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Basel II requires a backtest of a bank’s internal value at risk (VaR) model (IMA). Assume the bank’s ten-day 99% VaR is $1 million (minimum of 99% is hard-wired per Basel). The null hypothesis is: the VaR model is accurate. Out of 1,000 observations, 25 exceptions are observed (we saw the actual loss exceed the VaR 25 out of 1000 observations). (Binomial CDF p[x ≤ 24] = 99.996%)
　　A.     We will probably call the VaR model good (accurate) but we risk a Type I error.
　　B.     We will probably call the VaR model good (accurate) but we risk a Type II error.
　　C.     We will probably call the model bad (inaccurate) but we risk a Type I error.
　　D.     We will probably call the model bad (inaccurate) but we risk a Type II error.
　　Answer: C
　　The probability of 25 or more exceptions will only be observed 1 – 99.996%. So, we reject the model. Null = good model. To decide the model is bad model is to reject null and this implies a risk of type I error.