Underreaction, Trading Volume, and Momentum Profits in Taiwan Stock Market

Underreaction, Trading Volume, and Momentum Profits in Taiwan Stock Market Mei-Chen Lin * Abstract This paper uses a very short period to reexamine the momentum effect in Taiwan stock market, focusing on trading volume, size, and book-to-market factors. It is shown that price momentum exists in Taiwan stock market. In addition, trading volume predicts both the magnitude and the persistence of future price momentum. Specifically, the momentum strategy from buying past low-volume winners and selling past high-volume losers have better performance than the momentum strategy from buying past winners and selling past losers. Though Fama and French [27] three factors can partially explain the momentum profits, the momentum effect cannot be subsumed by the difference in risk factors. The profitability of the momentum strategy also cannot be completely explained as a reward for bearing the exposure to industry factors. The more prolonged accumulation of returns and lack of any observable return reversal support delayed reaction as a better explanation for the momentum returns. Besides, momentums in size and industry portfolios are as strong as individual stocks. Keywords: Momentum; Size; Book-to-market; and Industry 1. Introduction In recent years, a large volume of empirical evidence has presented that security's returns are predictable based on public available information. Among the evidence of the predictability, short-term price continuation and long-term overreaction are identified as two of the most puzzling anomalies. 1 The evidence of price continuation documents that a momentum portfolio, which is formed by buying winner stocks and shorting loser stocks at the same time, will be profitable [19,38,53]. Jegadeesh and Titman [38] originally show that past winners continue to outperform past losers over the following 3-12 months. The momentum results have been extended in several studies. For example, Moskowitz and Grinblatt [49] find that best-perform- * Department of Finance, National United University, No. 1, Lien Da, Kung-Ching Li, Miao-Li 360, Taiwan; Address Correspondence to Mei-Chen Lin. E-mail: meclin@nuu.edu.tw. 1 Daniel, Hirshleifer, and Subrahmanyam [20] classify the anomalies as follows: 1. public event-based return predictability, 2. short-term price continuation, 3. long-term price reversal, 4. Unconditional excess volatility on asset prices relative to fundamentals, and 5. short-run post-earnings announcement stock price ``drift'' in the direction indicated by the earnings surprise, but abnormal stock price performance in the opposite direction of long-term earnings changes. 1115

Mei-Chen Lin ing industries continue to outperform the worst performing industries. In contrast, the overreaction evidence shows that asset prices overreact to information release over longer horizons of perhaps 3-5 years, and past winners (losers) tend to be future losers (winners) [3,5,12,14,19,22,23,27,28,40, 50,52]. Therefore, a contrarian strategy that buys stocks performing poorly over the past periods and sells stocks performing well over the same period will earn subsequent excess returns. Except for the evidence of short-term momentum (3 to 12 months) and long-term overreaction (3 to 5 years), several studies examine the short-term price movements based on a very short (i.e., daily, weekly, or, at most, monthly) period. For example, Brown and Harlow [10] detect large price reversal for losers, but winners do not show any decline after the first month. Based on weekly data, Howe [36] finds strong support for the overreaction hypothesis for both winners and losers over the subsequent ten weeks. With daily data, Bremer and Sweeney's [8] findings indicate that losers earn return of 3.95 percent over the five days after the event. In contrast, winners show virtually no excess returns in the period immediately following the event. In addition, Lehmann [43] provides some evidence of nonzero return autocorrelations at a very short horizon such as a day. However, among these anomalies, the return momentum effect is probably the most difficult to explain with the traditional risk-based asset pricing theory. For example, Fama and French [27] document that their three-factor model can explain the overreaction evidence, but not the continuation of short-term returns. Jegadeesh and Titman [38] conjecture that individual stock momentum is driven by investor underreaction to information. Additionally, Chan, Jegadeesh, and Lakonishok [15] show that intermediate-horizon return continuation can be partially explained by underreaction to earnings news. Moskowitz and Grinblatt [49] suggest that industry momentum drive much of individual stock momentum. More recently, Hong and Stein [34] and Hong, Lim, and Stein's [35] document that short-term price continuation is a consequence of the gradual diffusion of private information. Furthermore, motivated by several papers that suggest that past trading volume may provide valuable information about a security [11,21, 48], Lee and Swaminathan [42] integrate price momentum and trading volume and conclude that past volume predicts both the magnitude of persistence of future price momentum. This article further examines momentum in Taiwan stock returns, focusing on the role of industry, size, book-to-market (B/M) factors, and trad- 1116

ing volume. This research is motivated by the following facts. First, since the successful momentum strategies are mostly based on empirical research for the NYSE data, the apparent success of these strategies may due to institutional factors or may result from data mining. Then, as argued in Jegadeesh and Titman [39], it is important to test the robustness of momentum profits on different samples. Second, with the surge of institutional interest in emerging capital markets, it is important to understand how well these markets operate. Whereas, little attention has been focused on the informational efficiency of capital markets in developing countries. 2 For example, not much is known about whether Taiwan stock market also exhibits momentum or not. Third, the institutional setting and trading practices in Taiwan are quite different from New York. For example, there are no specialists and for many stocks there is no continuous trading. For these reasons, the paper studied all companies listed on the Taiwan Stock Exchange for the two decades between 1981 and 2001 to crosscheck if the momentum strategies are also profitable in the less-developed market such as Taiwan. In addition, Taiwan, which has been one of the highest turnover-ratio markets in the world, will provide more robust evidence about how past trading volume to interact with past returns in the prediction of future stock returns. This article further examines the usefulness of trading volume in predicting future returns for various price momentum strategies. 2 This study focuses on returns in a short window (a few days) around an event. One advantage of this approach is that because daily-expected returns are close to zero, the model for expected returns does not have a big effect on inferences about abnormal returns. Conversely, the long-term return anomalies are sensitive to model and statistical approach [see 28]. The other advantage of focusing on the short-term (i.e. daily) behavior of stock return is because mean reversion in stock market is primarily a long-term phenomenon, and the findings of long-term overreaction is often subject to the criticism that stock prices move toward their fundamental values in the long run. The focus on daily returns also does help to avoid mean reversion in the stock market, and any findings of short-term overreactions in the stock markets provide more robust evidence of the overreaction hypothesis. Overall, it is found the evidence of short-term momentum profits, a result similar to Fung, Leung, and Patterson [29]. 2 A recent exception is the work of Harvey [33] 2 Some literature addresses the impacts of Asia financial crisis on the stock volatility [16,37] and exchange rate [45]. 1117

