Continuing Overreaction and Momentum in a Market with Price Limits

Transcription

1 Continuing Overreaction and Momentum in a Market with Price Limits Hsiang-Hui Chu a, Kuan-Cheng Ko a,*, Shiou-Wen Lee a, Nien-Tzu Yang b a Department of Banking and Finance, National Chi Nan University, Puli, Taiwan b Department of Business Management, National United University, Miaoli, Taiwan This version: January 2017 Abstract In this paper, we document strong return predictability for continuing overreaction in Taiwan, a market without the existence of momentum for conventional momentum strategies. Using signed volume to proxy for the level of continuing overreaction, we show that the strategy of buying stocks with upward continuing overreaction and short selling those with downward continuing overreaction generates both intermediate-term continuations and long-term reversals in this market. The evidence is consistent with the prediction of the model based on investor overconfidence and biased self-attribution in predicting future stock returns. We further examine the impact of price limits on this overreaction-based return predictability by isolating the information embedded in signed volumes for limit-hit and non-hit days, respectively. The findings indicate that the imposition of price limits seems to restrain investors overreaction behavior and that trading volume in non-hit days is a cleaner measure to capture the level of investor overconfidence in generating intermediate-term continuations and long-term reversals. JEL Classification: G11; G12; G14 Keywords: Continuing overreaction; Momentum; Price limits; Taiwan stock market * Kuan-Cheng Ko acknowledges the financial support from the Ministry of Science and Technology of Taiwan (grant number: MOST H MY2). Corresponding author. kcko@ncnu.edu.tw; Address: No. 1, Daxue Rd., Puli, Taiwan; Tel: ext. 4695; Fax: The authors can be reached via . Hsiang-Hui Chu: hhchu@ncnu.edu.tw; Shiou-Wen Lee: s @mail1.ncnu.edu.tw; Nien-Tzu Yang: nanzy@nuu.edu.tw.

2 Continuing Overreaction and Momentum in a Market with Price Limits This version: January 2017 Abstract In this paper, we document strong return predictability for continuing overreaction in Taiwan, a market without the existence of momentum for conventional momentum strategies. Using signed volume to proxy for the level of continuing overreaction, we show that the strategy of buying stocks with upward continuing overreaction and short selling those with downward continuing overreaction generates both intermediate-term continuations and long-term reversals in this market. The evidence is consistent with the prediction of the model based on investor overconfidence and biased self-attribution in predicting future stock returns. We further examine the impact of price limits on this overreaction-based return predictability by isolating the information embedded in signed volumes for limit-hit and non-hit days, respectively. The findings indicate that the imposition of price limits seems to restrain investors overreaction behavior and that trading volume in non-hit days is a cleaner measure to capture the level of investor overconfidence in generating intermediate-term continuations and long-term reversals. JEL Classification: G11; G12; G14 Keywords: Continuing overreaction; Momentum; Price limits; Taiwan stock market

3 1. Introduction Behavioral theories propose that intermediate-term momentum in stock markets is induced because of investors irrational reaction to information. Among the vast literature, investor overconfidence is one leading explanation of momentum. This line of research is initiated by Daniel, Hirshleifer, and Subrahmanyam (hereafter DHS, 1998), who propose a theoretical model of investor overconfidence and biased self-attribution to explain both under- and overreactions in stock markets. Follow-up studies provide several measures and empirical tests to demonstrate evidence in support of the DHS model. In particular, Hou, Peng, and Xiong (2009) argue that contemporaneous with up markets, investor overconfidence can give rise to excess trading volume. Thus the overreaction-driven momentum is more pronounced among stocks with high volume and following up markets. Asem and Tian (2010) propose that investor overconfidence is strengthened when the market continues in the same direction. Confirming the prediction of the DHS model, they show that market continuations enhance momentum profits while market transitions decrease the profitability of momentum. Byun, Lim, and Yun (2016) indicate that an important implication of the DHS model is that the formative process of investors overconfidence is related to their behavior of continuing overreaction. In the DHS model, overconfident investors initially overreact to their private information; their confidence is enhanced upon subsequent arrivals of public signals due to biased self-attribution and leads to further overreaction to the information. They thus propose a direct measure of continuing overreaction using weighted signed volumes to verify the credibility of the DHS model in explaining momentum profits. In particular, they construct a trading strategy by buying stocks with large positive continuing overreaction and short selling those with large negative continuing overreaction and show that the proposed strategy generates 1

