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Industry momentum strategies and autocorrelations in stock returns
Journal of Empirical Finance 11 (2004) 185 – 202 www.elsevier.com/locate/econbase
Industry momentum strategies and autocorrelations in stock returns Ming-Shiun Pan a,*, Kartono Liano b, Gow-Cheng Huang c a
Department of Finance and Information Management and Analysis, J.L. Grove College of Business, Shippensburg University, 1871 Old Main Drive, Shippensburg, PA 17257-2299, USA b Department of Finance and Economics, Mississippi State University, Mississippi State, MS 39762, USA c Department of Accounting and Finance, Alabama State University, Montgomery, AL 36117, USA Accepted 19 February 2003
Abstract In this study, we examine the sources of profits to momentum strategies of buying past winner industry portfolios and selling short past loser industry portfolios. We decompose the profit into (1) own-autocovariances in industry portfolio returns, (2) cross-autocovariances among industry portfolio returns, and (3) cross-sectional dispersion in mean portfolio returns. Our empirical results show that the industry momentum effect is mainly driven by the own-autocorrelation in industry portfolio returns, not by return cross-autocorrelations or by cross-sectional differences in mean returns. Indeed, the industry momentum strategy generates statistically significant profits only when own-autocorrelations are positive and statistically significant. The evidence is consistent with several behavioral models (e.g. Journal of Financial Economics 45 (1998) 307; Journal of Finance 53 (1998) 1839; Journal of Finance 54 (1999) 2143) that suggest positive own-autocorrelations in stock returns and hence the price momentum. D 2003 Elsevier B.V. All rights reserved. JEL classification: G12; G14 Keywords: Momentum strategies; Industry; Autocorrelation
1. Introduction Numerous studies have uncovered stock return anomalies based on trading strategies. For example, Jegadeesh and Titman (1993) find that trading strategies which buy past 6- to 12-month winners and short sell past losers earn significant profits over the subsequent 6* Corresponding author. Tel.: +1-717-477-1683; fax: +1-717-477-4067. E-mail address: [email protected] (M.-S. Pan). 0927-5398/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jempfin.2003.02.001
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to 12-month period. Moskowitz and Grinblatt (1999) further show that such momentum effects are mainly driven by industry factors in the sense that the profitability of individual stock momentum strategies can be substantially explained by industry momentum. That is, momentum strategies that buy stocks from past winning industries and sell stocks from past losing industries are highly profitable and can capture almost all the profits from individual stock momentum strategies. They also show superior returns to industry momentum strategies after adjusting for size, book-to-market, and microstructure effects. While Moskowitz and Grinblatt (1999) show the existence of an industry momentum effect, the sources of its profitability are unclear. They conjecture that such an effect might be due to ‘‘. . .there are. . . hot and cold sectors of the economy, and investors may simply herd toward (away from) these hot (cold) industries and sectors, causing price pressure that could create return persistence.’’ (p. 1287). This conjecture is consistent with a number of plausible explanations. For instance, Conrad and Kaul (1998) claim that momentum profits are primarily due to cross-sectional variation in unconditional mean returns.1 According to Conrad and Kaul’s arguments, if realized returns are strongly correlated to expected returns, then past winners (losers) that have higher (lower) returns tend to yield higher (lower) expected returns in the future. Thus, momentum strategies that buy past winner industries and short sell past loser industries would be profitable. Alternatively, the price momentum can also be explained by several existing behavioral models (e.g. Barberis et al., 1998; Daniel et al., 1998; Hong and Stein, 1999), which attempt to provide a theoretical framework for the empirical return anomalies documented in the finance literature. Hong and Stein (1999) propose a framework under which there are two types of investors: news watchers and momentum traders. Hong and Stein show that stock prices underreact to information in the short run if information diffuses gradually across news watchers. Their model indicates that this initial underreaction will induce trading from momentum traders, thereby exploring slow price movement. Eventually, prices will reverse to fundamentals in the long run when more and more momentum traders enter the market to earn a profit. Consequently, the Hong and Stein model implies positive autocorrelations in returns in the short run but negative autocorrelations in the long run. Like Hong and Stein, short-term underreaction is also present in the Barberis et al. (1998) model. However, Barberis et al. obtain the underreaction by assuming that investors exhibit a conservatism bias, meaning that investors are conservative in updating their priors. In contrast, Daniel et al. (1998) argue that the positive autocorrelation in returns is due to overreaction, not underreaction. According to the theory of Daniel et al., overconfidence, which would lead investors to overreact to information initially, together with continuing overreaction to news induced by attribution bias will result in positive autocorrelations in short lags and negative autocorrelations in long lags. In short, these behavioral models all suggest that positive autocorrelations in returns can cause the momentum effect. Finally, profits to momentum strategies can arise because of cross-sectional correlations among stocks (Lo and MacKinlay, 1990a). Lo and MacKinlay show that momentum 1 However, Jegadeesh and Titman (2002) suggest that Conrad and Kaul’s results suffer from small sample biases, and when these biases are corrected for in the tests, the variation in mean returns explains very little of the momentum profits.
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profits are negatively related to cross-sectional serial correlations, meaning that positive (negative) cross-autocorrelations lead to losses (profits) for a trading strategy that buys winner stocks and short sells loser stocks. Under this scenario, if winner stocks are negatively cross-serially correlated with loser stocks, then a strategy can generate profits by buying past winners and short selling past losers. Lewellen (2002) finds that the profitability of portfolio-based momentum strategies is mainly due to negative cross-serial correlations among portfolio returns. In this study, we attempt to identify the sources of profits to industry momentum strategies documented by Moskowitz and Grinblatt (1999). To this end, we follow Lo and MacKinlay (1990a) and decompose profits to momentum strategies applied onto industry portfolios into three sources: (1) the autocorrelation in industry portfolio returns; (2) the negative of cross-serial correlation among industry portfolios, so that positive cross-serial correlation contributes negatively to the profit; and (3) the cross-sectional variation in unconditional means. Our empirical results based on weekly data from 1962 to 1998 show that the industry momentum effect is primarily due to return own-autocorrelations, not to either return cross-autocorrelations or cross-sectional differences in mean returns. Indeed, the industry momentum strategies yield statistically significant profits only when return autocorrelation components are positive and significant. Thus, our finding indicates that momentum is caused by positive autocorrelation as suggested by the behavioral models, not by cross-serial correlation or by cross-sectional variation in unconditional means. The rest of the paper is organized as follows. Section 2 describes the momentum strategies that we follow in formulating trading rules and discusses the decompositions of momentum profits into various sources. Section 3 describes the data of industry portfolio returns and provides a test for autocorrelations in returns of industry portfolios. Section 4 presents industry momentum profits and analyzes the robustness of the results. The conclusion is in the final section.
2. Momentum strategies and sources of profits The primary motivation of momentum strategies is to exploit profits from trading strategies that long winners and short losers. Most prior studies (e.g. Jegadeesh and Titman, 1993; Conrad and Kaul, 1998; among many others) formulate trading strategies by buying or selling securities at time t, based on their performance at time t 1, with k horizons between time t 1 and t. As Conrad and Kaul show, the profitability of such trading strategies depends on the first-order own-autocovariances of security returns, the first-order cross-autocovariances, and the variation in the mean returns of individual securities. That is, formulating trading strategies in this way does not allow one to determine the impact of autocovariances at higher orders on the profits. Instead, we follow Lo and MacKinlay (1990a) and consider a strategy that buys industry portfolios at time t that were winners at time t k and short (sell) industry portfolios at time t that were losers at time t k. Formulating the momentum strategy in this manner permits us to decompose the profit into the kth-order own-autocovariance and cross-autocovariance of industry portfolio returns. As such, we can evaluate the relation between industry momentum profits and own- and cross-autocorrelation coefficients of industry portfolio returns at
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various lags, rather than just the first-order own- and cross-autovariances. See Eq. (5) below for more detail. Specifically, the momentum portfolio is constructed with investment weights in industry i determined as: wi;t ðkÞ ¼ ð1=N ÞðRi;tk Rm;tk Þ;
ð1Þ
where N is the number ofP industries available, Ri,t k is the return for industry i at time t k, and Rm;tk ¼ ð1=N Þ Ni¼1 Ri;tk is the return for an equal-weighted market portfolio at time t k. Eq. (1) shows that the investment weights are determined based on the performance of industries against the equal-weighted market index. The momentum strategy will buy winner industries at time t that outperform the market index at time t k and sell short industries at time t that underperform the market index at time t k. Several points concerning the investment weights should be noted. First, by construction, the investment weights lead to a zero-cost, arbitrage portfolio since the weights sum P to zero, i.e., Ni¼1 wi;t ðkÞ ¼ 0. Further, the total long and short position at time t, It(k), is given by It ðkÞ ¼
N X
Awi;t ðkÞA:
ð2Þ
i¼1
Second, Eq. (1) suggests that bigger winners and losers (in terms of their performances against the equal-weighted market index) will receive greater weights. Assigning greater weights to the more extreme performers allows us to capture the stock market momentum effect, whereby extreme price movements are to be followed by extreme movements in the same direction. Third, unlike most prior studies (e.g. Jegadeesh and Titman, 1993; Moskowitz and Grinblatt, 1999; among others) that focus on extreme losers and winners, we include all industry portfolios in formulating momentum strategies. As Fama and French (1996) document (see their Table VII), momentum profits tend to become smaller for average performance deciles. Thus, a momentum strategy that buys top winners and sells bottom losers might overestimate the profits. Finally, we can easily decompose momentum profits into different components based on investment weights in Eq. (1). The profit from the momentum strategy at time t, pt(k), is
pt ðkÞ ¼
N X
wi;t ðkÞRi;t
i¼1
¼
N 1X ðRi;tk Rm;tk ÞRi;t N i¼1
¼
N 1X Ri;tk Ri;t Rm;tk Rm;t : N i¼1
ð3Þ
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Assuming that unconditional mean returns are constant, i.e., l u E[Rt], and autocovariance matrix Wk u E[(Rt k l)(Rt l)], we can obtain the decompositions of the expected profit by taking expectations on both sides: E½pt ðkÞ ¼
¼
N 1X E½Ri;tk Ri;t E½Rm;tk Rm;t N i¼1
N 1X ðCov½Ri;tk ; Ri;t þ l2i Þ ðCov½Rm;tk ; Rm;t þ l2m Þ N i¼1
¼ Cov½Rm;tk ; Rm;t þ
N N 1X 1X Cov½Ri;tk ; Ri;t þ ðl lm Þ2 : N i¼1 N i¼1 i
ð4Þ
Eq. (4) indicates that the expected profits of momentum strategies come from three sources: (1) the negative of the kth-order autocovariance of the equal-weighted market index, (2) the average of the kth-order autocovariances of the industry portfolios, and (3) the variance of the mean returns of industry portfolios. Based on a multifactor model for stock returns, Moskowitz and Grinblatt (1999) show that momentum strategies based on industry portfolios generate almost identical average profits to those of individual stocks. Furthermore, they show that industry momentum accounts for a large portion of the profits from an individual stock momentum strategy. Moskowitz and Grinblatt’s results also suggest that return autocovariances largely contribute to momentum trading profits. Several recent studies (e.g. Barberis et al., 1998; Daniel et al., 1998; Hong and Stein, 1999) have developed behavioral models to establish links between return autocovariances and momentum. Barberis et al. hypothesize that a conservatism bias causes investors not to update their priors sufficiently in response to new information concerning a firm or an industry. As a result, security prices initially underreact to public information and produce trends in returns over short horizons, meaning that stock returns are positively autocorrelated. Like Barberis et al., Hong and Stein’s model also generates underreaction and postive return autocorrelations. However, they suggest that the underreaction arises because (1) heterogeneous investors observe different private information sets that diffuse gradually over time and across the investing public and (2) investors are boundedly rational in the sense that they can only incorporate a small subset of the available information into the pricing process. In contrast, Daniel et al. argue that positive serial correlation at short horizons is due to overreaction, not underreaction. The Daniel et al. model suggests that investors trade based on private information signals and tend to be overconfident in extracting information signals. As a result, stock prices overreact initially. Furthermore, when public information arrives, investors update their priors with an attribution bias. This attribution bias leads investors to become more overconfident if the noisy public information confirms what they already believe, but to adjust their confidence only slightly if the public information disconfirms their priors. Daniel et al. show that the overconfidence, together with the attribution bias, cause continuing overreaction and
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hence momentum at short horizons. In short, according to these behavioral models, momentum (or positive autocorrelation in stock returns) could arise because of investors’ underreaction or continuing overreaction to news. Alternatively, Lo and MacKinlay (1990a) show that momentum could be due to crossautocorrelations in returns and not due to return own-autocorrelations. To see this, Eq. (4) can be rewritten as ( ) N 1 X E½pt ðkÞ ¼ Cov½Rm;tk ; Rm;t 2 Cov½Ri;tk ; Ri;t N i¼1 þ
N N N 1X 1X Cov½R ; R þ ðl lm Þ2 i;tk i;t N 2 i¼1 N i¼1 i
¼ Ck þ Ok þ r2 ðlÞ:
ð5Þ
Eq. (5) shows that the profitability of the momentum strategy depends not only on the autocovariances of individual industry portfolios, denoted by Ok, but also on the crossautocovariances, denoted by Ck. Eq. (5) also shows that own-autocorrelation contributes to momentum profits positively, while cross-autocorrelation contributes to momentum negatively. Thus, momentum profits can be found if own-autocovariances and crossautocovariances are both negative and the latter dominates. In other words, the analogy between positive autocorrelation and momentum, as suggested by the behavioral models discussed previously, does not necessarily hold. The results reported by Lewellen (2002), in which he intends to determine the sources of momentum profits, seem to support the view that momentum is driven by cross-autocovariances in stock returns. Lewellen finds that industry, size, and book-to-market portfolios exhibit similar momentum in returns as that for individual stocks. His results also suggest that momentum is due to crossautocovariances because both the average own- and cross-autocovariances among the portfolios are negative, and the latter is more negative than the former. Apparently, Lewellen’s finding is inconsistent with the behavioral models, which imply that stock returns are positively serially correlated. He hypothesizes that the negative cross-serial covariance results from investors underreact to firm-specific news but overreact to macroeconomic news. Finally, Conrad and Kaul (1998) assert that momentum profits are mainly driven by the variation in the mean returns of individual equities, not by the time-series predictability in stock returns. They interpret momentum as variations in risk across assets. Intuitively, if realized returns are strongly correlated to expected returns, then momentum strategies that buy past winners and short sell past losers will yield positive profits because winners (losers) that have higher (lower) realized returns tend to yield higher (lower) expected returns in the future. To see this, consider the case that stock returns are both serially and cross-sectionally uncorrelated (i.e. stock returns are not predictable), then both the first and the second terms in Eq. (5) become zero and hence the entire momentum profit is due to the cross-sectional variation in mean returns. Thus, in the absence of predictability in stock returns, momentum can still arise as long as there are significant variations in mean returns
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or time-varying risk premiums. Theoretically, Berk et al. (1999) develop a dynamic model that relates a firm’s conditional expected return to the movements of its systematic risk. Berk et al.’s analysis also suggests that variables such as size and book-to-market can summarize changes in firms’ risks well. Their model implies that the momentum effect is related to the predictability of the movements in firms’ risks and hence their expected returns. Nevertheless, Fama and French (1996) show that abnormal momentum returns remain after adjusting for risk under their three-factor model of market return, size, and book-to-market, although the three-factor can capture most of asset pricing anomalies such as long-horizon return reversals. Furthermore, Jegadeesh and Titman (2002) show that the variation in mean returns explains very little of the momentum profits.
