Improved Risk Reporting with Factor-Based Diversification Measures

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

Executive Summary

Table 1: Time-Series Analysis of the Relationship Performances/Diversification for the S&P500 These two tables display the diagnostics of the linear regression between the annualised performance of the S&P500 computed on different periods and its ENC and ENB. Each diversification measure is computed weekly over the whole historical data period of the S&P500. Annualised performances of the S&P500 are calculated at a weekly frequency on each quarter, each semester, each year, each 2-year period, each 5-year period and each 10-year period immediately following the dates of computation of each diversification measure. (a) ENC ∆ t Following Quarter Following Semester Following Year Following 2-Y Following 5-Y Following 10-Y

Coefficients

0.22

0.22

0.28

0.33

0.28

0.27

R-Squared

0.36%

0.70%

2.37%

6.88%

12.52%

22.13%

t-stat

3.20

4.47

8.28

14.30

19.32

25.84

p-value

0.14%

0.00%

0.00%

0.00%

0.00%

0.00%

(b) ENB

∆ t

Following Quarter

Following Semester

Following Year

Following 2-Y

Following 5-Y

Following 10-Y

Coefficients

0.39

0.30

0.21

0.25

0.33

0.42

R-Squared

0.86%

0.96%

0.99%

2.86%

11.02%

32.00%

t-stat

4.98

5.25

5.31

9.02

17.98

33.25

p-value

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

more meaningful measure of diversification compared to the entropy of the distribution of the dollar contributions to the portfolio from correlated assets. After having approached the problem from a time-series perspective, we then test the link between diversification measures and the performance of equity indices from a cross-sectional perspective. To do so, we conduct an analysis of the relationship between the performance of the 14 equity indices during the sub-prime crisis and their diversification measures computed at some point before the crisis started. The indices we consider in this analysis are the S&P 500 and 13 other popular equity indices, namely the CAC 40 index, the DAX 30 index, the Dow Jones 30 index, the Euro Stoxx 50 index, the Euro Stoxx 300 index, the FTSE 100 index, the FTSE All World index, the Hang Seng index, the Nasdaq 100 index, the SPI index, the Stoxx Europe 200 index, the Stoxx Europe 600 index and the Topix

100 index. For each of these indices, we compute the ENC measure and the ENB measure on the longest available time period. We seek to perform the analysis on a period of particularly severe market correction in order to test whether the indices that were the best diversified in terms of the effective number of uncorrelated risk contributions (that is to say with the highest ENB) at some date prior to the start of the crisis tend to perform the best during the subsequent bear market period. Our choice for a sample period including a recent severe bear market is the period ranging from the beginning of September 2008 until the end of February 200 – a period starting when the US subprime crisis propagated to the banking sector and turned into a global financial crisis, and finishing when a first relief was obtained as the United States and other developed countries issued their first economic rescue plans.

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An EDHEC-Risk Institute Publication