4 significant abnormal returns. Further, despite its usefulness in the U.S. market, continuing overreaction has no return predictability in Japan, a market whose participants have been documented to lack biased self-attribution (Kitayama, Takagi, and Matsumoto, 1995). But is the lack of biased self-attribution necessarily the only reason to result in the unprofitability of continuing overreaction outside the U.S. market? Besides differences in culture and market participants, the Japanese market also differs from the U.S. market in terms of trading mechanism. Unlike the U.S. market that imposes trading halts in extreme conditions, the Tokyo Stock Exchange (TSE) imposes price limits for individual stocks. When investors are overconfident about their own information, their trading is more likely to trigger price limit events. As trading is allowed at the limit price but not beyond whenever the stock price hits the upper or lower boundary, trading volume will be limited at price limits even the magnitude of investor overconfidence is high. In such condition, the signed volume at price limit events would be underweighted in Byun, Lim, and Yun s (2016) continuing overreaction measure. Therefore, understanding the validity of Byun, Lim, and Yun s (2016) continuing overreaction measure in markets outside the U.S., especially those with the imposition of price limits, is an important issue to the literature. In this study, we extend Byun, Lim, and Yun s (2016) research by investigating whether continuing overreaction is a useful predictor of future returns in the Taiwan stock market, and further, whether price limits have important impacts on the usefulness of continuing overreaction. We choose this particular market for three reasons. First, like the Japanese market, the Taiwan Stock Exchange (TWSE) imposes price limit rules for individual stocks. A major difference in the price limit rule between Japan and Taiwan markets is that the former utilizes a fixed amount of daily price changes for stocks within a given price range while the latter sets a fixed 2

5 percentage of up and down price movements for all stocks, leading to a narrower price limit rule in Taiwan. 1 Also, the price limits are easier to observe in Taiwan because the Taiwan Economic Journal (TEJ), a local data vendor in Taiwan, records price limit events in the database. Thus using the Taiwan data enables us to directly identify and compare trading volumes for days with and without price limits. Second, unlike Japanese investors that are generally viewed as conservative and collectivistic, investors in Taiwan have been documented to exhibit overconfident trading behavior. Barber, Lee, Liu, and Odean (2009) show that individual investors in Taiwan account for over 90% of the trading volume with an annual turnover rate of 300% to 600% and attribute such active trading behavior to investor overconfidence. Lin, Ko, Feng, and Yang (2016) provide supportive evidence for the overconfidence hypothesis by showing that the traditional price momentum is profitable during periods of market continuations but not periods of market transitions. Taking the two advantages together, the Taiwan stock market serves as a natural experimental environment to examine the usefulness of continuing overreaction in explaining momentum considering the impacts of price limits. Third, a similarity between Japan and Taiwan stock markets is the lack of momentum, which is a long-debate phenomenon in the literature. Hameed and Kusnadi (2002), Chui, Titman, and Wei (2003, 2010) and Du, Huang, and Liao (2009) all indicate that the standard momentum strategy of Jegadeesh and Titman (1993) fails to be profitable in this market. But little is known about the underlying reason of the absence of the momentum effect in Taiwan. Analyzing the profitability of the momentum strategy based on continuing overreaction enables us to revisit the 1 See Kim and Rhee (1997) and Chung and Gan (2005) for detailed discussion on the price limit rules imposed by TSE. According to Chung and Gan (2005), the daily price limit ranges from 10% to 60% in Japan. In contrast, the price limits in Taiwan were fixed to be +/ 5% before January 1989, +/ 7% during January 1989 to May 30, 2015, and +/ 10% afterwards. 3

6 momentum effect in Taiwan, and more specifically, to examine whether investor overconfidence could be a possible source to induce return continuation in this market. We first confirm the usefulness of the standard continuing overreaction measure in predicting future stock returns in Taiwan and find that its effectiveness persists up to 9 months after portfolio formation. This continuing overreaction-oriented momentum strategy is subject to strong reversals in January months, thus its profitability is more pronounced in non-january months. We further confirm that this strategy exhibits reversals starting from the second year after the portfolio formation, thus supporting the notion that profitability of the continuing overreaction-oriented momentum is better explained by the DHS model. We also verify in cross-sectional regressions that the impact of continuing overreaction in inducing subsequent return continuation is robust to the inclusion of several determinants of momentum and stocks returns. In particular, the impact of continuing overreaction remains strong when we control for return consistency of Grinblatt and Moskowitz (2004) and information discreteness of Da, Gurun, and Warachka (2014), measures that are used to capture the return patterns over the formation periods. The profitability of continuing overreaction is also unaffected by small firm, idiosyncratic volatility, illiquidity, and turnover effects. After we eliminate the information embedded in these variables, the residual continuing overreaction still remains a strong predictor of future stock returns. We further examine the impact of price limits on continuing overreaction in explaining future stock returns by discriminating signed volumes of non-hit days from those of limit-hit days. We develop two continuing overreaction measures using data on non-hit and limit-hit signed volumes and construct momentum strategies based on the two measures, respectively. We find that the intermediate-term momentum and long-term reversal is pronounced only in the 4

