《金融投资学》教学资源（英文文献）bad news travel slowly

THE JOURNAL OF FINANCE.VOL.LV.NO.1.FEBRUARY 2000 Bad News Travels Slowly: Size,Analyst Coverage,and the Profitability of Momentum Strategies HARRISON HONG,TERENCE LIM,and JEREMY C.STEIN* ABSTRACT Various theories have been proposed to explain momentum in stock returns.We test the gradual-information-diffusion model of Hong and Stein (1999)and estab- lish three key results.First,once one moves past the very smallest stocks,the profitability of momentum strategies declines sharply with firm size.Second,hold- ing size fixed,momentum strategies work better among stocks with low analyst coverage.Finally,the effect of analyst coverage is greater for stocks that are past losers than for past winners.These findings are consistent with the hypothesis that firm-specific information,especially negative information,diffuses only grad- ually across the investing public. SEVERAL RECENT PAPERS HAVE DOCUMENTED that,at medium-term horizons rang- ing from three to 12 months,stock returns exhibit momentum-that is,past winners continue to perform well,and past losers continue to perform poorly. For example,Jegadeesh and Titman (1993),using a U.S.sample of NYSE/ AMEX stocks over the period from 1965 to 1989,find that a strategy that buys past six-month winners(stocks in the top performance decile)and shorts past six-month losers (stocks in the bottom performance decile)earns ap- proximately one percent per month over the subsequent six months.Not only is this an economically interesting magnitude,but the result also ap- pears to be robust:Rouwenhorst (1998)obtains very similar numbers in a sample of 12 European countries over the period from 1980 to 1995.1 Hong is from the Stanford Business School,Lim is from Goldman Sachs,and Stein is from the MIT Sloan School of Management and the National Bureau of Economic Research.This research is supported by the National Science Foundation and the Finance Research Center at MIT.We are grateful to Joseph Chen for research assistance and to Ken French,Paul Pfleiderer, Geert Rouwenhorst,David Scharfstein,Ken Singleton,Rene Stulz,three anonymous referees. and seminar participants at MIT,Yale,UCLA,Berkeley,Stanford,Illinois,the Norwegian School of Management,and the Stockholm School of Economics for helpful comments and suggestions. Data on analyst coverage were provided by I/B/E/S Inc.under a program to encourage aca- demic research.Thanks also to Lisa Meulbroek for sharing the data on options listings 'Rouwenhorst(1997)finds that momentum strategies also earn significant profits on aver- age in a sample of 20 emerging markets.See Haugen and Baker(1996)for confirmatory evi- dence from the United States and several European countries. 265

Bad News Travels Slowly: Size, Analyst Coverage, and the Profitability of Momentum Strategies HARRISON HONG, TERENCE LIM, and JEREMY C. STEIN* ABSTRACT Various theories have been proposed to explain momentum in stock returns. We test the gradual-information-diffusion model of Hong and Stein ~1999! and estab￾lish three key results. First, once one moves past the very smallest stocks, the profitability of momentum strategies declines sharply with firm size. Second, hold￾ing size fixed, momentum strategies work better among stocks with low analyst coverage. Finally, the effect of analyst coverage is greater for stocks that are past losers than for past winners. These findings are consistent with the hypothesis that firm-specific information, especially negative information, diffuses only grad￾ually across the investing public. SEVERAL RECENT PAPERS HAVE DOCUMENTED that, at medium-term horizons rang￾ing from three to 12 months, stock returns exhibit momentum—that is, past winners continue to perform well, and past losers continue to perform poorly. For example, Jegadeesh and Titman ~1993!, using a U.S. sample of NYSE0 AMEX stocks over the period from 1965 to 1989, find that a strategy that buys past six-month winners ~stocks in the top performance decile! and shorts past six-month losers ~stocks in the bottom performance decile! earns ap￾proximately one percent per month over the subsequent six months. Not only is this an economically interesting magnitude, but the result also ap￾pears to be robust: Rouwenhorst ~1998! obtains very similar numbers in a sample of 12 European countries over the period from 1980 to 1995.1 * Hong is from the Stanford Business School, Lim is from Goldman Sachs, and Stein is from the MIT Sloan School of Management and the National Bureau of Economic Research. This research is supported by the National Science Foundation and the Finance Research Center at MIT. We are grateful to Joseph Chen for research assistance and to Ken French, Paul Pfleiderer, Geert Rouwenhorst, David Scharfstein, Ken Singleton, René Stulz, three anonymous referees, and seminar participants at MIT, Yale, UCLA, Berkeley, Stanford, Illinois, the Norwegian School of Management, and the Stockholm School of Economics for helpful comments and suggestions. Data on analyst coverage were provided by I0B0E0S Inc. under a program to encourage aca￾demic research. Thanks also to Lisa Meulbroek for sharing the data on options listings. 1 Rouwenhorst ~1997! finds that momentum strategies also earn significant profits on aver￾age in a sample of 20 emerging markets. See Haugen and Baker ~1996! for confirmatory evi￾dence from the United States and several European countries. THE JOURNAL OF FINANCE • VOL. LV, NO. 1 • FEBRUARY 2000 265

266 The Journal of Finance While the existence of momentum in stock returns does not seem to be too controversial,it is much less clear what might be driving it.Some (e.g., Conrad and Kaul(1998))have suggested a risk-based interpretation of mo- mentum.This is certainly a logical possibility,although there is little evidence that cuts clearly in favor of a risk story.In this vein,Fama and French(1996) note that momentum effects are not subsumed by their three-factor model. Turning to "behavioral"(i.e.,non-risk-based)explanations,there are a num- ber of theories that can give rise to positive medium-term return auto- correlations.In some of these,prices initially overreact to news about fundamentals,then continue to overreact further for a period of time.The positive-feedback-trader model of DeLong et al.(1990)fits in this camp,as does the overconfidence model of Daniel,Hirshleifer,and Subrahmanyam (1998).In other models,momentum is a symptom of underreaction-prices adjust too slowly to news. The set of underreaction theories can be further subdivided according the exact mechanism that is at work.In Barberis,Shleifer,and Vishny (1998), there is a representative investor who suffers from a conservatism bias,and who does not update his beliefs sufficiently when he observes new public information.In Hong and Stein(1999)the emphasis is instead on heteroge- neities across investors,who observe different pieces of private information at different points in time.Hong and Stein make two key assumptions:(1) firm-specific information diffuses gradually across the investing public;and (2)investors cannot perform the rational-expectations trick of extracting in- formation from prices.Taken together,these two assumptions generate un- derreaction and positive return autocorrelations. Our goal in this paper is to test the Hong-Stein version of the underreac- tion hypothesis.In other words,we look for evidence that momentum re- flects the gradual diffusion of firm-specific information.2 To do so,we begin by sorting stocks into different classes,for which information is a priori more or less likely to spread gradually.The central prediction is then that stocks with slower information diffusion should exhibit more pronounced momentum.3 One natural sorting variable-which forms the basis for our first set of tests-is firm size.It seems plausible that information about small firms gets out more slowly;this would happen if,for example,investors face fixed costs of information acquisition,and hence choose in the aggregate to devote more effort to learning about those stocks in which they can take large positions. 2A recent paper that can be thought of in a similar spirit is Chan,Jegadeesh,and Lakon- ishok(1996).They show that momentum strategies are profitable even after controlling for post-earnings-announcement drift (Bernard and Thomas (1989,1990),Bernard (1992)).This suggests that momentum at least in part reflects the adjustment of stock prices to the sort of information that (unlike earnings news)is not made publicly available to all investors simultaneously. 3 To obtain this prediction,we are assuming that smart-money arbitrage does not completely eliminate differences in momentum across stocks.This property holds in a wide range of set- tings.For example,if there is a pool of arbitrageurs that operate across all stocks,it suffices to assume that they are risk-averse and hence prefer to hold diversified portfolios