3. Data and autocorrelation analysis 3.1. Data To exploit the profitability of momentum strategies based on industry portfolios, we focus on weekly returns. The use of a weekly series enables us to increase the sample size and hence the power of the test. It also minimizes the possible overestimation of the momentum profitability due to spurious serial correlations associated with asynchronous trading and the bid – ask spread when higher frequency (e.g. daily) data are used. The weekly stock returns are derived from daily CRSP return files for the sample period from July 11, 1962, to December 30, 1998 using all NYSE, AMEX, and NASDAQ stocks. Firms are grouped into 20 industry portfolios according to their twodigit Standard Industry Classification (SIC) codes.2 Industry portfolio returns are calculated as the equally weighted average of returns of individual firms. From this daily return data, we generate an artificial daily closing price series for each of the 20 industry portfolios. The weekly return of each industry portfolio is then computed as the return from Wednesday’s closing price to the following Wednesday’s close.3 We use Wednesday close weekly returns because Chordia and Swaminathan (2000) find that return autocorrelations based on closing prices of any weekdays other than Wednesday are either too low or too high. Table 1 shows some summary statistics for the industry portfolios and market indexes. The average weekly return ranges from 0.475% for the electrical equipment industry to 0.279% for the petroleum industry. The average weekly return on the equal-weighted portfolio constructed from the 20 industry portfolios is 0.392% (or 20.4% per year), and the equal-weighted CRSP index is 0.358% (or 18.6% per year). Most of the industry portfolios have similar volatility as measured by standard deviation, though the petroleum industry 2
We use the same two-digit SIC groupings as those employed by Moskowitz and Grinblatt (1999). If Wednesday’s price is missing, then Thursday’s price is used. There are 41 cases in which Thursday’s price is used for the entire 1904-week sample period. Thus, the return at week t could be measured from Thursday to Wednesday if only the previous week’s price is missing, from Wednesday to Thursday if only the current week’s price is missing, or from Thursday to Thursday if both weeks’ prices are missing. Simple returns are used throughout the study, except for the variance ratio analysis that employs continuously compounded returns. 3
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Table 1 Summary statistics of weekly returns for industry portfolios, 1962 – 1998 Industry
SIC Codes
Mean (%)
Standard Deviation
Skewness
Kurtosis
D-stat.
1. Mining 2. Food 3. Apparel 4. Paper 5. Chemical 6. Petroleum 7. Construction 8. Prim. Metals 9. Fab. Metals 10. Machinery 11. Electrical Eq. 12. Transport Eq. 13. Manufacturing 14. Railroads 15. Other Transport 16. Utilities 17. Dept. Stores 18. Retail 19. Financial 20. Other Equal-Weighted Index Equal-Weighted CRSP Index
10 – 14 20 22 – 23 26 28 29 32 33 34 35 36 37 38 – 39 40 41 – 47 49 53 50 – 52, 54 – 59 60 – 69 Other
0.456 0.396 0.474 0.396 0.379 0.279 0.384 0.398 0.384 0.442 0.475 0.369 0.368 0.349 0.417 0.350 0.348 0.338 0.407 0.423 0.392
0.027 0.023 0.025 0.025 0.024 0.013 0.024 0.022 0.017 0.023 0.025 0.017 0.023 0.021 0.023 0.023 0.021 0.023 0.022 0.025 0.020
0.211 0.345 0.405 0.255 0.264 0.139 0.171 0.590 0.289 0.569 0.113 0.731 0.378 0.476 0.723 0.214 0.316 0.458 0.479 0.457 0.703
4.432 4.723 5.526 5.838 4.173 4.426 3.733 6.403 5.223 5.958 3.992 6.237 5.742 5.192 6.737 3.765 6.098 5.632 5.688 5.400 6.715
0.974* 0.971* 0.968* 0.973* 0.971* 0.961* 0.974* 0.958* 0.951* 0.960* 0.966* 0.962* 0.959* 0.968* 0.961* 0.979* 0.967* 0.970* 0.966* 0.967* 0.956*
0.358
0.020
0.599
5.990
0.957*
This table reports summary statistics of weekly returns for 20 industry portfolios. The industries are formed using the two-digit SIC codes from July 1962 – December 1998. Equal-weighted index is the equally weighted average return of the 20 industry portfolios, which has a 0.994 correlation with the equal-weighted CRSP stock return index. Kurtosis is coefficient of excess kurtosis. D-statistic is Kolmogorov – Smirnov D-statistic for testing normality. Asterisk indicates statistically significant at the 5% level.
has a relatively low volatility. In addition, all industry portfolios appear to be negatively skewed and have excess kurtosis, indicating that they are not normally distributed. Unlike Conrad and Kaul’s (1998) finding on individual securities, the variation in mean returns of industry portfolios is only 0.000223 1,000 1, which appears to be too small to generate any significant industry-based momentum profit. Thus, the profitability of a momentum strategy based on industry portfolios should be driven by their cross-autocorrelations and/or own-autocorrelations, not by the variation in their mean returns. 3.2. Autocorrelation analysis Table 2 shows the autocorrelations of industry portfolio returns at several lags. The autocorrelations at short lags (one to four weeks) are all positive and large, which is consistent with Lo and MacKinlay (1990b). Positive portfolio autocorrelations at short lags may partially reflect the lead-lag effect between large and small stocks that is associated with the delayed reaction of small stocks to news (see e.g. Lo and MacKinlay, 1990a; Boudoukh et al., 1994; McQueen et al., 1996; Richardson and
Table 2 Autocorrelations and variance-ratio analysis of the random walk hypothesis for industry portfolios Autocorrelation at Lag
Variance Ratio Test Statistic at Lag
1
2
4
12
26
2
1. Mining 2. Food 3. Apparel 4. Paper 5. Chemical 6. Petroleum 7. Construction 8. Prim. Metals 9. Fab. Metals 10. Machinery 11. Electrical Eq. 12. Transport Eq. 13. Manufacturing 14. Railroads 15. Other Transport 16. Utilities 17. Dept. Stores 18. Retail 19. Financial 20. Other Equal-Weighted CRSP Index
0.30 0.25 0.31 0.15 0.24 0.25 0.26 0.34 0.33 0.33 0.29 0.25 0.31 0.22 0.26 0.17 0.25 0.25 0.30 0.29 0.32
0.14 0.13 0.16 0.09 0.09 0.09 0.12 0.18 0.17 0.17 0.14 0.15 0.16 0.10 0.09 0.07 0.16 0.11 0.16 0.13 0.15
0.10 0.07 0.09 0.02 0.05 0.03 0.09 0.12 0.10 0.11 0.08 0.07 0.11 0.04 0.06 0.02 0.06 0.05 0.08 0.08 0.09
0.02 0.01 0.01 0.01 0.01 0.00 0.04 0.03 0.01 0.03 0.03 0.03 0.00 0.05 0.03 0.05 0.03 0.04 0.01 0.02 0.02
0.00 0.00 0.01 0.02 0.03 0.04 0.03 0.01 0.04 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.01 0.00 0.01
1.304 1.260 1.316 1.155 1.243 1.252 1.259 1.342 1.331 1.339 1.295 1.258 1.314 1.222 1.266 1.173 1.261 1.253 1.306 1.291 1.321
3 (7.01) (5.55) (6.46) (3.01) (5.46) (5.75) (5.76) (6.46) (7.33) (6.66) (8.03) (4.84) (5.98) (4.51) (4.48) (4.15) (4.61) (4.86) (6.16) (5.64) (6.26)
1.500 1.437 1.532 1.269 1.387 1.394 1.429 1.574 1.558 1.563 1.487 1.447 1.527 1.361 1.418 1.281 1.452 1.413 1.516 1.477 1.530
5 (8.11) (6.61) (7.69) (3.70) (6.15) (6.35) (6.73) (7.73) (8.64) (7.81) (9.06) (5.95) (7.14) (5.25) (5.03) (4.75) (5.66) (5.68) (7.38) (6.55) (7.33)
1.783 1.670 1.844 1.393 1.586 1.570 1.699 1.927 1.880 1.889 1.738 1.697 1.838 1.555 1.644 1.392 1.724 1.610 1.806 1.746 1.822
(9.42) (7.65) (9.17) (4.13) (6.97) (6.84) (8.22) (9.50) (10.04) (9.31) (9.84) (7.10) (8.68) (6.17) (5.96) (4.92) (6.89) (6.45) (8.75) (7.80) (8.61)
13
27
2.204 (9.44) 2.025 (7.85) 2.352 (9.89) 1.566 (4.15) 1.935 (7.34) 1.641 (5.07) 2.185 (9.25) 2.561 (10.98) 2.454 (10.67) 2.430 (10.11) 2.168 (9.49) 2.067 (7.57) 2.395 (9.87) 1.763 (5.81) 1.934 (6.18) 1.521 (4.23) 2.117 (7.52) 1.833 (6.15) 2.228 (9.13) 2.160 (8.40) 2.267 (9.03)
2.264 (7.38) 2.114 (6.40) 2.541 (8.57) 1.583 (3.29) 1.996 (5.79) 1.824 (4.78) 2.292 (7.45) 2.734 (9.36) 2.851 (10.03) 2.586 (8.58) 2.564 (9.05) 2.154 (6.29) 2.622 (8.75) 1.679 (3.89) 1.990 (5.17) 1.580 (3.44) 2.104 (5.82) 1.727 (4.12) 2.332 (7.55) 2.150 (6.40) 2.400 (7.63)
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Industry
This table reports serial correlations for industry portfolios and Lo and MacKinlay’s (1988) variance-ratio statistics for testing the significance of serial correlation. Oneweek is taken as a base observation interval. The variance ratio estimates are given in the main rows, with heteroskedasticity-robust z-statistics given in parentheses. Under the hypothesis that returns are serially uncorrelated, the variance ratio estimate is one, and the test statistics are asymptotically N(0,1). 193
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Peterson, 1999).4 Nevertheless, the magnitude of positive autocorrelations suggests that momentum strategies might work, especially at short lags. On the other hand, autocorrelations at higher lags (12 and 26 weeks) are in general negative (especially for 12 weeks) and are much smaller in magnitude. Also reported in Table 2 are Lo and MacKinlay’s (1988) variance ratio analysis for testing the significance of the autocorrelations of returns. Since Lo and MacKinlay’s variance ratio estimate at lag k is approximately a linear combination of the first k 1 autocorrelation coefficients, it permits us to detect serial uncorrelations. We calculate the variance ratio test statistic that is robust to heteroskedasticity for k equals 2, 3, 5, 13, and 27 weeks. All the heteroskedasticity-robust standard normal z-statistics are substantially higher than critical values at any conventional significance levels, suggesting that none of the price series of industry portfolios follow a random walk. Consistent with the autocorrelation coefficients, the increasing variance ratio estimates along lag k indicate that autocorrelations are in general positive. Thus, the variance ratio analysis also suggests the profitability of a momentum strategy.
