Europian Mom Strategy

European Momentum Strategies, Information Diffusion, and Investor Conservatism John A. Doukas and Phillip J. McKnight* February 12, 2003

Abstract In this paper we conduct an out-of-sample test of two behavioral theories that have been proposed to explain momentum in stock returns. We test the gradual-information-diffusion model of Hong and Stein (1999) and the investor conservatism bias model of Barberis, Shleifer and Vishny (1998) in a sample of 13 European stock markets during the period 1988 to 2001. These two models predict that momentum comes from the (i) gradual dissemination of firm-specific information and (ii) investors’ failure to update their beliefs sufficiently when they observe new public information. The findings of this study are consistent with the predictions of the behavioral models of Hong and Stein’s (1999) and Barberis et al. (1998). The evidence shows that momentum is the result of the gradual diffusion of private information and investors’ psychological conservatism reflected on the systematic errors they make in forming earnings expectations by not updating them adequately relative to their prior beliefs and by undervaluing the statistical weight of new information.

*Department of Finance, Stern School of Business, New York University, 44 West 4th Street, New York, NY 10012, Tel:(212) 998-0432, Fax:(212) 994-422, E-mail: [email protected], Department of Accounting and Finance, Cardiff Business School, Cardiff, UK CF10 3EU, Tel: 02920 876804, Fax: 02920 876804 E-mail [email protected], respectively. We are grateful for the financial support provided by INQUIRE, EUROPE and The Leverhulme Trust. The authors also gratefully acknowledge the contribution of Thomson Financial for providing earnings per share forecast data, available through the Institutional Brokers Estimate System I/B/E/S. This data has been provided as part of a broad academic program to encourage earnings expectations research.

European Momentum Strategies, Information Diffusion, and Investor Conservatism Several recent papers have shown that stock returns are related to past performance-that is, past losers tend to be future winners and past winners are future losers. Jagadeesh and Titman (1993, 2001), and Asness (1994), using U. S. samples of stocks, find that when portfolios are formed over a short-term (from three months to a year) horizon, stock returns performance persists. 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 approximately one percent per month. Rouwnehorst (1998) finds stock return momentum in a sample of 12 European countries over the 1980-1995 period.

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While there has been considerable evidence in support of momentum in stock returns it

remains unclear whether the medium-term continuation pattern in stock returns reflects risk or market’s improper response to information. Conrad and Kaul (1998), for instance, suggest a riskbased explanation. Fama and French (1996), however, show that their three-factor model fails to explain this return pattern. The seminal work of Ball and Brown (1968), and more recent evidence by Chan, Jagadeesh, and Lakonishok (1996), suggest that momentum is a symptom of underreaction.

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That is, prices adjust slowly to new information. More recently, several non-risk based theories have been developed to explain momentum in stock returns. The model of Barberis, Shleifer, and Vishny (1998) shows that momentum is rooted in investors’ conservatism bias, and that investors do not update their beliefs adequately based on the strength and weight of new information. That is, investors place more emphasis on the strength of the information than on its statistical weight, relative to a rational Bayesian. Hong and Stein (1999) attribute momentum to the gradual diffusion of firm-specific information and the inability of investors to 3

extract each other's private information from prices. Hong, Lim, and Stein (2000), test the gradual diffusion of firm-specific information hypothesis of Hong and Stein (1999), using U.S. stock returns.

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Momentum strategies are also found to earn significant gains in emerging markets (Rouwenhorst (1997)). There is some evidence that tax-loss selling creates seasonal variation in the momentum effect (Grinblatt and Moskowitz (1999)), but Roll (1983) refers to such explanations as “stupid” because investors would have to be stupid not to buy in December and sell in January at higher prices. 3 Other non-risk based theories that produce momentum include the positive-feedback-trader model of Delong et al. (1990) and the overconfidence model of Daniel, Hirshleifer, and Subrahanyam (1998). 2

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Consistent with the hypothesis that firm-specific information spreads gradually across investors, they find that momentum strategies work better for stocks with low analyst coverage. They also find that (i) the profitability of momentum strategies is inversely related to firm size and (ii) the effect of analyst coverage is greater for stocks that are past losers than for past winners. In these two models (Barberis et al. (1998) and Hong and Stein (1999)), momentum is due to initial underreaction followed by a correction. Unlike other behavioral models, the common feature in the momentum explanations of Barberis et al. (1998) and Hong and Stein (1999) is that stock price underreaction is the outcome of insufficient investor reaction due to (i) conservatism behavior and (ii) slow diffusion of information, respectively. Conservatism means that investors react insufficiently, pushing prices up too little. In this paper, we empirically examine these two models of momentum. The first objective of this paper is to test the Hong and Stein (1999) version of the underreaction hypothesis by studying return patterns in an international context. Specifically, we investigate whether momentum reflects the gradual diffusion of firm-specific information using residual analyst coverage as a proxy for the rate of 4

information diffusion. While Hong, Lim, and Stein (2000), provide evidence in support of the idea that momentum strategies work better in low-analyst-coverage stocks, it cannot be ruled out that this result is limited to the U.S market. Without testing the robustness of these findings outside the environment in which they were found, it is difficult to determine whether these empirical results are merely spurious correlations that they may not be confirmed across capital markets. This paper fills a gap in the literature in this respect. Using international data over the period January 1988 to January 2001, we expect to shed more light on whether momentum strategies continue to be profitable and overcomes the criticism that observed empirical regularities arise from data mining. The second goal of this study is to investigate whether momentum is consistent with the model of Barberis et al. (1998) implying that investors exhibit conservatism and underreact to information that has a high weight when 5

adjusting their beliefs. We use the dispersion in analyst forecasts as a proxy for the weight of information. It follows that a consensus forecast revision (i.e., strength of information) with low

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Hong, Lim, and Stein (2000) use residual analyst coverage to proxy for the rate of information diffusion as well. The Barberis, Shleifer, and Vishny (1998) theory builds on Griffin and Tversky’s (1992) seminal work on the weighing of evidence and formation of beliefs in human thought. Edwards (1968) provides evidence consistent with the view that individuals are conservative in the sense that they do not adjust their beliefs sufficiently. That is, the adjustment process of updating human beliefs does not adequately take into account the weight of new information. 5

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dispersion (i.e., higher weight of information) is expected to have more pronounced effects on stock prices. We address these issues by focusing on international return momentum strategies using an aggregate sample of 3,084 firms provided by Institutional Brokers Estimate System (I/B/E/S) for 13 European countries. The main results of the paper are as follows. First, we find evidence in support of the view that average stock returns are related to past performance. Our evidence confirms the findings of Rouwenhorst (1998) and indicates that short-term momentum in stock returns has continued to be present in 13 European markets during the 1988 to 2001 period. This pattern in stock returns is not limited to a particular stock market, but is present and significant in eight of 13 European stock markets. Second, we provide evidence consistent with the gradual-information-diffusion model of Hong and Stein’s (1999). Specifically, we find not only that momentum is associated with size but also analyst coverage; that is, when holding size fixed, we find that momentum strategies work better in stocks with low analyst coverage indicating that the findings of Hong, Lim, and Stein (2000) are not merely due to chance. Third, we uncover that analysts’ forecast dispersion is inversely related with the profitability of momentum strategies. This finding is consistent with the model of Barberis et al. (1998) predicting that investors do not update their beliefs adequately. Our evidence suggests that investors do not place adequate emphasis on the statistical weight of new information. The remainder of the paper is organized as follows. Section I provides a discussion for the possible sources of momentum. Section II provides a description of our data set, summary statistics, and trading strategies. Section III examines the gradual-information-diffusion hypothesis and the presents the results. Section IV conducts additional tests and sheds light on the view that investors tend to exhibit conservatism and underweight the statistical importance of information in adjusting their beliefs. Section V concludes the paper.

I. Size, Analyst Coverage, and Analysts’ Earnings Forecast Dispersion The Hong and Stein (1999) model assumes that private information diffuses slowly through the population of newswatchers. As these investors are unable to extract each other's private information from prices, the slow diffusion of information creates momentum. The main prediction of their model is

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that stocks with slow information diffusion will display pronounced momentum. Firm size, then, appears to be a natural candidate for testing the slow diffusion of information hypothesis.

