On robust mean-variance portfolios

Abstract

We derive closed-form portfolio rules for robust mean–variance portfolio optimization where the return vector is uncertain or the mean return vector is subject to estimation errors, both uncertainties being confined to an ellipsoidal uncertainty set. We consider different mean–variance formulations allowing short sales, and derive closed-form optimal portfolio rules in static and dynamic settings.

Keywords:

• Robust optimization
• mean–variance portfolio theory
• ellipsoidal uncertainty
• adjustable robustness

Notes

No potential conflict of interest was reported by the authors.

1 Garlappi et al. [18] treat the problem RMVP3 that we address further below without a riskless asset. Their solution requires the numerical solution of a quartic polynomial.