A study of robust portfolio optimization with European options using polyhedral uncertainty sets

Abstract

We consider the problem of maximizing the worst-case return of a portfolio when the manager can invest in stocks as well as European options on those stocks, and the stock returns are modeled using an uncertainty set approach. Specifically, the manager knows a range forecast for each factor driving the returns and a budget of uncertainty limiting the scaled deviations of these factors from their nominal values. Our goal is to understand the impact of options on the optimal portfolio allocation. We present theoretical results regarding the structure of that optimal allocation, in particular with respect to portfolio diversification. Specifically, we show that the presence of options only leads to limited diversification across the financial instruments available. We compare our robust portfolio to several benchmarks in numerical experiments and analyze how the optimal allocation varies with the budget of uncertainty. Our results indicate that our approach performs very well in practice.