Improved Risk Reporting with Factor-Based Diversification Measures

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

Appendices

C. Tables Table 1: Correlations in % Among the Diversification Measures ENC

ENB-MLT

ENB-PCA

ENB-FFF

ENC

100.00

11.82

-11.18

1.64

ENB-MLT

11.82

100.00

1.58

-29.10

ENB-PCA

-11.18

1.58

100.00

10.43

ENB-FFF 100.00 This table displays the correlations (in %) of increment of the Effective Number of Constituents (ENC) and increments of the various versions of the Effective Number of Uncorrelated Bets (ENB) for the S&P500. The ENB has been computed with a PCA approach, an MLT approach, and uncorrelated Fama-French factors. The PCA and MLT methods are based on a robustified version of the sample covariance matrix estimated with rolling-windows of 52 weeks of constituents’ returns between December 1959 until the end of December 2012. Then the correlations that are reported in the table are computed with diversifications measures obtained at a weekly frequency from December 1959 to December 2012. Table 2: Cross-Sectional Analysis of the Relationship Between the Number of Constituents of 14 Equity Indices and their Diversification Measures ENC ENB Coefficients 0.42 0.49 R-Squared (%) 96.06% 99.25% t-stat 16.39 38.26 p-value (%) 0.00% 0.00% This table displays the diagnostics of the linear regression between the amount of constituents composing the 14 equity indices and the ENC and ENB of each index. The amount of constituents are the indices’ facial number of constituents. The diversification measures are the averages of diversification measures computed over the largest historical data-set available for each equity index. 1.64 -29.10 10.43

Table 3: Correlations in % Between Diversification Measures and Economic Indicators Correlation S&P500 GARCH Vol. Credit Spread Int. Rate Term Spread FFF1

FFF2

FFF33

FFF4

ENC

1.90

-10.97

-7.95

-0.69

3.21

2.39

9.94

5.61

-4.42

ENB 2.05 This table displays the correlations (in %) of three diversification measures of the S&P500 and several economic indicators. The diversification measures are the Effective Number of Constituents (ENC) and the Effective Number of Uncorrelated Bets (ENB) computed using an MLT approach. The economic indicators are the cumulated returns of the S&P500, the GARCH Volatility, the Term Spread, the Credit Spread, the Interest Rate and the four Fama-French factors (FFF). These correlations have been computed on the period ranging from January 1959 to December 2012. -2.64 -0.72 -3.9 2.56 -3.52 -3.42 -6.38 -2.4

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An EDHEC-Risk Institute Publication