Stochastic Portfolio Theory: an Overview

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Stochastic Portfolio Theory is a °exible framework for analyzing portfolio behavior and
equity market structure. This theory was introduced by E.R. Fernholz in the papers (Journal of
Mathematical Economics, 1999; Finance & Stochastics, 2001) and in the monograph Stochastic
Portfolio Theory (Springer 2002). It was further developed in the papers Fernholz, Karatzas
& Kardaras (Finance & Stochastics, 2005), Fernholz & Karatzas (Annals of Finance, 2005),
Banner, Fernholz & Karatzas (Annals of Applied Probability, 2005), and Karatzas & Kardaras
(2006). This theory is descriptive, as opposed to normative; it is consistent with observable
characteristics of actual portfolios and markets; and it provides a theoretical tool which is
useful for practical applications.
As a theoretical tool, this framework o®ers fresh insights into questions of stock 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 over a
decade.

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