7 non-hit continuing overreaction strategy. The strategy constructed based on limit-hit continuing overreaction, however, generates negative but insignificant profits in both intermediate and long terms. This finding implies that the imposition of price limits seems to restrain investors overreaction behavior in Taiwan. The weighted signed volume in non-hit days is thus a cleaner measure of continuing overreaction that better captures the patterns associated with intermediate-term continuations and long-term reversals. In a further investigation, we examine the time-series patterns of the continuing overreaction-based momentum conditional on market dynamics to document supportive evidence for the DHS model in explaining its profitability. In particular, we follow Asem and Tian (2010) and Lin, Ko, Feng, and Yang (2016) to define the dynamic of the market for each holding month of the strategy and show that the strategy generates pronounced profits only when the market continues in the same direction, during which the magnitude of investor overconfidence is enhanced. Furthermore, we control for the impacts of the time-varying market risk and down markets and find that the profitability of the continuing overreaction-based momentum is not subject to the momentum crash documented by Daniel and Moskowitz (2016). The remainder of this paper is organized as follows. Section 2 describes the construction of variables and the momentum strategy, as well as the data used in this study. In Section 3, we investigate whether continuing overreaction is associated with future stock returns in both short and long terms in the Taiwan stock market. We consider the impact of price limits on continuing overreaction in inducing momentum profits in Section 4 and investigate the robustness of our results in Section 5. Section 6 provides our conclusions. 2. Data and the construction of continuing overreaction and momentum 5

8 To investigate whether continuing overreaction is related to future stock returns in Taiwan, we use all common stocks listed on the Taiwan Stock Exchange (TWSE), including OTC stocks, for the sample period from January 1971 to December 2015 as our sample. We obtain data on return, trading volume, and accounting variables from the Taiwan Economic Journal (TEJ), which is a local data vendor in Taiwan. We begin by following Byun, Lim, and Yun (2016) to construct an empirical measure of continuing overreaction in which monthly trading volume is used as a proxy of the magnitude of investor overconfidence or overreaction. The use of trading volume is motived by its positive relation with overconfidence that has been documented by the vast literature (Benos, 1998; Odean, 1998; Barber and Odean, 2001; Statman, Thorley, and Vorkink, 2006; Glaser and Weber, 2009; Grinblatt and Keloharju, 2009; Hou, Peng, and Xiong, 2009). In addition to trading volume, the sign of contemporaneous return is important to identify the direction of overreaction. Byun, Lim, and Yun (2016) thus propose the signed volume measure, in which high trading volume accompanied by a positive (negative) return is assumed to be related to investor overconfidence toward positive (negative) private information. In particular, they define stock i s signed volume in month t, SV i,t, as SV Vol i, t, if ri, t 0 0, if r 0 Voli, t, if ri, t 0 i, t i, t (1) where Vol i,t is stock i s dollar trading volume in month t, which is calculated as the sum of daily trading volume within the month, and r i,t is stock i s return in month t. 2 2 Byun, Lim, and Yun (2016) declare that the results for the U.S. market are robust when weekly or daily signed volumes are used. We will show that our results are robust to the use of daily signed volumes in Section 4 when we consider the impacts of price limits. 6

9 In addition to investor overconfidence, biased self-attribution is a key driver of continuing overreaction characterized by an increasing trend of overconfidence in the DHS model. To capture this feature, Byun, Lim, and Yun (2016) assign increasing weights to signed volumes in more recent months of the formation period and aggregate across these weighted signed volumes with a normalization. They then construct the measure of continuing overreaction for every stock in a particular month, denoted as CO, in the following form: CO 12 J 1 it, 12 J 1 wj SVi, t J, Voli, t J /12 (2) where SV i,t J is stock i s signed volume in month t J, and w J is a weight that takes a value of 12 J+1 in month t J (i.e., w 12 = 1,, w 1 = 12). Based on this construction, large positive (negative) value of CO signifies higher level of overconfidence of investors in reacting positive (negative) information in the past. We then follow the conventional approach advocated by Jegadeesh and Titman (1993) to construct the momentum strategy based on individual stocks values of CO. At the beginning of each month t, we rank individual stocks according to their values of CO and allocate them into quintiles. We allocate stocks with CO values ranked at the top 20% into the winner portfolio and those with CO values ranked at the bottom 20% into the loser portfolio. The continuing overreaction-based strategy thus involves buying the winner portfolio and short selling the loser portfolio with equal weights, and the strategy is held for the subsequent K months (K = 3, 6, 9, 12). 3 For a given month t, the momentum profit is calculated as the difference in returns between winner and loser 3 Unlike conventional U.S. evidence of strong short-term return reversals in the month following portfolio formation (Jegadeesh, 1990; Lo and MacKinlay, 1990), the Taiwan stock market has been documented to exhibit positive autocorrelations in the short term because of the imposition of price limits. Thus we do not impose the 1-month skip between formation and holding periods in our main results. The results based on the imposition of the 1-month skip are virtually unchanged and are available upon request. 7

