A study of robust portfolio optimization with European options using polyhedral uncertainty sets. (2021) - Ashrafi, Hedieh
Highlights: We combine two techniques to address risk in portfolio management: robust optimization and European options. We study three models: a strong guarantee model, a weak guarantee model and a combined strong and weak guarantee model. We provide theoretical insights into diversification, focusing on the number of calls and puts for each asset at optimality. We show our models perform very well compared to benchmarks including those in Zymler et al. [24] in a case study. in a case study. 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.