A Note on Consistent Estimation of a Capital Market Equation

Abstract

In recent years the model of capital asset valuation (CAPM) proposed by Sharpe (1964), Lintner (1965), and Mossin (1966) has become the predominant representation of capital markets for empirical work and in the development of normative financial theory. In light of the model's popularity, the contradictory empirical evidence contained in studies of capital market behavior is disturbing. Researchers report findings of deviations of estimated parameters from theoretical values (Black et al., 1972; Fama and MacBeth, 1973; Miller and Scholes, 1972), non-linear rather than linear riskreturn relationships (Fama and MacBeth, 1973; Jensen, 1972), and indications of the incompleteness of the model's measure of risk (Fama and MacBeth, 1973; Rao and Miller, 1968). Further, the observed results have not been attributed to the econometric problems known to exist (Miller and Scholes, 1972). In this paper we argue that the conventional approach to testing the CAPM is subject to a peculiar in variables problem and cannot be expected to be successful even if the underlying model is valid. The CAPM is an equilibrium condition with equilibrium asset prices implicitly deflating the risk and the return measures denominated in rates of return. If disequilibrium observations are employed, then erroneous prices deflate both regressor and regressand in the regression model of the CAPM. As Casson (1973) has shown, estimated model parameters will not be consistent. The effect of this problem is difficult to relate to previous empirical evidence. The ,B estimates employed in these studies were produced by -a method that exhibits an equivalent errors in deflating variable problem. Our findings, however, indicate that reported results cannot be considered inconsistent with the validity of the hypothesized relationship. Finally, we show that the CAPM regression model can be recast in terms of asset prices rather than rates of return in order to produce consistent estimates of the parameters of interest.