Non-normality of rates of return on financial assets and portfolio management.

Summary We study the properties of the distribution of rates of return on financial securities and assess their impact on portfolio management. First, we estimate the distributional characteristics of the rates of return and extend this by studying the in-sample properties of the semi-moment estimators. With the latter we develop and study a normality test adapted to finance, which we use to estimate the speed of convergence of the distribution of rates of return to normality as a function of the horizon. We assess the impact of the non-normality of the rates of return on the empirical performance of the CAPM, through the semi-components. Finally, we study portfolio selection methods under non-normality and establish one based on distances between densities, using Gram-Charlier developments to obtain the distribution of portfolio returns, conditional on stock weights.