HISTORICAL LOSS SUMMARY Measuring reoccurring [historical] loss events Date 1
Date 2
05/19/08 01/14/08 10/29/07 03/07/08 03/06/08 10/09/07 03/05/08 03/03/08 10/08/07 10/05/07
03/09/09 11/20/08 10/15/08 03/06/09 03/05/09 10/10/08 03/03/09 03/02/09 10/09/08 10/08/08
RISK ASSESSMENT Daily Estimates
Max Loss -15.80% -14.30% -13.31% -12.94% -12.79% -12.63% -12.41% -11.94% -11.43% -9.55%
Table 1 displays annualised return, risk (standard deviation), Sharpe
ratio and asymmetry statistics for representative indices used to proxy asset class returns. We also display three estimates of annual T-VaR (downside risk) at the 99.5m percent confidence level. These are annualised estimates based upon monthly and daily total returns.
TABLE 1. DESCRIPTIVE STATISTICS AND ALTERNATIVE ANNUAL 99.5 T-VAR METRICS DECEMBER 1997 TO DECEMBER 2010
ASYMMETRY
SECTOR/CLASS TOTAL RETURN
US Treasury US Corp. AA US Corp. BBB US High Yield ABS MBS
Municipal (tX. Eqv.) Gilts
Sterling Corp. A ENERGY
6.17 6.64 7.42 8.76 4.60 6.00 7.90 5.95 3.68
Global High YIELD 9.71 SPX
2.79 5.21
RISK (STDEV)
5.31 5.68 6.46
10.82 2.69 2.90 4.31 3.90 7.47
10.92 16.31 32.62
SHARPE RATIO
0.637 0.679 0.716 0.552 0.676 1.107 1.186 0.811 0.119 0.634 0.000 0.074
SKEW- NESS
-0.012 -0.73 -1.38 -1.32 -0.82 0.06
-0.35 0.02
-2.20 -1.66 -0.64 0.11
KURT- OSIS
0.75 2.50 9.82 9.08 4.46 2.06 0.89 0.24
11.41 10.25 0.77 0.69
8.71
10.24 21.89 2.25 2.00 6.31 4.93
14.96 20.79 42.82 89.38
99.5% T-VAR
SNEOP DIP 8.33
11.01 11.74 13.47 25.54 4.49 4.21 8.62 7.01
19.67 25.05 47.65 93.94
LEVY 14.45
19.43 22.34 65.00 9.64
19.06 20.23 10.63 41.00 56.14 93.23 90.55
For this time period, the S&P 500 (SPX) shows the lowest annualised
total return and second-highest risk level. Its return distribution is slightly asymmetric. At the 99.5 percent confidence level, SNEOP and DIP annual T-VaRs are 42.82 percent and 47.65 percent, respectively. The Levy estimated annual T-VaR is 93.23 percent. Whereas this is the largest T-VaR shown, of greater importance is its relative value to other assets’ T-VaR in contrast to their other risk metrics.
Location [mu | delta]
Dispersion [sigma | gamma] Tail index [alpha] Skewness [beta]
Annual T-VaR Confidence Interval 99.0% 99.5% 99.9%
SNEOP 0.022 0.279
- -
SNEOP 8.23 9.45
12.00 DIP
10.23 11.27 13.56
[% portfolio loss]
Table 2 displays the rank correlations among the four risk metrics (standard deviation of total return and the three measures of downside risk) of the 120 asset indices used in this analysis. SNEOP and DIP rankings are highly correlated (both calculated from the same normal distribution mean and variance). Accordingly, their rank correlations to the standard deviation of total return are nearly identical.
TABLE 2. ASSET CLASS RISK METRIC CORRELATIONS RISK METRIC STDEV
StDev
SNEOP DIP
LEVY 1
0.94 0.96 0.67
SNEOP 1
0.97 0.66
DIP 1 0.67 1 Levy rankings are the least correlated to standard deviation (it is only
one of four parameters defining Levy T-VaR), meaning that the rank ordering of the assets with regard to their risk changes considerably. From a practical standpoint (and all else being equal), the greater an asset’s risk relative to the average risk of all indices, the ‘less favoured’ it will be in an MV framework other than at the maximum return allocation. As risk metrics change, it is useful to determine whether an assets’ relative risk positioning changes for better or worse.
In Chart 3, we plot individual indices’ relative risk based on standard
deviation and Levy as risk measures. For example, index U8AX, Municipal 15+ Year, annual Levy T-VaR is approximately 1.5 times the average T-VaR of all indices, whereas its standard deviation of total return is about only one times the average of all indices. All else being
CHART 3. RELATIVE RISK COMPARISON: STANDARD DEVIATION VERSUS LEVY 3.00
SMALL CAP CMBS IM00 2.50 H0A0 PRECMTLS 2.00 CMOO CMOZ U8AX 1.50 CMOQ CMOP 1.00 M0A0 U2AX 0.50 U1A0 UK03 G1O2 0.00 0.00 0.50 1.00 1.50 STANDARD DEVIATION 2.00 2.50 3.00 C1A4 U3AX C3A2 G3O2 C9Z0 R0H0 U9AX UR33 U7AX U4AX G0QI C3A4 G7O2 GS09 G8O2 HI00 EAFE LEVY
DIP
Levy 0.032 0.163 1.849 -0.259
Levy 12.88 21.83 55.10
44 | INTELLIGENT INSURER | September 2011
LEVY
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72