Risk-managed 52-week high industry momentum, momentum crashes, and hedging macroeconomic risk

Transcription

1 Risk-managed 52-week high industry momentum, momentum crashes, and hedging macroeconomic risk Klaus Grobys¹ This draft: January 23, 2017 Abstract This is the first study that investigates the profitability of Barroso and Santa-Clara s (2015) riskmanaging approach for George and Hwang s (2004) 52-week high momentum strategy in an industrial portfolio setting. The findings indicate that risk-managing adds value as the Sharpe ratio increases, and the downside risk remarkably decreases. Even after controlling for the spread of the traditional 52-week high industry momentum strategy in association with standard riskfactors, the risk-managed version generates economically and statistically significant payoffs. Notably, the risk-managed strategy is partially explained by changes in cross-sectional return dispersion, whereas the traditional strategy does not appear to be exposed to such economic risks. Keywords: asset pricing, momentum crash, industry momentum, optionality effect, 52-week high momentum JEL classification: G12, G14 ¹ K. Grobys Department of Accounting and Finance, University of Vaasa, Wolffintie 34, Vaasa, Finland klaus.grobys@uwasa.fi; grobys.finance@gmail.com 1

2 1. Introduction The persistence and pervasiveness of the momentum anomaly, documented first by Jegadeesh and Titman (1993), has been discussed in the literature for more than two decades. Moskowitz and Grinblatt (1999) extended Jegadeesh and Titman s (1993) study by proposing industrial momentum strategies, and argued that stock price momentum is primarily driven by industry factors. George and Hwang (2004) proposed further extensions to the traditional momentum strategy, referred to as 52-week high momentum strategies. The 52-week high momentum strategy invests in stocks that are near to their 52-week high prices and sells stocks that exhibit the largest distances to their 52-week high prices. George and Hwang (2004) compare their strategy to both strategies Jegadeesh and Titman s (1993) traditional stock momentum, and Moskowitz and Grinblatt s (1999) industrial momentum. They argue that the 52-week high momentum returns will yield higher returns than those achieved through the normal momentum strategy. In a recent paper, Daniel and Moskowitz (2016) show that momentum returns are subject to remarkable crashes occurring during strong market reversals during bear market states. Barroso and Santa-Clara (2015) emphasize that in 2009, the traditional momentum strategy in line with Jegadeesh and Titman (1993) experienced a crash of % in three months. They argue furthermore that it takes decades to recover from these sudden crashes, and momentum returns do not compensate an investor with reasonable risk aversion for these strings of enormous negative payoffs. In their paper, the authors propose a strategy to manage the downside risk of momentum strategies by estimating the risk of momentum by using the realized variance of daily returns. They find that the variance of the zero-cost portfolio is highly predictable. The Sharpe ratio of their proposed risk-managed momentum portfolio is 83% higher and, as a consequence, risk-managed momentum may even be a much greater puzzle than the traditional strategy. While Plessis and Hallerbach (2015) explore two types of volatility weightings applied to cross-sectional and time-series momentum strategies, employing 49 US industry portfolios, there is no study available that investigates the effects of Barroso and Santa- Clara s (2015) recently proposed risk-managing approach in an industrial portfolio setting, employing George and Hwang s (2004) 52-week high momentum strategy. This is the first paper that extends Barroso and Santa-Clara s (2015) risk-managed momentum to industrial portfolios employing George and Hwang s (2004) 52-week high 2

