Stochastic Portfolio Theory is a novel methodology, developed by E.R. Fernholz, for analysing
portfolio behaviour and equity market structure, constructing portfolios and understanding
the structure of equity markets. It thus has immediate applications to 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 market structure. 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 portfolio behaviour, stock market diversity, portfolio
generating functions and the concept of how to select stocks by their rank. We will also
contribute to both the theoretical as well as the practical aspects of Fernholz theory and
tackle some of the unsolved problems in Stochastic Portfolio Theory. We will also describe
how this new and fast-evolving theory can be applied, in particular, to equity management.