While the existence of momentum in stock returns does not seem to be too controversial, it is much less clear what might be driving it. Some ~e.g., Conrad and Kaul ~1998!! have suggested a risk-based interpretation of mo￾mentum. This is certainly a logical possibility, although there is little evidence that cuts clearly in favor of a risk story. In this vein, Fama and French ~1996! note that momentum effects are not subsumed by their three-factor model. Turning to “behavioral” ~i.e., non-risk-based! explanations, there are a num￾ber of theories that can give rise to positive medium-term return auto￾correlations. In some of these, prices initially overreact to news about fundamentals, then continue to overreact further for a period of time. The positive-feedback-trader model of DeLong et al. ~1990! fits in this camp, as does the overconfidence model of Daniel, Hirshleifer, and Subrahmanyam ~1998!. In other models, momentum is a symptom of underreaction—prices adjust too slowly to news. The set of underreaction theories can be further subdivided according the exact mechanism that is at work. In Barberis, Shleifer, and Vishny ~1998!, there is a representative investor who suffers from a conservatism bias, and who does not update his beliefs sufficiently when he observes new public information. In Hong and Stein ~1999! the emphasis is instead on heteroge￾neities across investors, who observe different pieces of private information at different points in time. Hong and Stein make two key assumptions: ~1! firm-specific information diffuses gradually across the investing public; and ~2! investors cannot perform the rational-expectations trick of extracting in￾formation from prices. Taken together, these two assumptions generate un￾derreaction and positive return autocorrelations. Our goal in this paper is to test the Hong–Stein version of the underreac￾tion hypothesis. In other words, we look for evidence that momentum re￾flects the gradual diffusion of firm-specific information.2 To do so, we begin by sorting stocks into different classes, for which information is a priori more or less likely to spread gradually. The central prediction is then that stocks with slower information diffusion should exhibit more pronounced momentum.3 One natural sorting variable—which forms the basis for our first set of tests—is firm size. It seems plausible that information about small firms gets out more slowly; this would happen if, for example, investors face fixed costs of information acquisition, and hence choose in the aggregate to devote more effort to learning about those stocks in which they can take large positions. 2 A recent paper that can be thought of in a similar spirit is Chan, Jegadeesh, and Lakon￾ishok ~1996!. They show that momentum strategies are profitable even after controlling for post-earnings-announcement drift ~Bernard and Thomas ~1989, 1990!, Bernard ~1992!!. This suggests that momentum at least in part reflects the adjustment of stock prices to the sort of information that ~unlike earnings news! is not made publicly available to all investors simultaneously. 3 To obtain this prediction, we are assuming that smart-money arbitrage does not completely eliminate differences in momentum across stocks. This property holds in a wide range of set￾tings. For example, if there is a pool of arbitrageurs that operate across all stocks, it suffices to assume that they are risk-averse and hence prefer to hold diversified portfolios. 266 The Journal of Finance

Size,Analyst Coverage,and Profitability 267 Unfortunately,even if firm size is in fact a useful measure of the rate of information diffusion,it is likely to capture other things as well,potentially confounding our inferences.For example,Merton(1987)and Grossman and Miller(1988)argue that market making or arbitrage capacity may be less in small-capitalization stocks.On the one hand,if there are supply shocks,this could lead to a greater tendency toward reversals (i.e.,negatively correlated returns)in small stocks,which would obscure the gradual-information-flow effect we are interested in.On the other hand,one might argue that what- ever behavioral phenomenon is driving positive serial correlation in returns, less arbitrage means that it will have a bigger impact in small stocks,lead- ing us to overstate the importance of gradual information flow as the spe- cific mechanism at work.The bottom line is that although it is certainly interesting to see how momentum profits vary with firm size,this probably does not by itself constitute a clean test of our central hypothesis. As an alternative proxy for the rate of information flow,we consider an- alyst coverage.The idea here is that stocks with lower analyst coverage should,all else equal,be ones where firm-specific information moves more slowly across the investing public.Thus our second set of tests boils down to checking whether momentum strategies work better in low-analyst-coverage stocks.The one important caveat is that analyst coverage is very strongly correlated with firm size (Bhushan (1989)).So in this second set of tests,we control for the influence of size on analyst coverage by sorting stocks into groups according to their residual analyst coverage,where the residual comes from a regression of coverage on firm size.4 To preview,we obtain the predicted results for both firm size and residual analyst coverage.First,with respect to size,once one moves past the very smallest capitalization stocks(where thin market making capacity does in- deed appear to be an issue)the profitability of momentum strategies de- clines sharply with market capitalization.Second,holding size fixed, momentum strategies work particularly well among stocks that have low analyst coverage.Moreover,size and coverage interact in a plausible fash- ion:The marginal importance of analyst coverage is greatest among small stocks.Beyond being statistically significant,these effects are also of an economically interesting magnitude.For example,across our entire sample, momentum profits are roughly 60 percent greater among the one-third of the stocks with the lowest residual coverage,as compared to the one-third with the highest residual coverage. In addition to these basic findings,we uncover another interesting regu- larity.There is a strong asymmetry,in that the effect of analyst coverage is much more pronounced for stocks that are past losers than for stocks that 4 Our use of residual analyst coverage as a forecaster of stock returns links us to work by Brennan,Jegadeesh,and Swaminathan(1993).They are interested in understanding a higher frequency phenomenon-the fact that at daily and weekly horizons,small stocks seem to lag large stocks (Lo and MacKinlay (1990)).They show that holding size fixed,low-coverage stocks also tend to lag high-coverage stocks,which they interpret as evidence that analysts are im- portant in helping stocks adjust to common information.Note that this is quite different from our story,which focuses on the role of analysts in propagating firm-specific information

