An Explanation of Momentum in. Canadian Stocks

Transcription

1 An Explanation of Momentum in Canadian Stocks TONY C.T. HOU Napier University Edinburgh, Scotland (UK) and Cardiff University Cardiff, Wales (UK) PHILLIP J. MCKNIGHT Napier University Edinburgh, Scotland (UK) (A Previous Version of This Paper Was Entitled Return Continuation in Canadian Stocks.) 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. Address for correspondence: Phil McKnight, Department of Finance, Edgewood College, 1000 Edgewood College Drive, Madison, Wisconsin Phone: Tony C.T. Hou Tel: +44-(0) , address: houc@cf.ac.uk 1

2 An Explanation of Momentum in Canadian Stocks Abstract This paper examines the drivers of momentum in Canadian stocks. We find that momentum is negatively related to book-to-market and analyst coverage whereas size appears to play no role in explaining the momentum effect. We further document that analyst coverage is more important than book-to-market in explaining momentum. In contrast to prior research, we only find partial support for the Fama and French s (1998) book-to-market argument, that is, most of the continuation effect is explained by low book-to-market stocks. Keywords: momentum, size, book-to-market, analyst coverage, and industry. JEL classification: G12, G14, G19 2

3 An Explanation of Momentum in Canadian Stocks 1. INTRODUCTION Prior research has found that the strategy of buying past stock winners and selling past stock losers can generate abnormal returns (Jegadeesh and Titman, 1993). Specifically, Jegadeesh and Titman (1993, 2001) found that buying six-month past winners and selling six-month past losers can yield on average one percent per month. Foerster, Prihar, and Schmitz (1994) using Canadian data from 1978 to 1993 document evidence of momentum in stock returns. A follow up study by Rouwenhorst (1998) for a sample of European stocks find similar results, suggesting that this phenomenon is not limited to the US or Canadian capital markets. Although previous studies have made important contributions by documenting the existence of momentum in stock returns in the U.S., European markets, and Canadian markets, research is still in its early stages as to providing explanations as to what may be driving these returns. Fama and French (1996) use a three-factor model in an attempt to explain this return pattern, however, they conclude that, at least over the short-term, these factors offer little explanation. Hong, Lim and Stein (2000) test the gradual diffusion of firm-specific information hypothesis put forth by Hong and Stein (1999) using U.S. data. They find that momentum is higher for stocks followed by fewer analysts, a finding consistent with the gradual diffusion of firm-specific 3

4 information hypothesis. Hong et al. (2000) also conclude that after purging the size effect, analyst coverage appears to be more important than size in driving the momentum found in U.S. stocks. More recently, Doukas and McKnight (2004) show that momentum in European stocks has been persistent, and that size and coverage explain much of the momentum. In summary, momentum in U.S. and European stocks appears to be a result of information being disseminated more slowly to the investing public. As to whether analysts coverage is real or merely a sample-specific result of chance found in the U.S. and European markets remains an empirical question. Thus, the purpose of this paper is twofold. First, extending the works of Foerster et al (1994), we perform an independent verification and examine the Hong and Stein (1999) version of the underreaction hypothesis within a Canadian context. Similar to Hong et al (2000), we use residual analyst coverage as a proxy for the rate of information diffusion and explore whether momentum reflects the gradual diffusion of firm-specific information. Second, extending the works Assoe and Sy (2003) and Cao and Wei (2002), we examine in more depth and test whether size, book-to-market, and industry can offer alternative explanations into any return pattern found in Canadian stocks. 1 In summary, the importance of this study is as follows. While Hong et al. (2000) and Doukas and McKnight (2004) provide evidence that momentum is primarily attributable to low-analyst-coverage stocks, it cannot be ruled out that this result is limited to the U.S. and European stock 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 applicable to the U.S. and European stock market. Canada is an important market because its economy is massively dependent on trade with 4

