Alpha Momentum and Price Momentum*

Transcription

1 Alpha Momentum and Price Momentum* Hannah Lea Huehn 1 Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg Hendrik Scholz 2 Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg First Version: July 1, 2013 Current Version: September 15, Hannah Lea Hühn, Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg, Chair of Finance and Banking, Lange Gasse 20, Nürnberg, Germany, phone: , fax: , hannah.l.huehn@fau.de Hendrik Scholz, Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg, Chair of Finance and Banking, Lange Gasse 20, Nürnberg, Germany, phone: , fax: , hendrik.scholz@fau.de * We are grateful for helpful comments and suggestions from Bernhard Breloer, Bruno Arthur, Jean- Sebastien Michel, Martin Rohleder, Sheridan Titman, Marco Wilkens, Jeffrey Wurgler, Haoyo Xu, and the participants of the International Ph.D. Seminar 2013 in Augsburg, the 22 nd International Business Research Conference 2013 in Madrid, the Midwest Finance Association Conference 2014 in Orlando and the Southwest Finance Association Conference 2014 in Dallas and the 2014 Financial Management Association (FMA) European Conference in Maastricht.

2 Alpha Momentum and Price Momentum Abstract We analyze a novel alpha momentum strategy that invests monthly in stocks based on threefactor-alphas. Our ranking thus accounts only for this stock-specific component which we estimate using daily returns during a recent formation period. In contrast to the common price momentum strategy, factor-related return contributions have no impact on our ranking. Our empirical analysis for the U.S. and for Europe shows that i) past alphas have power in predicting the cross-section of individual stock returns, ii) alpha momentum exhibits less dynamic factor exposures within the investment period and is, therefore, less volatile and iii) alpha momentum dominates price momentum in the U.S. but not in Europe. Connecting both alpha momentum and price momentum to behavioral explanations, we find that underreaction to firm-specific news drives alpha momentum more strongly than price momentum and that momentum trading resulting in an overreaction drives price momentum more strongly than alpha momentum. In addition, we find both strategies to be sensitive to investor sentiment. Keywords: Alpha momentum; price momentum; stock-specific return; factor-related return; overshooting; slow information diffusion; reversal JEL Classification: G11, G12, G14 II

3 1. Introduction The price momentum effect is one of the most widely studied phenomena in financial research. Academic studies regularly analyze a common price momentum strategy, which was first documented by Jegadeesh and Titman (1993). They show that stocks with superior returns in recent months exhibit superior performance in subsequent months and vice versa. However, Grundy and Martin (2001) argue that the performance of price momentum depends strongly on realizations of the underlying factors driving stock returns. Based on monthly return data over the previous 60 months, Grundy and Martin (2001) implement a momentum strategy that ranks stocks on a stock-specific return component. To the best of our knowledge, there is no study analyzing a stock-specific momentum strategy estimated based on daily returns. Our paper contributes to the literature by comparing the common price momentum strategy and our (daily) alpha momentum strategy in the U.S. and in Europe. Moreover, we examine simultaneously the impact of past alpha and past return in asset pricing tests. Our results indicate that past alphas have power in predicting the cross-section of individual stock returns. Studying the profitability of both strategies in a portfolio context, we find alpha momentum to exhibit less dynamic three-factor exposures and, therefore, to be less volatile. Finally, we find that alpha momentum dominates price momentum in the U.S. Apart from academic research showing the profitability of price momentum, there are many studies trying to explain this phenomenon. In the last decade, researchers have turned their focus on behavioral explanations. Such models assume that price momentum is due to an underreaction to firm-specific news or an overreaction due to momentum trading. Among others, Barberis et al. (1998) and Hong and Stein (1999) show that investors tend to underreact to firm-specific news. Therefore, prices adjust slowly to this information and momentum can be identified. On the other hand, Hong and Stein (1999) also give evidence that stock prices can overreact due to so-called momentum traders pushing prices of past 1

4 winner stocks above, and of past loser stocks below, their fundamental value. Furthermore, Daniel et al. (1998) document that investors might become overconfident and drive stock prices away with a time lag from their fundamental value. These overshooting momentum profits are then reversed in the long run. Our paper contributes to the literature by connecting alpha momentum and price momentum to these behavioral explanations. When we look at the long-term performance of these strategies, we find that alpha momentum does not reverse as strongly as price momentum. Our findings indicate that price momentum could be predominately due to an overreaction to momentum trading and alpha momentum could be more strongly related to an underreaction to firm-specific news. Moreover, we find alpha momentum and price momentum to be sensitive to investor sentiment. Since Jegadeesh and Titman (1993) have documented the price momentum effect in the U.S., various studies analyzing the profitability of price momentum strategies in different countries and asset classes have been published. Among others, Rouwenhorst (1998), Fama and French (2012) and Asness et al. (2013) find evidence of stock momentum in countries worldwide. Moreover, Asness et al. (1997), Chan et al. (2000) and Bhojraj and Swaminathan (2006) show that momentum strategies based on country indices earn significant abnormal returns. Additionally, Moskowitz and Grinblatt (1999), Swinkels (2002), Scowcroft and Sefton (2005) and Chen et al. (2012) report the profitability of momentum strategies based on sector indices in different countries worldwide. Shleifer and Summers (1990) and Menkhoff et al. (2012) find evidence of momentum in currencies, Erb and Harvey (2006) and Gorton et al. (2008) in commodities. Asness et al. (2013) detect momentum, among other things, in global bond futures and Jostova et al. (2013) in corporate bonds. However, Blitz et al. (2011) show that momentum profits vanished in the U.S. after the stock market collapsed in In addition, Daniel and Moskowitz (2014) detect that price momentum strategies perform poorly after market declines and when market volatility is high. Their study is in line with Grundy and Martin (2001), who argue that price momentum 2

5 strategies depend strongly on the performance of the underlying factor realizations driving stock returns. Accordingly, momentum strategies only perform well if factor realizations persist and are often quite volatile. To diminish the impact of these factors, Grundy and Martin (2001) implement a momentum strategy which does not rank stocks on raw returns but on stock-specific components. Using 60 months of return data, they estimate a modified Fama and French (1993) alpha for a six-month formation period applying a dummy variable approach. The strategy buys stocks with high dummy alphas and sells stocks with low dummy alphas. They find this strategy to be less volatile than common price momentum strategies. Stock-specific momentum strategies have also been examined by Gutierrez and Prinsky (2007), Blitz et al. (2011) and Chaves (2012). In contrast to Grundy and Martin (2001), these studies do not rank stocks based on dummy alphas but on monthly residual returns. Similar, Da et al. (2014) implement short-term reversal strategies that are corrected for Fama and French (1993) factors and cash-flow news. In summary, these studies analyzing stock-specific momentum (reversal) strategies apply three to five years of monthly return data to run Fama and French (1993) regressions. Then, only the last (six) twelve monthly returns of the formation period are used to calculate the respective stock-specific component using the coefficients which are estimated over three to five years. In our empirical analysis, we follow Grundy and Martin (2001) and implement a momentum strategy by ranking stocks on their stock-specific component during the formation period. Nevertheless, in contrast to Grundy and Martin (2001) we estimate alpha by considering daily stock returns only during the formation period. Thus, we run Fama and French (1993) regressions based on a clearly higher number of return observations and estimate all regression parameters solely based on the recent formation period. Doing so, possible variations in the factor exposure of stocks before and within the formation period do not impact our results. Finally, we do not need to restrict our sample to stocks with at least 36 months of return history and therefore can include recently issued stocks into our empirical analysis. 3

