The relationship between size, book-to-market equity ratio, earnings–price ratio, and return for the Hong Kong stock market

Global Finance Journal 13 (2002) 163 – 179

The relationship between size, book-to-market equity ratio, earnings–price ratio, and return for the Hong Kong stock market Keith S.K. Lam* Faculty of Business Administration, University of Macau, P.O. Box 3001, Macau, SAR, China Accepted 18 January 2002

Abstract In this paper, we investigate the relation between stock returns and
, size (ME), leverage, book-tomarket equity ratio, and earnings – price ratio (E/P) in Hong Kong stock market using the Fama and French (FF) [J. Finance 47 (1992) 427] approach. FF find that two variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with
, size, leverage, book-to-market equity, and E/P ratios. In this paper, similar to previous studies in Hong Kong and US stock markets, we find that
is unable to explain the average monthly returns on stocks continuously listed in Hong Kong Stock Exchange for the period July 1984– June 1997. But three of the variables, size, book-to-market equity, and E/P ratios, seem able to capture the cross-sectional variation in average monthly returns over the period. The other two variables, book leverage and market, are also able to capture the cross-sectional variation in average monthly returns. But their effects seem to be dominated by size, book-to-market equity, and E/P ratios, and considered to be redundant in explaining average returns when size, book-to-market equity, and E/P ratios are also considered. The results are consistent across subperiods, across months, and across size groups. These suggest that the results are not driven by extreme observations or abnormal return behavior in some of the months or by size groups. D 2002 Elsevier Science Inc. All rights reserved. JEL classification: G12; G15 Keywords: CAPM;
; Book-to-market equity ratio; Earnings – price ratio; Size effect

* Tel.: +853-3974753; fax: +853-838320. E-mail address: [email protected] (K.S.K. Lam). 1044-0283/02/$ – see front matter D 2002 Elsevier Science Inc. All rights reserved. PII: S 1 0 4 4 - 0 2 8 3 ( 0 2 ) 0 0 0 4 9 - 2

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1. Introduction There are many empirical evidences against the traditional Sharpe, Lintner, and Black (SLB) CAPM model. For instance, the size effect of Banz (1981), the leverage effect of Bhandari (1988), the book-to-market ratio effect of Stattman (1980), Rosenberg, Reid, and Lanstein (1985), and Chan, Hamao, and Lakonishok (1991), and the earnings–price (E/P) ratios effect of Basu (1983). Banz (1981) finds that small size (market equity) firms have higher average returns than large size firms even after adjusted for their systematic risks. So, market equity (ME, a stock’s price times shares outstanding), adds to the explanation of the average returns. Bhandari (1988) documents that there is a positive relation between leverage and average returns in tests that include both size (ME) and
. Stattman (1980) and Rosenberg et al. (1985) find that average returns in the US stock markets are positively related to the ratio of a firm’s book value of common stock to its market value, BE/ME. Chan et al. (1991) also find a similar positive BE/ME and average returns relation in the Japan stock market. Basu (1983) finds that (E/P) ratios have additional explanation power on US stocks on top of size and
. Ball (1978) argues that E/P can serve as a proxy for unnamed factors in expected returns. The reason being that, when stocks have relatively higher risks and expected returns, their prices are likely to be lower relative to earnings and thus the E/P is likely to be higher too. Chan et al. (1991) and Daniel, Titman, and Wei (1997) find that book-to-market equity can explain the cross-sectional variation of stock returns in the Japanese market. Chui and Wei (1998) examine the relationship between expected stock returns and
, book-to-market equity, and size in five Pacific Basin emerging markets. They find that the relationship between average stock return and
is weak for all five markets. But the book-to-market equity can explain the cross-sectional variation of expected returns in Hong Kong, Korea, and Malaysia, while the size effect is significant in all five markets except Taiwan. An alternative body of test to CAPM is the arbitrage pricing theory (APT) developed by Ross (1976, 1977) and later extended by Chamberlin and Rothschild (1983), Connor (1982), Dybvig (1983), Grinlatt and Titman (1983), Huberman (1982), and Ingersoll (1984). By imposing the ‘‘no arbitrage condition’’ in equilibrium together with other assumptions, the APT states that security returns are a linear function of an unknown number of unspecified factors, not just linearly related to
, the systematic risk. There are numerous tests done on the APT using US stock data. For example, Chen (1983), Dhrymes, Friend, and Gultekin (1984, 1985), Gehr (1975), and Roll and Ross (1980) find that there are three to four factors priced in the US stock market. Hughes (1982) and Lam (1988) test the Canadian stock market and find that three to four factors significantly explain stock returns. Antoniou, Garrett, and Priestley (1998) investigate the UK stock market and find that three factors are priced. Similar to other tests, the empirical evidences from the APT tests suggest that there is more than one factor explaining returns in stock market. All of the above researches suggest that expected returns of stocks are not only explained by
, the systematic risk of stocks. A single factor model seems no longer appropriate to describe the relation between risk and return. It is also clear from the empirical evidences

