter the winner (loser) portfolio in month t. Abnormal return for each event month is the average of the mean abnormal returns of all stocks with monthly return data for 30 months, t - 5 to t + 24, across all calendar months. Buy and hold abnormal return is the difference between the cumulative raw return and cumulative expected return for each stock for each event month. The expected returns are computed using the loadings on Fama-French three factors over the five year period between t - 71 to t Stocks with less than 24 monthly 21

23 observations are excluded for the purpose of estimation of the three factor loadings. Figure 3 presents the plots of the buy and hold abnormal returns. [Figure 3 around here] The buy and hold returns for the winner stocks in the identification period, months t -5 to t show that in the post 1998 period they reach substantially higher levels on average spiraling at a much faster rate compared to the pre 1999 period and they eventually flatten out in the holding and post holding periods, months t + 1 to t As a consequence, an investor looking to profit from buying past winners in the post identification period could find it is too late for her. Very similar pattern is exhibited by the returns of loser stocks. However, front running the traditional momentum traders on the short end seems more difficult to implement. This is not a surprising finding in light of the existing literature that associates higher asymmetry of information, transaction costs and other limits to arbitrage with shorting of the stocks in the lowest performance decile. The evidence is consistent with improved market efficiency in the period 1999 to 2010, regardless of which of our two explanations of learning are at work. We still refrain from labeling momentum as a behavioral phenomenon, and its substantial decline a proof of improved investors rationality. It is however interesting to note that Brav and Heaton (2002) point out even if irrationality perpetrates financial anomalies, their disappearance hinges on rational learning, an ability of rational arbitrageurs to identify observed price patterns and wipe out any return potential in excess of risk based expectations. 22

24 III. Conclusion This paper evaluates the persistence of momentum or lack thereof over the last half a century. We document that trading strategies, which buy past winners and sell past losers, though remarkably profitable up until 1998, fail to generate significant abnormal returns in the period 1999 to These results are robust across extreme size and liquidity subsamples of stocks, periods of unusual volatilities in the capital market, seasonality, and up and down market conditions. We also document that past returns can no longer explain cross-sectional variation in stock returns in the post 1998 period. We suggest two possible explanations of learning, not necessarily mutually exclusive, for the declining momentum profits. The first explanation is that momentum profits decline post 1998 to insignificant levels as investors learn to value firms more accurately thereby reducing mispricing, and the second explanation is that investors learn about exploitable market anomalies and arbitrage the profits away. Specifically, we believe that the unprecedented growth in sophisticated traders such as hedge funds and the intense competition among them in the period 1999 to 2010 is one of the possible channels through which our second explanation has worked. Higher level of competition amongst traders to arbitrage the momentum profits and improvements in market efficiency predict intensified reaction to both past winner and loser stocks in the identification period, exhaustion or at the least a substantial reduction in return continuation in the holding period, and weakened return reversal in the post holding period. We indeed find that the buy and hold returns for the winner stocks, (and to a large extent, for the 23

25 loser stocks) in the identification period, months t - 5 to t in the post 1998 period reach substantially higher (lower) levels, on average, spiraling upward (downward) at a much faster rate compared to the pre 1999 period, and eventually flatten out in the holding and post holding periods, months t + 1 to t This evidence is consistent with improved market efficiency in the period 1999 to 2010, but it does not allow us to distinguish between the two proposed explanations of learning. 24

26 References Amihud, Yakov, 2002, Illiquidity and stock returns: Cross-section and time-series effects, Journal of Financial Markets 5, Barberis, Nicholas, Andrei Shleifer, and Robert Vishny, 1998, A model of investor sentiment, Journal of Financial Economics 49, Brav, Alon, and J.B. Heaton, 2002, Competing theories of financial anomalies, Review of Financial Studies 15, Chordia, T., and L. Shivakumar, 2002, Momentum, business cycle, and time-varying expected returns, The Journal of Finance 57, Chordia, Tarun, Sahn-Wook Huh, and Avanidhar Subrahmanyam, 2007, The cross-section of expected trading activity, Review of Financial Studies 20, Conrad, J, and G Kaul, 1998, An anatomy of trading strategies, Review of Financial Studies 11, Cooper, M. J., R. C. Gutierrez, and A. Hameed, 2004, Market states and momentum, The Journal of Finance 59, Daniel, K., D. Hirshleifer, and A. Subrahmanyam, 1998, Investor psychology and security market under- and overreactions, The Journal of Finance 53, Daniel, K., and Tobias J. Moskowitz, 2008, Momentum crashes, SSRN elibrary. Fama, Eugene F., and Kenneth R. French, 1992, The cross-section of expected stock returns, The Journal of Finance 47,

27 Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, Fama, Eugene F., and Kenneth R. FrencH, 1996, Multifactor explanations of asset pricing anomalies, The Journal of Finance 51, Fowler, David J., and C. Harvey Rorke, 1983, Risk measurement when shares are subject to infrequent trading : Comment, Journal of Financial Economics 12, Friedman, Benjamin M., 1979, Optimal expectations and the extreme information assumptions of rational expectations macromodels, Journal of Monetary Economics 5, Hendershott, Terrence, Charles M. Jones, and Albert J. Menkveld, 2011, Does algorithmic trading improve liquidity?, The Journal of Finance 66, Hong, H., and J. C. Stein, 1999, A unified theory of underreaction, momentum trading, and overreaction in asset markets, The Journal of Finance 54, Hwang, Soosung, and Alexandre Rubesam, 2008, The disappearance of momentum, SSRN elibrary. Jegadeesh, N., and S. Titman, 2001, Profitability of momentum strategies: An evaluation of alternative explanations, The Journal of Finance 56, Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and selling losers: Implications for stock market efficiency, The Journal of Finance 48, Johnson, T. C., 2002, Rational momentum effects, The Journal of Finance 57, Schwert, G. William, 2003, Chapter 15 anomalies and market efficiency, in M. Harris G.M. Constantinides, and R. M. Stulz, eds.: Handbook of the economics of finance (Elsevier). 26

