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 α-stable distribution, with 1<α<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 α-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.
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Belkacem et al. (2000) studied this question.
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