Residual Momentum and Investor Underreaction in Japan

Transcription

1 Residual Momentum and Investor Underreaction in Japan Rosita P. Chang University of Hawai i rositac@hawaii.edu (1 808) Kuan-Cheng Ko National Chi Nan University kcko@ncnu.edu.tw (886) Shinji Nakano T&D Asset Management Co., Ltd s-nakano@tdasset.co.jp (81 3) S. Ghon Rhee University of Hawai i rheesg@hawaii.edu (1 808) & National Central University (Visiting Professor) Current Draft: October 2016 We would like to express our thanks to David Blitz, Phillip Brown, Zhi Da, Raymond da Silva Rosa, Kartick Gupta, Allaudeen Hameed, Ro Gutierrez, Bruce Grundy, Janice How, Petko Kalev, Qianqiu Liu, Suman Neupane, David Ng, Elizabeth Ooi, Vikash Ramiah, David Solomon, Terry Walter, Peter Verhoeven, Charles Yang, and David Yermack for their comments. We also gained significant benefits from seminar participants of National Central University, Renmin University, Griffith University, Queensland University of Technology, University of South Australia, and University of Western Australia. An earlier version of this paper was presented at the Asian Finance Association 2015 Annual Meeting in June 2015, Changsha, China and the 25 th Anniversary Special Conference of the Korea America Finance Association in June 2016, Seoul, Korea. Rhee is grateful for the 2016 Shidler Summer Research Grant of University of Hawai i. 1

2 Residual Momentum and Investor Underreaction in Japan Abstract We document that the residual momentum strategy, which is constructed to hedge out the risk exposure to the Fama-French factors, is profitable in Japan for short-term holding periods. Residual momentum profits over long-term holding periods are insignificant but do not reverse, unlike traditional total return momentum strategies observed in the U.S. market. The findings in both short- and long-term holding periods are attributed to investor underreaction. The role of investor underreaction remains robust to the control of the confounding variables (such as institutional ownership, idiosyncratic volatilities, and firm age) that are known to lead investor limited attention. JEL Classification: G11; G12; G14. Keywords: Residual momentum; Total return momentum; Japanese market; Investor underreaction; Information discreteness. 2

3 I. Introduction Since the publication of the study by Jegadeesh and Titman (1993), the existence of momentum profits has been widely documented as one of the most pronounced and prevalent anomalies in both U.S. and international stock markets. Despite ample evidence of pronounced momentum profits around the world, the failure of the momentum strategy in the Japanese market is one remarkable exception (Chan, Hameed, and Tong, 2000; Griffin, Ji, and Martin, 2003; Chui, Titman, and Wei, 2010; Fama and French, 2012; Asness, Moskowitz, and Pedersen, 2013; Li and Wei, 2016). In this paper, we compile surprising evidence that the residual momentum strategy, which is constructed to hedge out the risk exposure to the Fama and French factors, is profitable in Japan for short-term holding periods ranging from three to 12 months. We also demonstrate that the residual momentum profits over long-term holding periods ranging from two to five years do not reverse in Japan while they remain insignificant. The residual momentum strategy is traced back to Gutierrez and Prinsky (2007), who introduce two types of momenta: abnormal-return momentum and relative-return momentum. The latter is identical to Jegadeesh and Titman s (1993) total return momentum, whereas the former is the same as the residual momentum later elaborated by Blitz, Huij, and Martens (2011). While observing the success of residual momentum in the U.S. market, Gutierrez and Prinsky (2007) and Blitz et al. (2011) offer different underlying reasons. 1 Gutierrez and Prinsky (2007) believe that institutional investors overreact to traditional momentum strategies while they underreact to residual momentum strategies largely because of their career and reputational concerns. In contrast, Blitz et al. (2011) propose that residual momentum strategies work because time-varying exposures to Fama-Franch factors are minimized as residual returns are used to 1 It should be pointed out that Gutierrez and Prinsky (2007) focus on long-term residual momentum profits whereas Blitz et al. (2010) focus on short-term profits. 3

4 identify winners and losers for portfolio decisions. Blitz et al. (2011) owe this explanation to Grundy and Martin (2001) who observe that the traditional total return momentum has substantial time-varying exposures to Fama-French factors and significant profits can be attained through hedging away these exposures. The Japanese market is a major beneficiary of this residual momentum approach as demonstrated by Chaves (2012), but Chaves does not investigate underlying causes for residual momentum profits in Japan. The first goal of this paper is to investigate whether the residual momentum strategy advanced by Gutierrez and Prinsky (2007) and Blitz et al. (2011) generates significant momentum profits exclusively focusing on the Japanese market. 2 We document that the residual momentum strategy is profitable in Japan for short-term holding periods ranging from three to 12 months. We also find that the residual momentum profits over long-term holding periods ranging from two to five years are insignificant. Nevertheless, an important finding is that long-term momentum profits do not reverse in Japan while the magnitude of residual momentum profits is significant and sustain in the U.S. market (Gutierrez and Prinsky, 2007). Naturally, the agency cost based explanation for the institutional investor behavior is irrelevant in Japan due to the lack of long-term return reversals. Naturally, the main goal of this study is to identify the sources of residual momentum profits in the short-term holding period and no reversal in the long-term profits in Japan. These findings in both short- and long-term holding periods lead us to believe that investor underreaction is the underlying reason. The empirical confirmation of investor underreaction is the second goal of this paper, which has not been done in the past for the Japanese market. Specifically, we utilize the information discreteness (ID) measure based on the 2 Chaves (2012) is credited for investigating the Japanese market but Japan is just one of 21 countries investigated and the length of the portfolio holding period is not even specified. 4