6 We start our empirical analysis by implementing asset pricing tests to examine the relation of past alphas and past returns with individual future stock returns. Our results indicate that past alphas have power in predicting the cross-section returns in the U.S. and in Europe. Based on these results, we build zero-investment portfolios that buy recent winner and sell loser stocks according to past alpha or past return. We then analyze the performance of these alpha momentum and price momentum strategies and find alpha momentum to outperform price momentum in the U.S. and to be clearly less volatile in Europe. Furthermore, the difference between both strategies can be attributed to time-dependent differences in the overlap between stocks in the zero-investment portfolios of our alpha momentum strategy and the common price momentum strategy. Our results reveal that this overlap decreases when factor-related return contributions have a relatively high impact on stock returns during the ranking period. The alpha momentum strategy exhibits less dynamic factor exposure within the investment period and is, therefore, less volatile. Finally, we find alpha momentum to dominate price momentum in the U.S. but that there is no such clear dominance in Europe. Looking at the long-term profitability of alpha momentum and price momentum, our findings support behavioral explanations which assume that the momentum effect is caused by an underreaction to new information and by an overreaction due to momentum trading. We find evidence for both of these explanations in our empirical analysis. However, the impact of both effects is different for alpha momentum and price momentum. First, when we look at a momentum strategy using only a subset of stocks that are in the winner or loser decile according to their past alpha, but not according to their past returns, we see that the performance of this strategy reverses moderately in the U.S. while it constantly increases in Europe over 60 months. Thus we assume that this pattern could be predominantly due to an underreaction to firm-specific news. Second, the performance of a momentum strategy using a subset of stocks that are in the winner or loser decile based on their past return, but not on their past alpha, reverses strongly after a few months. Thus, this effect could be more strongly driven by an overshooting of these stocks due to momentum trading and a subsequent 4

7 reversal. Finally, a strategy that buys stocks that are in the winner or loser deciles of both strategies outperforms in the first months but reverses in the long-run. This effect could be due to an underreaction to firm-specific news in combination with an overreaction due to momentum trading. Finally, focusing on behavioral explanations of the momentum effect, we find both alpha momentum and price momentum to be sensitive to investor sentiment. Both strategies yield the highest risk-adjusted returns in periods of optimistic sentiment in the U.S. as well as in Europe. Our study proceeds as follows. Section 2 provides the methodology for constructing the alpha momentum as well as the common price momentum strategy and presents the applied performance evaluation models. Section 3 describes our database and documents main results of our empirical analysis. Section 4 connects alpha momentum and price momentum to behavioral explanations of the momentum effect. Section 5 concludes. 2. Portfolio construction and performance evaluation In our empirical analysis we focus on the following momentum strategies: common price momentum according to Jegadeesh and Titman (1993) and our (daily) alpha momentum strategy. To begin with, we describe the construction of these strategies and main differences between them. A common price momentum strategy sorts stocks into deciles based on their past cumulative raw returns (henceforth past returns) typically determined using monthly returns during a J-month formation period and is which denote the raw return of stock i in formation month : (1+ ) (1) The common price momentum strategy consists of a zero-investment portfolios that buys stocks with the highest and sells stocks with the lowest past returns over the J preceding 5

8 month. These stocks are held for K months, skipping a month between the formation period and the holding period to avoid possible short-term reversals (see, e. g. Jegadeesh, 1990; Lehmann 1990). Jegadeesh and Titman (1993) implement various strategies that differ with regard to the formation months J and holding periods K, where J, K {3, 6, 9, 12}. According to the three-factor Fama and French (1993) model, the return of a stock i in excess of the risk-free return in month can be divided into different components: (2) where is the excess return on the market index and and are the returns on the size and value factors in month. According to Equation (2), the excess return of a stock can thus be decomposed into a stock-specific component ( ) and a factor-related return contribution ( ). By ranking stocks on their past returns, the common price momentum strategy depends strongly on time-dependent realizations of the factor-specific return contribution during the formation period. For instance, if the market excess return is positive over the formation period, price momentum strategies tend to buy high-beta stocks and to sell low-beta stocks. In general, these strategies remain profitable throughout the investment period, if market excess returns remain positive. However, if market conditions change between formation and holding period, the common price momentum strategy performs poorly. To diminish the influence of factor exposures, similar to Grundy and Martin (2001), we implement an alpha momentum strategy by ranking stocks on their stock-specific component during the formation period. However, we are the first to estimate the alpha by considering daily stock returns only during the formation period. 1 In particular, at the end of each month t, we estimate the coefficients of the three-factor Fama and French (1993) model of each stock i based on daily stock returns over the J-month formation period: 1 We also implement alpha momentum strategies based on t-alphas to account for errors when estimating the coefficients of the Fama and French (1993) model. The main results are similar to those presented in this paper and are available upon request. 6

9 (3) where is the return of stock i on day d in excess of the risk-free rate, is the daily excess return of the market index and and are the daily returns on the Fama and French (1993) size and value factors. To account for possible infrequent trading, we follow Dimson (1979) and also include leaded and lagged factor returns into the Fama and French (1993) model to estimate the factor exposures. 2 Our alpha momentum strategy consist of a zero-investment portfolio that buys stocks in the deciles with the highest past daily threefactor alphas (henceforth past alphas) and sells stocks in the deciles with the lowest past alphas. To measure and compare the performance of the common momentum strategy and our alpha momentum strategy during the investment period, we look at their average returns, Sharpe ratios, FF alphas and risk-adjusted returns. To estimate alphas of the momentum strategies during the investment period, we first employ a Fama and French (1993) threefactor-regression according to Equation (2) but use the return of the zero-investment momentum portfolio in month t instead of the individual stock excess return. Doing so, this unconditional model assumes that factor exposures are constant over time. Second, we measure risk-adjusted profits of the momentum strategies accounting for dynamic factor exposures. In the literature, there are different approaches to determine the risk-adjusted performance of a strategy with dynamic factor exposures. On the one hand, Grundy and Martin (2001) run Fama and French (1993) regressions using six monthly returns beginning with the investment month to estimate the factor exposures of the momentum strategy. On the other hand, Daniel and Moskowitz (2014) use daily returns over a two months period after investment to estimate the strategies factor loadings. Thus, these two approaches implicitly assume that the factor exposures of the momentum strategy are constant 2 In line with Chordia et al. (2001) and Fama and French (1992), we include one lead and one lag in our regression model. Other studies apply more leads and lags. Among others, Cornell and Green (1981) and Brown and Warner (1985) include three lags and three leads into their regressions. Hong and Sraer (2012) use five and Daniel and Moskowitz (2014) ten lagged variables. 7

10 during these estimation periods of six or two months. However, the stock composition of momentum portfolios changes every month. Thus, Wang and Wu (2011) estimate the factor exposure of the momentum strategy for each investment month t separately based on individual stocks. They run rolling regressions from month t 37 to t 2 for each individual stock. They then use the betas of the stocks in the winner and loser decile to determine average betas of the momentum strategy. In this way, they account for monthly changing stock compositions and resulting time-dependent factor exposures of the strategies. Similar to Wang and Wu (2011), we determine factor exposures of the momentum strategy (,, ) in month t as the average factor exposures of the respective stocks in the momentum portfolios. Like Grundy and Martin (2001), we use six months beginning with the investment month t to estimate these factor exposures from month t to t + 5 but apply daily data. Based on this, the risk-adjusted performance of the zero-investment momentum portfolio p in investment month t is calculated as: (4) 3. Empirical analysis 3.1 Data Our study covers U.S. stock data from December 1979 to December Furthermore, we study European stock data from December 1989 to December 2011, which is ten years shorter for reasons of data availability. 3 We construct our dataset using stock constituent lists from Thomson Reuters Datastream. All stock data is extracted in US dollars. Appendix A explains in detail the construction of our dataset and the implementation of various screening procedures following Ince and Porter (2006). 3 We are able to evaluate the performance of our strategies after January 1982 for the U.S. and January 1992 for Europe for two reasons. First, we need one year to estimate the alphas. Second, we implement strategies with holding periods up to 12 months and skip a month between the formation period and the investment period. 8

11 To implement our alpha momentum strategy and to measure the performance of price momentum and alpha momentum, we run Fama and French (1993) regressions using monthly and daily factor realizations. For the U.S., we extracted these factors from the Kenneth R. French homepage. 4 For Europe, Kenneth R. French only provides monthly factor returns. Hence, we determine monthly and daily factor returns for Europe by ourselves. 5 Appendix B describes in detail how we construct the Fama and French (1993) factors for Europe. 3.2 Return predictability of past return and past alpha Our empirical analysis starts with a study of the determinants of future returns in the crosssection of individual stocks. To gain a first indication regarding the profitability of alpha and price momentum strategies we here focus whether individual stock returns are related either to past alpha or to past returns. In our cross-sectional regressions, we control for various other stock characteristics commonly used in asset pricing tests. In particular, each month t, we run cross-sectional regressions of future one-month, six-month or twelve-month stock returns on the past twelve-month return over month t 13 to t 2 according to Equation (1) or (and) the estimated daily alpha over month t 13 to t 2 according to Equation (3). Additionally, we include control variables for size (log(me)) and book-to-equity-market-ratio (log(b/m)) according to Fama and French (1992) and the past return in month t 1 following Novy-Marx (2013). Like in Gutierrez and Kelley (2008) and Loughran and Wellman (2011) size is measured as the market value of stocks in June of year t. Furthermore, book-to-market-equity is calculated as the book value in fiscal year t 1 divided by the market value in December of year t 1. Similar to Novy-Marx (2013), we exclude financial firms and trim independent variables at the 1% and 99% levels. 4 5 We thank Kenneth R. French for providing these factors on his website. Andrea Frazzini recently updated his data library homepage and now provides daily and monthly factor returns for Europe. Nevertheless, this factor returns are constructed using the Compustat/XpressFeed Global database and not Thomson Reuters Datastream. Moreover, the factor construction differs from the methodology described by Fama and French (2012). We therefore prefer construction factor return by ourselves. 9

