《金融投资学》教学资源（英文文献）The time-series relations.pdf

6 J.Lewellen Journal of Financial Economics 54 (1999)5-43 1.Introduction Empirical research consistently finds a positive cross-sectional relation be- tween average stock returns and the ratio of a firm's book equity to market equity(B/M).Stattman (1980)and Rosenberg et al.(1985)document the associ- ation between expected returns and B/M,which remains significant after con- trolling for beta,size,and other firm characteristics(Fama and French,1992). The explanatory power of B/M does not appear to be driven entirely by data snooping or survival biases;it is found in stock markets outside the United States(Chan et al,1991;Haugen and Baker,1996)and in samples drawn from sources other than Compustat(Davis,1994).As a whole,the evidence provides considerable support for the cross-sectional explanatory power of B/M. At least two explanations have been offered for the empirical evidence. According to asset-pricing theory,B/M must proxy for a risk factor in returns. The significance of B/M in competition with beta contradicts the capital asset pricing model (CAPM)of Sharpe(1964),Lintner(1965),and Black(1972),or more precisely,the mean-variance efficiency of the market proxy.However,the evidence might be consistent with the intertemporal models of Merton (1973) and Breeden (1979).In these models,the market return does not completely capture the relevant risk in the economy,and additional factors are required to explain expected returns.If a multifactor model accurately describes stock returns,and B/M is cross-sectionally correlated with the factor loadings,then the premium on B/M simply reflects compensation for risk. A positive relation between B/M and risk is expected for several reasons. Chan and Chen (1991)and Fama and French (1993)suggest that a distinct distress factor'explains common variation in stock returns.Poorly performing, or distressed,firms are likely to have high B/M.These firms are especially sensitive to economic conditions,and their returns might be driven by many of the same macroeconomic factors (such as variation over time in bankruptcy costs and access to credit markets).In addition,following the arguments of Ball (1978)and Berk(1995),B/M might proxy for risk because of the inverse relation between market value and discount rates.Holding book value constant in the numerator,a firm's B/M ratio increases as expected return,and consequently risk,increases. Alternatively,B/M might provide information about security mispricing.The mispricing view takes the perspective of a contrarian investor.A firm with poor stock price performance tends to be underpriced and have a low market value relative to book value.As a result,high B/M predicts high future returns as the underpricing is eliminated.Lakonishok et al.(1994)offer a rationale for the association between past performance and mispricing.They argue that investors naively extrapolate past growth when evaluating a firm's prospects. For example,investors tend to be overly pessimistic about a firm which has had low or negative earnings.On average,future earnings exceed the market's

1. Introduction Empirical research consistently "nds a positive cross-sectional relation between average stock returns and the ratio of a "rm's book equity to market equity (B/M). Stattman (1980) and Rosenberg et al. (1985) document the association between expected returns and B/M, which remains signi"cant after controlling for beta, size, and other "rm characteristics (Fama and French, 1992). The explanatory power of B/M does not appear to be driven entirely by data snooping or survival biases; it is found in stock markets outside the United States (Chan et al., 1991; Haugen and Baker, 1996) and in samples drawn from sources other than Compustat (Davis, 1994). As a whole, the evidence provides considerable support for the cross-sectional explanatory power of B/M. At least two explanations have been o!ered for the empirical evidence. According to asset-pricing theory, B/M must proxy for a risk factor in returns. The signi"cance of B/M in competition with beta contradicts the capital asset pricing model (CAPM) of Sharpe (1964), Lintner (1965), and Black (1972), or more precisely, the mean-variance e$ciency of the market proxy. However, the evidence might be consistent with the intertemporal models of Merton (1973) and Breeden (1979). In these models, the market return does not completely capture the relevant risk in the economy, and additional factors are required to explain expected returns. If a multifactor model accurately describes stock returns, and B/M is cross-sectionally correlated with the factor loadings, then the premium on B/M simply re#ects compensation for risk. A positive relation between B/M and risk is expected for several reasons. Chan and Chen (1991) and Fama and French (1993) suggest that a distinct &distress factor' explains common variation