5 frog-in-the-pan (FIP) hypothesis advanced by Da, Gurun, and Warachka (2014) to proxy for the degree of investor underreaction. The FIP hypothesis predicts that investors underreact to information arriving gradually and continuously in small amounts but overreact to information arriving in large amounts at discrete time intervals. We find that the profitability of the residual momentum is attributed to investor underreaction to information and the significant momentum profits are concentrated in stocks with continuous rather than discrete information arrival. Our findings have important implications for the literature on the momentum effect in Japan. First, we indicate that the time-varying exposure to risk factors is an important considen for momentum strategies in Japan. This result is not surprising because Asness (2011) documents that returns to the total return momentum strategy in Japan is the most volatile (with the largest standard deviation of 20.2% and with the lowest average return of 0.7% per year) among several major markets in the United States, United Kingdom, and non-u.k. European region. As the time-varying risk exposures are hedged out, the residual momentum strategies in Japan exhibit higher and more stable profitability with smaller standard deviation. Second, the pronounced profitability of the residual momentum is indicative of investor underreaction to firm-specific information. This finding in Japan is consistent with the gradual-information-diffusion hypothesis: firm-specific information diffuses gradually across the investing public (Barberis, Shleifer, and Vishny, 1998; Hong and Stein, 1999; Hong, Lim, and Stein, 2000; Blitz et al., 2011). This paper s contributions are summarized in three important aspects: First, short-term residual momentum profits are significant. Long-term profits remain insignificant but do not reverse. Second, investor underreaction emerges as the main underlying force that explains short-term momentum profits while investor overreaction is not applicable in Japan because 5

6 reversals are not observed in long-term momentum profits. Third, the role of investor underreaction remains robust after controlling confounding variables (e.g., low institutional ownership, low idiosyncratic volatilities, and young firm age) that are known to lead investor limited attention. II. Residual Momentum vs. Total Return Momentum A. Data Our sample consists of all common stocks listed on the Tokyo Stock Exchange (TSE) from January 1975 to December We obtain daily and monthly returns as well as accounting variables for all sample stocks from the database compiled by the PACAP Research Center. As a proxy for the risk-free interest rate, we use a combined series of the call money rate (from January 1975 to November 1977) and the 30-day Gensaki (repo) rate (from December 1977 to December 2011). Both the call money and repo rates are also retrieved from the PACAP database. B. Construction of Momentum Strategies We follow the procedures proposed by Blitz et al. (2011) to construct the standard residual momentum strategy. At the beginning of each month t, we perform the time-series regression for each individual stock using the Fama-French three-factor model expressed as follows: ri,t r f,t=α i+mi MKT t+sismb t+hi HML t+ε i,t, (1) where r i,t is the return on stock i in month t; r f,t is the risk-free rate in month t; MKT t, SMB t, and HML t are the realized returns on the market and two mimicking portfolios for size and book-to-market in month t, respectively; 3 α i, m, s i, and i h i are the coefficients to be estimated; 3 We follow the procedure of Fama and French (1993) to construct SMB and HML factors based on individual firm size and BM with an annual rebalancing starting from October of each year because many TSE-listed firms have the 6

7 and ε i,t is the residual return of stock i in month t. We use a three-year window to estimate Equation (1): at the beginning of each month t, the regressions are estimated over the period from t 36 to t 1. 4 Once we obtain the residual returns ( ε i,t ) from Equation (1), we calculate the average residual return over the past 12 or 6 months excluding the most recent month (i.e., from t 12 to t 2 or from t 6 to t 2) standardized by the standard deviation of the residual returns over the same period. We construct the residual momentum strategy (denoted as rmom 12,2 and rmom 6,2, respectively) by ranking individual stocks based on their values of the average standardized residual return into deciles. rmom 6,2 is considered because of Novy-Marx s (2012) findings that U.S. market momentum is not driven by firms performance six to two months prior to portfolio formation. Stocks with an average standardized residual return ranked at the top 10% are defined as winners, and those ranked at the bottom 10% are defined as losers. These portfolios are equally weighted. As performed by Jegadeesh and Titman (1993, 2001), the momentum strategy involves taking a long position in the winner portfolio and taking a short position in the loser portfolio for the subsequent K months (K = 3, 6, 9, and 12) using the overlapping approach. Specifically, the momentum return in month t is calculated as the return difference between the winner and loser portfolios, averaged across K separate positions, each formed in one of the K consecutive prior months from t K to t 1. We test the average returns with t-statistics adjusted end of March as their fiscal year-end and the accounting information becomes available before September (Daniel, Titman, and Wei, 2001). 4 We also apply a five-year window to replicate the analyses following representative studies (Fama and French, 1992; Shanken, 1992; Brennan, Chordia, and Subrahmanyam, 1998; Avramov and Chordia, 2006). The results remain virtually unchanged. 7

