A testable version of the Pareto-stable CAPM

The Capital Asset Pricing Model (CAPM) under the Pareto-stable assumptions was first developed by Fama [1] and Ross [2]. Fama treated a restricted case and neither he nor Ross gave ah expression of the coefficient beta that could lead to an empirical use of the stable CAPM. Using new developments on the multivariate structure of stable laws [3], we give a self-contained version of the Pareto-stable CAPM with several convenient expressions of beta [4]. Some of these expressions provide us with straightforward estimators of beta. We also address the issue of the Best Linear Unbiased Estimator (BLUE). Unfortunately, the BLUE program is solved only in Fama's restricted case. We have used the backtesting procedure proposed by Black in [5] in order to test our various estimators of beta. Black's procedure tends to show that leverage effects linked to beta can be efficiently exploited on the French market. Therefore, a simple statistical test based on this procedure was devised to determine whether beta's predictive power could still be improved with the stable hypothesis. Although no improvement has been realized so far, the statistical estimation of the stable beta is still an open issue and the testing procedure may prove to be of use for other new estimators.