I was just going over a past exam and stumbled upon this question. If you have already had the discussion on this question, could you please redirect me to the relevant forum (I can't seem to find this specific question in the past paper forum discussions). Here is the question:

You are backtesting a bank’s VaR model. Currently, the bank calculates a 1-day VaR at the 99% confidence level, and you are recommending that it switch to a 95% confidence level. Which of the following statements concerning this switch is correct?

a. The 95% VaR model is less likely to be rejected using backtesting than the 99% VaR model.

b. When validating with backtesting at the 90% confidence level, there is a smaller probability of incorrectly rejecting a 95% VaR model than a 99% VaR model.

c. The decision to accept or reject a VaR model based on backtesting results is more reliable with a 95% confidence level VaR model than with a 99% confidence level model.

d. When backtesting using a 90% confidence level, there is a smaller probability of committing a type I error when backtesting a 95% VaR model than with a 99% VaR model.

Correct answer: c

Explanation: The concept tested here is the understanding of the difference between the VaR parameter for confidence (here, namely 95% vs. 99%) and the validation procedure confidence level, and how they interact with one another. Using a VaR confidence level creates a narrower rejection region by allowing a greater number of exceptions to be generated. This in turn increases the power of the backtesting process and makes for a more reliable test

Why is (a) false? I thought that with a lower confidence interval, the 95% level would allow for more exceptions before rejecting the null hypothesis. Given the same confidence level for the backtest (e.g. 90%), shouldn't this be true?

Thanks

Ro