Answer: GBP 7,930

## Explanation Using Euler's theorem for credit risk, the contribution of each loan to the portfolio VaR can be calculated as: \[ Q_i = \frac{\Delta F_i}{\Delta x_i} \] Where: - \(Q_i\) is the contribution of loan i to portfolio VaR - \(\Delta F_i\) is the increase in portfolio VaR when loan i's VaR increases by 1% - \(\Delta x_i\) is the percentage increase in loan i's VaR (1% = 0.01) From the given data: **For Loan 1:** \[ Q_1 = \frac{58.1}{0.01} = 5,810 \] **For Loan 2:** \[ Q_2 = \frac{65.6}{0.01} = 6,560 \] **For Loan 3:** We know that the total portfolio VaR equals the sum of individual contributions: \[ F = Q_1 + Q_2 + Q_3 \] \[ 20,300 = 5,810 + 6,560 + Q_3 \] \[ Q_3 = 20,300 - 5,810 - 6,560 = 7,930 \] Therefore, the contribution of Loan 3 to the portfolio VaR is GBP 7,930, which corresponds to option D. This calculation demonstrates the application of Euler's theorem, which states that for homogeneous risk measures, the total portfolio risk equals the sum of the marginal contributions of each component when each component's risk is increased by a small amount.

Author: LeetQuiz .