12 After running monthly cross-sectional regressions, we calculate average factor exposures of the time series of each coefficient. Due to overlapping return intervals, we use Newey- West (1987) corrected standard errors to calculate t-statistics that are robust to heteroskedasticity and autocorrelation. (Insert Table 1 about here) Panel A of Table 1 shows that the past twelve-month return has no impact on future returns of individual stock over the evaluation period from 1982 to 2011 in the U.S. Coefficients on the past twelve-month returns are insignificant for all three future return intervals. On the other hand, factor exposures on past twelve-month alphas are significant on the 10%-level for the one-month future return. Nevertheless, the significance of past alpha in the cross-section of individual stock returns vanishes when we look at longer future return intervals. Finally, when we include both past return and past alpha into our cross-sectional regressions, we see that the factor exposures of past alpha stay positive and significant for the one-month and the six-month future return. On the other hand, coefficients on past returns still remain insignificant. Panel B of Table 1 repeats the results for our European sample. Both past return and past alpha have significant impact on the one-month future return. However, the influence of past alpha on the cross-section of returns gets insignificant when we include both past return and past alpha into our regression. Moreover, when we turn our focus on longer return intervals, we see that coefficients on past returns become insignificant. On the other hand, the impact of past alpha stays positive and becomes significant even after including both past return and past alpha into our cross-sectional regressions. In summary, our monthly regressions show that especially past alphas have power in predicting the cross-section of returns for the one-month and six-month future return. We thus assume that strategies constructed based on past alphas should generate positive abnormal returns. In the next section, we therefore turn our focus on the performance of momentum 10

13 strategies based on past alpha. Moreover, we compare the performance of this alpha momentum strategy to the performance of the conventional price momentum strategy. 3.3 Performance of momentum strategies in portfolio context In this section, we compare the performance of common price momentum with that of our alpha momentum strategy. For the sake of brevity, we focus on the implementation of the following two strategies. Both define stocks in the winner decile and in the loser decile based on a twelve-month formation period (J = 12). We skip a month after formation to account for short-term reversal effects. 6 Due to the fact that the impact of past return and past alpha decreases in the cross-section of returns when we look at longer future return intervals, we implement momentum strategies with a one- and with a six-month holding period (K = 1,6). The K = 6-strategies consist of six overlapping portfolios (cohorts) which are constructed based on the past returns (past alphas) at the end of month t and in the previous K 1 months. Moreover, these strategies are broadly used in the empirical literature. 7 Table 2 compares the alpha momentum strategy and the common price momentum strategy for J12/K1 and J12/K6. Panel A shows for the U.S., that alpha momentum outperforms common price momentum. For the full investment period from 1982 to 2011, alpha momentum exhibits higher average returns, higher Sharpe ratios, higher FF alphas and higher risk-adjusted returns. For instance, when we compare the J12/K6 strategies, the Sharpe ratio of alpha momentum is approximately three times as high (17.45%) as that of price momentum (6.18%). When we look at sub-periods, we find that alpha momentum outperforms price momentum from 1992 onwards. However, both effects disappear in the U.S. when we turn our focus at the most recent sub-period. In Panel B, we see different 6 7 We also implement momentum strategies with shorter formation periods (J = 3,6) and with other holding periods in the investment periods (K = 3,12). The main results are similar to those presented in this paper. The results based on other formation periods and holding periods are available upon request. We also implement Grundy and Martin (2001) momentum (GM momentum) based on dummy alphas estimated with 60 monthly returns. Our daily alpha momentum strategy outperforms the GM momentum strategy. The main results are available upon request. To implement this strategy, we use U.S. stock data from December 1974 to December 2011 and European stock data from December 1984 to December

14 patterns for our European sample. The common price momentum strategy outperforms our alpha momentum strategy in terms of average returns, FF alphas and risk-adjusted returns over the full investment period and in all sub-periods. Nevertheless, the Sharpe ratios of the alpha momentum are higher than the respective Sharpe ratios of the common price momentum strategy, because alpha momentum exhibits lower return volatility. (Insert Table 2 about here) Our results indicate that there are performance differences between alpha momentum and price momentum. To discover these differences, we now look at the stock composition of the winner and loser deciles of these two strategies over time. In particular, we first compare the percentage of stocks that are allocated simultaneously to both the price momentum strategy and to our alpha momentum strategy. Figure 1 plots all price momentum winner (loser) stocks with respect to their position in alpha momentum deciles. For instance, the.α-decile ( 0.α-decile ) area shows the percentage of all price momentum winner (loser) stocks that are also alpha momentum winner (loser) stocks. Therefore, this area shows a time-dependent overlap between price momentum stocks and alpha momentum stocks. The.α-decile ( 9.α-decile ) area presents the percentage of all price momentum winner (loser) stocks that can be located in the second (ninth) decile when we rank by alpha, and so on. It is obvious that the number of overlapping stocks between price momentum and alpha momentum varies over time. On average, we find an overlap of approximately 62% for the U.S. (Panel A) and 66% for Europe (Panel B). When we compare price momentum loser stocks with price momentum winner stocks, we find that loser stocks are more often located in deviating alpha momentum deciles. In addition, we include a line into each plot of Figure 1 showing the negative absolute difference between the average monthly factor-related return components of alpha (price) momentum and price (alpha) momentum for the winner (loser) stocks. Our figure reveals that the overlap between alpha momentum and price momentum varies most when the absolute difference between the average factor-related return components is large. (Insert Figure 1 about here) 12

15 Our results indicate that there are differences in the performance and stock composition between alpha momentum and price momentum. Moreover, these differences arise from variations in the factor-related return contributions. In Section 3.4, we therefore focus on the differences in the factor exposures between alpha momentum and price momentum. 3.4 Dynamic factor exposures of momentum strategies In context with price momentum strategies, the ranking of stocks is influenced by the realizations of the underlying factors driving stock returns. For instance, if the market excess return is positive over the formation period, price momentum strategies favor buying highbeta stocks and selling low-beta stock and vice versa. As factor realizations vary over time, factor exposures of the price momentum strategy also vary. Therefore, the unconditional Fama and French (1993) model cannot sufficiently identify the risk of momentum strategies, because it assumes constant factor exposures over time. In terms of variance, only up to 8.61% (6.78%) of the variation of the price momentum strategy can be explained by this model in the U.S. (Europe). The alpha momentum strategy should be less dependent on changes of the factor realizations, because it sorts stocks only on their stock-specific component. Accordingly, the explanatory power of the unconditional Fama and French (1993) is higher for our alpha momentum strategy with up to 20.31% (12.61%) for the U.S. (Europe). Following Wang and Wu (2011), we account for time-varying factor exposures of price momentum and alpha momentum when measuring risk-adjusted returns. Figure 2 shows the average factor exposures over time of price momentum and alpha momentum calculated based on individual stocks from month t to t + 5. Obviously, the factor exposures of both strategies vary strongly for the U.S. (Panel A) and Europe (Panel B). Thus by ranking stocks on their stock-specific component, we also generate a strategy with time-varying factor exposures. Nevertheless, the volatility of the factor exposures of price momentum is clearly higher than that of alpha momentum. 13

