Analysis Of Common Risk Factors In The Returns

Published Date: 02 Nov 2017

ABSTRACT

This research study investigates the validity of Fama-French three-factor model of stock returns for Tel Aviv Stock Exchange (TASE), Israel. Further, the research identifies three common risk factors in returns on stocks: an overall market factor, a factor related to firm size, and a factor related to book-to-market equity.

Empirical results show indications of pervasive market, size, and book-to-market factors in TASE stock returns. Thus, in the context of TASE, empirical results establish that the amount of variance in the average cross-sectional returns, explained by these three factors (market, size, and value), is comparatively more than the amount of variance explained by the market factor alone. Thus, we conclude that the empirical results in this research are reasonably consistent with the Fama-French 3-factor model.

INTRODUCTION

Capital Asset Pricing Model (CAPM) is used in pricing of risky securities. It is a cross-sectional relationship between mean excess returns and exposures to the market factor [Connor and Sehgal (2001)]. However, Fama and French (1992) observed that the cross-section of average returns on US common stocks had little relation to either the market s of the asset pricing model [Sharpe (1964); Lintner (1965)] or the consumption s of the inter-temporal asset-pricing model [Breeden (1979); Reinganum (1981); Breeden, Gibbons, and Litzenberger (1989)]. In subsequent studies Fama and French empirically showed that variables that have no special standing in asset-pricing theory show reliable power to explain the cross-section of average returns. Some of the most commonly used average-return variables include: size (stock price times number of shares (ME)), leverage, earnings/price ratio (E/P), and book-to-market equity (the ratio of the book value of a firm's common stock, BE, to its market value, ME) [Banz (1981); Bhandari (1988); Basu (1983); and Rosenberg, Reid, and Lanstein (1985)].

Fama and French (1992a) analyzed the joint roles of market  (the slope in the regression of a stock's return on a market return), size, E/P (earnings-price ratio), leverage, and book-to-market equity in the cross-section of average stock returns. They empirically established that , used alone or in combination with other variables, contained little information about the average returns. However, they observed that when used alone, size, E/P, leverage, and book-to-market equity have explanatory power. Further research studies indicated that among these variables, size (ME) and book-to-market equity (BE/ME), when used in combinations, showed to absorb the apparent roles of leverage and E/P in average returns.

In context of NYSE, AMEX, and NASDAQ, Fama-French (1992a) empirically established that size and book-to-market equity are significant in explaining the cross-section of average stock returns. Fama and French (1993) argued that systematic differences in average returns for rationally priced stocks should be due to differences in risk. This was confirmed by constructing portfolios to mimic risk factors related to market, size, and value, which significantly explained random returns from well-diversified stock portfolios. Finally, it was observed that under rational pricing assumptions, the market, size, and value factors proxy for sensitivity to pervasive risk factors in returns.

In this research we use time-series regressions approach [Black, Jensen, and Scholes (1972)] to regress monthly stock returns on market portfolio returns while mimicking risk factors related to size and book-to-market equity (BE/ME). The slopes of the time-series regression are factor loadings that, unlike size or BE/ME, have a clear interpretation as risk-factor sensitivities for stock returns. Time-series regressions approach is used in this research to address two important asset-pricing issues. Firstly, if assets are priced rationally, variables that are related to average returns, such as size and book-to-market equity, must proxy for sensitivity to common risk factors in returns. Secondly, the excess stock returns (monthly stock returns minus the 91-days T-bill’s implied yield) are used as dependent variables and excess market returns as explanatory variables. In such regressions, a well-specified asset-pricing model produces intercepts that are indistinguishable from 0 [Merton (1973)]. Therefore, the estimated intercepts provide a simple return metric and a formal test of how well different combinations of the common factors capture the cross-section of average returns.

DATA

The explanatory variables in the time-series regressions include excess returns on a market portfolio of stocks and mimicking portfolios for the size, and book-to-market factors in returns. The returns to be explained are for 25 stock portfolios formed on the basis of size and book-to-market equity.

The Sample Securities

This research is based on a sample of 265 stocks that are actively traded on Tel-Aviv Stock Exchange (TASE), Israel’s only stock exchange. TASE fulfils a major role in the Israeli economy and is a key player in the nation’s economic growth. TASE lists some 622 companies, about 60 of which are also listed on stock exchanges in other countries. In addition, it lists some 180 exchange-traded funds (ETFs), 60 government bonds, 500 corporate bonds, and more than 1000 mutual funds.

Our share price data consists of month-end adjusted share prices of 265 companies from July 2004 to June 2012. The price data has been adjusted for capitalization changes such as bonus rights and stock splits. The adjusted share price series has been converted into return series using arithmetic returns. The return calculations have been done using the capital gain component only and we have not used the data on dividends. However, over our sample period, dividend yields on Israel’s stocks were very small. Equity capital was released to shareholders mostly through cash-based acquisitions, or reinvested. We believe that the exclusion of dividends from the return calculations has no marked effect on our results or conclusions there from.

Risk-free Proxy

The implied yield on the month-end auction of 91-days treasury bills (T-bills) has been used as a risk-free proxy. The data related to implied yield on month-end auction of 91-days T-bill (also known as Makam in Israel) is obtained from Bloomberg’s financial database.

Company Attributes

The accounting information has been obtained for the sample companies for the financial years 2003 to 2011. Generally, the financial year and calendar year for companies listed in Israel is same, from January of year t to December of year t. The book value per share and number of shares outstanding for the sample companies are recorded in June-end of each year. The data source is Bloomberg, a provider of financial statement related information for companies worldwide. The accounting information combined with share price data has been used to construct measures of size and value employed in the study, as discussed in the next section. Additionally annual profit information measured as Profit before Depreciation and Taxes (PBDT) has been collected for the sample companies for the financial years 2003 to 2011. The choice of profit figure has been guided by the fact that PBDT figures are seldom negative, making them amenable for growth rate calculations. The earnings information is used in a latter section to explore the economic foundation for common risk factors in stock returns.

TESTS OF THE CAPM, FAMA-FRENCH MODEL, AND VARIANTS

The Size and Value Sorted Portfolios

In order to study the economic fundamentals, French and Fama (1992b) use six portfolios formed from sorts of stocks on ME (size factor) and BE/ME (value factor). We use the same six portfolios formed from sorts of stocks on ME and BE/ME to ensures a correspondence between the study of common risk factors in returns carried out here and the complementary study of economic fundamentals by Fama and French (1992a). The six portfolios are meant to mimic the underlying risk factors in returns related to size and value factors.

