Answer: GBP 7,930

## Explanation D is correct. In its application to credit risk, Euler’s theorem states that: \[ Q_i = \frac{\Delta F_i}{\Delta x_i} x_i \] and that (in the limit, as \(\Delta x_i\) goes to zero): \[ F = \sum_{i=1}^{n} Q_i \] Where: - \( F \) is a (homogeneous) risk measure for a portfolio - \( x_i \) is the same risk measure calculated for one component position in the portfolio - \( \Delta x_i \) is a small change in this risk measure - \( \Delta F_i \) is the resultant change in the portfolio’s risk measure ### Calculations Using the information given: \[ \Delta F_1 = 58.1 \\ Q_1 = \frac{58.1}{1\%} = 5,810 \] \[ \Delta F_2 = 65.6 \\ Q_2 = \frac{65.6}{1\%} = 6,560 \] \[ F = Q_1 + Q_2 + Q_3 \\ 20,300 = 5,810 + 6,560 + Q_3 \\ Q_3 = 7,930 \] ## Incorrect Options - **A is incorrect.** This is the proportion of portfolio VaR equivalent to the proportion of Loan 3’s amount to the total amount of all of the loans: \[ 20,300 \times \frac{160,000}{180,000 + 200,000 + 160,000} = 6,014.82 \] - **B is incorrect.** - **C is incorrect.** This is the proportion of portfolio VaR equivalent to the proportion of Loan 3’s individual VaR to the sum of the individual loan VaRs: \[ 20,300 \times \frac{9,500}{10,000 + 8,000 + 9,500} = 7,012.73 \]

Author: LeetQuiz Editorial Team