NO.PZ2018122701000034
问题如下：
A bank conducted a backtest of its 95% daily value at risk (VaR) and observed 19 exceptions - i.e., the number of days where the daily P&L loss exceeded the VaR - over the last year which included 250 trading days (T = 250). If we use the normal distribution to approximate the binomial for purposes of model verification, what is our accept/reject opinion of the model under a 90% two-tailed test?
选项：
A.Accept with a test statistic of 1.25
B.Accept with a test statistic of 1.89
C.Reject with a test statistic of 1.25
D.Reject with a test statistic of 1.89
解释：
D is correct.
考点Backtesting VaR
解析Null hypothesis is H0: Model is good with E[exceptions] = (1 - 95%) × 250 = 12.5 exceptions
The standard error (standard deviation) of the binomial variable = SQRT[p(1-p)T] = SQRT(5% × 95% × 250) = 3.446
The test statistic is [19 - 12.5] / 3.446 = 1.89
In words, we observed 6.5 more exceptions (19 - 12.5) than expected if the model is good, which is 1.89 standard deviations away from the expected number of exceptions. Since we know that a 95% one-tailed normal confidence interval implies a 1.645 cutoff, we know that 1.645 is also the cutoff for a 90% two-tailed since the normal is symmetrical, this falls outside the acceptance region. We reject the null, assuming that luck does not explain this, and find the model faulty.
计算的是90%的情况，为什么用的均值和标准差是95%的？
