Q3. A bank has two $10 million one-year loans. Possible outcomes are as the following table shows. If a default occurs, losses between 0% and 100% are equally likely. If a loan does not default, a profit of 0.2 million will be made. 3.1 What is the 99% one-year VaR and ES of each project? 3.2 What is the 99% one-year VaR and ES for the portfolio? Single Project Portfolio of Two Projects 100% Outcome Neither Loan Defaults Loan 1 defaults, loan 2 does not default Loan 2 defaults, loan 1 does not default Both loans default Probability Loss (M) 97.50% -0.40 1.25% [0, 9.8] 1.25% 0.00% 100% 99% 98.75% 99% 97.5% 1 $0.2 SO $10 $0.4 $0.2 $0 $9.8 3.1. Answer: 3.2. Answer: * You will see, in spite of the fact that there are clearly very attractive diversification benefits from combining the loans into a single portfolio-particularly because they cannot default together, the portfolio's VaR is bigger than the sum of two individual project's VaR adding up, which is a limitation of the VaR measurement. Q3. A bank has two $10 million one-year loans. Possible outcomes are as the following table shows. If a default occurs, losses between 0% and 100% are equally likely. If a loan does not default, a profit of 0.2 million will be made. 3.1 What is the 99% one-year VaR and ES of each project? 3.2 What is the 99% one-year VaR and ES for the portfolio? Single Project Portfolio of Two Projects 100% Outcome Neither Loan Defaults Loan 1 defaults, loan 2 does not default Loan 2 defaults, loan 1 does not default Both loans default Probability Loss (M) 97.50% -0.40 1.25% [0, 9.8] 1.25% 0.00% 100% 99% 98.75% 99% 97.5% 1 $0.2 SO $10 $0.4 $0.2 $0 $9.8 3.1. Answer: 3.2. Answer: * You will see, in spite of the fact that there are clearly very attractive diversification benefits from combining the loans into a single portfolio-particularly because they cannot default together, the portfolio's VaR is bigger than the sum of two individual project's VaR adding up, which is a limitation of the VaR measurement