Mei-Chen Lin In related papers, though Fung, Leung, and Patterson [29] and Hameed and Yuanto [31] addressed similar issues with the Basin Pacific data, my data cover a longer period and more numbers of firms, which provide more robust evidence about the findings. With monthly data, Hameed and Yuanto [31] documneted that momentum strategy does not yield significant returns. The difference between Hameed and Yuanto [31] and this paper may mainly come from the difference of data frequency, the numbers of portfolios formed [three for Hameed and Yuanto 31 and five for this paper], and the numbers of firms analyzed [94 for Hameed and Yuanto 31 and 653 for this paper]. Besides, in spite of simialr results, the portfolio weight used by Fung, Leung, and Patterson [29] is different from this paper. Different with the return-based weights used by Fung, Leung, and Patterson [29], this paper formed equal-weighted portfolios because to get a more robust result and to avoid any potential bias from implementing testing procedure, it is worth to do further research with different procedures [39]. With an extension of Fung, Leung, and Patterson [29] and Hameed and Yuanto [31], this paper also intends to find the potential sources of short-term momentum strategies since, as noted by Lo et al. [46] and Rhee and Chang [5], the behaviors of returns are affected by microstructure issues as well as government intervention, and accordingly the sources of momentum profits may vary with countries. It is found that, in Taiwan stock market, the profitability of momentum strategy cannot be completely explained as a reward for bearing the exposure to the three factors of the Fama and French [27] model, nor by exposure to industry factors. The more prolonged accumulation of returns and lack of any observable return reversal support that market underreaction better characterizes price momentum than overreaction. The results are consistent with Fung, Leung, and Patterson [29], who document that the consistent patterns of portfolio returns across Pacific Basin markets may be exploited by momentum trading strategies. This result also confirms with previous studies that stock prices in Pacific Basin countries are slow to respond economic information [4,29,46]. Besides, due to there is much evidence that size, B/M, and industry difference capture risk factors in returns [25,26], I also extend these results with individual stocks to size, book-to-market (B/M), and industry portfolios. It is found that momentum in size and industry portfolios are as strong as individual stocks. The insignificance of B/M is consistent with Chiu and Wei [17], in which they find that B/M effect does not exist in Taiwan stock market. The paper is organized as follows. Section 2 briefly describes the data and the methodology. Section 3 then analyzes the results, finding strong 1118

price momentum effects. Section 4 provides possible explanations based on some firm-specific characteristics, such as size, book-to-market ratios. This section also briefly describes some of the behavioral explanations for the momentum effect, and Section 5 provides the conclusions. 2. Data and Methodology The data consist of all common stocks listed on the Taiwan Security Exchange (TWSE) during the period January 1981 through December 2001. Daily stock returns, daily turnover ratio, firm size, and book-to-market (B/M) ratio are all taken from the Taiwan Economic Journal. The momentum investment strategy adopted in the paper is the equal-weighted portfolio based on extreme stocks [13,22,23]. This strategy buys only a fixed proportion of stocks among all stocks in the market that have been performed extremely badly over a certain ranking period, and sells the same amount of money on same proportion of stocks that performed extremely well. Each stock is assigned an equal weight in the portfolio. To avoid potential survivorship biases [e.g., 9], this paper does not require all securities included in a particular strategy at time t-p to have prices available at time t. If a security is included in a q-period strategy based on its past p-period performance, but it survives for less than q periods in the future (because of trading suspension or being delisted), its holding period return from time t up to its last trading week is calculated. To minimize small-sample biases in estimators of the components of the profits to the trading strategies, and to increase the power of the tests, overlapping holding periods are used here. To avoid the bias in cumulative abnormal returns (CAR) due to cumulation 3, the buy-and-hold subsequent return is used. Furthermore, since there is evidence of heteroskasticity for stock returns, the t-statistics are corrected using White-heteroskasdasticity method. 3. Momentum Returns to Individual Stocks 3.1 Price Momentum Table 1 summarizes results from several price momentum portfolio strategies over the next K days (1, 2, 3, 4, 5, 10, 15, and 20). To create this 3 The long-term performance measures calculated by cumulating single-period returns over long periods are upwardly biased because of bid-ask spreads and the bias per period is approximately s 2 /4 [7,18]. 1119

Mei-Chen Lin table, all common stocks are first ranked and then assigned to one of five portfolios on the basis of their returns over the previous J days (1, 2, 3, 4, or 5). Similar to Jegadeesh and Titman [38], daily equal-weighted portfolio returns are computed for each portfolio. For each portfolio formation period (J) and holding period (K), the equal-weighted average daily returns of buying the extreme winners (R5), buying the extreme losses (R1), and buying the extreme winners and selling the extreme losers (R5-R1) are presented. 4 It is found that the returns to the winners on the first day following the formation of the portfolio ranges from 0.235% (t=12.597) with J=5 to 0.419% (t=7.736) with J=1. 5 This suggests that, regardless of the holding periods, the short-term (one-day) price continuation for the winners is pronounced and statistically significant in Taiwan stock market. This table reports the average daily profits from momentum strategies that are formed by buying losers and selling winners based on their past performance during 1981 to 2001. At the beginning of each day, all stocks are sorted based on past J month returns and divided into 5 portfolios. R1 represents the loser portfolio with the lowest returns, and R5 represents the winner portfolio with the highest returns during the previous J days. K repre- Table 1 Returns to Price Momentum Portfolios for Various Formation and Holding Period J=1 J=2 J=3 J=4 J=5 K R5 R1 R5-R1 R5 R1 R5-R1 R5 R1 R5-R1 R5 R1 R5-R1 R5 R1 R5-R1 1 0.419-0.169 0.587 0.336-0.105 0.441 0.291-0.078 0.368 0.259-0.061 0.320 0.235-0.050 0.284 (12.597) (-5.489) (22.438) (10.581) (-3.338) (18.958) (9.373) (-2.424) (16.419) (8.464) (-1.915) (15.041) (7.736) (-1.565) (13.869) 2 0.600-0.164 0.764 0.517-0.094 0.611 0.453-0.070 0.253 0.419-0.048 0.468 0.387-0.027 0.414 (9.943) (-2.823) (20.746) (8.707) (-1.570) (16.365) (7.700) (-1.142) (13.913) (7.170) (-0.792) (12.703) (6.584) (-0.443) (11.354) 3 0.760-0.133 0.893 0.665-0.060 0.725 0.596-0.032 0.628 0.556-0.009 0.565 0.520 0.016 0.504 (8.740) (-1.574) (19.707) (7.724) (-0.695) (15.230) (6.926) (-0.367) (12.574) (6.444) (-0.105) (11.273) (5.994) (0.180) (9.956) 4 0.902-0.084 0.986 0.780-0.007 0.807 0.721 0.021 0.700 0.682 0.044 0.638 0.641 0.067 0.574 (7.989) (-0.767) (18.990) (7.137) (-0.059) (14.462) (6.401) (0.185) (11.671) (6.029) (0.387) (10.462) (5.637) (0.594) (9.088) 5 1.036-0.024 1.061 0.924 0.052 0.872 0.840 0.079 0.760 0.800 0.101 0.698 0.764 0.123 0.641 (7.497) (-0.182) (18.351) (6.705) (0.384) (13.579) (6.054) (0.576) (11.006) (5.750) (0.733) (9.761) (5.469) (0.896) (8.596) 10 1.641 0.277 1.364 1.554 0.338 1.216 1.485 0.341 1.144 1.464 0.339 1.125 1.447 0.336 1.111 (6.510) (1.176) (16.210) (6.165) (1.418) (12.784) (5.853) (1.415) (10.930) (5.751) (1.409) (10.072) (5.663) (1.398) (9.383) 15 2.262 0.593 1.670 3.174 0.644 1.530 2.114 0.641 1.474 2.070 0.636 1.434 2.047 0.643 1.404 (6.536) (1.868) (15.532) (6.271) (2.009) (12.605) (6.063) (1.981) (11.058) (5.940) (1.900) (10.064) (5.870) (1.976) (9.293) 20 2.768 1.012 1.756 2.684 1.055 1.630 2.623 1.056 1.567 2.586 1.057 1.529 2.559 1.053 1.505 (6.501) (2.573) (13.998) (6.285) (2.656) (11.401) (6.121) (2.635) (9.961) (6.038) (2.625) (9.057) (5.975) (2.613) (8.401) 4 The originally number of portfolio is (T-J-K) times 5, and T=5943. R1 and R5 represent the average returns by averaging (T-J-K) portfolios. 5 Asness [3] and Fama and French [27] begin the subsequent test period one month after the formation period ends, in order to avoid contaminating the momentum strategy with very short-term reversals. In the paper's results, very short-term reversals do not exist. Therefore, even after the bid-ask spread effect, the strategy of buying past winners and selling losers still earns positive profits. 1120