Unfortunately, even if firm size is in fact a useful measure of the rate of information diffusion, it is likely to capture other things as well, potentially confounding our inferences. For example, Merton ~1987! and Grossman and Miller ~1988! argue that market making or arbitrage capacity may be less in small-capitalization stocks. On the one hand, if there are supply shocks, this could lead to a greater tendency toward reversals ~i.e., negatively correlated returns! in small stocks, which would obscure the gradual-information-flow effect we are interested in. On the other hand, one might argue that what￾ever behavioral phenomenon is driving positive serial correlation in returns, less arbitrage means that it will have a bigger impact in small stocks, lead￾ing us to overstate the importance of gradual information flow as the spe￾cific mechanism at work. The bottom line is that although it is certainly interesting to see how momentum profits vary with firm size, this probably does not by itself constitute a clean test of our central hypothesis. As an alternative proxy for the rate of information flow, we consider an￾alyst coverage. The idea here is that stocks with lower analyst coverage should, all else equal, be ones where firm-specific information moves more slowly across the investing public. Thus our second set of tests boils down to checking whether momentum strategies work better in low-analyst-coverage stocks. The one important caveat is that analyst coverage is very strongly correlated with firm size ~Bhushan ~1989!!. So in this second set of tests, we control for the influence of size on analyst coverage by sorting stocks into groups according to their residual analyst coverage, where the residual comes from a regression of coverage on firm size.4 To preview, we obtain the predicted results for both firm size and residual analyst coverage. First, with respect to size, once one moves past the very smallest capitalization stocks ~where thin market making capacity does in￾deed appear to be an issue! the profitability of momentum strategies de￾clines sharply with market capitalization. Second, holding size fixed, momentum strategies work particularly well among stocks that have low analyst coverage. Moreover, size and coverage interact in a plausible fash￾ion: The marginal importance of analyst coverage is greatest among small stocks. Beyond being statistically significant, these effects are also of an economically interesting magnitude. For example, across our entire sample, momentum profits are roughly 60 percent greater among the one-third of the stocks with the lowest residual coverage, as compared to the one-third with the highest residual coverage. In addition to these basic findings, we uncover another interesting regu￾larity. There is a strong asymmetry, in that the effect of analyst coverage is much more pronounced for stocks that are past losers than for stocks that 4 Our use of residual analyst coverage as a forecaster of stock returns links us to work by Brennan, Jegadeesh, and Swaminathan ~1993!. They are interested in understanding a higher frequency phenomenon—the fact that at daily and weekly horizons, small stocks seem to lag large stocks ~Lo and MacKinlay ~1990!!. They show that holding size fixed, low-coverage stocks also tend to lag high-coverage stocks, which they interpret as evidence that analysts are im￾portant in helping stocks adjust to common information. Note that this is quite different from our story, which focuses on the role of analysts in propagating firm-specific information. Size, Analyst Coverage, and Profitability 267

268 The Journal of Finance are past winners.In other words,low-coverage stocks seem to react more sluggishly to bad news than to good news.This makes intuitive sense in the context of a theory based on the flow of firm-specific information.Think of a firm that has no analyst coverage but is sitting on good news.To the extent that its managers prefer higher to lower stock prices,they will push the news out the door themselves,via increased disclosures,etc.On the other hand,if the same firm is sitting on bad news,its managers will have much less incentive to bring investors up to date quickly.Thus the marginal contribution of outside analysts in getting the news out is likely to be greater when the news is bad. Although all of our evidence is consistent with the sort of gradual- information-flow model in Hong and Stein(1999),it is also possible to put forward an alternative explanation of the data.In particular,it may be that analyst coverage is a proxy for differences in transactions costs that are somehow not well captured by firm size.To take a concrete example,con- sider two stocks A and B of equal size,where A is harder to sell short than B,and also attracts fewer analysts.Since short-sales constraints can impede the adjustment of prices to negative information,(Diamond and Verrecchia (1987))this could explain why the low-coverage stock A reacts more slowly- especially to bad news-than the high-coverage stock B. In an effort to confront this alternative hypothesis,we experiment with two further proxies for transactions costs:share turnover and a dummy vari- able for the existence of listed options on a given stock.The latter variable might be expected to be particularly useful in picking up cross-sectional dif- ferences in ease of shorting,since investors who are not adept at directly shorting a stock can use put options as a substitute.As it turns out,our results are robust to both of these controls.Nevertheless,although these checks are helpful,we recognize that we do not have a perfect measure of transactions costs at the individual stock level,and so cannot definitively rule out all variations of the alternative hypothesis.This is an inevitable shortcoming of our approach. The remainder of the paper is organized as follows.In Section I we de- scribe our data and analyze in detail the cross-sectional determinants of analyst coverage.Section II contains our main results on momentum strat- egies sorted by firm size and residual coverage.In Section III we present complementary results based on an alternative,much more parametrically structured,regression approach.Section IV concludes. I.Cross-Sectional Determinants of Analyst Coverage Our data come from three primary sources.The stock return and turnover data are from the CRSP Monthly Stocks Combined File,which includes NYSE, AMEX,and Nasdag stocks.Throughout,we exclude ADRs,REITs,closed- end funds,and primes and scores-that is,stocks that do not have a CRSP share type code of 10 or 11.The data on analyst coverage are from the I/B/E/S Historical Summary File,and are available on a monthly basis be- ginning in 1976.For each stock on CRSP,we set the coverage in any given

