Standard mean-variance analysis is based on the assumption of normal return distributions. However, a growing body of literature suggests that the market oscillates between two different regimes - one with low volatility and the other with high volatility. In such a case, even if the return distributions are normal in both regimes, the overall distribution is not - it is a mixture of normals. Mean-variance analysis is inappropriate in this framework, and one must either assume a specific utility function or, alternatively, employ the more general and distribution-free Second degree Stochastic Dominance (SSD) criterion. This paper develops the SSD rule for the case of mixed normals: the SSDMN rule. This rule is a generalization the mean-variance rule. The cost of ignoring regimes and assuming normality when the distributions are actually mixed normal can be quite substantial - it is typically equivalent to an annual rate of return of 2-3 percent.
- Portfolio optimization
- Stochastic dominance
All Science Journal Classification (ASJC) codes
- Computer Science(all)
- Modelling and Simulation
- Management Science and Operations Research
- Information Systems and Management