Improved Risk Reporting with Factor-Based Diversification Measures

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

Executive Summary

measures. For each diversification measure (ENC and ENB), we thus obtain six sets of statistics, corresponding to the six periods of calculation of the average diversification measures. Since the FTSE 100 index appeared as a clear outlier, we compute these linear regressions without this outlier. Hence, the straight line drawn on Figure 1 corresponds to the coefficients calculated from the linear regressions without the outlier. We analyse in more detail the results for diversification measures computed at the end of August 2008; however, the results obtained on the other periods of computation of the diversification measures follow the same trend. The statistical analysis shows a clear positive linear relationship between the performance of the index on the period starting on September 2008 and ending at the end of February 2009, and each one of the two diversification measures computed at the end of August 2008. We observe that the positive relationship is statistically more significant for the ENB measure than for the ENC measure. Indeed, the regression based on ENB measures has a 92% confidence level and a 24.7% R-squared compared to the regression based on ENC measures, which only have an 84% confidence level and a 17.12% R-squared. In addition, the slope for the performance-to-ENB relationship is steeper (almost twice as steep) than the slope for the performance-to-ENC relationship. Overall, our results suggest that the higher the ENB of an index prior to the worst of the crisis, the more likely it was to perform better during September 2008-February 2009 compared to an index that had a lower ENB at the same date. This is again consistent with the interpretation of the ENB as a meaningful diversification

measure. Therefore, we conclude from this cross-sectional analysis that in a period of severe bear markets, equity indices that were the best diversified in terms of uncorrelated sources of risks (i.e. high ENB) prior to the period of market downturn exhibited better resistance than equity indices that enjoyed a lower degree of diversification. Diversification Measures for US Pension Funds We use the P&I Top 1,000 database to obtain information on the asset allocation of each of the 1,000 largest US pension funds as of 30 September 2002, 30 September 2007 and 30 September 2012. We exclusively focus on the portion allocated to their defined- benefit plan; if they also have a defined- contribution plan, we do not analyse the amount they allocate to this plan. In order to represent the different asset classes pension fund assets are invested in, we consider the following (arguably arbitrary) partition of the asset allocation: domestic fixed income; international fixed income; High-yield bond; inflation-linked bond; domestic equity; international equity; global equity; private equity; real-estate; commodity; mortgage; and cash. Once the partition is completed, we choose appropriate benchmarks for each asset class and use the MLT approach (Meucci et al. (2013)) to turn correlated asset class returns into uncorrelated factor returns. We estimate the ENB diversification measure for each pension fund in the database as of 30 September 2002, 30 September 2007 and 30 September 2012. We also compute the ENC, defined as the entropy of the asset class exposure, as of the same dates. This definition, which is maximised

11

An EDHEC-Risk Institute Publication