8 for autocorrelation and heteroskedasticity using Newey and West s (1987) correction of standard errors. To contrast with the residual momentum strategies, we construct Jegadeesh and Titman s (1993) total return momentum strategies (denoted as MOM 12,2 and MOM 6,2 ) by using the average total return over the past 12 or 6 months excluding the most recent month to measure past performance. Again, the momentum profits to the strategies involve buying the top decile and short selling the bottom decile with 3-, 6-, 9-, and 12-month holding periods. C. Short-Term Profits of Momentum Strategies Panels A and B of Table 1 report the average returns of the two residual and total return momentum strategies for the holding periods of 3, 6, 9, and 12 months. The risk-adjusted returns are measured by Jensen s alphas from the Fama-French three-factor model. The most dramatic finding from the third row of both Panels A and B is that the residual momentum strategy yields significant profits, whereas the total momentum strategy does not. In particular, momentum profits for the rmom 6,2 strategy in Panel B are significant for all holding periods, which indicates no reversal. The rmom 12,2 strategy produces profits only for the first six months, but the profits disappear afterward. In contrast, the total return momentum strategy yields no significant profits for all holding periods and displays faster and stronger reversals as indicated by negative profits. The stable momentum profits for the rmom 6,2 strategy suggest that its profitability is not transient and is more persistent over time than the rmom 12,2 strategy. Apparently, Novy-Marx s (2012) findings from the U.S. market are not supported in Japan. 5 [Insert Table 1] 5 This finding is consistent with the results of Goyal and Wahal (2015), who document no evidence in supporting Novy-Marx s (2012) result in international stock markets, including Japan. 8

9 We also observe that total return-based momentum produces negative s for all holding periods under MOM 12,2 and MOM 6,2, which is a stark contrast from the residual momentum s positive s reported in Panels A and B. Our findings reveal that the failure of the momentum in Japan is primarily due to the time-varying exposures to the Fama-French factors. Once the risk exposures are hedged out, we observe significant and persistent profits for the residual momentum strategy, particularly when recent past returns (rmom 6,2 ) are used to evaluate a stock s performance. D. Long-Term Profits of Momentum Strategies The literature generally asserts that investor overreaction results in long-term reversals but investor underreaction does not (Daniel, Hirshleifer, and Subrahmanyam, 1998; George and Hwang, 2004; Blitz et al., 2011; Da et al., 2014). Therefore, it is important to observe that the long-term residual momentum profits do not exhibit reversals and they are generated by investor underreaction in Japan. Hence, we compute the residual momentum profits for the longer holding periods from two to five years after the portfolio formation. The risk-adjusted returns and s to both residual and total return momentum strategies are reported in Panels C and D of Table 1. The most interesting finding is that profits to the residual momentum strategies (for both rmom 12,2 and rmom 6,2 ) display no reversals for up to five years, whereas profits to the total return momentum strategies (MOM 12,2 and MOM 6,2 ) exhibit significant reversals. These trends are confirmed by the evidence that none of residual momentum profits across all long-term holding horizons is significant, whereas all total return momentum profits are negative. It is interesting to observe that Japanese and U.S. markets exhibit dramatic contrasts: First, for the short-term holding period, Gutierrez and Prinsky (2007) report that both residual and total 9

10 return momentum strategies are similar by producing significant returns whereas our results indicate that only residual return momentum yields significant positive returns in Japan. For the long-term holding period, Gutierrez and Prinsky (2007) report that total return momentum reverse strongly while residual return momentum continues in the U.S. market. Our results indicate that: (i) total return momentum reverses (which is consistent with those of Gutierrez and Prinsky (2007)); but (ii) residual momentum does not reverse whereas the U.S. market residual momentum continues. Overall, the lack of reversals and stronger persistence of the residual momentum profits point to investor underreaction, which is examined further in the following section. III. Why Residual Momentum Works in Japan? A. The Frog-in-the-Pan (FIP) Hypothesis and Information Discreteness In a recent study, Da et al. (2014) test the FIP hypothesis to explain momentum profits. Motivated by the notion that a series of gradual and small price changes attracts less attention than sudden dramatic price changes, they propose a proxy for information discreteness (ID) that captures the relative frequency of small signals. 6 Specifically, ID is defined by the signs of daily returns underlying the cumulative residual returns during the formation period. Their findings indicate that continuous information (i.e., lower IDs) induces stronger return continuation and momentum profits that do not reverse in the long run because investors tend to underreact to such information. We hypothesize that if the profitability of the residual momentum in Japan is induced by investor underreaction, it is stronger among stocks with lower IDs than those with higher IDs. To 6 Huynh and Smith (2015) propose an alternative attention measure based on news of individual stocks. They compile evidence in support of investor underreaction in explaining momentum returns in four regions, including the United States, Europe, Japan, and Asia Pacific. 10