sents daily holding periods. Numbers in parentheses are t statistics corrected for heteroscedasticity and autocorrelation based on the consistent estimate of Newey and West (1987). All returns are measured in percent. The long-term ' price continuation for the winners is also pronounced. The average subsequent return of winners is consistently positive and significant for the first twenty days following the formation of the portfolio. In particular, the average return of the winner increase as the holding period following the initial return is extended, suggesting continual growth in the average returns of these winners. The average return of the winners reaches 2.768% (t=6.501) for J=1 and 2.559% for J=5 within twenty days. These results provide strong momentum evidence of the winner categories. The pattern for the losers is completely different for the winners. In particular, although there is significant price continuation on the first day following the initial reaction, no significant evidence of long-term momentum is found in the loser categories. On the contrary, when the holding periods are extended to 15 days, the evidence of price reversals for the losers is statistically significant. For example, the J=2 loser yields a fifteenth-day return of 0.644% (t=2.009). Other holding periods also provide similar results. These price-reversal results offer strong evidence that stock prices overreact to bad news. However, momentum profits from buying past winners and selling past losers are always significant positive, regardless of holding periods. Overall, my results confirm prior findings on price momentum. 6 Note that, for a given holding period, the returns to winners are decreasing with the length of the formation period. This implies the shorter the formation period, the stronger the magnitude and persistence of future price momentum. 7 By contrast, for a given holding period, the returns to losers are increasing with the lengthening of the formation period. This suggests that the price reversals for losers will be more imminent with longer formation periods. 6 Though the profits reported are eliminated when considering transaction costs, yet, these initial studies produced significant advancements in the understanding of return behavior even in the absence of reported economic profits. Assume that the minimum transaction cost of buying R5 and selling R1 is 1.17% (transaction tax 0.35%, commission fee 0.1425% per transaction), momentum profits of larger than 1.17% are found in some combination of (J, K) (For example, (J, K) = (1, 10), (1, 15), (1, 20), (2, 10), (2, 10), (2, 15), (3, 15), (3, 20), (4, 15), (4, 20), (5, 15), and (5, 20)). Thus, reducing the frequency of trades lessens the effect of transaction costs. 7 This implies that the profits do not increase with holding period. Another evidence comes from the finding with weekly data (not reported), it can be found that, when J = 1 and 2 (4) weeks, the profits from momentum strategy will decrease gradually after three (two) weeks following the formation of the portfolio. 1121

Mei-Chen Lin In sum, Table 1 confirms the existence of price momentum strategy in Taiwan stock market. I also extend prior results by documenting significant long-term ' price reversals for the losers in fifteen and twenty days. Nevertheless, winners exhibit significant price continuation. These results are somewhat consistent with the findings of Brown and Harlow [10] that losers have large price reversal, but winners do not show any decline after the first month. 8 These results are also consistent with those of Fung, Leung, and Patterson [29], who suggest that the daily returns of winner portfolios are positively autocorrelated while loser portfolios exhibit price reversals. 3.2 Volume-Based Price Momentum Table 2 reports returns to portfolios formed based on past returns and past trading volume. Trading volume (Volume) is defined as the average daily turnover in percentage during the portfolio formation period, where daily turnover is the ratio of the number of shares traded each day to the number of shares outstanding at the end of the day. At each day, all eligible stocks are sorted and then assigned to one of five portfolios according to their previous J day's returns (R1 to R5). The portfolios of stocks with the highest J-day returns are re-sorted by trading volume, thereby creating five volume portfolios (V1 to V5) within the highest J-day returns group. V1 represents the lowest trading volume portfolio, and V5 represents the highest trading volume portfolio. In this manner, 25 portfolios are constructed. The average daily returns over the next K days (K = 1, 2, 3, 4, 5, 10, 15, 20) are shown in the table. Several interesting results are obtained from Table 2. First, conditional on past returns, low volume stocks generally perform better than high volume stocks over the next 20 days. This is seen in the consistently negative returns 8 Taiwan Security Exchange (TSEC) occasionally restricts down price limits to 3.5% to reduce the non-economic impacts on stock markets. During this sample period, TSEC narrowed the down price limits four times. They include 921 earthquake (from 9/27/1999 to 10/8/1999), change of the reins of government (from 3/20/2000 to 3/25/2000), turbulent political situation (from 10/20/2000 to 12/31/2000), and US911 event (from 9/19/2001 to 9/21/2001). When price limits are restricted to 3.5% to reduce the non-economic impacts on stock markets, similar patterns of returns from momentum strategy would be found. But the returns mainly come from the price continual decrease of losers rather than from the continual increase of winners. The difference occurs because stricter price limits will constrain price adjustment during this panic time. Thus, it takes longer time for losers to reverse themselves. Basically, price may reflect both fundamental volatility resulting from information release and excess volatility due to investor's irrationality. If price limits restrain fundamental volatility and hurt information release process, they are useless. These results confirm with the view that price limits are ineffective when price volatility is due to fundamental information release. 1122

