TUTORIAL ON STOCHASTIC PORTFOLIO THEORY.
(Columbia University and INTECH Investment Management LLC)
The goal of this series of four one-hour lectures is to introduce Stochastic Portfolio Theory, a rich and flexible framework for analyzing portfolio behavior and equity market structure, and to explore some of its applications to portfolio management and performance measurement.
The first three lectures are intended for a general audience; very little background is assumed.The third lecture will be of particular interest to portfolio managers who wish to learn of new methods of measuring the impact of size on their equity portfolios. The last lecture is designed for a more mathematically advanced audience, although all relevant background materialwill be I ntroduced throughout.
Here is a detailed summary of the four one-hour lectures:
Lecture 1: The Model for a Stock PriceLogarithms; basic probability theory, random variables, mean and variance; random walks; Brownian motion; drift; stock price models; rates of return and growth rates.
Lecture 2: Introduction to Stochastic Portfolio TheoryMultiple stocks; portfolio rate of return and growth rate; Excess Growth Rate (EGR); relative growth rates and numeraire independence of EGR; the EGR of the market portfolio.
Lecture 3: Size and the Distribution of CapitalStability of markets; the size effe ct; market diversity and diversity-weighted portfolios; the distributional component of return.
Lecture 4: The Mathematics of Stochastic Portfolio TheoryDefinitions; why the EGR of an all-long portfolio is nonnegative; portfolio generating functions; diversity and relative arbitrage; local times and ranked generating functions.
E.R. FERNHOLZ (2002) Stochastic Portfo
lio Theory. Springer Verlag, NY.
E.R. FERNHOLZ & I. KARATZAS (2009) Stochastic Portfolio Theory: An Overview.
Handbook of Numerical Analysis XV (A. Bensoussan & Q. Zhang, Editors). North-Holland, Amsterdam and Boston.