Improved Risk Reporting with Factor-Based Diversification Measures

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

3. Empirical Analysis for Equity Indices

their first economic rescue plans. Therefore, we compare the annualised performances of the indices on the period starting at the beginning of September 2008 and ending at the end of February 2009 and their average diversification measures computed on six different periods. The average diversification measures are computed on periods immediately preceding the calculation of the index performance 7 . In Figure 7, we plot the annualised performances of the 14 equity indices between September 2008 and February 2009 with respect to each diversification measure computed at the date immediately preceding the period of bear market at the end of August 2008. We perform linear regressions in order to test the robustness of the relationship between performance and diversification measures. For each diversification measure (ENC and ENB), we 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 in Figure 7, we compute these linear regressions without this outlier. Our results are displayed in Table 4. In addition, the straight line drawn on Figure 7 corresponds to the coefficients calculated from the linear regressions without the outlier. We analyse in more details 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 displays a 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 a 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 suggests that the higher was 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 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 indices that were the most diversified in terms of uncorrelated sources of risks (i.e., high ENB) prior to the period of market downturn performed better than the others. However, even though there seems to be a positive relationship, it is not statistically proven that indices that were the best diversified in terms of constituents (i.e., high ENC) prior to the period of market downturn, performed better than the other equity indices. Hence, diversifying in terms constituents seem to be less rewarded than diversifying in terms of uncorrelated bets during bear market. For comparison purposes, we conduct the same analysis during a bull market period, focussing on the recovery period that started in the beginning of March 2009

7 - These periods being at the end of August 2008, during August 2008, during the quarter preceding September 2008, during the semester preceding September 2008, during the year starting on September 2007 and ending at the end of August 2008 and during the two-year period starting on September 2006 and ending at the end of August 2008.

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An EDHEC-Risk Institute Publication