are past winners. In other words, low-coverage stocks seem to react more sluggishly to bad news than to good news. This makes intuitive sense in the context of a theory based on the flow of firm-specific information. Think of a firm that has no analyst coverage but is sitting on good news. To the extent that its managers prefer higher to lower stock prices, they will push the news out the door themselves, via increased disclosures, etc. On the other hand, if the same firm is sitting on bad news, its managers will have much less incentive to bring investors up to date quickly. Thus the marginal contribution of outside analysts in getting the news out is likely to be greater when the news is bad. Although all of our evidence is consistent with the sort of gradual￾information-flow model in Hong and Stein ~1999!, it is also possible to put forward an alternative explanation of the data. In particular, it may be that analyst coverage is a proxy for differences in transactions costs that are somehow not well captured by firm size. To take a concrete example, con￾sider two stocks A and B of equal size, where A is harder to sell short than B, and also attracts fewer analysts. Since short-sales constraints can impede the adjustment of prices to negative information, ~Diamond and Verrecchia ~1987!! this could explain why the low-coverage stock A reacts more slowly— especially to bad news—than the high-coverage stock B. In an effort to confront this alternative hypothesis, we experiment with two further proxies for transactions costs: share turnover and a dummy vari￾able for the existence of listed options on a given stock. The latter variable might be expected to be particularly useful in picking up cross-sectional dif￾ferences in ease of shorting, since investors who are not adept at directly shorting a stock can use put options as a substitute. As it turns out, our results are robust to both of these controls. Nevertheless, although these checks are helpful, we recognize that we do not have a perfect measure of transactions costs at the individual stock level, and so cannot definitively rule out all variations of the alternative hypothesis. This is an inevitable shortcoming of our approach. The remainder of the paper is organized as follows. In Section I we de￾scribe our data and analyze in detail the cross-sectional determinants of analyst coverage. Section II contains our main results on momentum strat￾egies sorted by firm size and residual coverage. In Section III we present complementary results based on an alternative, much more parametrically structured, regression approach. Section IV concludes. I. Cross-Sectional Determinants of Analyst Coverage Our data come from three primary sources. The stock return and turnover data are from the CRSP Monthly Stocks Combined File, which includes NYSE, AMEX, and Nasdaq stocks. Throughout, we exclude ADRs, REITs, closed￾end funds, and primes and scores—that is, stocks that do not have a CRSP share type code of 10 or 11. The data on analyst coverage are from the I0B0E0S Historical Summary File, and are available on a monthly basis be￾ginning in 1976. For each stock on CRSP, we set the coverage in any given 268 The Journal of Finance

Size,Analyst Coverage,and Profitability 269 month equal to the number of I/B/E/S analysts who provide fiscal year 1 earnings estimates that month.If no I/B/E/S value is available (i.e.,the CRSP cusip is not matched in the I/B/E/S database),we set the coverage to zero.Finally,the options-listing data come from the Options Clearing Cor- poration,and cover options listed on the CBOE,NYSE,AMEX,Philadelphia, Pacific,and Midwest exchanges. Table I provides an overview of the extent of analyst coverage for both our full sample (Panel A)as well as for five size-based subsamples (Panel B). The first striking thing that emerges from the table is how many firms show up as having zero analysts.This is especially true in the first few years of the sample period,1976 to 1978.For example,in 1976,77.3 percent of all firms appear as having zero analysts.There is a marked deepening of cov- erage around 1980,with the fraction of uncovered firms dropping to 58.2 percent.After that,things change much more smoothly,with the fraction of uncovered firms declining gradually to 36.9 percent in 1996. While the numbers no doubt largely reflect the reality that many firms are simply not covered by analysts,we worry that they may also be some- what contaminated by measurement error.It is possible that the I/B/E/S data set is missing information on some firms'analysts.Alternatively,it is possible that I/B/E/S has the data,but has assigned a different cusip num- ber to a firm than CRSP.In this case,we would mistakenly code the CRSP firm as having no analysts.In principle,such measurement error should make our tests err on the side of conservatism-it should be harder to discern significant differences across stocks that we classify as low coverage versus high coverage.Because of this concern,and because the number of zeros is so much higher in the first few years,all the tests we present below use a sample period that runs from 1980 to 1996.5 However,it should be noted that none of our results are materially altered if we begin in 1976 instead. A second key fact that comes out of Table I is that for the smallest firms, there is simply no variation in coverage.Consider those firms that are smaller than the 20th percentile NYSE/AMEX firm.As can be seen,almost all of them have zero analysts-82 percent are not covered in 1988,which is roughly the midpoint of the sample period we use.Consequently,we simply cannot use this part of the population to test any hypotheses having to do with analyst coverage.Hence,all our coverage-related tests begin with a subsam- ple that excludes those firms that are below the 20th percentile NYSE/ AMEX breakpoint in any given month.5 Note that there is much more variation in analyst coverage in the next size class,which runs from the 20th to the 40th percentile of NYSE/AMEX-in 1988,only 41.7 percent of the firms in this class are not covered,and a substantial fraction have as many as three or four analysts. 5 For reasons that we explain later,we typically measure analyst coverage six months before we actually begin to implement our momentum strategies.Since our sample period for mea- suring returns begins in 1980,we use analyst data as far back as 1979. 6The cutoff point is around $30 million in market capitalization as of the midpoint of the sample period,and rises to almost $60 million by 1996

month equal to the number of I0B0E0S analysts who provide fiscal year 1 earnings estimates that month. If no I0B0E0S value is available ~i.e., the CRSP cusip is not matched in the I0B0E0S database!, we set the coverage to zero. Finally, the options-listing data come from the Options Clearing Cor￾poration, and cover options listed on the CBOE, NYSE, AMEX, Philadelphia, Pacific, and Midwest exchanges. Table I provides an overview of the extent of analyst coverage for both our full sample ~Panel A! as well as for five size-based subsamples ~Panel B!. The first striking thing that emerges from the table is how many firms show up as having zero analysts. This is especially true in the first few years of the sample period, 1976 to 1978. For example, in 1976, 77.3 percent of all firms appear as having zero analysts. There is a marked deepening of cov￾erage around 1980, with the fraction of uncovered firms dropping to 58.2 percent. After that, things change much more smoothly, with the fraction of uncovered firms declining gradually to 36.9 percent in 1996. While the numbers no doubt largely reflect the reality that many firms are simply not covered by analysts, we worry that they may also be some￾what contaminated by measurement error. It is possible that the I0B0E0S data set is missing information on some firms’ analysts. Alternatively, it is possible that I0B0E0S has the data, but has assigned a different cusip num￾ber to a firm than CRSP. In this case, we would mistakenly code the CRSP firm as having no analysts. In principle, such measurement error should make our tests err on the side of conservatism—it should be harder to discern significant differences across stocks that we classify as low coverage versus high coverage. Because of this concern, and because the number of zeros is so much higher in the first few years, all the tests we present below use a sample period that runs from 1980 to 1996.5 However, it should be noted that none of our results are materially altered if we begin in 1976 instead. A second key fact that comes out of Table I is that for the smallest firms, there is simply no variation in coverage. Consider those firms that are smaller than the 20th percentile NYSE0AMEX firm. As can be seen, almost all of them have zero analysts—82 percent are not covered in 1988, which is roughly the midpoint of the sample period we use. Consequently, we simply cannot use this part of the population to test any hypotheses having to do with analyst coverage. Hence, all our coverage-related tests begin with a subsam￾ple that excludes those firms that are below the 20th percentile NYSE0 AMEX breakpoint in any given month.6 Note that there is much more variation in analyst coverage in the next size class, which runs from the 20th to the 40th percentile of NYSE0AMEX—in 1988, only 41.7 percent of the firms in this class are not covered, and a substantial fraction have as many as three or four analysts. 5 For reasons that we explain later, we typically measure analyst coverage six months before we actually begin to implement our momentum strategies. Since our sample period for mea￾suring returns begins in 1980, we use analyst data as far back as 1979. 6 The cutoff point is around $30 million in market capitalization as of the midpoint of the sample period, and rises to almost $60 million by 1996. Size, Analyst Coverage, and Profitability 269