4. Profits to momentum strategies and robustness tests 4.1. Profits to momentum strategies Since it is well known that autocorrelations at higher lags cannot be estimated precisely, a study that includes higher order autocorrelations in the analysis may not correctly measure the relation between momentum profits and the pattern of autocorrelations. Thus, we do not perform the analysis for lags longer than 26 weeks. Table 3 reports expected profits to momentum strategies implemented on industry portfolios for five different lags, with k equals 1 week, 2 weeks, 4 weeks, 12 weeks, and 26 weeks. For lag 1, the average of the expected profit is 0.00173 cents, 0.00107 cents for lag 2, 0.0009 cents for lag 4, 0.00005 cents for lag 12, and 0.00002 cents for lag 26. The profits appear to become smaller for higher lags, which could simply reflect the result that autocorrelations decline when lags increase. The z-statistics,5 which are asymptotically standard normal under the null hypothesis that the ‘‘true’’ profits are zero, are significantly different from zero at the 1% level for lags up to 4 weeks. At higher lags, they are not significant. The result of significant profits up to 4 weeks is consistent with those of Moskowitz and Grinblatt (1999), in which they show a very strong one-month momentum effect in industries. Their result also shows that the significance of intermediate-term (6-month) momentum industry strategies is partly due to the one-month effect. Table 3 also contains the three components that make up the average profit, Ck, Ok, and r2(l). It is noteworthy that for all lags, Ck and Ok are opposite in their signs, meaning 4 Positive portfolio autocorrelation could also result from non-synchronous trading (see e.g. Lo and MacKinlay, 1990b). However, Mech (1993) shows that nontrading can explain only a small part of portfolio autocorrelations. 5 The z-statistics are corrected for heteroskedasticity and autocorrelations up to eight lags based on the adjustments outlined in Newey and West (1987).
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Table 3 Profits to momentum strategies for industry portfolios Lag k
E[pt(k)]
Ck
Ok
r2(l)
1
0.0173 (12.697) 0.0107 (8.394) 0.0090 (7.439) 0.0005 (0.389) 0.0002 (0.181)
0.1121 ( 6.762) 0.0527 ( 4.034) 0.0263 ( 2.283) 0.0074 (0.738) 0.0027 ( 0.255)
0.1292 (7.468) 0.0632 (4.596) 0.0351 (2.904) 0.0071 ( 0.676) 0.0027 (0.238)
0.0002
647.98
746.82
1.16
0.0002
492.52
590.65
1.87
0.0002
292.22
390.00
2.22
0.0002
1480.00
1420.00
40.00
0.0002
1350.00
1350.00
100.00
2 4 12 26
%[ Ck]
%[Ok]
%[r2(l)]
This table contains the decomposition of average profits of momentum strategies that long past winner industry portfolios and short past loser industry portfolios. Expected profit is given by E[pt(k)] = Ck + Ok + r2(l), where Ck mainly depends on the average kth-order cross-autocovariance of the returns for the 20 industry portfolios, Ok depends on the average kth-order own-autocovariance, and r2(l) is the cross-sectional variance of the mean returns. The numbers in parentheses are z-statistics that are asymptotically N(0, 1) under the null hypothesis that the relevant parameter is zero, and are robust to autocorrelation and heteroskedasticity. All profit estimates are multiplied by 1,000.
that a positive (negative) autocorrelation is associated with a positive (negative) cross autocorrelation. Consistent with the autocorrelation coefficient estimates, all the estimates of the component Ok that mainly depends on own-autocorrelations are positive, except for lag 12. Also, the z-statistics show that the Ok estimates are significant up to lag 4. Similar to the own-autocorrelations, the Ck component that captures cross-autocorrelations is also significant up to lag 4. Comparing the two components, Ck and Ok, suggests that ownautocorrelations of industry portfolios are more important than their cross-autocorrelations in determining the profitability of momentum strategies.6 Specifically, for the short lags that show significant positive profits, the difference between the percentage contributions of Ok and Ck are close to 100%, with a larger percentage contribution for Ok. Therefore, our result indicates that own-autocorrelations account for most of the momentum profits, which supports Moskowitz and Grinblatt’s (1999) assertion that it is the serial correlation in industry return components that drives the industry momentum.7
6
The larger impact of portfolio own-autocorrelations than cross-autocorrelations in influencing the profitability of trading strategies could be related to the argument that cross-autocorrelations are simply due to portfolio return autocorrelations (see e.g. Boudoukh et al., 1994; Hameed, 1997). Richardson and Peterson (1999), however, provide evidence showing that cross-autocorrelations are not an artifact of portfolio autocorrelations. 7 Assuming that stock returns follow a multifactor linear process, Moskowitz and Grinblatt analytically decompose industry momentum profits into three sources, including the variation in mean returns across industries, the first-order serial covariance of Fama and French’s (1993) size, book-to-market, and market factor portfolios, and the first-order serial covariance of industry return components. They find that the cross-sectional variance of mean industry monthly returns is too small to contribute significantly to the industry momentum profits. They also find that none of the first-order serial covariance for six-month returns of the three Fama and French factor-mimicking portfolios is significantly different from zero. Given these results, they assert that the main source of the industry momentum profits must be from the positive serial covariance in industry return components. Using a different decomposition method, our study indeed provides a direct support to Moskowitz and Grinblatt’s argument.
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The finding of significant positive profits to momentum strategies based on industry portfolios seems in contrast with that reported in Lo and MacKinlay (1990a), in which they document positive expected profits from contrarian strategies that are implemented on individual securities. Since the profitability to trading strategies depends largely on autocorrelations, this seemingly conflicting result appears to relate to positive autocorrelations in portfolio returns, while individual returns are generally negatively autocorrelated (see Lo and MacKinlay, 1990a). Unlike Conrad and Kaul (1998), we find that the variation in industry portfolio mean returns has little contribution to the momentum profits, which is consistent with Moskowitz and Grinblatt (1999). For instance, the percentage contributions are only 1.16%, 1.87%, and 2.22% for lags 1, 2, and 4, respectively. Although this percentage contribution increases to 40 percent for lag 12 and to 100 percent for lag 26, the corresponding expected profits, however, are not significant. Note that our estimate of the cross-sectional variance in mean weekly returns of industry portfolios is 0.000223 1,000 1, which is about 24 times smaller than the estimate of 0.00535 1,000 1 reported in Conrad and Kaul based on a sample of 6,524 firms during the 1962 – 1989 period. 4.2. Bootstrapping analysis Our statistical inference is based on the z-statistic, which is assumed to follow a standard normal distribution. To check the sensitivity of our significance tests against this assumption, we perform a bootstrap test. To this end, we shuffle (with replacement) the returns of industry portfolios simultaneously so that both own-autocorrelations and crossautocorrelations are eliminated.8 We calculate the expected profits and the profit components of Ck and Ok as well as their corresponding z-statistics for each bootstrap sample. A total of 1,000 replications are implemented. The results from the bootstrap analysis are given in Table 4. The Kolmogorov –Smirnov D-statistics (not reported) cannot reject the normality hypothesis for any of the z-statistic series, suggesting that the corrections adjusting for autocorrelation and heteroskedasticity are appropriate. The bootstrap p-value at any lag provides the same statistical inference as the z statistic; that is, there are significant positive profits for momentum strategies up to lag 4. Concerning the above finding, an important caveat should be noted. The evaluation of the statistical significance of a trading strategy may suffer from the bias of drawing the conclusion based solely on the result from a single lag (e.g. lag 1). To mitigate this bias, we calculate a Wald statistic that provides a joint test by taking into account the correlations between the expected average profits at the five lags (k = 1, 2, 4, 12, 26 weeks): Wald ¼ fE½pðkÞ TRUE½pðkÞgVX1 fE½pðkÞ TRUE½pðkÞg;
ð6Þ
where E is the expectation operator, pðkÞ is a 5 1 vector of sample average profits, TRUE½pðkÞ represents the vector of zero ‘‘true’’ profits under the null 8 Since our benchmark portfolio is an equally weighted average return of the 20 industry portfolios, randomizing industry portfolio returns will effectively create a serially uncorrelated market portfolio return series. Hence, both the profit components of Ck and Ok should be close to zero.
M.-S. Pan et al. / Journal of Empirical Finance 11 (2004) 185–202 Table 4 Average profits of trading strategies from bootstrapped returns Lag k E[p (k)] Ck t Sample E[pt(k)]
95%
99%
P-value
1
0.0173 0.0016 0.0022 0.000 (12.697) (2.031) (2.785) 2 0.0107 0.0015 0.0020 0.000 (8.394) (1.968) (2.636) 4 0.0090 0.0015 0.0022 0.000 (7.439) (1.952) (2.806) 12 0.0005 0.0015 0.0021 0.386 (0.389) (2.000) (2.742) 26 0.0002 0.0016 0.0021 0.530 (0.181) (1.970) (2.580) Wald Statistic = 772.448 ( q-value = 0.000)
197
Ok
Sample Ck
95%
99%
Sample Ok
95%
99%
0.1121 ( 6.762) 0.0527 ( 4.034) 0.0263 ( 2.283) 0.0074 (0.738) 0.0027 ( 0.255)
0.0152 (1.585) 0.0140 (1.503) 0.0150 (1.563) 0.0143 (1.528) 0.0141 (1.554)
0.0219 (2.332) 0.0202 (2.144) 0.0227 (2.197) 0.0195 (2.076) 0.0210 (2.244)
0.1292 (7.468) 0.0632 (4.596) 0.0351 (2.904) 0.0071 ( 0.676) 0.0027 (0.238)
0.0151 (1.588) 0.0156 (1.595) 0.0154 (1.582) 0.0154 (1.584) 0.0151 (1.626)
0.0240 (2.459) 0.0234 (2.343) 0.0220 (2.285) 0.0218 (2.224) 0.0212 (2.283)
This table reports average actual and various fractiles of the decompositions of average bootstrapped profits to momentum strategies that long winner industry portfolios and short loser industry portfolios. Expected profit is given by E[pt(k)] = Ck + Ok + r2(l), where Ck mainly depends on the average kth-order cross-autocovariance of the returns for the 20 industry portfolios, Ok depends on the average kth-order own-autocovariance, and r2(l) is the cross-sectional variance of the mean returns. The bootstrap samples are constructed by first shuffling (with replacement) the weekly return series, then calculating profits for the momentum strategies for a replication of 1,000 times. The percentage column reports upper fractiles of the bootstrapped distribution. The numbers in parentheses are z-statistics that are asymptotically N(0,1) under the null hypothesis that the relevant parameter is zero, and are robust to autocorrelation and heteroskedasticity. The p-value reports the probability that the 1,000 bootstrap average profits from the bootstrap distribution are greater than the sample average profits of the actual strategy shown in the second column. The Wald statistic is computed by using the covariance matrix that describes the dependences among the five profit estimates as derived from the bootstrap distribution. The Wald statistic distributes as a v2 variate with 5 degrees of freedom, with a critical value of 11.070 at the 5% level. The q value reports the probability that the Wald statistic from the bootstrap distribution is larger than the sample Wald statistic. All profit estimates are multiplied by 1,000.