16 (Insert Figure 2 about here) As described in Section 2, we hedge out the factor exposures for each investment month separately when determining risk-adjusted returns. In doing so, this hedging strategy explains up to 50.81% (46.88%) of the variance of the price momentum strategy and up to 44.03% (32.22%) of the alpha momentum strategy in the U.S. (Europe). Hence, this approach with time-varying factor loadings much better explains the return variations of both strategies. However, even after hedging out the factor exposures of price momentum and alpha momentum, we find that the two strategies generate differing positive abnormal returns. In the next section, we therefore study a possible dominance of price momentum or alpha momentum. 3.5 Dominance of momentum strategies To examine the dominance of price momentum and alpha momentum, we run two tests according to George and Hwang (2004). We first apply a pairwise nested comparison model which looks at the performance of alpha momentum conditional on the ranking on price momentum, and vice versa. (Insert Table 3 about here) Table 3 present the results of the nested pairwise comparisons when we rank on two criterions. The left of Table 3 contain the results, when we first rank stocks into quintiles according to price momentum and then further rank each quintile according to alpha momentum. The right columns stocks are first sorted according to alpha momentum and then further divided into quintiles according to price momentum. For the U.S. (Panel A), we find positive and significant risk-adjusted returns for alpha momentum in the highest price momentum quintiles (P3, P4, P5). However, within alpha momentum quintiles, the profitability of price momentum disappears. We find differing results for Europe (Panel B). Here, both alpha and price momentum yield significant profits 14

17 within some of the conditional ranked quintiles. Nevertheless, price momentum profits in alpha momentum quintiles are somewhat higher. To measure if our findings are not driven by rankings on more extreme returns (alphas), we double sort stocks according to the same criterion (see Bandarchuk and Hilscher, 2013). (Insert Table 4 about here) Table 4 shows the results when we double sort stocks according to the same criterion. For the U.S., Panel A of Table 4 reveals that it is not possible to realize positive and significant price momentum profits within price momentum quintiles. The same holds true for alpha momentum. Nevertheless, when we look at the European results in Panel B, double sorting according to both strategies leads to positive and partly significant returns. In summary, our findings reveal that alpha momentum sorts are more promising in predicting future performance in the U.S. and that there is no clear dominance of one strategy in Europe. To measure the robustness of our dominance results, we next employ cross-sectional regressions to test the profitability of a single strategy independent from the other strategy similar to Section 3.2. We explain the one-month future return of stock i in each month t by running cross-sectional regressions. However, in contrast to Section 3.2, we focus only on stocks that are located in the winner or loser decile. Thus, our dependent variables are four dummy variables indicating whether stock i is part of the winner or loser decile according to price momentum (alpha momentum) in month t. For the J12/K1 strategy, each investment month t we implement one cross-sectional regression for the one cohort held in that month. The J12/K6 strategy, however, consists of six overlapping cohorts each month. Thus following George and Hwang (2004) we run one cross-sectional regressions for each of the six cohorts held in month t. Within these cross-sectional regressions, the dummy variables change with regard to the stock composition in the respective winner or loser deciles of the six overlapping cohorts. More precisely, the respective dummy variables of a cross-sectional 15

18 regression are set to one if a stock is ranked in the winner or loser deciles in the respective cohort. Moreover, we control for market capitalization (log (ME)) and the past return in t 1 to get comparative results to George and Hwang (2004). 8 After running these monthly cross-sectional regressions, we first calculate average factor exposures of the dummy variables for the J12/K6 strategy over the six different crosssectional regressions for each cohort in each investment month t. Then time-series averages of all coefficients are measured. We use Newey-West (1987) corrected standard errors to calculate t-statistics that are robust to heteroskedasticity and autocorrelation. (Insert Table 5 about here) The results in Table 5 confirm the findings from our nested pairwise comparison test. In the U.S. (Panel A), alpha momentum dominates price momentum. Alpha momentum coefficients (A10 A1) are highly significant for J12/K1 and J12/K6. On the other hand, price momentum coefficients (P10 P1) are only significant at the 10%-level for J12/K1 and insignificant for J12/K6. For Europe, Panel B reveals that coefficients on price momentum dummies are higher than the respective coefficients on alpha momentum. However, coefficients on alpha momentum stay positive and significant for J12/K1 and J12/K6. That implies that both alpha momentum and price momentum are profitable in addition to the other strategy. 4. Sources of different momentum profits 4.1 Momentum effects for subsets of stocks and long-term performance Our empirical results in Section 4.2 show that the conditional as well as unconditional Fama and French (1993) framework cannot fully explain the profits of alpha momentum and price momentum. Both strategies exhibit positive and significant FF alphas and risk-adjusted 8 We also included book-to-equity-market-ratio (log(b/m)) as a control variable. The main results are similar to those presented in this paper and are available upon request. 16

19 returns based on the whole investment period in the U.S. and in Europe. We therefore turn our focus to behavioral models aiming to explain the momentum phenomenon. Behavioral explanations assume that price momentum is caused by an underreaction to firm-specific news or a delayed overreaction. Among others, Barberis et al. (1998) and Hong and Stein (1999) postulate that some investors tend to underreact to new information. Therefore, prices adjust slowly to this firm-specific news and price momentum can be identified. On the other hand, Daniel et al. (1998) argue that investors become overconfident about their trading abilities. Moreover, Hong and Stein (1999) presume that stock prices can overreact because so-called momentum traders do not trade based on fundamental information but past prices only. Both models imply that these investors push prices of past winner stocks above, and past loser stocks below, their fundamental value in the short-run. Resulting momentum profits are then reversed in the long-run. In their seminal paper, De Bondt and Thaler (1985) find that past loser stocks outperform past winner stocks over three to five years. Lee and Swaminathan (2000) and Jegadeesh and Titman (2001) also document that momentum strategies reverse in the long-run. If underreaction partly causes momentum, then alpha momentum should be more persistent than price momentum. To connect alpha momentum and price momentum profits to these behavioral explanations, we first construct subset portfolios to distinguish between winner or loser stocks according to only price momentum, only alpha momentum or according to both criterions at the same time. We then look at the performance of these strategies in the short-run. In a second step, we analyze the long-run performance of alpha momentum, price momentum and their subset portfolios. Similar to Gutierrez and Prinsky (2007) we look at different types of momentum by comparing the stocks in the winner and loser deciles according to price momentum and alpha momentum. First, we examine the performance of those stocks that are in winner and loser deciles according to price momentum but not in the respective decile according to alpha momentum. This Price Alpha momentum strategy buys (sells) the subset of stocks that 17

20 are in the winner (loser) decile based on their past return, but not based on their past alpha. Second, our so-called Alpha Price momentum strategy consists of a zero-investment portfolio of stocks that are winner stocks or loser stocks based on their past alpha, but not on their past return. Finally, the Price Alpha momentum portfolio contains stocks that are in the winner (loser) decile based on both past return and alpha. (Insert Table 6 about here) Panel A of Table 6 presents the results of the subset strategies described above for the U.S. For the entire evaluation period, Price Alpha momentum outperforms both Alpha Price momentum and Price Alpha momentum in terms of average returns, FF alphas and risk-adjusted returns. In addition, Alpha Price momentum outperforms Price Alpha momentum in terms of Sharpe ratios and risk-adjusted returns. Considering the sub-period from January 2002 to December 2011, the performance of Price Alpha momentum and Price Alpha momentum turns insignificant with monthly risk-adjusted returns of -0.55% and -0.35%, respectively, for the J12/K1 strategy. Only Alpha Price momentum produces positive and significant returns at the 1% level with a risk-adjusted monthly return of 1.13%. In Europe (Panel B), Price Alpha momentum outperforms Price Alpha momentum as well as Price Alpha momentum over the entire evaluation period and in all sub-periods. Additionally, Price Alpha momentum outperforms Alpha Price momentum in terms of Sharpe ratios and risk-adjusted returns. When comparing the results from the U.S. to the results from Europe, we find that momentum returns are lower in the U.S. We conclude that there seems to be faster information diffusion in the U.S. Moreover, trading strategies based on past returns are well known in the U.S. since the seminal paper of Jegadeesh and Titman in That could be a reason why the performance of Price Alpha momentum and Price Alpha momentum turns insignificant during the recent sub-period. Overall, these results support findings of behavioral explanations of the price momentum effect. The Price Alpha portfolio contains stocks that are in the winner (loser) decile 18