Table I 岂 Descriptive Statistics for Analyst Coverage Descriptive statistics for analyst coverage for NYSE,AMEX,and Nasdaq stocks,excluding ADRs,REITs,closed-end funds,and primes and scores during the period 1976 to 1996.Panel A reports for the even years between 1976 and 1996 the number of firms in the sample,their mean and median size,the number of analysts at various coverage percentiles,and the percentage of firms that had no coverage.Panel B reports for 1988 by firm size the same statistics as in Panel A. Panel A:All Stocks,1976-1996 Mean Median Percentage No.of Size Size No.of Analysts at Coverage Percentiles of firms Year Firms (millions) (millions) 10 20 30 40 50 60 70 80 90 uncovered 76 4402 183.6 18.7 0 0 0 0 0 0 0 77.3% 晨 78 4472 176.4 22.7 0 0 0 0 0 0 2 5 71.5% 80 4329 248.9 34.6 0 0 0 0 0 1 2 ￥ 9 58.2% 82 4754 249.3 30.3 0 0 0 0 a 2 5 11 59.3% 84 5049 332.3 44.4 0 0 0 0 1 3 6 12 50.8% Journal 86 5364 387.4 42.5 0 0 0 0 0 3 6 14 50.5% 88 5932 402.2 32.6 0 0 0 0 0 1 3 5 12 50.1% g 90 5567 500.7 34.5 0 0 0 0 7 13 45.4% 9 5438 672.8 49.8 0 0 0 0 1 3 6 3 46.7% 5890 802.9 81.1 0 0 0 0 3 7 13 40.0% Finance 96 6460 978.1 90.8 0 0 0 3 4 12 36.9% Panel B:Breakdown of Analyst Coverage by Firm Size for 1988 Mean Median Percentage No.of Size Size No.of Analysts at Coverage Percentiles of firms NYSE/AMEX Breakpoints Firms (millions) (millions) 10 20 30 40 50 60 70 80 90 uncovered Below the 20th percentile 2597 9.6 8.3 0 0 0 0 0 0 82.0% Between the 20th 40th percentiles 1363 45.1 42.5 0 0 0 0 1 1 2 3 4 41.7% Between the 40th 60th percentiles 937 147.1 133.3 0 4 5 9 21.5% Between the 60th 80th percentiles 607 554.0 495.8 4 6 7 8 10 12 14 17 7.7% Above the 80th percentile 431 4235.7 2390.7 13 1619 2123 26 28 30 5.6%

Table I Descriptive Statistics for Analyst Coverage Descriptive statistics for analyst coverage for NYSE, AMEX, and Nasdaq stocks, excluding ADRs, REITs, closed-end funds, and primes and scores during the period 1976 to 1996. Panel A reports for the even years between 1976 and 1996 the number of firms in the sample, their mean and median size, the number of analysts at various coverage percentiles, and the percentage of firms that had no coverage. Panel B reports for 1988 by firm size the same statistics as in Panel A. Panel A: All Stocks, 1976–1996 No. of Analysts at Coverage Percentiles Year No. of Firms Mean Size ~millions! Median Size ~millions! 10 20 30 40 50 60 70 80 90 Percentage of firms uncovered 76 4402 183.6 18.7 00000001 4 77.3% 78 4472 176.4 22.7 00000002 5 71.5% 80 4329 248.9 34.6 00000124 9 58.2% 82 4754 249.3 30.3 0 0 0 0 0 1 2 5 11 59.3% 84 5049 332.3 44.4 0 0 0 0 0 1 3 6 12 50.8% 86 5364 387.4 42.5 0 0 0 0 0 1 3 6 14 50.5% 88 5932 402.2 32.6 0 0 0 0 0 1 3 5 12 50.1% 90 5567 500.7 34.5 0 0 0 0 1 2 3 7 13 45.4% 92 5438 672.8 49.8 0 0 0 0 1 2 3 6 13 46.7% 94 5890 802.9 81.1 0 0 0 0 1 3 4 7 13 40.0% 96 6460 978.1 90.8 0 0 0 1 2 3 4 7 12 36.9% Panel B: Breakdown of Analyst Coverage by Firm Size for 1988 No. of Analysts at Coverage Percentiles NYSE0AMEX Breakpoints No. of Firms Mean Size ~millions! Median Size ~millions! 10 20 30 40 50 60 70 80 90 Percentage of firms uncovered Below the 20th percentile 2597 9.6 8.3 0 00000001 82.0% Between the 20th & 40th percentiles 1363 45.1 42.5 0 00011234 41.7% Between the 40th & 60th percentiles 937 147.1 133.3 0 01234579 21.5% Between the 60th & 80th percentiles 607 554.0 495.8 1 4 6 7 8 10 12 14 17 7.7% Above the 80th percentile 431 4235.7 2390.7 8 13 16 19 21 23 26 28 30 5.6% 270 The Journal of Finance