to the V5-V1 portfolio. For example, with a one-day portfolio formation period and one-day holding period (J = 1, K =1), low volume losers outperform high volume losers by 0.088% per day, whereas low volume winners outperform high volume winners by 0.137% per day. Similar results are found in almost every (J, K) cell. Obviously, firms that have low trading volume in the recent past tend to perform better than firms that have high trading volume do. Table 2 Returns to Portfolios Based on Price Momentum and Trading Volume J=1 J=2 J=3 J=4 J=5 V1 V5 V5-V1 V1 V5 V5-V1 V1 V5 V5-V1 V1 V5 V5-V1 V1 V5 V5-V1 1 R1-0.131-0.219-0.088-0.073-0.189-0.116-0. 042-0.166-0.124-0.028-0.160-0.131-0.009-0.135-0.126 (-4.508) (-6.272) (-3.807) (-2.519) (-5.135) (-4.962) (-1.430) (-4.404) (-5.185) (-0.987) (-4.161) (-5.436) (-0.327) (-3.509) (-5.126) R5 0.457 0.320-0.137 0.339 0.259-0.080 0.286 0.228-0.058 0.256 0.219-0.037 0.244 0.206-0.038 (12.530) (8.580) (-4.777) (10.022) (7.047) (-2.852) (8.947) (6.013) (-2.122) (8.118) (5.710) (-1.296) (7.848) (5.324) (-1.303) R5-R1 0.586 0.540 0.412 0.448 0.328 0.394 0.284 0.378 0.253 0.342 (16.347) (19.481) (12.576) (16.742) (10.929) (14.742) (10.375) (14.038) (9.880) (12.495) 2 R1-0.163-0.220-0.058-0.082-0.212-0.130-0.053-0.215-0.162-0.023-0.207-0.185 0.015-0.193-0.208 (-3.083) (-3.270) (-1.408) (-1.537) (-2.984) (3.063) (-0.993) (-2.942) (-3.687) (-0.430) (-2.787) (-4.041) (0.291) (-2.759) (-4.407) R5 0.713 0.415-0.298 0.558 0.377-0.181 0.458 0.348-0.110 0.420 0.335-0.085 0.376 0.324-0.048 (11.266) (5.836) (-5.922) (9.293) (5.189) (-3.564) (7.758) (4.663) (-2.109) (7.269) (4.446) (-1.570) (6.586) (4.188) (-1.203) R5-R1 0.875 0.635 0.640 0.589 0.511 0.562 0.443 0.543 0.361 0.516 (16.836) (15.410) (12.970) (13.016) (10.673) (11.716) (9.715) (10.974) (8.286) (10.048) 3 R1-0.141-0.209-0.068-0.070-0.204-0.135-0.032-0.221-0.189 0.013-0.208-0.222 0.071-0.202-0.273 (-1.868) (-2.119) (-1.176) (-0.920) (-1.965) (-2.236) (-0.430) (-2.081) (-2.991) (0.175) (-1.926) (-3.370) (0.967) (-1.863) (-4.096) R5 0.906 0.511-0.395 0.717 0.486-0.232 0.604 0.443-0.161 0.555 0.435-0.120 0.497 0.408-0.089 (10.376) (4.843) (-5.573) (8.448) (4.512) (-3.187) (7.240) (3.997) (-2.778) (6.720) (3.861) (-1.528) (6.055) (3.551) (-1.129) R5-R1 1.047 0.720 0.787 0.690 0.636 0.664 0.541 0.643 0.425 0.610 (16.412) (13.877) (12.645) (11.727) (10.302) (10.40) (8.963) (8.921) (7.186) (8.466) 4 R1-0.107-0.193-0.086-0.023-0.179-0.156 0.027-0.193-0.219 0.076-0.202 0.278 0.137-0.186-0.323 (-1.111) (-1.497) (-1.165) (-0.240) (-1.323) (-2.008) (0.278) (-1.398) (-2.713) (0.785) (-1.442) (-3.284) (1.440) (-1.326) (-3.771) R5 1.065 0.585-0.480 0.883 0.572-0.311 0.736 0.517-0.219 0.690 0.510-0.180 0.615 0.483-0.132 (9.619) (4.200) (-5.275) (8.142) (4.018) (-3.278) (6.830) (3.529) (-2.229) (6.473) (3.429) (-1.784) (5.793) (3.191) (-1.290) R5-R1 1.172 0.778 0.906 0.751 0.709 0.709 0.615 0.712-0.478-0.670 (16.084) (12.763) (12.454) (10.595) (9.524) (8.654) (8.268) (8.188) (6.462) (7.365) 5 R1-0.039-0.159-0.121 0.046-0.146-0.192 0.085-0.157-0.242 0.149-0.174-0.323 0.201-0.160 0.361 (-0.333) (-1.011) (-1.350) (0.397) (-0.886) (-2.041) (0.737) (-0.938) (-2.498) (1.279) (-1.026) (-3.193) (1.748) (-0.940) (-3.514) R5 1.218 0.668-0.550 1.009 0.639-0.371 0.858 0.581-0.278 0.801 0.574-0.227 0.729 0.551-0.178 (9.140) (3.880) (-5.005) (7.708) (3.620) (-3.213) (6.593) (3.200) (-2.330) (6.187) (3.315) (-1.849) (5.652) (2.952) (-1.426) R5-R1 1.256 0.827 0.964 0.785 0.773 0.738 0.652 0.748 0.528 0.711 (15.557) (11.917) (11.781) (9.422) (9.084) (7.668) (7.500) (7.310) (-6.038) (6.574) 10 R1 0.317 0.057-0.260 0.351 0.033-0.318 0.389-0.030-0.419 0.444-0.115-0.558 0.512-0.153-0.654 (1.583) (0.204) (-1.726) (1.771) (0.116) (-1.997) (1.950) (-0.103) (-2.557) (2.214) (0.387) (-3.271) (2.509) (-0.514) (-3.764) R5 1.836 1.094-0.742 1.584 1.051-0.533 1.437 1.084-0.353 1.433 1.092-0.341 1.360 1.088-0.272 (7.866) (3.403) (-3.847) (6.932) (3.193) (-2.648) (0.621) (3.229) (-1.700) (6.189) (3.233) (-1.581) (5.899) (3.188) (-1.241) R5-R1 1.519 1.037 1.233 1.017 1.048 1.114 0.989 1.206 0.859 1.241 (13.467) (9.535) (10.504) (7.709) (8.303) (7.427) (7.275) (7.403) (-6.069) (7.123) 15 R1 0.719 0.278-0.434 0.703 0.204-0.499 0.743 0.057-0.686 0.811-0.049 0.860 0.895-0.080-0.976 (2.617) (0.736) (-2.166) (2.615) (0.530) (-2.413) (2.726) (0.146) (-3.200) (2.956) (0.125) (-3.849) (3.252) (-0.203) (-4.306) R5 2.493 1.550-0.944 2.181 1.490-0.691 2.035 1.536-0.499 2.014 1.541-0.473 1.928 1.497-0.431 (7.787) (3.516) (-3.689) (6.971) (3.303) (-2.565) (6.432) (3.355) (-1.814) (6.372) (3.344) (-1.649) (6.121) (3.238) (-1.495) R5-R1 1.781 1.271 1.478 1.286 1.292 1.479 1.204 1.590 1.033 1.578 (12.991) (9.155) (10.181) (7.495) (8.129) (7.587) (6.947) (7.483) (5.744) (6.975) 20 R1 1.194 0.585-0.609 1.160 0.459-0.701 1.209 0.297-0.912 1.285 0.221-1.064 1.508 0.238-1.270 (3.523) (1.257) (-2.481) (3.451) (0.972) (-2.795) (3.553) (0.623) (-3.546) (3.744) (0.459) (-3.956) (4.431) (0.497) (-4.652) R5 3.018 1.963-1.055 2.619 1.878-0.741 2.517 1.903-0.614 2.530 1.930-0.560 2.705 1.976-0.729 (7.660) (3.631) (-3.387) (6.860) (3.401) (-2.290) (6.565) (3.399) (-1.859) (6.580) (3.416) (-1.727) (6.914) (3.528) (-2.092) R5-R1 1.824 1.378 1.459 1.418 1.309 1.607 1.245 1.709 1.197 1.737 (11.593) (8.420) (8.745) (6.989) (7.130) (6.955) (6.170) (6.744) (-5.551) (6.494) 1123

