CAPM, risk and portfolio selection in "alpha-stable markets"

Our main purpose in this paper is to derive the generalized equilibrium rel ationship between risk and return under the assumption that the asset retur ns follow a joint symmetric a-stable distribution, with 1 < alpha < 2. In o rder to justify such an investigation, we start by empirically evidencing t he fractal structure of stocks market through extensive tests of self-simil arity and stability. These tests allow us to model price changes with a-sta ble distributions. We then show that equilibrium rates of return on all ris ky assets are functions of their covariation with the market portfolio. The "stable" CAPM highlights a new measure of the quantity of risk which may b e interpreted as a generalized beta coefficient.