Understanding robust optimization by analyzing robust equity portfolios

Abstract

In this dissertation, we study the behavior of robust portfolios to further understand robust optimization. We analyze robust equity portfolios formed from robust optimization to find noticeable properties that can help us understand how robust optimization achieves robustness. First, since robust optimization focuses on the worst case, we begin by analyzing the worst case in financial markets. While the equity market exhibits distinct movements during its worst case such as increased correlation among individual stock returns, we confirm the importance of information during the worst case for gaining robustness. We also present an algorithm that uses worst-case information to form robust portfolios without solving robust optimization problems. Second, we examine the factor exposure of robust portfolios constructed from the robust formulation with an ellipsoidal uncertainty set on expected returns. We analytically derive that portfolios with increased robustness are more dependent on factor movements compared to classical mean-variance portfolios. Third, the dependency on market factors of robust portfolios is empirically confirmed. We perform a comprehensive test by observing robust portfolios with box and ellipsoidal uncertainty sets and also by using various risk levels, rebalancing periods, and constraints on portfolio weight. Our results show a strong connection between robustness and factor exposure. Last, we investigate the composition of robust portfolios to reveal properties at the individual stock level. Robust portfolios are shown to invest in less number of stocks and also to refrain from holding large positions. While robust portfolios only allocate small amounts to each stock, it appears to invest relatively more in low-beta stocks. The findings in this study will provide a better understanding of robust portfolio optimization as well as robust optimization in general, and the identified properties will be valuable for formulating improved robus...