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Enjoy · 2024年05月15日

这一题麻烦解释一下具体算法

* 问题详情,请 查看题干

NO.PZ202305230100005304

问题如下:

For a 100 bps increase in yield-to-maturity and using the weighted average duration and convexity, the expected percentage price change for the bond portfolio is closest to:

选项:

A.

–7.981%

B.

–8.949%

C.

–9.533%

解释:

B is correct. The portfolio weights for Bonds X, Y, and Z are 0.25, 0.25, and 0.50, respectively. The weighted average duration and convexity measures are calculated as follows:

Weighted-average duration = (0.25 × 3.6239) + (0.25 × 9.0036) + (0.50 × 12.7512) = 9.5325.

Weighted-average convexity = (0.25 × 16.2513) + (0.25 × 91.0278) + (0.50 × 179.8591) = 116.7493.

%ΔPVFull ≈ (–9.5325 × 0.01) + [0.5 × 116.7493 × (0.01)^2]

= –8.9487% ≈ –8.949%.

感觉这道题的算法很复杂,考试会考这么复杂的算术题吗?

1 个答案

吴昊_品职助教 · 2024年05月15日

嗨,从没放弃的小努力你好:


这道题考察了组合久期和组合凸度,是会考察的。 具体计算步骤如下:

1、我们先计算各债券市值权重,Wx=5m/20m=0.25;Wy=5m/20m=0.25;Wz=10m/20m=0.5

2、有了权重之后,分别计算出组合久期和组合凸度。

组合久期= (0.25 × 3.6239) + (0.25 × 9.0036) + (0.50 × 12.7512) = 9.5325

组合凸度=(0.25 × 16.2513) + (0.25 × 91.0278) + (0.50 × 179.8591) = 116.7493

3、有了组合久期和组合凸度之后,代入公式,即可得组合的价格变动:%ΔPVFull

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