21 based on both past return and past alpha. Therefore, the performance of this portfolio could be driven by an underreaction to firm-specific news (see Barberis et al., 1998; and Hong and Stein, 1999) as well as by an overreaction due to momentum trading. Momentum traders can push prices of winner and loser stocks away from their fundamental value (see Hong and Stein, 1999). Taken together, this would result in a higher performance of Price Alpha in the short run. In the next step, we turn our focus on the long-term performance of price momentum and alpha momentum. Similar to Gutierrez and Prinsky (2007), we therefore plot the performance of the different strategies over the five years following the investment point of time. Nevertheless, we use cumulative returns for the performance of the strategies in the event months, similar to Jegadeesh and Titman (1993). 9 Figure 3 plots the cumulative log return for the common price momentum strategy and our alpha momentum strategy. We see that both alpha momentum and price momentum reverse in the U.S. (Panel A) and in Europe (Panel B) in the long-run. Clearly, the reversal is more pronounced for the price momentum strategy. Against the background of the behavioral explanations, we find evidence that both price momentum and alpha momentum could be influenced by an underreaction to firm-specific news and by an overreaction due to momentum trading. The positive performance of price momentum during the first months is followed by negative performance in the long run. Since there is an overlap between alpha momentum and price momentum stocks, alpha momentum also reverses in the long run, but not as strongly as price momentum. Moreover, underreaction to firm-specific news or overreaction due to momentum trading seems to be slower in Europe. Figure 3 also presents separately the long-term performance of the three subset portfolios ( Price Alpha, Alpha Price and Price Alpha ). For the U.S. (Panel A), the cumulative return of Alpha Price increases for about ten months and then moderately 9 We also measure long-term performance with cumulative risk-adjusted returns. The main results are similar to those presented in this paper and are available upon request. 19

22 declines. Price Alpha performs similarly to Alpha Price momentum in the first months, but then reverses after about five months while Price Alpha immediately reverses after two months. For Europe (Panel B), we see that both Price Alpha and Price Alpha strongly increase in the first months. Nevertheless, both strategies reverse after nine months. Remarkably, Alpha Price slowly increases over the full event period. (Insert Figure 3 about here) Overall, we see that the performance of stocks which exclusively experience alpha momentum, but not price momentum, does not reverse strongly in the U.S. and increases steadily on in the long run in Europe. Thus, we conclude that the performance of Alpha Price could be primarily influenced by an underreaction to firm-specific news. Stocks that are in the winner (loser) decile based on both past return and alpha should contain fundamental information. Investors tend to underreact to this firm-specific news and prices move slowly towards their fundamental value. Nevertheless, those stocks that are in the winner (loser) decile based on alpha but not past return could be included in the second/ninth decile according to price momentum, and thus also experience some overreaction due to momentum trading. This could in any case explain the reversal of Alpha Price in the U.S. in the long run. On the other hand, the performance of the subset of stocks that are in the winner (loser) decile based on past return but not past alpha reverses quickly. This performance could be more strongly influenced by momentum traders who push prices of past winner and loser stocks away from their fundamental value, although there is no fundamental information. Finally, the intersection of both momentum strategies performs well in the first months but then reverses in the long run. This effect could be due to both an underreaction to firm-specific news and an overreaction due to momentum trading. Furthermore, these results of Price Alpha stocks are in line with a delayed overreaction to firm-specific news according to Daniel et al. (1998) who shows that investors become overconfident and overestimate signals about stock prices. These investors drive stock prices away from their 20

23 fundamental value with some time delay. Eventually, this performance reverses. Moreover, our results indicate, that new information diffuses faster in the U.S. than in Europe. 4.2 Investor sentiment and momentum In the last section, we have seen that the profitability of alpha momentum and price momentum could be connected to behavioral explanations. Now, we therefore turn our focus more closely on the behavior of investors. Specifically, we analyze to what extent investor sentiment is related alpha momentum and price momentum. Many studies show that investor sentiment has an impact on stock prices (among others, Barberis et al. 1998; Kumar and Lee 2006; Baker and Wurgler 2006). For example, Baker and Wurgler (2006) point out that investor sentiment influences the profitability of zero-costinvestment strategies based on several firm characteristics. Antoniou et al. (2013) connect sentiment to price momentum. They argue that investors tend to underreact to news that contradicts their preconceived sentiments due to cognitive dissonance. Therefore, the prices of loser (winner) stocks underreact to this firm-specific news in optimistic (pessimistic) periods. Their empirical findings indicate that price momentum strategies yield highly significant positive returns when the overall sentiment is optimistic. These profits can be traced back to the underperformance of loser stocks. The authors assume that selling loser stocks is costly and difficult due to short-selling constraints. This leads to positive returns in optimistic sentiment periods. In contrast, momentum profits vanish when the prevailing sentiment is pessimistic. The authors argue that winner and loser stocks earn equally positive returns because managers try to boost good news of loser stocks in times of investor pessimism. Similar to Antoniou et al. (2013), we analyze how sentiment affects both alpha momentum and price momentum. Hence, we extract the investor sentiment index provided by Jeffrey Wurgler for the U.S and the Consumer Confidence Index for Europe. 10 Like Antoniou et al. 10 We thank Jeffrey Wurgler for providing this index on his website: 21

24 (2013), we divide our evaluation of sentiment into optimistic, mild and pessimistic periods by computing weighted-rolling average of the sentiment index for the formation period over month t 1 to t 3. Our sample is then divided into three sentiment trends based on the 30 th and 70 th percentile. For the sake of brevity, we only report the results of the J12-K1 strategy. 11 (Insert Table 7 about here) Table 7 contains the risk-adjusted returns for alpha momentum and price momentum deciles in different sentiment periods. Our findings reveal that alpha momentum and price momentum yield highly significant risk-adjusted profits in optimistic periods for the U.S. (Panel A). Nevertheless, the monthly risk-adjusted return of price momentum is higher (1.62%) than that of alpha momentum (1.29%). Moreover, the significant profits primarily result from the underperformance of the loser stocks. For both strategies, momentum profits decrease for periods characterized by mild and pessimistic sentiments. However, price momentum profits become insignificant while alpha momentum profits decrease but stay positive and significant. In pessimistic periods, winner and loser stocks realize positive riskadjusted returns in roughly the same amount for price momentum. On the other hand, alpha momentum winner stocks outperform alpha momentum loser stocks. We observe similar patterns for Europe (Panel B). Nevertheless, price momentum and alpha momentum profits are significant in all sentiment states. Connecting these results to behavioral explanations, our findings indicate that price momentum in optimistic periods could be due to cognitive dissonance. Loser stocks underperform in times of optimistic sentiment and that is why momentum profits are high. On the other hand, given that alpha momentum stocks experience relatively more firm-specific news, they should be influenced more strongly by cognitive dissonance. Nevertheless, our findings do not support this hypothesis We also implement sentiment sorts for the J12-K6 strategy. The main results are similar to those presented in this paper. Moreover, unreported results show that the results remain robust when we use raw returns instead of risk-adjusted returns. All results are available upon request. 22

25 When we turn our focus to pessimistic periods, we find no sign of cognitive dissonance in the winner decile for the price momentum strategy. Risk-adjusted profits are similar for all deciles. On the other hand, the profits of alpha momentum deciles stay significant in pessimistic periods due to cognitive dissonance of the winner stocks. This implies that good news of these stocks are incorporated slowly when sentiment is low. Finally, momentum profits for both strategies could be more pronounced in periods of optimistic sentiment because momentum traders are sensitive to sentiment. Momentum traders strongly engage in arbitraging momentum stocks when sentiment is optimistic. Since price momentum profits should be influenced more strongly by momentum trading, they turn insignificant in times of pessimistic sentiment. On the other hand, alpha momentum profits stay positive and significant due to cognitive dissonance. 5. Conclusion This paper contributes to the extensive literature on momentum by comparing the common price momentum strategy to an alpha momentum strategy that ranks stocks based on threefactor-alphas estimated on the basis of daily returns. First, we find past alphas to have power in predicting the cross-section of individual returns. Moreover, we are able to build a strategy based on past alphas which shows lower return volatility and less extreme return reversal in the long-run. In addition, we gain further insight related to behavioral explanations of momentum. Our results reveal that past alpha is an economically and statistically significant predictor of the cross-section of individual stock returns in the U.S. and in Europe. Furthermore, we show that ranking stocks on past daily alphas instead of on past returns leads to similar profits. Nevertheless, the profits of the alpha momentum strategy are less volatile in the U.S. and in Europe. The performance differences between alpha momentum and price momentum can be explained by time-dependent differences between the stock composition of the zero- 23

