Optimal Portfolio Diversification via Independent Component Analysis
46 Pages Posted: 9 Dec 2018 Last revised: 29 Jan 2020
Date Written: January 28, 2020
A popular approach to enhance portfolio diversification is to use the factor-risk-parity portfolio, which is the portfolio whose return variance is spread equally among the principal components (PCs) of asset returns. Although PCs are unique and useful for dimension reduction, they are an arbitrary choice because any rotation of the PCs remains uncorrelated. This is problematic because we demonstrate that any portfolio is the factor-variance-parity portfolio corresponding to a specific rotation of the PCs. To overcome this problem, we rely on the factor-risk-parity portfolio based on the independent components (ICs), which are the rotation of the PCs that are maximally independent, and thus, account for higher moments in asset returns. We demonstrate that using the IC-variance-parity portfolio helps to reduce the return kurtosis. We also show how to exploit the near independence of the ICs to parsimoniously estimate the factor-risk-parity portfolio based on Value-at-Risk. Finally, we empirically demonstrate that portfolios based on ICs outperform those based on PCs, and the minimum-variance portfolio.
Keywords: Portfolio selection, risk parity, factor analysis, principal component analysis, higher moments
JEL Classification: G11
Suggested Citation: Suggested Citation