3 momentum strategy. This study employs 48 value-weighted Fama and French industry portfolios and sorts all available industries by the nearness to their 52-week high/low price into four portfolio groups (PG). The first PG 1 contains those industries that are nearest to their 52-week high process on the last trading day before portfolio formation, whereas PG 4 contains those that exhibit the largest distance to the 52-week high prices. The zero-cost strategy is long on PG 1 and short on PG 4. The variances of the zero-cost portfolio are forecasted in the same manner as detailed in Barroso and Santa-Clara (2015), and employed to estimate the scaling factor to either leverage or deleverage the invested amount in the strategy. Using a sample period from July 1928 until August 2015, the portfolios are risk-adjusted using the standard Fama and French (1993) three-factor model. Moreover, Daniel and Moskowitz s (2016) optionality regressions are employed to explore potential momentum crash risks. Finally, motivated by recent literature that establishes links between momentum and cross-sectional return dispersion (Connolly and Stivers, 2003, Stivers and Sun, 2010, Grobys, Kolari and Heinonen, 2017), the effects of changes in cross-sectional industry return dispersion on the 52-week high industry momentum and the risk-managed counterpart are explored in detail. Various robustness checks complete the study. This paper contributes to the literature in many important ways. First, this is the first paper that extends Barroso and Santa-Clara s (2015) risk-managing approach to George and Hwang s (2004) 52-week high momentum in an industry setting. Barroso and Santa-Clara (2015, p.112) emphasize that managing the risk of momentum not only avoids its worse crashes but also improves the Sharpe ratio in the months without crashes. Second, this is also the first paper that investigates the presence of crash risks in terms of potential optionality effects in the spirit of Daniel and Moskowitz (2016) in a 52-week high industry momentum, as proposed by George and Hwang (2004). Daniel and Moskowitz (2016) show that even though momentum appears to be persistent and Asness, Moskowitz, and Pedersen (2013) document the ubiquity of momentum payoffs across asset classes, momentum payoffs seem to be subject to remarkable crashes. There is no study available that investigates those crashes in the context of George and Hwang s (2004) 52-week high industry momentum setting. In doing so, I also explore the effects of Barroso and Santa-Clara s (2015) risk-managing approach on potential momentum crash risks. Finally, recent literature documents a link between momentum return and cross-sectional returns dispersion (Connolly and Stivers, 2003, Stivers and Sun, 2010, Grobys, Kolari and Heinonen, 2017). Chichernea et al. (2015, p.147) argue that RD is likely to capture the uncertainty associated 3

4 with economic transitions and the flexibility of adaptability to fundamental economic restructuring. This is the first study that investigates whether or not the payoffs of George and Hwang s (2004) 52-week high industry momentum strategy or the risk-managed version, employing Barroso and Santa-Clara s (2015) risk-managing strategy, is exposed to macroeconomic risk, proxied by cross-sectional industry return dispersion. The findings of this study indicate that the risk-managed 52-week high industry momentum strategy generates higher expected returns and lower volatility than the original version confirming Santa-Clara s (2015) finding in the U.S. stock market setting. This result also confirms Plessis and Hallerbach (2015), who document that weighting Moskowitz and Grinblatt s (1999) industrial momentum strategy with its own volatility increases the Sharpe ratio and decreases the downside risk. Notably, even though the risk-managed 52-week high industry momentum strategy is highly correlated with the traditional version, it generates 25 basis points risk-adjusted excess payoffs per month (i.e., after controlling for the traditional 52- week high industry momentum strategy) with a Newey-West (1987) t-statistic of 3.71 which suggests a robust result (see Harvey, Liu, and Zhu 2016). Surprisingly, neither the 52-week high industry momentum strategy nor the risk-managed counterpart, are subject to Daniel and Moskowitz s (2016) optionality effects. Finally, while the returns of the traditional 52-week high industry momentum strategy are not systematically varying with changes in cross-sectional industry return dispersion, the risk-adjusted counterpart appears to be a hedge for macroeconomics risk. This result is in line with Grobys, Kolari and Heinonen (2017), who establish a robust link between changes in the state of cross-sectional currency return dispersion and currency momentum in finding that momentum payoffs are significantly higher in bad economics states. This study finds that the payoff difference between high cross-sectional industry return dispersion and low cross-sectional industry return dispersion is positive and statistically significant on a common 5% significance level. This paper is organized as follows. The next section describes the data. The third section provides the empirical framework. The last section concludes. 4