in stock returns. Poorly performing, or distressed, "rms are likely to have high B/M. These "rms are especially sensitive to economic conditions, and their returns might be driven by many of the same macroeconomic factors (such as variation over time in bankruptcy costs and access to credit markets). In addition, following the arguments of Ball (1978) and Berk (1995), B/M might proxy for risk because of the inverse relation between market value and discount rates. Holding book value constant in the numerator, a "rm's B/M ratio increases as expected return, and consequently risk, increases. Alternatively, B/M might provide information about security mispricing. The mispricing view takes the perspective of a contrarian investor. A "rm with poor stock price performance tends to be underpriced and have a low market value relative to book value. As a result, high B/M predicts high future returns as the underpricing is eliminated. Lakonishok et al. (1994) o!er a rationale for the association between past performance and mispricing. They argue that investors naively extrapolate past growth when evaluating a "rm's prospects. For example, investors tend to be overly pessimistic about a "rm which has had low or negative earnings. On average, future earnings exceed the market's 6 J. Lewellen / Journal of Financial Economics 54 (1999) 5}43

J.Lewellen Journal of Financial Economics 54 (1999)5-43 expectation,and the stock does abnormally well.Thus,the mispricing argument says that B/M captures biases in investor expectations. Fama and French(1993)provide evidence of a relation between B/M and risk. Using the time-series approach of Black et al.(1972),they examine a multifactor model consisting of market,size,and book-to-market factors,where the size and book-to-market factors are stock portfolios constructed to mimic underlying risk factors in returns.If the model explains cross-sectional variation in average returns,the intercepts will be zero when excess returns are regressed on the three factors.Fama and French find,as predicted by the risk-based view,that the model does a good job explaining average returns for portfolios sorted by size, B/M,earnings-price ratios,and other characteristics.Further,they document a strong association between a stock's B/M ratio and its loading on the book-to-market factor. More recently,Daniel and Titman(1997)argue in favor of a characteristics- based model,consistent with the mispricing view.They suggest that the three- factor model does not directly explain average returns.Instead,the model appears to explain average returns only because the factor loadings are corre- lated with firms'characteristics(size and B/M).To disentangle the explanatory power of the factor loadings from that of the characteristics,Daniel and Titman construct test portfolios by sorting stocks first on B/M ratios and then on factor loadings.This sorting procedure creates independent variation in the two variables.Consistent with the mispricing story,Daniel and Titman find a stronger relation between expected returns and B/M than between expected returns and factor loadings.Daniel and Titman conclude that firm charac- teristics,in particular B/M,and not covariances determine expected stock returns. In this paper,I provide further evidence on the risk-and characteristics-based stories.In contrast to Fama and French(1993)and Daniel and Titman (1997), I focus on the time-series relations among expected return,risk,and B/M. Specifically,I ask whether a portfolio's B/M ratio predicts time-variation in its expected return,and test whether changes in expected return can be explained by changes in risk.Recently,Kothari and Shanken(1997)and Pontiff and Schall (1998)find that B/M forecasts stock returns at the aggregate level,but the predictive ability of B/M for individual stocks or portfolios has not been explored. The time-series analysis is a natural alternative to cross-sectional regressions. An attractive feature of the time-series regressions is that they focus on changes in expected returns,not on average returns.The mispricing story suggests that a stock's expected return will vary over time with B/M,but it says little about average returns if mispricing is temporary.Cross-sectional regressions,however, can pick up a relation between average returns and B/M.The time-series regressions also highlight the interaction between B/M and risk,as measured by time-variation in market betas and the loadings on the Fama and French