Size,Analyst Coverage,and Profitability 271 In Table II,we examine the cross-sectional determinants of analyst cov- erage.When we actually implement our trading strategies in the next sec- tion,we run a separate regression every month to create our measure of residual coverage.Because the regressions look so similar month to month, we only present one set in Table II for illustrative purposes,corresponding to December 1988,which is around the midpoint of our sample period. Again,note that in each case,the regression is run only on those stocks that are larger than the 20th percentile NYSE/AMEX breakpoint in the given month. The first point to note is that unlike some previous researchers who have run similar regressions (e.g.,Bhushan(1989)and Brennan and Hughes(1991)) we use as our left-hand side variable log(1 Analysts),rather than the raw number of analysts.We do this because we ultimately want to use the re- siduals from our analyst-coverage regressions to explain momentum,and it seems plausible that one extra analyst should matter much more in this regard if a firm has few analysts than if it has many. In Model 1,we use OLS,and the only two right-hand side variables are log (Size),where Size is current market capitalization,and a Nasdaq dummy variable.7 The size variable is clearly enormously important,generating an R2 of 0.61.In Model 2,we add 15 industry dummies to the regression.8 This has a small effect,raising the R2 to 0.63. In Models 3 and 4,we try adding the firm's book-to-market ratio.We do this because book-to-market is known to forecast returns (Fama and French (1992),Lakonishok,Shleifer,and Vishny (1994))and we want to make sure that any return-predicting power we get out of analyst coverage is not sim- ply capturing a book-to-market effect.As it turns out,the coefficient on book- to-market is positive and significant,but it adds nothing at all to the R2. Thus it is unlikely that any of the results we report below are driven by anything to do with book-to-market.?In Models 5 and 6,we undertake a similar experiment with beta.10 The coefficient on beta is positive and strongly significant,and in this case,the R2increases marginally,going from 0.61 to 0.63 when we exclude industry dummies. 7 The Nasdag dummy is the only variable whose behavior changes much over the sample period.In earlier years,it is strongly negative,which is why we include it in our baseline model.However,by the late 1980s,it is typically positive,though not always significantly so. 8 The dummies correspond to the following grouping of two-digit SIC codes:(1)SIC 01-09; (2)SIC10-14;(3)SIC15-19;(4)SIC20-21;(⑤)SIC22-23:(6)SIC24-27;(7)SIC28-32:(8) SIC33-34;(9)SIC35-39:(10)SIC40-48;(11)SIC49;(12)SIC50-52:(13)S1C53-59:(14)SIC 60-69:and(15)S1C70-79. s Even if high-coverage stocks do have higher mean returns because they have a higher loading on book-to-market,this cannot explain our central result,namely that high-coverage stocks exhibit less momentum. 10 Throughout,we calculate beta with the Scholes-Williams(1977)method,using daily re- turns and the value-weighted CRSP index in the prior calendar year.We require that 50 per. cent of single-day trade-only returns(computed using closing prices,not bid/ask averages)be available.This is the same approach used by CRSP in its NYSE/AMEX Excess Returns File

In Table II, we examine the cross-sectional determinants of analyst cov￾erage. When we actually implement our trading strategies in the next sec￾tion, we run a separate regression every month to create our measure of residual coverage. Because the regressions look so similar month to month, we only present one set in Table II for illustrative purposes, corresponding to December 1988, which is around the midpoint of our sample period. Again, note that in each case, the regression is run only on those stocks that are larger than the 20th percentile NYSE0AMEX breakpoint in the given month. The first point to note is that unlike some previous researchers who have run similar regressions ~e.g., Bhushan ~1989! and Brennan and Hughes ~1991!! we use as our left-hand side variable log~1 1 Analysts!, rather than the raw number of analysts. We do this because we ultimately want to use the re￾siduals from our analyst-coverage regressions to explain momentum, and it seems plausible that one extra analyst should matter much more in this regard if a firm has few analysts than if it has many. In Model 1, we use OLS, and the only two right-hand side variables are log ~Size!, where Size is current market capitalization, and a Nasdaq dummy variable.7 The size variable is clearly enormously important, generating an R2 of 0.61. In Model 2, we add 15 industry dummies to the regression.8 This has a small effect, raising the R2 to 0.63. In Models 3 and 4, we try adding the firm’s book-to-market ratio. We do this because book-to-market is known to forecast returns ~Fama and French ~1992!, Lakonishok, Shleifer, and Vishny ~1994!! and we want to make sure that any return-predicting power we get out of analyst coverage is not sim￾ply capturing a book-to-market effect. As it turns out, the coefficient on book￾to-market is positive and significant, but it adds nothing at all to the R2 . Thus it is unlikely that any of the results we report below are driven by anything to do with book-to-market.9 In Models 5 and 6, we undertake a similar experiment with beta.10 The coefficient on beta is positive and strongly significant, and in this case, the R2 increases marginally, going from 0.61 to 0.63 when we exclude industry dummies. 7 The Nasdaq dummy is the only variable whose behavior changes much over the sample period. In earlier years, it is strongly negative, which is why we include it in our baseline model. However, by the late 1980s, it is typically positive, though not always significantly so. 8 The dummies correspond to the following grouping of two-digit SIC codes: ~1! SIC 01–09; ~2! SIC 10–14; ~3! SIC 15–19; ~4! SIC 20–21; ~5! SIC 22–23; ~6! SIC 24–27; ~7! SIC 28–32; ~8! SIC 33–34; ~9! SIC 35–39; ~10! SIC 40–48; ~11! SIC 49; ~12! SIC 50–52; ~13! SIC 53–59; ~14! SIC 60–69; and ~15! SIC 70–79. 9 Even if high-coverage stocks do have higher mean returns because they have a higher loading on book-to-market, this cannot explain our central result, namely that high-coverage stocks exhibit less momentum. 10 Throughout, we calculate beta with the Scholes–Williams ~1977! method, using daily re￾turns and the value-weighted CRSP index in the prior calendar year. We require that 50 per￾cent of single-day trade-only returns ~computed using closing prices, not bid0ask averages! be available. This is the same approach used by CRSP in its NYSE0AMEX Excess Returns File. Size, Analyst Coverage, and Profitability 271

3 Table II Determinants of Analyst Coverage,12/1988 Dependent variable is log(1 Analyst coverage).Log Size is the log of a firm's year-end market value.NASD is a Nasdaq dummy.Book/Mkt is the ratio of a firm's year-end book-to-market value.Beta is a firm's market beta.P is a firm's share price.Var is the variance of a firm's return using the last 200 observations from year-end.R is the rate of return of a firm lagged k years for k=0,1,2,3,4.T-O is a firm's turnover defined as the prior six months'trading volume divided by shares outstanding.NASD T-O is the Nasdag dummy times firm turnover.OPT is a dummy for whether a firm has options trading on CBOE,NYSE,AMEX,Philadelphia,or Pacific stock exchanges.IND is a set of CRSP industry dummies.There are 2,012 observations.t-statistics are in parentheses. Model No. 5 Book/ NASD NASD Mkt Beta 1/P Var R R2 R R TO T-0 OPT IND P2 0.54 0.03 No 0.61 (52.67) (0.99) 2 0.56 0.04 Yes 0.63 Journal (52.90 (1.21) 3 0.55 0.05 0.12 No 0.61 (53.03 (1.50) (3.15) 4 0.57 0.07 0.17 Yes 0.63 (52.22) (2.00) (4.30) 5 0.50 0.07 0.38 No 0.64 Finance (48.41) (2.28) (11.54) 0.51 0.09 0.40 Yes 0.65 (46.11) (2.62) (10.94) 0.57 0.09 -0.52 -1.27 -0.50 -0.28 -0.28 -0.04 -0.16 Yes 0.65 (49.87) (2.59) (-3.12) (-3.23) (-9.46) (-6.06) (-6.00) (-0.85 (-3.46) 8 0.52 -0.02 3.82 -0.53 No 0.64 (51.46) (-0.54) (8.18) (-0.93) 9 0.50 -0.02 3.52 -0.37 0.12 No 0.64 (38.83) (-0.48) (7.32) -0.64)(2.48)