The decision to sort firms into three groups on BE/ME and only two on ME follows the evidence in Fama and French (1992a) that book-to-market equity has a stronger role in average stock returns than size. The splits are arbitrary, however, and we have not searched over alternatives. The hope is that the tests here and in Fama and French (1992b) are not sensitive to these choices. We see no reasons to argue that they are.

We construct six portfolios (S/L, S/M, S/H, B/L, B/M, B/H) from the intersection of the two size and three BE/ME groups. For example S/L portfolio contains stocks that are in the small size group and also in the low BE/ME group while B/H consists of big size stocks that also have high BE/ME ratios. In June of each year t from 2004 to 2011, all the sample stocks are ranked on the basis of size (price time shares). The median sample size is then used to split the sample companies into two groups: small (S) and big (B). Although the two groups contain equal number of stocks, the smaller group has just about 2.22% (in 2012) of the combined market value of the two size groups. We also break the sampled stock into three book-to-market equity groups based on the breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of BE/ME for TASE stocks. Book equity to market equity (BE/ME) for year t is calculated by dividing book equity at the end of financial year t - 1 by market equity at the end of financial year t – 1 (financial year closing in Israel is December). We do not use negative BE firms when calculating the break even points for BE/ME or when forming size-BE/ME portfolios. In addition, only firms with ordinary common equity (as classified by CRSP) are included in the tests. This means that ADRs, REITs, and units of beneficial interest are excluded.

Monthly equally-weighted returns on the six portfolios are calculated from t July of year t to June of year t+1, and the portfolios are re-formed in June of year t+1. The returns are calculated from July of year t to ensure that book equity for year t-1 is known. The six size-BE/ME portfolios are constructed to be equally-weighted, as suggested by Lakonishok, Shliefer and Vishny (1994). Fama and French (1996) documents that three factor model does a better job in explaining LSV for equally-weighted portfolios as compared with value-weighted portfolios. To be included in the tests, a firm must have CRSP stock prices for December of year t-1 and June of year t and book common equity for year t-1. Moreover, to avoid the survival bias we do not include firms which do not have at least two years data.

The Factor Portfolios

The Fama-French model involves the use of three factors for explaining common stock returns: the market factor (market index return minus risk-free return) proposed by the CAPM, the size factor and the value factor.

Our proxy for the market factor in stock returns is the excess market returns (RM-RF), where RM is the return on equally-weighted portfolio of the stocks in the six size-BE/ME portfolios plus the negative-BE stocks excluded from the portfolio and RF is the implied yield on the month-end auction of 91-days T-bills.

SMB (Small minus Big) is meant to mimic the risk factor in returns related to size. SMB is the difference each month between the simple average of the returns of the three small stock portfolios (S/L, S/M and S/H) and the average of the returns on the three big portfolios (B/L, B/M, B/H). It is the difference between the returns on small and big stock portfolios with about the same weighted-average BE/ME. Hence, SMB is largely clear of BE/ME effects, focused on the different behavior of small and big stocks.

HML (High minus Low) is meant to mimic the risk factor in returns related to value (that is book-to-market ratios). HML is the difference each month between the simple average of the returns on two high BE/ME portfolios (S/H and B/H) and the average returns on two low BE/ME portfolios (S/L and B/L); it is constructed to be relatively free of the size effect.

Explaining Common Variation in Returns with the Factor Portfolios

In this research we use the standard multivariate regression framework [Campbell et. al. (1997)] to test the Fama-French model in the context of Israel’s Stock Exchange. We estimate the following multivariate regression systems:

Hererepresent the excess returns to the portfolio j in month t,represent the excess returns to the market portfolio,represent the returns to the size portfolio, andrepresent the returns to the value portfolio. are the market, size, and value factor exposures of portfolio j,is the abnormal mean return of portfolio j, which equals zero under the hypothesized pricing model, andis the mean-zero asset-specific return of portfolio j. In this research we have also estimated and tested some variants of the French-Fama model by forcing some of the coefficients to be zero, i.e., excluding the variables from the regression model (1). In particular, we can restrictfor all j to estimate and test the Sharpe-Linter CAPM (model (3)).

EMPIRICAL ANALYSIS

The results in Table 1 to Table 5 summarize the empirical findings of this research on applicability of Fama-French 3-factor model in the context of Israeli stock market. The average excess returns on the portfolios that serve as dependent variables gives perspective on the range of average returns that different set of risk factors must explain. The average returns on the explanatory portfolios are the average premiums per unit of risk (regression slope) for the candidate common risk factors in returns.

Descriptive Statistics on the Return Series

In this research we use portfolios formed on size and BE/ME to determine if the mimicking portfolios, SMB and HML, are capable of capturing common factors in stock returns related to size and book-to-market equity. In addition, portfolios formed on size and BE/ME will produce a wide range of average returns that needs to be explained by competing asset-pricing equations [Fama and French, 1992a]. Later, in the diagnostics section, we use portfolios formed on E/P and D/P, variables that are also informative about average returns, to check the robustness of our results on the ability of our explanatory factors to capture the cross-section of average returns.

This research uses excess returns on 25 stock portfolios, formed on size and book-to-market equity, as dependent variables in the time-series regressions. The 25 size-BE/ME portfolios are formed much like the six size-BE/ME portfolios discussed earlier. In June of each year t we sort the sampled stocks by size and (independently) by book-to-market equity. For the size sort, ME is measured at the end of June. For the book-to-market sort, BE and ME is market equity at the end of December of t-1. We construct 25 portfolios from the intersections of the size and BE/ME quintiles and calculate equally-weighted monthly returns on the portfolios from July of t to June of t+1. The excess returns on these 25 portfolios for July 2004 to June 2012 are the dependent variables for stocks in the time-series regressions.

The results in Table 1 show that the number of firms (aggregating firms across all financial years) in each size quintile varies considerably. On an average, the smallest size quintile has 61 firms and the largest size quintile has 78 firms during each financial year. On the other hand, it is observed that there is no considerable difference in the average number of firms during each financial year within each BE/ME quintile. On an average, there are 70 firms during each financial year in the smallest and the largest BE/ME quintiles.