Mei-Chen Lin This table reports the average daily profits from momentum strategies based on past returns and past daily turnover during 1981 to 2001. At the beginning of each day, all stocks are sorted based on past J month returns and divided into 5 portfolios. R1 represents the loser portfolio with the lowest returns, and R5 represents the winner portfolio with the highest returns during the previous J days. K represents daily holding periods. The stocks are then independently sorted based on the turnover ratio over the past J days and divided into five portfolios. V1 represents the lowest trading volume portfolio, and R5 represents the highest trading volume portfolio. Numbers in parentheses are t statistics corrected for heteroscedasticity and autocorrelation based on the consistent estimate of Newey and West (1987). All returns are measured in percent. The findings that low volume firms earn higher expected returns are consistent with the liquidity hypothesis proposed by Datar et. al.[21]. According to the liquidity hypothesis of Amihud and Mendelson [2], the portfolio with lower liquidity should command a higher illiquidity premium and earn higher expected returns. To further examine if the liquidity hypothesis really exists in Taiwan stock market, Table 3 reports returns to portfolios formed based on past trading volume. Generally, the volume-based results also confirm the previous findings that low volume stocks outperform high volume stocks. This table reports the average daily profits from momentum strategies that are formed by buying low-volume stocks and selling high-volume stocks based on their past performance during 1981 to 2001. At the beginning of each day, all stocks are sorted based on past J daily turnover ratio and divided into five portfolios. V1 represents the lowest trading volume portfolio, and R5 represents the highest trading volume portfolio. Numbers in parentheses are t statistics corrected for heteroscedasticity and autocorrelation based on the consistent estimate of Newey and West (1987). All returns are measured in percent. A closer examination shows that low volume losers (R1V1) exhibit price reversal strongly in the next 20 days relative to high volume losers (R1V5). Moreover, the longer the formation period for the low-volume portfolios, the more imminent the future price reversals. However, on the contrary, the shorter the formation period for the high-volume portfolios, the more imminent the future price reversals. On the other hand, low volume winners (R5V1) generally outperform high volume winners (R5V5). These results agree with Lee and Swaminathan [42], in which they find that low (high) volume losers (winners) experience faster momentum reversals. 1124

Table 3 Returns for Volume-Based Momentum Portfolios K J=1 J=2 J=3 J=4 J=5 1 V5 0.039 0.041 0.034 0.034 0.031 (1.165) (1.220) (1.044) (1.020) (0.922) V1 0.069 0.073 0.070 0.067 0.068 (2.664) (2.827) (2.947) (2.834) (2.910) V1-V5 0.030 0.032 0.036 0.033 0.037 (2.029) (2.112) (1.997) (1.778) (1.985) 2 V5 0.092 0.092 0.079 0.078 0.076 (1.415) (1.404) (1.222) (1.191) (1.163) V1 0.146 0.152 0.149 0.145 0.148 (2.887) (3.023) (3.213) (3.148) (3.235) V1-V5 0.054 0.060 0.071 0.067 0.072 (1.871) (2.043) (1.963) (1.840) (1.936) 3 V5 0.146 0.149 0.127 0.129 0.127 (1.530) (1.550) (1.333) (1.341) (1.307) V1 0.226 0.232 0.231 0.225 0.225 (3.049) (3.3134) (3.391) (3.323) (3.345) V1-V5 0.080 0.083 0.104 0.096 0.098 (1.902) (1.922) (1.952) (1.768) (1.798) 4 V5 0.204 0.209 0.185 0.185 0.180 (1.631) (1.663) (1.474) (1.460) (1.412) V1 0.310 0.316 0.315 0.308 0.308 (3.196) (3.260) (3.536) (3.474) (3.501) V1-V5 0.106 0.107 0.130 0.123 0.129 (1.950) (1.905) (1.862) (1.732) (1.796) 5 V5 0.262 0.244 0.244 0.242 0.236 (1.714) (1.592) (1.579) (1.553) (1.508) V1 0.394 0.400 0.398 0.390 0.391 (3.310) (3.620) (3.634) (3.585) (3.621) V1-V5 0.132 0.156 0.153 0.147 0.155 (1.984) (1.855) (1.788) (1.695) (1.767) 10 V5 0.560 0.541 0.537 0.528 0.515 (2.039) (1.942) (1.913) (1.873) (1.827) V1 0.832 0.794 0.794 0.779 0.775 (3.870) (4.003) (4.026) (3.970) (3.964) V1-V5 0.272 0.253 0.257 0.251 0.260 (2.281) (1.681) (1.675) (1.618) (1.666) 15 V5 0.886 0.857 0.851 0.835 0.819 (2.381) (2.266) (2.236) (2.816) (2.417) V1 1.271 1.234 1.227 01.211 1.212 (4.340) (4.550) (4.557) (4.524) (4.544) V1-V5 0.385 0.377 0.376 0.377 0.393 (2.366) (1.872) (1.826) (1.810) (1.881) 20 V5 1.240 1.187 1.177 1.160 1.136 (2.750) (2.547) (2.514) (2.470) (2.425) V1 1.741 1.701 1.693 1.682 1.683 (4.790) (5.075) (5.088) (5.077) (5.098) V1-V5 0.501 0.514 0.516 0.523 0.547 (2.488) (2.082) (2.042) (2.048) (2.135) Therefore, buying low volume winners and selling will high volume losers enhance the performance of the price-momentum strategy. In sum, winners outperform losers, low volume stocks generally outper- 1125

Mei-Chen Lin form high volume stocks even after controlling for price momentum, and price momentum is more pronounced among low volume stocks. 3.3 Simple and Early Strategy The results in Table 2 suggest that the magnitude and persistence of price momentum are a function of past trading volume. Price reversals are only found in losers, and more pronounced among low volume losers (R1V1). Conversely, price momentum is found in winners, and more pronounced among low volume winners (R5V1). These observations suggest two-volume based price momentum strategies. The first one, which involves buying low volume winners and selling high volume losers, is referred to as the early-stage strategy. The early-stage strategy tries to capture the notion that stocks in low-volume winners and high-volume losers exhibit future price momentum in a greater degree over a longer horizon. The second strategy, which involves buying high-volume winners and selling low-volume losers, is referred to as the late-stage momentum strategy. The late-stage momentum strategy is aimed to capture the idea that the price momentum in low volume losers reverses faster. Table 4 campers the mean returns of the simple price momentum strategy (simple) to the early strategy (early) and the late stage (late) strategy. Table 3 shows that the simple strategy earns 1.061% with a one-day portfolio formation period and five-day holding period (J=1, K=5). The early strategy earns 1.377% and the late strategy earns 0.706% for J=1 and k=5. In comparison, the profits from early strategy are stronger than those from late strategy and simple strategy. Similar results are found in almost every (J, K) cell. This evidence shows that the magnitude of price momentum can be predicted based on firm characteristics, such as trading volume. Furthermore, the returns from these three strategies exhibit price continuation even after 20 trading days. Therefore, I might be tempted to conclude that price momentum is driven by investor underreaction to information (see next sections for further discuss). This table reports daily returns from early and late stage price momentum-trading volume strategies and compares them with the returns from a simple price momentum strategy for the period 1981 to 2001. The earlystage strategy involves buying low volume winners and selling high volume losers. The late-stage momentum strategy involves buying high-volume winners and selling low-volume losers. R1 represents the loser portfolio with the lowest returns, and R5 represents the winner portfolio with the highest re- 1126

