Essays on Hedge Fund Replication: Methodological Assessment and Development of the Factor Approach, Nonlinear Modeling and Policy Perspectives

This dissertation is concerned with hedge fund replication, a subject of a practical and theoretical importance, both from an investment and a risk management point of view. One of our goals is to extend known methodologies in order to enhance our understanding of an industry that is known for its secrecy and its lack of transparency. A second goal is to contribute to the quantitative finance literature with improved techniques for hedge fund replication. Hedge fund replication (HFR) is approached from the methodological as well as from practical and regulatory perspectives. The first two chapters provide the motivation and the theoretical and methodological foundations of this work. In the third chapter, we review and demonstrate the superiority of the linear tracking problem approach over more classical methodologies. This chapter also clarifies and explains in terms of portfolio management’s terminology how Bayesian filters, like the Kalman filter, actually proceed to find (close to) optimal solutions to the HFR tracking problem. We also demonstrate how practical concerns such as separating the funds’ beta and alpha are readily addressed by this dynamic approach. The fourth chapter extends the approach to nonlinear settings. We develop some advanced tools and algorithms which are needed to explore the presence and the replication of sources of nonlinearity in hedge fund returns. In the fifth chapter we introduce a methodology based on minimax filters (instead of Bayesian filters) which is robust to modeling misspecifications and therefore adapted for use independently of an underlying dynamic. We also introduce a new statistic, dubbed ζ, whose purpose is to detect the presence of unmodelled sources of performance. The sixth chapter addresses the problem of model and factor selection. Unlike most of the literature on the subject, we use a Bayesian variable selection approach. We develop a reversible-jump MCMC algorithm to estimate the posterior density of the models. The rationale for choosing this angle over the classical information criterion approach is also provided. Making use of the recent Madoff scandal, we examine in our last chapter the potential impact of HFR techniques on the regulatory framework of the asset management industry.