Each of the five portfolios in the smallest size quintile is less than 0.1% of the combined value of stocks in the 25 portfolios. In contrast, the portfolios in the largest size quintile have the largest fractions of value. Together, the five portfolios in the largest size quintile account for about 91.9% of combined value of stocks in the 25 portfolios. The portfolio of stocks in the largest size and lowest BE/ME quintiles (big successful firms) alone accounts for more than 71% of the combined value of the 25 portfolios. In addition, Table 1 shows that in the largest size quintile, both the number of stocks and the proportion of total value (of 25 stock portfolios) accounted for by a portfolio decrease from lower to higher BE/ME portfolios. Further, the results in Table 1 summarize the descriptive statistics for the 25 size-value sorted portfolios, E/P sorted portfolios, and D/P sorted portfolios.

The Dependent Returns

The 25 stock portfolios formed on size and book-to-market equity produce a wide range of average excess returns, from -3.632% to 1.747% per month. Fama-French (1992a) observed that there is a negative relation between size and average returns, and there is a strong positive relation between average returns and book-to-market equity. In context of stocks traded on TASE this observation was strongly confirmed. The average returns on largest BE/ME-quintile portfolios are comparatively higher than the average returns on the smallest BE/ME-quintile portfolios, irrespective of the size-quintile. On the other hand, the average returns on the smallest size-quintile are comparatively higher than the average returns on the largest size-quintile, irrespective of the BE/ME-quintile. However, within each size quintile, the average returns does not show any significant relationship with BE/ME. Thus, overall average returns across different BE/ME-quintiles show an increasing trend and the overall average returns across different size-quintiles show a decreasing trend.

The wide range of average returns on the 25 stock portfolios, and the size and book-to-market effects in average returns, present interesting challenges for competing sets of risk factors. The time-series regression analysis used in this research attempts to explain the cross-section of average returns with the premiums for the common risk factors in returns. It is observed that many portfolios in the bottom two size-quintiles produce average excess returns that are less than two standard errors from 0. This is mainly because stock returns have high standard deviations (around 9.98% per month for the bottom two size portfolios) and therefore large average returns often are not reliably different from 0 [Merton (1980)]. However, high volatility of stock returns does not mean that our asset-pricing tests will lack power. The common factors in returns will absorb most of the variation in stock returns, making the asset-pricing tests on the intercepts in the time-series regressions quite precise.

In the time-series regressions approach to asset-pricing tests, the average risk premiums for the common factors in returns are just the average values of the explanatory variables. The average value of RM-RF (the average premium per unit of market ) is -1.83% per month. This is large from an investment perspective (about -21.96% per year), and it is a marginal 2.58 standard errors from 0. The average SMB return (the average premium for the size-related factor in returns) is only 1.34% per month (t = -2.504). The book-to-market factor HML produces an average premium of 0.728% per month (t=1.149), that is large in both practical and statistical terms.

Common variation in returns

In the time-series regressions, the slopes and R2 values are direct evidence on whether different risk factors capture common variation in stock returns. The explanatory power of stock-market factors is examined in the following sections. The role of stock-market factors in returns is developed in three steps. We examine (a) regressions that use the excess market return, RM-RF, to explain excess stock returns, (b) regressions that use SMB and HML, the mimicking returns for the size and book-to-market factors, as explanatory variables, and (c) regressions that use RM-RF, SMB, and HML. The one- and two-factor regressions help explain why the three-factor regressions work well for stocks.

The results in Table 3 shows that the excess return on the market portfolio of stocks, RM-RF, captures some amount of variation in stock returns. The R2 values are near 0.7 for the big-stocks and low-book-to-market portfolios. For small-stock and high BE/ME portfolios, R2 values less than 0.6 are a rule. These are the stock portfolios for which the size and book-to-market factors, SMB and HML, will have their best shot at showing marginal explanatory power.

The results in Table 4 show that in the absence of competition from the market portfolio, SMB and HML typically capture substantial time-series variation in stock returns for the largest-size and smallest-value portfolio and smallest size and largest-value portfolio. Further, it can be observed that 7 of the 25 R2 values are above 0.1 and two are above 0.2. It is observed that for the portfolios in the smaller-size quintile, SMB and HML leave common variation in stock returns that is picked up by the market portfolio in Table 3. Thus it is observed that used alone, SMB and HML have little power to explain stock returns.

The results in Table 5 shows that when the excess market return is also used as a predictor variables in the regressions, each of the three stock-market factors capture significant amount of variation in the stock returns. The three stock-market factors capture strong common variation in stock returns. The market s for stocks are all more than 7.17 standard errors from 0. With just four exceptions, the t-statistics (absolute value) on the SMB slopes for stocks are greater than 1; 68% are greater than 2. SMB, the mimicking return for the size factor, clearly captures shared variation in stock returns that is missed by the market and by HML. Moreover, the slopes on SMB for stocks are related to size. In every book-to-market quintile, generally the slopes on SMB decrease from smaller- to larger-size quintiles.

Similarly, the slopes on HML, the mimicking return for the book-to-market factor are systematically related to BE/ME. In every size quintile of stocks, the HML slopes increase from smaller values for the lowest-BE/ME quintile to higher values for the highest-BE/ME quintile. For majority of the portfolios (64%), the HML slopes are more than one standard error from zero. Thus, HML clearly captures shared variation in stock returns, related to book-to-market equity that is missed by the market and by SMB.

Given the strong slopes on SMB and HML for stocks, it is not surprising that adding the two returns to the regressions results in large increases in R2. For stocks, the market alone produces only nine (of 25) R2 values greater than 0.7 (Table 3); in the three-factor regressions (Table 5), R2 values greater than 0.7 are more common (13 of 25). For the five portfolios in the smallest-size quintile, R2 increases from values between 0.220 and 0.561 in Table 3 to values between 0.416 and 0.620 in Table 5. The lowest three-factor R2 for stocks, 0.372 for the portfolio in the second-size quintile and third-BE/ME quintile, is almost equal to 0.323 generated by the market alone.

Adding SMB and HML to the regressions has an interesting effect on the market s for stocks. In the one-factor regression of Table 3, the  for the portfolio of stocks in the smallest-size and lowest-BE/ME quintiles is 0.790. At the other extreme, the univariate  for the portfolio of stocks in the biggest-size and highest-BE/ME quintiles is 0.951. In the three-factor regressions of Table 5, the s for these two portfolios are 0.919 and 0.931, respectively. In general, adding SMB and HML to the regression collapses the s for the stocks towards 1.0; low s move up towards 1.0 and high s move down. This behavior is due, of course, to correlation between the market and SMB or HML. SMB and HML have moderate correlation (-0.548), the correlations between RM-RF and SMB and HML are -0.093 and -0.062, respectively.