26 investment portfolios of our alpha momentum strategy and the common price momentum strategy. In contrast to the common price momentum strategy following Jegadeesh and Titman (1993), factor-related return contributions have less impact on our ranking of stocks. While the composition of the common price momentum portfolio depends on the performance of the factors driving stock returns during the formation period, our alpha momentum portfolios are composed based on stock-specific returns only. Consequently, the common price momentum strategy exhibits more dynamic three-factor exposures. Finally, alpha momentum dominates price momentum in the U.S. and there is no clear dominance of one strategy over the other in Europe. In addition, looking at the long-term profitability of price momentum and alpha momentum, our results support behavioral explanations which assume that the momentum effect is caused by an underreaction to firm-specific news as well as by an overreaction due to momentum trading. However, the impact of both behavioral explanations is different for each strategy. First, we see that the profits of strategies that consist of stocks that are in the winner (loser) decile based on past alpha but not past return slightly reverse in the U.S. but constantly increase in Europe in the long run. This pattern could be due to an underreaction to firmspecific news (see Barberis et al., 1998; and Hong and Stein, 1999). Second, we find that the performance of a strategy that selects stocks that are in the winner (loser) decile based on past return but not past alpha reverse quickly in the U.S. and slowly in Europe. The positive performance in the beginning could be induced by momentum traders who push prices of past winner and loser stocks away from their fundamental value (see Hong and Stein, 1999). Eventually, these profits reverse. Finally, the intersection of both alpha momentum and price momentum stocks performs well in the first months but then reverses the U.S. and in Europe. This effect could be due to both an underreaction to firm-specific news combined with an overreaction due to momentum trading. In further analyses, we show that both alpha momentum and price momentum might be sensitive to investor sentiment. Both strategies yield highly significant risk-adjusted returns in 24

27 periods of optimistic sentiment in the U.S. as well as in Europe. Risk-adjusted profits decrease in periods of mild and pessimistic sentiment and become insignificant in the U.S. for the price momentum strategy. Connecting these results to behavioral explanations, our findings indicate that price momentum in optimistic periods could be due to cognitive dissonance in the loser decile. Moreover, alpha momentum profits remain positive in pessimistic sentiment periods due to cognitive dissonance in the winner decile. Finally, our results support, that momentum traders more strongly engage in arbitraging momentum stocks when sentiment is optimistic. 25

28 Appendix A Screening procedures following Ince and Porter (2006) Following Ince and Porter (2006) and Schmidt et al. (2011), we extract active and dead stock constituent lists compiled by Thomson Reuters Datastream. Moreover, we use constituent lists compiled by Thomson Reuters Worldscope, as well as country-specific constituent lists. The inclusion of the dead lists prevents our dataset from suffering survivorship bias. Ince and Porter (2006) and Schmidt et al. (2011) argue that the use of raw returns from Thomson Reuters Datastream could lead to erroneous results. We therefore employ the common screening procedures used by the above-mentioned authors. In a first step, we implement static screens that account for certain stock characteristics. We only include stocks with Datastream identifier MAJOR=major listing, TYPE=EQ, GEOG/GEOGN=domestic market and stocks that are listed at one of the country-specific stock exchanges. Moreover, we employ a text search to eliminate non-common shares such as preferred stocks, trusts, warrants, rights, REITS, closed-end funds, ETFs and depository receipts. Finally, we do not consider stocks with an average market capitalization below $ 10 million. In a second step, we also implement dynamic screens. When a security is delisted or goes bankrupt, Thomson Reuters Datastream repeats the last available value of the stock. Therefore, we have to delete all zero daily/monthly returns in local currency from the end of our sample until the first non-zero return. In addition, every month we delete all stocks with an unadjusted price below $ In this way, our sample does not suffer from a bias induced by so-called penny stocks. Finally, we employ several return filters. We set all returns to missing that are greater than 890%. Additionally, we delete all daily/monthly returns that are greater than 300% in one month and drop by 50% or more in the next month, and vice versa. After applying the filters described above, our sample should be relatively free from data errors. 26

29 Appendix B Calculation of Fama and French (1993) factors in Europe Following Fama and French (1993), we sort European stocks on size and book-to-marketequity denoted in US dollars. Following Fama and French (1992) and Artmann et al. (2012), we exclude financial firms when constructing the factors due to special accounting standards and high leverage ratios. To determine breakpoints for the size and book-to-market-equity portfolios in Europe, we follow the approach of Fama and French (2012). First, we use the top 90% of market cap to split our sample into small and big stocks. Then our sample is divided into three book-to-market-equity portfolios based on the 30th and 70th percentile for big stocks only. Like Schmid et al. (2001), we define book value as Thomson Reuters Worldscope common equity plus deferred taxes. We only use stocks with book values greater than zero. Book-to-market-equity is thus defined as the book equity of the fiscal year ending in calendar year t 1 divided by the market value of December t 1. Size, on the other hand, is the Thomson Reuters Datastream market value (MV) at the end of June in calendar year t. Each June, we independently sort all stocks on size and book-to-market-equity. We then build six portfolios from the intersection of the two size and the three book-to-market-equity portfolios. We calculate monthly and daily value-weighted returns of the SMB-factor and the HML-factor as follows: (5) (6) where denotes the value-weighted return of the intersection of size class X and bookto-market-equity class Y on day (month) t based on portfolio formation in last June. 27

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33 Table 1 Monthly cross-sectional regressions of individual stock returns on different momentum strategies Panel A: U.S. (1) (2) (3) Mean t-value Mean t-value Mean t-value One-month future return Intercept 2.25 (3.74) 2.29 (3.74) 2.03 (3.53) log(me) (-2.63) (-2.36) (-2.13) log(b/m) 0.17 (1.53) 0.13 (1.11) 0.16 (1.42) R t (-5.52) (-5.71) (-5.74) R [t 13,t 2] 0.11 (0.35) (-0.50) α [t 13,t 2] (1.67) (1.74) Six-months future return Intercept (2.44) (2.44) (2.49) log(me) (-2.25) (-2.22) (-2.12) log(b/m) 1.18 (1.34) 1.05 (1.14) 1.15 (1.41) R t (-0.81) (-1.13) (-1.04) R [t 13,t 2] (-0.09) (-0.84) α [t 13,t 2] (0.78) (1.71) Twelve-months future return Intercept (2.78) (2.69) (2.88) log(me) (-2.39) (-2.25) (-2.45) log(b/m) 1.75 (1.09) 1.60 (0.98) 1.84 (1.25) R t (0.01) (-0.11) (-0.12) R [t 13,t 2] (-0.36) (-1.06) α [t 13,t 2] (0.27) (1.47) Panel B: Europe (1) (2) (3) Mean t-value Mean t-value Mean t-value One-month future return Intercept 0.48 (0.91) 0.30 (0.51) 0.47 (0.90) log(me) 0.05 (1.23) 0.11 (2.78) 0.06 (1.42) log(b/m) 0.41 (3.82) 0.43 (3.60) 0.40 (3.76) R t (-0.97) (-0.66) (-1.28) R [t 13,t 2] 1.35 (3.03) 1.39 (2.60) α [t 13,t 2] (5.82) (0.64) Six-months future return Intercept (0.91) (0.89) (0.94) log(me) (-0.94) (-0.64) (-0.83) log(b/m) 2.43 (1.42) 2.47 (1.48) 2.34 (1.42) R t (3.25) (3.32) (3.13) R [t 13,t 2] 4.95 (0.92) 2.18 (0.45) α [t 13,t 2] (1.81) (1.94) Twelve-months future return Intercept (1.32) (1.41) (1.35) log(me) (-0.75) (-0.61) (-0.62) log(b/m) 4.80 (1.95) 4.82 (1.85) 4.69 (1.95) R t (3.85) (3.80) (3.68) R [t 13,t 2] 5.08 (0.60) 1.53 (0.33) α [t 13,t 2] (2.55) (2.10) This table presents results from monthly cross-sectional regressions of returns on price momentum and alpha momentum. (7) The dependent variable is the raw monthly return of stock i in month t, t to t+6 and t to t+12. Independent variables are the market value, book-to market-equity, past performance measure over month t 1, past performance over t 13 to t 2 and past alpha over t 13 to t 2 of stock i in month t. The table reports the mean (%) of the monthly time series of each coefficient. We use Newey-West (1987) corrected standard errors to get t-statistics that are robust to heteroskedasticity and autocorrelation. 31

