Robust Portfolio Management with Uncertain Compounded Rates of Return

Lehigh University, Bethlehem PA

Investigators

Abstract

This grant provides funding to investigate the models, insights and algorithms arising in portfolio management when the uncertain rates of return and the investor's risk preferences are quantified using robust optimization techniques based on uncertainty sets. Robust optimization aims at protecting a system against unknown but bounded disturbances, and hence does not require the precise knowledge of the underlying probability distributions. Furthermore, it allows the expression of risk preferences through the degree of protection chosen by the user. The goal of this research is to explore a variety of analytical approaches that capture the uncertainty drivers observed in real life and the fund manager's attitude towards them, in a framework that is easy to implement by finance practitioners. A novel aspect of the PI's methodology is that she will model the continuously compounded rates of return, rather than the actual returns, as parameters belonging to uncertainty sets, in order to build upon the famous Lognormal model of asset prices while addressing its limitations, and increase the relevance of the robust optimization models for practitioners. If successful, these activities will lead to a comprehensive theory of portfolio management under uncertainty, which will be tightly connected to the information available in practice and the manager's behavior, and will mitigate the uncertainty faced by financial decision-makers while maintaining performance. The PI will analyze models of increasing difficulty, with and without derivatives, with and without short sales, to develop optimal asset allocation guidelines. This research will lead to a better understanding of the following issues: (i) What theoretical insights can be gained regarding the extent of which uncertainty, information and risk preferences affect the optimal strategy? (ii) What are the algorithmic benefits of the robust optimization approach over traditional methods, in particular, in regard to tractability for large-scale problems? The PI's conclusions will be validated through extensive numerical experiments using real data provided by her institution's Financial Services Laboratory.