hypothesis, and X is a measure of the covariance matrix of pðkÞ estimated with the bootstrap Xij ¼ r2 ½pðiÞ; pðjÞ:
ð7Þ
The Wald statistic distributes as a m2 variate with five degrees of freedom. As shown in Table 4, the calculated Wald statistic of 772.488 is so large that the null hypothesis of zero profit for all five lags can be rejected at any significance level. 4.3. Non-synchronous trading effects The results reported in the preceding subsections suggest that return autocorrelation is a major source of the momentum effect for industry portfolios. However, non-synchronous trading will result in positive return autocorrelation for stock portfolios and hence may
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overestimate momentum profit.9 The spurious autocorrelation induced by the nontrading effect is expected to become smaller for lower frequency data. To gauge the impact of nonsynchronous trading on industry momentum profits, we also evaluate trading strategies for the data of two- (bi-weekly) and four-week (monthly) intervals.10 Table 5 shows that significant profits still exist for both bi-weekly and monthly data. For both sampling intervals, the average profits are highly significant at short lags, such as lags 1 and 2.11 Unlike the weekly interval, significant profits can also be made at higher lags. For instance, for the lag order of about 1 year (i.e. lag 26 for the 2-week interval and lag 12 for the 4-week interval), the average profits are 0.00409 cents and 0.01124 cents, respectively, and are both significant. Significant profits available at such a long lag indicate a nominal impact from the lead-lag effect. In addition, Boudoukh et al. (1994) estimate that the firstorder serial correlation for weekly return induced by nontrading can be as high as 0.18, which is much smaller than the average of our first-order autocorrelation estimates of 0.28 (see Table 2). Thus, non-synchronous trading cannot explain the industry momentum effect completely. More importantly, the results contained in Table 5 continue to show that the Ok component, which mainly depends on own-autocorrelation, is the driving force for the industry momentum effect. Specifically, for the six lags that show significant profits (i.e. lags 1, 2, and 26 for the 2-week interval and lags 1, 2, and 12 for the 4-week interval), the own-autocovariances are positive and highly significant, except for lag 2 of the 4-week interval. Relative to the own-autovariances, the cross-autocovariances contribute very little to the profits of industry momentum strategies. Indeed, for the six lags that yield significant profits, most of the values of the cross-autocovariance components are negative, meaning that they contribute negatively to the profits. For the two lags that the Ck component is positive (i.e. lag 1 for the 2-week interval and lag 2 for the 4-week interval), the values are small compared to those of the Ok component. For instance, the magnitude of the Ck component for lag 2 of the 4-week interval is only about one-fourth as large as that of the Ok component. When we compare the contributions to the profits between the own-autocovariances and the variation in mean returns, the results also show that own-autocovariances are the main source of industry momentum. That is, for the cases that the profits are significant, the percentage contributions of the variance in mean returns
9 For a discussion on the impact of non-synchronous trading on portfolio return autocorrelation, see, for example, Lo and MacKinlay (1990b). Lo and MacKinlay also show that non-synchronous trading can explain only parts of return autocorrelations. 10 Non-overlapping data are used in this analysis, although we also conduct the investigation on overlapping data. While the conclusion about the profitability for momentum strategies from non-overlapping data is qualitatively the same as that from overlapping data, the profits for overlapping data are substantially larger. For instance, the average profit for the 4-week interval for overlapping data at lag 1 is 0.0507 cents, whereas it is only 0.0176 cents for the non-overlapping data (about three times smaller). Such a large difference in profits between the two data sets suggests that studies that use overlapping data (e.g. Conrad and Kaul, 1998) might have overestimated the profits from trading strategies. 11 The significant profit for the four-week interval at lag 1 is consistent with that of Moskowitz and Grinblatt (1999), in which they show significant profits can be earned for industry momentum portfolios that are formed at time t based on returns in the previous month and held for one month.
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Table 5 Profits to momentum strategies for lower frequency data Ck
Ok
r2(l)
Panel A: sampling interval = 2 weeks 1 0.1290 (16.220) 2 0.0682 (9.627) 6 0.0075 (1.221) 13 0.0098 (1.634) 26 0.0409 (4.442) 30 0.0122 ( 1.552)
0.0009 (0.717) 0.0001 ( 0.127) 0.0002 (0.168) 0.0027 ( 2.537) 0.0018 ( 1.959) 0.0023 (1.777)
0.1192 (14.318) 0.0594 (8.064) 0.0017 ( 0.263) 0.0035 (0.599) 0.0337 (3.567) 0.0234 ( 3.094)
0.0089 0.0089 0.0089 0.0089 0.0089 0.0089
Panel B: sampling interval = 4 weeks 1 0.1764 (10.132) 2 0.0514 (3.094) 3 0.0168 (0.979) 6 0.0262 (1.433) 12 0.1124 (5.531) 16 0.0185 (1.037)
0.0024 ( 1.239) 0.0043 (1.994) 0.0044 (2.091) 0.0010 (0.586) 0.0018 ( 0.976) 0.0007 (0.354)
0.1490 (8.205) 0.0172 (1.020) 0.0175 ( 1.004) 0.0046 ( 0.251) 0.0843 (4.062) 0.0120 ( 0.652)
0.0299 0.0299 0.0299 0.0299 0.0299 0.0299
Lag k
E[pt(k)]
Panels A and B report the decomposition of average profits of momentum for sampling intervals of 2- and 4weeks, respectively. Expected profit is given by E[pt(k)] = Ck + Ok + r2(l), where Ck mainly depends on the average kth-order cross-autocovariance of the returns for the 20 industry portfolios, Ok depends on the average kth-order own-autocovariance, and r2(l) is the cross-sectional variance of the mean returns. The numbers in parentheses are z-statistics that are asymptotically N(0, 1) under the null hypothesis that the relevant parameter is zero, and are robust to autocorrelation and heteroskedasticity. All profit estimates are multiplied by 1,000. The Bonferroni-adjusted critical values for multiple tests of the significance for 6 lags together at the 5 percent and 1 percent levels are 2.395 and 2.929, respectively.
are much smaller compared with those of the own-autocovariance component, except for lag 2 of the 4-week interval. 4.4. Positive autocorrelations in portfolio returns The results reported so far suggest that industry momentum strategies are profitable, especially for short horizons. Furthermore, the primary source of momentum is ownautocorrelations of industry portfolios, rather than cross-autocorrelations or the variation in mean returns of portfolios. However, it is noteworthy that in addition to nonsynchronous trading, positive autocorrelations in stock portfolio returns may also reflect lead-lag effects between small and large stocks within a portfolio that are related to delayed reactions of small firms to common factors. Thus, positive autocorrelations likely will be present in stock portfolios regardless of the grouping methods used. If the lead-lag effects are driving the positive autocorrelation and hence the industry momentum, grouping methods other than those based on industry will deliver the momentum effect as well. If other grouping methods can yield similar profits as do the industry grouping, the industry momentum effect may be attributable to positive autocorrelations (i.e. the lead-lag effect) of stock portfolios constructed in other arbitrary ways. To find out whether other grouping methods will yield momentum profits, we apply the momentum strategies to 20 portfolios that are formed based on the first alphabet of the
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Table 6 Profits to momentum strategies for alphabet-based portfolios Lag k
E[pt(k)]
Ck
Ok
r2(l)
1 2 4 12 26
0.0011 ( 5.789) 0.0006 ( 3.469) 0.0002 (1.211) 0.0001 (0.706) 0.0002 ( 1.098)
0.1230 ( 7.210) 0.0583 ( 4.279) 0.0341 ( 2.890) 0.0081 (0.749) 0.0029 ( 0.258)
0.1218 (7.129) 0.0577 (4.224) 0.0343 (2.895) – 0.0080 ( 0.736) 0.0027 (0.241)
0.00002 0.00002 0.00002 0.00002 0.00002
This table reports expected profits to momentum strategies applied to 20 alphabet-based portfolios. Expected profit is given by E[pt(k)] = Ck + Ok + r2(l), where Ck mainly depends on the average kth-order crossautocovariance of the returns for the 20 industry portfolios, Ok depends on the average kth-order ownautocovariance, and r2(l) is the cross-sectional variance of the mean returns. The numbers in parentheses are zstatistics that are asymptotically N(0,1) under the null hypothesis that the relevant parameter is zero, and are robust to autocorrelation and heteroskedasticity. All profit estimates are multiplied by 1,000.
names of the respective companies.12 It is reasonable to expect that the alphabet-based portfolios do not consist of an industry feature, though positive own-autocorrelations might remain. Table 6 contains the results from this analysis. Not surprisingly, the variation of mean returns of the 20 alphabet-based portfolios is very small and hence contributes almost nothing to the profits. Also, as expected, the Ok profit component, which is closely related to the average own-autocovariance of portfolios, is positive and also highly significant for the first three lags. The Ck component that captures crossautocovariance is also significant for the first three lags. However, the positive and significant own-autocovariance does not deliver positive profits. Indeed, the profits for the first two lags are negative and it is insignificantly different from zero for lag three. Furthermore, when compared with the industry portfolio results in Table 3, it appears that the Ok estimates for the alphabet-based portfolios are slightly smaller than those for the industry portfolios, while the converse is true for the Ck estimates. It is also important to note that Ck is greater than Ok for the alphabet-based grouping, but it is the opposite for the industry grouping. In other words, although both grouping methods result in positive and significant own-autocovariances, only the industry grouping that has a higher average own-autocovariance than cross-autocovariance produces significant profits to momentum strategies.
5. Conclusions This study attempts to identify the sources of profits to momentum strategies that buy past winner industry portfolios and sell short past loser industry portfolios. To this end, we calculate profits to momentum strategies applied to industry portfolios, and decompose the 12 Twenty portfolios are formulated based on the first alphabet of the names of companies. The groupings are as follows: A for portfolio 1, B for portfolio 2, C for portfolio 3, D for portfolio 4, E for portfolio 5, F for portfolio 6, G for portfolio 7, H for portfolio 8, I for portfolio 9, J and U for portfolio 10, K and O for portfolio 11, L for portfolio 12, M for portfolio 13, N for portfolio 14, P for portfolio 15, Q, V, X, Y, Z, and numbers for portfolio 16, R for portfolio 17, S for portfolio 18, T for portfolio 19, and W for portfolio 20. We constructed 20 portfolios in this way so that the number of stocks included in each of the portfolios is similar.
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profits into three components: own-autocorrelations in industry portfolio returns, crossserial correlations among industry portfolios, and variation in unconditional mean returns of these industry portfolios. Using weekly returns from 1962 –1998, we find that industry momentum strategies can generate significant, positive profits, especially for short horizons (less than 4 weeks). More importantly, our results show that the industry momentum effect is mainly due to own-autocorrelations in industry portfolio returns, and is not caused by cross-autocorrelations or by cross-sectional variation in mean returns. Consistent with the behavioral models by Barberis et al. (1998), Daniel et al. (1998) and Hong and Stein (1999), our results show that the industry momentum effect is statistically significant only for cases when return autocorrelations are positive and also statistically significant. Due to lead-lag effects, industry portfolios are expected to exhibit positive autocorrelations and hence a significant industry momentum. However, our robust analysis shows that microstructure influences (e.g. non-synchronous trading) and grouping methods cannot totally explain the industry momentum effect. Of course, our finding of significant industry momentum profits that arise from return autocorrelations does not necessarily imply market inefficiency. Positive profits could be a result of spurious autocorrelations in industry portfolios due to still unknown economic sources, other than microstructure influences and grouping methods. While stocks within an industry tend to be highly correlated, it is not obvious why industry portfolios have such high own-autocorrelations and low cross-autocorrelations, especially at short lags. In addition, the economic magnitude of the momentum profits may become insignificant when transactions costs are taken into account. This is particular true for the result from examining higher frequency data (e.g. weekly) because of high turnovers. Nevertheless, future work might explore the sources of return autocorrelation and cross-autocorrelation patterns for portfolios formed based on industry.
Acknowledgements We thank Robert Fok, Hung-Gay Fung, seminar participants at the 2001 Financial Management Association meetings and Shippensburg University, and two anonymous referees for helpful comments.