5 2. Data I downloaded daily and monthly data for 48 value-weighted industry portfolios, and monthly data for 25 value-weighted portfolios sorted by size and book-to-market ratio from Kenneth French website. The sample period is from July, until September 30, Moreover, I used the matrix of daily industry returns to calculate the daily price series for all industries. 3. Methodology 3.1. Portfolio analysis In the following, I describe how the 52-week high momentum strategy was implemented. In the first iteration, starting at August 1927, I sorted all industry portfolios for which data was available in to quartiles. The first quartile comprises one fourth of all available industries that exhibited the lowest relative distance to their 52-week high and the last trading day in July 1927, that is, the last trading day of the preceding month before portfolio formation. The fourth quartile comprises one fourth of all available industrial portfolios that exhibited the highest relative distance to their 52-week high and the last trading day in July. The zero-cost portfolio is long on PG 1 and short on PG 4. This procedure was updated at the beginning of each month. In Table 1 the descriptive statistics are reported. From Table 1 we observe that the sample average return (raw return) linearly decreases as we move from portfolio group 1 (PG 1) to portfolio group 4 (PG 4). The zero-cost strategy generates a payoff of 0.61% per month. The Newey-West t-statistic of 3.96 suggests a robust result (see Harvey, Liu, and Zhu 2016). The zero-cost portfolio exhibits a maximum (minimum) return of 26.03% (-48.59%) over the sample period. Moreover, the skewness is negative and implies a crash risk Risk-managing the 52-week high industry momentum strategy Next, I followed Barroso and Santa-Clara (2015) and used an estimate of the 52-week high industry momentum risk to scale the exposure to the strategy to have a constant risk over time. For each month t, I compounded the variance forecasts, from daily returns in the previous period j. Let, be the monthly returns of the 52-week high industry momentum strategy and,,{ } be the daily returns and the time series of the dates of the last trading sessions of each month. Then the variance forecasts were estimated as 5

6 = 21, /251. (1), In my notation, WML is the zero-cost 52-week high industry momentum portfolio. Then I used the forecasted variances to scale the returns as =,, (2), where, is the unscaled momentum payoff at time t,, is the scaled or risk-managed momentum, and is a constant corresponding to the target level of volatility. As documented in Barroso and Santa-Clara (2015), scaling corresponds to having a weight in the long and short legs that is different from one and which varies over time. Furthermore, I followed Barroso and Santa-Clara (2015) and chose = 12%. I also report the distribution of the weights over time (see Figure 1). The weights for the scaled 52-week high industry momentum range between 0.01 and 2.54 which is in line with the figures documented in Barroso and Santa-Clara (2015), who report weights varying between 0.13 and 2.00 for the scaling factor. The results reported in Table 1 are very similar to those documented in Table 3 in Barroso and Santa-Clara s (2015) research: As we move from the traditional to the risk-managed strategy, we observe that the kurtosis drops from (23.52) to 2.68 (5.65) for the momentum strategy (52- high momentum strategy) is implemented in stocks (industrial portfolios). Similarly, we observe that the skewness improves from (-2.05) to (-0.57) when comparing the results from Table 3 in Barroso and Santa-Clara s (2015) study with Table 1 in this study Risk-adjusting the plain and risk-managed 52-week high industry momentum strategies Next, to risk-adjust the payoff I first regressed the plain 52-week high zero-cost industry momentum portfolio successively on the standard risk-factors of the Fama and French (1993) three-factor model. The results are reported in Table 2. From Table 2 we observe that the intercept exhibit an economic magnitude of 0.92% per month and is statistically significant on any level. The strategy is negatively exposed to the stock index. Interestingly, the strategy is not significantly exposed to any other risk factor. Notably, the last row in Table 2 shows that the 6

7 loading against the industry momentum factor is virtually zero. This result implies that those two investment strategies are in essence statistically orthogonal. This result confirms George and Hwang (2004, p.2154), who find that Moskowitz and Grinblatt s (1999) industrial momentum and the 52-week high industry momentum strategy are two different strategies, and combining them would improve profits from momentum investing. Furthermore, the Fama and French (1993) three-factor is capable of explaining roughly one third of the strategy s return variation. Second, I employed the risk-managed version of the 52-week high zero-cost industry momentum portfolio and risk-adjusted the strategy by regressing the payoffs on the Fama and French (1993) three-factor model. The results are reported in Table 3. While the risk-adjusted payoffs are very similar to those of the plain strategy, we observe that the risk-managed version is slightly exposed to big stocks, implied by the significantly negative loading against the size factor in all model specifications. Like the plain strategy, the risk-managed strategy is statistically uncorrelated with the standard industry momentum strategy because the loading against the momentum factor is statistically not different from zero, irrespective of which model is taken into account. Unsurprisingly, once the spread of the plain 52-week high industry momentum portfolio is included in the regression model, we observe that the loading is significantly positive. The economic magnitude was estimated at 0.66% and economically large. Interestingly, even after controlling for the spread of the plain strategy, risk-managed counterpart exhibits a risk-adjusted average return of 25 basis points per month that remain unexplained by other risk-factors. Also, Tables 2 and 3 show that the loadings of the traditional 52-week high industry momentum strategy against the size and value factor are statistically not different from zero on a common 5% significance level. This result confirms Plessis and Hallerbach (2015), who find that the standard 12-1 industry momentum strategy is virtually uncorrelated with other standard risk-factors Potential optionality effects In a recent paper, Daniel and Moskowitz (2016, p. 242) document that in panic states, following multi-year market drawdowns and in periods of high market volatility, the prices of past losers embody a high premium. When poor market conditions ameliorate and the market starts to rebound, the losers experience strong gains, resulting in a momentum crash as momentum strategies short these assets. They argue that in bear market states, when market 7