Cross-Section of Average Stock Returns

When the excess market return is the only explanatory variable in the time-series regressions, the intercepts for stocks (Table 3) show the size effect of Banz (1981). It is observed that in all the BE/ME quintile the intercepts for the smallest-size portfolios exceed those for the biggest by 0.634% to 4.558% per month. The intercepts are also related to book-to-market equity. In every size quintile, the intercepts increase with BE/ME; the intercepts for the highest BE/ME quintile exceed those for the lowest by 0.536% to 4.460% per month. These results parallel the evidence in Fama and French (1992a) that market s, when used alone, leave the cross-sectional variation in average stock returns that is related to size and book-to-market equity.

In fact, as in Fama and French (1992a), the simple relation between average returns and  for the 25 stock portfolios used here is flat. A regression of average return on  yields a slope of -0.22 with a standard error of 0.31. The Sharpe (1964)-Lintner (1965) model ( suffices to describe the cross-section of average returns and the simple relation between  and average return is positive) fares no better here than in previous research studies. The two-factor time-series regressions of excess stock returns on SMB and HML produce similar intercepts for the 25 stock portfolios (Table 4). The two-factor regression intercepts are, however, large (around 0.5% per month) and close to or more than two standard errors from 0. Intercepts that are similar in size support the conclusion from the cross-section regressions in Fama-French (1992a) that size and book-to-market factors explain the strong differences in average returns across stocks. But the large intercepts also say that SMB and HML do not explain the average premium of stock returns over one-month bill returns. The excess market return to the time series regressions pushes the strong positive intercepts for stocks observed in the two-factor (SMB and HML) regressions to values close to 0. Only three of the 25 intercepts in the three-factor regressions differ from 0 by more than 0.2% per month; 16 are within 0.1% of 0. Intercepts close to 0 say that the regressions that use RM-RF, SMB, and HML to absorb common time-series variation in returns do a good job explaining the cross-section of average stock returns. There is an interesting story for the smaller intercepts obtained when the excess market return is added to the two-factor (SMB and HML) regressions. In the three-factor regressions, the stock portfolios produce slopes on RM-RF close to 1.

The average market risk premium (0.43% per month) then absorbs the similar strong positive intercepts observed in the regressions of stock returns on SMB and HML. In short, the size and book-to-market factors can explain the differences in average returns across stocks, but the market factor is needed to explain why stock returns are on average above the one-month bill rate.

Tests on the regression intercepts

We use the F-statistic of Gibbons, Ross, and Shanken (1989) to formally test the hypothesis that a set of explanatory variables produces regression intercepts for the 25 stock portfolios that are all equal to 0. The F-statistics, and bootstrap probability levels, for the three sets of intercepts produced by the explanatory variables in Tables 3 to Table 5 are summarized in Table 6.

The F-test rejects the hypothesis that RM-RF suffices to explain average returns at the 0.985 level. This confirms that the excess market return cannot explain the size and book-to-market effects in average stock returns. The large positive intercepts for stocks observed when SMB and HML are the only explanatory variables produce an F-statistic that rejects the zero-intercepts hypothesis at the 0.973 level. In terms of the F-test, the three stock-market factors, RM-RF, SMB, and HML, produce the best-behaved intercepts.

Nevertheless, the joint test that all intercepts for the 25 stock portfolios are 0 rejects at about the 0.94 level. The rejection comes largely from the lowest-BE/ME quintile of stocks. Among stocks with the lowest ratios of book-to-market equity (growth stocks), the smallest stocks have returns that are too low (0.129% per month, t=0.147) relative to the predictions of the three-factor model, and the biggest stocks have returns that are too high (-0.582% per month, t=-1.707). Put a bit differently, the rejection of a three-factor model in table 6 is due to the absence of a size effect in the lowest-BE/ME quintile.

The five portfolios in the lowest­ BE/ME quintile produce slopes on the size factor SMB that are strongly negatively related to size (Table 5). But unlike the other BE/ME quintiles, average returns in the lowest-BE ME quintile show no relation to size (Table 2). Despite its marginal rejection in the F-tests, our view is that the three-factor model does a good job on the cross-section of average stock returns. The rejection of the model simply says that because RM-RF, SMB, and HML absorb most of the variation in the returns on the 25 stock portfolios (the typical R2 values in Table 5 are above 0.60), even small abnormal average returns suffice to show that the three-factor model is just a model, that is, it is false.

To answer the important question of whether the model can be useful in applications, the interesting result is that only one of the 25 three-factor regression intercepts for stocks (for the portfolio in both the smallest-size and the lowest-BE/ME quintiles) is much different from 0 in practical terms. Indeed, our view is that the three-factor regressions that use RM-RF, SMB, and HML to explain average returns do surprisingly well, given the simple way the mimicking returns SMB and HML for the size and book-to-market factors are constructed. The regressions produce intercepts for stocks that are close to 0, even though SMB and HML surely contain some firm-specific noise as proxies for the risk factors in returns related to size and book-to-market equity.

DIAGNOSTICS

In this section, we validate the robustness of our inference about the common risk factors that explain the cross-section of expected stock returns. Firstly, we use residuals from the 3-factor time-series regressions to investigate if the regressions capture the variation through time in the cross-section of expected returns. We then examine if the three risk factors capture the January seasonals in stock returns. These tests address the concern that the evidence of size and book-to-market factors in the regressions above is spurious, arising only because we use size and book-to-market portfolios for both our dependent and explanatory returns. Lastly, we examine if the three risk factors are informative about average returns on portfolios formed on other variables, particularly, earnings/price and dividend/price ratios.

January Seasonal

Roll and Keim (1983) documented that returns on small stocks tend to be higher in January. Since then it is standard in tests of asset-pricing models to look for unexplained January effects. However, Lo et al. (1990) documented that if the seasonals are, in whole or in part, sampling error, the tests can contain a data snooping bias towards rejection. In the following section we test for January seasonals in the residuals from our three-factor regression. It was observed that except for the smallest stocks, January seasonals are weak at best. This can be mainly due to the absorbance of strong January seasonals in the returns on stocks by strong seasonals in the risk factors. The results in Table 7 show regressions of residual returns on a January dummy variable that is 1 in January and 0 in other months. The average returns for non-January months are captured by the regression intercepts, and the difference between average returns during January and non-January months is captured by the slopes on the dummy variable.