Table 4 Early and Late Stage Strategies Based on Price Momentum and Trading Volume K J=1 J=2 J=3 J=4 J=5 1 R5-R1(simple) 0.587 0.441 0.368 0.320 0.574 (22.438) (18.958) (16.419) (15.041) (9.088) R5V1-R1V5(early 0.677 0.528 0.452 0.415 0.379 (19.315) (16.108) (14.386) (13.125) (12.071) R5V5-R1V1(late) 0.452 0.333 0.269 0.247 0.215 (13.665) (10.835) (8.738) (8.247) (7.346) 2 R5-R1(simple) 0.764 0.611 0.523 0.468 0.641 (20.746) (16.365) (13.913) (12.703) (8.596) R5V1-R1V5(early 0.933 0.770 0.673 0.628 0.569 (16.821) (13.803) (11.808) (10.798) (9.792) R5V5-R1V1(late) 0.578 0.459 0.400 0.358 0.308 (10.770) (8.457) (7.265) (6.498) (5.478) 3 R5-R1(simple) 0.893 0.725 0.628 0.565 1.111 (19.707) (15.230) (12.574) (11.273) (9.383) R5V1-R1V5(early 1.115 0.922 0.825 0.763 0.699 (15.075) (11.974) (10.324) (9.315) (8.517) R5V5-R1V1(late) 0.652 0.555 0.475 0.422 0.336 (8.870) (7.437) (6.123) (5.328) (4.140) 4 R5-R1(simple) 0.986 0.807 0.700 0.638 0.284 (18.990) (14.462) (11.672) (10.402) (13.869) R5V1-R1V5(early 1.258 1.062 0.928 0.893 0.801 (13.717) (10.969) (9.2596) (8.652) (7.731) R5V5-R1V1(late) 0.692 0.595 0.490 0.434 0.346 (7.582) (6.312) (4.930) (4.266) (3.924) 5 R5-R1(simple) 1.061 0.872 0.760 0.698 0.414 (18.351) (13.759) (11.006) (9.761) (11.354) R5V1-R1V5(early 1.377 1.155 1.015 0.975 0.890 (12.708) (10.148) (8.612) (8.014) (7.321) R5V5-R1V1(late) 0.706 0.593 0.496 0.425 0.350 (6.502) (5.194) (4.122) (3.4485) (2.723) 10 R5-R1(simple) 1.364 1.216 1.144 1.125 0.504 (16.210) (12.784) (10.930) (10.072) (9.956) R5V1-R1V5(early 1.779 1.551 2.836 1.547 1.513 (10.302) (8.673) (6.987) (7.957) (7.577) R5V5-R1V1(late) 0.777 0.699-0.161 0.648 0.587 (4.060) (3.422) (-0.317) (2.932) (2.579) 15 R5-R1(simple) 1.669 1.530 1.474 1.434 1.404 (15.532) (12.605) (11.058) (10.064) (9.293) R5V1-R1V5(early 2.215 1.977 1.978 2.064 2.009 (10.020) (8.580) (8.327) (8.233) (7.828) R5V5-R1V1(late) 0.838 0.787 0.973 0.731 0.602 (3.233) (2.846) (2.749) (2.446) (1.986) 20 R5-R1(simple) 1.756 1.630 1.567 1.529 1.505 (14.200) (11.400) (9.961) (9.057) (8.401) R5V1-R1V5(early 2.434 2.160 2.221 2.309 2.466 (9.062) (7.760) (7.773) (7.586) (7.819) R5V5-R1V1(late) 0.769 0.718 0.695 0.645 0.467 (2.437) (2.151) (1.994) (1.788) (1.281) turn during the previous J days. K represents daily holding periods. V1 represents lowest trading volume portfolio, and R5 represents the highest trading volume portfolio. Numbers in parentheses are t statistics corrected for heteroscedasticity and autocorrelation based on the consistent estimate of Newey and West (1987). All returns are measured in percent. 1127

Mei-Chen Lin 3.4 Momentum Returns to Size, BM, and Industry Portfolios Jegadeesh and Titman [38] use individual firms in their tests and show that past winners continue to outperform past losers. Moskowitz and Grinblatt [49] present similar patterns in industry portfolios. Lewellen [44] extend these results to size and B/M portfolios because there is much evidence that they capture risk factors in returns [25,26]. He finds that momentum in size and B/M portfolios are as strong as individual stocks. Therefore, despite tests with individual stocks, this article also explores the profitability of portfolio-based momentum strategies. The industry, size, and B/M portfolios are constructed as follows. The daily returns of 13 industry portfolios are obtained from Taiwan Economic Journal. Ten size and B/M portfolios are based on the market value of equity and the ratio of book equity to market value in the previous year, respectively. Table 5 shows the momentum results for size, BM, and industry portfolios. The table reports profits for price-momentum strategies that use portfolios sorted by size, book-to-market, and industry. R1 represents the loser portfolio with the lowest returns, and R5 represents the winner portfolio with the highest returns during the previous J days. K represents daily holding periods. Numbers in parentheses are t statistics corrected for heteroscedasticity and autocorrelation based on the consistent estimate of Newey and West (1987). All returns are measured in percent. I find that momentum is strong in both individual stocks and portfolios. Specifically, there is significant long-term price continuation for the winners of industry portfolios and size-sorted portfolio. The average subsequent return of winners is consistently positive and significant even after twenty days following the formation of the portfolio. In particular, the average return of the winners increase as the holding period following the initial return is extended, suggesting continual growth in the returns of the industry and size-sorted portfolio. The average subsequent return to the winners of the size portfolio reaches 1.305% (t=3.556) for J=1 and 1.367% (t=3.611) for J=5 within twenty days. These results provide strong evidence that momentum in size and industry portfolios are as strong as momentum in individual stocks. For losers of the size portfolios, momentum exists (though it is not significant) on the first two days. But it quickly diminishes and turns to contrarian profits. When the holding periods are extended to 10 days or more, the evidence of overreaction for the losers is statistically significant. For example, the losers of the sized portfolio yield a 10-day the cumulative profit 1128