5 the U.S. Canadian companies also turn to the U.S. markets to raise capital whereas U.S. companies turn to Canada for financing opportunities as well. The similarities in economies provide an opportunity to perform an independent verification of the findings of prior research in determining whether momentum exists in Canadian stocks. This paper fills a gap in the literature in this respect. The results are as follows. First, we find evidence in support of the view that average stock returns in Canada are related to past performance. Second, we discover that size plays no role in explaining momentum, a finding inconsistent with prior research conducted in the U.S. and European stock markets (Hong et al, 2000; Doukas and McKnight, 2004). Third, we provide evidence that momentum is negatively related to analyst coverage, a finding consistent with the gradual-information-diffusion model of Hong and Stein s (1999). Fourth, we find that momentum is negatively related to book-to-market, a result which is partially inconsistent with the Fama and French (1998) book-to-market argument. Finally, by virtue of a three-way sort, the results suggest that analyst coverage is more important that book-to-market in explaining momentum. This paper is organized as follows. Section 2 provides a description of the methodology used in this study. Section 3 discusses the portfolio strategies used in this study and presents the empirical results relating to size, book-to-market, analyst coverage, and industry. Section 4 presents the results from Fama-MacBeth cross-sectional regressions. Section 5 concludes. 2. METHODOLOGY (i) Size, Book-to-Market, Analyst Coverage, and Industry 5

6 In this section, we discuss four variables as drivers of momentum in Canadian stocks. Our first test uses firm size as an explanation of momentum, a variable which has been examined in-depth in the U.S. markets. Prior research provides evidence that small size (market capitalization) firms have on average higher returns than large size firms. Hong et al. (2000) asserts that investors encounter more difficulty in generating public available information for smaller firms as opposed to larger ones and, as a result, firm-specific information should diffuse more slowly for small firms. 2 Moreover, market making activities or arbitrage capacity may be limited for smaller size firms (Merton, 1987; Grossman and Miller, 1988) as opposed to larger ones. Thus, if investors require more time to acquire relevant information for smaller firms, then firm size may serve as a reasonable substitute for the rate of information flow. As a result, we believe that small firms will generate higher future returns than large firms. Our next test examines the book-to-market (BE/ME) effect on momentum. High BE/ME stocks tend to be value firms, with presently low earnings growth (Lakonishok, Shleifer, Vishny, 1994; Fama and French, 1996; Fama, 1998). High book-to-market firms hold a value premium and should have higher future returns (Fama and French, 1996). Lakonishok, Shleifer, Vishny (1994) argue that abnormal returns from high BE/ME stocks are generated by investors, who incorrectly extrapolate the past earnings growth rates of firms. Moreover, Lakonishok et al. (1994) argue that investors may be overly optimistic about past winning stocks and more pessimistic regarding past losing stocks. Therefore, we expect that the momentum effect will be more pronounced in high BE/ME (value) stocks as opposed to low BE/ME (growth) stocks. 6

7 Another variable that plays a prominent role in this paper is analyst coverage. Here, we test the prediction of the Hong and Stein (1999) gradual-information-diffusion model. We do so because size may not be an adequate proxy for measuring the rate at which information is disseminate to the markets. Hong et al (2000) assert that analyst s coverage may be an alternative proxy to size in that stocks covered by fewer analysts may be those where information is disseminated more slowly to the investing public. In other words, where there is a greater degree of herding among analysts, we would expect markets to be more efficient in processing information. 3 Bhushan (1989) points out that size and analyst coverage are highly correlated, we factor for this potential limitation by using residual coverage. Hence, we expect momentum to be higher in stocks followed by fewer analysts. Finally, we control for industry influences on momentum (Cao and Wei, 2002). Firms in the same industry tend to be highly correlated because they operate in a similar macroeconomic environment. Moreover, analysts interest at certain points in time may be more concentrated in one industry (i.e., technology) than another. (ii) Data and Sample Characteristics Data for this study is gathered from the following sources. First, analyst coverage, industry and stock price information is gathered from the Institutional Brokers Estimate System (I/B/E/S) summary history files, which include stocks listed on the Toronto, Montreal, Vancouver and Alberta stock exchanges. Beta and book value data is colleted from DataStream, FAME, and annul reports. 4 Our data set spans the period January 1988 through December 2000 and we 7

8 exclude those firms trading below C$30 million in market capitalization to ensure small or illiquid stocks do not influence the results (Hong et al, 2000; Jegadeesh and Titman, 2001). 5 All stock related information is in Canadian dollars. Firm size is measured as the natural logarithm of the market value of a firm s equity. We computed BE/ME ratios by scaling the firm s book value by the market value of its equity. Similar to Hong et al (2000), an OLS regression is used to determine residual coverage, with the left-hand side variable being the log of 1 + the number of analysts and the right-hand side being the log of size. The residuals allow us to purge the size effect from analyst coverage in explaining momentum. Finally, we assign firms into ten industries according to the classification system provided by the I/B/E/S summary history file. Table 1 provides the descriptive statistics for market capitalization, BE/ME ratio, and analyst coverage. As shown in the table, coverage by I/B/E/S of Canadian firms has steadily increased from 917 in 1988 to 2429 for the year Interestingly, while the number of firms has increased linearly with time, firm size has shown no consistent pattern other than meandering up and down between the years 1988 and Median analyst coverage, on the other hand, resembles an inverted U-shaped relationship; that is, in 1988 median coverage was 5.0 and reached peaks of 6.0 in 1992 and 1995 before declining to 4.0 in the year After further examination of the data we found that coverage apparently trails corporate earnings. [Insert Table 1 about here] 3. PORTFOLIO STRATEGIES AND MOMENTUM 8

