• econophysics
• minimal spanning tree
• hierarchical clustering
• kalman filter
• hedge funds

In the present thesis we discuss some statistical methods for Hedge Funds.
We can split the work in two parts.
In the former part we apply some econophysics techniques, to obtain economic information about the hierarchical structures and the taxonomy of the
Hedge Funds strategies. We discuss some filtering procedures, based on hierarchical clustering, for the correlation matrix . As a result of the clustering
procedure, a hierarchical tree of the elements of the system is obtained. In particular, we focus our attention on two correlation based hierarchical clustering
procedures. The first one is the single linkage clustering method that is used to
detect a hierarchical organization of hedge funds. Using such method it is possible, in a unique way, to associate a Minimum Spanning Tree (the shortest tree
connecting all the elements in a graph) to hedge funds. The second procedure is
the average linkage which provides different economic information. These two
approaches reveal topological (throughout the MST) and taxonomic (throughout the hierarchical tree) aspects of the correlation present among indexes.
Hedge fund replication based on factor models is encountering growing interest, in particular a linear model has been proposed as a possible reduced
form model. This question concerns the latter part of this thesis. We apply
a technique borrowed from engeneering, the Kalman filter, to capture the dynamic linear factors (also known as betas) of hedge funds. The Kalman filter is
a computational algorithm that makes optimal use of data on a linear and near
linear system with Gaussian errors to continuously update the best estimate of
the systems past, current and even future state. Initially we test the filtering
procedure with a Monte Carlo Simulation and then we apply the algorithm to
hedge funds returns. Finally we compare this technique with the Ordinary Least
Squares regressions.