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.
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Submitted on : Thursday, June 9, 2011 - 9:01:15 AM Last modification on : Friday, September 6, 2019 - 1:14:36 AM
Lotfi Belkacem, Jacques Lévy-Vehel, Christian Walter. CAPM, Risk and Portfolio Selection in "alpha-Stable Markets". Fractals, World Scientific Publishing, 2000, 8 (1), pp.99-116. ⟨10.1142/S0218348X00000111⟩. ⟨inria-00599259⟩