Pettengill, Sundaram, and Mathur 105 low beta portfolios). This relationship provides important implications concerning empirical tests for a systematic relationship between beta and returns A systematic relationship must exist between beta and returns for beta to be a useful measure of risk. The SLB model prescribes a systematic and positive tradeoff between beta and expected return, but the above discussion refects a segmented relationship between realized returns and beta, i.e., a positive relation during positive market excess return periods and a negative relation during negative market excess return periods. If realized market returns were seldom less than the risk-free rate, this conditional relationship would have a trivial impact on tests of the relationship between beta and returns. This relationship, however, occurs frequently. A month-by-month comparison of the CRSP equally-weighted index(as the proxy for market return) and the 90-day T-bill rate(as the measure for the risk-free return) over the period 1936 through 1990 reveals that the t- bill rate exceeds the market return in 280 out of 660 total observations The existence of a large number of negative market excess return periods suggests that previous studies that test for an unconditional positive correlation between beta and realized returns are biased against finding a systematic relationship. This paper mploys testing procedures that account for the segmented relationship and finds a significant impact of beta on returns Ill. Previous Tests of the Relationship between Beta and Returns Extant literature examining the relationship between beta and returns has primarily tested for a positive linear relationship as prescribed by the SlB model Although the model postulates a positive tradeoff between risk(beta) and expected return, prior studies have examined the realized returns of equity portfolios forme from rankings of betas. They generally find a weak, but positive, relationship between returns and beta over the entire sample period, but these results are often found to be intertemporally inconsistent and weaker than the association between returns and other variables(e. g, size). These results are generally interpreted as evidence against the validity of a positive relationship between beta and returns The findings of the major studies in this area are briefly described here Fama and MacBeth,'s(1973)seminal study on the validity of the SLB model takes a three-step approach. In the first step, portfolios are formed based on esti mated beta for individual securities. The second step involves estimation of each portfolio's beta in a subsequent time period. In the final step using data from a third time period, portfolio returns are regressed on portfolio betas. Since, on average, for the period 1935 through 1968, a positive relationship exists between beta and monthly returns, Fama and MacBeth conclude that the SlB model ad- equately describes the risk-return behavior observed in capital markets. Schwert (1983), however, suggests that this evidence provides surprisingly weak support for a risk-return tradeoff Following Fama and MacBeth, a number of researchers have conducted em- pirical analyses that suggest that beta may not adequately measure a security'srisk Reinganum(1981)finds that".estimated betas are not systematically related to average returns across securities"and concludes".. that the slB model may lack
106 Journal of Financial and Quantitative Analysis significant empirical content"(p. 439). In a sample of daily returns, Reinganum finds a tendency for portfolio returns to decrease as beta increases. In contrast, for a sample of monthly returns, Reinganum finds a positive relationship between returns and beta, but argues that this apparent corroboration is spurious on two counts. First, the difference in returns across portfolios is not significant. Sec ond, the positive relationship between beta risk and return is not consistent across subl Tinic and West (1984)also reject the validity of the slB model based on ntertemporal inconsistencies. Using monthly data, they find a positive and signif- icant slope when regressing portfolio returns on portfolio betas when return data for the entire year are included. Tinic and West are, however, unable to reject the null hypothesis of no difference in returns across portfolios if return data from the month of January are excluded. Further, for several months of the year, nega- across months of the year led them to conclude that their resul the slb model tive slope coefficients are observed. This inconsistent support for doubt on the validity of the two-parameter model.. "and"... to the extent that the risk-return tradeoff shows up only in January, much of what now constitutes the received version of modern finance is brought into question"(Tinic and West (1984),p.573) Several other studies stress that the ability of beta to explain changes in return is weak relative to other variables. Lakonishok and Shapiro(1984),(1986)find an insignificant relationship between beta and returns. Further, Lakonishok and Shapiro find a significant relationship between returns and market capitalization values From these tests, Lakonishok and Shapiro conclude that an dividual securitys return did not appear to be specifically related to its degree of systematic risk”(1984),p.36 Fama and French(1992) study monthly returns and find an insignificant re- lationship between beta and average returns. In contrast, market capitalization and the ratio of book value to market value have significant explanatory power for portfolio returns. Fama and French state: We are forced to conclude that the SlB odel does not describe the last 50 years of average stock returns"(p 464) In summary, Reinganum finds therelationship between beta and cross-section- al returns to vary across subperiods. Tinic and West find the relationship between beta and the returns to vary with months in a year. Lakonishok and Shapiro and Fama and french find the relationship between beta and returns to be weaker than the relationship between returns and other variables. Collectively, these results have been taken as evidence that the slb model provides an inadequate expla nation for the risk-return behavior observed in capital markets. In contrast, the methodology described below accounts for the conditional relationship between beta and realized returns, and finds a systematic relationship between these vari- Although they argue in support of the SLB model, Fama and Mac Beth find similar inconsistency This result is consistent with Rozeff and Kinney(1976), who find the risk premium for Janua