Date of Award
PhD in Business
Department of Mathematical Sciences: Business Analytics
Dominique M. Haughton
Victoria R. Steblovskaya
Jose M. Marin Vigueras
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.
Weisang, Guillaume, "Essays on Hedge Fund Replication: Methodological Assessment and Development of the Factor Approach, Nonlinear Modeling and Policy Perspectives". 2011. 2.