Stochastic portfolio theory and its applications to equity management

Abstract

Stochastic portfolio theory is a novel methodology, developed by Fernholz (2002), for analysing stock and portfolio behaviour, and equity market structure, constructing portfolios and understanding the structure of equity markets. It thus has immediate applications to equity portfolio management and performance measurement. This theory successfully generalises well-known models for the stock price to provide models for portfolios and markets, leading to a better and more precise understanding of equity market structure. The aim of this dissertation is to present an exhaustive review of stochastic portfolio theory by imitating the work done and contributions made by Fernholz (2002) thus far. A detailed discussion of stochastic portfolio theory as well as how the implications di er from the conclusions and results of classic portfolio theory will be provided. In this dissertation, we will undertake a thorough investigation into stochastic portfolio theory; by focusing on the central, innovative ideas of the excess growth rate, long-term stock market and portfolio behaviour, stock market diversity of equity markets, portfolio generating functions, the concept of how to select stocks by their rank and the existence of relative arbitrage opportunities within the context of stochastic portfolio theory. Thus, we shall review the central concepts of stochastic portfolio theory, this will include a detailed explanation of the excess growth rate, long-term behaviour of portfolios, stock market diversity, portfolio generating functions and stocks selected by rank. We will also present examples of portfolios and markets with a wide variety of di erent properties. We will also show how this new and fast-evolving theory can be applied, in particular, to equity management, by considering the performance of certain functionally generated portfolios. Furthermore, several results and implications of stochastic portfolio theory will be discussed, and in this dissertation, we shall examine these results in far greater depth. Keywords and Phrases: Stochastic portfolio theory, Portfolios, Stock market and portfolio behaviour, Stock market diversity, Portfolio generating functions, Functionally generated portfolios, Rank-dependent portfolio generating functions, Local time, Relative arbitrage opportunities, Performance of functionally generated portfolios.