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Daniel, K.D., Hirshleifer, D., Subrahmanyam, A., 1998. Investor psychology and security market under- and overreactions. Journal of Finance 53, 1839 – 1885. Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3 – 56. Fama, E.F., French, K.R., 1996. Multifactor explanations of asset pricing anomalies. Journal of Finance 51, 55 – 84. Hameed, A., 1997. Time-varying factors and cross-autocorrelations in short-horizon stock returns. Journal of Financial Research 20, 435 – 458. Hong, H., Stein, J.C., 1999. A unified theory of underreaction, momentum trading, and overreaction in asset markets. Journal of Finance 54, 2143 – 2184. Jegadeesh, N., Titman, S., 1993. Returns to buying winners and selling losers: implications for stock market efficiency. Journal of Finance 48, 65 – 91. Jegadeesh, N., Titman, S., 2002. Cross-sectional and time-series determinants of momentum returns. Review of Financial Studies 15, 143 – 157. Lewellen, J., 2002. Momentum and autocorrelation in stock returns. Review of Financial Studies 15, 533 – 563. Lo, A.W., MacKinlay, A.C., 1988. Stock market prices do not follow random walks: evidence from a simple specification test. Review of Financial Studies 1, 41 – 66. Lo, A.W., MacKinlay, A.C., 1990a. When are contrarian profits due to stock market overreaction? Review of Financial Studies 3, 175 – 205. Lo, A.W., MacKinlay, A.C., 1990b. An econometric analysis of nonsynchronous trading. Journal of Econometrics 45, 181 – 211. McQueen, G., Pinegar, M., Thorley, S., 1996. Delayed reaction to good news and the cross-autocorrelation of portfolio returns. Journal of Finance 51, 889 – 919. Mech, T.S., 1993. Portfolio return autocorrelation. Journal of Financial Economics 34, 307 – 344. Moskowitz, T.J., Grinblatt, M., 1999. Do industries explain momentum? Journal of Finance 54, 1249 – 1290. Newey, W.K., West, K.D., 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703 – 708. Richardson, T., Peterson, D.R., 1999. The cross-autocorrelation of size-based portfolio returns is not an artifact of portfolio autocorrelation. Journal of Financial Research 22, 1 – 13.
Industry momentum strategies and autocorrelations in stock returns Ming-Shiun Pan a,*, Kartono Liano b, Gow-Cheng Huang c a
Department of Finance and Information Management and Analysis, J.L. Grove College of Business, Shippensburg University, 1871 Old Main Drive, Shippensburg, PA 17257-2299, USA b Department of Finance and Economics, Mississippi State University, Mississippi State, MS 39762, USA c Department of Accounting and Finance, Alabama State University, Montgomery, AL 36117, USA Accepted 19 February 2003
Abstract In this study, we examine the sources of profits to momentum strategies of buying past winner industry portfolios and selling short past loser industry portfolios. We decompose the profit into (1) own-autocovariances in industry portfolio returns, (2) cross-autocovariances among industry portfolio returns, and (3) cross-sectional dispersion in mean portfolio returns. Our empirical results show that the industry momentum effect is mainly driven by the own-autocorrelation in industry portfolio returns, not by return cross-autocorrelations or by cross-sectional differences in mean returns. Indeed, the industry momentum strategy generates statistically significant profits only when own-autocorrelations are positive and statistically significant. The evidence is consistent with several behavioral models (e.g. Journal of Financial Economics 45 (1998) 307; Journal of Finance 53 (1998) 1839; Journal of Finance 54 (1999) 2143) that suggest positive own-autocorrelations in stock returns and hence the price momentum. D 2003 Elsevier B.V. All rights reserved. JEL classification: G12; G14 Keywords: Momentum strategies; Industry; Autocorrelation
1. Introduction Numerous studies have uncovered stock return anomalies based on trading strategies. For example, Jegadeesh and Titman (1993) find that trading strategies which buy past 6- to 12-month winners and short sell past losers earn significant profits over the subsequent 6* Corresponding author. Tel.: +1-717-477-1683; fax: +1-717-477-4067. E-mail address: [email protected] (M.-S. Pan). 0927-5398/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jempfin.2003.02.001
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to 12-month period. Moskowitz and Grinblatt (1999) further show that such momentum effects are mainly driven by industry factors in the sense that the profitability of individual stock momentum strategies can be substantially explained by industry momentum. That is, momentum strategies that buy stocks from past winning industries and sell stocks from past losing industries are highly profitable and can capture almost all the profits from individual stock momentum strategies. They also show superior returns to industry momentum strategies after adjusting for size, book-to-market, and microstructure effects. While Moskowitz and Grinblatt (1999) show the existence of an industry momentum effect, the sources of its profitability are unclear. They conjecture that such an effect might be due to ‘‘. . .there are. . . hot and cold sectors of the economy, and investors may simply herd toward (away from) these hot (cold) industries and sectors, causing price pressure that could create return persistence.’’ (p. 1287). This conjecture is consistent with a number of plausible explanations. For instance, Conrad and Kaul (1998) claim that momentum profits are primarily due to cross-sectional variation in unconditional mean returns.1 According to Conrad and Kaul’s arguments, if realized returns are strongly correlated to expected returns, then past winners (losers) that have higher (lower) returns tend to yield higher (lower) expected returns in the future. Thus, momentum strategies that buy past winner industries and short sell past loser industries would be profitable. Alternatively, the price momentum can also be explained by several existing behavioral models (e.g. Barberis et al., 1998; Daniel et al., 1998; Hong and Stein, 1999), which attempt to provide a theoretical framework for the empirical return anomalies documented in the finance literature. Hong and Stein (1999) propose a framework under which there are two types of investors: news watchers and momentum traders. Hong and Stein show that stock prices underreact to information in the short run if information diffuses gradually across news watchers. Their model indicates that this initial underreaction will induce trading from momentum traders, thereby exploring slow price movement. Eventually, prices will reverse to fundamentals in the long run when more and more momentum traders enter the market to earn a profit. Consequently, the Hong and Stein model implies positive autocorrelations in returns in the short run but negative autocorrelations in the long run. Like Hong and Stein, short-term underreaction is also present in the Barberis et al. (1998) model. However, Barberis et al. obtain the underreaction by assuming that investors exhibit a conservatism bias, meaning that investors are conservative in updating their priors. In contrast, Daniel et al. (1998) argue that the positive autocorrelation in returns is due to overreaction, not underreaction. According to the theory of Daniel et al., overconfidence, which would lead investors to overreact to information initially, together with continuing overreaction to news induced by attribution bias will result in positive autocorrelations in short lags and negative autocorrelations in long lags. In short, these behavioral models all suggest that positive autocorrelations in returns can cause the momentum effect. Finally, profits to momentum strategies can arise because of cross-sectional correlations among stocks (Lo and MacKinlay, 1990a). Lo and MacKinlay show that momentum 1 However, Jegadeesh and Titman (2002) suggest that Conrad and Kaul’s results suffer from small sample biases, and when these biases are corrected for in the tests, the variation in mean returns explains very little of the momentum profits.
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profits are negatively related to cross-sectional serial correlations, meaning that positive (negative) cross-autocorrelations lead to losses (profits) for a trading strategy that buys winner stocks and short sells loser stocks. Under this scenario, if winner stocks are negatively cross-serially correlated with loser stocks, then a strategy can generate profits by buying past winners and short selling past losers. Lewellen (2002) finds that the profitability of portfolio-based momentum strategies is mainly due to negative cross-serial correlations among portfolio returns. In this study, we attempt to identify the sources of profits to industry momentum strategies documented by Moskowitz and Grinblatt (1999). To this end, we follow Lo and MacKinlay (1990a) and decompose profits to momentum strategies applied onto industry portfolios into three sources: (1) the autocorrelation in industry portfolio returns; (2) the negative of cross-serial correlation among industry portfolios, so that positive cross-serial correlation contributes negatively to the profit; and (3) the cross-sectional variation in unconditional means. Our empirical results based on weekly data from 1962 to 1998 show that the industry momentum effect is primarily due to return own-autocorrelations, not to either return cross-autocorrelations or cross-sectional differences in mean returns. Indeed, the industry momentum strategies yield statistically significant profits only when return autocorrelation components are positive and significant. Thus, our finding indicates that momentum is caused by positive autocorrelation as suggested by the behavioral models, not by cross-serial correlation or by cross-sectional variation in unconditional means. The rest of the paper is organized as follows. Section 2 describes the momentum strategies that we follow in formulating trading rules and discusses the decompositions of momentum profits into various sources. Section 3 describes the data of industry portfolio returns and provides a test for autocorrelations in returns of industry portfolios. Section 4 presents industry momentum profits and analyzes the robustness of the results. The conclusion is in the final section.
2. Momentum strategies and sources of profits The primary motivation of momentum strategies is to exploit profits from trading strategies that long winners and short losers. Most prior studies (e.g. Jegadeesh and Titman, 1993; Conrad and Kaul, 1998; among many others) formulate trading strategies by buying or selling securities at time t, based on their performance at time t 1, with k horizons between time t 1 and t. As Conrad and Kaul show, the profitability of such trading strategies depends on the first-order own-autocovariances of security returns, the first-order cross-autocovariances, and the variation in the mean returns of individual securities. That is, formulating trading strategies in this way does not allow one to determine the impact of autocovariances at higher orders on the profits. Instead, we follow Lo and MacKinlay (1990a) and consider a strategy that buys industry portfolios at time t that were winners at time t k and short (sell) industry portfolios at time t that were losers at time t k. Formulating the momentum strategy in this manner permits us to decompose the profit into the kth-order own-autocovariance and cross-autocovariance of industry portfolio returns. As such, we can evaluate the relation between industry momentum profits and own- and cross-autocorrelation coefficients of industry portfolio returns at
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various lags, rather than just the first-order own- and cross-autovariances. See Eq. (5) below for more detail. Specifically, the momentum portfolio is constructed with investment weights in industry i determined as: wi;t ðkÞ ¼ ð1=N ÞðRi;tk Rm;tk Þ;
ð1Þ
where N is the number ofP industries available, Ri,t k is the return for industry i at time t k, and Rm;tk ¼ ð1=N Þ Ni¼1 Ri;tk is the return for an equal-weighted market portfolio at time t k. Eq. (1) shows that the investment weights are determined based on the performance of industries against the equal-weighted market index. The momentum strategy will buy winner industries at time t that outperform the market index at time t k and sell short industries at time t that underperform the market index at time t k. Several points concerning the investment weights should be noted. First, by construction, the investment weights lead to a zero-cost, arbitrage portfolio since the weights sum P to zero, i.e., Ni¼1 wi;t ðkÞ ¼ 0. Further, the total long and short position at time t, It(k), is given by It ðkÞ ¼
N X
Awi;t ðkÞA:
ð2Þ
i¼1
Second, Eq. (1) suggests that bigger winners and losers (in terms of their performances against the equal-weighted market index) will receive greater weights. Assigning greater weights to the more extreme performers allows us to capture the stock market momentum effect, whereby extreme price movements are to be followed by extreme movements in the same direction. Third, unlike most prior studies (e.g. Jegadeesh and Titman, 1993; Moskowitz and Grinblatt, 1999; among others) that focus on extreme losers and winners, we include all industry portfolios in formulating momentum strategies. As Fama and French (1996) document (see their Table VII), momentum profits tend to become smaller for average performance deciles. Thus, a momentum strategy that buys top winners and sells bottom losers might overestimate the profits. Finally, we can easily decompose momentum profits into different components based on investment weights in Eq. (1). The profit from the momentum strategy at time t, pt(k), is
pt ðkÞ ¼
N X
wi;t ðkÞRi;t
i¼1
¼
N 1X ðRi;tk Rm;tk ÞRi;t N i¼1
¼
N 1X Ri;tk Ri;t Rm;tk Rm;t : N i¼1
ð3Þ
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Assuming that unconditional mean returns are constant, i.e., l u E[Rt], and autocovariance matrix Wk u E[(Rt k l)(Rt l)], we can obtain the decompositions of the expected profit by taking expectations on both sides: E½pt ðkÞ ¼
¼
N 1X E½Ri;tk Ri;t E½Rm;tk Rm;t N i¼1
N 1X ðCov½Ri;tk ; Ri;t þ l2i Þ ðCov½Rm;tk ; Rm;t þ l2m Þ N i¼1
¼ Cov½Rm;tk ; Rm;t þ
N N 1X 1X Cov½Ri;tk ; Ri;t þ ðl lm Þ2 : N i¼1 N i¼1 i
ð4Þ
