Rayleigh Portfolios and Penalised Matrix Decomposition

Francois Buet-Golfouse, Hans Roggeman, Islam Utyagulov

Abstract: Since the development and growth of personalised financial services online, effective tailor-made and fast statistical portfolio allocation techniques have been sought after. In this paper, we introduce a framework called Rayleigh portfolios, that encompasses many well-known approaches, such as the Sharpe Ratio, maximum diversification or minimum concentration. By showing the commonalities amongst these approaches, we are able to provide a solution to all such optimisation problems via matrix decomposition, and principal component analysis in particular. In addition, thanks to this reformulation, we show how to include sparsity upper bounds in such portfolios, thereby catering for two additional requirements in portfolio construction: robustness and low transaction costs. Importantly, modifications to the usual penalised matrix decomposition algorithms can be applied to other problems in statistics. Finally, empirical applications show promising results.