Modeling Stock Returns as Mixtures of Normals and Incorporating Black-Litterman Views in Portfolio Optimization

In this paper, we consider the basic problem of portfolio construction in financial engineering, and analyze how market-based and analytical approaches can be combined to obtain efficient portfolios. As a first step in our analysis, we model the asset returns as a random variable distributed according to a mixture of normal random variables. We then discuss how to construct portfolios that minimize the Conditional Value-at-Risk under this probabilistic model. Furthermore, we incorporate the market equilibrium information into this procedure through the well-known Black-Litterman approach via an inverse optimization framework. Our computational experiments on a real dataset show that this approach with an emphasis on the market equilibrium typically yields less risky portfolios than a purely market-based portfolio while producing similar returns on average.