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Enron Mail |
Vlady, I enclosed the file with 2 backtesting plots (you saw them before).
The following table shows what was the percentage of the days when PnL fell below VAR95, VAR90, VAR85. These results are based on the real NG forward prices from 1/1/99 to 6/7/00 for 2 different portfolios: -Portfolio 1 contained the positions equal to NG-PRICE-PRC portfolio positions on 6/6/00, -Portfolio 2 consists of the positions equal to STORAGE-PRC positions on 5/25/00. _____________________________________________________________________ Portfolio 1 VAR95 VAR90 VAR85 Implied Vols 2.93 4.11 5.57 Historical vols with Decay=1 7.62 12.02 15.54 Historical vols withDecay=0.97 6.75 12.02 15.54 Historical vols withDecay=0.94 6.45 12.02 15.54 _____________________________________________________________________ Portfolio 2 VAR95 VAR90 VAR85 Implied Vols 4.1 6.74 9.97 Historical vols with Decay=1 7.04 11.14 15.84 Historical vols withDecay=0.97 6.74 10.56 16.13 Historical vols withDecay=0.94 7.04 11.14 15.84 ____________________________________________________________________ This shows that when we have more observations (columns corresponding to VAR90 and VAR85) compared to the column corresponding to VAR95 the frequency of Curve Shift being lower than VAR becomes closer to the theoretical value (5%, 10% and 15%). The numbers in the column "VAR85" are very close to 15%. This is the argument in favor of using historical vols. And also the results do not depend on the decay factor in this experiment. Also notice: the numbers in column "VAR95" are higher than 5% and this is an indication of fat tails. Let me know if you have any questions. Tanya.
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