Backtesting Value at Risk. With kupiec test

Question

I have a certain problem with backtesting calculated earlier Value at Risk.

I've got calculated daily VaR with historical simulation method for stocks. I've used two values of alpha 0.05 and 0.1. Now, I want to backtest this values with Kupiec test. What alpha should I use for Kupiec test? When I'm using 0.05 alpha for VaR calculated with 0.1, I have to reject null hypothesis for all stocks. Is it normal? Or I should use 0.1 alpha for Kupiec test in this case for comparison between these two models.

Answer 1

When backtesting VaR results using Kupiec test you should choose the respective significance levels as your VaRs. Thus, using 0.05 alpha for VaR with 99% confidence level is not correct. From Dowd:

To implement the Kupiec test, we require data on n, p and x. The first are easily found from the sample size and VaR confidence level, and we can derive x from a set of paired observations of P/L and VaR each period.