Shortcomings in Advise versus the Art and Science of Investing in Hedge Funds

Abstract

Hedge Funds are often marketed as appealing alternative investment instruments. The quality of marketing arguments, used to seduce investors, are obviously function of the depth of market literacy of potential investors. In Italy, for instance, high returns, low volatility, and essentially no correlation with market indices, suffice to ease Investment Advisers task to seduce institutional investors with the potentially mined field of HF. Indeed neglecting the proper characteristics of HF instruments and extending with no precautions standard text book models and techniques like Markovitz portfolio optimization, may hide an unexpected risk. The risk of a sudden phase locking of the hedge fund investment with an extreme negative market move, thus amplifying the losses. Indeed, the full construct of Markovitz portfolio optimization is based on the hypothesis on normal multivariate joint distribution of the components. Only in this case the knowledge of the return, variance and correlation suffice to characterize the risk profile of the investment. However, even assuming Markovitz assumptions satisfied, zero correlation is extremely difficult to measure since blurred by measurement errors. Moreover the available data is extremely reduced to allow a satisfactory estimate of the parameters and any implied approach do not seems to be a feasible approach. It is thus important to understand how and to which extent the information embedded on the HF historical data bases can be used to build an efficient portfolio. In this article we will expose the problem of measuring correlations and how methods borrowed from theoretical physics, such as random matrices (Wigner 1960), can be used to noise undress raw correlation matrices. Cleaned correlation matrices are then visualized in the subdominant ultrametric space through their Minimum Spanning Tree representation in order to classify, via a similarity measure, funds in homogeneous clusters of management styles. In this case, assuming elliptic joint distribution of the returns, we will complete the portfolio diversification concept by maximizing dissimilarity of the fund managers investment style.