28 Zhang, X. F., 2006, Information uncertainty and stock returns, The Journal of Finance 61,

29 Frequency (%) Frequency (%) Distribution of Winners-Losers Monthly Returns Figure 1 Comparison of Distribution of Momentum Portfolios Returns following Up Markets Panel A and This figure plots the distribution of monthly returns of winner- loser portfolios, constructed as described in Table IV following up-markets as defined in Table VII for the first and the most recent subperiods. The solid line represents a fitted normal distribution and the dashed line represents fitted kernel density, estimated with bandwidth parameter of

30 Frequency (%) Frequency (%) Distribution of Winners-Losers Monthly Returns Figure 1-Continued Comparison of Distribution of Momentum Portfolios Returns following Up Markets Panel B and This figure plots the distribution of monthly returns of winner - loser portfolios, constructed as described in Table IV following up-markets as defined in Table VII for the second and the most recent subperiods. The solid line represents a fitted normal distribution and the dashed line represents fitted kernel density, estimated with bandwidth parameter of

31 Frequency (%) Frequency (%) Distribution of Winners-Losers Monthly Returns Figure 1-Continued Comparison of Distribution of Momentum Portfolios Returns following Up Markets Panel C and This figure plots the distribution of monthly returns of winner - loser portfolios, constructed as described in Table IV following up-markets as defined in Table VII for the first and the second subperiods. The solid line represents a fitted normal distribution and the dashed line represents fitted kernel density, estimated with bandwidth parameter of

32 Risk Adjusted Returns Risk Adjusted Returns Winners to 6 7 to to to 24 Month Losers 1 to 6 7 to to to 24 Month Figure 2 Post Holding Period Three-Factor Alphas of Winner and Loser Portfolios The top panel of this figure plots the Fama-French three-factor alphas earned over various post holding periods by winner portfolios as described in Table III in the three subperiods (first and second subperiods combined and third subperiod). The bottom panel of this figure plots the Fama-French three-factor alphas earned over various post holding periods by loser portfolios as described in Table III in the three subperiods (first and second subperiods combined and third subperiod). 31

33 Buy and Hold Abnormal Returns Buy and Hold Abnormal Returns Winners Losers Event Month Event Month Figure 3 Buy and Hold Abnormal Returns of New Entrants to Winner and Loser Portfolios-Event Study This figure plots the abnormal buy and hold returns of new entrants to winner and loser portfolios (constructed as in Table IV) over t = - 5 to t = 24. Our initial sample includes all NYSE, AMEX and NASDAQ stocks priced above $5 at the beginning of the holding period and with market capitalizations above the cut -off level of lowest NYSE decile. New winners (losers) are the stocks that enter the winner (loser) portfolio in month t=0 and are not included in the winner (loser) portfolios in any of the months t = - 5 to t = - 1. Abnormal return for each event month is the average of the mean abnormal returns of all stocks with monthly return data for 30 months, t - 5 to t + 24, across all calendar months. Buy and hold abnormal return is the difference between the cumulative raw return and cumulative expected return for each stock for each event month. The expected returns are computed using the loadings on Fama-French three factors over the five year period between t = -71 to t = Stocks with less than 24 monthly observations are excluded for the purpose of estimation of the loadings on the three factors. 32

34 Table I Raw Returns of Relative Strength Portfolios This table presents the average monthly returns earned by winner, loser and momentum portfolios constructed with all NYSE, AMEX and NASDAQ stocks after excluding stocks priced below $5 at the beginning of the holding period and stocks with market capitalizations less than the cut -off level of lowest NYSE decile. At the end of each month (t = 0) stocks are sorted into 10 equally weighted portfolios based on their cumulative returns earned in the past J months (t - J + 1 to t) and held for K months (t +1 to t + K). Panels A, B, and C report the mean of monthly average returns and the corresponding p-values earned by the winner (highest past return decile), loser (lowest past return decile), and winner-loser portfolios that buy winner and sells loser portfolios formed on the basis of the past J months cumulative returns and held for another K months for the period , , and , respectively. All the portfolios are equal weighted. Panel A J K= Winners ( ) ( ) ( ) ( ) 3 Losers ( ) ( ) ( ) ( ) 3 Winners-Losers ( ) ( ) ( ) ( ) 6 Winners ( ) ( ) ( ) ( ) 6 Losers ( ) ( ) ( ) ( ) 6 Winners-Losers ( ) ( ) ( ) ( ) 9 Winners ( ) ( ) ( ) ( ) 9 Losers ( ) ( ) ( ) ( ) 9 Winners-Losers ( ) ( ) ( ) ( ) 12 Winners ( ) ( ) ( ) ( ) 12 Losers ( ) ( ) ( ) ( ) 12 Winners-Losers ( ) ( ) ( ) ( ) 33