9 (i) Sorting by Size Our analysis begins with Table 2 which examines the influence size may have on momentum in Canadian stocks. We closely follow the methodology used by Hong et al (2000), who rank stocks over a six month period based on past performance and hold those stocks for six months, skipping a month between formation and holding periods to address any potential microstructure problems. The literature refers to this as a six-month/six-month trading strategy. Stocks are first sorted into 10 size deciles where size decile S1 contains the smallest size stocks and size decile S10 includes the largest size stocks. We then use a strategy; that is, stocks are sorted into three portfolios where the worst performing 30 percent of stocks are placed in portfolio P1, the middle performing 40 percent of stocks are placed in portfolio P2, and the best performing 30 percent are placed in portfolio P3. Momentum or the arbitrage is measured by P3 P1. Similar to Hong et al (2000), we use overlapping holding periods to increase the strength of our results. As for the results, we find that momentum exists in nine out of ten size decile portfolios. More importantly, moving across size deciles we do not find the smooth monotonic decline in returns as found by Hong et al (2000) in U.S. stocks. In fact, it appears that much of the momentum can be attributed to the three largest size deciles, S8, S9, and S10. For example, size decile S8 earns on average 2.78 percent per month and size deciles S9 and S10 earn an average monthly return of 1.41 and 2.05 percent, respectively. At this point, we do not find support for the gradual information diffusion hypothesis because the economic importance of size appears not to be a factor. 9

10 Another interesting finding which is inconsistent with Hong et al (2000) is that returns are driven by loser stocks in only four of the ten size decile portfolios. In other words, in five of the ten decile portfolios momentum is apparently coming from winning stocks. In this case, there is no clear pattern as to whether it is good news or bad news driving returns. The final observation we can offer from Table 2 relates to size and analyst coverage. As for size, we see that for the smallest size firms, in decile S1, the mean firm size is 330 million Canadian dollars where as in the largest size firms, in decile S10, the mean firm size is 36 billion Canadian dollars. We offer at least four explanations regarding the mean and median size levels found for each decile in Table 2, and in addition, why these levels may differ from that found by Hong et al (2000). First, stocks below 30 million Canadian dollars are deleted from the sample to ensure that the bid-ask bounce and/or smaller, illiquid stocks do not influence the results (Hong, et al, 2000; Jegadeesh and Titman, 2001). Second, we quote firms in Canadian rather than U.S. dollars or any other currency. Third, our time period of analysis is more recent, 1988 through Finally, during March of 2000 when equities reached a pinnacle, and stocks like Nortel Networks had market capitalizations of over 350 billion Canadian dollars. [Insert Table 2 about here] (ii) Sorting by Book-to-Market In Table 3, we use a n identical sorting strategy as found in section (i). However, in this section stocks are first sorted by book-to-market (BE/ME) rather than size. The first finding of interest is that momentum exist in seven of the ten 10

11 book-to-market decile portfolios. The returns in six of the ten book-to-market decile portfolios are positive and significant at the one percent level. More importantly, moving across book-to-market deciles we find that returns are the highest for the lowest BE/ME1 through BE/ME4 stocks. In particular, the BE/ME1 portfolio produces a very large 33.8 percent statistically positive yearly average return and the BE/ME3 portfolio provides a 35.1 percent statistically positive yearly average return. Moving across book-to-market deciles we also find that returns decline sharply in the BE/ME5 portfolio and then meander within a particular trading range. ****** The results in Table 3 contrast sharply with the results reported by Fama and French (1998). In this instance, we find that the lowest book-to-market stocks (i.e. BE/ME1, BE/ME2 BE/ME3, and BE/ME4) generate most of the returns found in Canadian stocks. Focusing on the loser portfolio (P1), we find only partial support for the Fama/French argument in that a value premium exists for stocks, especially distressed stocks. An alternative trading strategy is to hold the return portfolios (i.e. the P1, P2, and P3) constant. For example, in the loser portfolio (P1) we find that the difference between the BE/ME1 and the BE/ME10 book-to-market deciles generates a statistically positive monthly average return of 3.46 percent. As for the middle and best performing portfolios (P2 and P3), monthly average returns decrease significantly. Finally, the bulk of the momentum appears to be generated from the winner (P2-P1/P3-P1) stocks. Although this finding supports the Fama/French book-to-market argument, once we factor in the momentum effects found within each book-to-market portfolio the value premium explanation applicable to high book-to-market stocks does not supersede that of the small book-to-market stocks. This issue is further explored in Section iv. 11

