Answer-first summary for fast verification
Answer: AUD 307.66
## Explanation For key rate 01 (KR01), the magnitude of a shift in a key rate declines linearly to zero at the next key rate above and/or below. Given the key rates are 2-year, 5-year, and 10-year: - When the 5-year spot rate increases by 1 bp, the 4-year spot rate changes by: $$1 * \frac{4 - 2}{5 - 2} = 0.6667$$ - When the 5-year spot rate increases by 1 bp, the 7-year spot rate changes by: $$1 * \frac{10 - 7}{10 - 5} = 0.6$$ The change in portfolio value for a 1 bp change in the 5-year spot rate is calculated as: $$0.6667 * (-189.27) + 0.6 * (-302.45) = -126.18 + (-181.47) = -307.65$$ Taking the absolute value gives KR01 = AUD 307.66, which matches option C. This calculation shows how the portfolio value would decrease by AUD 307.66 for a 1 basis point increase in the 5-year key rate, considering the linear interpolation of rate changes to adjacent key rates.
Author: LeetQuiz .
Ultimate access to all questions.
A risk manager at a bank is measuring the sensitivity of a bond portfolio to non-parallel shifts in spot rates. The portfolio currently holds a 4-year zero coupon bond and a 7-year zero coupon bond with the following sensitivities to these respective spot rates:
| Spot rate | Change in portfolio value for 1-bp increase in spot rate (AUD) |
|---|---|
| 4-year | -189.27 |
| 7-year | -302.45 |
To model the non-parallel movement of the spot rate curve, the manager treats the 2-year, 5-year, and 10-year spot rates as key rates. Given this information, what is the portfolio's key rate 01 (KR01) for a 1-bp increase in the 5-year rate?
A
AUD 184.06
B
AUD 226.99
C
AUD 307.66
D
AUD 491.72
No comments yet.