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daiwin18 · 2022年10月19日

关于BPV的计算

NO.PZ2018113001000075

问题如下：

Matthew, a junior analyst, manages a portfolio W. The portfolio is fully invested in US Treasuries。Matthew intends to fully hedge this bond portfolio against a rise in interest rates。

Exhibit 1 presents selected data on Portfolio W, and the relevant Treasury futures contract, and the cheapest-to deliver (CTD) bond.

Based on Exhibit 1, the number of Treasury futures contracts Matthew should sell to fully hedge Portfolio W is closest to:

选项：

A.

652

B.

651

C.

745

解释：

B is correct

$BPVHR=\frac{BPV_T-BPV_P}{BPV_{CTD}}\times CF=\frac{0-111,924.57}{128.88}\times0.75=-651.33$

Matthew should sell 651 Treasury bond futures contracts.

中文解析：

本题考察的是利用期货合约调节组合的久期，直接带入上述公式计算即可。注意最后合约份数需要四舍五入取整数，负号代表卖出期货合约。

为什么通过这个公式BPV(p)=MDUR × 0.01% × MV(p)，计算得出的MV(p)跟题干的信息不相等。

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Hertz_品职助教 · 2022年10月19日

嗨，爱思考的PZer你好：

同学你好

问题：为什么通过这个公式BPV(p)=MDUR × 0.01% × MV(p)，计算得出的MV(p)跟题干的信息不相等

回答：

题干中能够通过BPV,以及MDur的信息推算出MV，并且有已知的MV数据可以对比的，是关于组合W的信息，也就是表格左侧的信息。

根据表格中的数据，按照同学说的反推出来的MV是和题干给的信息一致的，都为120349000.当然按照这个数据计算的组合的BPV也是和表格中的数据一致的。

另外，几乎没有题目会通过计算BPV的公式来反算MV的哈，因为MV一般是作为已知信息需要给到我们的。

----------------------------------------------
努力的时光都是限量版，加油！

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