Improved Risk Reporting with Factor-Based Diversification Measures

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

1. Introduction

world's 10 largest pension funds. In a first application to international equity indices, we use the minimal linear torsion approach (Meucci et al. (2013)) to turn correlated constituents into uncorrelated factors, and find statistical evidence of a positive (negative) time-series and cross-sectional relationship between the ENB risk diversification measure and performance in bear (bull) markets. We find a weaker relationship when using other diversification measures such as the effective number of constituents (ENC), thus confirming the relevance of the effective number of bets on uncorrelated risk factors as a meaningful measure of diversification. Finally, we find the predictive power of the effective number of bets diversification measure for equity market performance to be statistically and economically significant, comparable to predictive power of the dividend yield for example (Cochrane (1997)), with an explanatory power that increases with the holding period. In a second application to US pension fund policy portfolios, we find that better diversified policy portfolios in the sense of a higher number of uncorrelated bets tend to perform better on average in bear markets, even though top performers are, as expected, policy portfolios highly concentrated in the best performing asset class for the sample period under consideration. Overall, our results suggest that the effective number of (uncorrelated) bets could be a useful risk indicator to be added to risk reports for equity and policy portfolios. The rest of the paper is organised as follows. In Section 2, we review various measures of portfolio diversification, and argue in favour of risk- and

investment vehicles has been put in question. For example, Ang et al. (2009) argue in favour of replicating mutual fund returns with suitably designed portfolios of factor exposures such as the value, small cap and momentum factors. 1 Similar arguments have been made for private equity and real estate funds, for example. On the other hand, allocating to risk factors should provide a better risk management mechanism, in that it allows investors to achieve an ex-ante control of the factor exposure of their portfolios, as opposed to merely relying on ex-post measures of such exposures. In this paper, we first review a number of weight-based measures of (naive) diversification as well as risk-based measures of (scientific) diversification that have been introduced in the academic and practitioner literatures, and analyse the shortcomings associated with these measures. We then argue that the effective number of (uncorrelated) bets (ENB), formally defined in Meucci (2009a) as the dispersion of the factor exposure distribution , provides a more meaningful assessment of how well-balanced is an investor’s dollar (egg) allocation to various baskets (factors). We also provide an empirical illustration of the usefulness of this measure for intra-class and inter-class diversification. For intra-class diversification, we cast the empirical analysis in the context of various popular equity indices, with a particular emphasis on the S&P500 index. For inter- class diversification, we analyse policy portfolios for two sets of pension funds, the first set being a large sample of the 1,000 largest US pension funds and the second set being a small sample of the

1 - In the same vein, Hasanhodzic and Lo (2007) argue for the passive replication of hedge fund vehicles, even though Amenc et al. (2010) found that the ability of linear factor models to replicate hedge fund performance is modest at best.

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An EDHEC-Risk Institute Publication