12 A final observation made from Table 3 relates to the book-to-market and analyst coverage. As for book-to-market, we see that the lowest BE/ME1 portfolio has a mean ratio of 0.15 and monotonically increases to a mean average of 1.94 for the BE/ME10 portfolio. Based on the analyst coverage statistics also at the bottom of Table 3, the book-to-market sort appears coverage and size (not shown) neutral. [Insert Table 3 about here] Figure 1 illustrates the results by plotting the relationship between momentum and size, and book-to-market. As can be seen, there is a seemingly defined relationship between book-to-market and returns but no noticeable pattern found between size and returns. [Insert Figure 1 about here] (iii) Sorting by Residual Coverage In this section, we examine the impact of residual coverage on momentum in Canadian stocks. Stocks are first sorted by residual coverage, where residual coverage is found by regressing the log of 1 + the number analysts following the firm on the log of size. A strategy is used where the lowest (highest) covered 30 percent of stocks in NAF1 (NAF3) and the middle covered 40 percent of stocks in NAF2. Similar to the previous tables, our basic measure of momentum is P3 P1. Table 4 confirms that the momentum effect is greatest for low coverage stocks. To illustrate, the low coverage stocks (NAF1) produce a monthly 12

13 average return of 2.34%, whereas the high coverage stocks (NAF3) yield a monthly average return of 0.97%. The difference between the returns on these two portfolios is positive (1.37%) and statistically significant (t-value of 4.38). This finding is consistent with the information diffusion hypothesis (Hong and Stein, 1999). Turning to both the mean and medians for size and analyst coverage at the bottom of Table 4, we find that the residuals derived from the regression of coverage on size provides the desired characteristics. For example, sorting by residual analyst coverage, the mean and median of analysts in portfolio NAF1 (2.0 and 2.0 respectively) are considerably smaller than that found in portfolio NAF3 (11.9 and 11.0 respectively). More importantly, we also find that firm size across the NAF1 (low coverage) portfolios have a mean size of 4.5 billion Canadian dollars and increases only slightly to 5.9 billion Canadian dollars for the NAF3 (high coverage) portfolio. Although not perfect, we appear to have been somewhat successful in purging the size effect from coverage. [Insert Table 4 about here] (iv) Sorting by Book-to-Market and Analyst Coverage We continue our analysis by performing a two-way cut, where we sort by book-to-market ratios and then residual coverage. We know from Table 4 that residual coverage has a significantly greater impact on the momentum effect than firm size. Moreover, we also know from Table 3 that small book-to-market stocks have a seemingly larger effect on returns as opposed to the large book-to-market stocks. However, what we do not know is the relative 13

14 importance of analyst coverage over book-to-market. Thus, this step should allow us to impose a more equal book-to-market match across residual analyst coverage portfolios, and ascertain the marginal importance of analyst coverage over book-to-market in determining momentum. As can be seen in Table 5, we have achieved the desired characteristics with regard to book-to-market and analyst coverage. To illustrate, the mean book-to-market is 0.25 for portfolio BE/ME1,NAF1 (low book-to-market, low coverage) and 0.28 for BE/ME1,NAF3 (low book-to-market, high coverage). Moreover, there is considerable variation in analyst coverage across book-to-market classes. For example, mean analyst coverage is 2.7 for BE/ME1,NAF1 and 13.0 for BE/ME1,NAF3. On the other hand, there is also considerable variation in book-to-market across analyst coverage classes. Consistent with Table 3, we see that the lowest book-to-market and low covered stocks (BE/ME1,NAF1) generate significantly large positive monthly average returns of 5.02 percent. More importantly, we see a sharp decline in returns moving down coverage classes; the BE/ME1,NAF3 portfolio generates a monthly average return of 1.33 percent. Hence, as coverage increases, returns decrease a finding consistent with the information diffusion hypothesis. Table 5 also shows that holding book-to-market fixed and moving across coverage classes, momentum declines as coverage increases. To illustrate, the difference between the NAF1 and NAF3 portfolios in both the BE/ME1 and BE/ME2 book-to-market classes are large (3.69 and 1.52 percent, respectively) and statistically significant at the one percent level (t-value of 5.87 and 3.01, respectively). On the other hand, holding coverage fixed and moving across coverage classes, we also find that the difference between the returns is significant in only one of the three portfolios is significant (5.81). In summary, 14

