CAPM, Risk and Portfolio Selection in «Stable» Markets
Résumé
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 {\bf 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.