7.1 INTRODUCTION

Since the 1950s, mean variance optimization has been widely used to construct portfolios of traditional assets, such as stocks and bonds. Over the past 10 years, alternative investments such as hedge funds have risen in prominence. There are currently more than 6,000 registered hedge funds worldwide. Many have performed well in bull and bear markets and there has been a significant flow of assets into hedge funds.

It is natural to ask the question: how much of an investor s portfolio should be allocated to a specific hedge fund or a portfolio of hedge funds? The usual approach has been to incorporate hedge funds in a mean variance framework. However, many hedge funds have outperformed stocks and bonds (in a risk-adjusted sense) over the past few years; thus, a na ve optimizer would allocate nearly all assets to these funds rather than traditional assets. Many fund of funds have capped the allocation to hedge funds at 20 30% in an ad hoc way. This reflects the idea that there are subtle risks in hedge fund investing; we list some of these below:

• The true volatility of a hedge fund may be much larger than its historical volatility. Managers who trade illiquid assets tend to receive disproportionately large allocations according to mean variance theory. Since the assets do not trade much, portfolio returns tend to have a large serial correlation from month to month. This lowers the calculated historical volatility.