Answer: CVaR of Loan S > CVaR of Loan U > CVaR of Loan T

The correct answer is A: CVaR of Loan S > CVaR of Loan U > CVaR of Loan T. To understand this, let's break down the components involved in calculating the Credit Value at Risk (CVaR) for each loan. The CVaR is the expected loss beyond the Value at Risk (VaR) and is calculated using the formula: \[ 95\% \text{ CVaR} = 95\text{th percentile of the unrecovered credit loss} - \text{Expected Loss (EL)} \] Given that the 95th percentile of the unrecovered credit loss for all three loans is the same, the comparison of their CVaRs essentially comes down to comparing their expected losses. The expected loss is calculated by multiplying the Probability of Default (PD), the Loss Given Default (LGD), and the Exposure at Default (EAD). Here's how it's calculated for each loan: - **Loan S** (Investment grade, 2-year maturity): \[ \text{PD} = 1.5\% \] \[ \text{EL} = 0.015 \times 0.80 \times \text{SGD 55,000,000} = \text{SGD 660,000} \] - **Loan T** (Non-investment grade, 3-year maturity): \[ \text{PD} = 12.0\% \] \[ \text{EL} = 0.12 \times 0.90 \times \text{SGD 36,000,000} = \text{SGD 3,888,000} \] - **Loan U** (Investment grade, 4-year maturity): \[ \text{PD} = 3.5\% \] \[ \text{EL} = 0.035 \times 0.70 \times \text{SGD 50,000,000} = \text{SGD 1,225,000} \] Since the 95th percentile loss is constant across loans, the loan with the highest expected loss will have the highest CVaR, and the loan with the lowest expected loss will have the lowest CVaR. Comparing the expected losses: - Loan T has the highest expected loss (SGD 3,888,000). - Loan U has a lower expected loss (SGD 1,225,000). - Loan S has the lowest expected loss (SGD 660,000). Thus, the CVaR comparison is as follows: Loan S has the lowest CVaR, followed by Loan U, and Loan T has the highest CVaR. This leads us to the correct answer, which is A: CVaR of Loan S > CVaR of Loan U > CVaR of Loan T.

Author: LeetQuiz Editorial Team