15 although book-to-market may be important in explaining momentum in Canadian stocks, coverage appears to be the most instrumental driver. [Insert Table 5 about here] (v) Sorting by Industry Our final portfolio strategy is to examine whether the momentum effect can be explained by a given industry (Moskowitz and Grinblatt, 1999). Firms are assigned into an industry class as provided by I/B/E/S. Definitions are as follows: Industry 1 refers to financial services (IN1), Industry 2 refers to health care (IN2), Industry 3 to refers consumer non-durables (IN3), Industry 4 refers to consumer services (IN4), Industry 5 refers to consumer durables (IN5), Industry 6 refers to energy (IN6), Industry 7 refers to transportation (IN7), Industry 8 refers to technology (IN8), Industry 9 refers to basic industries (IN9), and Industry 10 refers to capital goods and utilities (IN10). We first sort stocks by industry and, as before, we use a trading strategy with the measure of momentum; P3 - P1. The primary reason for sorting by industry is that stocks in the same Industry may also be in a similar macroeconomic environment and, therefore, may be highly correlated. As a result, certain industries may be more responsible for driving momentum as opposed to other industries. Hence, the idea here is to show whether or not the momentum effect is confined to a particular industry. As shown by Table 6, we find that momentum is present in all but three industries, IN2, IN5 and IN6; or the health care, consumer durables, and energy industry. Our analysis also shows that momentum is large and statistically significant for industry IN3 (consumer non-durables), IN7 (transportation), and 15

16 IN8 (technology). Momentum is also moderately present in IN1 (financial services) and IN9 (basic industries). We also discover that with reference to median size, it is smaller firms (as exhibited by IN3 and IN8) rather than larger ones where much of the continuation effect is occurring. Interestingly, here our results seem to contradict the Fama/French argument regarding low and high book-to-market stocks; that is, low book-to-market stocks appear to have higher returns as opposed to high book-to-market stocks. This finding also supports an earlier conclusion reached from the results found in Table 3 in which it was found that low rather than high boot-to-market stocks appear to influence returns. [Insert Table 6 about here] 4. CROSS-SECTIONAL REGRESSION TESTS Finally, in this section we perform a Fama and MacBeth (1973) cross-sectional regression test on our sample of Canadian stocks. Firm returns, at time t, are regressed on a set of explanatory variables, including beta, firm size (the natural logarithm of the market value of the equity at time t 1), book-to-market ratio (the natural logarithm of the ratio of the matching year book value to the market value of the equity at time t-1), past returns (over the previous 6 months), and our measure of residual analyst coverage. Beginning with the univariate regressions, Table 7 shows that future stock returns are statistically significant and positively related to firm size, to book-to-market, to past returns, and statistically significant and negatively related to residual analyst coverage. Although the coefficients for beta are 16

17 negative they are not statistically significant in explaining future returns. The multivariate regressions produce similar results, with little significance lost between coefficients. The results of Table 7 are mixed with regard to supporting our analysis. For example, the size variable is both positive and significant with respect to future returns. Reflecting back on the results of Table 2, we also find that returns for size deciles S8, S9, and S10 are large and strongly significant. On the other hand, the results are mixed when comparing the findings of Table 7, the book-to-market variable, with those of Table 3. To illustrate, the book-to-market variable is positive and statistically, and can be explained by the fact that much of the momentum in Table 3 is coming from the loser stocks. This finding seems to support the Fama/French argument. However, we find that the momentum for the small book-to-market stocks is significantly larger than that found with the high book-to-market stocks. Thus, the book-to-market variable only partially supports the Fama/French argument. 7 In summary, book-to-market and analyst coverage appear to explain much of the momentum effect in Canadian stocks, with book-to-market prevailing over analyst coverage. [Insert Table 7 about here] 5. CONCLUSIONS In this study, we examine the effects of size, book-to-market, analyst coverage, and industry in explaining momentum in Canadian stocks. We generally conclude that the returns found in U.S. stocks and European are not limited to their respective capital markets. In this study we also find evidence of momentum in Canadian stocks, and that it is analyst coverage and 17

