Re: Ten-day 99% VaR has worked fine.

From: Glyn Holton
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Date: 01 Nov 2006
Time: 14:52:27

Comments

In the blog posting, I described two analyses (by Till and Finger). They looked at identical data, yet one came up with a standard deviation that was three times that of the other. If they expressed their results as value-at-risk figures, one would still be three times the other. Please understand that neither analysis was right or wrong. They were just two different (largely reasonable) approaches to the same statistical problem. There are numerous other sources of variability in VaR results. Perhaps the biggest is calculated correlations. That is a huge can of worms. The problems become most pronounce when you consider extreme cases, such as 10-day 99% VaR. While it is pretty reasonable to model asset returns as joint normal for the 90% or 95% quantile, that assumption is really not reasonable at the 99% quantile. But if we don't assume joint normality, what joint distribution should we assume? Whatever choice we make will profoundly affect results at the 99% quantile. Also, correlations are known to become exaggerated during extreme market moves. Accordingly, correlations you calculate from historical data will likely underestimate what will be experienced in a 99% quantile extreme market event. There are various ways this might be addressed, but as with the disparity between Till's and Finger's analyses, those solutions will produce a wide variety of differet outputs.

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