expectation, and the stock does abnormally well. Thus, the mispricing argument says that B/M captures biases in investor expectations. Fama and French (1993) provide evidence of a relation between B/M and risk. Using the time-series approach of Black et al. (1972), they examine a multifactor model consisting of market, size, and book-to-market factors, where the size and book-to-market factors are stock portfolios constructed to mimic underlying risk factors in returns. If the model explains cross-sectional variation in average returns, the intercepts will be zero when excess returns are regressed on the three factors. Fama and French "nd, as predicted by the risk-based view, that the model does a good job explaining average returns for portfolios sorted by size, B/M, earnings-price ratios, and other characteristics. Further, they document a strong association between a stock's B/M ratio and its loading on the book-to-market factor. More recently, Daniel and Titman (1997) argue in favor of a characteristicsbased model, consistent with the mispricing view. They suggest that the threefactor model does not directly explain average returns. Instead, the model appears to explain average returns only because the factor loadings are correlated with "rms' characteristics (size and B/M). To disentangle the explanatory power of the factor loadings from that of the characteristics, Daniel and Titman construct test portfolios by sorting stocks "rst on B/M ratios and then on factor loadings. This sorting procedure creates independent variation in the two variables. Consistent with the mispricing story, Daniel and Titman "nd a stronger relation between expected returns and B/M than between expected returns and factor loadings. Daniel and Titman conclude that "rm characteristics, in particular B/M, and not covariances determine expected stock returns. In this paper, I provide further evidence on the risk- and characteristics-based stories. In contrast to Fama and French (1993) and Daniel and Titman (1997), I focus on the time-series relations among expected return, risk, and B/M. Speci"cally, I ask whether a portfolio's B/M ratio predicts time-variation in its expected return, and test whether changes in expected return can be explained by changes in risk. Recently, Kothari and Shanken (1997) and Ponti! and Schall (1998) "nd that B/M forecasts stock returns at the aggregate level, but the predictive ability of B/M for individual stocks or portfolios has not been explored. The time-series analysis is a natural alternative to cross-sectional regressions. An attractive feature of the time-series regressions is that they focus on changes in expected returns, not on average returns. The mispricing story suggests that a stock's expected return will vary over time with B/M, but it says little about average returns if mispricing is temporary. Cross-sectional regressions, however, can pick up a relation between average returns and B/M. The time-series regressions also highlight the interaction between B/M and risk, as measured by time-variation in market betas and the loadings on the Fama and French J. Lewellen / Journal of Financial Economics 54 (1999) 5}43 7

8 J.Lewellen Journal of Financial Economics 54 (1999)5-43 (1993)size and book-to-market factors.Further,I can directly test whether the three-factor model explains time-varying expected returns better than the char- acteristics-based model.These results should help distinguish between the risk and mispricing stories. The empirical tests initially examine B/M's predictive ability without attempt- ing to control for changes in risk.I find that a portfolio's B/M ratio tracks economically and statistically significant variation in its expected return.An increase in B/M equal to twice its time-series standard deviation forecasts a 4.6%(annualized)increase in expected return for the typical industry port- folio,8.2%for the typical size portfolio,and 9.3%for the typical book-to- market portfolio.The average coefficient on B/M across all portfolios,0.99,is approximately double the cross-sectional slope,0.50,found by Fama and French(1992,p.439).B/M explains,however,only a small fraction of portfolio returns,generally less than 2%of total volatility. Return predictability indicates that either risk or mispricing changes over time.Of course,we cannot distinguish between these explanations without some model of risk.Following Daniel and Titman (1997),I examine B/M's explanatory power in competition with the Fama and French (1993)three- factor model.The multifactor regressions employ the conditional asset-pricing methodology of Shanken (1990),which allows both expected returns and factor loadings to vary over time with B/M.In these regressions,time-variation in the intercepts measures the predictive ability of B/M that cannot be explained by changes in risk.The mispricing view suggests that the intercepts will be positively related to B/M;the risk-based view implies that changes in the factor loadings will eliminate B/M's explanatory power,assum- ing the Fama and French factors are adequate proxies for priced risk in the economy. Empirically,the factors absorb much of the volatility of portfolio returns, which permits relatively powerful tests of the competing stories.I find that B/M explains significant time-variation in risk,but does not