Portfolio Selection via Independent Component Analysis

Different authors have remarked that the first two moments of the return distribution do not adequately summarize the investor’s preferences. However, higher-order moment portfolios perform poorly out-of-sample due to the estimation error and the curse of dimensionality. To circumvent this problem, we rely on minimum Modified Value-at-Risk portfolio based on independent components (ICs) which are the rotation of the principal components (PCs) that are independent as possible. On one hand, the ICs are useful for dimension reduction by retaining only the first high variance factors. On the other hand, we harness the near independence of the ICs to parsimoniously estimate the higher-order moments. Finally, out-of-sample studies reveal that minimizing the portfolio MVaR with this parsimonious estimation of the higher-order moments on the ICs yields solid financial performance in terms of higher-order risk. However, this strategy generally tends to generate higher turnover and less performing mean-variance trade-off.