Table II Determinants of Analyst Coverage, 12/1988 Dependent variable is log~1 1 Analyst coverage!. Log Size is the log of a firm’s year-end market value. NASD is a Nasdaq dummy. Book0Mkt is the ratio of a firm’s year-end book-to-market value. Beta is a firm’s market beta. P is a firm’s share price. Var is the variance of a firm’s return using the last 200 observations from year-end. Rk is the rate of return of a firm lagged k years for k 5 0,1,2,3,4. T-O is a firm’s turnover defined as the prior six months’ trading volume divided by shares outstanding. NASD * T-O is the Nasdaq dummy times firm turnover. OPT is a dummy for whether a firm has options trading on CBOE, NYSE, AMEX, Philadelphia, or Pacific stock exchanges. IND is a set of CRSP industry dummies. There are 2,012 observations. t-statistics are in parentheses. Model No. Log Size NASD Book0 Mkt Beta 10P Var R0 R1 R2 R3 R4 T-O NASD * T-O OPT IND R2 1 0.54 0.03 No 0.61 ~52.67! ~0.99! 2 0.56 0.04 Yes 0.63 ~52.90! ~1.21! 3 0.55 0.05 0.12 No 0.61 ~53.03! ~1.50! ~3.15! 4 0.57 0.07 0.17 Yes 0.63 ~52.22! ~2.00! ~4.30! 5 0.50 0.07 0.38 No 0.64 ~48.41! ~2.28! ~11.54! 6 0.51 0.09 0.40 Yes 0.65 ~46.11! ~2.62! ~10.94! 7 0.57 0.09 20.52 21.27 20.50 20.28 20.28 20.04 20.16 Yes 0.65 ~49.87! ~2.59! ~23.12! ~23.23! ~29.46! ~26.06! ~26.00! ~20.85! ~23.46! 8 0.52 20.02 3.82 20.53 No 0.64 ~51.46! ~20.54! ~8.18! ~20.93! 9 0.50 20.02 3.52 20.37 0.12 No 0.64 ~38.83! ~20.48! ~7.32! ~20.64! ~2.48! 272 The Journal of Finance

Size,Analyst Coverage,and Profitability 273 In Model 7,we add to the industry-dummy specification of Model 2 a number of variables that are considered in Brennan and Hughes(1991):1/P, where P is the price of a share;the variance of daily returns;and five years worth of annual lagged returns.Although many of the coefficients are indi- vidually significant,the overall impression is that these extra variables are not very important in explaining the variation in coverage-jointly they raise the R2 from 0.63 to 0.65.11 In Model 8,we take the baseline specification of Model 1 and add a turn- over measure,defined as the number of shares traded over the prior six months divided by total shares outstanding.(Because turnover numbers may not have the same interpretation in a dealer market,we allow the coefficient on turnover to be different for Nasdaq firms.)Turnover is significantly pos- itively correlated with coverage on all exchanges,and it raises the R2 some- what,from 0.61 to 0.64.However,with this regression,one needs to be especially careful in attaching any causal interpretation.On the one hand,it is possible that turnover causes coverage:Analysts may be more inclined to follow naturally high-turnover stocks if this makes it easier to generate bro- kerage commissions for their employers(Hayes (1996)).On the other hand, Brennan and Subrahmanyam (1995)find evidence of causality running in the other direction:More analysts reduce the adverse-selection costs of trad- ing,and thereby attract a greater volume of trade.As we argue in Sec- tion II.D below,depending on which story one believes,it may or may not make sense to control for turnover in generating our measure of residual analyst coverage. Continuing in a similar vein,Model 9 adds to the turnover measure of Model 8 another proxy for transactions costs,a dummy variable that takes on the value one if the stock in question has listed options.(About 25 percent of our sample firms have listed options in 1988,with the fraction rising to 49 percent by 1996.)As can be seen,the options-listing dummy has the expected positive sign and is statistically significant.However,unlike turn- over,it adds virtually nothing to the explanatory power of the regression- the R2 remains at 0.64,just as in Model 8. Overall,the results in Table II make it clear that although a number of other variables are significantly related to analyst coverage,firm size is by far the dominant factor.Thus,in addition to worrying about the influence of these other variables,it is also important to think about potential nonlin- earities in the relationship between log(1+Analysts)and log(Size).In this spirit,we proceed as follows.We start in Section II.B by using the simple size-based regression in Model 1 as our baseline method for generating re- 11 Interestingly,our results call into question the conclusions of Brennan and Hughes(1991), who obtain significant positive coefficients on 1/P.In our regressions,we tend to get the op- posite sign.We conjecture that this arises because we are using log(1+Analysts)on the left. hand side,rather than the raw number of analysts.Because 1/P is correlated with firm size, and because firm size is of such dominant importance,any differences in how one models the analyst-size relationship is likely to have a strong influence on the 1/P coefficient