10 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 for autocorrelation and heteroskedasticity using Newey and West s (1987) standard errors. 3. Continuing overreaction and momentum We start with the investigation of the credibility of continuing overreaction in generating momentum profits in the intermediate term. We verify the overconfidence hypothesis to underlie the continuing overreaction-based momentum by showing that the intermediate-term return continuation is followed by long-term reversals. We next demonstrate the effectiveness of continuing overreaction in relating future returns controlling for several predictors of momentum and stock returns Momentum profits regarding continuing overreaction in the intermediate term Table 1 reports the returns to the winner and loser portfolios formed on CO, as well as their differences with holding periods of 3, 6, 9, and 12 months. In addition to the return patterns for the entire sample period (Panel A), we also observe whether CO behaves differently in predicting stock returns in January and non-january subsamples (Panels B and C). For all holding horizons, the winner portfolio generates higher returns than loser portfolios in the full period. In particular, the momentum profits are significant at 0.364%, 0.307%, and 0.271% for 3-, 6-, and 9-month holding periods and become insignificant at 0.075% for the 12-month holding period. We also observe strong reversals in January months. The continuing overreaction strategy generates an average return ranging from % to % across different holding horizons in January months. As a result, the momentum profits in non-january months become 8

11 higher and more significant at 0.554%, 0.481%, 0.448%, and 0.239% for the four sets of holding horizons. [Insert Table 1 about here] The results indicate that the continuing overreaction-based strategy generates significantly positive profits for periods within 9 months subsequent to the portfolio formation in Taiwan. Moreover, the insignificant profit for the 12-month holding period shows that the positive impact of continuing overreaction on future stock returns is declining and implies the possibility that the profitability of the strategy may reverse beyond 1 year after the portfolio formation. According to the prediction of the DHS model, overconfidence-oriented momentum profitability is followed by subsequent reversals. We address this issue in next subsection Long-term return patterns of continuing overreaction An important implication of the DHS model is that if investors are overconfident about their information and the level of overconfidence is enhanced by biased self-attribution, stock prices would be corrected and thus exhibit reversal patterns in the long term. Because CO in essence is constructed to capture the aggressiveness of investors in trading stocks implied by trading volumes, it is important to demonstrate that CO leads to reversals to correct for the mispricing of stocks. To this end, we observe the return patterns of winner and loser portfolios formed on CO and the differences between winners and losers in the second to the fifth years after portfolio formation. Table 2 gives the results. [Insert Table 2 about here] Confirming our conjecture, the momentum strategy constructed based on CO generates negative returns in subsequent second to the fifth years with corresponding average returns of 9

12 -0.294%, %, %, and %, respectively. This evidence indicates that for the Taiwan stock market, the predictability of the CO measure is likely be the result of investors behavior of continuing overreaction, which eventually corrects in the long term Cross-sectional regressions of future returns In addition to continuing overreaction, several studies also investigate the role of information flows embedded in a stream of stock returns in predict future stock returns and propose alternative measures to capture these patterns. Jegadeesh and Titman (1993) propose the traditional momentum strategy based on the cumulative return of stock in the past. Motivated by the prediction of the disposition effect that investors are more likely to sell stocks with unrealized capital gains in their portfolio, Grinblatt and Moskowitz (2004) propose a measure of return consistency to predict momentum profits. Da, Gurun, and Warachka (2014), on the other hand, develop a measure of information discreteness to isolate the information flows associated with continuous information from those associated with discrete information. The literature also introduces the importance of firm size in momentum profits and the cross section of stock returns (Fama and French, 1992, 1993, 2008; Zhang, 2006). Ang, Hodrick, Xing, and Zhang (2006, 2009) and Bali, Cakici, and Whitelaw (2011), among others, show that idiosyncratic volatility predicts future stock returns. The illiquidity and turnover effects have been demonstrated as important determinants of stock returns and momentum profits (Lee and Swaminathan, 2000; Amihud, 2002; Sadka, 2006; Hou, Peng, and Xiong, 2009; Avramov, Cheng, and Hameed, 2015). Finally, the short-term reversal documented in Jegadeesh (1990) and Lo and MacKinlay (1990) is also an important control variable of momentum for the U.S. market. 10

13 To examine the robustness of CO in predicting future returns, we perform cross-sectional regression of future 6-month buy-and-hold returns on CO and aforementioned variables using the Fama and MacBeth (1973) procedure. The regression takes the following form: r CO PRET PosID NegID PosRC NegRC i, t 1, t i, t 2 i, t 3 i, t 4 i, t 5 i, t 6 i, t Npos _ neg SIZE IVOL ILLIQ TURN REV,(3) 7 i t, 8 i t, 9 i t, 10 i t, 11 i t, i t12 i t t,, 1, 6 where r i,t+1,t+6 is stock i s cumulative return from month t+1 to month t+6, CO i,t is the continuing overreaction measure defined in Section 2, PRET i,t is stock i s cumulative return from month t 12 to t 1, PosID i,t and NegID i,t are variables associated with information discreteness, 4 PosRC i,t and NegRC i,t are dummy variables of return consistency, 5 Npos_neg i,t is the number of months with positive return minus the number of months with negative return for stock i from month t 12 to t 1, 6 SIZE i,t is the natural logarithm of stock i s market capitalization at the end of month t, IVOL i,t is the standard deviation of residuals from the market model calculated using daily returns during month t, ILLIQ i,t is stock i s Amihud (2002) measure, which is the average ratio of the absolute daily return to the dollar trading volume in month t, TURN i,t is the average monthly turnover over the previous 12 months from month t 12 to t 1, and REV i,t is stock i s return in month t. We perform the cross-sectional regressions of Equation (3) every month and test the average slope coefficients using Newey and West s (1987) robust standard errors. We provide several 4 In particular, we follow Byun, Lim, and Yun (2016) by adopting the signed versions of information discreteness % pos % neg, if ri, t 12, t 1 0 % neg % pos, if ri, t 12, t 1 0 measure, in which PosIDit, and NegIDit,, 0, otherwise 0, otherwise where %pos and %neg are the percentages of days during the formation period from month t 12 to t 1 with positive and negative returns, respectively, and r i,t 12,t 1 is stock i s cumulative return from month t 12 to t 1. 5 We follow Grinblatt and Moskowitz (2004) and Byun, Lim, and Yun (2016) by defining PosRC i, t (NegRC i, t ) as dummies that takes a value of one if stock i has experienced positive (negative) monthly returns for at least eight of twelve months during the formation period from month t 12 to t 1 and past 12-month return is also positive (negative). 6 We follow Byun, Lim, and Yun (2016) by adopting this measure as another proxy of return consistency. 11