34 Table 2 Monthly performance of different momentum strategies Panel A: U.S. Price Momentum Alpha Momentum µ SR α 3F r 3F ajd. µ SR α 3F r 3F ajd. Full investment period 01/82-12/11 Mean J12-K t-value (2.49) (3.82) (2.72) (4.32) (5.00) (5.02) J12-K (0.99) (2.11) (1.45) (2.59) (3.49) (2.91) 01/82-12/91 J12-K (6.21) (6.85) (5.66) (5.99) (6.90) (5.70) J12-K (4.25) (5.93) (4.33) (4.27) (6.00) (3.88) 01/92-12/01 J12-K (1.73) (2.07) (2.00) (2.73) (3.35) (4.27) J12-K (0.62) (1.71) (1.08) (1.76) (2.81) (3.29) 01/02-12/11 J12-K (-0.55) (-0.43) (-1.12) (0.56) (0.95) (0.12) J12-K (-0.97) (-0.96) (-1.26) (-0.31) (-0.07) (-0.53) Panel B: Europe Price Momentum Alpha Momentum µ SR α 3F r 3F ajd. µ SR α 3F r 3F ajd. Full investment period 01/92-12/11 Mean J12-K t-value (4.53) (5.33) (6.06) (4.68) (6.09) (5.90) J12-K (3.10) (3.68) (4.89) (3.65) (4.56) (5.19) 01/92-12/01 J12-K (3.29) (3.40) (3.79) (2.74) (3.63) (3.60) J12-K (2.29) (2.45) (3.44) (2.09) (2.65) (3.40) 01/02-12/11 J12-K (3.09) (4.25) (4.99) (4.40) (5.38) (5.42) J12-K (2.07) (2.75) (3.48) (3.54) (4.16) (4.14) This table presents the monthly performance of 2x2 momentum strategies. For each month t, all stocks with returns for the formation period t 13 to t 2 are ranked according to two different criteria. The price momentum strategy indicates winner and loser stocks based on raw cumulative returns over the formation months. The alpha momentum strategy ranks stocks based on daily, three-factor-alphas estimated over the formation months. All portfolios are long in an equal-weighted winner portfolio and short in an equal-weighted loser portfolio. For the U.S., Panel A shows the performance of the different strategies from January 1982 to December For Europe, Panel B Table 2 shows the performance of the different strategies from January 1992 to December Table 2 presents the mean returns, Sharpe ratios, FF alphas and the risk-adjusted returns for the 12-month formation period and 1-month (6-months) holding period momentum strategies. All performance numbers are given in %. We use Newey-West (1987) corrected standard errors to get t-statistics that are robust to heteroskedasticity and autocorrelation. 32

35 Table 3 Monthly risk-adjusted performance of two-way dependent sort by price momentum and alpha momentum Panel A: U.S. Portfolios by price momentum Portfolios by alpha momentum Portfolios by alpha momentum Portfolios by price momentum A5 A1 A5 A1 P5 P1 P5 P1 Mean J12-K1 P J12-K1 A t-value (0.58) (-0.58) (1.57) (-0.39) (-0.79) (0.67) P A (0.58) (-1.36) (1.36) (-0.39) (-0.74) (0.43) P A (2.37) (0.01) (2.15) (0.12) (0.27) (-0.15) P A (4.11) (-0.02) (3.69) (0.21) (1.03) (-0.73) P A (2.35) (0.11) (2.89) (0.97) (2.40) (-1.05) Mean J12-K6 P J12-K6 A t-value (1.02) (-0.28) (1.64) (0.46) (-0.55) (0.85) P A (1.02) (-0.03) (1.08) (0.46) (-0.06) (0.42) P A (2.57) (0.68) (1.81) (0.22) (0.45) (-0.21) P A (3.33) (0.27) (2.79) (-0.07) (1.06) (-0.96) P A (1.25) (-0.13) (1.82) (0.26) (1.96) (-1.40) Panel B: Europe Portfolios by price momentum Portfolios by alpha momentum Portfolios by alpha momentum Portfolios by price momentum A5 A1 A5 A1 P5 P1 P5 P1 Mean J12-K1 P J12-K1 A t-value (-1.76) (-2.99) (2.13) (-1.14) (-2.68) (2.07) P A (-1.76) (-0.94) (-1.01) (-1.14) (-1.68) (0.37) P A (2.20) (0.24) (2.56) (4.33) (-0.42) (2.82) P A (2.62) (1.93) (1.54) (5.95) (0.65) (2.76) P A (4.20) (4.38) (3.23) (4.41) (1.27) (3.51) Mean J12-K6 P J12-K6 A t-value (-0.54) (-2.23) (2.35) (-0.02) (-2.12) (2.19) P A (-0.54) (-0.51) (-0.15) (-0.02) (-1.09) (0.84) P A (1.62) (1.17) (0.92) (3.78) (0.22) (2.09) P A (2.59) (2.17) (1.50) (5.20) (0.30) (2.83) P A (3.25) (3.84) (1.89) (3.50) (1.18) (2.38) This table presents the monthly risk-adjusted performance of two-way dependent sorts by price momentum and alpha momentum. For each month t, all stocks with returns for the formation period t 13 to t 2 are first sorted into quintiles according to price momentum (alpha momentum), then further ranked by alpha momentum (price momentum) within each group. The price momentum strategy indicates winner and loser stocks based on raw cumulative returns over the formation months. The alpha momentum strategy ranks stocks based on daily, three-factor-alphas estimated over the formation months. All portfolios are long in an equal-weighted winner portfolio and short in an equal-weighted loser portfolio. For the U.S., Panel A shows the performance of the different strategies from January 1982 to December For Europe, Panel B Table 3 shows the performance of the different strategies from January 1992 to December Table 3 presents the the risk-adjusted performance (%) for the 12-month formation period and 1-month (6-months) holding period momentum strategies. We use Newey-West (1987) corrected standard errors to get t-statistics that are robust to heteroskedasticity and autocorrelation. 33

36 Table 4 Monthly risk-adjusted performance of two-way dependent sort by price momentum and alpha momentum Panel A: U.S. Portfolios by price momentum Portfolios by price momentum Portfolios by alpha momentum Portfolios by alpha momentum P5 P1 P5 P1 A5 A1 A5 A1 Mean J12-K1 P J12-K1 A t-value (2.29) (0.66) (0.40) (2.15) (0.90) (0.06) P A (2.29) (1.91) (1.11) (2.15) (2.13) (0.22) P A (6.56) (6.48) (-0.16) (6.26) (5.22) (0.51) P A (8.08) (8.61) (0.93) (7.16) (8.01) (1.91) P A (5.46) (7.70) (1.19) (5.52) (8.19) (2.12) Mean J12-K6 P J12-K6 A t-value (2.48) (0.80) (0.41) (2.83) (1.17) (-0.03) P A (2.48) (2.89) (-0.07) (2.83) (3.00) (0.44) P A (7.85) (6.31) (1.09) (7.65) (6.16) (1.58) P A (7.99) (9.49) (0.37) (7.60) (8.47) (2.33) P A (3.60) (8.26) (0.38) (4.37) (7.48) (1.59) Panel B: Europe Portfolios by price momentum Portfolios by price momentum Portfolios by alpha momentum Portfolios by alpha momentum P5 P1 P5 P1 A5 A1 A5 A1 Mean J12-K1 P J12-K1 A t-value (-1.61) (-2.55) (2.23) (-1.52) (-2.84) (2.94) P A (-1.61) (-0.87) (-1.40) (-1.52) (-0.34) (-2.49) P A (2.65) (1.54) (1.42) (3.19) (0.88) (3.45) P A (5.12) (3.25) (3.20) (4.79) (3.36) (2.47) P A (4.36) (5.25) (2.86) (3.68) (3.75) (2.63) Mean J12-K6 P J12-K6 A t-value (-0.87) (-2.03) (2.08) (-0.51) (-2.11) (2.67) P A (-0.87) (-0.24) (-2.53) (-0.51) (0.42) (-2.67) P A (2.96) (1.59) (2.62) (3.42) (2.22) (2.77) P A (4.14) (3.23) (3.10) (3.79) (3.32) (2.72) P A (3.47) (4.34) (1.98) (2.86) (4.18) (1.64) This table presents the monthly risk-adjusted performance of two-way dependent sorts by price momentum and alpha momentum. For each month t, all stocks with returns for the formation period t 13 to t 2 are first sorted into quintiles according to price momentum (alpha momentum), then further ranked by price momentum (alpha momentum) within each group. The price momentum strategy indicates winner and loser stocks based on raw cumulative returns over the formation months. The alpha momentum strategy ranks stocks based on daily, three-factor-alphas estimated over the formation months. All portfolios are long in an equal-weighted winner portfolio and short in an equal-weighted loser portfolio. For the U.S., Panel A shows the performance of the different strategies from January 1982 to December For Europe, Panel B shows the performance of the different strategies from January 1992 to December Table 4 presents the the risk-adjusted performance (%) for the 12- month formation period and 1-month (6-months) holding period momentum strategies. We use Newey-West (1987) corrected standard errors to get t-statistics that are robust to heteroskedasticity and autocorrelation. 34