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presented in the previous studies that the same story applies to the Hong Kong stock market. Since Hong Kong stock market is the second largest equity market in Asia and an important stock market in the world, it is worthwhile to examine the risk-return relation utilizing a multifactor asset pricing approach. Ball’s argument, higher risk firms with higher expected returns and lower prices, can still be applied to those variables such as size (ME), leverage, and book-to-market equity ratio. It is because these variables, size (ME), leverage, and book-to-market equity ratio, are variables that extract risk and return information from prices by scaling stock prices using different methods (Keim, 1988). Fama and French (1992) (hereafter FF, 1992) find that two variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market
, size, leverage, book-to-market equity, and E/P ratios. The purpose of this paper is to investigate the relation between stock returns and size (ME), leverage, book-to-market equity (BE/ME), and (E/P) ratio using the FF (1992) approach. Under the FF (1992) tests, we find that
is unable to explain the average returns on stocks listed in the Stock Exchange of Hong Kong (SEHK) for the period July 1984–June 1997. This is consistent with the findings of previous studies. But three of the accounting variables, size, book-to-market equity, and E/P, seem able to capture the cross-sectional variation in average returns over the period. The other two variables, book leverage and market leverage, are also able to capture the cross-sectional variation in average returns. But their effects seem to be dominated by size, book-to-market equity, and E/P, and considered to be redundant in explaining average returns when size, book-to-market equity, and E/P are also considered. The results are consistent across subperiods and across months, which suggest that the results are not driven by extreme observations or the abnormal return behavior in some of the months. This paper is organized as follows. In Section 2, we will discuss the data, methodologies, and the estimation of
. In Section 3, we will discuss the test results and the investigation of the relations between average returns and
’s, size, E/P, leverage, and book-to-market equity. In Section 4, the final section, we will summarize and conclude the chapter.

2. Data, methodologies, and estimation of b 2.1. Data and methodologies All of the data are taken from the Pacific Basin Capital Markets (PACAP) Databases compiled by the University of Rhode Island. The data set contains 100 firms continuously listed in the SEHK for the entire test period, July 1980–June 1997. Financial firms, which on average have higher leverage, are not excluded in the tests. It is because test results do not change significantly by excluding financial firms. We follow FF (1992) in defining size and explanatory variables related to accounting information. For accounting variables, we match the accounting data for all fiscal year-ends in calendar year t
1 (July 1980–June 1997) with the returns for July of year t to June of t + 1. The purpose of matching t
1 accounting variable with t to t + 1 returns is to ensure that the

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accounting variables are known before the returns they are used to explain. The minimum 6month gap between fiscal yearend and the return tests is a conservative time to allow for the release of accounting information after the fiscal year-end. In fact, most of the firms announced their financial results within this 6-month period. We use a firm’s market equity for June of year t to compute its size (ME). For accounting variables, we use a firm’s market equity at the end of December of year t
1 to compute its book-to-market, leverage, and E/P ratios for t
1. Thus, a firm must have stock price for December of year t
1 and June of year t in order to be included in the return tests for July of year t. In addition, firms must also have monthly returns for at least 18 out of the 48 months between July 1980 and June 1984 to allow for the estimation of ‘‘preranking
’’ (discussed in Section 2.2 below). Besides, firms must have data on total book assets (A), book equity (BE), and earnings (E), for its fiscal year ending in (any month of) calendar year t
1 for the estimation of explanatory variables. On top of meeting the above three criteria, firms must also need to have monthly returns for at least 78 out of the 156 months (50%) between July 1984 and June 1997 in order to be included in the data set. The purpose of the last criterion is to minimize the size and effect of missing observations. Ultimately, 100 firms meet the four selecting criteria and qualified to be included in the data set. The FF (1992) tests employ the Fama and MacBeth (1973) (hereafter FM) approach by performing cross-sectional regression on monthly returns against the explanatory variables in the following equation: Rit ¼ a þ b1t
it þ b2t lnðMEit Þ þ b3t lnðBE=MEit Þ þ b4t lnðA=BEit Þ þ b5t EðþÞ=P þ b6t E=P dummy þ eit

ð1Þ

where Rit is the return of individual stocks,
it is the preranking
(the method of estimation will be discussed in Section 2.2), ln(MEit) is natural log of the size (ME) of a firm, ln(BE/ MEit) is the natural log of a firm’s book-to-market equity ratio, ln(A/BEit) is the natural log of a firm’s book asset to market equity ratio, E(+)/P is the earnings to price ratio for positive earnings firms, E/P dummy is the dummy variable for positive and negative earnings firms with E/P dummy equals one when a firm earns negative earnings and zero when a firm earns positive earnings, and eit is the residual error of the regression. Twelve regressions (Eqs. (1) to (12)) are performed with different combinations of the variables (for details, refer to Table 3). The time-series means of the monthly regression slopes of the 156 monthly regressions (b1t to b6t) are then tested by standard t-test for their explanation power on stock returns. 2.2. Estimation of preranking and postranking
’s Portfolio
’s (preranking
’s) are estimated for portfolios and then assign the portfolio
to each stock in the portfolio as the stock’s
. Since the accounting information and variables can be measured precisely for individual stocks, there is no need to run the FM regressions using portfolios. Rather FM regressions will be run using individual stocks.