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It is

reasonable to assume that information about smaller firms filters through the financial markets more slowly than for larger ones. Smaller firms are more likely to be followed by fewer analysts, as the cost of information acquisition is considerably higher for smaller as opposed to larger firms. It is also generally believed that the payoff structure of analysts tends to direct their research efforts into stocks that are likely to generate more “news” and as a result greater trading activity. Investors are, then, expected to invest in stocks with greater analyst coverage where information is expected to be more current and easily accessible. Consequently, it is expected that momentum profits should decrease as one moves from the smallest to the largest decile in stocks. Although firm size may be a useful proxy for the rate at which information is disseminated to the markets, it is likely to capture other confounding events. For example, it could be argued that market making and arbitrage capacity (Merton (1987), and Grossman and Miller (1988)) would be less in smaller firms. Hong et al. (2000) argue that firm size may not represent an appropriate variable that measures the rate by which information is disseminated to the markets, and that alternative proxies such as analyst coverage should be used to test the information diffusion hypothesis. The importance of analyst coverage over size is best explained by transaction costs associated with the time and effort put forth by analysts in providing coverage, a cost not well captured by firm size. For instance, analysts may have little incentive to track smaller firms in an attempt to protect their reputation capital and compensation by avoiding large forecast errors in earnings that are more likely to exist in smaller than larger firms. Low analyst coverage could, therefore, cause stock prices to adjust more slowly to information. This is especially the case when information is negative and managers have little incentive to push out bad news, a condition that would most likely be followed by a stock price correction. Therefore, the effect of analyst coverage should be more pronounced in past losers than past winners. As in Hong et al. (2000), we use the residual analyst coverage as an alternative proxy for testing the information diffusion hypothesis. The choice of the residual analyst coverage is dictated by the observation that there is a strong correlation between firm size and analyst coverage (Bhushan

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This variable has been the subject of recent empirical investigations in both the U.S. (Jegadeesh and Titman

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(1989)). If momentum reflects the gradual diffusion of firm-specific information, as the model of Hong and Stein (1999) predicts, momentum should be more pronounced in small capitalization firms and firms with low analyst coverage. Consistent with the information diffusion story, among firms with low analyst coverage, momentum is also expected to be stronger in prior losers continuing to lose than past winners continuing to win. Our second empirical test is designed to examine whether momentum is consistent with the model of Barberis et al. (1998), suggesting that momentum is rooted in investors’ conservatism bias and failure to update their beliefs adequately by using both the strength and weight of new information. According to the theory of Barberis et al. (1998), which relies on the weighing of evidence and formation of beliefs in human thought of Griffin and Tversky (1992), investors do not adequately take into account the weight of new information. That is, investors place more emphasis on the strength of the information than on its statistical weight, relative to a rational Bayesian. We use the dispersion in analysts’ earnings forecasts, as a proxy for the weight of information. Theory suggests that forecast dispersion reflects uncertainty about a firm’s future economic performance (Barron, Kim, Lim, and Stevens (1998)). When the future prospects of a firm are more (less) uncertain, disagreement among analysts regarding growth in future earnings will be higher (lower). If investors fail to adequately take into account the weight of new information, as the model of Barberis et al. (1998) predicts, momentum should be more pronounced in stocks with low analyst dispersion (i.e., stocks with higher weight of information). Therefore, the investor conservatism bias hypothesis amounts to testing how momentum 7

profits vary with the weight of information (i.e., dispersion in analysts’ earnings forecasts). We test these two hypotheses using a sample of 3,084 firms provided by Institutional Brokers Estimate System (I/B/E/S) for 13 European countries.

II. Data, Descriptive Statistics, and Trading Strategies A. Data

(1993), Hong, Lim, and Stein, 2000)) and European markets (Rouwenhorst (1998)). 7 Similarly, Dische (2002) uses dispersion in analysts’ earnings forecasts to proxy the weight of information. His tests, however, were limited to Germany.

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Our sample period runs from January 1988 through January 2001. The data on analyst coverage 8

are from Institutional Brokers Estimate System (I/B/E/S). We exclude those countries where analyst 9

coverage began only recently and few firms were covered. The sample consists of monthly returns in local currency converted to pound sterling using exchange rate information taken from DataStream. The sample used in the analysis excludes all firms below £1 and £25 million in market capitalization in order to ensure that the bid-ask bounce and/or smaller, illiquid stocks do not influence the results (Jegadeesh and Titman (2001)). The total number of firms after adjustments for pricing and size are 3,084 covering 13 European countries (firms), which consist of Austria (76), Belgium (86), Denmark (107), Finland (100), France (411), Germany (568), Italy (165), Netherlands (155), Norway (102), Spain (149), Sweden (216), Switzerland (160), and United Kingdom (789). Our primary data source is the I/B/E/S from which we use both the summary and detail history files. These I/B/E/S data files contain pricing data, number of analysts providing fiscal year one earnings estimates, and earnings forecasts.

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The consensus forecast is obtained at the first trading day of

each month. We set coverage equal to the number of analyst providing earnings estimates for the fiscal year one period. When such a value is missing we assume coverage is equal to zero. Because size and the number of analyst coverage exhibit a strong positive correlation (Bhushan (1989)), an OLS regression is employed to calculate residuals with the left-hand side variable being the log (1 + Analysts) and the right-hand side the log (Size), where size is market capitalization.

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The residuals

allow us to purge the size effect from analyst coverage in explaining momentum (Hong et al. (2000)). Unlike prior research (Bhushan (1989), and Brennan and Hughes (1991)), we use the log (1 + Analysts) rather than the raw number of analysts. It is important to note that since we use the residuals from the analyst-coverage regression to explain momentum, it is believed that one additional analyst should have a significant impact, especially when firms are followed by fewer analysts (Hong et al. (2000)).

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Although I/B/E/S data is available for 1987, it was excluded from the analysis because there were considerably fewer analyst coverage observations. 9 These countries are Greece, Ireland, and Portugal. 10 When we unadjust the data for stock splits, the results remain essentially unchanged. 11 In the regressions, we did account for book-to-market effects as well. As in Hong et al. (2000), the coefficient on book-to-market, although positive and significant, adds nothing to the overall R 2.

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Finally, we use the dispersion in analysts’ earnings forecasts for the fiscal year one period to measure the magnitude of divergence of opinion among investors (Diether, Malloy, and Scherbina, (2002)). The analyst dispersion is a useful measure for it allows us to capture the weight of information and, therefore, test whether momentum in stock returns is associated with investors’ failure to adequately account for the weight of information, as predicted by Barberis et al. (1998). Analyst dispersion is defined as the standard deviation in earnings forecasts scaled by the stock price per share at the beginning of the forecast’s fiscal year. Both the standard deviation in earnings forecasts and pricing values are obtained from I/B/E/S Summary History file.

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To be included in the analysis,

stocks must be followed by at least two analysts since we use the standard deviation in earnings forecasts. B. Descriptive Statistics Panel A of Table 1 provides a summary of the analyst coverage for the entire sample of European firms as reported in the I/B/E/S database. An interesting feature that is apparent in our sample is that analyst coverage has increased considerably over the years. For instance, 38.1 percent of European firms were uncovered in January 1988 while the number of uncovered firms declined sharply to 6.3 percent in January 2001. Surprisingly, the percent of uncovered European firms appears to be considerably lower than that documented by Hong et al. (2000) for U. S. firms. For instance, they report that 36.9 percent of U. S. firms were uncovered in 1996 (last year of their sample) while only 18.1 percent of European firms were no covered by analysts in the same year. That is, the depth of analyst coverage in European firms is considerably larger than one would expect. Of course, there is a considerable size difference between the two samples. The U.S. sample contained 6460 firms while the European sample had only 4002 firms in 1996. Panel B of Table 1, reports descriptive statistics for mean analyst coverage and momentum by country. Mean analyst coverage varies across countries. Austrian and Scandinavian stocks have lower analyst coverage than other European stocks. Dutch stocks have the highest mean coverage during the 1988-2001 period. It is interesting to note that mean analyst coverage exhibits an inverted U shape

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We compared the forecasts provided by the Detail History file and Summary History file and found them to be similar. However, we did not use the Detail History file primarily because it provided fewer observations than that reported by the Summary History file.

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relationship with time. That is, mean coverage by country rises until about 1997 and begins to decrease afterwards. A possible explanation for this finding is that analysts tend to track earnings that exhibited an inverted-U shape during this period as well.

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Panel B of Table 1, reports momentum returns by country. Relative strength portfolios are formed using a six-month/six-month strategy and breaking performance down into three (P1, P2, P3) and five (P1, P2, P3, P4, P5) equally weighted portfolios. Generally, we find that momentum profits continue to be present in most European stock markets and that the source of the continuation effect is not confined to a particular stock market. These results are consistent with those found by Rouwenhorst (1998), suggesting that European momentum is not limited to a particular time period. [Insert Table I About Here] C. Trading Strategies The momentum portfolios are constructed as in Jagadeesh and Titman (1993). In particular, we concentrate on the six-month/six-month strategy and sort the entire sample in terms of raw returns. Stocks are assigned into portfolios based on their six-month past return period. These portfolios are equally weighted at formation and are held for six-months.

Specifically, we use two momentum

strategies. The first strategy sorts the entire sample into three portfolios: P1, P2, and P3. P1 includes the worst performing 30 percent, P2 includes the middle 40 percent, and P3 includes the best performing 30 percent. In this case, the basic measure of momentum is P3 – P1. This measure has also been used in previous studies (Hong et al. (2000) and Rouwenhorst (1998)).

Since we are

interested in confirming the existence of momentum in European stock returns per se, we also employ a broader strategy that sorts stocks into five portfolios: P1, P2, P3, P4 and P5. P1 includes the worst performing 20 percent, P3 includes the middle 20 percent, and P5 includes the best performing 20 percent. The basic measure of momentum is P5 – P1. This alternative measure of momentum is closer to the spirit of Jagadeesh and Titman (1993), who short stocks into 10 deciles according to past performance and measure the return difference of the deciles (i.e., P10 – P1).

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The earning per share results are not reported here, but are available upon request. Using the Jagadeesh and Titman (1993), P10 – P1 momentum measure has the tendency to reduce the degree of diversification in the decile portfolios and, therefore, produce large standard errors (see also Hong et al. (2000)). 14

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III. Size and Residual Coverage In this section our primary objective is to test the Hong and Stein (1999) version of the underreaction hypothesis. In particular, we examine whether momentum reflects the gradual diffusion of firm-specific information. We use residual analyst coverage as a proxy for the rate of information diffusion as in Hong et al. (2000). Residual analyst coverage is measured on the month the performance-ranking period begins.