8 volatility is high, the down-market betas of the past losers are low, but the up-market betas are very large which results in these momentum crashes. The negative skewness of the 52-week high industry momentum strategy, as reported in Table 1, could be an indication that this strategy may be subject to optionality effects. To investigate potential optionality effects of the plain or risk-managed 52-week high zero-cost industry momentum, I used the same optionality regression as in Daniel and Moskowitz s (2016), that is, I estimated the following regression equation: = + +, +,, +,,,, +,, (3) where denotes the zero-cost portfolio of either the 52-week high industry momentum strategy or the risk-managed counterpart at time t. Furthermore, denotes the risk-adjusted return of the unconditional model and denotes the unconditional market sensitivity (e.g., beta)., denotes the value-weighted market factor in excess returns (e.g., excess CRSP returns),, is an ex-ante bear market indicator that has a value of 1 if the cumulative market return in the 24 months leading up to the start of month t is negative, and a value of zero otherwise. The binary variable, is a contemporaneous up-market indicator that has a value of 1 if the excess market return is greater than zero, and a value of zero otherwise. From Table 4 we observe that both strategies do not exhibit the optionality effect, as documented in Daniel and Moskowitz (2016). The point estimates are virtually zero and statistically insignificant. We also observe that only the loading against the market factor is statistically significantly negative. On the one hand, it may be surprising that both strategies the plain 52-week high zero-cost industry momentum portfolio and risk-managed counterpart do not respond to rebounds in bear market states, like the plain momentum strategy implemented among U.S. stocks. On the other hand, the regression results reported in Table 2 and 3 suggest that both strategies are statistically uncorrelated with the plain industry momentum strategy. 8

9 week high industry momentum strategy and cross-sectional return dispersion Chichernea, Holder, and Petkevich, (2015a, 2015b) have established a robust link between cross-sectional return dispersion and the accrual anomaly in both stock and bond markets. In the spirit of Gomes et al. (2003) and Zhang (2005), they employ cross-sectional return dispersion as a macro state variable that encapsulates general investing conditions faced by firms. Another study that is of relevance for this paper is that of Connolly and Stivers (2003), who document that cross-sectional stock return dispersion is associated with momentum payoffs in equity markets. Further, Stivers and Sun (2010) employ cross-sectional return dispersion in stock returns as macroeconomic state variable and find that cross-sectional return dispersion in stock returns is negatively related to subsequent momentum premiums. However, no study has investigated yet the potential relation of the 52-week high industry momentum strategy and cross-sectional industry return dispersion. To explore a potential link between cross-sectional industry return dispersion and the 52- week high industry momentum strategy, respectively, the risk-managed counterpart, I first followed Maio (2016) and estimated the corresponding measure of the cross-sectional return dispersion process in an industrial portfolio setting as follows: =,, (4), where, denotes the monthly value-weighted industry portfolio return of industry i at time t, and = 48. The times series of the three month moving average of is reported in Figure A.1 in the appendix. Next, I regressed the returns of the 52-week high industry momentum strategy successively on and, as well as on the three-month moving averages and to investigate the sensitivities of the 52-week high industry momentum strategies to contemporaneous or lagged cross-sectional industry dispersion measurements. From Table 5 it becomes evident that once cross-sectional industry dispersion is included in the regression model, the intercept of the respective regression models are statistically not different from zero, irrespective of what measure is accounted for. This result is surprising because the correlation between the plain 52-week high industry momentum strategy and cross-sectional industry dispersion does not appear to be statistically significant either. 9