11 test this hypothesis, we apply a double-sorting procedure based on individual stock ID values and past residual returns to observe the momentum profits within each ID group. We use ID as a proxy for underreaction in assuming that any signals with absolute values below a lower threshold during the first period are not processed by FIP investors until the second period when the information is realized in a two-period model. We follow the Da et al. (2014) approach to distinguish continuous information from discrete information during the formation period of the momentum strategy by defining the ID measure as follows: ID = sgn(pret) [%neg %pos], (2) where PRET is denoted as the cumulative return during the formation period. We use the cumulative residual return and total return calculated based on the formation periods (from t 6 to t 2) to proxy for PRET for residual and total return momentum strategies, respectively; %neg and %pos denote the percentages of days with positive and negative residual (or total) returns during the formation period. The sign of PRET is denoted as sgn(pret), which equals +1 when PRET > 0 and 1 when PRET < 0. By construction, a higher value of ID signifies discrete information, whereas a lower value of ID indicates continuous information. According to Equation (2), higher percentages of positive (negative) returns culminating in positive (negative) PRETs yield lower values of ID. In such cases, positive (negative) PRET is formed by a large number of small positive (negative) returns with continuous information. A higher value of ID, however, implies that the positive (negative) PRET is generated by a few large positive (negative) returns, whereas the majority of daily returns are negative (positive). Such small amounts of large positive (negative) returns in generating the positive (negative) PRET tend to be discrete information. The median ID score for our sample stocks is , indicating that investor underreaction is prevailing in Japan. 11

12 B. Momentum Profits Conditional on Information Discreteness To examine whether the FIP hypothesis explains the return patterns of momentum strategies in Japan, we adopt a double-sorting procedure based on individual stock past residual (or total) returns and ID values. 7 In each month t, we first sort individual stocks into quintiles according to their ID values. Within each ID group, we further allocate stocks into quintiles based on their standardized residual or total returns over month t 6 to t 2 (rmom 6, 2 or MOM 6,2 ). For each ID group, we calculate equally weighted momentum profits as the differences between the winner and the loser portfolios for the subsequent K months (K = 3, 6, 9, and 12) using the overlapping approach. We report average monthly momentum profits with Fama-French risk adjustment (i.e., Jensen s alpha) and s of both residual and total return momentum strategies conditional on the ID measure in Table 2. Panel A reports results for the momentum profits based on individual stocks residual returns estimated over the past six to two months (rmom 6,2 ), whereas Panel B reports those for the total return momentum profits over the past six to two months (MOM 6,2 ). Figures 1 and 2 present graphical illustns of the risk-adjusted returns and s of residual and total return momentum strategies across several holding horizons and ID groups. Specifically, the residual momentum profits and corresponding s are remarkably higher in the continuous ID group than in the rest of the ID groups. Despite the differences across ID groups, the residual momentum generates positive returns and s in most cases. In contrast, the returns and s of the total return momentum are mostly negative, with the sole exception of the continuous ID group. [Insert Table 2 and Figures 1 and 2] 7 Hereafter, we report only the results for rmom 6,2 and MOM 6,2 strategies to save space. The results for other formation periods are qualitatively identical. These results are available upon request. 12

13 The overall results support the FIP hypothesis in explaining the profits from the residual momentum strategy (rmom 6,2 ); the momentum profit for the average 3-month holding period is 0.428% per month for the bottom quintile ID group stocks, but it declines to % per month for the top quintile ID counterparts. The results are consistent with the FIP hypothesis that the profitability of the residual momentum based on recent past performance is explained by investor underreaction to stock information. In contrast, total return momentum profits are insignificant for all holding periods. In addition, the s of the rmom 6,2 strategy for the bottom quintile ID group stocks are consistently greater than those stocks with higher ID measures. Even for the total return momentum strategy, MOM 6,2, we observe that ID measures do affect the s. Only the bottom quintile ID group has positive s, whereas all other ID groups exhibit negative s. C. Direct Evidence on Information Discreteness: Earnings Forecast Error Although our results in Table 2 confirm that the FIP hypothesis explains the residual momentum profits, we want to demonstrate the crucial role of investor underreaction in the Japanese market. After reviewing a few alternatives, we decide to demonstrate the direct link between investor underreaction and earnings forecast errors. 8 The intuition underlying this test is that, if low ID scores indeed capture limited investor attention, analysts would be slow in adjusting their forecasts for low ID firms, resulting in larger forecast errors for such firms. To confirm this prediction, we obtain analysts annual earnings per share (EPS) forecasts for Japan from the Institutional Brokers Estimate System (I/B/E/S). Following Livnat and Mendenhall (2006) and Da et al. (2014), we define earnings surprises (denoted as SURP) as the difference 8 For example, Griffin and Tversky (1992) and Barberis, Shleifer, and Vishny (1998) suggest that investors underreact to sporadic news. DellaVigna and Pollet (2009) show that investors tend to underreact to firms post-earnings announcement on Friday. George and Hwang (2004) and Li and Yu (2012) indicate that the nearness to the 52-week high price is a proxy for underreaction. Frazzini (2006) demonstrates that the disposition effect induces underreaction to news using mutual fund data. 13