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However, we first examine the influence of size on momentum

across 10 size deciles because smaller firms may have slower information diffusion. A. Momentum Portfolios Based on Size Table II provides evidence in support of momentum within the entire universe of European stocks. Panel A presents the country-neutral strategy that buys top-30 percent (P3) best performing stocks and shorts bottom-30 percent (P1) worst performing stocks. Panel B reports the strategy that buys top20 percent (P5) best performing stocks and shorts bottom-20 percent (P1) worst performing stocks. The first column in Panel A indicates that there is significant momentum in the entire sample. The momentum strategy of P3 - P1 generates a 0.73 percent return per month (with a t-statistic = 2.90) whereas in Panel B, the momentum strategy of P5-P1 is associated with a return difference of 0.89 percent per month (with a t-statistic = 3.34) for all stocks. We next sort the firms into 10 size decile subsamples with the smallest firms placed in size class 1 and the largest in size class 10. As shown in Panel A of Table II, we find that size deciles one and two generate the highest average returns of 1.16 (with a t-statistic = 4.49) percent and 1.09 (with a t-statistic = 3.87) percent per month, respectively. The subsequent size decile momentum profits tend to meander and decline monotonically until they effectively become marginal and statistically insignificant in the largest stocks. Similarly, as reported in Panel B, the general pattern of momentum (P5 – P1) is a mirror image of that found in Panel A. An interesting feature that emerges from these results is that the (P5 – P1) trading strategy, generates a higher monthly average return across all size deciles. For example, in Panel B, the decile 1 return differential is 1.43 percent (with a t-statistic = 5.02) and the decile 2 return difference is 1.32 percent (with a t-statistic = 4.32), with momentum profits declining monotonically as size increases. Another

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Hong et al. (2000) found that their results were basically insensitive to the exact point as to when residual analyst coverage was measured; that is, whether it was zero, 12, or 18 months prior to the ranking period, the results were

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interesting aspect of the results listed in Table II, especially in Panel A, is that a most of the return continuation is driven by prior worst performing (loser) stocks which is consistent with the slow information diffusion story of Hong and Stein (1999) and the evidence of Hong et al. (2000). For example, in size decile 1 of Panel A (B), about 63 (52) percent of the 1.16 (1.14) percent return is driven by smaller/loser stocks. After the fourth size decile, momentum profits decrease monotonically and become essentially zero in the largest stocks. This sharp decline in momentum gains after the fourth size decile suggests that smaller firms are subject to slower information diffusion and this could be attributed to low analyst coverage and they have smaller investor base (i.e., thinner market making capacity) causing considerable supply-shock driven price reversals. These results provide additional support that size may in fact be a useful measure of the rate of information diffusion. Furthermore, these results demonstrate that most of the momentum effect seems to be associated with loser as opposed to winner stocks. For instance, the column corresponding to the first size class (1) in Panel A, generates a momentum gain (P3 – P1= winners - losers) of 1.16 percent per month. About 63 percent of the total momentum gain is associated with the difference between average performers and losers, P2 – P1. A similar pattern emerges in all the other deciles with significant momentum profits. This result corroborates the view that stock price underreaction, is more likely to be associated with negative than positive news. [Insert Table II About Here] B. Momentum Portfolios Based on Residual Analyst Coverage Our next partition is based on residual analyst coverage. Three subsamples are created using residuals derived from a month-by-month cross-sectional regression of log (1 + Analysts) on the log (Size) and log (B/M). Size is the firm’s year-end market value. Book-to-market (B/M) is the ratio of a firm’s year-end book-to-market value. As exhibited in Panels A and B of Table III the subsamples contain stocks of the same size yet maintaining a healthy spread in analyst coverage. In Panel A, the Cov1 subsample or those stocks with low-coverage have median coverage of 3.0 whereas the highcoverage Cov3 subsample has a median coverage of 19.0. As for size matching, Cov1 has a mean size (£950 million) that is not very different from that found in Cov3 (£910 million), yet a larger mean

very similar. We have confirmed this in the European data set. Therefore, we measure residual coverage the month

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size for Cov2. The median size for the low coverage stocks Cov1 is £130 million while for the high coverage stocks Cov3 is £230 million. Similar mean size variation is observed in Panel B, but the size variation is less pronounced in terms of median size. Although the relationship between size and analyst coverage is not linear, we remedy this shortcoming later on and, therefore, it does not alter our conclusions. Table III reports results based on our two basic momentum strategies. Panel A shows the momentum returns from buying P3 winners (top-30 percent) and selling P1 losers (bottom-30 percent) while Panel B lists momentum returns from buying P5 winners (top – 20 percent) and selling P1 losers (bottom – 20 percent). There are at least two interesting findings that emerge from Table III. First, consistent with the slow diffusion of information theory of Hong and Stein (1999), the momentum profits are larger in stocks with low residual coverage than in stocks with high residual coverage. This result holds for both strategies as shown in Panels A and B. For example, the P3 - P1 momentum measure, reported in Panel A, generates a 0.88 percent per month average return (with a t-statistic = 3.22) for the subsample of low coverage stocks, Cov1, while it generates 0.59 percent per month average return (with a t-statistic = 2.39) for the high-residual-coverage stocks, Cov3. The P5 - P1 momentum strategy, reported in Panel B, demonstrates an even larger monthly average return continuation of 1.12 percent (with a t-statistic = 3.80) for the low-residual-coverage stocks, Cov1, in comparison to the 0.81 percent (t-statistic = 2.98) for the high-residual coverage stocks, Cov5. While the P3 – P1 momentum measure produces a 10.56 percent average annual return for the low analyst coverage stocks, Cov1, the P5 – P1 strategy produces a 13.44 percent average annual return. Sorting stocks into more extreme past performance portfolios appears to have a greater effect on the magnitude of momentum profits.

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Second, the evidence in Table III also shows that the influence of residual analyst coverage on the P3 – P1 (P5 – P1) momentum measure is heavily affected by loser stocks in P1. P1/Low Cov1 underperform P1/High Cov3 by 0.60 (0.71) percent per month. The difference between P1/Low Cov1 and P1/High Cov3 (i.e., Cov1 – Cov3) is significant with a t-statistic of -2.16. This seems to suggest that one can profit by simply buying the stocks in portfolio P1/High Cov3 and selling the stocks in

the performance ranking period begins.

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portfolio P1/High Cov1. That is, the high-low analyst coverage investment strategy (i.e., loser-analyst spread trade strategy or LAST strategy of Hong et al. (2000)) is profitable in the European markets as well even though it is size-neutral and momentum-neutral. A significant but smaller spread is observed in the average performers, P2, and winner, P3, stocks. The gains of the “pure” analyst coverage spread strategies, especially in loser stocks, suggest that momentum returns of 0.60 (0.71) percent per month are unlikely to be driven by a risk factor. Overall, these results are consistent with the view that analysts play a crucial role in disseminating bad news.

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This draws additional support from our previous results showing that most of the

momentum gains stem from loser stocks. Therefore, analyst coverage seems to be far more important in loser than winner stocks. Managers of firms with good news have strong incentives to spread such news out as fast as possible making analysts less important. However, firms with bad news are likely to hold back such news and, therefore, analysts are expected to play a more important role in firms where managers are likely to be less forthcoming. [Insert Table III About Here] C. Momentum Portfolios on Two Way Cuts: Size and Residual Analyst Coverage In this section we repeat our analysis relying on firm size and residual analyst coverage. The motivation behind this two-way cut is twofold. First, there is evidence that smaller stocks are, on average, covered by fewer analysts and, therefore, are less researched.

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It is reasonable, then, to

assume that the marginal value of analyst coverage is greater in smaller stocks. Second, this two-way partition will also allow us to achieve better size matches across residual coverage classes since the analyst coverage-firm size relationship is estimated separately for each size-based subsample. In other words, this procedure permits the analyst-size relationship to be piecewise linear. The results in Table IV confirm the generally held view that fewer analysts cover smaller stocks than larger stocks. This holds for all three analyst coverage classes. As expected, the evidence also shows that there is a better size match across residual coverage classes. For example, for the

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Beta-adjusted returns, not reported here, but available upon request, produce similar results. Even though it is generally believed that analysts are rarely pessimistic about the growth prospects of firms, analyst recommendations can still be a strong signal as smart investors are expected to deflate them. For instance, a “buy” recommendation can be interpreted as a “hold” while a “hold” as a “sell” recommendation. 18 See, for instance, Doukas, Kim, Pantzalis (2002), among others. 17

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smallest size class, the mean (median) size is £55 (£52) million in Cov1 compared to £58 (£54) million in Cov3. Moreover, we also retain a good spread in analyst coverage between Cov1 and Cov3, where the mean (median) analyst following is 2.0 (2.0) for Cov1 stocks and 14.4 (13.0) for Cov3 stocks. Consistent with our previous findings, Table IV reveals that momentum returns decrease monotonically with size. For instance, for stocks in the low coverage class, Cov1, the P3-P1 momentum profit in the Small (30 percent) stocks is 1.14 percent per month (with a t-statistic= 4.02) while in the Medium (40 percent) stocks is 0.85 percent per month (with a t-statistic= 2.86) and in the Large (30 percent) is 0.31 percent per month (with a t-statistic=1.20) percent. Even though less pronounced, this pattern of momentum return difference between small and large capitalization stocks is common in the other two analyst coverage classes (Cov2 and Cov3). These results are consistent with those found by Hong et al. (2000) and in support of the view that the marginal importance of analysts should decline with size. Consequently, analyst coverage appears to have a stronger influence on momentum in stocks where the gradual information diffusion is likely to be important (i.e., small stocks) and where momentum effects are expected to be more pronounced (i.e., low coverage stocks). Another interesting feature of the results is that as we move to high coverage stocks (Cov3) from low coverage stocks (Cov1), for a given size class, the magnitude of the momentum profits seem to drop systematically. The difference, between firms with the fewest analysts (Cov1) and those with the most analysts (Cov3) is only a fraction (0.19 percent) of the total momentum effect (1.14 percent), suggesting that analyst coverage on its own is unlikely to reflect the full extent of importance of gradual information flow of information. Overall, the European evidence provides additional credence to the Hong and Stein (1999) version of the underreaction hypothesis predicting that momentum in stock returns mirrors the gradual diffusion of firm-specific information. Our findings are consistent with those documented by Hong at al. (2000), who find evidence in support of the slow information diffusion explanation of the medium-term return continuation in stock returns, suggesting that momentum is a symptom of the (1) slow diffusion

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of firm-specific information and (2) inability of investors to extract information from prices that is not limited to the U. S. capital market.