18 book-to-market driving the returns. However, we do not find firm size as an explanation of momentum as found by Hong et al (2000) for U.S. stocks, and Rouwenhorst (1998) and Doukas and McKnight (2004) for European stocks. Generally, we find that momentum in Canadian stocks is negatively related to firm book-to-market and analyst coverage. The negative relation between Canadian stock returns and book-to-market ratios seem to contradict the Fama and French (1992, 1996 and 1998) argument. We further find that analyst coverage is more important than firm size in explaining the momentum effect. However, when we sort by book-to-market and then analyst coverage, it appears that analyst coverage rather than book-to-market is more important in explaining the bulk of the returns in Canadian stocks. Hence, we provide support for the information diffusion hypothesis of Hong and Stein (1999). As for size, our findings do not coincide with those found by Hong et al (2000) in the U.S. markets and Doukas and McKnight (2004) in European markets. Size appears to play no role in explaining the continuation effect in Canadian stocks. Finally, when we examine the book-to-market effect more closely, our results confirm the existence of a value premium for poorly performing firms. However, we also find, in terms of momentum, that once sort stocks into book-to-market deciles the lowest book-to-market stocks out perform the highest book-to-market stocks by a significant margin (month average return of 1.96 percent and significant at the one percent level). As a result, our tests performed in Table 3 do not fully support the Fama/French book-to-market argument. There are at least two avenues for future research. First, one avenue for future research is to extend the dataset and perform a value-weighted test; that is, to see how momentum may differ with regard to value-weighted as opposed 18

19 to equal-weighed returns. Second, another avenue for possible research is to extend the dataset to incorporate stock returns after the March 2000 stock market correction. In doing so, we can exam momentum in both pre and post market correction periods, of which may provide a deeper understanding of the momentum phenomenon. REFERENCES Assoe, K. and O. Sy (2003), Profitability of the Short-Run Contrarian Strategy in Canadian Stock Markets, Canadian Journal of Administrative Science, Vol 20, pp Bhushan, R. (1989), Firms Characteristics and Analyst Following, Journal of Accounting and Economics, Vol. 11, pp Brennan, M., and P. Hughes (1991), Stock Prices and the Supply of Information, Journal of Finance, Vol. 46, pp Cao, M and J. Wei (2002), Uncovering Sector Momentums, Canadian Investment Review, Winter, Vol

20 Cleary, S. and M. Inglis (1998), Momentum in Canadian Stock Returns, Canadian Journal of Administrative Science, Vol. 15, pp Doukas, J. A. and P. J. McKnight (2004), European Momentum Strategies, Information Diffusion, and Investor Conservatism, European Financial Management, Forthcoming. Fama, E.F. and K.R. French (1992), The Cross-Section of Expected Stock Returns, Journal of Finance, No. 47, pp Fama, E.F. and K.R. French (1996), Multifactor Explanations of Asset Pricing Anomalies, Journal of Finance, No. 51, pp Fama, E.F. (1998), Market Efficiency, Long-term Returns, and Behavioural Finance, Journal of Financial Economics, No. 49, pp Fama, E.F. and K.R. French (1998), Value versus Growth: The International Evidence, Journal of Finance, No. 53, pp

21 Fama, E.F. and J. MacBeth (1973), Risk, Return, and Equilibrium: Empirical Tests, Journal of Political Economy, No. 81, pp Grinblatt M. and T.J. Moskowitz (1999), Do Industries Explain Momentum, Journal of Finance, No. 54, pp Grossman, S.J. and M.H. Miller (1988), Liquidity and Market Structure, Journal of Finance, No. 43, pp Hong, H., T. Lim and J.C. Stein (2000), Bad News Travels Slowly: Size, Analyst Coverage, and the Profitability of Momentum Strategies, Journal of Finance, No. 55, pp Hong, H. and J.C. Stein (1999), A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets, Journal of Finance, No. 54, pp Jegadeesh, N. and S. Titman (1993), Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance, 21

