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I have a sorted historical P&L vector of 250 days and say, I want to calculate the 90% VaR on this distribution. I will look for the 225 element (90% * 250 = 225) and this will be my Value at Risk.

Now how to back test the VaR model ? If I look for the number of days in last year that the Loss exceeded the VaR, it will always be 25 days, since by construction, it's the number which corresponds to the quantile of the VaR...

And in case the VaR model is not valid, what is usually done ?

Am I missing something please ? Thanks

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you should backtest in the future. Thus you calculate your VaR based on the last 250 business days and then look at the return tomorrow. You have to do this in a rolling/sliding fashion. Your approach is in-sample and what you should do is out-of-sample.

The number of violations should be binomial. Furthermore you could do a runs test to test whether your violations do not cluster too much.

Having said this: the model will be ok but not good. In volatile times you will have too many violations. But it will be better than a Gaussian model as you capture the tails better.

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  • $\begingroup$ Thank you for your answer. And in case, my VaR model is not Ok (the loss exceeded the VaR more than 10% of times, what's is usually done to correct it ? $\endgroup$
    – user7120
    Mar 5, 2014 at 11:51
  • $\begingroup$ An answer for a full Var model is another question, it depends on the asset class (bonds, equity, multi assets, HF). Post a question and you will get some references. $\endgroup$
    – Richi Wa
    Mar 5, 2014 at 12:30

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