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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/13943 |
| Date | 25 February 2014 |
| Creators | Bonney, Lisa |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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