14 between a firm s actual EPS and the median of analyst forecasts issued within 90 days before the earnings announcement. This difference is then standardized by the firm s share price on its earnings announcement date. We then perform cross-sectional regressions of SURP on a set of variables including ID, past performance, and other variables that may affect the accuracy of analyst forecasts in the following forms: and SURP i,t = β 0 + β 1 ID i,t + β 2 PRET i,t + β 3 ID i,t PRET i,t + ε it,, (3) SURP i,t = β 0 + β 1 ID i,t + β 2 PRET i,t + β 3 ID i,t PRET i,t + β 4 COV i,t + β 5 BM i,t + β 6 SIZE i,t + β 7 TURN i,t + β 8 IO i,t + β 9 AGE i,t + ε it,, (4) where ID is the information discreteness defined using residual or total returns. PRET is residual or total returns. COV is analyst coverage, which is the number of analysts following the firm. BM is book-to-market and SIZE is market capitalization. TURN is turnover, which is defined as the monthly trading volume divided by the total number of shares outstanding. IO is institutional ownership. The IO of a given stock is defined as the number of shares held by institutions divided by the total number of shares outstanding. AGE is firm age, proxied by the number of years the firm has been listed on TSE. We obtain all necessary data from the PACAP database. The FIP hypothesis predicts a negative β 3 coefficient for the interaction between ID and PRET. In particular, a negative β 3 coefficient indicates that past winners (losers) with lower ID have larger positive (negative) forecast errors, implying analysts underreaction to the earnings forecasts. As reported in Panel A of Table 3, the β 3 coefficient of Equation (3) is significantly negative at , with a t-statistic of -3.21, confirming the prediction that analysts are slower in incorporating continuous residual information into their forecasts than discrete residual 14

15 information. This observation remains the same when additional control variables are included in the regression model. This result indicates that the underreaction of analysts to continuous residual information is a special channel that drives the relation between residual momentum and ID. The same applies for the total return momentum, which is reported in Panel B. The β 3 coefficients are significantly negative in both specifications at and -3.50, suggesting that the results of Da et al. (2014) regarding analyst underreaction to the information embedded in total return are also robust in Japan. 9 Finally, Table 3 indicates that firms with higher analyst coverage and institutional ownership and lower BM and turnover are subject to higher earnings forecast errors, which suggests that various firm characteristics may also be related to analyst underreaction. [Insert Table 3] IV. Investor Underreaction and Time Variation of Momentum Profits Because the Japanese economy has experienced dramatic changes over the past three decades, our next task is to examine the crucial role of investor underreaction in the time variation of residual momentum profits. Time-varying patterns of momentum profits in the U.S. market have been compiled in several recent studies: (i) business cycles by Chordia and Shivakumar (2002); (ii) up and down markets by Cooper, Gutierrez, and Hameed (2004); (iii) return dispersions by Strivers and Sun (2010); (iv) market volatilities by Wang and Xu (2015); (v) market liquidity by Avramov, Cheng, and Hameed (2015); and (vi) momentum crashes by Daniel and Moskowitz (2016). Our goal in this section is to assess the role of investor underreaction as we consider these six conditioning variables in the Japanese market even though they are not necessarily mutually exclusive. 9 The large difference observed in estimated β 3 coefficients in Panels A and B may be attributed to the fact that residual returns are net of Fama-French factors whereas total returns are not. 15

16 A. Effects of Business Cycles Chordia and Shivakumar (2002) suggest from the risk-based perspective that the profitability of momentum is explained by common macroeconomic variables that are associated with business cycles. The authors indicate that the returns of the total return momentum in the U.S. market are significantly positive during expansionary periods and insignificantly negative during recessionary periods. However, Blitz et al. (2011) demonstrate that the residual momentum in the United States generates significantly positive returns regardless of business cycles because the strategy has hedged out the exposures to the systematic risk by construction. To examine the impact of business cycles on our results, we follow Chordia and Shivakumar (2002) in classifying holding periods as expansionary or recessionary periods, based on the Cabinet Office (Japan) definition, and calculate the profits to the momentum strategies conditional on the ID values in each of these environments. 10 Panel A of Table 4 presents the risk-adjusted momentum profits to the rmom 6,2 across quintile ID subgroups during different periods of business cycles. To save space, we report the results only for the lowest ID quintile group (labeled as the continuous group) and the highest ID quintile group (labeled as the discrete group) stocks. Four findings emerge: first, the momentum profits to the rmom 6,2 strategy are greater for the continuous group stocks than the discrete group stocks regardless of expansionary and recessionary periods the Japanese market experiences; second, residual momentum profits are greater for the continuous group stocks than the discrete group stocks for all holding periods of 3, 6, 9, and 12 months; third, residual momentum profits for the continuous group are significant only for the holding period of three months during recessionary periods, whereas expansionary periods exhibit significant profits for 10 Refer to 16

17 all holding periods; and fourth, the s of the continuous group stocks are consistently greater than those for the discrete group stocks. In contrast, momentum profitability of total return momentum remains insignificant for both expansionary and recessionary periods. Although they are insignificant, the overall patterns appear similar to those of residual momentum profits. [Insert Table 4] To summarize, the overall results in Panel A of Table 4 suggest that concentrating on expansionary periods enhances the profitability of the residual momentum in Japan when it is induced by investor underreaction. This evidence is consistent with Chordia and Shivakumar s (2002) observation that business cycles play an important role in explaining the momentum premium. B. Effects of Market States Cooper et al. (2004) establish the link between market states and the profit to the total return momentum for the U.S. market. They indicate that the total return momentum is profitable only in up markets because investor biases are more accentuated after market gains. Because investor underreaction represents a form of behavioral bias, we expect that the underreaction-driven residual momentum profits would be enhanced subsequent to up markets. To consider the effects of market states, we follow Cooper et al. (2004) and classify each holding period as UP or DOWN market state. Specifically, at the beginning of each month t, we calculate the buy-and-hold return on the value-weighted market index over the 12 months prior to the holding period of the momentum strategy. If this return is positive (negative), we classify the market state of month t as UP (DOWN). 11 We then calculate the risk-adjusted momentum returns 11 We also replicate the analysis by using the buy-and-hold market returns over the past 24 or 36 months and obtain 17