provide incremental information about expected return.In general,the loadings on the size and book-to-market factors vary positively with a portfolio's B/M ratio,and statistical tests strongly reject the hypothesis of constant risk.The results for market betas are more difficult to characterize:across different portfolios, B/M predicts both significant increases and significant decreases in beta. Overall,B/M contains substantial information about the riskiness of stock portfolios. In contrast,the intercepts of the three-factor model do not vary over time with B/M.For the industry portfolios,the average coefficient on B/M (that is, variation in the intercept)has the opposite sign predicted by the overreaction hypothesis and is not significantly different from zero.Across the 13 portfolios, eight coefficients are negative and none is significantly positive at conventional levels.The results are similar for size and book-to-market portfolios:the

(1993) size and book-to-market factors. Further, I can directly test whether the three-factor model explains time-varying expected returns better than the characteristics-based model. These results should help distinguish between the risk and mispricing stories. The empirical tests initially examine B/M's predictive ability without attempting to control for changes in risk. I "nd that a portfolio's B/M ratio tracks economically and statistically signi"cant variation in its expected return. An increase in B/M equal to twice its time-series standard deviation forecasts a 4.6% (annualized) increase in expected return for the typical industry portfolio, 8.2% for the typical size portfolio, and 9.3% for the typical book-tomarket portfolio. The average coe$cient on B/M across all portfolios, 0.99, is approximately double the cross-sectional slope, 0.50, found by Fama and French (1992, p. 439). B/M explains, however, only a small fraction of portfolio returns, generally less than 2% of total volatility. Return predictability indicates that either risk or mispricing changes over time. Of course, we cannot distinguish between these explanations without some model of risk. Following Daniel and Titman (1997), I examine B/M's explanatory power in competition with the Fama and French (1993) threefactor model. The multifactor regressions employ the conditional asset-pricing methodology of Shanken (1990), which allows both expected returns and factor loadings to vary over time with B/M. In these regressions, time-variation in the intercepts measures the predictive ability of B/M that cannot be explained by changes in risk. The mispricing view suggests that the intercepts will be positively related to B/M; the risk-based view implies that changes in the factor loadings will eliminate B/M's explanatory power, assuming the Fama and French factors are adequate proxies for priced risk in the economy. Empirically, the factors absorb much of the volatility of portfolio returns, which permits relatively powerful tests of the competing stories. I "nd that B/M explains signi"cant time-variation in risk, but does not provide incremental information about expected return. In general, the loadings on the size and book-to-market factors vary positively with a portfolio's B/M ratio, and statistical tests strongly reject the hypothesis of constant risk. The results for market betas are more di$cult to characterize: across di!erent portfolios, B/M predicts both signi"cant increases and signi"cant decreases in beta. Overall, B/M contains substantial information about the riskiness of stock portfolios. In contrast, the intercepts of the three-factor model do not vary over time with B/M. For the industry portfolios, the average coe$cient on B/M (that is, variation in the intercept) has the opposite sign predicted by the overreaction hypothesis and is not signi"cantly di!erent from zero. Across the 13 portfolios, eight coe$cients are negative and none is signi"cantly positive at conventional levels. The results are similar for size and book-to-market portfolios: the 8 J. Lewellen / Journal of Financial Economics 54 (1999) 5}43

J.Lewellen Journal of Financial Economics 54 (1999)5-43 9 average coefficients are indistinguishable from zero,and roughly half are negative.Importantly,the inferences from the multifactor regressions are not driven by low power.For all three sets of portfolios,statistical tests can reject economically large coefficients on B/M.In short,the three-factor model measures risk sufficiently well to explain time-variation in expected returns. As an aside,I find that the book-to-market factor,HML,explains common variation in returns that is unrelated to its industry composition.Daniel and Titman(1997)argue that HML does not proxy for a distinct risk factor,but explains return covariation only because similar types of firms become mis- priced at the same time.For example,a bank with high B/M will covary positively with