NO.PZ2023091701000051
问题如下：
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:
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?
选项：
A.AUD 184.06
B.AUD 226.99
C.AUD 307.66
D.AUD 491.72
解释：
C is correct. For a key rate (or partial) 01, the magnitude of a shift in a key rate declines linearly to zero at the next key rate above and/or below. Therefore, if the 5-year spot rate increases by 1 bp, the 4-year and 7-year spot rates change as follows:
4-year spot rate:
7-year spot rate:
The change in the value of the portfolio for a 1 bp change in the 5-year spot rate is therefore:
0.6667∗−189.27+0.6∗−302.45=307.6563
A is incorrect. This incorrectly calculates the changes in the 4-year and 7-year rates as 0.3333 and 0.4 respectively.
B is incorrect. This incorrectly calculates the change in the 7-year rate as 0.3333.
D is incorrect. This incorrectly calculates the forward bucket 01 for the portfolio, assuming the 4-year and 7-year rates change by 1.
请问一下这个题目中4/7 year spot rate 是怎么求出来的