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Stocks are sorted into five portfolios by size (ME). The preranking
’s are estimated on 12–48 monthly returns in the 4 years before July of year t (July 1980–June 1984). The preranking
’s are estimated using Dimson (1979) approach as in equation below:1 Rit ¼ a þ
it
2 RMt
2 þ
it
1 RMt
1 þ
it RMt þ
itþ1 RMtþ1 þ
itþ2 RMtþ2 þ þeit

ð2Þ

where
it
j is the lag j (1 and 2) stock
and RMt
j is the lag j (1 and 2) value-weighted market return from the PACAP database. The
’s are estimated as the sum of the slopes in the regression of the return on a portfolio on the current and two lead and lag months’ market returns as in equation below:
i ¼
it
2 þ
it
1 þ
it þ
itþ1 þ
itþ2

ð3Þ

Two lead and two lag market returns are included in the regression because the first order and second order autocorrelations of the monthly market returns for the entire period, July 1980–June 1997, are significantly different from zero. They are
0.0327 (t =
4.5930) and 0.0740 (t = 10.3780), respectively. Since size and
are found to be highly correlated in the US stock market, FF (1992) investigate risk-return relation by disentangling the size and b
effect. Even though the size and
correlation in Hong Kong stock market is quite low (0.08), We still follow FF by disentangling the size and
effect as follows. To allow for variation in
that is unrelated to size, we subdivide each size decile into five portfolios by preranking
’s. Therefore, there are 25 size-
portfolios formed (a relatively smaller 5  5 portfolio size is chosen because of a relatively smaller sample size in our data set). We then calculate the equally weighted monthly returns of each portfolio for the next 12 months, from July t to June t + 1. Postranking
’s are then estimated using the equally weighted portfolio month returns computed for the full testing period from July 1984–June 1997 (156 months) using both the value-weighted and equally weighted market indexes.2 Postranking
’s are estimated using the same approach as the preranking
’s, i.e., Dimson
’s with current plus two lead and lag market returns. The postranking
is then assigned to each stock in the portfolio for use in the later FM cross-sectional regression tests. The findings are reported in Section 3.

3. Relations between returns, b’s, and other explanatory variables Table 1 shows that the range of postranking
’s is magnified by forming portfolios on size and preranking
rather than on size alone. The postranking
’s range from 1.14 for the largest size portfolio to 0.84 for the second smallest size portfolio (first column of Panel B of Table 1). The spread of the range is 0.30. However, the spread of the postranking
produced 1

We also try on the Scholes – Williams
suggested by Scholed and Williams (1977). The test results are very similar to those using the Dimson
. So, they are not reported here. 2 Since the results on using value-weighted and equally weighted market index are very similar, we only report those using value-weighted market index in this paper.

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Table 1 Average returns, postranking
’s and average size for portfolio formed on size and then
: stocks sorted on ME (down) then preranking (Dimson)
(across): July 1984 to June 1997 All

High



-2


-3


-4

Low


Panel A: Average monthly returns (%) All 2.71 2.96 Large ME 3.31 3.53 ME-2 2.97 3.36 ME-3 2.97 2.86 ME-4 2.46 2.71 ME-5 1.54 2.09

2.65 3.91 2.94 2.40 1.92 1.98

2.41 3.17 2.60 3.94 1.63 1.04

2.72 2.82 3.08 2.87 2.96 1.75

2.78 3.23 2.87 2.95 3.20 0.99

Panel B: Postranking
’s All 0.99 Large ME 1.14 ME-2 0.85 ME-3 1.07 ME-4 0.84 ME-5 1.07

1.20 1.43 0.94 1.18 1.20 1.30

1.04 1.10 1.03 1.02 0.92 1.17

0.99 1.28 1.04 1.39 0.40 0.91

1.01 1.19 0.81 1.25 0.90 0.86

0.70 0.75 0.47 0.55 0.70 1.22

Panel C: Average size (ln(ME)) All 6.83 Large ME 9.17 ME-2 7.41 ME-3 6.45 ME-4 5.70 ME-5 4.82

6.82 9.66 7.18 6.32 5.86 4.60

6.74 9.09 7.47 6.43 5.64 4.60

6.72 8.88 7.50 6.45 5.78 4.97

6.71 8.80 7.24 6.41 5.52 4.97

7.15 9.37 7.61 6.66 5.60 4.85

by any
sort by size decile is greater than the spread of the postranking
produced by size sort alone (except the second high
group). For example, the second smallest spread of the postranking
is 0.44 (1.25–0.81) of the second lowest
-size portfolio (fifth column of Panel B of Table 1), which is 47% more than the spread of the postranking
by size alone. The spread of the postranking
is 1.3 across the 25
-size portfolio (1.43–0.40) which is 4.33 times the spread obtained with size portfolios alone. Similar to FF (1992), we find two important facts worth to mention here. First, the order of the postranking
’s closely resemble those of the preranking
’s. This is an evidence, which suggests that the preranking
’s captures the ordering of the true postranking
’s. Second, the average value of size (ln(ME)) are flat across
-sorted portfolio in any size decile (Panel C of Table 1). This indicates that the size-
sort produces strong variation in postranking
’s that is unrelated to size, which allows us to separate the effect of
and size on average returns. Thus, in Hong Kong, same as those in the US, the effect of
and size on average returns can be disentangled by controlling either size or
. Table 2 presents the results on average returns, postranking
’s, and other explanatory variables on size sorted portfolio (Panel A) and preranking
sorted portfolios (Panel B). From Panel A, we can see the familiar negative size-return relation of Banz (1981), average returns vary inversely with size, is not observed in Hong Kong. The relation between average

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Table 2 Properties of portfolios formed on size or preranking (Dimson)
: July 1984 to June 1997 Large 1