10 Next, I investigated the impact of cross-sectional industry dispersion on the riskmanaged 52-week high industry momentum strategy. The results are reported in Table 6. Unlike the plain strategy, the first four rows of Table 6 suggest that the risk-managed version exhibits statistically significant loadings against the lagged measures and. At the first glance this result suggests that in increase in cross-sectional industry dispersion is associated with a decrease in payoffs of the risk-managed strategy. However, once the vector of excess returns of the CRSP index is included in the regression models, the sensitivity against the respective measure of cross-sectional industry dispersion becomes statistically insignificant. A possible explanation for this phenomenon is a multicollinearity problem. The correlation between the excess returns of the CRSP index and, respectively, is 0.21 and 0.16 with Newey-West (1987) t-statistics of 2.56 and 3.05 indicating statistical significance on a 5% and 1% level. In order to investigate the effect of changes in cross-sectional industry dispersion on 52- week high industry momentum in more detail, I followed the empirical setup in Stambaugh et al. (2012) to design the empirical tests. To investigate profits from various anomalies in the U.S. stock market, the authors divided time series observations for investor sentiment into above and below median values corresponding to high and low investor sentiment. In the same manner, I divided intertemporal observations for cross-sectional industry return dispersion into above and below median values indicating states of high and low cross-sectional industry return dispersion to examine 52-week high industry momentum profits. As in Stivers and Sun (2010) and Chichernea et al. (2015a), I utilized for the sorting procedure the three-month moving averages of cross-sectional industry return dispersion. High (low) dispersion months have three-month cross-sectional industry return dispersion values above (below) their respective sample medians. Average returns are compounded separately for the high and low dispersion months. The results are reported in Table 7. Chichernea et al. (2015a) have argued that states of high cross-sectional stock return dispersion correspond to times of economic stress. Notably, the significant positive difference in average returns between bad and good states of the economy, as reported in Table 7, suggests an insurance-like explanation for the profitability of the risk-managed 52-week high industry momentum strategy because the payoffs are considerably higher in bad states of the economy, that is, in states where the cross-sectional dispersion is high. Interestingly, this finding is line with Grobys, Kolari and 10

11 Heinonen (2017), who find that the currency momentum strategy varies systematically with states of cross-sectional currency return dispersion. Their findings indicate that the payoff differential of the currency momentum strategy between states of high and low cross-sectional currency return dispersion is positive and both statistically and economically significant, implying that currency momentum may act as hedge for global economic risk. On the other hand, the plain strategy does not significantly vary with economic states because the return difference between good and bad state is small and statistically not significant, irrespective of whether or not the market factor is controlled for. Both findings are interesting issues for future research because they are contrary to Connolly and Stivers (2003) and Stivers and Sun s (2010) findings that equity market momentum appears to be procyclical Robustness checks To investigate whether or not the results are sample specific, I divided the sample into two subsamples of equal length and repeat the analysis presented in Table 2 and 3 for the second subsample running from March 1973 to August The results, reported in Table A.2 and A.3 in the appendix, show that the point estimate for the average net risk-managed excess return after controlling for standard risk factors and the plain 52-week high zero-cost industry momentum spread is 0.25% per month, like the estimate for the whole sample reported in Table 3. Next, I employed a different measure of cross-sectional return dispersion to check how sensitive the findings are when employing a different measure of cross-sectional equity return dispersion in the spirit of Maio (2016). In doing so, I downloaded 25 value-weighted Fama and French portfolios sorted by size and book-to-market ratio from Kenneth French website. In Figure A.1 in the appendix, both time series are plotted, the three-month moving average of cross-sectional industry return dispersion, and the corresponding measure using portfolios sorted by size and book-to-market ratio. Visual inspection of Figure A.1 shows that both time series exhibit very similar evolutions. Indeed, the sample correlation is estimated at 0.63, and with a Newey-West (1987) t-statistic of statistically significant on any level. A principal component analysis shows furthermore that the first eigenvalue explains 82% of the overall variation implying that, indeed, both measures are proxies for the same underlying risk. Then again, I divided intertemporal observations for currency RD into above and below median values indicating high and low cross-sectional industry return dispersion to examine 52-week high 11

