# Portfolio

# Selecting the Optimum Portfolio

## Introduction

By employing a modified utility-based model - that accommodates both real estate's relative illiquidity and investor attitudes towards risk - this chapter seeks to provide a better understanding of its role within a mixed-asset portfolio. However, before an assessment of the risk and return characteristics of real estate within a mixed-asset portfolio is undertaken, a review of mean-variance portfolio theory and utility-based decision making is required.

In order to solve any decision problem an investor has to define both an opportunity set and a preference function. Defining the opportunity set is the focus of the first section of this chapter. It discusses the possible constructions of an investor's opportunity set and how, with some very general assumptions about preferences, an investor can limit this set to the efficient frontier.

Assuming that mean-variance space is the relevant space for portfolio analysis, the risk and return characteristics of a portfolio of securities are examined. This was undertaken initially by studying the attributes of combinations of two risky assets. It was then extended by analysing combinations of all possible risky assets, delineating that subset of portfolios preferred by all investors who exhibit risk avoidance as well as prefer more to less.

Relaxing the mean-variance assumption, the next section proceeds to review the expected utility theorem, discussing how to choose amongst an investor's opportunity set or, alternatively, how to specify an investor's preference function.

Finally, in considering real estate's relative illiquidity and investor attitudes towards risk, a modified utility-based model is then employed in an attempt to better understand its role within a mixed-asset portfolio.