22 No. 48, pp Jegadeesh, N. and S. Titman (2001), Profitability of Momentum Strategies: An Evaluation of Alternative Explanations, Journal of Finance, No. 56, pp Lakonishok, J., A. Shleifer and R.W. Vishny (1994), Contrarian Investment, Extrapolation and Risk, Journal of Finance, No. 49, pp Merton, R.C. (1987), A Simple Model of Capital Market Equilibrium with Incomplete Information, Journal of Finance, No. 42, pp Rouwenhorst, K.G. (1998), International Momentum Strategies, Journal of Finance, No. 53, pp

23 Table 1 Descriptive Statistics: January 1988 Though December 2000 Date Number of Firms Mean Size (Millions) Summary Statistics for All Canadian Stocks Median Size Mean (Millions) Analyst Median Analyst Mean BE/ME Ratio Median BE/ME Ratio

24 Table 2 Mean Portfolio Returns Sorting by Market Capitalization Declines Stocks are first sorted into 10 size deciles where size decile S1 contains the smallest size stocks and size decile S10 includes the largest size stocks. We then use a strategy; that is, stocks are sorted into three portfolios where the worst performing 30 percent of stocks are placed in portfolio P1, the middle performing 40 percent of stocks are placed in portfolio P2, and the best performing 30 percent are placed in portfolio P3. Momentum or the arbitrage is measured by P3 P1. Stocks are ranked over a six month period based on past performance and held for six months, skipping a month between formation periods. t-statistics in parentheses are adjusted for autocorrelation. Size Deciles Portfolio Small Large S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S1-S10 P (-0.25) P (-2.99) P (-2.89) P3-P (0.89) (2.25) (2.81) (4.32) (2.45) (5.02) (1.78) (6.67) (3.86) (4.17) (-3.68) 24

25 P2 P P3 P1 Mean size (C$) Median size (C$) Mean analyst Median analyst

26 Table 3 Mean Portfolio Returns Sorting by Book-to-Market Ratio Deciles Stocks are first sorted into 10 book-to-market (BE/ME) deciles where decile BE/ME1 contains the smallest book-to-market stocks and decile BE/ME10 includes the highest book-to-market stocks. We then use a strategy; that is, stocks are sorted into three portfolios where the worst performing 30 percent of stocks are placed in portfolio P1, the middle performing 40 percent of stocks are placed in portfolio P2, and the best performing 30 percent are placed in portfolio P3. Momentum or the arbitrage is measured by P3 P1. Stocks are ranked over a six month period based on past performance and held for six months, skipping a month between formation periods. t-statistics in parentheses are adjusted for autocorrelation. Book-to-Market Ratio Deciles Small Large BE/ME10- Portfolio BE/ME1 BE/ME2 BE/ME3 BE/ME4 BE/ME5 BE/ME6 BE/ME7 BE/ME8 BE/ME9 BE/ME10 BE/ME1 P P P P3-P (3.42) (2.46) (4.40) (3.28) (1.63) (3.50) (0.88) (2.83) (2.88) (1.28) (-3.37) (4.20) (2.62) (2.20) 26

27 P2 P P3 P1 Mean BE/ME Median BE/ME Mean analyst Median analyst

28 Table 4 Mean Portfolio Returns Sorting by Analyst Coverage Stocks are first sorted into three portfolios using a strategy, where the lowest covered 30 percent of stocks are in NAF1 and the highest covered stocks are in NAF3, with the middle covered 40 percent of stocks in NAF2. We then use a strategy; that is, stocks are sorted into three portfolios where the worst performing 30 percent of stocks are placed in portfolio P1, the middle performing 40 percent of stocks are placed in portfolio P2, and the best performing 30 percent are placed in portfolio P3. Momentum or the arbitrage is measured by P3 P1. Stocks are ranked over a six month period based on past performance and held for six months, skipping a month between formation periods. t-statistics in parentheses are adjusted for autocorrelation. Analyst Coverage Low High NAF1 NAF3 Portfolio NAF1 NAF2 NAF3 P (-0.93) P (3.81) P (3.55) P3-P (6.49) (4.30) (3.68) (4.38) Mean size Median size Mean analyst Median analyst

