Outperforming the Market: Stochastic Portfolio Theory in the Face of Transaction Costs

Abstract

The question of investment strategy and portfolio optimization is always relevant in the world of mathematical finance. Banks, hedge funds, and portfolio managers are always trying to outperform the market and have greater returns, using mathematical models to aid in their investment decisions. There are many different ways to model a stock market in order to choose which stocks to invest in. One such model is presented by E. Robert Fernholz in his monograph Stochastic Portfolio Theory. He provides a descriptive mathematical framework for the behavior of stocks, and then further describes a method for the creation of portfolios that take advantage of market structure in order to outperform the market. This framework makes very few assumptions about the market and stocks; moreover, it is a descriptive theory, rather than a normative one. As such, it should apply practically to the real world and work using actual stock data.

However, the model does not take into account some frictions present in real world stock markets. This thesis analyzes the performance of Fernholz’s theory using S&P500 stock data to determine the impact transaction costs have on the framework. Several portfolios are analyzed and compared to determine how much worse they perform in the presence of transaction costs. We then compare portfolios to determine which ones are the most sensitive to transaction costs. Two evaluation metrics, the mean relative loss and the annualized returns, are examined in order to determine a portfolio’s sensitivity to these costs. Finally, we determine which portfolios have the best performance when faced with transaction costs.