You are back-testing a 10-day, 95% VaR model using 300 realizations, each over a 10-

day period. The test is conducted at a 10% critical level.

1) If we observe eleven (11) 10-day periods during which the realized loss is greater

than the VaR, do we reject the VaR model according to the binomial test? What is

the smallest number of exceptions above which we can accept the VaR model?

2) If we observe twenty-one (21) 10-day periods during which the realized loss is

greater than the VaR, do we reject the VaR model according to the binomial test?

What is the largest number of exceptions below which we can accept the VaR

model?