Title: High dimensional portfolio optimization by wavelet thresholding
Authors: Sebastien Van Bellegem - Universite catholique de Louvain (Belgium) [presenting]
Abstract: The static mean-variance portfolio optimization takes the form of a quadratic programming problem under a linear constraint and uses the mean return vector and the cross-covariance matrix of an $N$-dimensional stationary process as inputs. Due to the fact that the process cannot be observed directly the mean return vector and the covariance matrix need to be replaced by estimates. In high-dimensional settings, e.g. when the number of assets is large relative to the sample size, the empirical covariance matrix is badly conditioned. Inversion of the covariance matrix is therefore unstable and portfolio optimization behaves poorly. We show that wavelet can achieve some decorrelation of the stationary process. We exploit this property and introduce a new thresholding rule of the empirical covariance matrix in the wavelet domain, based on a generalization of Tree Structured Wavelet (TSW) denoising. The consistency of the denoising procedure is established and we derive an optimal thresholding rule. Simulation studies show the good performance of the final optimizer compared to benchmarks and optimizers based on other regularization methods (such as e.g. Tikhonov).