ROLLING ANNUAL TOTAL RETURNS Dec-97 Jun-98 Dec-98 Jun-99 Dec-99 Jun-00 Dec-00 Jun-01 Dec-01 Jun-02 Dec-02 Jun-03 Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10
30.0 25.0 20.0 15.0 10.0 5.0 0.0 -5.0 -10.0 -15.0
Time frame scanned December 31, 1997
December 31, 2010
BLOCK PERIOD ANALYSIS
Period length to scan: Inception DESCRIPTIVE STATISTICS # Observations: Minimum: Maximum:
3400
-2.113 2.353
Range: Mean:
4.466 0.022
Standard deviation: 0.279 Test statistic p-value Excess kurtosis: Skewness:
6.037 -0.196
71.907 -4.666
0.000 0.000
10% x x
Jarque-Bera 5184.801 4.605
Chi-2 Goodness of Fit 186.818 Anderson-Darling
26.269
18.549 0.631
0.000 0.000 NA
10% x x x
Histogram options #bins
=bin width 0.060
Distribute bins equally: (Outliers highlighted)
5% x x
5% x x x
2.50% x x
2.50% x x x
x Outliers ignored x
1% x x
NORMALITY TESTS Test statisticCritical value p-value Test indicates normality at [x] significance level 10%
1% x x x
H_0: Normality Chart 2 displays additional details. The opposite (right) graph contrasts
the fit of the alpha-stable distribution (used for the Levy methodology) and the normal distribution to the left-tail (100 smallest) observed total returns. The graph below displays the historic exceedance loss plot of the portfolio. Mid-teen total return losses were not uncommon and price-only (valuation losses) had a still greater frequency.
The tables directly overleaf in Chart 2 show T-VaR estimates for the
three differing downside risk metrics. Neither SNEOP nor DIP estimates adequately account for the magnitude of downside loss. For example, at the 99.5 confidence level, the difference between their respective T-VaRs, 9.45 and 11.27, to the observed loss exceedance is considerable. These metrics are more insensitive to extreme events. Levy metrics appear to provide more conservative estimates for extreme event outcomes.
LOG [ABS (% returns)] MAXIMUM LOSS ON INDEX WITHIN ONE YEAR AT EVERY POINT IN TIME
0.0% -2.0% -4.0% -6.0% -8.0% -10.0% -12.0% -14.0% -16.0% -18.0%
75 (choose between 5 and 100 bins)
RETURN SERIES HISTOGRAM VS. FITTED NORMAL AND STABLE DISTRIBUTION
2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00
-1.50-1.00
Histogram Fitted normal Fitted stable
-0.500.000.501.001.50 % returns
TAIL FIT GRAPH-EMPIRICAL LEFT TAIL OF RETURN SERIES VS. FITTED NORMAL AND STABLE DIST. -0.37-0.27
0.03 0.13 0.23
Empirical Fitted normal Fitted stable
Dec-97 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Jan-01 Jul-01 Jan-02 Jul-02 Jan-03 Jul-03 Jan-04 Jul-04 Jan-05 Jun-05 Jan-06 Jul-06 Jan-07 Jun-07 Jan-08 Jul-08 Jan-09 Jul-09 Jan-10 Jul-10 HISTORIC LOSS EXCEEDANCE PLOT
-1.54 -3.54 -5.54 -7.54 -9.54 -11.54 -13.54 -15.54
CHART 2. REPRESENTATIVE PORTFOLIO DETAILS -0.17-0.07
September 2011 | INTELLIGENT INSURER | 43
% returns
LOG (CDF)
Density
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