Answer: CNY 3.03 million

The correct answer to the question is option C, which is CNY 3.03 million. To estimate the standard deviation of losses on the portfolio, the risk manager uses a formula that calculates the standard deviation of losses for each individual loan. The formula is given by \( \sigma_i = \sqrt{P_i(1 - P_i)[L_i(1 - R_i)]} \), where \( P_i \) is the probability of default, \( L_i \) is the exposure at default (amount borrowed), and \( R_i \) is the recovery rate. For Loan 1: - \( P_1 = 2\% \) (0.02) - \( L_1 = CNY 15 million \) - \( R_1 = 40\% \) (0.4) The standard deviation of losses for Loan 1 is calculated as: \[ \sigma_1 = \sqrt{0.02(1 - 0.02)[15(1 - 0.4)]} = 1.26 \] For Loan 2: - \( P_2 = 2\% \) (0.02) - \( L_2 = CNY 20 million \) - \( R_2 = 25\% \) (0.25) The standard deviation of losses for Loan 2 is calculated as: \[ \sigma_2 = \sqrt{0.02(1 - 0.02)[20(1 - 0.25)]} = 2.1 \] The variance of losses on the portfolio is then calculated using the formula: \[ \text{Var}(\text{Losses}) = \sigma_1^2 + 2 \cdot \rho_{1,2} \cdot \sigma_1 \cdot \sigma_2 + \sigma_2^2 \] where \( \rho_{1,2} \) is the default correlation between Loan 1 and Loan 2, which is 0.6. Plugging in the values, we get: \[ \text{Var}(\text{Losses}) = 1.26^2 + 2 \cdot 0.6 \cdot 1.26 \cdot 2.1 + 2.1^2 = 9.1728 \] The standard deviation of the portfolio losses is the square root of the variance: \[ \sigma_{\text{portfolio}} = \sqrt{9.1728} = 3.0287 \] This value is rounded to CNY 3.03 million, which corresponds to option C. The other options (A, B, and D) are incorrect as they do not match the calculated standard deviation of losses for the portfolio.

Author: LeetQuiz Editorial Team