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[Insert Table IV About Here] D. Cross-Sectional Regression Analysis The slow information diffusion hypothesis states that stocks that are small and that have low analyst coverage should exhibit more positive medium-term return autocorrelation. Following Hong, Lim and Stein (2000), we test this hypothesis by first estimating the serial correlation coefficient of each stock, and then regress it on measures of the stock’s analyst coverage and firm size. Specifically, for each stock with complete return data from year t through year t+3, we estimate its serial correlation coefficient, RHOit. This is the regression coefficient of six-month returns, net of risk free-rate, on lagged six-month returns. Then we regress RHOit on the log(1+Analyst coverage) and log(Size) variables. The regression results are reported in Table V. Panel A, presents the coefficients on the analyst coverage and size variables from cross-sectional regressions estimated each year 1988 to 1998.

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We also report results based on a pooled regression inclusive of year dummies. In general, the regression results show that coverage and firm size have a negative association with a stock’s serial correlation. Size appears to have a more significant relation with a stock’s serial correlation than analyst coverage. In Panel B, we report results by including an interaction variable, [log(1+Analyst coverage) * log(Size)]. The inclusion of the interaction term in this set of regressions stems from our previous finding suggesting that the marginal importance of analyst coverage decreases with firm size. The interaction term is mostly positive, as expected, indicating that the negative impact of coverage on serial correlation tends to be weaker for larger firms. Overall, the regression results provide supplemental evidence in support of the slow information diffusion explanation of the medium-term return continuation in stock returns. [Insert Table V About Here]

19

Results based on P5 – P1 momentum returns are similar to those reported in Table IV and are available upon request. 20 We stop in 1998 because we require three years of data after year t to estimate RHOit.

14

IV. Momentum Returns and Dispersion in Analyst Forecasts: A Test of the Investors’ Conservatism Bias Hypothesis In this section we investigate whether momentum is consistent with the Barberis et al. (1998) version of underreaction hypothesis. This model implies that investors exhibit conservatism and underreact to information that has a high weight when adjusting their beliefs. In particular, this view claims that investors do not update their expectations adequately based on the strength and weight of new information. In contrast with the stock price underreaction explanation of Hong et al. (1999), that stems from the slow diffusion of firm-specific information (low analyst coverage), Barberis et al, (1998) argue that momentum is the result of systematic errors that investors make when they use publicly available information to form expectations about future cash flows.

21

Namely, investors exhibit

conservatism and underreact to information that has high weight when they adjust their beliefs in forming cash flow expectations. Drawing on the seminal work of Griffin and Tversky (1992) on weighing of evidence and formation of beliefs in human thought, investors should determine how positive (negative) is the new information (analysts’ recommendation) and how credible (i.e., the weight) the recommendation is. That is, investors should distinguish between the strength (i.e., upward or downward changes in earnings forecasts) and the weight of the recommendation (i.e., the credibility of the analysts’ recommendation).

22

As mentioned earlier, we use the dispersion in analysts’ earnings forecasts as a proxy for the weight (credibility) of information.

23

An important function of security analysts is to provide information

that reduces information asymmetries. Consequently, informational asymmetries are more likely to exist when analysts release different forecasts (i.e., when there is disagreement among analysts’

21

This stems from investors’ two key updating biases: the tendency to underweight new information relative to priors (i.e., conservatism) and the expectation that small samples can reflect the properties of the parent population (i.e., representativeness). Especially, the kind of bias where investors put too little weight on the base rate of new information. 22 Griffin and Tversky (1992), illustrate how people form beliefs using the example of a letter of recommendation for a prospective graduate student. They suggest that the admissions committee should distinguish between the how positive the content of the letter is (strength of new information about the applicant) and how credible the writer of the letter is (i.e., the weight of the new information). 23 Since dispersion in analysts’ earnings forecasts measures differences of opinion (see, e.g., Diether, Malloy, and Scherbina (2002), Harris and Raviv (1993)), we argue that when dispersion among analysts is low (high) the strength of information is high (low).

15

earnings forecasts). Higher dispersion in earnings forecasts, then, would weaken the credibility of analysts’ earnings forecasts (i.e., weight of information). On the other hand, lower dispersion would strengthen the credibility of analysts’ earnings forecasts. If investors do not process new information based on these two aspects, it follows that a consensus forecast revision (i.e., strength of information) with low dispersion (i.e., higher weight of information) should have more pronounced effects on stock prices. Consequently, momentum strategies that recognize the potential value of dispersion should be even more profitable if investors systematically underestimate the importance of low divergence of opinion among analysts (i.e., the weight of new information) about firms’ cash flow prospects. A. Portfolios Sorted by Analysts’ Earnings Forecast Dispersion To test the prediction of the Barberis et al. (1998) theory, we classify firms by the strength (monthly consensus earnings revisions) and weight (dispersion) of analysts’ earnings forecasts and sort them into corresponding portfolios. Dispersion serves as a proxy for the uncertainty of a firm’s future earnings (Barron, Kim, Lim, and Stevens (1998)). Low (high) dispersion among analyst forecasts reflects small (large) uncertainty about the firm’s prospects. That is, the larger (smaller) the dispersion in earnings forecasts among analysts the lower (higher) the credibility (i.e., the weight of new information) of the forecasts.

24

Earnings news for each firm is measured by the earnings revision ratio,

which is the monthly change in average consensus forecasts. Revision ratios are estimated as the average monthly earnings forecast change in expected earnings per share as a percentage of the absolute mean value of the prior consensus forecasts. Stocks are then ranked in descending order by their monthly earnings revision ratio and shorted according to their rank into three (five) equally weighted portfolios. Then, the stocks of each earnings momentum portfolios are sorted independently by their dispersion into the corresponding equally weighted portfolios. Dispersion is defined as the standard deviation of analysts’ current-fiscal year annual earnings per share forecasts scaled by the absolute value of the mean earnings forecast at the beginning of the forecast’s fiscal year.

24

25

Since turnover is another measure of differences of opinion (Harris and Raviv (1993) and Lee and Swaminathan (2000)) and shown by Diether, Malloy, and Scherbina (2002) to have a strong positive relation with dispersion in analysts’ forecasts, it could be used as an alternative measure that permits to determine the weight of information in testing the investor conservatism bias hypothesis. Specifically, high (low) turnover stocks should earn higher (lower) returns consistent with the prediction of the investor conservatism bias hypothesis of Barberis et al. (1998). 25 We obtain similar results when the standard deviation of analysts’ current-fiscal year annual earnings per share forecasts is standardized by the firm’s share price. These results are available upon request.

16

Table VI, reports momentum returns based on earnings–revision portfolios and dispersion in consensus forecasts for two basic investment strategies. The first one identifies with buying P3 winners (i.e., stocks with upward earnings revisions)

(top-30 percent) and selling P1 losers (i.e.,

stocks with downward earnings revisions) (bottom-30 percent), reported in Panel A, while the second strategy identifies with buying P5 winners (i.e., stocks with upward earnings revisions)

(top – 20

percent) and selling P1 losers (i.e., stocks with downward earnings revisions) (bottom – 20 percent), listed in Panel B. Before we concentrate on the return results, it is important to examine whether these portfolios have the desired characteristics with respect to dispersion. The pattern that emerges by comparing high and low dispersion stocks, shown in Panel A, is that low dispersion (D1) stocks exhibit smaller dispersion than high dispersion (D3) stocks, as expected. Specifically, the low dispersion stocks have a mean (median) dispersion of 0.034 (0.032), however, as we move across dispersion classes we find that high dispersion stocks have a mean (median) dispersion of 0.832 (0.264). This pattern holds with remarkable uniformity in Panel B of Table VI, while the momentum profits are much more distinct. For instance, the low dispersion (D1) stocks have a mean (median) dispersion of 0.030 (0.026) while the high dispersion (D5) stocks have a mean (median) dispersion of 1.115 (0.297). The clear pattern that emerges from Table V is that momentum is pronounced in stocks with low dispersion. The momentum profit of the strategy D1/P3 – P1 is 0.0107 percent per month (with a tstatistic = 5.31) while the gains for the strategy D3/P3 – P1 is 0.53 (with a t-statistic = 1.87). Similarly, the gains for D1/P5 – P1 is 0.0147 percent per month (with a t-statistic = 6.89) while the gains for the strategy D3/P5 – P1 is 0.0032 (with a t-statistic = 0.92). Second, the momentum profit of the low dispersion strategy with the most favorable earnings revision D1/P3 is 0.0129 percent per month (with a t-statistic= 9.27) while the gains for the high dispersion strategy with the least favorable earnings revision D1/P1 is 0.0022 (with a t-statistic= 1.48). A similar momentum return difference is reported in Panel B, for the portfolios D1/P5 and

D1/P1. For instance, the gain for D1/P5 portfolio is 0.0134

percent per month (with a t-statistic= 9.00) while for D1/P1 portfolio is –0.0013 percent per month (with a t-statistic= -0.85).