12 industry momentum profits. The results are reported in Table A.4. in the appendix. We observe that the return difference between turbulent and calm states of the economy for the risk-adjusted risk-managed 52-week high industry momentum strategy is 0.40% per month and statistical significant on a standard 5% significance level. As a consequence, this robustness check confirms the study s previous finding. 4. Conclusion This study investigates the profitability of the risk-managed 52-week high momentum strategy in an industrial portfolio setting. The empirical results confirm that volatility-weighting adds value: The average return increases, the volatility decreases, and the kurtosis and downside risk considerably decreases. The risk-managed strategy generates 25 basis points per month excess payoffs unexplained by standard risk-factors, even after controlling for the spread of the traditional 52-week high industry momentum strategy. The average payoff of the risk-managed version seems to be partially explained by changes in cross-sectional industry return dispersion, while the average payoff of the traditional 52-week high industry momentum strategy are statistically unrelated to changes in economic conditions as proxied by cross-sectional industry return dispersion. Future research may explore the effects of other weighting schemes on 52- week high momentum strategy implemented in both, stocks and industrial portfolios. 12

13 References Asness, Clifford, Moskowitz, Tobias & Pedersen, Lasse, Value and Momentum Everywhere. The Journal of Finance 68, Barroso, Pedro & Santa-Clara, Pedro, Momentum Has Its Moments. Journal of Financial Economics 116, Chichernea, D. C., A. D. Holder, and A. Petkevich, 2015a. Does return dispersion explain the accrual and investment anomalies? Journal of Accounting and Economics 60, Chichernea, D. C., A. D. Holder, and A. Petkevich, 2015b. Why do bondholders care about accruals? The role of time-varying macroeconomic conditions. Proceedings of the 64th Midwest Finance Association Meeting. Connolly, R., and C. Stivers, Momentum and reversals in equity index returns during periods of abnormal turnover and return dispersion. Journal of Finance 58, Daniel, K., Moskowitz, T., Momentum Crashes. Journal of Financial Economics 122, George, T., Hwang, C.Y., The 52-week high and momentum investing. Journal of Finance 59, Grobys, K., Kolari, J., Heinonen, J.-P., Is currency momentum a hedge for global economic risk? Working paper. Harvey, C. R., Y. Liu, and H. Zhu, and the cross-section of expected returns. Review of Financial Studies 29, Jegadeesh, N., Titman, S., Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance 48,

14 Maio, P., Cross-sectional return dispersion and the equity premium. Journal of Financial Markets 29, Moskowitz, T. J. and M. Grinblatt, Do Industries Explain Momentum? Journal of Finance 54, Newey, W. K. and K.D. West, A Simple, Positive Semi-definite, Heteroskedsticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55, Plessis, J.P.D. and W.G. Hallerbach, Volatility Weighting Applied to Momentum Strategies. Journal of Alternative Investments, forthcoming. Stambaugh, R. F., J. Yu, and Y. Yuan, The short of it: Sentiment and anomalies. Journal of Financial Economics 104, Stivers, C., and L. Sun, Cross-sectional return dispersion and time variation in value and momentum premiums. Journal of Financial and Quantitative Analysis 45,

15 Tables Table 1. Descriptive statistics ( ) Risk-managed ( ) Raw return *** (3.96) 0.66*** (5.86) Median Maximum Minimum Std.Dev Skewness Kurtosis JB-statistic (p-value) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) *** Statistically significant on a 1% level. 15

16 Table 2. Risk-adjusting the 52-week high zero-cost industry momentum portfolio This Table reports the risk-adjusted payoffs of the plain 52-weeks high zero-cost industry portfolios. The sample is from July 1928 until August Intercept 0.85*** (6.75) CRSP excess -0.39*** (-6.18) SMB HML MOM R-squared *** -0.34*** * 0.27 (7.78) (-8.22) (-0.87) (1.67) 0.92*** (7.62) -0.34*** (-8.21) (-0.87) -0.18* (-1.67) *** Statistically significant on a 1% level. *Statistically significant on a 10% level (-0.31)

