Testing the CAPM across observed and fundamental returns

Abstract

The Capital Asset Pricing Model (CAPM) describes a relationship between risk and expected forward-looking returns. Existing research tests the model using realized returns as the proxy for exante expectations. However, recent studies cast doubt on the ability of expost observed returns to proxy for exante expectations. Using an alternative specification to proxy for investor expectations, I test the CAPM in the context of pricing size and book/market equities. The results indicate that the CAPM retains additional merit with an improved measure of expectations. However, the value premium appears large and significant across both specifications of expected returns.

Notes

¹ Stambaugh (1982) considers various asset classes and shows that CAPM inferences are similar across a variety of market portfolio constructions.

² Fama and French (2002) explain that the specification in Equation 2 requires that the dividend/price ratio is stationary, with a constant mean. They also discuss that the specification is robust to reasonable forms of nonstationarity. In unreported analyses, Phillips–Perron tests reject the null hypothesis of a nonstationary unit root nominal dividend/price process at the 10% level for 22 of the 25 test portfolios used within the study. These results are available from the author on request. The results are qualitatively unchanged when the analyses are conducted over only the 22 test portfolios that are confirmed to have a stationary dividend/price ratio.

³ Mean excess returns of the 25 dependent test portfolios are reported, along with CAPM parameter estimates, in Table 3.

⁴ From Table 1, SDs of fundamental returns on a portfolio basis appear larger than the observed return counterparts. Therefore, the insignificant α estimates may be due to higher SEs, and not necessarily supportive of the CAPM. I thank an anonymous referee for this point. At minimum, this analysis indicates the alternative proxies for expectations lead to different CAPM related inferences.

⁵ Small sample concerns exist across the entire analysis as well. However, the significant findings across the full sample for the fundamental return series suggest significant power to analyse the CAPM. Further, the 25 test portfolios cover a large number of equities, as described in the data section.