26

Taken together, these results suggest that analyst dispersion (i.e., the

26

Another interesting observation is that the difference between D1/P1 and D3/P1 (D1/P1 and D5/P1) stocks, as shown in the last column of Panel A and B, is mostly insignificant. This indicates that a profitable momentum-neutral strategy does not exist. This alternative strategy is simply to buy the stocks with low dispersion and least favorable

17

weight/validity/credibility of new information) has an incremental impact on the profits of the momentum portfolios. Our findings are consistent with the claim of Barberis at al. (1998) that investors display conservatism and underreact to information that has a high weight in adjusting their expectations about firm cash flows. This evidence provides empirical support for the version of stock price underreaction that believes it is caused by investors who tend to place too much emphasis on the content (analysts’ earnings recommendation) and too little on the weight (credibility/analyst dispersion) of new information in adjusting their expectations. [Insert Table VI About Here] B. Portfolios Sorted by Size and Dispersion In this section we form portfolios based on size and analyst dispersion. In this vein, we allow the dispersion-size relationship to be piecewise linear, where the size effect is essentially purged. As exhibited in Table VII, the size match across dispersion classes is nearly perfect. For example, the mean (median) size for the Small 30/low dispersion (D1) stocks is £63 (£58) million compared to £60 (£55) million for the Small 30/high dispersion (D3) stocks. Moreover, we also retain a good spread in dispersion between the two classes, where the mean (median) dispersion is 0.037 (0.035) for the low dispersion (D1) stocks and increasing to 0.981 (0.347) for the high dispersion (D3) stocks. Beginning with the Small 30 stocks and moving from the low (D1) to the high (D3) dispersion classes we find that the Small 30 and D1/low dispersion stocks generate an average monthly return of 1.22 percent whereas the Small 30 and D3/high dispersion stocks produce an average monthly return of just 0.66 percent per month. On an annualized basis these returns are 134.64 percent and 7.92 percent, respectively. Similar to the momentum pattern found by moving from low to the high dispersion classes, moving across size classes we find that momentum profits decrease considerably with size increases. For example, where the Small 30 and D1/low dispersion stocks generate an average monthly return of 1.22 percent (with a t-statistic = 5.22), the Large 30 and D1/low dispersion stocks produce a return of just 0.92 percent per month (with a t-statistic =4.48). Again, on an

earnings revisions (D1/P1) and sell the stocks with high dispersion (D3/P1) (or short the stocks in D5/P1 and buy the stocks in D1/P1). This result contradicts the evidence of Diether et al. (2002) who show that US firms with high (low) dispersion earn low (high) returns. The most profitable momentum-neutral strategy, however, emerges in stocks with the most favorable earnings revisions (i.e., buy D1/P3 and sell D5/P3 and/or buy D1/P5 and sell D5/P5).

18

annualized basis these returns are 14.64 percent and 10.04 percent, respectively. Since dispersion and momentum gains decrease with size increases, it appears that size has an important bearing on the gains of the dispersion momentum strategy. As shown in the last row, low dispersion stocks with the most favorable earnings revisions are associated with higher momentum gains. These gains are larger for medium and large capitalization stocks. [Insert Table VII About Here] Overall, the results of this section provide the evidence that the dispersion in analysts’ earnings forecasts is inversely related with the profitability of momentum strategies. This finding is consistent with the model of Barberis, Shleifer, and Vishny (1998) predicting that momentum is the result of systematic errors that investors make by not updating their earnings expectations adequately relative to their prior beliefs and by undervaluing the statistical weight of new information. To the extent that the dispersion effect reflects the psychological aspect of investors’ conservatism, it is expected to persist.

V. Conclusions Several non-risk based theories (Delong et al. (1990), Barberis et al. (1998), Daniel, Hirshleifer, and Subrahanyam (1998), and Hong and Stein (1999)) have been developed to explain momentum in stock returns. A common feature in the models of Barberis et al. (1998) and Hong and Stein (1999)) is that momentum is due to initial underreaction followed by a correction. Barberis et al. (1998) argue that momentum originates in investors’ conservatism bias, and that investors do not update their beliefs adequately based on the strength and weight of new information. The Hong and Stein (1999) model shows that momentum comes from the gradual diffusion of firm-specific information and the inability of investors to extract each others’ private information from prices. Hong et al. (2000) have produced evidence in support of the gradual-information-diffusion model of Hong and Stein (1999), using U. S. stock returns. In this paper, we conduct an empirical investigation of these two behavioral models in a sample of 13 European countries during the period 1988 to 2001. This is an out-of-sample test designed to address Fama’s (1998) concern that “… these models simply rationalize those existing patterns that

19

they were specifically designed to capture. Rather, the acid test should be the “out-of-sample” one:”. Our first result is in support of the view that average stock returns are related to past performance. This evidence confirms the previous findings of Rouwenhorst (1998) and indicates that short-term momentum in stock returns has persisted in 13 European markets during the period 1988 to 2001. This pattern in stock returns is not limited to a particular stock market, but is present and significant in eight of 13 European stock markets. Second, the European evidence is consistent with the gradual-information-diffusion model of Hong and Stein’s (1999) and remarkably similar to findings for the U. S. by Hong at al. (2000). Specifically, we find not only that momentum is associated with size but also analyst coverage; namely, when holding size fixed, we find that momentum strategies work better in stocks with low analyst coverage indicating that the findings of Hong et al. (2000) are unlikely to be due to chance. Third, we find that analysts’ forecast dispersion is inversely related with the profitability of momentum strategies. This finding is consistent with the model of Barberis et al. (1998) predicting that investors fail to update their beliefs adequately. This evidence suggests that investors do not place adequate emphasis on the statistical weight of new information. Overall, the results of this study are consistent with the predictions of the behavioral models of Hong and Stein’s (1999) and Barberis et al. (1998). The out-of-sample evidence suggests that momentum is the result of the gradual diffusion of private information and investors’ psychological conservatism reflected on the systematic errors they make in forming earnings expectations by not updating them adequately relative to their prior beliefs and by undervaluing the statistical weight of new information.

20

REFERENCES Atiase, R. and L. Bamber, 1994, Trading volume reaction to annual earnings announcements: The incremental role of predisclosure information asymmetry. Journal of Accounting and Economics 17, 309-329. Ball, R. and P. Brown, 1968, An empirical evaluation of accounting income numbers. Accounting Research 6, 159-78.

Journal of

Barberis, N., A. Shleifer, and R. Vishny, 1998, A model of investor sentiment, Journal of Financial Economics 49, 307-343. Barron, O., O. Kim, S. Lim, and D. Stevens, Using analyst forecasts to measure properties of analysts’ information environment, Accounting Review (forthcoming 2002). Bhushan, R, 1989, Firm characteristics and analyst following, Journal of Accounting and Economics 37; 39-65. Brennan, M., and A. Subrahmanyam, 1995, Investment analysis and price formation in security markets. Journal of Financial Economics 38: 361-381. Brennan, M., and P.Hughes, 1991, Stock prices and the supply of information. Journal of Finance 46: 1665-1691. Chan, L. K.C., N. Jegadeesh, and J. Lakonishok, 1996, Momentum strategies, Journal of Finance 51, 1681-1713. Conrad, J., and K. Gautam, 1997, An anatomy of trading strategies, Review of Financial Studies 11, 489-519. Daniel, K., D. Hirshleifer, and A. Subrahmanyam, 1998, Investor psychology and security market under- and overreactions. Journal of Finance 53: 1839-1885. Delong, J.B., A. Shleifer, L.H. Summers, and R. Waldmann, 1990, Positive feedback investment strategies and destabilizing rational speculation, Journal of Finance 45, 379-395. Diether, K. B., C. J. Malloy, and A. Scherbina, 2002, Differences of opinion and the cross-section of stock returns, Journal of Finance 57, 21. Dische, A., 2002, Dispersion in analyst forecasts and the profitability of earnings momentum strategies, European Financial Management 8, 211-228. Doukas, J., C. Kim, C. Pantzalis, 2002, A test of the errors-in-expectations explanation of the value/glamour stock returns performance: Evidence from analysts’ forecasts. Journal of Finance 57, 2143-2165. Fama, E., 1998, Market efficiency, long-term returns, and behavioral finance. Journal of Finance 49: 283-306. Fama, E.F., and K. French, 1996, Multifactor explanations of asset pricing anomalies, Journal of Finance 51, 55-84. Griffin, D., and A. Tversky, 1992, The weighing of evidence and the determinants of confidence. Cognitive Psychology 24, 411-435.