2

3

4

Small 5

2.97% 0.85 7.38
3.04 0.03 3.07 0.03 0.10 20

2.97% 1.06 6.41
2.83 0.44 3.27 0.07 0.11 20

2.46% 0.83 5.60
2.82 0.58 3.41 0.15 0.11 20

1.54% 1.08 4.56
2.92 0.63 3.55 0.28 0.09 20

Panel B: Portfolios formed on preranking
Return 2.84% 2.75%
1.21 1.02 ln(ME) 6.62 6.24 ln(BE/ME)
2.85
3.20 ln(A/ME) 0.42 0.58 ln(A/BE) 3.27 3.79 E/P dummy 0.12 0.19 E(+)/P 0.10 0.10 Firms 20 20

2.57% 1.06 7.52
2.63 0.37 3.00 0.05 0.09 20

2.58% 0.88 6.69
2.89 0.07 2.96 0.04 0.11 20

2.81% 0.79 6.14
3.27 0.11 3.38 0.13 0.09 20

Panel A: Portfolios formed on size Return 3.31%
1.14 ln(ME) 9.16 ln(BE/ME)
3.21 ln(A/ME)
0.12 ln(A/BE) 3.09 E/P dummy 0.00 E(+)/P 0.08 Firms 20

returns and size is positive instead of negative. However, the relation between average returns and postranking
’s is, in general, flat. Thus, the results in Panel A suggest an insignificant risk-return relation rather than a positive risk-return relation predicted by the traditional CAPM. The insignificant risk-return result is consistent with some of the studies in Hong Kong stock market (e.g., Lam, 2000). In Panel B, average returns do not show any trend related to preranking
’s or postranking
’s. The spread of the average returns is small (0.27%, from 2.84% to 2.58%) and the returns vary randomly across the five
sorted portfolios. The evidence in Panel B shows that, if we sort portfolios by
, the negative risk-return relation in Hong Kong stock market disappears. This phenomenon can be further explained by the figures shown in Panel A of Table 1. There is an obvious positive size-return relation for each
portfolio (columns 1–6). However, there is no obvious trend for
and return when we look across the rows in Panel A of Table 1. That is, when size is controlled for, there is no obvious risk-return relation. The evidences seem to suggest that there is a positive size-return relation. But the familiar negative
-return in Hong Kong stock market disappeared when size is controlled. Table 3 presents the time-series averages of the slopes from the month-by-month FM regressions of stock returns on size, postranking
, and other explanatory variables (leverage, BE/ME, and E/P). There are 156 monthly regressions and thus 156 slopes coefficients of the explanatory variables of the regressions. The mean slope coefficients of the 156 slope

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Table 3 Average slopes (t-statistics) from monthly-by-monthly regression of stock returns on (Dimson)
, size, book-tomarket equity, leverage, and E/P: July 1984 to June 1997 Reg




(1) t p (2) t p (3) t p (4) t p (5) t p (6) t p (7) t p (8) t p (9) t p (10) t p (11) t p (12) t p

0.0017 (0.2916) (.7710)

0.0013 (0.2272) (.8205)

ln(ME)

ln(BE/ME)

ln(A/ME)

ln(A/BE)


0.0130* * (
6.9576) (.0001)

0.0096* * (22.2742) (.0001)

E/P dummy

E(+)/P

0.0486* * (26.1130) (.0001)

0.1694* * (18.0484) (.0001)

0.0507* * (26.2314) (.0001) 0.0518* * (26.6733) (.0001) 0.0521* * (27.0709) (.0001) 0.1766* * (26.5712) (.0001)

0.1694* * (17.9310) (.0001) 0.1749* * (17.7546) (.0001) 0.1766* * (17.6086) (.0001)

0.0014 (1.0086) (.2792) 0.0014 (1.0815) (.2812)
0.0046* * (
5.0542) (.0001)

0.0077* * (24.2829) (.0001) 0.0080* * (24.6540) (.0001) 0.0080* * (24.7577) (.0001) 0.0081* * (24.3867) (.0001) 0.0084* * (24.7309) (.0001)

0.0089* * (21.9940) (.0001) 0.0157* * (23.6281) (.0001)

0.0095* * (22.5369) (.0001)

0.0094* * (23.2549) (.0001) 0.0164* * (23.9580) (.0001) 0.0094* * (23.4719) (.0001)

0.0099* * (23.6166) (.0001) 0.0497* *

(17.8550) (.0001)

** Significant at 1% level.

coefficients are then tests for their explanatory power on average returns by performing standard t tests. Same as the results in Tables 1 and 2, the results in Table 3 show that postranking
’s have no explanatory power on stock returns for the period July 1984–June 1997. The result is also consistent with the test results of the traditional CAPM tests using monthly returns. The

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Table 4 Overall and average monthly correlation matrix between variables for the period July 1984 to December 1997 (Dimson
) ln(ME)

ln(A/ME)

ln(A/BE)

E/P

Panel A: Overall correlation matrix of variables ln(ME) 1.00 .08
.19
1.00 .02 ln(BE/ME) 1.00 ln(A/ME) 1.00 ln(A/BE) E/P


.31 .10 .39 .20 1.00

.01 .04
.82 .18
.11 1.00


.03 .01 .21

Panel B: Average monthly correlation matrix of variables ln(ME) 1.00 .09
.08
1.00 .01 ln(BE/ME) 1.00 ln(A/ME) 1.00 ln(A/BE) E/P