14 sets of explanatory variables to examine how robust is the impact of CO conditional on different combinations of the variables. Table 3 presents the results. [Insert Table 3 about here] In univariate regressions, CO is positively related to future stock returns with statistical significance. The average coefficient on CO reported in Model (1) is with a t-statistic of The significance of CO remains unchanged when PRET is included in the regressions as shown in Model (2). Also, the insignificantly negative coefficient on PRET is consistent with the evidence of prior studies that past return does not induce momentum in Taiwan. In Models (3) and (4), we separately consider the incremental effect of CO beyond the impacts of information discreteness and return consistency and find that the predictability of CO remains to be significant. In Models (5) to (7), we include variables associated with information discreteness (PosID and NegID), return consistency (PosRC and NegRC), and alternative return consistency measure (Npos_neg) with additional control variables of SIZE, IVOL, ILLIQ, TURN, and REV. Again, although these variables are shown to be related to future 6-month returns in the cross section, the pronounced impact of CO always remain in all specifications. When we include all variables together (Model (8)), we find that after controlling for these firm characteristics, only continuing overreaction and information discreteness have significant impacts on future returns while return consistency does not. This finding is not surprising and implies that information discreteness may generate return predictability through different channel via limited attention while the continuing overreaction is motivated by overconfidence and biased self-attribution, and the two phenomena may coexist in the Taiwan stock market as the two measures to capture different information sets embedded in trading volumes and past returns. 12

15 3.4. Residual continuing overreaction To demonstrate the validity of CO in predicting future returns, we perform the cross-sectional regressions of CO on a set of variables every month to isolate the information embedded in our CO measure from that embedded in alternative determinants of momentum and stock returns. The model specification takes the following form: CO PRET ID RC Npos _ neg SIZE IVOL ILLIQ i, t 0 1 i, t 2 i, t 3 i, t 4 i, t 5 i, t 6 i, t 7 i, t (4) 8 TURN. i, t 9 REVi, t i, t The variables are defined as in Equation (3), and we obtain the residual continuing overreaction ) to capture the pure effect of CO controlling for the impacts of these variables. We use this ( it, residual CO to form the momentum strategy as described in Section 2 with intermediate- and long-term holding horizon. We report and test the returns of winner, loser, and the momentum portfolios in Table 4. [Insert Table 4 about here] The momentum profits are significantly positive within 1-year hold periods and become insignificant afterwards. In particular, the 3-, 6-, 9-, and 12-month momentum profits are significant at 0.317%, 0.289%, 0.297%, and 0.202%, respectively. The significance of long-term reversals disappears in this residual CO strategy, with corresponding profits of 0.104%, 0.080%, %, and 0.010% for the second to the fifth years after portfolio formation. This evidence indicates that the intermediate-term return continuation implied in the CO measure is distinct from the information embedded in other measures and firm characteristics. The long-term reversal pattern, however, seems to be absorbed by other effects. 13

16 4. Continuing overreaction and price limits An important feature of the Taiwan stock market is the imposition of price limits. To investigate whether and how price limits affect the predictability of continuing overreaction in explaining momentum in Taiwan, we construct two measures of continuing overreaction by isolating the information embedded in non-hit and limit-hit days and investigate whether the two measures exhibit return predictability across different holding periods Continuing overreaction based on daily frequency Because price limit events are triggered on the daily basis, it is important to verify the effectiveness of continuing overreaction based on the construction using daily frequencies before we formally examine their impact on CO in explaining momentum. We define the signed volume of individual stocks in Equation (1) for every trading day and calculate the continuing overreaction measure of Equation (2) in month t using based on daily signed volumes, expressed as CO D it, 12 k 1 12 k 1 w SV Vol k i, d k / i, d k 12, (5) where SV i,d k and Vol i,d k are stock i s signed and trading volumes on day d k, and w k is a weight that takes a value of 12 k+1 on day d k, in which 12 is the number of trading days over past 12 months. Because the setting of w k may produce large dispersion in weights across trading days than w J we use in Equation (1), we also repeat the calculation by assigning the same w J to the trading days within the same month (that is, w J ranges from 1 to 12) to reduce the artificial effect of weights and obtain similar results in unreported tables. 14

