A Survey of Stochastic Portfolio Theory

The purpose of these lectures is to offer an overview of Stochastic Portfolio Theory, a rich and flexible framework for analyzing portfolio behavior and equity market structure. This theory was developed in the book by E.R. Fernholz (Stochastic Portfolio Theory, Springer 2002) and was studied further in the papers Fernholz (Journal of Mathematical Economics, 1999; Finance & Stochastics, 2001), Fernholz, Karatzas & Kardaras [FKK] (Finance & Stochastics, 2005), Fernholz & Karatzas [FK] (Annals of Finance, 2005), Banner, Fernholz & Karatzas [BFK] (Annals of Applied Probability, 2005), and Karatzas & Kardaras (preprint, 2006). It is descriptive as opposed to normative, is consistent with the observable characteristics of actual portfolios, and provides a theoretical tool which is useful for practical applications. As a theoretical tool, this framework provides fresh insights into questions of market structure and arbitrage, and can be used to construct portfolios with controlled behavior. As a practical tool, Stochastic Portfolio Theory has been applied to the analysis and optimization of portfolio performance and has been the basis of successful investment strategies for close to 20 years. I am indebted to my audience at Bowling Green, in particular to my colleagues Gabor Szekely, Gordon Wade, Haowen Xi and Craig Zirbel for the invitation to deliver the Eugene Lukacs lectures, for their interest and stimulating questions during the lectures, and for their hospitality. Many thanks are due to Constantinos Kardaras who read an early version of these notes and for offered many valuable suggestions, and to Adrian Banner for his many corrections to the manuscript.