The results in Table 7 confirm that there are January seasonals in excess stock returns, and these seasonals are related to size. The slopes on the January dummy are all less than 0.35% per month and more than 1.50 standard errors from 0 for the portfolios in the smallest quintiles. For the portfolios in the second size quintile, the slopes on the January dummy are all less than -0.965% per month and more than 1.25 standard errors from 0. Similarly, the slopes on the January dummy are all less than -2.81% per month and more than 1.15 standard errors from 0 for the portfolios in the third size quintiles. For the portfolios in the fourth size quintile, the slopes on the January dummy are all less than -3.086% per month and more than 1.65 standard errors from 0. Lastly, the slopes on the January dummy are all less than -2.61% per month and more than 1.33 standard errors from 0 for the portfolios in the largest size quintiles. When the returns are controlled for BE/ME-effect, the extra January returns are comparatively lower. However, the January seasonal in stock returns are neither related to book-to-market equity nor to the size. Further, the results in Table 7 indicate that the risk factors have extra January returns in excess of 1.64% and at-least 1.75 standard errors from 0. The seasonals in the size and book-to-market factors are especially strong. The average SMB and HML returns in January are 1.92% and 1.64% per month greater than in other months, and the extra January returns are 1.75 and 1.83 standard errors from 0. Indeed, like the excess returns on the 25 stock portfolios, the extra January returns on the risk factors are generally must larger and more reliably different from 0 than the average returns for non-January months. Thus, the results in Table 7 show that the January seasonals in our risk factors largely absorb the seasonals in stock returns. In the regressions of the five-factor residuals on the January dummy, only the stock portfolios in the smallest-size quintile produce systematically positive slopes; even these slopes are only one-quarter to one-tenth the positive January seasonals in the raw excess returns on the portfolios. Further, we observe no relationship between the three-factor residuals for the size quintiles and the January seasonals, however, the slopes on the January dummy for these stock portfolios are small and mostly within two standard errors of 0. Overall, we can state that, whether spurious or real, the January seasonals in the returns on stocks seems to be largely explained by the corresponding seasonals in the risk factors of our three-factor model.

Portfolios formed on E/P

The most commonly used diagnostics to confirm the inference about role of size and book-to-market risk factors in returns is to examine whether these variables explain the returns on portfolios formed on other variables that are informative about average returns. The results in Table 8 summarize the one-factor (RM-RF) and three-factor (RM-RF, SMB, and HML) regression results for the portfolios formed on earnings/price (E/P) and dividend/price (D/P) ratios.

Jaffe et al. (1989) and Fama-French (1992a) documented that average returns on the E/P portfolios have U-shape. However, the results in Table 8 indicate that the returns do not strictly follow the U-shape pattern and the portfolio of firms with negative earnings and the portfolio of firms in the highest-E/P quintile do not strictly have high average returns compared to the middle-E/P quintiles.

Basu (1983) stated that the one-factor Sharpe-Lintner model leaves the relation between average return and E/P largely unexplained. The results in Table 8 indicate that for the positive-E/P portfolios, the intercepts in the one-factor regressions increases monotonically, from -1.455% per month (t=-2.592) for the lowest-E/P quintile to -1.021% (t=-1.667) for the third quintile. The intercepts in the one factor regressions are -1.386% per month (t=-2.149) for the fourth-quintile and -1.109% per month (t=-1.386) for the fifth-quintile. The R-square values in Table 10 indicate that the one factor model fails to explain the expected market returns for the portfolios formed on earnings/price (E/P) ratio. This can be explained by the fact that the market s for the positive-E/P portfolios are all close to 1.0, so one-factor model cannot explain the positive relation between E/P and average returns.

On the other hand, the three-factor model, with RM-RF, SMB, and HML as the explanatory variables, leaves no residual E/P-effect in average returns. The three-factor intercepts for the five positive-E/P portfolios are in the range -1.332 to -0.769 (t’s from -2.255 to -0.972). Interestingly, the three-factor regressions say that the increasing pattern in the average returns on the positive-E/P portfolios is due to their loadings on the book-to-market factor HML. The lowest positive-E/P quintile has an HML slope, 0.064, unlike those produced by portfolios in the lowest-BE/ME quintile in the three-factor regressions in Table 5. The results in Table 1 confirms that there is also a positive relation between E/P and BE/ME for our 25 portfolios formed on size and BE/ME.

Fama and French (1992b) find that low BE/ME is characteristic of growth stocks, that is, stocks with persistently high earnings on book equity that result in high stock prices relatively to book equity. High BE/ME, on the other than, is associated with distress, that is, persistently low earnings on book equity that result in low stock prices. The loadings on HML in the three-factor regressions of Table 8 then say that low-E/P stocks have the low average returns typical of (low-BE/ME) growth stocks, while high-E/P stocks have the high average returns associated with distress (high-BE/ME). The negative-E/P portfolio produces the only hint of evidence against the three-factor model. Inspite of the portfolio’s high average excess return (0.72% per month), the three-factor model says that its average return is 0.3% per month too low, given its strong loadings on SMB (1.13, like the smallest-size portfolios in Table 6) and HML (0.46, like the higher-BE/ME portfolios in Table 6). In other words, according to the three-factor model, the average return on this portfolio should be higher because its return behaves like those of small relatively depressed, stocks. The three-factor intercept for the negative-E/P portfolio is, however, only 1.68 standard error from 0.

In short, E/P portfolios produce a strong spread in average returns, which seems to be absorbed by the three common risk factors in stock returns. The E/P portfolios are thus interesting corroboration of our inferences that (a) there are common risk factors in stock returns related to size and book-to-market equity, and (b) RM-RF, SMB, and HML, the mimicking returns for market, size, and BE/ME risk factors, capture the cross-section of average stock returns.

Portfolios formed on D/P

Keim (1983) stated that the average returns drop from the zero-dividend portfolio to the lowest positive-D/P portfolio, and then increases across the positive-D/P portfolios (follow U-shaped pattern). However, in context of TASE, the U-shaped pattern is not strictly observed, but the average returns are much weaker for the D/P portfolios than for the E/P portfolios.

The results in Table 8 confirm Keim’s (1983) finding that the one-factor Sharpe-Lintner model leaves a pattern in average returns that looks like a tax penalty on dividends. It can be observed from Table 8 that the one-factor intercepts increases, though not monotonically, from the lowest to the highest-D/P portfolios. This suggests that pre-tax returns on higher-D/P stocks must be higher on equalize after-tax risk-adjusted returns.

The apparent tax effect in average returns does not survive in the three-factor regressions that use RM-RF, SMB, and HML to explain returns. The three-factor intercepts for the five positive-D/P portfolios are much closer to 0 compared to the one-factor intercepts and show no relation to D/P.

