The Relevance of the Distributional Form of Common Stock Returns to the Construction of Optimal Portfolios

In this paper, we compare the robustness in application of the Gaussian assumption of security return distributions to the robustness of the general stable assumption. Using actual stock return data to simulate the “real world,†a stock market is constructed in which stock returns conform to a Gaussian distribution as well as to a stable Pareto-Levy distribution. Using these two sets of stock returns, efficient frontiers are generated under both assumptions of parametric environments. It is shown that the Gaussian assumption, and its incumbent statistical techniques, is preferable to the general stable assumption.