关于key rate对邻近的辐射影响

问题如下：

A portfolio depends on a 3.5-year, risk-free rate interest rate and no other rates or risk factors. It is calculated that the portfolio will increase in value by USD 500 for each one-basis-point increase in the rate. The rates that are modeled are the three month, six-month, one-year, two-year, three-year, five-year, ten-year, and thirty year rates. What is the delta of the portfolio with respect to each of these rates?

解释：

The portfolio has a delta with respect to the 3- and 5-year rates and no other rates. When the 3-year rate changes by one basis point, the 3.5-year rate changes by 0.75 basis points. When the 5-year rate changes by one basis point, the 3.5-year rate changes by 0.25 basis points. The deltas with respect the 3- and 5-year rates are therefore USD 375 and USD 125, respectively.

题目问：投资组合取决于 3.5 年期的无风险利率，没有其他利率或风险因素。 根据计算，利率每增加一个基点，投资组合的价值将增加 500 美元。 建模的利率是三个月、六个月、一年、两年、三年、五年、十年和三十年的利率。 相对于这些利率中的每一个，投资组合的 delta 是多少？

3.5年和3年 比3.5年和5年更加接近，所以肯定是3年对portfolio的影响更大一些。

解答这类题目的思路是用3年和5年去凑一个3.5年，假设3年的影响比重为x，那么5年的影响比重则为1-x，得到

3x+5(1-x)=3.5，得x=0.75