This fifth Lyxor White Paper tackles the issue of how Quantitative Methods can help in building a portfolio of Hedge Funds. To address this question one has to bear in mind that most of the so-called 'Portfolio Theory' has been developed under 'Perfect Markets' assumptions, with large cap equities, government bonds and FX markets in mind. 'Perfect Markets' share three essential characteristics:

1. Any relevant information when disclosed to somebody has to be disclosed to everybody;

2. Liquidity is high, market impact is limited and transaction costs are negligible;

3. Distributions of returns are close to be normal.

When it comes to hedge funds, these assumptions might hardly be satisfied. Hence, 'Portfolio Theory' is to be used with care.

Information issues are usually addressed by setting up tight due-diligence procedures. However history teaches that, in practice, putting in place and maintaining the necessary level of rigor in those processes is no easy task. Another possibility consists in accessing hedge funds through so-called managed account platforms. Such platforms provide simple yet efficient solutions to ensure that most due diligence rules are permanently enforced. Investments are made within a transparent fund envelope, following predefined investment guidelines which are enforced independently of the hedge fund manager. On top of that, some of these platforms help in standardizing and improving hedge fund liquidity. Putting aside the debate on the tracking error between hedge fund strategies and their platform equivalent, they provide a very satisfactory way to create an investment universe where both information and liquidity issues are controlled rigorously.

However, even managed under such 'secured' format, the distribution of hedge fund returns can be far from Gaussian. Running dynamic strategies, hedge funds can indeed generate option-like payoffs and hence asymmetric and fat tailed returns. Traditional Mean-Variance approaches are then doomed to be inadequate. Hence, one has to look for other approaches which, in turn, open the door to new unexpected pitfalls, some of them being developed in this White Paper. As an example, trying to account uncritically for skewness and kurtosis with monthly data, can lead to situations where the number of parameters to be estimated is much larger than the number of available data...

This White Paper has been written with a view to help investors understand, compare and find their way among the different available quantitative techniques. Our results suggest that even if those methods can provide useful insights, each of them only brings partial answers. As a consequence, we claim that hedge fund investment still cannot be considered as a commoditized job. It remains an expert field in which delegation and incentives structures have to be carefully designed. We hope you will find this study both interesting and useful in practice.

Nicolas Gaussel
Publishing Director
PhD, Global Head of Quantitative Asset Management