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Grinblatt and Moskowitz, 1999, The cross-section of expected returns and its relation to past returns, Working paper, University of Chicago. Grossman, S. J., and M. H. Miller,1988, Liquidity and market structure, Journal of Finance 43,617-633. Harris, M., and A. Raviv, 1993, Differences of opinion make a horse race, Review of Financial Studies 6, 475-506. Hong, H., T. Lim, and J. Stein, 2000, Bad news travels slowly: Size, analyst coverage, and the profitability of momentum strategies. Journal of Finance 55: 265-295. Hong, H., and J. Stein, 1999, A unified theory of underreaction, momentum trading and overreaction in asset markets. Journal of Finance 54: 2143-2184. Jegadeesh, N., and S. Titman, 1993, Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance 48: 65-91. Jegadeesh, N., and S. Titman, 2001, Profitability of momentum strategies: An evaluation of alternative explanations. Journal of Finance 56, 699-720. Jensen, M. C., and W. H. Meckling, 1976, Theory of the firm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics 3: 305-360. Lee, C. M., and B. Swaminathan, 2000, Price momentum and trading volume, Journal of Finance 55, 2017-2069. Lim, T., 1998, Rationality and analysts’ forecast bias. Working paper, Amos Tuck School. Roll, R., 1983, Vas its Das? Journal of Portfolio Management 9: 18-28. Rowenhorst, G., 1997, Local return factors and turnover in emerging stock markets. Working paper, Yale University. Rowenhorst, G., 1998, International momentum strategies. Journal of Finance 53: 267-284. Womack, K., 1996, Do Brokerage analysts’ recommendations have investment value? Journal of Finance 51: 137-167.

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Table I Descriptive Statistics for Analyst Coverage and Momentum Returns Panel A reports descriptive statistics for firm size and mean analyst coverage broken down into percentiles for all I/B/E/S quoted European firms before any size or price adjustments from January 1988 through January 2001. Panel B reports analyst coverage and momentum returns by country. Panel B reports descriptive statistics for mean analyst coverage and momentum by country for all European firms in the sample for which complete data exist and before any size and pricing adjustments (except for momentum returns where stocks below £1per share and £25 million in market capitalization are deleted from the sample) for the years January 1988 through January 2001 as reported by I/B/E/S. The relative momentum portfolios are formed based on six-month lagged raw returns and held for six months, with each portfolio reporting average monthly returns. Performance is broken down into three (five) equally weighted portfolios: Portfolio P1 (P1) contains the worst performing 30 percent (20 percent) of stocks in the portfolio whereas Portfolio P3 (P5) contains the best performing 30 percent (20 percent) of stocks in the sample, with P3 - P1 (P5 – P1) the basic measure of momentum.

Panel A: Analyst Coverage by Percentile

Year 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Number of I/B/E/S Mean Quoted Firm Firms Size (£) 3226 3398 3228 3401 3616 3604 3602 3989 4022 4302 4402 4500 4543 4075

353 373 383 320 314 365 446 466 554 668 882 1080 1340 1370

Percent of Firms Uncovered

Median Firm Size (£)

10

20

30

40

50

60

70

80

90

46 51 56 49 41 49 70 72 79 80 91 92 126 118

0 0 0 0 0 0 0 0 0 0 0 0 0 1

0 0 0 0 0 1 1 1 1 1 1 1 1 1

0 0 1 1 1 2 2 2 2 2 2 1 1 2

1 1 2 2 2 3 3 3 3 3 2 2 2 3

1 3 4 4 4 4 4 4 5 4 4 3 3 4

2 4 5 5 5 6 7 7 7 6 5 5 5 6

4 6 8 8 9 9 10 10 11 9 8 7 7 9

7 10 11 12 13 15 16 16 17 15 12 11 11 12

13 15 17 18 19 22 23 24 24 24 21 18 17 19

Number of Analysts at Coverage Percentiles

38.1% 31.2% 25.8% 25.0% 24.9% 19.3% 19.2% 19.6% 18.1% 18.9% 14.9% 14.1% 11.7% 6.3%

Table I Panel B:Mean Analyst Coverage and Momentum by Country B1: Mean Analyst Coverage by Country Year

Austria

Belgium

Germany

Spain

France

Italy

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

3.6 3.5 5.1 5.7 5.5 6.2 5.7 6.8 7.4 6.5 4.3 2.7 3.1 3.2

4.5 4.8 5.8 5.7 6.0 6.9 8.1 11.0 11.4 11.2 9.3 5.9 6.1 6.7

6.7 8.8 9.8 10.9 11.3 8.9 10.1 11.0 11.3 10.5 9.4 5.2 6.3 6.8

5.7 6.0 8.7 9.2 14.3 13.8 13.4 14.5 17.2 15.9 13.5 8.5 7.7 8.6

4.4 6.3 8.4 7.9 8.9 12.3 13.9 16.5 15.8 14.1 12.2 9.9 6.6 7.2

4.1 5.5 8.1 9.0 10.0 12.1 11.2 12.3 13.1 13.4 11.8 7.4 6.5 5.1

5.5 7.0 8.8 12.5 13.9 14.5 16.5 17.1 16.6 17.6 17.1 13.1 9.2 10.2

Mean Coverage

4.95

7.38

9.07

11.21

10.31

9.25

12.82

Nether. Switzer..

UK

Denmark

Finland

Norway Sweden

5.6 6.9 8.6 8.4 9.4 11.7 10.9 11.2 12.4 10.5 8.9 8.4 7.9 7.7

7.6 7.9 7.7 7.1 7.3 7.7 7.4 7.2 7.5 6.8 6.5 6.5 6.5 6.6

3.9 4.4 5.3 4.7 4.7 4.9 5.6 6.7 6.1 6.7 7.1 6.9 6.9 5.7

2.2 2.4 2.6 3.5 3.5 4.2 6.8 7.0 8.1 8.9 9.1 8.1 7.5 7.4

3.6 4.2 5.9 6.7 9.1 10.0 9.5 10.2 8.3 8.3 6.1 6.8 6.6 5.4

1.7 2.3 2.9 4.4 5.3 5.3 5.7 7.0 7.4 7.6 6.7 6.8 6.3 5.6

9.17

7.16

5.68

5.80

7.19

5.35

0.0048 (2.00) 0.0065 (2.54)

0.0098 (3.30) 0.0102 (3.03)

0.0025 (0.61) 0.0043 (0.96)

0.0065 (1.40) 0.0103 (1.91)

0.0033 (0.86) 0.0049 (1.22)

B2: Momentum Returns by Country P3 – P1 (t-stat) P5 – P1 (t-stat)

0.0070 (1.63) 0.0078 (1.71)

0.0065 (2.27) 0.0091 (2.85)

0.0032 (3.20) 0.0121 (3.65)

-0.0007 (-0.19) -0.0012 (-0.34)

0.0086 (2.74) 0.0111 (3.37)

0.0036 (0.96) 0.0032 (0.81)

0.0079 (2.89) 0.0098 (3.18)

0.0031 (1.00) 0.0022 (0.64)

Table II European Momentum Strategies Based on Raw Returns and Sorting by Size: 1/1988-1/2001 Panel A incorporates all stocks for the sample of European firms excluding all stocks trading below £1 per share and with £25 million in market capitalization. The relative momentum portfolios are formed based on six-month lagged raw returns and held for six months, with each portfolio reporting average monthly returns. Stocks are ranked in ascending order on the basis of six-month lagged returns. Performance is broken down into three equally weighted portfolios: P1, P2, and P3. Portfolio P1 contains the worst performing 30 percent of stocks in the portfolio, Portfolio P2 contains the middle performing 40 percent of stocks, and Portfolio P3 contains the best performing 30 percent of stocks in the sample. Each portfolio is segregated into size deciles with the smallest firms in size class 1 and the largest size firms in class 10. Size (mean and median) is in millions with t-statistics reported in parentheses.

Past Returns

All Stocks

P1 (Worst) 0.0014 (0.75) P2 0.0060 (4.09) P3 (Best) 0.0087 (5.39) P3 – P1 0.0073 (2.90) P2 – P1

Panel A: Size Class (Decile Breakpoints) 1

2

3

4

5

6

7

8

9

-0.0005 (-0.26) 0.0078 (4.95) 0.0111 (6.32) 0.0116 (4.49)

0.0008 (0.37) 0.0062 (3.89) 0.0117 (5.94) 0.0109 (3.87)

0.0022 (1.03) 0.0064 (4.09) 0.0114 (6.23) 0.0092 (3.24)

0.0015 (0.67) 0.0069 (4.23) 0.0118 (5.77) 0.0103 (3.46)

0.0011 (0.52) 0.0066 (4.07) 0.0092 (5.16) 0.0081 (3.01)

0.0019 (0.91) 0.0048 (3.10) 0.0069 (3.89) 0.0050 (1.84)

0.0010 (0.44) 0.0053 (3.24) 0.0062 (3.66) 0.0053 (1.91)

0.0028 (1.28) 0.0051 (3.52) 0.0049 (3.23) 0.0021 (0.84)

0.0049 (1.25) 0.0023 (3.73) 0.0058 (3.19) 0.0024 (0.99)

0.629

0.495

0.456

0.524

0.679

0.580

0.811

1.095

53 52 6.8 6.7

81 81 8.1 8.0

121 120 9.2 9.0

178 180 10.5 10.4

267 272 11.1 11.0

423 427 12.9 12.8

742 723 14.8 15.1

10 0.0024 (1.25) 0.0057 (3.81) 0.0060 (4.09) 0.0036 (1.53) 0.917

P3 – P1 Mean size Median size Mean analyst Median analyst

32 32 6.5 6.3

1558 1365 16.9 17.4

8023 6150 19.9 21.5

SC1 - SC10 -0.0029 (-1.07) 0.0021 (0.94) 0.0051 (2.21) 0.0080 (3.23)

Table II European Momentum Strategies Based on Raw Returns and Sorting by Size: 1/1988-1/2001 Panel B incorporates all stocks for the sample of European firms excluding all stocks trading below £1 and with £25 million in market capitalization. The relative momentum portfolios are formed based on six-month lagged raw returns and held for six months, with each portfolio reporting average monthly returns. Stocks are ranked in ascending order on the basis of six-month lagged returns. Performance is broken down into five equally weighted portfolios: P1, P2, P3, P4, and P5. Portfolio P1 contains the worst performing 20 percent of stocks in the portfolio, Portfolio P3 contains the middle performing 20 percent of stocks, and Portfolio P5 contains the best performing 20 percent of stocks in the sample. Each portfolio is segregated into size deciles with the smallest firms in size class 1 and the largest firms in size class 10. Size (mean and median) is in millions. t-statistics are reported in parentheses.