.33 .11 .39 .20 1.00


.12 .05
.82 .19
.17 1.00

.00 .00 .27




ln(BE/ME)

average slope coefficient of
in regression (1) is 0.0017 per month with an insignificant t-statistic of 0.2916. Size (ln(ME)) is also insignificantly related to average returns. The average slope from the monthly regressions of returns on size alone (regression (2)) is 0.0014 with a t-statistic of 1.0086. Size and average returns are still insignificantly related even when
’s are included in the regressions (regression (3)). The insignificant size-return result is contradictory to the findings in the US stock market done by Lakonishok and Shapiro (1986). The book-to-market variable, ln(BE/ME), shows significant explanatory power on stock returns. If stock returns are regressed on the ln(BE/ME) (regression (4)), the average monthly coefficient of the regressions is
0.0046 with a significant t-statistic of
5.50542. The relation between the ln(BE/ME) and monthly stock returns is strongly negative. The ln(BE/ ME) and return relation turns to positive when size and E/P are included in the regressions (regressions (7), (10), and (12)). The signs of the coefficients change because ln(BE/ME) and size are negatively correlated (see Table 4).3

3 In addition to simple multiple regressions, stepwise regressions are also run on data of Table 3. All three types of stepwise regressions, the all-possible, forward, and backward stepwise regressions, are used in the tests. The stepwise regressions are done on both monthly and whole sample data. The R2 and Cp (total mean squared error) criteria are used to find the ‘‘best’’ regression model for the all-possible model. The results of the stepwise regressions show that the best models include all seven variables. One exception is the backward stepwise regression, which excludes
in the best model. The coefficients of the variables are all significant at 5% level. Besides, the magnitudes of the coefficients of the variables are similar to those presented in Table 3. In general, the stepwise regression, an approach to capture the maximum explanatory power of equation on p. 5, supports and reconfirms the results of the simple multiple regression approach used in Table 3.

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But the book-to-market effect is not strong enough to replace the size effect. The coefficient of size remains strongly significantly (t = 21.9940) even when book-to-market equity is included in the regression (regression (7)). Table 5 (Panel A) presents the average returns formed on ranked value of BE/ME. The relation between BE/ME and return is negative with a spread of 2.24% per month for the largest (4.12%) and the smallest portfolios (1.88%). The spread is larger that the spread of return between largest and smallest size sorted portfolios in Table 2 (Panel A) (1.77% per month). The sign of the slope coefficient of size remains positive when ln(BE/ME) is included in the regression (regression (7)). The correlation and the average monthly correlation between size and ln(BE/ME) are both negative (
0.19, Panel A, and
0.08, Panel B of Table 4). It is this negative correlation that change the sign of the average ln(BE/ME) coefficient when both variables are included in the regression. However, the correlation is not high enough to cause one effect to dominate the other. There are a few firms which have negative BE. We exclude them from all the regressions. The returns for the negative BE firms, like those of the high BE/ME firms, are high. Negative BE and high BE/ME firms are both signals of poor earning prospects. For negative BE and high BE/ME firms, prices will fall due to poor earnings performance and thus returns will be Table 5 Properties of portfolios formed on book-to-market equity (BE/ME) and earnings – price ratio (E/P): July 1984 to June 1997 Panel A: Stocks sorted on book-to-market equity (BE/ME) Return
(Dimson)
(SW) ln(ME) ln(BE/ME) ln(A/ME) ln(A/BE) E/P dummy E(+)/P Firms

Large 1

2

3

4

Small 5

2.43% 0.99 0.86 5.50
0.74 0.95 1.69 0.16 0.13 17

1.88% 1.01 0.88 6.49
2.34 0.44 2.78 0.06 0.12 19

2.02% 1.00 0.84 6.91
2.88 0.33 3.21 0.04 0.11 21

2.87% 0.98 0.83 7.23
3.39 0.12 3.51 0.07 0.08 22

4.12% 0.98 0.87 6.83
4.92
0.14 4.78 0.21 0.05 21

Panel B: Stocks sorted on earnings – price ratio (E/P) Return
(Dimson)
(SW) ln(ME) ln(BE/ME) ln(A/ME) ln(A/BE) E/P dummy E(+)/P Firms