17 We first examine whether the CO D measure has incremental predictability for future stock returns beyond alternative determinants of momentum and stock returns by performing the cross-sectional regressions of Equation (3) but replacing the standard CO measure with the CO D measure. As Table 5 shows, the coefficients on CO D are generally positive and significant across all specifications of control variables. This result indicates that the creditability of continuing overreaction in explaining future 6-month stock returns in Taiwan is not affected by the data frequency used for the variable construction. [Insert Table 5 about here] We also calculate momentum profits generated by the CO D measure with holding periods in intermediate and long terms and report the results in Panel A of Table 6. In particular, the strategy constructed based on CO D generates significantly positive returns in 3-, 6-, and 9-month holding periods and significantly negative returns the second- and the fifth-year holding periods. These patterns are consistent with the results based on the standard CO measure reported in Tables 1 and 2. [Insert Table 6 about here] We also compute the residual CO D measure by obtaining the residuals from cross-sectional regressions of CO D on a set of variables as in Equation (4). We then calculate momentum profits for the strategy constructed based on the residual CO D with the results presented in Panel B of Table 6. Consistent with the results reported in Table 4, the residual CO D generates significantly positive momentum profits within the 1-year holding periods and insignificant profits from the second to the fifth years. Overall, the results from Tables 5 and 6 indicate that the intermediate-term momentum and long-term reversals induced by continuing overreaction in Taiwan is not sensitive to the way we construct the continuing overreaction measure. 15

18 4.2. Continuing overreaction measures controlling for price limits The price limit, by its design, is imposed to prevent investors from overreacting to information. Despite the pros and cons of price limits and the price behavior surrounding the event (Kim and Rhee, 1997; Cho, Russell, Tiao, and Tsay, 2003; Kim, Yagüe, and Yang, 2004; Kim and Yang, 2004, 2008; Chan, Kim, and Rhee, 2005), the information content of trading volume at price limits is seldom discussed in the literature. On the one hand, Seasholes and Wu (2007) show that price limits are attention-grabbing events that can catch investors attention and further induce subsequent buying behavior on stocks they have not previously owned. In such case, high trading volume at price limits could enhance the level of investor overreaction. On the other hand, if price limits do prevent investors from overreacting to information, high trading volume at price limits is not followed by subsequent trading behavior. That is, there is no continuing overreaction and thus the subsequent momentum phenomenon would be refrained. Another important feature of price limits is that when price limit events are triggered, trading is allowed at the limit price but not beyond. Thus, trading volumes in limit-hit and non-lit days are not directly comparable because trading volume is limited on limit-hit days. Unlike the standard CO D measure that is constructed using signed and trading volumes for all trading days, considering the impact of price limits needs to isolate the volume information embedded in trading on limit-hit and non-hit days. This motivates us to construct two measures of continuing overreaction that separately consider trading volumes with and without hitting price limits. To do so, we define a stock s non-hit signed volume as in Equation (1) by counting non-hit days only. Similarly, we define limit-hit signed volume using data on limit-hit days only. We then calculate non-hit and limit-hit CO measures using Equation (5) based on the two sets of data, respectively. 16

19 We observe the return patterns generated by the two CO measures for the holding periods of intermediate and long terms. The results for non-hit and limit-hit COs are reported in Panels A and B of Table 7, respectively. Several interesting findings emerge. First, the momentum strategy constructed based on non-hit CO generates significantly positive profits within the 9-month holding periods and strong reversal in the second year after portfolio formation. The returns remain negative but become insignificant after the second-year holding period. The momentum strategy constructed based on limit-hit CO, however, yields negative returns in both intermediate and long terms. This evidence suggests that the predictability of the standard continuing overreaction measure is concentrated in stocks with more non-hit signed volumes. [Insert Table 7 about here] Second, after taking a close look at the returns of winner and loser portfolios identified by the two CO measures, we find that the inverse-u shaped return pattern is observable only among past winners with higher volumes at up limit events (limit-hit CO winners) but not past winners with higher volumes on non-hit days (non-hit CO winners). In particular, the return of non-hit CO winners increases within 1 year after portfolio formation and becomes smaller afterwards. The relatively flat pattern across intermediate and long terms of limit-hit CO winners, however, indicates that there is no sharp changes in future returns. The evidence indicates that high trading volumes accompanied by positive returns on non-hit days tend to enhance investors overconfidence, which would be corrected eventually. Another notable finding is that limit-hit CO winners have lower returns than non-hit CO winners, especially in the intermediate term. This observation confirms the notion that the magnitude of overconfidence for non-hit CO winners is strengthened while limit-hit CO winners experience faster price corrections. 17