29 Table 5 Mean Portfolio Returns Sorting by Book-to-Market Ratio and Analyst Coverage Stocks are first sorted by book-to-market and then by coverage using a strategy, where the lowest covered 30 percent of stocks are in NAF1 (BE/ME1) and the highest covered stocks are in NAF3 (BE/ME3), with the middle covered 40 percent of stocks in NAF2 (BE/ME). We then use a strategy; that is, stocks are sorted into three portfolios where the worst performing 30 percent of stocks are placed in portfolio P1, the middle performing 40 percent of stocks are placed in portfolio P2, and the best performing 30 percent are placed in portfolio P3. Momentum or the arbitrage is measured by P3 P1. Stocks are ranked over a six month period based on past performance and held for six months, skipping a month between formation periods. t-statistics in parentheses are adjusted for autocorrelation. Book-to-Market Ratio Rank Analyst Coverage BE/ME1 BE/ME2 BE/ME3 BE/ME1 BE/ME3 NAF1 P3-P1= P3-P1= P3-P1= P3-P3= (5.35) (4.13) (2.27) (5.81) Mean BE/ME Ratio Median BE/ME Ratio Mean coverage Median coverage NAF2 P3-P1= P3-P1= P3-P1= P3-P1= (2.26) (2.38) (2.65) (1.28) Mean BE/ME Ratio Median BE/ME Ratio Mean coverage Median coverage NAF3 P3-P1= P3-P1= P3-P1= P3-P1= (1.93) (2.51) (2.66) (-0.06) Mean BE/ME Ratio Median BE/ME Ratio Mean coverage Median coverage NAF1 NAF3 P3-P1= (5.87) P3-P1= (3.01) P3-P1= (0.38) 29

30 Table 6 Mean Portfolio Returns Sorting by Industry Stocks are first sorted into 10 industry deciles. Industry 1 refers to financial services (IN1), Industry 2 refers to health care (IN2), Industry 3 to refers consumer non-durables (IN3), Industry 4 refers to consumer services (IN4), Industry 5 refers to consumer durables (IN5), Industry 6 refers to energy (IN6), Industry 7 refers to transportation (IN7), Industry 8 refers to technology (IN8), Industry 9 refers to basic industries (IN9), and Industry 10 refers to capital goods and utilities (IN10). We then use a strategy; that is, stocks are sorted into three portfolios where the worst performing 30 percent of stocks are placed in portfolio P1, the middle performing 40 percent of stocks are placed in portfolio P2, and the best performing 30 percent are placed in portfolio P3. Momentum or the arbitrage is measured by P3 P1. Stocks are ranked over a six month period based on past performance and held for six months, skipping a month between formation periods. t-statistics in parentheses are adjusted for autocorrelation. Industry Portfolio IN1 IN2 IN3 IN4 IN5 IN6 IN7 IN8 IN9 IN10 P P P P3-P (3.78) (0.62) (2.88) (3.14) (1.39) (0.15) (2.85) (3.13) (3.29) (2.53) 30

31 P2 P P3 P1 Mean size Median size Mean BE/ME Ratio Median BE/ME Ratio Mean analyst Median analyst

32 Table 7 Fama-MacBeth Regressions: Explaining the Cross-Section of Individual Stock Returns Table 7 contains the results of a Fama and MacBeth (1973) cross-sectional regression test on our sample of Canadian stocks. Firm returns, at time t, are regressed on a set of explanatory variables, including beta (Beta), firm size (ln(me) or the natural logarithm of the market value of the equity at time t 1), book-to-market ratio (ln(be/me) or the natural logarithm of the ratio of the matching year book value to the market value of the equity at time t-1), past returns (R_6-6), and our measure of residual analyst coverage. Newey-West adjusted t-statistics are in parentheses. Beta In (ME) In (BE/ME) R Residual _ 6: 6 Coverage (-0.80) (3.91) (7.99) (4.41) (-4.64) (5.77) (8.51) (5.50) (8.08) (3.69) (6.46) (9.39) (-6.77) (6.18) (8.93) (3.01) (-6.22) (-0.79) (5.54) (7.98) (3.71) (-6.03) 32

33 Figure 1 Momentum, Size, and Book-to-Market Monthly Average Retuns: P3 - P Deciles: 1 = Small (Low); 10 = Large (High) Size Bk-to-Mkt 33

34 Notes 1 Fama and French (1996) have shown that stock momentum is correlated with size and book-to-market variables. 2 It is important to note that firm size may capture other confounding events as well. 3 We refer to herding as a concentration of analysts. 4 We also compared stock pricing data from both I/B/E/S file and DataStream files as a robustness check. However, we do not find any inconsistencies between the two datasets. 5 We also used other market capitalization thresholds, such as C$50 million. However, the impact of increasing the size threshold had only marginal impact on momentum. 34