Many research studies have attributed the increasing pattern in the average returns on the positive-D/P portfolios to the increasing patterns in their loadings on the book-to-market factor HML. However, in context of TASE, we observe no relationship between the loading on the book-to-market factor, HML, and D/P quintile.

Further, the 3-factor model says that low-D/P stocks have low average returns typical of growth stocks, whereas high-D/P stocks have high average returns associated with relative distress. The results in Table 1 confirms that there is a positive relationship between D/P and BE/ME for our 25 portfolios form on size and BE/ME.

The zero-dividend portfolio produces the strongest evidence against the three-factor model. The three factor model says that the high average excess return on this portfolio (-1.986% per month) is -0.325% too low (t=-1.017), given its strong loading (-0.176) on SMB, the mimicking return for the size factor. In other words, because the return on the zero-dividend portfolio varies like the return on a portfolio of small stocks, the three-factor model says that the high return on this portfolio is not high enough. But the three-factor intercept for the zero-dividend portfolio is small in practical terms. Moreover, the three-factor model produces intercepts from the five positive-D/P portfolios that are all close to 0, both statistically and practically. We conclude that, overall, the D/P portfolios are consistent with our inference that the three stock-market factors, RM-RF, SMB, and HML, capture the cross-section of average stock returns.

CONCLUSION

This research study investigates the common risk factors in stock returns and tests whether these factors explain the cross-section of average returns. In the context of TASE, we have studied three risk factors that are often cited in research studies: market risk factor, size risk factor (ME) and value risk factor (BE/ME).

The time-series regression results in this research study suggest that size and book-to-market effects explain a significant amount of variance in the context of stocks listed on TASE, Israel’s only stock exchange. The results indicate that there are common return factors related to size and book-to-market equity that help capture the cross-section of average stock returns in a way that is consistent with multi-factor asset pricing models. Thus, the results here confirm Fama and French’s claim that size and BE/ME are related to systematic patterns in relative profitability and growth that could well be the source of common risk factors in returns.

Table 1

Descriptive statistics for 25 stock portfolios formed on size and book-to-market equity: FY 2003-2011

Size Quintile

Book-to-market equity (BE/ME) quintiles

Low

2

3

4

High

Low

2

3

4

High

Average Annual averages of firms size

Average of annual B/E ratios for portfolio

Small

26953.65

25200.96

22759.25

28827.81

26207.18

-4.45

-0.48

-4.42

-6.78

-3.19

2

65364.06

73054.59

68032.92

67387.27

65916.38

-43.28

-723.48

-8.37

3.99

-160.52

3

129378.24

134847.09

143405.30

137155.84

136815.57

23.07

-9569.84

73.86

13.83

11.44

4

390354.26

344213.86

350515.11

353838.13

332771.38

-3.13

121.59

8.89

8.03

19.31

Big

12450086.84

2728998.94

1601965.39

2358729.52

1377136.76

12.28

9.73

8.95

11.75

0.26

Average of annual percent of market value in portfolio

Average of annual number of firms in portfolio

Small

0.052

0.067

0.046

0.054

0.092

49

68

51

48

89

2

0.131

0.166

0.158

0.196

0.264

51

58

59

74

102

3

0.249

0.291

0.484

0.511

0.338

49

55

86

95

63

4

0.873

1.094

1.087

1.056

0.927

57

81

79

76

71

Big

71.353

9.320

4.653

5.185

1.351

146

87

74

56

25

Average of annual E/P ratios (in percent) for portfolio

Average of annual D/P ratios (in percent) for portfolio

Small

0.03

-0.29

0.05

0.67

-48.30

0.00

0.71

0.10

1.05

0.11

2

-0.04

0.11

0.02

0.12

0.12

0.03

0.10

0.03

0.07

0.08

3

-0.05

0.01

-0.03

0.14

0.30

0.02

0.10

0.10

0.09

0.16

4

-0.12

2.36

0.06

0.22

0.09

0.01

0.06

0.12

0.09

0.04

Big

0.03

0.07

0.15

0.10

11.73

0.03

0.06

0.08

0.05

0.07

Table 2

Summary statistics for the monthly dependent and explanatory returns (in percent): 2003 to 2011

Descriptive Statistics

Autocorrelation for lag

Correlations

Name

Mean

Std. Deviation

t (mn)

1

2

12

RM

RM-RF

SMB

HML

Explanatory Variables

RM

1.352

6.524

2.030

0.302

0.265

0.087

1

RM – RF

-1.828

6.945

-2.580

0.380

0.329

0.070

0.977

1

SMB

1.336

5.227

2.504

-0.052

0.110

-0.045

-0.065

-0.093

1

HML

0.728

6.209

1.149

-0.155

-0.139

-0.163

-0.058

-0.062

-0.548

1

Dependent variables: Excess Returns on 25 stock portfolios formed on ME and BE/ME

Size

Quintile

Book-to-Market equity (BE/ME) quintiles

Low

2

3

4

High

Low

2

3

4

High

Means

Standard Deviation

Small

-2.098

-0.765

-1.402

-1.022

1.747

9.555

9.742

9.551

9.527

17.070

2

-2.228

0.565

-1.648

-1.915

-0.878

9.384

34.559

8.005

7.602

7.000

3

-3.632

-2.968

-2.350

-1.792

-1.827

9.793

9.030

7.565

7.890

8.278

4

-3.387

-2.285

-2.323

-2.544

-1.791

10.397

8.287

9.104

9.472

8.824

Big

-2.656

-2.411

-2.601

-2.379

-2.386

6.557

6.644

8.719

7.581

9.430

t-statistics for means

Small

-2.013

-0.719

-1.438

-0.983

1.003

2

-2.327

0.160

-1.886

-2.468

-1.229

3

-3.399

-3.220

-2.847

-2.225

-2.163

4

-2.985

-2.702

-2.500

-2.632

-1.989

Big

-3.969

-3.556

-2.923

-3.075

-2.319

Table 3

Regression of excess stock returns (in percentage) on the excess stock-market return, RM-RF: July 2004 to June 2012

R(t) - RF(t) = a + b[RM(t)-RF(t)] + e(t)

Dependent Variable: Excess returns on 25 stock portfolios formed on size and book-to-market equity

Book-to-Market equity (BE/ME) Quintiles

Low

2

3

4

High

Low

2

3

4

High

a

t-statistics (a)