Past Returns

All Stocks

P1 (Worst) 0.0004 (0.22) P2 0.0043 (2.76) P3 0.0059 (3.98) P4 0.0071 (4.84) P5 (Best) 0.0093 (5.53) P5 – P1 0.0089 (3.34) P2 – P1 P5 – P1

Panel B: Size Class (Decile Breakpoints) 1

2

-0.0024 -0.0006 (-1.18) (-0.28) 0.0050 0.0035 (2.91) (1.89) 0.0072 0.0064 (4.22) (3.89) 0.0096 0.0091 (6.19) (5.32) 0.0119 0.0126 (6.01) (5.83) 0.0143 0.0132 (5.02) (4.32) 0.517

0.310

3 0.0011 (0.45) 0.0055 (3.13) 0.0056 (3.47) 0.0091 (5.30) 0.0120 (6.31) 0.0109 (3.54) 0.404

4

5

-0.0004 -0.0003 (-0.16) (-0.14) 0.0046 0.0047 (2.60) (2.75) 0.0071 0.0075 (4.04) (4.35) 0.0096 0.0070 (5.22) (4.05) 0.0127 0.0098 (5.91) (5.34) 0.0131 0.0101 (4.04) (3.45) 0.382

0.495

6

7

8

9

10

0.0010 (0.45) 0.0043 (2.49) 0.0043 (2.62) 0.0058 (3.57) 0.0074 (3.84) 0.0064 (2.15)

-0.0006 (-0.24) 0.0044 (2.42) 0.0048 (2.71) 0.0058 (3.47) 0.0070 (3.96) 0.0076 (2.53)

0.0023 (1.03) 0.0041 (2.31) 0.0051 (3.84) 0.0054 (3.44) 0.0049 (3.14) 0.0026 (0.98)

0.0017 (0.82) 0.0049 (2.95) 0.0054 (3.36) 0.0058 (3.83) 0.0044 (2.84) 0.0027 (1.04)

0.0009 (0.42) 0.0055 (3.72) 0.0059 (3.91) 0.0055 (3.81) 0.0061 (3.94) 0.0052 (2.06)

0.512

0.657

0.692

1.185

0.884

SC1 - SC10 -0.0033 (-1.14) -0.0005 (-0.21) 0.0013 (0.56) 0.0041 (1.95) 0.0058 (2.29) 0.0091 (3.37)

Table III European Momentum Strategies Based on Raw Returns and Sorting by Residual Analyst Coverage: 1/1988-1/2001 Panel A includes all stocks in the sample of European firms excluding all stocks trading below £1 and with £25 million in market capitalization. The relative momentum portfolios are formed based on six-month lagged returns and held for six months, with each portfolio reporting average monthly returns. Based on six month lagged returns, stocks are ranked in ascending order. Portfolio P1 is the worst performing 30 percent portfolio, Portfolio P2 is the middle performing 40 percent, and Portfolio P3 is the best performing 30 percent. The least covered firms are in Cov1 whereas the most covered firms are in Cov3. Residual coverage is determined by regressing the log(1+Analysts) on market capitalization and log (Size) (mean and median). t-statistics are reported in parentheses.

Panel A: Residual Analyst Coverage Past Returns

All Stocks

Low Cov1

Medium Cov2

High Cov3

Cov1-Cov3

P1 (Worst)

0.0014 (0.75) 0.0060 (4.10) 0.0087 (5.39) 0.0073 (2.90)

-0.0016 (-0.74) 0.0036 (2.27) 0.0072 (4.19) 0.0088 (3.22)

0.0017 (0.89) 0.0062 (4.19) 0.0081 (5.09) 0.0064 (2.56)

0.0045 (2.44) 0.0081 (5.43) 0.0104 (6.19) 0.0059 (2.39)

-0.0060 (-2.16) -0.0045 (-2.10) -0.0032 (-1.35) 0.0028 (1.08)

950 130 3.9 3.0

1800 330 11.5 10.0

910 230 20.5 19.0

P2 P3 (Best) P3 – P1

Mean size Median size Mean analyst Median analyst

Table III European Momentum Strategies Based on Raw Returns and Sorting by Residual Analyst Coverage: 1/1988-1/2001 Panel B includes all stocks in the sample of European firms excluding all stocks trading below £1 and with £25 million in market capitalization. The relative momentum portfolios are formed based on six-month lagged returns and held for six months, with each portfolio reporting average monthly returns. Based on six month lagged returns, stocks are ranked in ascending order. Portfolio P1 is the worst performing 20 percent portfolio, Portfolio P3 is the middle performing 20 percent, and Portfolio P5 is the best performing 20 percent. The least covered firms are in Cov1 whereas the most covered firms are in Cov5. Residual coverage is determined by regressing the log(1+Analysts) on market capitalization and log(Size) (mean and median) is in millions. t-statistics are reported in parentheses.

Panel B: Residual Analyst Coverage Past Returns P1 (Worst) P2 P3 P4 P5 (Best) P5 – P1

All Stocks

Low Cov1

Cov2

0.0004 (0.22) 0.0043 (2.76) 0.0059 (3.98) 0.0071 (4.84) 0.0093 (5.53) 0.0089 (3.34)

-0.0029 (-1.28) 0.0015 (0.83) 0.0033 (2.12) 0.0045 (2.82) 0.0083 (4.46) 0.0112 (3.80)

-0.0006 (-0.28) 0.0023 (1.25) 0.0044 (2.73) 0.0068 (4.01) 0.0083 (4.49) 0.0089 (3.03)

630 120 2.8 2.0

1800 200 7.3 6.0

Mean size Median size Mean analyst Median analyst

Middle Cov3

Cov4

-0.0001 0.0029 (-0.05) (1.41) 0.0046 0.0055 (2.83) (3.34) 0.0063 0.0079 (4.10) (5.01) 0.0066 0.0079 (4.40) (5.34) 0.0082 0.0090 (5.05) (5.19) 0.0083 0.0061 (3.18) (2.29) 1800 360 11.5 10.0

1600 390 15.9 14.0

High Cov5 0.0042 (2.04) 0.0069 (4.27) 0.0081 (5.40) 0.0092 (5.62) 0.0123 (6.78) 0.0081 (2.98) 630 200 22.1 21.0

Cov1-Cov5 -0.0071 (-2.31) -0.0054 (-2.57) -0.0048 (-2.50) -0.0047 (-2.04) -0.0040 (-1.57) 0.0031 (1.09)

Table IV European Momentum Strategies Based Raw Returns and Sorting by Size and Residual Analyst Coverage: 1/1988-1/2001 Table IV includes all stocks in the sample of European firms excluding all stocks trading below £1 and with £25 million in market capitalization. The relative momentum portfolios are formed based on six-month lagged returns and held for six months, with each portfolio reporting average monthly returns. Based on six month lagged returns, stocks are ranked in ascending order. Portfolio P1 is the worst performing 30 percent portfolio, Portfolio P2 is the middle performing 40 percent, and Portfolio P3 is the best performing 30 percent. The least covered firms are in Cov1 whereas the most covered firms are in Cov3. Residual coverage is determined by the regression of the log(1+Analysts) and market capitalization. The small 30 column contains the smallest size firms whereas the large 30 column represent the largest size firms. Size (mean and median) is in millions with t-statistics reported in parenthesis.

Firm Size Residual Coverage Class

Small 30

Medium 40

Large 30

Low: Cov1 Mean size Median size Mean Cov class Median Cov class Median: Cov2 Mean size Median size Mean Cov class Median Cov class

P3 - P1 = 0.0114 (4.02) 55 52 2.0 2.0 P3 - P1 = 0.0105 (3.93) 58 54 5.4 5.0

P3 - P1 = 0.0085 (2.86) 240 210 3.8 4.0 P3 - P1 = 0.0071 (2.47) 270 230 9.6 9.0

P3 - P1 = 0.0031 (1.20) 5200 1600 10.2 10.0 P3 - P1 = 0.0020 (0.85) 4100 1700 17.6 17.0

High: Cov3 Mean size Median size Mean Cov class Median Cov class

P3 - P1 = 0.0095 (3.35) 58 54 14.4 13.0

P3 - P1 = 0.0054 (2.17) 260 220 20.4 19.0

P3 - P1 = 0.0026 (1.04) 2300 1200 26.0 25.0

Cov1 – Cov3

P3 - P1 = 0.0019 (0.67)

P3 - P1 = 0.0031 (1.07)

P3 - P1 = 0.0005 (0.19)

Table V European Cross-Sectional Momentum Regressions, 1988-1998 This table includes all stocks in the sample of European firms with all stocks below £1 and £25 million deleted from the sample. The dependent variable is RHO: regression coefficient of six-month returns (net of risk-free rate) on lagged six month returns. Panel A: Independent variables are log(1 + analyst coverage) and the log(Size). Panel B: Independent variables are log(1 + analyst coverage), log(Size), and the interaction of log(1 + Analyst coverage) and the log(Size). tstatistics are adjusted for serial correlation.