20 Third, we observe similar patterns for non-hit and limit-hit CO losers. Non-hit CO losers have low returns ranging from 1.635% to 1.697% within subsequent year; the return reverses to 2.049% in the second year after portfolio formation. The returns of limit-hit CO losers are relatively stable across different holding periods. This finding indicates that investors overconfidence in trading non-hit CO losers is enhanced, but their overconfidence is refrained in trading limit-hit CO losers. To conclude, our empirical findings from Table 7 indicate that continuing overreaction exist only among stocks that have more signed volumes at non-hit days. Price limit events seem to restraint investors from overconfident trading. High signed volumes at limit-hit days seem to be helpful in cooling down investors overconfident trading, leading to faster price correction immediately after their aggressive trading. 5. Robustness tests We provide three robustness tests to verify the usefulness of continuing overreaction in inducing intermediate-term momentum and long-term reversals in Taiwan. First, the literature proposes that overconfidence and biased self-attribution are stronger when the market continues in the same direction. Thus the investigation based on market dynamics is important to strengthen our linkage with the overconfidence hypothesis. Second, Grundy and Martin (2001) and Daniel and Moskowitz (2016) both highlight the importance of the time-varying exposure of momentum to the market risk. We also investigate whether the continuing overreaction-based momentum in Taiwan is affected by time-varying market risk. Finally, we investigate whether our results are robust to alternative continuing overreaction measure constructed based on idiosyncratic volatility. 18

21 5.1. Continuing overreaction and market dynamics Cooper, Gutierrez, and Hameed (2004) propose that investor biases are more accentuated after market gains, further inducing the profitability of the price momentum following positive market returns. Extending Cooper, Gutierrez, and Hameed s (2004) finding, Asem and Tian (2010) propose that it is the dynamic of market states, rather than the market state itself, that predicts momentum profits. 7 In particular, they propose that the degree of overconfidence on the buying (selling) behavior is enhanced when the markets continue in the UP (DOWN) market state. As a result, momentum profits should be higher when the markets continue in the same state (from UP to UP or from DOWN to DOWN) than when they transit to a different state (from UP to DOWN or from DOWN to UP). We follow Asem and Tian (2010), Hanauer (2014) and Lin, Ko, Feng, and Yang (2016) by first defining whether a given holding month of momentum belongs to UP or DOWN market state. We define a given holding month t of momentum as past UP (DOWN) market if the buy-and-hold return on the TAIEX, which is the proxy of the market index in Taiwan, over month t 12 to month t 1 is nonnegative (negative). Following past DOWN markets, we further classify month t as market continuation (transition) if the TAIEX return in the subsequent month is negative (nonnegative). Analogously, we define month t as market continuation (transition) following UP markets if the TAIEX return in the subsequent month is nonnegative (negative). We then calculate average momentum profits for strategies constructed based on CO D, non-hit and limit-hit CO measures separately for periods of market continuation and transition, 7 Hanauer (2014) and Lin, Ko, Feng, and Yang (2016) also provide supportive evidence for market dynamics in explaining momentum profits in Japan and Taiwan, two markets that have been widely documented to have no momentum. 19

22 respectively. 8 Our prediction is that if the continuing overreaction-based momentum is induced because of investor overconfidence and biased self-attribution, its profitability is strengthened during periods of market continuation and is weaken during periods of market transition. Table 8 gives the results. [Insert Table 8 about here] The results for CO D and non-hit CO share similar patterns, as shown in Panels A and B. Consistent with our prediction, the intermediate-term momentum and long-term reversals for CO D and non-hit CO strategies are higher during periods of market continuation than during periods of market transition. Taking the CO D strategy for example, its momentum profits during market continuations increase to 0.729%, 0.766%, 0.696%, and 0.552% for 3-, 6-, 9-, and 12-month holding periods, respectively. The magnitude of reversal for the second to the fifth years when the market continues in the same direction is also enhanced compared with the numbers reported in Table 6. The corresponding returns for the two strategies during periods of market transition, however, are insignificant across all holding horizons. The results thus serve as further evidence to support the DHS model in explaining the predictability of CO D and non-hit CO in Taiwan. For the limit-hit CO strategy presented in Panel C, we observe no particular difference in intermediate-term returns between periods of market continuation and transition. However, the strategy exhibits significantly negative returns in the long terms when the market continues in the same direction. This evidence suggests that the price corrections of limit-hit CO winners and losers are stronger and persist in the long term during market continuation. 8 We also show that the results for the standard CO measure constructed based on monthly data are similar to those conducted based on CO D. The results are not reported to save space and are available upon request. 20