Table 5 Price Momentum Returns to Size, B/M, and Industry Portfolios J=1 J=2 J=3 J=4 J=5 K R5 R1 R5-R1 R5 R1 R5-R1 R5 R1 R5-R1 R5 R1 R5-R1 R5 R1 R5-R1 Panel A : Size portfolios 1 0.310-0.036 0.167 0.109-0.037 0.146 0.118-0.029 0.147 0.109-0.004 0.113 0.105 0.018 0.124 (4.369) (1.178) (7.327) (3.702) (1.211) (6.651) (4.068) (0.954) (6.821) (3.774) (0.124) (5.188) (3.587) (-0.600) (5.809) 2 0.212-0.018 0.230 0.198-0.017 0.214 0.194-0.006 0.200 0.197 0.005 0.191 0.188 0.012 0.176 (3.587) (-0.316) (6.798) (3.573) (-0.283) (6.071) (3.489) (-0.104) (5.506) (3.516) (0.092) (5.184) (3.298) (0.203) (4.585) 3 0.295 0.019 0.276 0.269 0.030 0.239 0.265 0.040 0.2250 0.262 0.048 0.214 0.252 0.063 0.189 (3.674) (0.228) (6.493) (3.355) (0.357) (5.211) (3.259) (0.475) (4.579) (3.185) (0.561) (4.212) (3.044) (0.733) (3.603) 4 0.358 0.090 0.268 0.340 0.095 0.244 0.325 0.099 0.226 0.317 0.130 0.187 0.308 0.124 0.184 (3.444) (0.842) (5.519) (3.254) (0.877) (4.439) (3.064) (0.902) (3.762) (2.975) (1.179) (2.986) (2.853) (1.130) (2.819) 5 0.428 0.134 0.293 0.399 0.149 0.249 0.377 0.167 0.210 0.380 0.193 0.187 0.370 0.190 0.181 (3.385) (1.028) (5.400) (3.129) (1.136) (3.958) (2.930) (1.261) (3.063) (2.920) (1.458) (2.590) (2.819) (1.427) (2.339) 10 0.705 0.440 0.265 0.675 0.463 0.211 0.675 0.506 0.169 0.660 0.550 0.110 0.659 0.519 0.139 (3.133) (1.945) (3.534) (2.990) (2.046) (2.306) (2.961) (2.211) (1.643) (2.876) (2.398) (0.965) (2.842) (2.434) (1.131) 15 0.922 0.743 0.249 1.012 0.737 0.275 1.036 0.778 0.258 1.023 0.809 0.214 1.050 0.763 0.287 (3.289) (2.480) (2.677) (3.349) (2.459) (2.412) (3.385) (2.571) (2.025) (3.325) (2.661) (1.489) (3.381) (2.490) (1.846) 20 1.305 1.044 0.261 1.340 1.070 0.270 1.359 1.087 0.2721 0.349 1.081 0.267 1.376 1.014 0.353 (3.556) (2.851) (2.565) (3.643) (2.908) (2.087) (3.635) (2.924) (1.842) (3.585) (2.892) (1.597) (3.611) (2.700) (1.966) Panel B : B/M portfolios 1 0.003 0.072 0.069-0.006 0.040 0.046-0.054 0.117 0.171 0.001 0.093 0.092-0.017 0.074 0.091 (0.061) (0.994) (0.904) (-0.137) (0.837) (0.887) (-1.109) (1.605) (2.120) (0.015) (1.331) (1.171) (-0.330) (1.046) (1.145) 2-0.002 0.088 0.090-0.048 0.099 0.148-0.062 0.162 0.223 0.001 0.155 0.155-0.020 0.090 0.110 (0.024) (0.866) (0.928) (-0.576) (0.996) (1.348) (-0.718) (1.198) (1.528) (0.009) (1.179) (1.088) (-0.218) (0.665) (0.746) 3-0.005 0.185 0.190-0.058 0.133 0.190-0.079 0.186 0.265-0.021 0.137 0.159-0.001 0.084 0.086 (-0.040) (1.230) (1.325) (-0.498) (0.870) (1.157) (-0.658) (0.974) (1.305) (-0.167) (0.720) (0.781) (-0.010) (0.434) (0.402) 4 0.015 0.174 0.159-0.026 0.120 0.146-0.023 0.098 0.121 0.028 0.069 0.041 0.026 0.074 0.048 (0.103) (1.042) (1.122) (-0.183) (0.669) (0.821) (-0.153) (0.470) (0.579) (0.178) (0.338) (0.193) (0.157) (0.354) (0.215) 5 0.038 0.180 0.142 0.005 0.031 0.026-0.020 0.035 0.055-0.006 0.010 0.0016 0.064 0.044-0.020 (0.224) (1.048) (0.553) (0.620) (0.095) (-0.532) (0.554) (0.376) (-0.094) (0.062) (0.521) (-0.005) (0.987) (0.603) (-0.190) 10 0.195 0.320 0.126 0.169 0.030-0.139 0.153 0.126-0.027 0.186 0.184-0.001 0.282 0.219-0.063 (0.671) (1.048) (0.553) (0.620) (0.095) (-0.532) (0.554) (0.376) (-0.094) (0.662) (0.521) (-0.005) (0.987) (0.603) (-0.190) 15 0.535 0.382-0.153 0.498 0.133-0.366 0.514 0.300-0.214 0.547 0.499-0.048 0.580 0.490-0.090 (1.494) (0.983) (0.562) (1.413) (0.319) (-1.127) (1.434) (0.703) (-0.612) (1.493) (1.106) (-0.125) (1.540) (1.074) (-0.219) 20 0.635 0.500-0.135 0.614 0.318-0.297 0.487 0.597 0.110 0.520 0.737 0.217 0.545 0.842 0.297 (1.436) (1.084) (-0.402) (1.434) (0.650) (-0.757) (1.112) (1.194) (0.257) (1.164) (1.394) (0.463) (1.197) (1.499) (0.573) Panel C : Industry portfolios 1 0.142-0.071 0.212 0.146-0.048 0.194 0.123-0.037 0.160 0.135-0.029 0.165 0.114-0.033 0.147 (4.681) (-2.333) (8.713) (4.855) (-1.559) (8.177) (4.195) (-1.223) (7.214) (4.491) (-0.999) (7.237) (3.785) (-1.140) (6.464) 2 0.239-0.080 0.319 0.252-0.049 0.301 0.203-0.043 0.245 0.216-0.046 0.263 0.190-0.031 0.221 (4.310) (-1.423) (8.846) (4.466) (-0.843) (7.734) (3.596) (-0.746) (6.281) (3.742) (-0.830) (6.478) (3.291) (-0.561) (5.295) 3 0.317-0.037 0.354 0.319-0.023 0.343 0.261-0.030 0.291 0.267-0.035 0.302 0.258 0.005 0.253 (3.973) (-0.460) (7.965) (3.923) (-0.280) (6.952) (3.155) (-0.366) (5.362) (3.159) (-0.433) (5.277) (3.066) (0.056) (4.250) 4 0.367 0.012 0.355 0.375 0.021 0.354 0.319 0.011 0.308 0.329 0.027 0.302 0.332 0.044 0.288 (3.524) (0.112) (6.885) (3.537) (0.196) (5.910) (2.917) (0.104) (4.606) (2.984) (0.253) (4.168) (3.012) (0.417) (3.830) 5 0.442 0.049 0.393 0.460 0.061 0.400 0.400 0.058 0.342 0.402 0.057 0.345 0.416 0.081 0.335 (3.470) (0.389) (6.739) (3.555) (0.471) (5.836) (3.043) (0.455) (4.397) (2.976) (0.444) (4.033) (3.063) (0.625) (3.728) 10 0.793 0.295 0.498 0.828 0.256 0.572 0.753 0.257 0.496 0.758 0.261 0.498 0.787 0.227 0.559 (3.458) (1.329) (5.655) (3.521) (1.138) (5.397) (3.155) (1.142) (4.169) (3.109) (1.161) (3.728) (3.219) (1.005) (3.930) 15 1.192 0.514 0.678 1.199 0.495 0.704 1.145 0.441 0.704 1.187 0.462 0.726 1.201 0.460 0.741 (3.753) (1.730) (5.891) (3.693) (1.640) (5.034) (3.499) (1.476) (4.516) (3.532) (1.541) (4.115) (3.572) (1.528) (3.947) 20 1.503 0.801 0.702 1.535 0.824 0.711 1.449 0.768 0.681 1.513 0.735 0.778 1.548 0.706 0.842 (3.852) (2.194) (5.253) (3.858) (2.220) (4.372) (3.610) (2.100) (3.756) (3.681) (1.994) (3.699) (3.760) (1.911) (3.838) for J=1 is 0.440% (t=1.945). Overall, momentum profits from buying past winners and selling past losers (R5-R1) are statistically significant. In particular, there is also continual growth in the momentum returns as the holding period is extended, suggesting the long-persistent profits from the momentum strategy. 1129

