TR-2004-11 Robust Portfolio Management

In this paper we present robust models for index tracking and active portfolio management. The goal of these models is to control the effect of statistical errors in estimating market parameters on the performance of the portfolio. The proposed models allow one to impose additional side constraints such as bounds on the portfolio holdings, constraints on the portfolio beta, limits on cash exposure, etc. The optimal portfolios are computed by solving second-order cone programs. Since the complexity of solving a second-order cone program is comparable to that of solving a convex quadratic program, it follows that the effort required to compute the optimal robust portfolio is comparable to that of computing the Markowitz optimal portfolio. We report on the performance of our robust strategies in tracking the S&P 500 index over 1994-2003. We find that our robust strategy is able to track the index with a significantly smaller number of assets than a non-robust mean-variance index tracking strategy. We propose a simple strategy for managing the cost of the robust index tracking strategy in markets with transaction costs. Our computational results also suggest that the robust active portfolio management strategy significantly outperforms the S&P 500 index without a significant increase in volatility.