No abstract

A long standing puzzle in the Capital Asset Pricing Model (CAPM) has been the inability of empirical work to validate it. Roll (1977) was the first to point out this problem, and recently, Fama and French (1992, 1993) bolstered Roll's original critique with additional empirical results. Does this mean the CAPM is dead? This paper presents a new empirical approach to estimating the CAPM, taking into account the differences between observable and expected returns for risky assets and for the market portfolio of all traded assets, as well as inherent nonlinearities and the effects of excluded variables. Using this approach, we provide (1965) , and Black (1972) in its various formulations provides predictions for equilibrium expected returns on risky assets. More specifically, one of its formulations states that an individual asset's (or a group of assets) expected excess return over the risk-free interest rate equals a coefficient, denoted by ~, times the (meanvariance efficient) market portfolio's expected excess return over the risk-free interest rate. This relatively straightforward relationship between various rates of return is difficult to implement empirically because expected returns and the efficient market portfolio are unobservable e. Despite this formidable difficulty, a substantial number of tests have nonetheless been performed, using a variety of ex-post values and proxies for the unobservable ex-ante variables. Recognizing the seriousness of this situation quite early, Roll (1977) emphasized correctly that tests following such an approach provide no evidence about the validity of the CAPM. The obvious reason is that ex-post values and proxies are only approximations and therefore not the variables one should actually be using to test the CAPM. The primary purpose of this paper is to provide a new approach to testing the CAPM that overcomes this deficiency. Recently, Fama and French (1992, 1993) conducted extensive tests of the CAPM and found that the relation between average stock return and is flat, and that average firm size and the ratio of book-to-market equity do a good job capturing the cross-sectional variation in average stock returns. These findings suggest, among other things, that a formal accounting of the effects of "excluded variables" my resurrect the CAPM. This will be the central issue in this paper. According to Fama and French (1993), some questions that need to be addressed are: (i) How are the size and book-to-market factors in returns driven by the stochastic behavior of earnings? (ii) How does profitability, or any other fundamental, produce common variation in returns associated with size and book-to-market equity that is not