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