CAPM, Risk and Portfolio Selection in "alpha-Stable Markets"

Abstract : Our main purpose in this paper is to derive the generalized equilibrium relationship between risk and return under the assumption that the asset returns follow a joint symmetric \alpha-stable distribution, with 1< \alpha <2. In order to justify such an investigation, we start by empirically evidencing the fractal structure of stocks market through extensive tests of self-similarity and stability. These tests allow us to model price changes with \alpha-stable distributions. We then show that equilibrium rates of return on all risky assets are functions of their covariation with the market portfolio. The "stable" CAPM highlights a new measure of the quantity of risk which may be interpreted as a generalized beta coefficient.