18 and s of the rmom 6,2 and MOM 6,2 strategies conditional on ID separately for the UP and DOWN markets and report the results in Panel B of Table 4. The pronounced momentum profits to the rmom 6,2 strategies are generally concentrated in the continuous group stocks following UP market states. In terms of the rmom 6,2 strategy in Panel B, the 3-, 6-, 9-, and 12-month monthly risk-adjusted returns of the continuous group stocks following UP markets are 0.577%, 0.446%, 0.438%, and 0.394%, respectively. The profits decrease to %, %, %, and %, respectively, after experiencing the DOWN market state. Furthermore, the discrete group stocks do not generate significant momentum profits following both the UP and DOWN market states. The evidence in favor of market states predicting the time-series patterns of the continuous group stocks supports our intuition that investor underreaction plays a key role in explaining the behavioral biases following a string of market gains. When the degree of behavioral bias is low, i.e., following periods of market declines, return continuation disappears because investors have a lower tendency to underreact to firm information. C. Effects of Market Return Dispersions Recent theoretical and empirical work suggests that (i) the momentum profits are procyclical, implying that they are larger during stronger economic times; and (ii) cross-sectional dispersion in stock returns is countercyclical in the U.S. market (Gomes, Kogan, and Zhang, 2003; Stivers, 2003; Avaramov and Chordia, 2006). As a result, it is not surprising that Stivers and Sun (2010) report a negative relation between the return dispersion (RD) and subsequent momentum profits. Using the RD as a conditioning variable, we examine the role of investor underreaction in Japan. Following Stivers and Sun (2010), we calculate the cross-sectional similar results. The results are available upon request. 18

19 standard deviation of the monthly stock returns using size-bm sorted portfolios as the RD measure for each month. To identify whether a given month t of the holding month for the momentum strategies belongs to high or low RD, we calculate a three-month RD moving average from t 3 to t 1. If the value of this three-month RD moving average in month t is higher than the median value of the time-series over our sample period, we classify month t as high RD; otherwise, it is classified as low RD. We then calculate the risk-adjusted momentum returns and s of the rmom 6,2 and MOM 6,2 strategies conditional on ID separately for periods of high and low RD and report the results in Panel C of Table 4. The results in Panel C support our prediction that investor underreaction matters in yielding both residual and total return momentum profits in Japan. The continuous group stocks (with low ID measures) exhibit significant momentum profits during both high and low RD periods, whereas discrete group stocks (with high ID measures) display insignificant profits during both periods. 12 D. Effects of Market Volatilities Motivated by the observation that high stock market volatilities during periods of dramatic market declines are followed by a string of dramatic losses of momentum strategies, Wang and Xu (2015) confirm that market volatility is negatively correlated with the momentum profit in the U.S. market. Following Wang and Xu (2015), we compare the relative strength between short- and long-term market volatilities: for each month t, we calculate the volatilities of the daily returns on the value-weighted market index over the past 12 months (from month t 12 to t 1) and 36 months (from month t 36 to t 1). If the lagged 12-month volatility is larger (smaller) than the lagged 36-month volatility, we define month t as high (low) market volatility. 12 Interestingly, the negative relation is not observed between RD and momentum profits in Japan unlike in the U.S. market, whereas the role of investor underreaction is clearly demonstrated. 19

20 We examine the effect of ID on residual and total return momentum separately for periods of high and low market volatilities to confirm the role of investor underreaction in Japan. The results in Panel D of Table 4 indicate that both market volatilities and investor underreaction are key variables in determining residual momentum profits. Conditional on low market volatilities and low ID, residual momentum profits are 0.386%, 0.350%, 0.341%, and 0.303% per month for K = 3-, 6-, 9-, and 12-month holding periods. s are highest for low ID stocks when market volatility is low. Insignificant profits are reported for high market volatilities and high ID. Although total return momentum profits are either insignificant or negative in reaction to market volatilities, we still observe that the magnitude of momentum profits and s within the same ID group is higher when market volatility is low. Moreover, the s of the total return momentum are all positive in periods of low market volatilities and negative in periods of high market volatilities, suggesting that market volatilities at least produce some variation to discriminate between momentum profits in Japan. E. Effects of Market Liquidity Avramov et al. (2015) report that momentum strategies generate large (weak) profits in liquid (illiquid) market states, which contradicts the conventional arbitrage prediction. In particular, the authors find a negative relation between total return momentum and illiquidity for markets in the United States, Japan, and the Eurozone. Nevertheless, whether the explanatory ability of market liquidity for momentum profits in Japan is related to underreaction has yet to be confirmed. To investigate this issue, we follow Chordia, Subrahmanyam, and Tong (2014) and Avramov et al. (2015) by employing Amihud s (2002) measure of stock illiquidity (ILLIQ). We n define a stock s ILLIQ in month t as t R 1 id, /( Pid, Nid, ) / n d = t, where n t is the number of trading days in month t, R id, is the absolute value of stock i s return on day d, P id, is stock i s 20

