Improved Risk Reporting with Factor-Based Diversification Measures

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

Appendices

Table 8: Factors’ Exposures in % with the PCA Approach F 1 F 2 F 3 F 4

F 5

F 6

F 7

F 8

F 9

F 10

F 11

US Bonds

-2.00 -0.41 1.26 15.20 40.20 16.84 3.28 -14.70 -58.06 65.25 -2.76

Global Bonds

-0.39 -6.00 -0.87 38.02 51.41 -5.48 -38.02 62.86 20.61 -4.68 1.40

US HY Bonds

9.58 -0.98 -0.76 13.06 17.99 1.20 91.78 29.94 8.18 -4.77 -1.15

US IL Bonds

-0.96 -3.63 2.27 20.52 48.48 17.64 3.85 -65.58 49.82 -9.97 -0.78

US MBS

-0.78 -0.07 -0.44 9.97 23.00 11.68 -1.12 -10.61 -59.45 -74.74 0.51

US Eq.

39.95 11.39 -27.21 -24.96 0.08 70.82 -7.99 15.46 8.07 -1.27 -39.07

Ex-US Eq.

39.81 -7.50 -36.57 55.78 -24.09 -34.97 -1.93 -16.02 -6.56 1.60 -42.44

Global Eq.

39.97 1.20 -32.51 16.67 -11.08 16.11 -2.72 -2.67 -0.91 2.81 81.61

Private Eq.

48.71 12.58 -8.18 -55.04 41.07 -51.49 -2.94 -4.39 -2.51 -0.56 -0.56

Real Est.

47.27 27.95 79.48 21.26 -12.02 6.96 -4.40 -0.76 -0.83 0.07 0.57

Commo.

22.74 -93.93 21.74 -11.74 -1.82 6.33 -1.25 0.59 -2.12 0.20 -0.25

Total Position (%)

243.90 -59.40 -1.80 98.76 173.23 55.64 38.54 -5.89 -43.77 -26.06 -2.91 - - - - - - - - - - -

Variance (%)

0.37 0.10 0.06 0.03 0.01 0.01 0.01 0.00 0.00 0.00 0.00

Percent Explained (%)

63.35 17.01 9.46 4.26 2.15 1.59 1.33 0.51 0.25 0.08 0.02

Cumulative (%)

63.35 80.36 89.82 94.08 96.23 97.82 99.15 99.66 99.91 99.98 100.00

Sharpe Ratio 0.20 0.10 0.14 0.33 0.95 0.11 0.33 -0.19 -0.32 -0.67 0.02 This table displays the exposures (in %) with respect to asset classes of each factor obtained with the PCA approach applied to the sample covariance matrix estimated with 787 weekly returns from September 1997 to the end of September 2012.

Table 9: Factors’ Exposures in % with the MLT Approach F 1 F 2 F 3 F 4

F 5

F 6

F 7

F 8

F 9

F 10

F 11

US Bonds

190.48 -32.15 -16.78 -43.95 -61.83 5.67 23.64 -24.20 3.50 0.21 2.27

Global Bonds

-32.15 129.79 10.37 -22.08 -7.13 9.55 -31.59 15.41 4.78 -1.46 -2.14

US HY Bonds

-16.78 10.37 125.05 -9.50 1.02 14.37 -1.60 -28.78 -3.80 -6.03 -2.10

US IL Bonds

-43.95 -22.08 -9.50 135.79 -6.80 8.18 9.37 -16.23 4.02 -1.40 -2.88

US MBS

-61.83 -7.13 1.02 -6.80 161.21 -2.60 0.97 -3.21 2.91 0.29 0.93

US Eq.

5.67 9.55 14.37 8.18 -2.60 605.12 370.93 -837.62 -69.90 -15.51 8.55

Ex-US Eq.

23.64 -31.59 -1.60 9.37 0.97 370.93 636.22 -925.62 -6.57 -14.19 -14.46

Global Eq.

-24.20 15.41 -28.78 -16.23 -3.21 -837.62 -925.62 1866.27 -51.04 4.13 -10.42

Private Eq.

3.50 4.78 -3.80 4.02 2.91 -69.90 -6.57 -51.04 208.60 -45.50 -8.37

Real Est.

0.21 -1.46 -6.03 -1.40 0.29 -15.51 -14.19 4.13 -45.50 132.92 -0.93

Commo.

2.27 -2.14 -2.10 -2.88 0.93 8.55 -14.46 -10.42 -8.37 -0.93 106.27

Total Position (%)

46.86 73.37 82.22 54.52 85.75 96.74 47.10 -11.31 38.64 52.52 76.74 - - - - - - - - - - -

Variance (%)

0.00 0.01 0.01 0.01 0.00 0.07 0.08 0.07 0.10 0.13 0.11

Percent Explained (%)

0.65 1.66 1.89 1.05 0.32 12.12 13.06 11.32 17.44 21.70 18.80

Cumulative (%)

0.65 2.30 4.20 5.25 5.57 17.69 30.75 42.07 59.51 81.20 100.00

Sharpe Ratio 0.25 0.40 0.50 0.62 0.92 -0.06 -0.02 0.03 0.21 0.21 -0.05 This table displays the exposures (in %) with respect to asset classes of each factor obtained with the MLT approach applied to the sample covariance matrix estimated 787 weekly returns from September 1997 to the end of September 2012.

62

An EDHEC-Risk Institute Publication