Eq. (4) indicates that the expected profits of momentum strategies come from three sources: (1) the negative of the kth-order autocovariance of the equal-weighted market index, (2) the average of the kth-order autocovariances of the industry portfolios, and (3) the variance of the mean returns of industry portfolios. Based on a multifactor model for stock returns, Moskowitz and Grinblatt (1999) show that momentum strategies based on industry portfolios generate almost identical average profits to those of individual stocks. Furthermore, they show that industry momentum accounts for a large portion of the profits from an individual stock momentum strategy. Moskowitz and Grinblatt’s results also suggest that return autocovariances largely contribute to momentum trading profits. Several recent studies (e.g. Barberis et al., 1998; Daniel et al., 1998; Hong and Stein, 1999) have developed behavioral models to establish links between return autocovariances and momentum. Barberis et al. hypothesize that a conservatism bias causes investors not to update their priors sufficiently in response to new information concerning a firm or an industry. As a result, security prices initially underreact to public information and produce trends in returns over short horizons, meaning that stock returns are positively autocorrelated. Like Barberis et al., Hong and Stein’s model also generates underreaction and postive return autocorrelations. However, they suggest that the underreaction arises because (1) heterogeneous investors observe different private information sets that diffuse gradually over time and across the investing public and (2) investors are boundedly rational in the sense that they can only incorporate a small subset of the available information into the pricing process. In contrast, Daniel et al. argue that positive serial correlation at short horizons is due to overreaction, not underreaction. The Daniel et al. model suggests that investors trade based on private information signals and tend to be overconfident in extracting information signals. As a result, stock prices overreact initially. Furthermore, when public information arrives, investors update their priors with an attribution bias. This attribution bias leads investors to become more overconfident if the noisy public information confirms what they already believe, but to adjust their confidence only slightly if the public information disconfirms their priors. Daniel et al. show that the overconfidence, together with the attribution bias, cause continuing overreaction and
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hence momentum at short horizons. In short, according to these behavioral models, momentum (or positive autocorrelation in stock returns) could arise because of investors’ underreaction or continuing overreaction to news. Alternatively, Lo and MacKinlay (1990a) show that momentum could be due to crossautocorrelations in returns and not due to return own-autocorrelations. To see this, Eq. (4) can be rewritten as ( ) N 1 X E½pt ðkÞ ¼ Cov½Rm;tk ; Rm;t 2 Cov½Ri;tk ; Ri;t N i¼1 þ
N N N 1X 1X Cov½R ; R þ ðl lm Þ2 i;tk i;t N 2 i¼1 N i¼1 i
¼ Ck þ Ok þ r2 ðlÞ:
ð5Þ
Eq. (5) shows that the profitability of the momentum strategy depends not only on the autocovariances of individual industry portfolios, denoted by Ok, but also on the crossautocovariances, denoted by Ck. Eq. (5) also shows that own-autocorrelation contributes to momentum profits positively, while cross-autocorrelation contributes to momentum negatively. Thus, momentum profits can be found if own-autocovariances and crossautocovariances are both negative and the latter dominates. In other words, the analogy between positive autocorrelation and momentum, as suggested by the behavioral models discussed previously, does not necessarily hold. The results reported by Lewellen (2002), in which he intends to determine the sources of momentum profits, seem to support the view that momentum is driven by cross-autocovariances in stock returns. Lewellen finds that industry, size, and book-to-market portfolios exhibit similar momentum in returns as that for individual stocks. His results also suggest that momentum is due to crossautocovariances because both the average own- and cross-autocovariances among the portfolios are negative, and the latter is more negative than the former. Apparently, Lewellen’s finding is inconsistent with the behavioral models, which imply that stock returns are positively serially correlated. He hypothesizes that the negative cross-serial covariance results from investors underreact to firm-specific news but overreact to macroeconomic news. Finally, Conrad and Kaul (1998) assert that momentum profits are mainly driven by the variation in the mean returns of individual equities, not by the time-series predictability in stock returns. They interpret momentum as variations in risk across assets. Intuitively, if realized returns are strongly correlated to expected returns, then momentum strategies that buy past winners and short sell past losers will yield positive profits because winners (losers) that have higher (lower) realized returns tend to yield higher (lower) expected returns in the future. To see this, consider the case that stock returns are both serially and cross-sectionally uncorrelated (i.e. stock returns are not predictable), then both the first and the second terms in Eq. (5) become zero and hence the entire momentum profit is due to the cross-sectional variation in mean returns. Thus, in the absence of predictability in stock returns, momentum can still arise as long as there are significant variations in mean returns
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or time-varying risk premiums. Theoretically, Berk et al. (1999) develop a dynamic model that relates a firm’s conditional expected return to the movements of its systematic risk. Berk et al.’s analysis also suggests that variables such as size and book-to-market can summarize changes in firms’ risks well. Their model implies that the momentum effect is related to the predictability of the movements in firms’ risks and hence their expected returns. Nevertheless, Fama and French (1996) show that abnormal momentum returns remain after adjusting for risk under their three-factor model of market return, size, and book-to-market, although the three-factor can capture most of asset pricing anomalies such as long-horizon return reversals. Furthermore, Jegadeesh and Titman (2002) show that the variation in mean returns explains very little of the momentum profits.
3. Data and autocorrelation analysis 3.1. Data To exploit the profitability of momentum strategies based on industry portfolios, we focus on weekly returns. The use of a weekly series enables us to increase the sample size and hence the power of the test. It also minimizes the possible overestimation of the momentum profitability due to spurious serial correlations associated with asynchronous trading and the bid – ask spread when higher frequency (e.g. daily) data are used. The weekly stock returns are derived from daily CRSP return files for the sample period from July 11, 1962, to December 30, 1998 using all NYSE, AMEX, and NASDAQ stocks. Firms are grouped into 20 industry portfolios according to their twodigit Standard Industry Classification (SIC) codes.2 Industry portfolio returns are calculated as the equally weighted average of returns of individual firms. From this daily return data, we generate an artificial daily closing price series for each of the 20 industry portfolios. The weekly return of each industry portfolio is then computed as the return from Wednesday’s closing price to the following Wednesday’s close.3 We use Wednesday close weekly returns because Chordia and Swaminathan (2000) find that return autocorrelations based on closing prices of any weekdays other than Wednesday are either too low or too high. Table 1 shows some summary statistics for the industry portfolios and market indexes. The average weekly return ranges from 0.475% for the electrical equipment industry to 0.279% for the petroleum industry. The average weekly return on the equal-weighted portfolio constructed from the 20 industry portfolios is 0.392% (or 20.4% per year), and the equal-weighted CRSP index is 0.358% (or 18.6% per year). Most of the industry portfolios have similar volatility as measured by standard deviation, though the petroleum industry 2
We use the same two-digit SIC groupings as those employed by Moskowitz and Grinblatt (1999). If Wednesday’s price is missing, then Thursday’s price is used. There are 41 cases in which Thursday’s price is used for the entire 1904-week sample period. Thus, the return at week t could be measured from Thursday to Wednesday if only the previous week’s price is missing, from Wednesday to Thursday if only the current week’s price is missing, or from Thursday to Thursday if both weeks’ prices are missing. Simple returns are used throughout the study, except for the variance ratio analysis that employs continuously compounded returns. 3
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Table 1 Summary statistics of weekly returns for industry portfolios, 1962 – 1998 Industry
SIC Codes
Mean (%)
Standard Deviation
Skewness
Kurtosis
D-stat.
1. Mining 2. Food 3. Apparel 4. Paper 5. Chemical 6. Petroleum 7. Construction 8. Prim. Metals 9. Fab. Metals 10. Machinery 11. Electrical Eq. 12. Transport Eq. 13. Manufacturing 14. Railroads 15. Other Transport 16. Utilities 17. Dept. Stores 18. Retail 19. Financial 20. Other Equal-Weighted Index Equal-Weighted CRSP Index
10 – 14 20 22 – 23 26 28 29 32 33 34 35 36 37 38 – 39 40 41 – 47 49 53 50 – 52, 54 – 59 60 – 69 Other
0.456 0.396 0.474 0.396 0.379 0.279 0.384 0.398 0.384 0.442 0.475 0.369 0.368 0.349 0.417 0.350 0.348 0.338 0.407 0.423 0.392
0.027 0.023 0.025 0.025 0.024 0.013 0.024 0.022 0.017 0.023 0.025 0.017 0.023 0.021 0.023 0.023 0.021 0.023 0.022 0.025 0.020
0.211 0.345 0.405 0.255 0.264 0.139 0.171 0.590 0.289 0.569 0.113 0.731 0.378 0.476 0.723 0.214 0.316 0.458 0.479 0.457 0.703
4.432 4.723 5.526 5.838 4.173 4.426 3.733 6.403 5.223 5.958 3.992 6.237 5.742 5.192 6.737 3.765 6.098 5.632 5.688 5.400 6.715
0.974* 0.971* 0.968* 0.973* 0.971* 0.961* 0.974* 0.958* 0.951* 0.960* 0.966* 0.962* 0.959* 0.968* 0.961* 0.979* 0.967* 0.970* 0.966* 0.967* 0.956*
0.358
0.020
0.599
5.990
0.957*
This table reports summary statistics of weekly returns for 20 industry portfolios. The industries are formed using the two-digit SIC codes from July 1962 – December 1998. Equal-weighted index is the equally weighted average return of the 20 industry portfolios, which has a 0.994 correlation with the equal-weighted CRSP stock return index. Kurtosis is coefficient of excess kurtosis. D-statistic is Kolmogorov – Smirnov D-statistic for testing normality. Asterisk indicates statistically significant at the 5% level.
has a relatively low volatility. In addition, all industry portfolios appear to be negatively skewed and have excess kurtosis, indicating that they are not normally distributed. Unlike Conrad and Kaul’s (1998) finding on individual securities, the variation in mean returns of industry portfolios is only 0.000223 1,000 1, which appears to be too small to generate any significant industry-based momentum profit. Thus, the profitability of a momentum strategy based on industry portfolios should be driven by their cross-autocorrelations and/or own-autocorrelations, not by the variation in their mean returns. 3.2. Autocorrelation analysis Table 2 shows the autocorrelations of industry portfolio returns at several lags. The autocorrelations at short lags (one to four weeks) are all positive and large, which is consistent with Lo and MacKinlay (1990b). Positive portfolio autocorrelations at short lags may partially reflect the lead-lag effect between large and small stocks that is associated with the delayed reaction of small stocks to news (see e.g. Lo and MacKinlay, 1990a; Boudoukh et al., 1994; McQueen et al., 1996; Richardson and
Table 2 Autocorrelations and variance-ratio analysis of the random walk hypothesis for industry portfolios Autocorrelation at Lag
Variance Ratio Test Statistic at Lag
1
2
4
12
26
2
1. Mining 2. Food 3. Apparel 4. Paper 5. Chemical 6. Petroleum 7. Construction 8. Prim. Metals 9. Fab. Metals 10. Machinery 11. Electrical Eq. 12. Transport Eq. 13. Manufacturing 14. Railroads 15. Other Transport 16. Utilities 17. Dept. Stores 18. Retail 19. Financial 20. Other Equal-Weighted CRSP Index
0.30 0.25 0.31 0.15 0.24 0.25 0.26 0.34 0.33 0.33 0.29 0.25 0.31 0.22 0.26 0.17 0.25 0.25 0.30 0.29 0.32
0.14 0.13 0.16 0.09 0.09 0.09 0.12 0.18 0.17 0.17 0.14 0.15 0.16 0.10 0.09 0.07 0.16 0.11 0.16 0.13 0.15
0.10 0.07 0.09 0.02 0.05 0.03 0.09 0.12 0.10 0.11 0.08 0.07 0.11 0.04 0.06 0.02 0.06 0.05 0.08 0.08 0.09
0.02 0.01 0.01 0.01 0.01 0.00 0.04 0.03 0.01 0.03 0.03 0.03 0.00 0.05 0.03 0.05 0.03 0.04 0.01 0.02 0.02
0.00 0.00 0.01 0.02 0.03 0.04 0.03 0.01 0.04 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.01 0.00 0.01
1.304 1.260 1.316 1.155 1.243 1.252 1.259 1.342 1.331 1.339 1.295 1.258 1.314 1.222 1.266 1.173 1.261 1.253 1.306 1.291 1.321
3 (7.01) (5.55) (6.46) (3.01) (5.46) (5.75) (5.76) (6.46) (7.33) (6.66) (8.03) (4.84) (5.98) (4.51) (4.48) (4.15) (4.61) (4.86) (6.16) (5.64) (6.26)
1.500 1.437 1.532 1.269 1.387 1.394 1.429 1.574 1.558 1.563 1.487 1.447 1.527 1.361 1.418 1.281 1.452 1.413 1.516 1.477 1.530
5 (8.11) (6.61) (7.69) (3.70) (6.15) (6.35) (6.73) (7.73) (8.64) (7.81) (9.06) (5.95) (7.14) (5.25) (5.03) (4.75) (5.66) (5.68) (7.38) (6.55) (7.33)
1.783 1.670 1.844 1.393 1.586 1.570 1.699 1.927 1.880 1.889 1.738 1.697 1.838 1.555 1.644 1.392 1.724 1.610 1.806 1.746 1.822
(9.42) (7.65) (9.17) (4.13) (6.97) (6.84) (8.22) (9.50) (10.04) (9.31) (9.84) (7.10) (8.68) (6.17) (5.96) (4.92) (6.89) (6.45) (8.75) (7.80) (8.61)
13
27
2.204 (9.44) 2.025 (7.85) 2.352 (9.89) 1.566 (4.15) 1.935 (7.34) 1.641 (5.07) 2.185 (9.25) 2.561 (10.98) 2.454 (10.67) 2.430 (10.11) 2.168 (9.49) 2.067 (7.57) 2.395 (9.87) 1.763 (5.81) 1.934 (6.18) 1.521 (4.23) 2.117 (7.52) 1.833 (6.15) 2.228 (9.13) 2.160 (8.40) 2.267 (9.03)
2.264 (7.38) 2.114 (6.40) 2.541 (8.57) 1.583 (3.29) 1.996 (5.79) 1.824 (4.78) 2.292 (7.45) 2.734 (9.36) 2.851 (10.03) 2.586 (8.58) 2.564 (9.05) 2.154 (6.29) 2.622 (8.75) 1.679 (3.89) 1.990 (5.17) 1.580 (3.44) 2.104 (5.82) 1.727 (4.12) 2.332 (7.55) 2.150 (6.40) 2.400 (7.63)
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Industry
This table reports serial correlations for industry portfolios and Lo and MacKinlay’s (1988) variance-ratio statistics for testing the significance of serial correlation. Oneweek is taken as a base observation interval. The variance ratio estimates are given in the main rows, with heteroskedasticity-robust z-statistics given in parentheses. Under the hypothesis that returns are serially uncorrelated, the variance ratio estimate is one, and the test statistics are asymptotically N(0,1). 193
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Peterson, 1999).4 Nevertheless, the magnitude of positive autocorrelations suggests that momentum strategies might work, especially at short lags. On the other hand, autocorrelations at higher lags (12 and 26 weeks) are in general negative (especially for 12 weeks) and are much smaller in magnitude. Also reported in Table 2 are Lo and MacKinlay’s (1988) variance ratio analysis for testing the significance of the autocorrelations of returns. Since Lo and MacKinlay’s variance ratio estimate at lag k is approximately a linear combination of the first k 1 autocorrelation coefficients, it permits us to detect serial uncorrelations. We calculate the variance ratio test statistic that is robust to heteroskedasticity for k equals 2, 3, 5, 13, and 27 weeks. All the heteroskedasticity-robust standard normal z-statistics are substantially higher than critical values at any conventional significance levels, suggesting that none of the price series of industry portfolios follow a random walk. Consistent with the autocorrelation coefficients, the increasing variance ratio estimates along lag k indicate that autocorrelations are in general positive. Thus, the variance ratio analysis also suggests the profitability of a momentum strategy.
