Portfolio optimization when asset returns have the Gaussian mixture distribution
In this paper we consider a portfolio optimization problem where the underlying asset returns are distributed as a mixture of two multivariate Gaussians; these two Gaussians may be associated with distressed and tranquil market regimes. In this context, the Sharpe ratio needs to be replaced by other non-linear objective functions which, in the case of many underlying assets, lead to optimization problems which cannot be easily solved with standard techniques. We obtain a geometric characterization of efficient portfolios, which reduces the complexity of the portfolio optimization problem.
portfolio optimization gaussian mixture distribution sharpe ratio mixture of normals distribution market distress hedge fund portfolio lower partial moment efficient frontier hodges modified sharpe ratio exponential utility correlation switching regime switching asset allocation commodity trading advisor probability of shortfall distress sensitivities fund of funds