We propose a portfolio selection model in a single-period setting which takes into account asymmetry of returns distribution. We assume that an agent is non satiate, risk averse and displays prudence (according to the definition given in Kimball). We assume also that the agent's preferences are represented by Expected Utility with a cubic utility function. This implies that the agent displays a skewness preference, ceteris paribus. The asymmetry on returns distribution arises from a stochastically independent noise added to the symmetric distribution of asset returns. By assuming that the agents in the markets have homogeneous beliefs on returns distribution and that all agents display skewness preference, we derive an equilibrium relation which extends the classical Capital Asset Pricing Model (CAPM) to evaluate skewness. The equilibrium model is drawn on individual agent's choice and is based on a three-fund separation property. The extended CAPM presents for each risky asset a discount on positive systematic skewness, which is the ratio given by co-skewness of the asset return to market skewness. This implies that, for a given variance, an agent can trade in some expected return for positive systematic skewness. This is consistent with the result obtained by Kraus & Litzenberger from different assumptions on returns and preferences. We provide also some numerical examples.