Small

-0.567

1.139

0.156

0.949

3.893

-0.642

1.459

0.196

1.329

2.445

2

-0.805

3.608

-0.381

-0.356

0.444

-0.989

1.044

-0.511

-0.704

0.859

3

-1.548

-1.053

-0.543

-0.006

0.091

-2.194

-1.854

-1.274

-0.015

0.219

4

-0.863

-0.471

-0.151

-0.294

0.162

-1.554

-0.964

-0.370

-0.678

0.319

Big

-1.201

-0.978

-0.696

-0.680

-0.665

-3.208

-2.420

-1.348

-1.610

-0.917

B

t-statistics (b)

Small

0.790

0.982

0.852

1.018

1.174

6.497

9.151

7.648

10.354

5.269

2

0.778

1.664

0.654

0.852

0.723

6.831

3.441

6.377

12.035

9.985

3

1.076

1.047

0.933

0.977

1.049

11.090

13.174

15.909

16.313

17.993

4

1.303

0.992

1.188

1.231

1.068

17.052

14.507

20.784

20.315

15.052

Big

0.796

0.784

1.042

0.929

0.951

15.197

13.871

14.406

15.721

9.771

R2

S (e)

Small

0.332

0.499

0.377

0.561

0.220

0.847

0.748

0.765

0.684

1.531

2

0.325

0.102

0.323

0.602

0.510

0.783

3.324

0.714

0.487

0.498

3

0.595

0.645

0.752

0.736

0.773

0.676

0.546

0.408

0.411

0.401

4

0.777

0.688

0.819

0.813

0.704

0.532

0.470

0.393

0.416

0.488

Big

0.708

0.668

0.685

0.722

0.532

0.360

0.388

0.497

0.406

0.699

Table 4

Regression of excess stock returns (in percentage) on the excess stock-market return, RM-RF: July 2004 to June 2012

R(t) - RF(t) = a + s[SMB(t)] + h[HML(t)] + e(t)

Dependent Variable: Excess returns on 25 stock portfolios formed on size and book-to-market equity

Book-to-Market equity (BE/ME) Quintiles

Low

2

3

4

High

Low

2

3

4

High

A

t-statistics (a)

Small

-1.259

-0.781

-2.005

-1.396

-1.646

-1.135

-0.673

-1.916

-1.251

-1.001

2

-2.666

1.036

-1.852

-2.240

-1.090

-2.634

0.510

-1.947

-2.678

-1.414

3

-2.990

-2.267

-1.862

-1.826

-1.299

-2.620

-2.304

-2.217

-2.082

-1.433

4

-2.121

-1.032

-1.584

-1.634

-1.521

-1.904

-1.215

-1.603

-1.600

-1.563

Big

-1.623

-1.491

-1.490

-1.369

-1.676

-2.438

-2.152

-1.626

-1.728

-1.554

S

t-statistics (s)

Small

-0.275

-0.041

0.292

-0.175

1.804

-0.862

-0.122

1.307

-0.545

5.145

2

0.373

1.708

0.030

0.130

0.063

1.728

3.941

0.109

0.730

0.383

3

-0.612

-0.365

-0.826

0.010

-0.323

-1.866

-1.738

-3.422

0.054

-1.672

4

-1.397

-0.731

-0.447

-0.527

-0.208

-4.363

-4.032

-2.120

-2.420

-1.000

Big

-0.610

-0.501

-0.650

-0.588

-0.422

-4.292

-3.391

-3.326

-3.478

-1.857

H

t-statistics (h)

Small

-0.623

0.044

0.294

0.483

1.350

-1.971

0.133

1.564

1.519

4.574

2

-0.084

-3.780

0.177

0.208

0.176

-0.460

-10.363

0.655

1.383

1.270

3

-0.199

-0.293

0.098

0.028

-0.133

-0.613

-1.658

0.411

0.177

-0.814

4

-0.261

-0.381

-0.196

-0.284

0.009

-0.823

-2.495

-1.102

-1.548

0.054

Big

-0.301

-0.345

-0.334

-0.309

-0.331

-2.515

-2.777

-2.029

-2.169

-1.698

R2

S (e)

Small

0.027

0.000

0.008

0.009

0.233

1.016

1.063

0.961

1.022

1.510

2

0.039

0.714

0.000

0.000

0.000

0.929

1.865

0.871

0.768

0.708

3

0.020

0.018

0.110

0.000

0.008

1.045

0.904

0.769

0.805

0.832

4

0.172

0.131

0.026

0.040

0.000

1.020

0.780

0.908

0.937

0.893

Big

0.148

0.101

0.088

0.097

0.024

0.611

0.636

0.841

0.728

1.004

Table 5

Regression of excess stock returns (in percentage) on the excess stock-market return, RM-RF: July 2004 to June 2012

R(t) - RF(t) = a + b[RM(t)-RF(t)] + s[SMB(t)] + h[HML(t)] + e(t)

Dependent Variable: Excess returns on 25 stock portfolios formed on size and book-to-market equity

Book-to-Market equity (BE/ME) Quintiles

Low

2

3

4

High

Low

2

3

4

High

A

t-statistics (a)

Small

0.129

0.965

-0.749

0.328

0.297

0.147

1.260

-0.937

0.464

0.233

2

-1.535

3.260

-0.685

-1.006

-0.048

-1.887

1.972

-0.897

-2.038

-0.091

3

-1.238

-0.846

-0.465

-0.442

0.142

-1.693

-1.399

-1.015

-1.012

0.322

4

-0.211

0.268

0.036

0.032

-0.031

-0.379

0.582

0.084

0.071

-0.058

Big

-0.582

-0.459

-0.108

-0.138

-0.417

-1.707

-1.145

-0.209

-0.334

-0.547

b

t-statistics (b)

Small

0.919

1.156

0.913

1.142

1.412

7.413

10.706

8.527

11.447

8.298

2

0.822

1.617

0.773

0.897

0.758

7.546

7.308

7.173

13.579

10.824

3

1.160

1.033

0.925

1.006

1.048

11.253

12.765

14.319

17.216

17.764

4

1.264

0.945

1.178

1.211

1.083

16.116

15.318

20.697

20.192

15.340

Big

0.757

0.750

1.005

0.895

0.931

16.606

13.982

14.570

16.178

9.351

s

t-statistics (s)