17 Table 3. Risk-adjusting the risk-managed 52-week high zero-cost industry momentum portfolio This Table reports the risk-adjusted payoffs of the risk-managed 52-weeks high zero-cost industry portfolios. The sample is from July 1928 until August Intercept CRSP SMB HML MOM 52-week R-squared excess high 0.81*** -0.24*** 0.14 (7.74 (-7.36) 0.85*** -0.19*** -0.20** (8.57) (-7.72) (-2.30) (-1.49) 0.86*** -0.19*** -0.20** (8.53) (-7.72) (-2.29) (-1.49) (-0.46) 0.25*** 0.04*** -0.11*** *** 0.73 (3.71) (2.64) (-2.58) (1.13) (-0.21) (12.72) *** Statistically significant on a 1% level. ** Statistically significant on a 1% level. * Statistically significant on a 10% level. 17

18 Table 4. Optionality regressions Coeff. Variable Plain strategy Risk-managed strategy α *** (7.55) 0.97*** (8.25) α I (-0.20) -0.67* (-1.66) β R, -0.26*** (6.53) -0.21*** (-5.87) β I, R, (-1.14) (-0.02) β, I, I, R, (-1.14) (-0.82) R Log likelihood ***Statistically significant on a 1% level. 18

19 Table 5. The 52-week high zero-cost industry momentum and cross-sectional return dispersion This Table reports the risk-adjusted payoffs of the plain 52-weeks high industry momentum strategy controlled for cross-sectional return dispersion. The sample is from July 1928 until August

20 Intercept CRSP excess R-squared 1.32 (1.21) (-0.60) (1.03) (-0.10) (0.87) (-0.23) (0.84) 0.08 (0.07) *** 0.24 (0.92) (-0.02) (-8.69) *** 0.24 (0.87) (0.36) (-6.90) *** 0.24 (0.71) (0.20) (-7.14) *** 0.24 (0.92) (0.27) (-6.39) *** Statistically significant on a 1% level. 20

21 Table 6. The risk-managed 52-week high zero-cost industry momentum and cross-sectional return dispersion This Table reports the risk-adjusted payoffs of the risk-managed 52-weeks high industry momentum strategy controlled for cross-sectional return dispersion. The sample is from July 1928 until August

22 Intercept CRSP excess R-squared 1.39*** (3.23) (-1.59) *** (4.64) -0.72** (-1.98) *** (3.52) -0.97* (-1.69) *** (4.66) -0.74** (2.03) *** *** 0.15 (3.09) (-0.86) (-8.66) 1.10*** *** 0.15 (4.09) (-1.12) (-7.58) 1.22*** *** 0.15 (3.43) (-1.14) (-7.83) 1.22*** *** 0.15 (4.49) (-1.56) (-7.37) *** Statistically significant on a 1% level. ** Statistically significant on a 1% level. * Statistically significant on a 10% level. 22

23 Table week high zero-cost industry momentum and states of low versus high crosssectional return dispersion This table reports average excess returns for the 52-week high zero-cost industry momentum strategy in months classified as representing a high or low industry return dispersion state. A period is classified as a low (high) state if the estimated three-month moving average at time 1 of the measure for currency RD is below (above) its median value. The regression equations in Panel B control for the excess returns of the CRSP index. The t-statistics are based on heteroscedasticity and autocorrelation consistent standard errors in Newey and West (1987). The columns headed High-Low test the hypothesis that the difference of the estimated parameters in the high state minus low state equals zero. The sample is from July 1928 until August Panel A. Raw returns High state Low state High-Low Plain strategy 0.74*** (6.97) 0.48* (1.67) 0.26 (0.83) Risk-managed strategy 0.97*** (7.28) 0.37** (2.04) 0.60*** (2.71) Panel B. Risk-adjusted returns High state Low state High-Low Plain strategy 0.98*** (8.89) Risk-managed 1.11*** strategy (8.70) *** Statistically significant on a 1% level. ** Statistically significant on a 1% level. * Statistically significant on a 10% level. 0.71*** (2.84) 0.50*** (3.08) 0.27 (0.96) 0.61*** (2.99) 23

