Min-Max Portfolio Optimization

Modern investment processes often use quantitative models based on Markowitz’s mean-variance approach for determining optimal portfolio holdings. A major drawback of using such techniques is that the optimality of the portfolio structure only holds with respect to a single set of expected returns. Becker, Marty, and Rustem introduced the robust min-max portfolio optimization strategy to overcome this drawback. It computes portfolio holdings that guarantee a worst case risk/return tradeoff whichever of the specified scenarios occurs. This paper extends the approach to include transaction costs. We illustrate the advantages of the min-max strategy on balanced portfolios. The importance of considering transaction costs when rebalancing portfolios is shown. The experimental results illustrate how a portfolio can be insured against a possible loss without sacrificing too much upside potential.