Small

0.488

0.919

0.511

0.773

2.144

1.823

3.941

3.014

3.589

7.948

2

0.571

2.097

0.671

0.346

0.245

3.307

5.980

2.886

3.305

2.211

3

0.351

-0.116

-0.059

0.252

-0.071

1.576

-0.907

-0.420

2.723

-0.763

4

-0.347

-0.503

-0.164

-0.236

0.053

-2.051

-5.145

-1.815

-2.480

0.473

Big

-0.427

-0.321

-0.408

-0.373

-0.175

-5.915

-3.771

-3.735

-4.249

-1.094

h

t-statistics (h)

Small

-0.770

-0.141

0.459

0.300

1.605

-3.135

-0.659

3.218

1.518

7.085

2

0.065

-3.489

0.054

0.370

0.312

0.447

-11.848

0.251

4.203

3.354

3

-0.385

-0.107

-0.050

0.209

0.056

-1.885

-0.990

-0.389

2.693

0.718

4

-0.463

-0.210

0.017

-0.065

0.205

-2.983

-2.557

0.223

-0.819

2.180

Big

-0.164

-0.210

-0.153

-0.147

-0.112

-2.704

-2.943

-1.662

-1.999

-0.811

R2

S (e)

Small

0.416

0.574

0.440

0.620

0.557

0.782

0.681

0.718

0.629

1.142

2

0.400

0.817

0.372

0.663

0.554

0.730

1.484

0.680

0.443

0.469

3

0.616

0.642

0.747

0.755

0.774

0.650

0.543

0.408

0.392

0.396

4

0.802

0.753

0.826

0.821

0.714

0.495

0.414

0.382

0.402

0.474

Big

0.784

0.709

0.721

0.763

0.528

0.306

0.360

0.462

0.371

0.694

Table 6

F-statistics testing the intercepts in the excess-return regressions against 0 and matching probability levels of bootstrap and F-distributions

Regression (from Table 3, Table 4, and Table 5)

Model 1

Model 2

Model 3

F-statistic

2.47

2.24

2.13

Probability Levels

Bootstrap

0.985

0.973

0.941

F-distribution

0.986

0.979

0.946

Table 7

Tests for January seasonal in the dependent returns, explanatory returns, and residuals from the three-factor regression: July 2004 to June 2012 [R(t)=a + b*JAN(t) + e]

A

B

t(a)

t(b)

R2

RM

-2.500

-3.548

8.059

3.302

0.094

SMB

1.057

1.918

3.343

1.750

0.021

HML

1.073

1.641

-4.141

-1.828

0.024

Portfolios

Excess Stock Returns

3-Factor Regression Residuals

Smallest-size quintile

A

B

t(a)

t(b)

R2

a

b

t(a)

t(b)

R2

Small

-2.641

-2.455

6.511

1.747

0.024

-0.144

-0.176

1.732

0.610

-0.008

2

-1.409

-1.294

7.739

2.051

0.037

0.038

0.054

-0.461

-0.186

-0.012

3

-2.279

-2.339

10.533

3.121

0.084

-0.280

-0.375

3.365

1.300

0.007

4

-1.488

-1.381

5.596

1.499

0.015

0.310

0.476

-3.719

-1.650

0.020

Big

0.617

0.346

13.563

2.195

0.039

-0.138

-0.115

1.660

0.400

-0.009

Size quintile 2

A

B

t(a)

t(b)

R2

a

b

t(a)

t(b)

R2

Small

-2.739

-2.770

6.134

1.791

0.023

0.177

0.232

-2.127

-0.804

-0.004

2

-3.314

-0.965

46.554

3.913

0.131

-1.006

-0.664

12.071

2.299

0.043

3

-1.975

-2.172

3.923

1.246

0.007

0.162

0.228

-1.947

-0.790

-0.005

4

-2.393

-3.004

5.740

2.080

0.034

0.093

0.200

-1.116

-0.694

-0.005

Big

-1.159

-1.560

3.381

1.313

0.008

0.188

0.384

-2.251

-1.331

0.008

Size quintile 3

A

B

t(a)

t(b)

R2

a

b

t(a)

t(b)

R2

Small

-4.002

-3.593

4.435

1.149

0.004

0.270

0.400

-3.240

-1.385

0.011

2

-3.642

-3.886

8.088

2.491

0.052

0.024

0.043

-0.291

-0.148

-0.010

3

-2.733

-3.198

4.605

1.555

0.017

0.190

0.450

-2.276

-1.557

0.017

4

-2.471

-3.051

8.150

2.905

0.073

-0.006

-0.014

0.068

0.048

-0.011

Big

-2.420

-2.810

7.116

2.385

0.047

0.071

0.172

-0.854

-0.594

-0.007

Size quintile 4

A

B

t(a)

t(b)

R2

A

b

t(a)

t(b)

R2

Small

-4.312

-3.789

11.106

2.817

0.077

-0.227

-0.442

2.722

1.532

0.016

2

-2.702

-3.086

5.000

1.648

0.018

0.151

0.349

-1.806

-1.209

0.005

3

-3.210

-3.478

10.639

3.328

0.096

-0.147

-0.370

1.766

1.283

0.007

4

-3.329

-3.412

9.414

2.786

0.066

-0.014

-0.034

0.173

0.118

-0.010

Big

-2.911

-3.398

13.441

4.529

0.170

-0.449

-0.953

5.383

3.301

0.094

Biggest-size quintile

A

B

t(a)

t(b)

R2

A

b

t(a)

t(b)

R2

Small

-3.013

-4.359

4.277

1.787

0.023

0.090

0.280

-1.075

-0.971

-0.001

2

-2.753

-3.924

4.095

1.685

0.019

0.146

0.389

-1.748

-1.348

0.009

3

-3.019

-3.274

5.023

1.572

0.015

0.195

0.406

-2.340

-1.406

0.010

4

-2.793

-3.496

4.965

1.794

0.023

0.134

0.347

-1.612

-1.203

0.005

Big

-2.797

-2.614

4.923

1.329

0.009

0.203

0.280

-2.440

-0.972

-0.001

Table 8

Summary statistics for equally-weighted monthly excess returns (in percent) on portfolios formed on dividend/price (D/P) and earnings/price (E/P), and regressions of excess portfolio returns on (i) the excess market return (RM-RF) and (ii) the excess market return (RM-RF) and the mimicking returns for the size (SMB) and book-to-market equity (HML) factors: July 2004 to June 2012.

Portfolios formed on E/P

Portfolios formed on D/P

Portfolio

Mean

Std. Dev.

t(mm)

Mean

Std. Dev.

t(mm)

≤ 0

-2.419

7.569

-3.132

-1.986

8.146

-2.388

Low

-2.600

6.565

-3.881

-2.191

5.982

-3.589

2

-2.114

6.383