Mei-Chen Lin The results for B/M portfolios are completely different from the size-sorted and industry portfolios. There is no significant momentum or contrarian profits for B/M portfolios. These results are quite consistent with the results in next section that B/M factor has no explanatory power based on the Fama-French [25] three-factor model (see next section). The insignificance of B/M also confirms with Chiu and Wei [17], in which they find that B/M effect does not exist in Taiwan stock market. 4. Sources of Momentum Profits 4.1 Fama-French Risk Adjustments Table 6 provides evidence on the possible source of returns for the various volume-based price momentum strategies. The results from time-series regressions based on the following Fama-French [25] three-factor model are reported: (r i -r f )=a i +b i (r m -r f )+s i SMB+h i HML+ei, where r i is the daily return from portfolio i; r f is the daily return on the one-year term rate; r m is the value-weighted return on the Taiwan stock market index; SMB is the Fama-French small firm factor; HML is the Fama-French book-to-market value factor; b i, s i, h i are the corresponding factor loading; and a i is the intercept of the portfolio. Numbers in parentheses are t statistics corrected for heteroscedasticity and autocorrelation based on the consistent estimate of Newey and West (1987). For parsimony, Table 4 only reports the results for symmetrical combinations of portfolio formation and holding periods (J and K =1, 2, 3, 4, and 5 days). The estimated intercept coefficients from these regressions (a i ) are interceptable as the risk-adjusted return of the portfolio relative to three-factor model. The risk-adjusted profitability of a momentum strategy must reflect momentum in a component of stock returns not associated with exposure to the Fama-French factors. Focusing on these intercepts, it is clear that our earlier results cannot be completely explained by the Fama-French three factors. Specifically, the intercepts corresponding to R5-R1 are positive for both high and low volume categories. The results are consistent with the findings of Fama and French [27] that their three-factor model cannot explain the continuation of short-term returns. 1130

Table 6 Three-Factor Regressions of Daily Excess Returns on Price Momentum-Volume Portfolio V1 V5 V5-V1 V1 V5 V5-V1 V1 V5 V5-V1 Panel A: J=1, K=1 a b s R1-0.1635-0.2491-0.1020 0.0640 0.0884 0.0245-0.0497-0.1013-0.0573 (0.0001) (0.0001) (0.0001) (0.0022) (0.0003) (0.0210) (0.0201) (0.0170) (0.0409) R5 0.4330 0.2905-0.1589 0.0891 0.1142 0.0251-0.1230-0.1107-0.0135 (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0478) (0.0006) (0.0203) (0.0456) R5-R1 0.6128 0.55601 0.0251 0.0257-0.0796-0.0087 (0.0001) (0.0001) (0.1080) (0.0933) (0.0165) (0.0884) H Adj R 2 R1 0.0265 0.0521 0.0258 0.0041 0.0049 0.0009 (0.3772) (0.1791) (0.3301) R5 0.0070 0.0217 0.0148 0.0087 0.0061 0.0002 (0.8302) (0.6249) (0.6727) R5-R1 0.0196 0.0305 0.0016 0.0003 (0.0829) (0.0691) Panel B: J=2, K=2 a b s R1-0.1250-0.2664-0.1578 0.8816 1.2494 0.3678-0.7650-1.0663-0.3010 (0.0002) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) R5 0.5400 0.3217-0.2347 0.8651 1.3988 0.5337-0.6640-1.1053-0.4411 (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) R5-R1 0.6814 0.6045 0.0165 0.1493-0.1007-0.0393 (0.0001) (0.0001) (0.0960) (0.0001) (0.0673) (0.0741) H Adj R 2 R1 0.1333 0.1738 0.0406 0.3697 0.1738 0.0708 (0.1001) (0.0901) (0.3719) R5 0.1014 0.1325 0.0312 0.3243 0.4017 0.0996 (0.1255) (0.1222) (0.5828) R5-R1 0.0320 0.0414 0.0009 0.0090 (0.5337) (0.4171) Panel C: J=3, K=3 a b s R1-0.9108-1.0999-1.0584-0.1782-0.1463-0.3021-0.8647-1.0585-0.9160 (0.0830) (0.0095) (0.0210) (0.0733) (0.0601) (0.0905) (0.1086) (0.0514) (0.0871) R5-0.2451-0.4352-1.0594 0.1322 0.2046 0.4064-0.9081-0.9912-0.8053 (0.0204) (0.0274) (0.0214) (0.0945) (0.0162) (0.1006) (0.0928) (0.0582) (0.0332) R5-R1 1.5350 1.5340 0.3801 0.2758-0.0796-0.0087 (0.0245) (0.0247) (0.0834) (0.0623) (0.0165) (0.0884) h Adj R 2 R1 0.2128 0.2008 0.1771 0.003 0.00096 0.0007 (0.3772) (0.1791) (0.3301) R5 0.1679 0.2156 0.2368 0.0003 0.0006 0.0008 (0.3282) (0.2452) (0.1604) R5-R1 0.2340 0.1743 0.0016 0.0003 (0.1555) (0.2986) Panel D: J=4, K=4 a b s R1-1.1490-1.4378-1.5178-0.0550-0.1257-0.1915-0.7799-0.8428-0.7931 (0.0789) (0.0943) (0.0753) (0.0672) (0.0516) (0.0932) (0.0435) (0.0702) (0.0848) R5-0.5166-0.7377-1.4501 0.0356 0.1802 0.2655-0.8137-0.6364-0.5530 (0.0460) (0.0916) (0.0899) (0.0494) (0.0519) (0.0508) (0.0482) (0.1228) (0.1494) R5-R1 1.8614 1.9291 0.1403 0.0663-0.6965-0.9366 (0.0290) (0.0238) (0.0444) (0.0681) (0.0879) (0.0767) h Adj R 2 R1 0.4308 0.3670 0.2918 0.0001 0.0000 0.0000 (0.2637) (0.3514) (0.4456) R5 0.3063 0.3571 0.4064 0.0001 0.0001 0.0000 (0.4283) (0.3677) (0.2924) R5-R1 0.4801 0.3655 0.0000 0.0001 (0.2090) (0.3388) Panel E: J=5, K=5 a b s 1131