Improved Risk Reporting With Factor-Based Diversification Measures

Summary:

This paper analyses various measures of portfolio diversification, and explores the implication in terms of advanced risk reporting techniques. We use the minimal linear torsion approach (Meucci et al. (2013)) to turn correlated constituents into uncorrelated factors, and focus on the effective number of (uncorrelated) bets (ENB), the entropy of the distribution of risk factor contribution to portfolio risk, as a meaningful measure of the degree of diversification in a portfolio. In an attempt to assess whether a relationship exists between the degree of diversification of a portfolio and its performance in various market conditions, we empirically analyse the diversification of various equity indices and pension fund policy portfolios. We find strong evidence of a significantly positive time-series and cross-sectional relationship between the ENB risk diversification measure and performance in bear markets.