Improved Risk Reporting with Factor-Based Diversification Measures

Improved Risk Reporting with Factor-Based Diversification Measures — February 2014

5. Conclusion

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. Our work can be extended in several dimensions. In particular, the analysis developed in this paper could be used not only to measure, but also to manage, diversification within an equity or policy portfolio. We encourage interested readers

to look at Meucci et al. (2013) and Deguest et al. (2013) for a thorough empirical and theoretical analysis of the properties of portfolios designed to maximise the effective number of bets. Regarding the empirical analysis of diversification for equity portfolios, another natural extension of our work would consist in comparing the degree of diversification for various weighting schemes based on the same investment universe. While we have looked at cap-weighted and equally- weighted equity index portfolios only, it would be useful to also assess the degree of diversification achieved by minimum variance portfolios or risk parity portfolios, amongst other examples of so-called smart beta indices. Yet another useful extension of the paper would consist in repeating the analysis we have conducted for pension funds for endowments. We leave this extension for further research.

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An EDHEC-Risk Institute Publication