21 closing price on day d, and N id, is stock i s number of shares traded on day d. To explain the momentum return in month t, we construct the one-month-lag market-wide measure of illiquidity, MKTILLIQ, as the value-weighted average of each stock s Amihud measure of illiquidity in month t 1. We identify a given month as high (low) liquidity if the value of MKTILLIQ in that month is lower (higher) than the median value of MKTILLIQ in our sample period. We then examine the effect of ID on residual and total return momentum separately for periods of high and low market liquidities in Japan. Panel E of Table 4 confirms that market liquidity has a significant impact on the profitability of both residual and total return momentum strategies in Japan. Specifically, we observe that momentum profits are larger during the period of high market liquidity, which is consistent with the overall results compiled by Avramov et al. (2015). The highest momentum profits and s are concentrated in low ID stocks following high market liquidity. This evidence suggests that investor underreaction provides incremental explanatory power for momentum profits in Japan beyond the effect of market liquidity. F. Underreaction and Momentum Crashes By observing infrequent and persistent strings of extreme momentum losses, Daniel and Moskowitz (2016) propose the crashes of momentum strategies in panic states, that is, following DOWN markets contemporaneous with market rebounds and when market volatility is high. 13 Although Daniel and Moskowitz (2016) indicate the existence of momentum crashes in Japan, whether the crashes are related to investor attention and whether limited investor attention explains the momentum profits in normal times in Japan still remain unexplored in the literature. We follow Daniel and Moskowitz (2016) by defining a given month t as a panic state if (i) the 13 Barroso and Santa-Clara (2015) also show that momentum has a very high excess kurtosis and a pronounced left skew, implying huge crash risk. 21

22 cumulative return to the value-weighted market index over the 24 months prior to month t is negative; (ii) the return to the value-weighted market index in month t is positive; and (iii) the variance of the daily returns on the value-weighted market index measured over the 126 days prior to month t is higher than the median of the time series. The remainder is defined as normal states. This screening process results in 364 months of normal states and 61 months of panic states in Japan. We then observe how ID interacts with normal/panic states for residual and total return momentum in Panel F of Table 4. Interestingly, we find that the residual momentum generates remarkably negative s during panic states, particularly for stocks with low ID. For the total return momentum, the negative momentum profits and s are concentrated in low ID stocks during panic periods. This evidence indicates that the momentum strategies experience more severe losses during panic periods if investors are unaware of the market information of the stocks. For normal states, both residual and total return momentum strategies generate significant risk-adjusted returns and the highest s in the low ID group. This evidence strengthens our previous findings that momentum profits in Japan are largely attributed to limited investor attention, particularly during normal states. An implication of our results is that although the residual momentum is constructed by hedging out the risk exposure to time-varying factor and market risks, extreme market risk still has a large incremental impact on the profitability of the residual momentum. More importantly, the effect of momentum crashes is enhanced and pronounced only when market participants perception is limited. Our results contribute to the literature by providing an understanding of the source of momentum crashes documented by Daniel and Moskowitz (2016). 22

23 V. Confounding Effects of Limited Attention Variables Because information discreteness (ID) captures investors limited attention, it is important to investigate the roles of other variables that are closely related to limited attention in assessing the momentum profits in Japan. We consider three such variables: institutional ownership, idiosyncratic volatilities, and firm age. A. Institutional Ownership Stocks with higher levels of institutional ownership (IO) are expected to receive more investor attention than those with lower levels of IO. If the residual momentum is induced by limited investor attention, we expect its profit to be higher among stocks with lower IO. Because the IO data are reported on an annual basis, we use the proportion of institutional ownership reported in previous year to classify individual stocks into IO quintiles. Within each of the five IO groups, we subdivide individual stocks into quintiles according to their values of the average past six-month residual or total returns to construct rmom 6,2 and MOM 6,2 strategies controlling for the effects of IO. We report risk-adjusted returns and s of rmom 6,2 and MOM 6,2 strategies separately for the five quintile IO groups in Panel A of Table 5. The results show that the residual momentum profits and s are higher among stocks with low IO than those with high IO. This finding confirms our prediction that the residual momentum is more profitable when investor attention is limited. [Insert Table 5] B. Idiosyncratic Volatilities Da et al. (2014) document a positive relation between ID and IVOL and suggest that continuous information corresponds to low ID and low IVOL. 14 Given the observation reported 14 Zhang (2006), however, proposes that the momentum effect is stronger in stocks with higher idiosyncratic 23