23 5.2. Time-varying exposure to market risk Grundy and Martin (2001) and Daniel and Moskowitz (2016) both propose that momentum is subject to the time-varying exposure of to the market risk. They show that momentum has a striking decline in market beta following market declines, especially when the contemporaneous market return is positive. As a result, momentum could be subject to severe losses in such situation. This phenomenon is referred to as the famous momentum crashes pointed out by Daniel and Moskowitz (2016). We provide our second robustness test to examine whether the profitability of the continuing overreaction-based momentum in Taiwan is subject to the time-varying market risk. To do so, we follow Daniel and Moskowitz s (2016) approach by considering a conditional CAPM with indicators on past market state, which takes the regression in the following form: WML I r I r (6) K, t 1 B, t 1 2 m, t 3 B, t 1 m, t where WML t is the momentum profit with the K-month holding period in month t, I B,t 1 is an ex ante bear market indicator that takes the value of if the cumulative TAIEX return in the past 24 months is negative and is zero otherwise, r m,t is the TAIEX return in excess of the risk-free rate in month t. The intercept from Equation (6) represents the risk-adjusted momentum profit accounting for the time-varying market risk, and 1 captures the incremental return in bear markets. We perform the regression of Equation (6) separately for strategies constructed based on CO D, non-hit and limit-hit COs and report the results in Table 9. [Insert Table 9 about here] The results from Panels A and B indicate that the risk-adjusted abnormal returns for the CO D and non-hit CO strategies remain significantly positive in intermediate terms and negative in long terms. Thus the profitability of the two strategies is not affected by the effects of bear 21

24 markets and time-varying market risk. In addition, the coefficients on 1 are negative but insignificant with 1-year holding periods. Despite its insignificance, the 1 coefficient in absolute value is very close to the coefficient. That is, the momentum profit in bear markets ( + 1 ) controlling for time-vary market risk is about zero and insignificant. For long-term profits, the two strategies have negative s and positive 1s with similar magnitude in absolute value, indicating that the long-term reversal is more pronounced in bull markets than in bear markets. It is also notable that the coefficients on 2 and 3 do not exhibit consistent patterns and are insignificant in most cases, indicating that the return predictability of CO D and non-hit CO is unlikely to be explained by the market risk and is not subject to changes in market risk. For the limit-hit CO strategy, as presented in Panel C, the coefficients on are all negative across different holding horizons with significance in the intermediate term. The coefficients on 1, on the contrary, are all positive but insignificant. This evidence suggests that the price correction of the limit-hit CO strategy is stronger in bull markets than in bear markets. Unlike CO D and non-hit CO strategies, the limit-hit CO strategy has significantly positive coefficients on 3, indicating a striking increase in market beta of the strategy in bear markets Alternative measure of continuing overreaction based on idiosyncratic volatility In addition to trading volume, excess volatility is another important feature of investor overconfidence (DHS, 1998; Odean, 1998). To consider the information of volatility in forming investor overconfidence, we follow Byun, Lim, and Yun (2016) by replacing trading volume (Vol i,t ) with idiosyncratic volatility (IVOL i,t ) in equations (1) and (2) to obtain the alternative continuing overreaction measure (denoted as CO IVOL ). IVOL i,t is defined as in Section 3.3. We then construct the momentum strategy by forming quintile portfolios based on stocks values of 22

25 CO IVOL and observe their returns for holding periods within subsequent 5 years. In addition to raw returns, we also report risk-adjusted returns for this momentum strategy using Equation (6). We report the results in Table 10. Similar to the results for CO and CO D measures in Tables 1 and 6, the CO IVOL momentum generates significant return continuation in the intermediate term and reversals in the long term. This observation is robust to the consideration of time-varying market risk. Overall, the results from Table 10 provide additional support for the DHS model in explaining momentum and reversals in Taiwan. More importantly, our evidence is not sensitive to the way we construct our measure of continuing overreaction. [Insert Table 10 about here] 6. Conclusions Motivated by the argument of DHS (1998) that continuing overreaction built on investor overconfidence and biased self-attribution induces stock return predictability, Byun, Lim, and Yun (2016) propose the measure of continuing overreaction using weighted signed volumes and relate it to future stock predictability. Based on a sample of all common stocks listed on the TWSE, a market without the existence of traditional momentum phenomenon, we empirically show that Byun, Lim, and Yun s (2016) continuing overreaction predicts both intermediate-term momentum and long-term reversals in Taiwan. This market provides an interesting setting in examining this issue because of the imposition of price limits, a trading mechanism that is designed to prevent investors from overreacting to information. We investigate the impact of price limits on continuing overreaction in explaining intermediate-term momentum and long-term reversals by constructing two measures of continuing overreaction, non-hit and limit-hit COs, to isolate the information embedded in signed 23

26 volumes. We find that only the non-hit CO induces future profitability that is characterized by intermediate-term momentum and long-term reversals. Stocks with high signed volumes contemporaneous with positive and negative past returns, i.e., winners and losers of limit-hit CO, however, exhibit faster price corrections with no momentum. These findings indicate that the imposition of price limits seems to restrain investors overreaction behavior in Taiwan. The weighted signed volume in non-hit days is thus a cleaner measure of continuing overreaction that better captures the patterns associated with intermediate-term continuations and long-term reversals. The evidence in favor of the DHS model in explaining momentum is further verified by linking continuing overreaction with market dynamics. The continuing overreaction-based momentum strategy generates pronounced profits and long-term reversals only when the market continues in the same direction, during which the magnitude of investor overconfidence is enhanced. Finally, we show the profitability of the strategy is robust to time-varying market risk and the way we construct continuing overreaction. 24

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