4. Profits to momentum strategies and robustness tests 4.1. Profits to momentum strategies Since it is well known that autocorrelations at higher lags cannot be estimated precisely, a study that includes higher order autocorrelations in the analysis may not correctly measure the relation between momentum profits and the pattern of autocorrelations. Thus, we do not perform the analysis for lags longer than 26 weeks. Table 3 reports expected profits to momentum strategies implemented on industry portfolios for five different lags, with k equals 1 week, 2 weeks, 4 weeks, 12 weeks, and 26 weeks. For lag 1, the average of the expected profit is 0.00173 cents, 0.00107 cents for lag 2, 0.0009 cents for lag 4, 0.00005 cents for lag 12, and 0.00002 cents for lag 26. The profits appear to become smaller for higher lags, which could simply reflect the result that autocorrelations decline when lags increase. The z-statistics,5 which are asymptotically standard normal under the null hypothesis that the ‘‘true’’ profits are zero, are significantly different from zero at the 1% level for lags up to 4 weeks. At higher lags, they are not significant. The result of significant profits up to 4 weeks is consistent with those of Moskowitz and Grinblatt (1999), in which they show a very strong one-month momentum effect in industries. Their result also shows that the significance of intermediate-term (6-month) momentum industry strategies is partly due to the one-month effect. Table 3 also contains the three components that make up the average profit, Ck, Ok, and r2(l). It is noteworthy that for all lags, Ck and Ok are opposite in their signs, meaning 4 Positive portfolio autocorrelation could also result from non-synchronous trading (see e.g. Lo and MacKinlay, 1990b). However, Mech (1993) shows that nontrading can explain only a small part of portfolio autocorrelations. 5 The z-statistics are corrected for heteroskedasticity and autocorrelations up to eight lags based on the adjustments outlined in Newey and West (1987).
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Table 3 Profits to momentum strategies for industry portfolios Lag k
E[pt(k)]
Ck
Ok
r2(l)
1
0.0173 (12.697) 0.0107 (8.394) 0.0090 (7.439) 0.0005 (0.389) 0.0002 (0.181)
0.1121 ( 6.762) 0.0527 ( 4.034) 0.0263 ( 2.283) 0.0074 (0.738) 0.0027 ( 0.255)
0.1292 (7.468) 0.0632 (4.596) 0.0351 (2.904) 0.0071 ( 0.676) 0.0027 (0.238)
0.0002
647.98
746.82
1.16
0.0002
492.52
590.65
1.87
0.0002
292.22
390.00
2.22
0.0002
1480.00
1420.00
40.00
0.0002
1350.00
1350.00
100.00
2 4 12 26
%[ Ck]
%[Ok]
%[r2(l)]
This table contains the decomposition of average profits of momentum strategies that long past winner industry portfolios and short past loser industry portfolios. Expected profit is given by E[pt(k)] = Ck + Ok + r2(l), where Ck mainly depends on the average kth-order cross-autocovariance of the returns for the 20 industry portfolios, Ok depends on the average kth-order own-autocovariance, and r2(l) is the cross-sectional variance of the mean returns. The numbers in parentheses are z-statistics that are asymptotically N(0, 1) under the null hypothesis that the relevant parameter is zero, and are robust to autocorrelation and heteroskedasticity. All profit estimates are multiplied by 1,000.
that a positive (negative) autocorrelation is associated with a positive (negative) cross autocorrelation. Consistent with the autocorrelation coefficient estimates, all the estimates of the component Ok that mainly depends on own-autocorrelations are positive, except for lag 12. Also, the z-statistics show that the Ok estimates are significant up to lag 4. Similar to the own-autocorrelations, the Ck component that captures cross-autocorrelations is also significant up to lag 4. Comparing the two components, Ck and Ok, suggests that ownautocorrelations of industry portfolios are more important than their cross-autocorrelations in determining the profitability of momentum strategies.6 Specifically, for the short lags that show significant positive profits, the difference between the percentage contributions of Ok and Ck are close to 100%, with a larger percentage contribution for Ok. Therefore, our result indicates that own-autocorrelations account for most of the momentum profits, which supports Moskowitz and Grinblatt’s (1999) assertion that it is the serial correlation in industry return components that drives the industry momentum.7
6
The larger impact of portfolio own-autocorrelations than cross-autocorrelations in influencing the profitability of trading strategies could be related to the argument that cross-autocorrelations are simply due to portfolio return autocorrelations (see e.g. Boudoukh et al., 1994; Hameed, 1997). Richardson and Peterson (1999), however, provide evidence showing that cross-autocorrelations are not an artifact of portfolio autocorrelations. 7 Assuming that stock returns follow a multifactor linear process, Moskowitz and Grinblatt analytically decompose industry momentum profits into three sources, including the variation in mean returns across industries, the first-order serial covariance of Fama and French’s (1993) size, book-to-market, and market factor portfolios, and the first-order serial covariance of industry return components. They find that the cross-sectional variance of mean industry monthly returns is too small to contribute significantly to the industry momentum profits. They also find that none of the first-order serial covariance for six-month returns of the three Fama and French factor-mimicking portfolios is significantly different from zero. Given these results, they assert that the main source of the industry momentum profits must be from the positive serial covariance in industry return components. Using a different decomposition method, our study indeed provides a direct support to Moskowitz and Grinblatt’s argument.
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The finding of significant positive profits to momentum strategies based on industry portfolios seems in contrast with that reported in Lo and MacKinlay (1990a), in which they document positive expected profits from contrarian strategies that are implemented on individual securities. Since the profitability to trading strategies depends largely on autocorrelations, this seemingly conflicting result appears to relate to positive autocorrelations in portfolio returns, while individual returns are generally negatively autocorrelated (see Lo and MacKinlay, 1990a). Unlike Conrad and Kaul (1998), we find that the variation in industry portfolio mean returns has little contribution to the momentum profits, which is consistent with Moskowitz and Grinblatt (1999). For instance, the percentage contributions are only 1.16%, 1.87%, and 2.22% for lags 1, 2, and 4, respectively. Although this percentage contribution increases to 40 percent for lag 12 and to 100 percent for lag 26, the corresponding expected profits, however, are not significant. Note that our estimate of the cross-sectional variance in mean weekly returns of industry portfolios is 0.000223 1,000 1, which is about 24 times smaller than the estimate of 0.00535 1,000 1 reported in Conrad and Kaul based on a sample of 6,524 firms during the 1962 – 1989 period. 4.2. Bootstrapping analysis Our statistical inference is based on the z-statistic, which is assumed to follow a standard normal distribution. To check the sensitivity of our significance tests against this assumption, we perform a bootstrap test. To this end, we shuffle (with replacement) the returns of industry portfolios simultaneously so that both own-autocorrelations and crossautocorrelations are eliminated.8 We calculate the expected profits and the profit components of Ck and Ok as well as their corresponding z-statistics for each bootstrap sample. A total of 1,000 replications are implemented. The results from the bootstrap analysis are given in Table 4. The Kolmogorov –Smirnov D-statistics (not reported) cannot reject the normality hypothesis for any of the z-statistic series, suggesting that the corrections adjusting for autocorrelation and heteroskedasticity are appropriate. The bootstrap p-value at any lag provides the same statistical inference as the z statistic; that is, there are significant positive profits for momentum strategies up to lag 4. Concerning the above finding, an important caveat should be noted. The evaluation of the statistical significance of a trading strategy may suffer from the bias of drawing the conclusion based solely on the result from a single lag (e.g. lag 1). To mitigate this bias, we calculate a Wald statistic that provides a joint test by taking into account the correlations between the expected average profits at the five lags (k = 1, 2, 4, 12, 26 weeks): Wald ¼ fE½pðkÞ TRUE½pðkÞgVX1 fE½pðkÞ TRUE½pðkÞg;
ð6Þ
where E is the expectation operator, pðkÞ is a 5 1 vector of sample average profits, TRUE½pðkÞ represents the vector of zero ‘‘true’’ profits under the null 8 Since our benchmark portfolio is an equally weighted average return of the 20 industry portfolios, randomizing industry portfolio returns will effectively create a serially uncorrelated market portfolio return series. Hence, both the profit components of Ck and Ok should be close to zero.
M.-S. Pan et al. / Journal of Empirical Finance 11 (2004) 185–202 Table 4 Average profits of trading strategies from bootstrapped returns Lag k E[p (k)] Ck t Sample E[pt(k)]
95%
99%
P-value
1
0.0173 0.0016 0.0022 0.000 (12.697) (2.031) (2.785) 2 0.0107 0.0015 0.0020 0.000 (8.394) (1.968) (2.636) 4 0.0090 0.0015 0.0022 0.000 (7.439) (1.952) (2.806) 12 0.0005 0.0015 0.0021 0.386 (0.389) (2.000) (2.742) 26 0.0002 0.0016 0.0021 0.530 (0.181) (1.970) (2.580) Wald Statistic = 772.448 ( q-value = 0.000)
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Ok
Sample Ck
95%
99%
Sample Ok
95%
99%
0.1121 ( 6.762) 0.0527 ( 4.034) 0.0263 ( 2.283) 0.0074 (0.738) 0.0027 ( 0.255)
0.0152 (1.585) 0.0140 (1.503) 0.0150 (1.563) 0.0143 (1.528) 0.0141 (1.554)
0.0219 (2.332) 0.0202 (2.144) 0.0227 (2.197) 0.0195 (2.076) 0.0210 (2.244)
0.1292 (7.468) 0.0632 (4.596) 0.0351 (2.904) 0.0071 ( 0.676) 0.0027 (0.238)
0.0151 (1.588) 0.0156 (1.595) 0.0154 (1.582) 0.0154 (1.584) 0.0151 (1.626)
0.0240 (2.459) 0.0234 (2.343) 0.0220 (2.285) 0.0218 (2.224) 0.0212 (2.283)
This table reports average actual and various fractiles of the decompositions of average bootstrapped profits to momentum strategies that long winner industry portfolios and short loser industry portfolios. Expected profit is given by E[pt(k)] = Ck + Ok + r2(l), where Ck mainly depends on the average kth-order cross-autocovariance of the returns for the 20 industry portfolios, Ok depends on the average kth-order own-autocovariance, and r2(l) is the cross-sectional variance of the mean returns. The bootstrap samples are constructed by first shuffling (with replacement) the weekly return series, then calculating profits for the momentum strategies for a replication of 1,000 times. The percentage column reports upper fractiles of the bootstrapped distribution. The numbers in parentheses are z-statistics that are asymptotically N(0,1) under the null hypothesis that the relevant parameter is zero, and are robust to autocorrelation and heteroskedasticity. The p-value reports the probability that the 1,000 bootstrap average profits from the bootstrap distribution are greater than the sample average profits of the actual strategy shown in the second column. The Wald statistic is computed by using the covariance matrix that describes the dependences among the five profit estimates as derived from the bootstrap distribution. The Wald statistic distributes as a v2 variate with 5 degrees of freedom, with a critical value of 11.070 at the 5% level. The q value reports the probability that the Wald statistic from the bootstrap distribution is larger than the sample Wald statistic. All profit estimates are multiplied by 1,000.