37 Table 5 Dominance of momentum strategies in the cross-section of returns Panel A: U.S. r t Mean t-value J12-K1 Intercept 2.03 (4.13) r t (-2.71) log(size) (-6.25) P (1.56) P (-1.28) A (2.03) A (-1.94) P10 P (1.79) A10 A (2.82) J12-K6 Intercept 2.00 (4.27) r t (-2.67) log(size) (-6.46) P (0.10) P (-0.36) A (1.53) A (-2.48) P10 P (0.33) A10 A (2.44) Panel B: Europe r t Mean t-value J12-K1 Intercept 0.64 (1.25) r t (0.61) log(size) (-0.03) P (3.33) P (-2.72) A (2.06) A (-2.49) P10 P (3.87) A10 A (2.82) J12-K6 Intercept 0.66 (1.29) r t (0.74) log(size) 0.11 (0.14) P (1.85) P (-2.08) A (1.46) A (-3.12) P10 P (2.56) A10 A (2.81) This table presents results from monthly cross-sectional regressions of returns on price momentum and alpha momentum. (8) The dependent variable is the one-month future return of stock i in each month t. Independent variables are the market capitalization and the past return in month t 1. P10 (P1) is a dummy variable that equals 1 if stock i s past performance over t 13 to t 2 is ranked in the winner (loser) decile. A10 (A1) is a dummy variable that equals 1 if stock i s past daily alpha over t 13 to t 2 is ranked in the winner (loser) decile. The table reports the mean (%) of the monthly time series of each coefficient. We use Newey-West (1987) corrected standard errors to get t-statistics that are robust to heteroskedasticity and autocorrelation. 35

38 Table 6 Monthly performance of different momentum strategies Panel A: U.S. Price Alpha Price Alpha Alpha Price µ SR α 3F r 3F ajd. µ SR α 3F r 3F ajd. µ SR α 3F r 3F ajd. All investment periods 01/82-12/11 Mean J12-K t-value (1.39) (2.12) (1.19) (3.30) (4.42) (3.60) (4.17) (5.56) (5.25) J12-K (0.01) (0.90) (0.22) (1.65) (2.63) (1.99) (3.33) (5.33) (3.58) 01/82-12/91 J12-K (4.57) (4.92) (4.17) (6.76) (7.56) (6.15) (2.51) (2.87) (1.76) J12-K (3.22) (4.08) (3.59) (4.78) (6.78) (4.38) (2.28) (2.83) (1.39) 01/92-12/01 J12-K (0.86) (1.04) (0.37) (2.08) (2.69) (2.88) (2.18) (3.15) (3.79) J12-K (-0.57) (0.11) (-0.67) (1.07) (2.37) (1.98) (1.88) (2.65) (3.10) 01/02-12/11 J12-K (-0.55) (-0.50) (-1.28) (-0.49) (-0.33) (-0.99) (3.53) (3.49) (3.31) J12-K (-1.13) (-1.28) (-1.69) (-0.89) (-0.83) (-1.05) (2.33) (2.62) (1.61) 36

39 Table 6 continued Monthly performance of different momentum strategies Panel B: Europe Price Alpha Price Alpha Alpha Price µ SR α 3F r 3F ajd. µ SR α 3F r 3F ajd. µ SR α 3F r 3F ajd. All investment periods 01/92-12/11 Mean J12-K t-value (3.78) (4.34) (4.16) (4.77) (5.75) (6.38) (2.85) (4.74) (3.59) J12-K (2.57) (3.06) (3.40) (3.36) (3.96) (5.17) (3.28) (6.09) (4.00) 01/92-12/01 J12-K (3.04) (2.94) (3.16) (3.04) (3.46) (3.89) (1.25) (2.70) (2.04) J12-K (2.47) (2.42) (2.97) (2.20) (2.49) (3.50) (1.70) (4.39) (2.90) 01/02-12/11 J12-K (2.33) (3.25) (2.65) (3.85) (4.89) (5.80) (3.37) (3.98) (3.12) J12-K (1.40) (1.57) (1.94) (2.62) (3.37) (3.89) (3.10) (4.35) (2.83) This table presents the monthly performance of 2x3 momentum strategies. For each month t, all stocks with returns for the formation period t 13 to t 2 are ranked according to three different criteria. The Price Alpha momentum strategy indicates winner and loser stocks that exclusively exhibit cumulative return momentum. Price Alpha is the intersection of those stocks that can be located in the two extreme deciles of both price momentum and alpha momentum. The Alpha Price momentum is based on a subset of alpha but not price momentum stocks. All portfolios are long in an equalweighted winner portfolio and short in an equal-weighted loser portfolio. For the U.S., Panel A shows the performance of the different strategies from January 1982 to December For Europe, Panel B shows the performance of the different strategies from January 1992 to December Table 6 presents the mean returns, Sharpe ratios, FF alphas and the risk-adjusted returns for the 12-month formation period and 1-month (6-months) holding period momentum strategies. All performance numbers are given in %. We use Newey-West (1987) corrected standard errors to get t-statistics that are robust to heteroskedasticity and autocorrelation. 37

40 Table 7 Monthly risk-adjusted performance of different momentum strategies Panel A: U.S. Price momentum P1 P2 P9 P10 P10 P1 Mean J12-K1 Optimistic t-value (-1.16) (0.44) (5.78) (6.46) (3.63) Mild (0.91) (1.84) (5.56) (6.07) (1.62) Pessimistic (2.12) (2.79) (5.63) (4.24) (-0.20) Opt.-Pes (2.71) Alpha momentum A1 A2 A9 A10 A10 A1 Mean J12-K1 Optimistic t-value (-0.36) (0.21) (5.49) (4.91) (3.88) Mild (0.47) (1.10) (6.38) (5.12) (3.21) Pessimistic (1.85) (2.70) (6.39) (5.05) (1.80) Opt.-Pes (1.47) Panel B: Europe Price momentum P1 P2 P9 P10 P10 P1 Mean J12-K1 Optimistic t-value (-2.11) (0.11) (5.31) (6.13) (6.09) Mild (-3.90) (-4.22) (4.58) (4.04) (5.99) Pessimistic (0.65) (-0.11) (2.53) (2.85) (1.55) Opt.-Pes (3.23) Alpha momentum A1 A2 A9 A10 A10 A1 Mean J12-K t-value (-1.97) (-0.90) (5.06) (5.15) (6.22) (-4.34) (-3.69) (3.73) (3.44) (6.62) (0.31) (-0.74) (3.02) (2.48) (1.97) 1.75 (3.03) This table presents the monthly risk-adjusted performance of the winner, loser and zero-investment momentum strategies in different sentiment periods. For each month t, all stocks with returns for the formation period t 13 to t 2 are ranked according to two different criteria. The price momentum strategy indicates winner and loser stocks based on raw cumulative returns over the formation months. The alpha momentum strategy ranks stocks based on daily, three-factor-alphas estimated over the formation months. All portfolios are long in an equal-weighted winner portfolio and short in an equal-weighted loser portfolio. For the U.S., Panel A shows the performance of the different strategies from January 1982 to December For Europe, Panel B shows the performance of the different strategies from January 1992 to December Table 7 presents the riskadjusted performance (%) for 12-month formation period and 1-month holding period momentum strategies. We use Newey- West (1987) corrected standard errors to get t-statistics that are robust to heteroskedasticity and autocorrelation. 38

41 Panel A: U.S. Panel B: Europe Figure 1: This figure shows the overlap between stocks of price momentum and alpha momentum for the formation months t 13 to t 2 for the U.S. (Panel A) and Europe (Panel B). We show the percentage of price momentum winner and loser stocks and their position in the alpha momentum deciles (left scale). The black line presents the negative absolute difference in the monthly factor-related returns between alpha momentum and price momentum for the winner stocks and the difference between alpha momentum and price momentum for the loser stocks (right scale). 39