In Model 7, we add to the industry-dummy specification of Model 2 a number of variables that are considered in Brennan and Hughes ~1991!: 10P, where P is the price of a share; the variance of daily returns; and five years’ worth of annual lagged returns. Although many of the coefficients are indi￾vidually significant, the overall impression is that these extra variables are not very important in explaining the variation in coverage—jointly they raise the R2 from 0.63 to 0.65.11 In Model 8, we take the baseline specification of Model 1 and add a turn￾over measure, defined as the number of shares traded over the prior six months divided by total shares outstanding. ~Because turnover numbers may not have the same interpretation in a dealer market, we allow the coefficient on turnover to be different for Nasdaq firms.! Turnover is significantly pos￾itively correlated with coverage on all exchanges, and it raises the R2 some￾what, from 0.61 to 0.64. However, with this regression, one needs to be especially careful in attaching any causal interpretation. On the one hand, it is possible that turnover causes coverage: Analysts may be more inclined to follow naturally high-turnover stocks if this makes it easier to generate bro￾kerage commissions for their employers ~Hayes ~1996!!. On the other hand, Brennan and Subrahmanyam ~1995! find evidence of causality running in the other direction: More analysts reduce the adverse-selection costs of trad￾ing, and thereby attract a greater volume of trade. As we argue in Sec￾tion II.D below, depending on which story one believes, it may or may not make sense to control for turnover in generating our measure of residual analyst coverage. Continuing in a similar vein, Model 9 adds to the turnover measure of Model 8 another proxy for transactions costs, a dummy variable that takes on the value one if the stock in question has listed options. ~About 25 percent of our sample firms have listed options in 1988, with the fraction rising to 49 percent by 1996.! As can be seen, the options-listing dummy has the expected positive sign and is statistically significant. However, unlike turn￾over, it adds virtually nothing to the explanatory power of the regression— the R2 remains at 0.64, just as in Model 8. Overall, the results in Table II make it clear that although a number of other variables are significantly related to analyst coverage, firm size is by far the dominant factor. Thus, in addition to worrying about the influence of these other variables, it is also important to think about potential nonlin￾earities in the relationship between log~1 1 Analysts! and log~Size!. In this spirit, we proceed as follows. We start in Section II.B by using the simple size-based regression in Model 1 as our baseline method for generating re- 11 Interestingly, our results call into question the conclusions of Brennan and Hughes ~1991!, who obtain significant positive coefficients on 10P. In our regressions, we tend to get the op￾posite sign. We conjecture that this arises because we are using log~1 1 Analysts! on the left￾hand side, rather than the raw number of analysts. Because 10P is correlated with firm size, and because firm size is of such dominant importance, any differences in how one models the analyst-size relationship is likely to have a strong influence on the 10P coefficient. Size, Analyst Coverage, and Profitability 273

274 The Journal of Finance sidual analyst coverage.Next,in Section II.C we rerun all of our tests sep- arately for each of the size classes(except the very smallest)in Table I.In this case,we run a separate cross-sectional analyst regression each month for firms in the 20th-40th NYSE/AMEX percentiles,for firms in the 40th- 60th percentiles,and so on.Among other things,this approach allows the relationship between log(1 +Analysts)and log(Size)to take on a piecewise linear form,hopefully correcting any deficiencies that arise from imposing an overly simple linear structure on the entire sample. Moreover,in Section II.D we also report on sensitivity checks that take into account the potential for analyst coverage to be correlated with some of the other variables considered in Table II.For example,we experiment with alternative definitions of residual coverage based on Model 2,which in- cludes the industry dummies,and Models 8 and 9,which include turnover and the options-listing dummy.Furthermore,we redo our tests in terms of beta-adjusted returns in case the pronounced relationship between beta and analyst coverage is affecting the results. II.Momentum Strategies,Cut Different Ways A.Cuts on Raw Size We begin our analysis of momentum strategies in Table III.In this table, unlike in the tables that come later,we look at the entire universe of stocks without dropping those below the 20th NYSE/AMEX percentile.In so doing,we closely follow the methodology of Jegadeesh and Titman(1993) in many respects.In particular,we focus on their preferred six-month/six- month strategy,we couch everything in terms of raw returns,and we equal- weight these returns.But there are three noteworthy differences.First, our sample period from 1980 to 1996 is more recent.Second,we do not exclude Nasdag stocks.And third,our measure of momentum differs from theirs.They sort stocks into 10 deciles according to past performance,and then measure the return differential of the most extreme deciles-which they denote by P10-P1.In contrast,we place less emphasis on the tails of the performance distribution.We sort our sample into only three parts based on past performance:P1,which includes the worst-performing 30 per- cent;P2 which includes the middle 40 percent;and P3,which includes the best-performing 30 percent.Our basic measure of momentum is then P3 -P1.This is similar to the measure used by Moskowitz (1997)and Rouwenhorst (1997). We use this alternative,broader-based measure of momentum in order to generate better signal-to-noise properties for our tests.Unlike Jegadeesh and Titman (1993),we are not so much interested in establishing the exis- tence of momentum per se,but in comparing momentum effects across sub- samples of stocks.In some cases,we look at as many as 12 subsamples, when we sort by size and residual analyst coverage simultaneously.(See Table V below.)If we also were to use 10 performance deciles,we would end

sidual analyst coverage. Next, in Section II.C we rerun all of our tests sep￾arately for each of the size classes ~except the very smallest! in Table I. In this case, we run a separate cross-sectional analyst regression each month for firms in the 20th–40th NYSE0AMEX percentiles, for firms in the 40th– 60th percentiles, and so on. Among other things, this approach allows the relationship between log~1 1 Analysts! and log~Size! to take on a piecewise linear form, hopefully correcting any deficiencies that arise from imposing an overly simple linear structure on the entire sample. Moreover, in Section II.D we also report on sensitivity checks that take into account the potential for analyst coverage to be correlated with some of the other variables considered in Table II. For example, we experiment with alternative definitions of residual coverage based on Model 2, which in￾cludes the industry dummies, and Models 8 and 9, which include turnover and the options-listing dummy. Furthermore, we redo our tests in terms of beta-adjusted returns in case the pronounced relationship between beta and analyst coverage is affecting the results. II. Momentum Strategies, Cut Different Ways A. Cuts on Raw Size We begin our analysis of momentum strategies in Table III. In this table, unlike in the tables that come later, we look at the entire universe of stocks without dropping those below the 20th NYSE0AMEX percentile. In so doing, we closely follow the methodology of Jegadeesh and Titman ~1993! in many respects. In particular, we focus on their preferred six-month0six￾month strategy, we couch everything in terms of raw returns, and we equal￾weight these returns. But there are three noteworthy differences. First, our sample period from 1980 to 1996 is more recent. Second, we do not exclude Nasdaq stocks. And third, our measure of momentum differs from theirs. They sort stocks into 10 deciles according to past performance, and then measure the return differential of the most extreme deciles—which they denote by P10 2 P1. In contrast, we place less emphasis on the tails of the performance distribution. We sort our sample into only three parts based on past performance: P1, which includes the worst-performing 30 per￾cent; P2 which includes the middle 40 percent; and P3, which includes the best-performing 30 percent. Our basic measure of momentum is then P3 2 P1. This is similar to the measure used by Moskowitz ~1997! and Rouwenhorst ~1997!. We use this alternative, broader-based measure of momentum in order to generate better signal-to-noise properties for our tests. Unlike Jegadeesh and Titman ~1993!, we are not so much interested in establishing the exis￾tence of momentum per se, but in comparing momentum effects across sub￾samples of stocks. In some cases, we look at as many as 12 subsamples, when we sort by size and residual analyst coverage simultaneously. ~See Table V below.! If we also were to use 10 performance deciles, we would end 274 The Journal of Finance