1. The multiplicative factor m_c used in the specific risk charge in (15.3) has value between 3 and 4, and is based on back-testing over the past 250 days. Specifically, the bank evaluates the number of exceptions in this period, where an exception is defined as a day where the market value loss exceed the calculated 1-day, 99% confidence level VaR. For the minimum value of m_c=3 the bank must have less than 5 exceptions, while the bank must use the maximum m_c=4 for 10 or more exceptions.

(a) Using the one tailed binomial test of section 12.10, what is the probability that the bank has 5 or more exceptions if their VaR calculation is correct?

(b) Using the same model, what is the probability that the bank has 10 or more exceptions if their VaR calculation is correct?