HML simply because the factor is weighted towards underpriced financial firms.The time-series regressions provide evidence to the contrary.As an alternative to HML,I estimate the regressions with an 'industry-neutral' book-to-market factor.This factor is constructed by sorting stocks on their industry-adjusted B/M ratios,defined as the firm's B/M minus the industry average,so the factor should never be weighted towards particular industries. The results using the industry-neutral factor are similar to those with HML. Thus,HML's explanatory power does not appear to be driven by industry factors in returns. The remainder of the paper is organized as follows.Section 2 introduces the time-series regressions.Section 3 describes the data to be used in the empirical tests.Section 4 estimates the simple relation between expected returns and B/M, and Section 5 tests whether the predictive ability of B/M can be explained by changes in risk,as measured by the Fama and French(1993)three-factor model. Section 6 summarizes the evidence and concludes. 2.Distinguishing between characteristics and risk Book-to-market explains cross-sectional variation in average returns after controlling for beta.Fama and French(1993)provide evidence that B/M relates to common risk factors in returns.In contrast,Daniel and Titman(1997)argue that the Fama and French factors appear to be priced only because the loadings are correlated with firm characteristics,like B/M.This section introduces the time-series methodology used in the current paper and discusses,more gener- ally,asset-pricing tests of the risk and mispricing stories. I also replicate the empirical tests using size in place of B/M,with similar results.There is some evidence that size and expected returns are negatively related in time series.In conditional three-factor regressions,size captures significant time-variation in risk,but does not contain additional information about expected returns.Details are available on request.I thank Ken French for suggesting these tests

average coe$cients are indistinguishable from zero, and roughly half are negative. Importantly, the inferences from the multifactor regressions are not driven by low power. For all three sets of portfolios, statistical tests can reject economically large coe$cients on B/M. In short, the three-factor model measures risk su$ciently well to explain time-variation in expected returns.1 As an aside, I "nd that the book-to-market factor, HML, explains common variation in returns that is unrelated to its industry composition. Daniel and Titman (1997) argue that HML does not proxy for a distinct risk factor, but explains return covariation only because similar types of "rms become mispriced at the same time. For example, a bank with high B/M will covary positively with HML simply because the factor is weighted towards underpriced "nancial "rms. The time-series regressions provide evidence to the contrary. As an alternative to HML, I estimate the regressions with an &industry-neutral' book-to-market factor. This factor is constructed by sorting stocks on their industry-adjusted B/M ratios, de"ned as the "rm's B/M minus the industry average, so the factor should never be weighted towards particular industries. The results using the industry-neutral factor are similar to those with HML. Thus, HML's explanatory power does not appear to be driven by industry factors in returns. The remainder of the paper is organized as follows. Section 2 introduces the time-series regressions. Section 3 describes the data to be used in the empirical tests. Section 4 estimates the simple relation between expected returns and B/M, and Section 5 tests whether the predictive ability of B/M can be explained by changes in risk, as measured by the Fama and French (1993) three-factor model. Section 6 summarizes the evidence and concludes. 2. Distinguishing between characteristics and risk Book-to-market explains cross-sectional variation in average returns after controlling for beta. Fama and French (1993) provide evidence that B/M relates to common risk factors in returns. In contrast, Daniel and Titman (1997) argue that the Fama and French factors appear to be priced only because the loadings are correlated with "rm characteristics, like B/M. This section introduces the time-series methodology used in the current paper and discusses, more generally, asset-pricing tests of the risk and mispricing stories. 1 I also replicate the empirical tests using size in place of B/M, with similar results. There is some evidence that size and expected returns are negatively related in time series. In conditional three-factor regressions, size captures signi"cant time-variation in risk, but does not contain additional information about expected returns. Details are available on request. I thank Ken French for suggesting these tests. J. Lewellen / Journal of Financial Economics 54 (1999) 5}43 9