Une méthode asymptotique pour tester la validité du modèle d’équilibre d’actifs financiers (MEDAF) avec pour exemple la bourse de Paris An asymptotic method to test the validity of the capital asset pricing model (CAPM) with the Paris Stock Exchange as an example

ABSTRACT

One of the problems in testing the validity of the two-parameter CAPM is the determination of an efficient proxy market portfolio to represent the true market portfolio. We test the mean-variance efficiency of a pre-specified market portfolio by using a method proposed by Roll (1976) for testing the linear relation between the rate of return of an asset and its beta, and hence the mean-variance efficiency of a proxy market portfolio. This procedure exploits the asymptotic exact linearity condition of the rate of return and beta by measuring the rate of decrease of cross-sectional residual variance with respect to increasing time-series sample size. The technique is applied to samples of companies on the Paris Stock Exchange for the period 1969-1978: 144 companies and twenty-nine different time series. The results indicate that although the sum of the squared residuals of a CAPM-type regression declines as the number of time observations increases, the sum of the squared residuals does not approach zero as the temporal sample size increases, as would be required for the market proxy of our pre-specified sample to be efficient.