M. Senneret, Y. Malevergne, P. Abry, G. Perrin, L. Jaffrès
Asset allocation is one of the most crucial and difficult tasks in financial engineering. In many allocation strategies, the estimation of large covariance or precision matrices, estimated on multivariate observations from short time windows is a mandatory but difficult step. In this contribution, a large selection of covariance and precision matrix estimation procedures is organized into classes of estimation principles to allow a comparative review of their performance. To complete this overview, several additional estimators are explicitly derived and studied theoretically. Rather than the estimation performance evaluated from simulated data, the performance of the estimation methods is empirically evaluated by financial criteria (volatility, Sharpe ratio, …), to quantify the quality of the asset allocation in the mean-variance framework.
This paper is published in the September 2016 Special Issue “Financial Signal Processing and Machine Learning for Electronic Trading” of the IEEE Journal on Selected Topics in Signal Processing. It was also presented in the 1st Financial Management Agora, set up by the AFG to foster exchanges between practitioners and academic researchers.