Robust Portfolio Selection Problems

TLDR

This paper formulates and solves robust portfolio selection problems to mitigate sensitivity to statistical and modeling errors in market parameter estimates. The authors introduce uncertainty structures for market parameters, reformulate the resulting robust portfolio problems as second‑order cone programs, and provide a simple recipe for efficiently computing robust portfolios from raw data at a chosen confidence level. They show that the uncertainty structures align with confidence regions of the statistical estimation procedures and demonstrate that the proposed recipe yields robust portfolios efficiently.

Abstract

In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce “uncertainty structures” for the market parameters and show that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as secondorder cone programs and, therefore, the computational effort required to solve them is comparable to that required for solving convex quadratic programs. Moreover, we show that these uncertainty structures correspond to confidence regions associated with the statistical procedures employed to estimate the market parameters. Finally, we demonstrate a simple recipe for efficiently computing robust portfolios given raw market data and a desired level of confidence.