Panel A Year

Coverage

t-statistics

Size

t-statistics

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

0.125 -0.006 -0.045 -0.077 0.004 0.052 0.008 -0.123 -0.022 -0.028 -0.113

3.483 -0.164 -1.527 -2.127 0.131 1.912 0.319 -4.219 -1.054 -0.906 -1.725

-0.033 -0.009 -0.010 -0.006 -0.010 -0.019 -0.016 -0.006 -0.010 -0.015 0.019

-8.393 -2.079 -2.854 -1.472 -2.494 -5.403 -4.660 -1.719 -3.675 -3.716 2.270

Pooled

-0.023

-2.217

-0.010

-7.932

Table V European Cross-Sectional Momentum Regressions, 1988-1998 This table includes all stocks in the sample of European firms with all stocks below £1 and £25 million deleted from the sample. The dependent variable is RHO: regression coefficient of six-month returns (net of risk-free rate) on lagged six month returns. Panel A: Independent variables are log(1 + analyst coverage) and the log(Size). Panel B: Independent variables are log(1 + analyst coverage), log(Size), and the interaction of log(1 + Analyst coverage) and the log(Size). tstatistics are adjusted for serial correlation.

Panel B Size

t-statistic

Interaction Cov. * Size t-statistic

Year

Coverage

t-statistic

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

0.450 -0.127 -0.257 -0.052 -0.181 -0.076 -0.146 -0.330 0.075 0.079 0.237

3.090 -0.858 -2.403 -0.404 -1.560 -0.713 -1.477 -3.142 1.093 0.774 1.124

-0.034 -0.008 -0.009 -0.006 -0.010 -0.019 -0.015 -0.006 -0.010 -0.016 0.017

-8.647 -2.018 -2.727 -1.479 -2.415 -5.251 -4.473 -1.546 -3.808 -3.853 1.974

-0.016 0.006 0.010 -0.001 0.009 0.006 0.007 0.010 -0.004 -0.005 -0.016

-2.300 0.844 2.059 -0.199 1.659 1.249 1.621 2.045 -1.488 -1.101 -1.748

Pooled

-0.081

-2.166

-0.010

-7.699

0.002

1.615

Table VI European Momentum Strategies Based on Earnings Revisions and Sorting by Dispersion: 1/1988-1/2001 Panel A includes all stocks in the sample of European firms excluding all stocks trading below £1 and with £25 million in market capitalization. This panel reports monthly returns by portfolios formed on the basis of monthly analyst consensus earnings revisions and held for one month. Portfolio returns are estimated for stocks tracked with a minimum of two analysts. Stocks are ranked into three portfolios in descending order where Portfolio P1 represents the least favorable stocks (30 percent) with downward earnings revisions, Portfolio P2 represents the middle 40 percent, and Portfolio P3 represents the most favorable stocks (30 percent) with upward earnings revisions. Dispersion is defined as the ratio of the standard deviation of analysts’ current-fiscal-year annual earnings per share forecasts scaled by the absolute value of the mean earnings forecast, as reported by the I/B/E/S Summary History File. Low dispersion stocks are in D1 whereas high dispersion stocks are in D3. Size (mean and median) is in millions with t-statistics reported in parenthesis.

Panel A: Analysts’ Earnings Forecast Dispersion Earnings Revision Portfolios

All Stocks

Low D1

D2

High D3

D1 - D3

P1 (Least Favorable)

0.0031 (3.07)

0.0022 (1.48)

0.0034 (2.06)

0.0036 (1.78)

-0.0014 (-0.57)

P2

0.0080 (8.98)

0.0090 (6.64)

0.0086 (5.81)

0.0065 (3.64)

0.0024 (1.09)

P3 (Most Favorable)

0.0116 (11.89)

0.0129 (9.27)

0.0128 (7.99)

0.0089 (4.48)

0.0040 (1.64)

P3 – P1

0.0085 (6.13)

0.0107 (5.31)

0.0094 (4.15)

0.0053 (1.87)

0.0054 (2.27)

0.034 0.032 1600 300

0.093 0.085 1500 250

0.832 0.264 800 170

Mean Dispersion Median Dispersion Mean Size Median Size

Table VI European Momentum Strategies Based on Earnings Revisions and Sorting by Dispersion: 1/1988-1/2001 Panel B includes all stocks in the sample of European firms excluding all stocks trading below £1 and with £25 million in market capitalization. This panel reports monthly returns by portfolios formed on the basis of monthly analyst consensus earnings revisions and held for one month. Portfolio returns are estimated for stocks tracked with a minimum of two analysts. Stocks are ranked into three portfolios in descending order where Portfolio P1 represents the least favorable stocks (20 percent) with downward earnings revisions, Portfolio P3 represents the middle 20 percent, and Portfolio P5 represents the most favorable stocks (20 percent) with upward earnings revisions. Dispersion is defined as the ratio of the standard deviation of analysts’ current-fiscal-year annual earnings per share forecasts scaled by the absolute value of the mean earnings forecast, as reported by the I/B/E/S Summary History File. Low dispersion stocks are in D1 whereas high dispersion stocks are in D3. Size (mean and median) is in millions with t-statistics reported in parenthesis.

Panel B: Analysts’ Earnings Forecast Dispersion Earnings Revision Portfolios

All Stocks

P1 (Least Fav.) 0.0029 (1.61) P2 0.0066 (4.16) P3 0.0091 (6.10) P4 0.0108 (7.21) P5 (Most Fav.) 0.0118 (6.80) P5 – P1 0.0089 (3.55)

Mean Dispersion Median Dispersion Mean Size Median Size

Low D1

D4

High D5

D2

D3

D1 – D5

-0.0013 (-0.85) 0.0045 (3.21) 0.0088 (5.94) 0.0124 (9.07) 0.0134 (9.00) 0.0147 (6.89)

0.0014 (0.84) 0.0057 (4.00) 0.0090 (6.03) 0.0123 (8.67) 0.0134 (8.19) 0.0120 (4.99)

0.0023 (1.34) 0.0072 (4.69) 0.0082 (5.28) 0.0103 (6.91) 0.0131 (7.61) 0.0108 (4.45)

0.0031 (1.51) 0.0067 (4.17) 0.0080 (4.86) 0.0107 (6.95) 0.0106 (5.74) 0.0075 (2.74)

0.0045 (1.95) 0.0062 (3.47) 0.0066 (3.12) 0.0088 (5.00) 0.0075 (3.25) 0.0030 (0.92)

-0.0058 (-2.09) -0.0017 (-0.74) 0.0022 (0.85) 0.0036 (1.62) 0.0059 (2.14) 0.0117 (4.45)

0.030 0.026 1400 260

0.064 0.052 1600 280

0.103 0.084 1600 250

0.178 0.135 1200 220

1.115 0.297 890 180

Table VII European Momentum Strategies Based on Earnings Revisions, Sorting by Size and Dispersion: 1/1988-1/2001 Table VI incorporates all stocks for the sample of European firms excluding all stocks trading below £1 and with £25 million in market capitalization. Panel A includes all stocks in the sample of European firms excluding all stocks trading below £1 and with £25 million in market capitalization. This table reports monthly average returns by portfolios formed on the basis of monthly analyst consensus earnings revisions and held for six months. Portfolio returns are estimated for stocks tracked with a minimum of two analysts. Stocks are ranked into three portfolios in descending order where Portfolio P1 represents the least favorable stocks (30 percent) with downward earnings revisions, Portfolio P2 represents the middle 40 percent, and Portfolio P3 represents the most favorable stocks (30 percent) with upward earnings revisions. The small 30 column contains the smallest size firms whereas the large 30 column represent the largest size firms. Dispersion is defined as the ratio of the standard deviation of analysts’ current-fiscal-year annual earnings per share forecasts scaled by the absolute value of the mean earnings forecast, as reported by the I/B/E/S Summary History File. Low dispersion stocks are in D1 whereas high dispersion stocks are in D3. Size (mean and median) is in millions with t-statistics reported in parentheses.

Analysts’ Forecast Dispersion

Firm Size Small 30

Medium 40

Large 30

Low: D1 Mean Size Median Size Mean dispersion Median dispersion

P3 - P1 = 0.0122 (5.22) 63 58 0.037 0.035

P3 - P1 = 0.0111 (5.02) 280 240 0.035 0.033

P3 - P1 = 0.0092 (4.48) 4000 1800 0.032 0.029

Median: D2 Mean Size Median Size Mean dispersion Median dispersion

P3 - P1 = 0.0130 (4.83) 62 57 0.114 0.103

P3 - P1 = 0.0093 (3.78) 280 230 0.096 0.087

P3 - P1 = 0.0066 (3.04) 4400 1600 0.077 0.069

High: D3 Mean Size Median Size Mean dispersion Median dispersion

P3 - P1 = 0.0066 (1.89) 60 55 0.981 0.347

P3 - P1 = 0.0049 (1.67) 270 230 0.951 0.272

P3 - P1 = 0.0036 (1.40) 3500 1400 0.518 0.186

D1 – D3

P3 - P1 = 0.0056 (1.95)

P3 - P1 = 0.0062 (2.38)

P3 - P1 = 0.0056 (2.43)