0

High 1

2

3

4

Low 5

4.04% 1.03 0.93 4.97
3.48 0.63 4.11 1.00 0.00 11

0.25% 0.97 0.83 6.03
2.18 0.78 2.96 0.00 0.28 15

1.40% 0.99 0.83 6.72
2.39 0.46 2.84 0.00 0.12 17

2.20% 1.00 0.85 7.35
2.83 0.24 3.07 0.00 0.09 19

3.49% 1.01 0.86 7.34
3.14 0.07 3.21 0.00 0.06 19

4.78% 0.96 0.85 6.61
3.78
0.07 3.71 0.00 0.02 19

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high. Thus, the positive BE/ME-return relation (high return due to low stock price for high BE/ME firms) is consistent with the hypothesis that book-to-market equity captures crosssectional variation in average returns that is related to relative distress. In order to gain more insight into the relation between book-to-market equity and average return, we use two leverage variables, ln(A/BE) and ln(A/ME), as a replacement of ln(BE/ ME) in the regressions. The ln(A/BE) variable, the ratio of book assets to book equity, is taken to be a measure of book leverage. Where as the ln(A/ME) variable, the ratio of book assets to market equity, is taken to be a measure of market leverage. The natural logs of the leverage ratios are used for two reasons. First, it is believe that, especially in the US market, logs are a good function form for capturing leverage effects in average returns (FF, 1992). Second, using natural logs enable us to easily interpret the relation between the roles of leverage and book-to-market equity in average returns. In fact, the different between the natural log of market and book leverage is exactly equal to the book-tomarket equity (ln(A/ME)
ln(A/BE) = ln(BE/ME)). Both the leverage variables, ln(A/BE) and ln(A/ME), show significant explanatory power on stock returns. The average monthly slope coefficients of the regressions of stock returns on leverage variables (regression (5)) are significant and they are
0.0130 and 0.0096 with t-statistic of
6.9576 and 22.2742, respectively. The different between the two leverage ratios (ln(A/ME)
ln(A/BE)) is
0.0034, which is very close to the value of the monthly slope coefficient of ln(BE/ME) (
0.0046). The evidence shows that the different between the market and book leverages, which is the bookto-market equity, helps to explain the average returns. Thus, we can interpret the results in two ways. First, the average returns can be explained by the book-to-market equity, BE/ME, which is a distress effect. Second, the average returns can be explained by a leverage effect, which is captured by the different between market leverage and book leverage. Finally, the E/P and the E/P dummy (represents the negative earnings and E/P firms) variables are also strong and positively related to stock returns. The average monthly slope coefficients of the regression (6) of stock returns on the E/P and the E/P dummy are 0.0486 and 0.1694 with t-statistic of 26.1130 and 18.0484, respectively. The positive E/P-return relation is consistent with Ball’s (1978) argument that E/P ratio is positively related to returns. He argues that if current earnings proxy for future earnings, highrisk stocks with high-expected returns will have low prices relative to their earnings. Since the argument is only valid for firms with positive earnings, the slope coefficient of E/P is thus for positive earnings firms only. The negative earnings firms are represented by a dummy variable (E/P dummy). Both average monthly slope coefficients are strongly positive with a value of 0.0486 (t = 26.1130) and 0.1694 (t = 18.0484), respectively. Adding either size, or size and book-to-market equity, or leverages, or size and leverages to the regressions does not affect the positive significant effect of E/P on average returns. Besides, our findings are against the evidence provided by FF (1992), which find that the effect of size is negative throughout all regressions. Rather, we find that the effect of size is positive throughout all regressions. The result on the change of sign on average monthly slope coefficient of ln(BE/ME) when other explanatory variables are included in the regressions seems to suggest that those

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variables, especially size and E/P, can proxy for book-to-market equity. To check where book-to-market equity is dominated by size and E/P, we further perform regressions on average stocks with book-to-market equity, E/P, and E/P dummy (regression (12)). The magnitude of the slope coefficients of size, book-to-market equity, and E/P are very close with or without size or book-to-market equity variable included in the regressions ((9), (10), and (12)). Thus, there is not enough evidence to suggest that either size and E/P dominates book-to-market equity or size and book-to-market equity dominates E/P. In general, we find that
has no explanatory power on average returns. The results are similar to those of FF (1992). FF (1992) suggests two possible explanations for the poor performance of
in their paper. The first possible explanation is the high correlation between
and other explanatory variables which obscures the relation between average returns and
. The second possible reason is the noise, the measure error, in the
estimates, which obscures the
-return relation. For the first possible explanation, we can find the answer by investigating the correlation matrix presented in Table 4. Both the overall correlations (Panel A) and the average monthly cross-sectional correlations (Panel B) between
and the other explanatory variables, which is the average of the full period monthly correlation of variables, are low. The correlation between ln(BE/ME) and the leverage ratios are expected to be high because the latter ratios are the proxy for the former variable. Besides ln(BE/ME) and the leverage ratios, the largest correlation is in the average monthly correlation matrix between size (ln(ME)) and market leverage (ln(A/ME)) (Panel B) with a value of
0.33. The smallest correlation is also in the average monthly correlation matrix between (i) size and E/P and (ii)
and E/P both with a value of zero. These correlation values are considered to be small. Thus, the explanatory power of
does not seem to be obscured by its high correlation with other explanatory variables. For the second possible explanation, the noise problem, we can investigate Tables 1 and 2. In Table 1, we can see that most of the postranking
in each size decile follows the order of the preranking
. Besides, from Table 2, we also notice that the preranking
also closely follows the order of the postranking
. We take this as an evidence that postranking
’s are informative of the preranking
’s and the measurement error in
estimation is low. In addition, we can also examine the precision of the estimation of the postranking
’s for the full thirteen years period (July 1984–June 1997). All of the postranking
’s are significant at the 5% significant level ( F-statistics range from 9.3540 to 224.3620). These evidences suggest that the noise problem in postranking
estimation is very insignificant. After discussing the possible explanations for the poor performance of
in explaining returns, we can then summarize the empirical findings on the FF (1992) tests. First, there is no significant relation between
and return when either size or
is controlled. Second, the significant roles of market and book leverages in average returns are captured well by the book-to-market equity variable. Third, average return seems can be explained by the combination of size, book-to-market equity, and E/P variables. To check whether the results are driven by extreme observations of some of the subperiods, we subdivide the data into two roughly equal subperiods, July 1984–December 1990 and January 1991–June 1997, and perform tests on these two subperiods. We do five regressions

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on average returns against different explanatory variables. The five regressions to regress average return on namely (i) ln(ME) and ln(BE/ME); (ii)
, ln(ME), and ln(BE/ME); (iii) ln(BE/ME), E/P, and E/P dummy; (iv) ln(ME), E/P, and E/P dummy; and (v) ln(ME), ln(BE/ ME), E/P, and E/P dummy. The regression results are presented in Table 6. All the coefficients for regressions (i) to (v) are significant at the 5% level except three of the intercept terms. The magnitude of the coefficients do not change significant over subperiods with magnitude on the E/P and E/P dummy coefficients much higher than the

Table 6 Subperiod average monthly returns on SEHK value-weighted and subperiod means of intercepts and slopes from the monthly FM cross-sectional regressions of returns on (i) size (ln(ME)) and book-to-market equity (ln(BE/ ME)); (ii) (Dimson)
, ln(ME), and ln(BE/ME); (iii) ln(ME), E/P, and E/P dummy; (iv) ln(ME), E/P, and E/P dummy; and (v) ln(ME), ln(BE/ME), E/P, and E/P dummy 7/84 – 6/97 (156 obs.)

