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Institutional Investment - March 10, 2014

Improved Risk Reporting with Factor-Based Diversification Measures

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. This relationship, however, is highly linear, and the top performing portfolios in severe bear markets are typically portfolios concentrated in safe assets, as opposed to well-diversified portfolios. We also find statistical and economic evidence that this diversification measure has predictive power for equity market returns, a predictive power which becomes substantial over long holding period.

Overall our results suggest that the ENB measure could be a useful addition to the list of risk indicators reported for equity and policy portfolios.

This research was produced as part of the "New Frontiers in Risk Assessment and Performance Reporting" research chair at EDHEC-Risk Institute, in partnership with CACEIS.