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Answer: CVaR of Loan S > CVaR of Loan U > CVaR of Loan T
## Explanation Since the 95th percentile of the unrecovered credit loss for the three loans are the same and the 95% CVaR is derived as follows: **95% CVaR = 95th percentile of the unrecovered credit loss – Expected Loss** Therefore, we only need to consider the expected loss to compare the CVaR values. ### Step 1: Determine PD for each loan - **Loan S**: Investment grade (BBB), 2-year maturity → PD = 1.5% - **Loan T**: Non-investment grade (BB-), 3-year maturity → PD = 12.0% - **Loan U**: Investment grade (A), 4-year maturity → PD = 3.5% ### Step 2: Calculate Expected Loss (EL) EL = PD × LGD × Exposure - **Loan S**: EL = 0.015 × 0.80 × SGD 55,000,000 = SGD 660,000 - **Loan T**: EL = 0.12 × 0.90 × SGD 36,000,000 = SGD 3,888,000 - **Loan U**: EL = 0.035 × 0.70 × SGD 50,000,000 = SGD 1,225,000 ### Step 3: Compare CVaR Since the 95th percentile is the same for all loans: - **CVaR_S** = Same 95th percentile - 660,000 - **CVaR_T** = Same 95th percentile - 3,888,000 - **CVaR_U** = Same 95th percentile - 1,225,000 **Order from highest to lowest CVaR**: CVaR_S > CVaR_U > CVaR_T This matches **Option A**: CVaR of Loan S > CVaR of Loan U > CVaR of Loan T
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A credit analyst at a bank is asked to estimate the credit VaR (CVaR) for three loans in the bank's credit portfolio. The analyst assembles the following loan information:
| Loan | Maturity (years) | Exposure (SGD) | Loss given default | S&P rating |
|---|---|---|---|---|
| S | 2 | 55,000,000 | 0.8 | BBB |
| T | 3 | 36,000,000 | 0.9 | BB- |
| U | 4 | 50,000,000 | 0.7 | A |
In addition, the annual probability of default (PD) based on loan rating and maturity is provided in the table below:
| Loan maturity (years) | 2 | 3 | 4 |
|---|---|---|---|
| PD (investment grade) | 1.5% | 2.5% | 3.5% |
| PD (non-investment grade) | 5.0% | 12.0% | 18.0% |
Assuming the 95th percentile of the unrecovered credit loss for the three loans are the same, which of the following is correct about the comparison of the 95% CVaR of the loans?
A
CVaR of Loan S > CVaR of Loan U > CVaR of Loan T
B
CVaR of Loan T > CVaR of Loan U > CVaR of Loan S
C
CVaR of Loan T > CVaR of Loan S > CVaR of Loan U
D
CVaR of Loan U > CVaR of Loan S > CVaR of Loan T
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