24 Figures Figure 1. Scaling of the risk-managed 52-week high industry zero-cost portfolio This figure plots the investment weights for the 52-week high zero-cost industry portfolio over time. To scale the payoffs, we use a time window of months to estimate the variance forecast. The sample period is from August 1927 to August ,5 2 1,5 1 0,

25 Figure 2. Cross-sectional return dispersion of industry portfolios This figure plots the three-month moving average of the cross-sectional return dispersion of the 48 Fama and French value-weighted industry portfolios. The sample period is from August 1927 to August ,5 3 2,5 2 1,5 1 0,

26 Appendix Table A.1. Descriptive statistics for cross-sectional industry return dispersion measures Mean Median Maximum Minimum Std.Dev. Skewness Kurtosis JB-test (p-value) (0.00) (0.00) 26

27 Table A.2. Risk-adjusting the 52-week high zero-cost industry momentum portfolio This Table reports the risk-adjusted payoffs of the plain 52-weeks high zero-cost industry portfolios. The sample is from March 1973 until August Intercept CRSP excess SMB HML MOM R-squared 0.72*** -0.35*** 0.17 (4.59) (-5.13) 0.81*** -0.34*** -0.22* (5.30) (-5.15) (-1.88) (-1.38) 0.81*** (5.11) -0.34*** (-5.14) (-1.89) (-1.38) *** Statistically significant on a 1% level. *Statistically significant on a 10% level (-0.49)

28 Table A.3. Risk-adjusting the risk-managed 52-week high zero-cost industry momentum portfolio This Table reports the risk-adjusted payoffs of the risk-managed 52-weeks high zero-cost industry portfolios. The sample is from March 1973 until August Intercept CRSP SMB HML MOM 52-week R-squared excess high 0.82*** -0.23*** 0.09 (5.30) (-4.69) 0.89*** -0.20*** -0.24** (5.81) (-4.28) (-2.35) (-1.28) 0.89*** -0.20*** -0.24** (5.79) (-4.26) (-2.34) (-1.27) (-0.17) 0.25*** 0.06*** -0.06** *** 0.78 (2.88) (2.76) (-2.13) (0.63) (-1.28) (10.30) *** Statistically significant on a 1% level. ** Statistically significant on a 1% level. * Statistically significant on a 10% level. 28

29 Table A week high zero-cost industry momentum and states of low versus high crosssectional return dispersion employing portfolios sorted by size and book-to-market ratio This table reports average excess returns for the 52-week high zero-cost industry momentum strategy in months classified as representing a high or low industry return dispersion state. A period is classified as a low (high) state if the estimated three-month moving average at time 1 of the measure for currency RD is below (above) its median value. For compounding the three-month moving average of crosssectional return dispersion, I employed 25 value weighted Fama and French portfolios sorted by size and book-to-market ratio. The data were downloaded from Kanneth French website. The regression equations in Panel B control for the excess returns of the CRSP index. The t-statistics are based on heteroscedasticity and autocorrelation consistent standard errors in Newey and West (1987). The columns headed High-Low test the hypothesis that the difference of the estimated parameters in the high state minus low state equals zero. The sample is from July 1928 until August Panel A. Raw returns High state Low state High-Low Plain strategy 0.61*** (6.64) 0.61** (2.18) (-0.02) Risk-managed strategy 0.85*** (7.32) 0.50*** (2.64) 0.36* (1.66) Panel B. Risk-adjusted returns High state Low state High-Low Plain strategy 0.87*** (8.40) Risk-managed 1.01*** strategy (8.77) *** Statistically significant on a 1% level. ** Statistically significant on a 1% level. * Statistically significant on a 10% level. 0.82*** (3.40) 0.61*** (3.62) 0.05 (0.17) 0.40** (1.96) 29

30 Figure A.1. Three-month moving averages of cross-sectional return dispersion This figure plots the three-month moving averages of the cross-sectional return dispersion of the 48 Fama and French value-weighted industry portfolios (RD 1) and three-month moving averages of the crosssectional return dispersion of the 25 Fama and French value-weighted portfolios sorted by size and bookto-market ratio. 4,5 4 3,5 3 2,5 2 RD 1 RD 2 1,5 1 0,