Is it possible to deduce a 1y HSVAR 99% from a 1m HSVAR 99% just by applying the time scaling factor square-root of 12?
For normal log-returns it is consistent but what about historical VaR? Is there any article dealing with that subject?
Historical VaR and time scaling
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nsande
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- Joined: Thu Jan 01, 2004 12:00 am
Historical VaR and time scaling
It is, subject to the usual caveat of i.i.d. , identical independent draws.
I have appended a paper by Danielsson and Zigrand where they discuss the square root of time rule when these assumptions are not valid.
[url=/User%20Files/25/SSRN-id567123.pdf]Attached File: SSRN-id567123.pdf[/url]
I have appended a paper by Danielsson and Zigrand where they discuss the square root of time rule when these assumptions are not valid.
[url=/User%20Files/25/SSRN-id567123.pdf]Attached File: SSRN-id567123.pdf[/url]
"For all intents and purposes, politics is to keep the populace alarmed, so they demand safety measures. They are bombarded by an endless array of imaginary hobgoblins..." H.L. Mencken, publicist and author 1880-1956.
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aaron
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- Joined: Thu Jan 01, 2004 12:00 am
Historical VaR and time scaling
I'm not sure exactly what you mean. A 99%-HSVaR should have at least 300 months of data, and 25 years is too long to be relevant in most markets.
In any event, to apply the square root rule, the most important condition is that the returns are independent. This should be true of monthly returns of pure financial assets (i.e., non-seasonal with zero storage costs and use value) if you have good, liquid quotes.
If the monthly returns are independent, then the annual standard deviation will be the square root of 12 times the monthly standard deviation. If the monthly returns are lognormal, then the shape of the annual distribution is the same as the shape of the monthly, which is why the VaR point will be the same number of standard deviations below the mean. However, for any reasonably bell-shaped distribution, you won't get much VaR movement from distribution shape change.
In any event, to apply the square root rule, the most important condition is that the returns are independent. This should be true of monthly returns of pure financial assets (i.e., non-seasonal with zero storage costs and use value) if you have good, liquid quotes.
If the monthly returns are independent, then the annual standard deviation will be the square root of 12 times the monthly standard deviation. If the monthly returns are lognormal, then the shape of the annual distribution is the same as the shape of the monthly, which is why the VaR point will be the same number of standard deviations below the mean. However, for any reasonably bell-shaped distribution, you won't get much VaR movement from distribution shape change.