这一题麻烦解释一下具体算法

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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：

–7.981%

–8.949%

–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？

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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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努力的时光都是限量版，加油！

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NO.PZ202305230100005304 问题如下 For a 100 bps increase in yielto-maturity anusing the weighteaverage ration anconvexity, the expectepercentage prichange for the bonportfolio is closest to: A.–7.981% B.–8.949% C.–9.533% B is correct. The portfolio weights for Bon X, Y, anZ are 0.25, 0.25, an0.50, respectively. The weighteaverage ration anconvexity measures are calculatefollows:Weighteaverage ration = (0.25 × 3.6239) + (0.25 × 9.0036) + (0.50 × 12.7512) = 9.5325.Weighteaverage 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%. 为何不是分别计算每个资产的ration和convexity，然后再根据每个资产的权重，将每个资产的ration和convexity相加

2024-09-25 23:11 2 · 回答

这一题麻烦解释一下具体算法

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