Hedge Fund Modelling and Analysis using MATLAB

CHAPTER 4 Mean-Variance Optimisation

Hedge fund analysis primarily involves ascertaining relevant statistical properties of the hedge fund returns distribution in order to make informed decisions about the characteristics and performance of a hedge fund. We have already looked in detail at the two most prominent statistical parameters most often cited: the mean and standard deviation. In 1952, H.M. Markowitz introduced the topic of modern portfolio theory which opened up the possibility of being able to optimise a portfolio of assets so as to minimise the portfolio risk for an acceptable level of portfolio return. Clearly, such a technique is extremely valuable to hedge fund managers, especially when dealing with asset allocation and the efficient distribution of wealth across a portfolio.

Chapter 4 introduces the main ideas behind mean-variance optimisation and shows how a simple hedge fund optimisation problem to minimise the portfolio variance can be set up and solved. The chapter also looks at a common modification of the minimum variance optimisation problem in terms of maximising the Sharpe ratio.

4.1 PORTFOLIO THEORY

4.1.1 Mean-Variance Analysis

All hedge fund managers would like to achieve the highest possible return from their investment portfolios; however, this has to be weighed up against the amount of risk they are willing to accept. Figure 4.1 shows the risk-return scatter plot for the 10 hypothetical hedge funds with monthly returns.

Figure 4.1 Risk-return ...