The worst-case risk of a portfolio

We show how to compute in a numerically efficient way the maximum risk of a portfolio, given uncertainty in the means and covariances of asset returns. This is a semidefinite programming problem, and is readily solved by interior-point methods for convex optimization developed in recent years. While not as general, this approach is more accurate and much faster than Monte Carlo methods. The computational effort required grows gracefully, so that very large problems can be handled. The proposed approach is extended to portfolio selection, allowing for the design of portfolios which are robust with respect to model uncertainty. • Contact: [email protected] • First draft: February 1999; Second draft: August 1999; This version: September 2000 • Research supported in part by NSF Grant ECS-9707111, by AFOSR Grant F4962098-1-0147, by MURI Grant 49620-95-1-0525, and by the Portuguese Government under Praxis XXI