(a) The probability that the loss from a portfolio will be larger than $5 million in one quarter is estimated to be 10%. First, what is the one-quarter 95% VaR assuming the change in the portfolio value is normally distributed with zero mean? Second, what is the one-quarter 95% VaR assuming that the power law applies with a = 4? (4 marks) (b) A bank has made a large number of retail loans. The 1-year default probability on each loan is z%. The bank uses a Gaussian copula for time to default. The 99.97% "worse case default rate" for the percentage of loans that default in the portfolio is 0.325899. The copula correlation is 0.3. What is z? (4 marks) (C) Suppose that daily changes in a portfolio value are normally distributed with mean $3 million and standard deviation of $6 million. Compute both the five-day 99.5% VaR and ES where the first-order autocorrelation of daily changes is 0.2. (4 marks) (a) The probability that the loss from a portfolio will be larger than $5 million in one quarter is estimated to be 10%. First, what is the one-quarter 95% VaR assuming the change in the portfolio value is normally distributed with zero mean? Second, what is the one-quarter 95% VaR assuming that the power law applies with a = 4? (4 marks) (b) A bank has made a large number of retail loans. The 1-year default probability on each loan is z%. The bank uses a Gaussian copula for time to default. The 99.97% "worse case default rate" for the percentage of loans that default in the portfolio is 0.325899. The copula correlation is 0.3. What is z? (4 marks) (C) Suppose that daily changes in a portfolio value are normally distributed with mean $3 million and standard deviation of $6 million. Compute both the five-day 99.5% VaR and ES where the first-order autocorrelation of daily changes is 0.2. (4 marks)