24 by Da et al. (2014), we expect residual momentum profit to be higher in stocks with low IVOL if it is induced by limited investor attention. The estimation of IVOL involves regressing the daily stock returns on the daily market excess returns over the year ending at the portfolio formation date. We obtain the standard deviation of residual returns from the regression. To avoid potential estimation errors, we require a stock to have at least 30 observations over the estimation window. We then form 5 5 groups based on a sequential sorting procedure that first conditions on IVOL and then on the average past six-month residual or total return. We report the risk-adjusted returns and s of rmom 6,2 and MOM 6,2 strategies separately for the five IVOL groups in Panel B of Table 5. Panel B results indicate that (i) the low IVOL groups show greater momentum profits (both residual and total return profits), whereas high IVOL groups exhibit negative profits; and (ii) the of the residual momentum decreases monotonically with IVOL. This evidence again is consistent with our previous finding that the residual momentum is driven by limited investor attention. C. Firm Age Barry and Brown (1985) and Zhang (2006) propose that firms with a long history have more information available to the market. Hence, old firms attract more investor attention than young firms. Using the same definition of AGE introduced in regression equation (4), we form 5 5 portfolios to construct momentum strategies conditional on firm age. We expect that the residual momentum is more profitable in young stocks than in old stocks. Panel C of Table 5 confirms this conjecture. Both residual and total return momentum profits are significantly positive, whereas s are much greater for young stocks. volatility (IVOL) because of a higher degree of information uncertainty. 24

25 D. Fama-MacBeth Cross-Sectional Regressions Although our main findings are consistent with the prediction of the FIP hypothesis, Table 5 indicates that other limited attention variables may also explain the profitability of the residual momentum. To contrast with these alternative explanations, we perform Fama-MacBeth cross-sectional regressions to evaluate the impact of ID on future returns separately for residual and total return momentum strategies, expressed in the following form: r i,t+j = β 0 + β 1 ID i,t + β 2 PRET i,t + β 3 PRET i,t ID i,t + αx i,t + α I PRET i,t X i,t + ε it,, (5) where r i,t+j is the subsequent j-month cumulative residual or total return of stock i and j = 6 or 12. X i,t is a set of control variables that are associated with the cross-sectional differences in momentum profits, including IO, IVOL, AGE, BM, SIZE, and TURN. The specification enables us to compare the relative explanatory power of variables for the profits of residual and total return momentum strategies. In particular, a negative β 3 coefficient supports the FIP hypothesis because it implies that continuous information leads to higher momentum profits than discrete information. Table 6 reports the coefficient estimates from Equation (5) for residual and total return momentum strategies. Consistent with our expectation, the β 3 coefficient is significantly negative in every specification for both momentum strategies. In addition to ID, IVOL and BM also provide incremental explanatory power for momentum profits. This power is indicated by the significantly negative coefficients on their interaction terms with PRET. These patterns are robust to both residual and total return momentum strategies. [Insert Table 6] E. Further Examination of Information Discreteness on Momentum Profits 25

26 The results reported in previous subsections reveal that several firm characteristics also account for the profitability of the residual momentum in Japan. These variables are often used to measure the degree of information uncertainty and thus may proxy for investor attention. To ensure that our evidence regarding ID is distinct from these alternative information measures, we investigate the incremental effect of ID controlling for alternative investor attention measures. In particular, we perform the following cross-sectional regression. As indicated in the previous section, we observe that IO, IVOL, and AGE are good measures of limited attention, but for the cross-sectional regression, we capture firm size and TSE section listing additionally as potential variables that proxy investor attention: ID = + IO + IVOL + AGE + SIZE + SECTION + (6) it, δ0, t δ1, t it, δ2, t it, δ3, t it, δ4, t it, δ5, t it, εit,. We compute residual IDs by retrieving the residuals from Equation (6) to measure the incremental effect of ID. We then form residual momentum and total return momentum conditional on residual ID using the 5 5 sorted procedure. Table 7 generally shows that the residual momentum continues to generate significant positive profits for the low residual ID group even though they are slightly smaller than the results compiled in Table 2, whereas total momentum profits remain insignificant. These results confirm that residual IDs net of other potential variables proxying limited attention of investors are equally effective in generating residual momentum profits. [Insert Table 7] VI. Conclusions Using a sample of all stocks listed on the TSE covering the sample period from 1975 to 2011, we demonstrate that the residual momentum strategy, which is constructed to hedge out the risk exposure to the Fama and French factors, is profitable in Japan for short-term holding 26

27 periods ranging from three to 12 months. We also demonstrate that the residual momentum profits over long-term holding periods ranging from two to five years do not reverse. Short-term momentum without long-term reversals in Japan reminds of the question George and Hwang (2004) raise about the traditional view that short-term momentum and long-term reversals are sequential components of the process by which the market absorbs news. The findings in both short- and long-term holding periods are attributed to investor underreaction in Japan. 15 Consistent with the FIP hypothesis of Da et al. (2014), we find that the profits to the residual momentum in Japan are concentrated in stocks with more continuous rather than discrete information. In addition, this pronounced momentum profit is not followed by long-term reversals, consistent with the prediction of the underreaction hypothesis. Finally, we find that the residual momentum with continuous information displays predictable time-varying patterns according to the business cycle, market state, market volatilities, return dispersion, market liquidity, and momentum crashes. Additional tests indicate that residual momentum profits and s are greater among stocks with low institutional ownership, low idiosyncratic volatilities, and young age. These findings are expected because these three variables capture investor limited attention. Nevertheless, the role of investor underreaction remains robust after controlling for these confounding variables (e.g., low institutional ownership, low idiosyncratic volatilities, and young firm age). 15 A welcome addition to the literature in this area is Byun, Lim, and Yun (2016). They report that continuous overreaction advocated by Daniel et al. (1998) is not applicable in Japan due to the lack of biased self-attribution. 27