7/84 – 12/90 (78 obs.)

1/91 – 12/97 (78 obs.)

Mean

Mean

S.D.

t(mean)

S.D.

t(mean)

Mean

S.D.

t(mean)

0.1467 0.0045 0.0060

1.5586 17.1826* * 15.7659* *


0.0138 0.0065 0.0071

0.1121 0.0029 0.0031


1.0843 20.1304* * 20.3060* *

(ii) Rit = a + b1t
it + b2tln(MEit) + b3tln(BE/MEit) + eit a 0.0050 0.1314 0.4791 0.0260 0.1479 b1 0.0456 0.0247 23.0846* * 0.0530 0.0292 b2 0.0077 0.0040 24.2439* * 0.0088 0.0045 b3 0.0089 0.0050 22.0404* * 0.0106 0.0059

1.5516 16.0697* * 17.1573* * 15.8429* *


0.0159 0.0381 0.0065 0.0071

0.1096 0.0162 0.0029 0.0031


1.2807 20.8272* * 20.1024* * 20.3059* *

(iii) a b3 b4 b5

Rit = a + b3tln(BE/MEit) + b4tE(+)/P + b5tE/P dummy + eit 0.0280 0.0884 3.9560* * 0.0301 0.0986 2.7000 0.0094 0.0050 23.4719* * 0.0108 0.0059 16.2288* * 0.1756 0.1229 17.8550* * 0.1919 0.1138 14.8939* * 0.0497 0.0234 26.5712* * 0.0559 0.0263 18.7911* *

0.0259 0.0080 0.1594 0.0435

0.0775 0.0034 0.1300 0.0182

2.9477 * 20.5008* * 10.8269* * 21.1259* *

(iv) a b2 b4 b5

Rit = a + b2t ln(MEit) + b4tE(+)/P + b5tE/P dummy + eit 0.0268 0.1411 2.3708 * 0.0456 0.1580 0.0080 0.0040 24.7577* * 0.0091 0.0046 0.1694 0.1180 17.9310* * 0.1893 0.1128 0.0507 0.0241 26.2314* * 0.0581 0.0269

0.0080 0.0068 0.1496 0.0432

0.1199 0.0030 0.1204 0.0184

0.5870 20.1166* * 10.9686* * 20.7795* *

0.0026 0.0068 0.0079 0.1577 0.0448

0.1256 0.0030 0.0034 0.1296 0.0188

0.1824 20.1857* * 20.2825* * 10.7473* * 21.1126* *

(i) Rit = a + b2tln(MEit) + b3tln(BE/MEit) + eit a 0.0061 0.1316 0.5749 0.0259 b2 0.0077 0.0039 24.2829* * 0.0088 b3 0.0089 0.0050 21.9940* * 0.0106

(v) Rit = a + b2t a 0.0189 b2 0.0081 b3 0.0094 b4 0.1749 b5 0.0518

2.5478 * 17.6460* * 14.8141* * 19.1177* *

ln(MEit)+ + b3tln(BE/MEit) + b4tE(+)/P + b5tE/P dummy + eit 0.1373 1.7185 0.0352 0.1471 2.1125 * 0.0041 24.3867* * 0.0093 0.0047 17.3924* * 0.0050 23.2549* * 0.0108 0.0059 16.2418* * 0.1231 17.7546* * 0.1922 0.1144 14.8341* * 0.0243 26.6733* * 0.0587 0.0271 19.1480* *

* Significant at 5% level. * * Significant at 1% level.

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Table 7 Monthly average slope on regression (i) and (v) of Table 6 (Dimson
) (a) Monthly average slope on regression: (i) Rit = a + b2tln(MEit) + b3tln(BE/MEit) + eit (i) July 1984 – June 1997 January February ln(ME) 0.0021 0.0019 ln(BE/ME) 0.0025 0.0022

ln(ME) ln(BE/ME)

July 0.0025 0.0029

March 0.0018 0.0021

April 0.0022 0.0025

May 0.0025 0.0030

June 0.0024 0.0028

September 0.0030 0.0034

October 0.0036 0.0041

November 0.0025 0.0029

December 0.0030 0.0035

March 0.0033 0.0040

April 0.0040 0.0048

May 0.0039 0.0047

June 0.0043 0.0051

August 0.0049 0.0056

September 0.0058 0.0066

October 0.0068 0.0076

November 0.0042 0.0048

December 0.0040 0.0046

1997 February 0.0026 0.0028

March 0.0022 0.0023

April 0.0025 0.0027

May 0.0035 0.0038

June 0.0031 0.0033

August 0.0024 0.0027

September 0.0023 0.0026

October 0.0033 0.0037

November 0.0033 0.0037

December 0.0048 0.0054

August 0.0026 0.0030

(ii) July 1984 – December 1990 January February ln(ME) 0.0033 0.0032 ln(BE/ME) 0.0040 0.0038

ln(ME) ln(BE/ME)