hypothesis, and X is a measure of the covariance matrix of pðkÞ estimated with the bootstrap Xij ¼ r2 ½pðiÞ; pðjÞ:
ð7Þ
The Wald statistic distributes as a m2 variate with five degrees of freedom. As shown in Table 4, the calculated Wald statistic of 772.488 is so large that the null hypothesis of zero profit for all five lags can be rejected at any significance level. 4.3. Non-synchronous trading effects The results reported in the preceding subsections suggest that return autocorrelation is a major source of the momentum effect for industry portfolios. However, non-synchronous trading will result in positive return autocorrelation for stock portfolios and hence may
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overestimate momentum profit.9 The spurious autocorrelation induced by the nontrading effect is expected to become smaller for lower frequency data. To gauge the impact of nonsynchronous trading on industry momentum profits, we also evaluate trading strategies for the data of two- (bi-weekly) and four-week (monthly) intervals.10 Table 5 shows that significant profits still exist for both bi-weekly and monthly data. For both sampling intervals, the average profits are highly significant at short lags, such as lags 1 and 2.11 Unlike the weekly interval, significant profits can also be made at higher lags. For instance, for the lag order of about 1 year (i.e. lag 26 for the 2-week interval and lag 12 for the 4-week interval), the average profits are 0.00409 cents and 0.01124 cents, respectively, and are both significant. Significant profits available at such a long lag indicate a nominal impact from the lead-lag effect. In addition, Boudoukh et al. (1994) estimate that the firstorder serial correlation for weekly return induced by nontrading can be as high as 0.18, which is much smaller than the average of our first-order autocorrelation estimates of 0.28 (see Table 2). Thus, non-synchronous trading cannot explain the industry momentum effect completely. More importantly, the results contained in Table 5 continue to show that the Ok component, which mainly depends on own-autocorrelation, is the driving force for the industry momentum effect. Specifically, for the six lags that show significant profits (i.e. lags 1, 2, and 26 for the 2-week interval and lags 1, 2, and 12 for the 4-week interval), the own-autocovariances are positive and highly significant, except for lag 2 of the 4-week interval. Relative to the own-autovariances, the cross-autocovariances contribute very little to the profits of industry momentum strategies. Indeed, for the six lags that yield significant profits, most of the values of the cross-autocovariance components are negative, meaning that they contribute negatively to the profits. For the two lags that the Ck component is positive (i.e. lag 1 for the 2-week interval and lag 2 for the 4-week interval), the values are small compared to those of the Ok component. For instance, the magnitude of the Ck component for lag 2 of the 4-week interval is only about one-fourth as large as that of the Ok component. When we compare the contributions to the profits between the own-autocovariances and the variation in mean returns, the results also show that own-autocovariances are the main source of industry momentum. That is, for the cases that the profits are significant, the percentage contributions of the variance in mean returns
9 For a discussion on the impact of non-synchronous trading on portfolio return autocorrelation, see, for example, Lo and MacKinlay (1990b). Lo and MacKinlay also show that non-synchronous trading can explain only parts of return autocorrelations. 10 Non-overlapping data are used in this analysis, although we also conduct the investigation on overlapping data. While the conclusion about the profitability for momentum strategies from non-overlapping data is qualitatively the same as that from overlapping data, the profits for overlapping data are substantially larger. For instance, the average profit for the 4-week interval for overlapping data at lag 1 is 0.0507 cents, whereas it is only 0.0176 cents for the non-overlapping data (about three times smaller). Such a large difference in profits between the two data sets suggests that studies that use overlapping data (e.g. Conrad and Kaul, 1998) might have overestimated the profits from trading strategies. 11 The significant profit for the four-week interval at lag 1 is consistent with that of Moskowitz and Grinblatt (1999), in which they show significant profits can be earned for industry momentum portfolios that are formed at time t based on returns in the previous month and held for one month.
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Table 5 Profits to momentum strategies for lower frequency data Ck
Ok
r2(l)
Panel A: sampling interval = 2 weeks 1 0.1290 (16.220) 2 0.0682 (9.627) 6 0.0075 (1.221) 13 0.0098 (1.634) 26 0.0409 (4.442) 30 0.0122 ( 1.552)
0.0009 (0.717) 0.0001 ( 0.127) 0.0002 (0.168) 0.0027 ( 2.537) 0.0018 ( 1.959) 0.0023 (1.777)
0.1192 (14.318) 0.0594 (8.064) 0.0017 ( 0.263) 0.0035 (0.599) 0.0337 (3.567) 0.0234 ( 3.094)
0.0089 0.0089 0.0089 0.0089 0.0089 0.0089
Panel B: sampling interval = 4 weeks 1 0.1764 (10.132) 2 0.0514 (3.094) 3 0.0168 (0.979) 6 0.0262 (1.433) 12 0.1124 (5.531) 16 0.0185 (1.037)
0.0024 ( 1.239) 0.0043 (1.994) 0.0044 (2.091) 0.0010 (0.586) 0.0018 ( 0.976) 0.0007 (0.354)
0.1490 (8.205) 0.0172 (1.020) 0.0175 ( 1.004) 0.0046 ( 0.251) 0.0843 (4.062) 0.0120 ( 0.652)
0.0299 0.0299 0.0299 0.0299 0.0299 0.0299
Lag k
E[pt(k)]
Panels A and B report the decomposition of average profits of momentum for sampling intervals of 2- and 4weeks, respectively. Expected profit is given by E[pt(k)] = Ck + Ok + r2(l), where Ck mainly depends on the average kth-order cross-autocovariance of the returns for the 20 industry portfolios, Ok depends on the average kth-order own-autocovariance, and r2(l) is the cross-sectional variance of the mean returns. The numbers in parentheses are z-statistics that are asymptotically N(0, 1) under the null hypothesis that the relevant parameter is zero, and are robust to autocorrelation and heteroskedasticity. All profit estimates are multiplied by 1,000. The Bonferroni-adjusted critical values for multiple tests of the significance for 6 lags together at the 5 percent and 1 percent levels are 2.395 and 2.929, respectively.
are much smaller compared with those of the own-autocovariance component, except for lag 2 of the 4-week interval. 4.4. Positive autocorrelations in portfolio returns The results reported so far suggest that industry momentum strategies are profitable, especially for short horizons. Furthermore, the primary source of momentum is ownautocorrelations of industry portfolios, rather than cross-autocorrelations or the variation in mean returns of portfolios. However, it is noteworthy that in addition to nonsynchronous trading, positive autocorrelations in stock portfolio returns may also reflect lead-lag effects between small and large stocks within a portfolio that are related to delayed reactions of small firms to common factors. Thus, positive autocorrelations likely will be present in stock portfolios regardless of the grouping methods used. If the lead-lag effects are driving the positive autocorrelation and hence the industry momentum, grouping methods other than those based on industry will deliver the momentum effect as well. If other grouping methods can yield similar profits as do the industry grouping, the industry momentum effect may be attributable to positive autocorrelations (i.e. the lead-lag effect) of stock portfolios constructed in other arbitrary ways. To find out whether other grouping methods will yield momentum profits, we apply the momentum strategies to 20 portfolios that are formed based on the first alphabet of the
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Table 6 Profits to momentum strategies for alphabet-based portfolios Lag k
E[pt(k)]
Ck
Ok
r2(l)
1 2 4 12 26
0.0011 ( 5.789) 0.0006 ( 3.469) 0.0002 (1.211) 0.0001 (0.706) 0.0002 ( 1.098)
0.1230 ( 7.210) 0.0583 ( 4.279) 0.0341 ( 2.890) 0.0081 (0.749) 0.0029 ( 0.258)
0.1218 (7.129) 0.0577 (4.224) 0.0343 (2.895) – 0.0080 ( 0.736) 0.0027 (0.241)
0.00002 0.00002 0.00002 0.00002 0.00002
This table reports expected profits to momentum strategies applied to 20 alphabet-based portfolios. Expected profit is given by E[pt(k)] = Ck + Ok + r2(l), where Ck mainly depends on the average kth-order crossautocovariance of the returns for the 20 industry portfolios, Ok depends on the average kth-order ownautocovariance, and r2(l) is the cross-sectional variance of the mean returns. The numbers in parentheses are zstatistics that are asymptotically N(0,1) under the null hypothesis that the relevant parameter is zero, and are robust to autocorrelation and heteroskedasticity. All profit estimates are multiplied by 1,000.
names of the respective companies.12 It is reasonable to expect that the alphabet-based portfolios do not consist of an industry feature, though positive own-autocorrelations might remain. Table 6 contains the results from this analysis. Not surprisingly, the variation of mean returns of the 20 alphabet-based portfolios is very small and hence contributes almost nothing to the profits. Also, as expected, the Ok profit component, which is closely related to the average own-autocovariance of portfolios, is positive and also highly significant for the first three lags. The Ck component that captures crossautocovariance is also significant for the first three lags. However, the positive and significant own-autocovariance does not deliver positive profits. Indeed, the profits for the first two lags are negative and it is insignificantly different from zero for lag three. Furthermore, when compared with the industry portfolio results in Table 3, it appears that the Ok estimates for the alphabet-based portfolios are slightly smaller than those for the industry portfolios, while the converse is true for the Ck estimates. It is also important to note that Ck is greater than Ok for the alphabet-based grouping, but it is the opposite for the industry grouping. In other words, although both grouping methods result in positive and significant own-autocovariances, only the industry grouping that has a higher average own-autocovariance than cross-autocovariance produces significant profits to momentum strategies.
5. Conclusions This study attempts to identify the sources of profits to momentum strategies that buy past winner industry portfolios and sell short past loser industry portfolios. To this end, we calculate profits to momentum strategies applied to industry portfolios, and decompose the 12 Twenty portfolios are formulated based on the first alphabet of the names of companies. The groupings are as follows: A for portfolio 1, B for portfolio 2, C for portfolio 3, D for portfolio 4, E for portfolio 5, F for portfolio 6, G for portfolio 7, H for portfolio 8, I for portfolio 9, J and U for portfolio 10, K and O for portfolio 11, L for portfolio 12, M for portfolio 13, N for portfolio 14, P for portfolio 15, Q, V, X, Y, Z, and numbers for portfolio 16, R for portfolio 17, S for portfolio 18, T for portfolio 19, and W for portfolio 20. We constructed 20 portfolios in this way so that the number of stocks included in each of the portfolios is similar.
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profits into three components: own-autocorrelations in industry portfolio returns, crossserial correlations among industry portfolios, and variation in unconditional mean returns of these industry portfolios. Using weekly returns from 1962 –1998, we find that industry momentum strategies can generate significant, positive profits, especially for short horizons (less than 4 weeks). More importantly, our results show that the industry momentum effect is mainly due to own-autocorrelations in industry portfolio returns, and is not caused by cross-autocorrelations or by cross-sectional variation in mean returns. Consistent with the behavioral models by Barberis et al. (1998), Daniel et al. (1998) and Hong and Stein (1999), our results show that the industry momentum effect is statistically significant only for cases when return autocorrelations are positive and also statistically significant. Due to lead-lag effects, industry portfolios are expected to exhibit positive autocorrelations and hence a significant industry momentum. However, our robust analysis shows that microstructure influences (e.g. non-synchronous trading) and grouping methods cannot totally explain the industry momentum effect. Of course, our finding of significant industry momentum profits that arise from return autocorrelations does not necessarily imply market inefficiency. Positive profits could be a result of spurious autocorrelations in industry portfolios due to still unknown economic sources, other than microstructure influences and grouping methods. While stocks within an industry tend to be highly correlated, it is not obvious why industry portfolios have such high own-autocorrelations and low cross-autocorrelations, especially at short lags. In addition, the economic magnitude of the momentum profits may become insignificant when transactions costs are taken into account. This is particular true for the result from examining higher frequency data (e.g. weekly) because of high turnovers. Nevertheless, future work might explore the sources of return autocorrelation and cross-autocorrelation patterns for portfolios formed based on industry.
Acknowledgements We thank Robert Fok, Hung-Gay Fung, seminar participants at the 2001 Financial Management Association meetings and Shippensburg University, and two anonymous referees for helpful comments.
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