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Oudi · 2022年12月23日

想问一下这个题目的128.88是怎么得来的?

  1. CFA III
  2. Derivative

NO.PZ2018113001000076

问题如下：

Matthew, a junior analyst, manages a portfolio W. The portfolio is fully invested in US Treasuries。Matthew intends to decrease the portfolio’s modified duration to 3.00。

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, to achieve Matthew’s objective, the number of Treasury futures contracts Matthew should sell is closest to:

选项：

A.

440

B.

441

C.

398

解释：

B is correct

BPVT =MDurT × 0.0001 × MVP = 3×0.0001×120,349,000 = 36,104.70

BPVHR=BPVT−BPVPBPVCTD×CF=36,104.70−111,924.57128.88×0.75=−441,22<span>BPVHR=\frac{BPV_T-BPV_P}{BPV_{CTD}}\times CF=\frac{36,104.70-111,924.57}{128.88}\times0.75=-441,22

Matthew should sell 441 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。

想问一下这个题目的128.88是怎么得来的?

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1 个答案

Hertz_品职助教 · 2022年12月25日

嗨，爱思考的PZer你好：


同学你好

128.88的确是可以计算出来的：

我们知道BPV的计算公式为：BPV = MV*MD*1BP

然后注意的是这里的期货合约的报价是按照面值100进行报价的，因此在求期货合约的MV的时候，需要用143.20先除以100，得到1块钱的面值，然后再乘以contract size才能得到期货合约的MV。

因此BPV=143.20/100 * 100,000 * 9 * 1bp=128.88.

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努力的时光都是限量版，加油！

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NO.PZ2018113001000076 问题如下 Matthew, a junior analyst, manages a portfolio W. The portfolio is fully investein US Treasuries. Matthew inten to crease the portfolio’s mofieration to 3.00.Exhibit 1 presents selecteta on Portfolio W, anthe relevant Treasury futures contract, anthe cheapest-to liver (CT bon Baseon Exhibit 1, to achieve Matthew’s objective, the number of Treasury futures contracts Matthew shoulsell is closest to: A.440 B.441 C.398 B is correctBPVT =MrT × 0.0001 × MVP = 3×0.0001×120,349,000 = 36,104.70BPVHR=BPVT−BPVPBPVCTCF=36,104.70−111,924.57128.88×0.75=−441,22 spBPVHR=\frac{BPV_T-BPV_P}{BPV_{CT}\times CF=\frac{36,104.70-111,924.57}{128.88}\times0.75=-441,22 spBPVHR=BPVCTBPVT​−BPVP​​×CF=128.8836,104.70−111,924.57​×0.75=−441,22 spMatthew shoulsell 441 Treasury bonfutures 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。 老师，您好！题中给出的128.88是债券期货的BPV吗？还是债券CTBPV?如果是债权期货的BPV，那么用债券期货调整债券组合的久期（或BPV）时，计算需要多少份期货合约的计算公式应该如下Nf = (BPV_T - BPV_P) / BPV_f，如果题目中的128.88是债券期货的合约，则代入计算得到(36104.7-111924.57) / 128.88 = -588.3。如果128.88是CT券的BPV, 则需要通过conversion factor转换计算对应债券期货的BPV_f = BPV_ct/ CF，那么计算需要多少份期货合约的计算公式应该如下Nf = (BPV_T - BPV_P) / (BPV_ct/ CF) = -441.22。题目中显然是把128.88当做CTBPV来处理的。但是128.88 = 143200 * 9 * 0.0001得到的，即应该是债券期货的BPV。那么到底该怎么理解呢？麻烦老师一下，谢谢！

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