Answer: AUD307.66

The portfolio's key rate duration (KR01) for a 1-bp increase in the 5-year rate is calculated by considering the sensitivity of the bond portfolio to changes in the 5-year spot rate. The key rate duration measures the change in the value of a bond or a portfolio of bonds for a 1 basis point change in the specific key rate. In this case, the risk manager has identified the 2-year, 5-year, and 10-year spot rates as key rates. The 4-year and 7-year zero coupon bonds in the portfolio have sensitivities to their respective spot rates, which are -189.27 and -302.45 for a 1-bp increase in the spot rate. To find the KR01 for the 5-year rate, we need to determine how the 4-year and 7-year spot rates would change in response to a 1-bp increase in the 5-year rate. The change in the 4-year spot rate is calculated by the ratio of the distance between the 4-year and the 5-year key rates to the distance between the 2-year and the 5-year key rates, which is \( \frac{4 - 2}{5 - 2} = 0.6667 \). Similarly, the change in the 7-year spot rate is calculated by the ratio of the distance between the 7-year and the 10-year key rates to the distance between the 7-year and the 5-year key rates, which is \( \frac{10 - 7}{10 - 5} = 0.6 \). The overall change in the portfolio value for a 1 bp change in the 5-year spot rate is then the sum of the changes in the value of the individual bonds due to the change in their respective spot rates: \[ 0.6667 \times (-189.27) + 0.6 \times (-302.45) = -307.6563 \] This calculation results in a portfolio value decrease of approximately AUD 307.66, which corresponds to option C. This value represents the key rate duration for the 5-year rate, indicating that for a 1 basis point increase in the 5-year spot rate, the portfolio value would decrease by approximately AUD 307.66.

Author: LeetQuiz Editorial Team