Determining an Efficient Frontier in a Stochastic Moment Setting

Abstract

We analyze the problem of portfolio optimization under uncertainty in the assets return distribution. After characterizing the problem using a general formulation involving the product space of the return distribution with the parameter distribution, we propose the use of penalty functions to solve the resulting program. The connection to some important existing approaches is shown, and we then focus on two specific proposals with an important practical feature: the stability of the resulting portfolio composition under changing input variables. With high transaction costs and missing liquidity in some Brazilian markets, this stability feature is of great practical relevance. Finally, we show with an example from the Brazilian market that the penalty function approach does indeed increase stability, and seems to be a promising alternative whose long-range performance should be analyzed.

Keywords

• portfolio optimization
• model risk
• penalty function
• stable portfolios
• resampling