July 0.0042 0.0047

(iii) January 1991 – June January ln(ME) 0.0030 ln(BE/ME) 0.0033

ln(ME) ln(BE/ME)

July 0.0029 0.0033

(Non – January) February – December 0.0025 0.0029

(Non – January) February – December 0.0044 0.0051

(Non – January) February – December 0.0030 0.0033

(b) Monthly average slope on regression: (v) Rit = a + b2tln(MEit) + b3tln(BE/MEit) + b4tE(+)/P + b5tE/P dummy + eit (i) July 1984 – June 1997 January February E/P 0.0294 0.0334 ln(BE/ME) 0.0026 0.0023 ln(ME) 0.0022 0.0128

E/P ln(BE/ME) ln(ME)

July 0.0384 0.0030 0.0027

August 0.0381 0.0031 0.0027

(ii) July 1984 – December 1990 January February E/P 0.0586 0.0664 ln(BE/ME) 0.0040 0.0039 ln(ME) 0.0036 0.0034

March 0.0315 0.0022 0.0019

April 0.0369 0.0026 0.0023

May 0.0339 0.0030 0.0027

June 0.0311 0.0029 0.0026

September 0.0429 0.0035 0.0031

October 0.0512 0.0042 0.0038

November 0.0361 0.0030 0.0027

December 0.0399 0.0036 0.0031

March 0.0719 0.0040 0.0036

April 0.0956 0.0049 0.0043

May 0.0979 0.0048 0.0041

June 0.0970 0.0052 0.0045

(Non – January) February – December 0.0376 0.0030 0.0027

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Table 7 (continued) (b) Monthly average slope on regression: (v) Rit = a + b2tln(MEit) + b3tln(BE/MEit) + b4tE(+)/P + b5tE/P dummy + eit (ii) July 1984 – December 1990 July August E/P 0.0818 0.0947 ln(BE/ME) 0.0048 0.0056 ln(ME) 0.0044 0.0051

September 0.1111 0.0067 0.0061

October 0.1348 0.0077 0.0073

November 0.0823 0.0048 0.0045

December 0.0774 0.0046 0.0043

(iii) December 1991 – June 1997 January February E/P 0.0346 0.0386 ln(BE/ME) 0.0034 0.0030 ln(ME) 0.0031 0.0027

March 0.0318 0.0025 0.0023

April 0.0354 0.0029 0.0026

May 0.0364 0.0040 0.0037

June 0.0307 0.0035 0.0032

September 0.0263 0.0027 0.0024

October 0.0373 0.0039 0.0034

November 0.0363 0.0039 0.0034

December 0.0495 0.0057 0.0050

E/P ln(BE/ME) ln(ME)

July 0.0353 0.0034 0.0031

August 0.0282 0.0029 0.0025

(Non – January) February – December 0.0919 0.0052 0.0047

(Non – January) February – December 0.0351 0.0035 0.0031

other coefficients. The results confirm that our previous results are consistent across subperiods and are not driven by any one of the two subperiods. We further check whether the results are driven by abnormal behavior of some of the months in the sample period. We calculate the average monthly slope coefficients of regression (i) and (v) of Table 6 and present the results in Table 7. All the average monthly coefficients, ln(ME), ln(BE/ME), and E/P, are significant at the 5% level. It seems that, in October of subperiod 1 and in December of subperiod 2, the average monthly slope coefficients are slightly higher than the overall average slope coefficients across all variables. But since all the slope coefficients are highly significant and the October and December magnitudes are not too high, the results do not seem to suggest that the FF (1992) test results are driven by the abnormal figures of some of the months (e.g., January) in the sample period. Finally, we check whether the results are driven by the well-known January and size effect. We run the regressions in Table 3 by months and size groups and compare the results between January and non-January and among the five size groups. We find that, despite some slight variations on the magnitude of the coefficients, the signs of the coefficients of all regressions are the same. It implies that the test results are not driven by January or firm size.

4. Summary and conclusions In general,
seems not able to explain the average returns on SEHK stocks for the period July 1984–June 1997. This is consistent with the findings of the previous studies. However, three accounting variables, size, book-to-market equity, and E/P ratios, seem able to capture the cross-sectional variation in average returns over the period. Other variables, book and

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market leverage, seem also able to capture the cross-sectional variation in average returns but their effects are dominated by size, book-to-market equity and E/P ratios and thus regarded to be redundant. It seems that a three factor model, ln(ME), ln(BE/ME), and E/P, is more appropriate for the description of asset pricing behavior in Hong Kong stock market. If our three factor model is correct, size, book-to-market equity, and E/P ratios can serve as proxy for risk. There are at least two practical implications for our three-factor model. The model can be used as benchmark portfolio for portfolio performance evaluation by investors and fund managers. Investors and fund managers can evaluate their portfolios by comparing their portfolio returns to the benchmark model with similar size, book-to-market equity, and E/P characteristics. If their portfolio returns are higher than the benchmark, they are able to outperform and beat the market. If not, they are then outperformed and beaten by the market. Second, investors and firms can estimate a better and more precise b as their cost of capital to serve as their discounting rate in calculating net present value of their investments.

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