3. [20 marks] A bank has two $10m one-year loans Outcome Neither loan defaults Loan 1 defaults, Loan 2 does not default Loan 2 defaults, Loan 1 does not default Both loans default Probability 95% 2.5% 2.5% 0% If Loan 1 defaults, the loss will be either $5m or $10m, with equal probability. If Loan 2 defaults, the loss will be either $2m, $4m, $6m, $8m or $10m, with equal probability. For each loan, a profit of $1m will be made in case of no default. (a) Calculate the one-year 97% VaR for the portfolio of two loans. (b) Calculate the one-year 97% ES for the portfolio of two loans. 3. [20 marks] A bank has two $10m one-year loans Outcome Neither loan defaults Loan 1 defaults, Loan 2 does not default Loan 2 defaults, Loan 1 does not default Both loans default Probability 95% 2.5% 2.5% 0% If Loan 1 defaults, the loss will be either $5m or $10m, with equal probability. If Loan 2 defaults, the loss will be either $2m, $4m, $6m, $8m or $10m, with equal probability. For each loan, a profit of $1m will be made in case of no default. (a) Calculate the one-year 97% VaR for the portfolio of two loans. (b) Calculate the one-year 97% ES for the portfolio of two loans