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Betty-Che · 2024年01月17日

portfolio的convexity是怎么算的

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ202112010200000102

问题如下：

The manager estimates that accelerated economic growth in Australia will increase the level of government yields-to-maturity by 50 bps.

Under this scenario, which of the three portfolios experiences the smallest decline in market value?

选项：

A.

Bullet portfolio

B.

Barbell portfolio

C.

Equally weighted portfolio

解释：

A is correct. The change in portfolio value due to a rise in Australian government rate levels may be calculated using Equation:

%∆PVFull ≈ -(ModDur × ΔYield) + [½ × Convexity × (ΔYield)2],where ModDur and Convexity reflect portfolio duration and convexity, respectively. Therefore, the bullet portfolio declines by 2.093%, or -2.093% = (-4.241 × 0.005) + [0.5 × 22.1 × (0.0052)],

followed by a drop of 2.343% for the equally weighted portfolio, or

-2.343% = (-4.779 × 0.005) + [0.5 × 37.4 × (0.0052)],

and a drop of 2.468% for the barbell portfolio, or

-2.468% = (-5.049 × 0.005) + [0.5 × 45.05 × (0.0052)].

如题，barbells和equal weighted的convexity是怎么算的，看答案好像是直接平均的，这样合理吗


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已采纳答案

pzqa015 · 2024年01月18日

嗨，从没放弃的小努力你好：


不是简单平均，是加权平均的


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

pzqa015 · 2024年01月18日

嗨，爱思考的PZer你好：



2Y的convexity是4.9，4.5年的convexity是22.1，9年的convexity是85.2.

barbell portfolio由2年和9年债，各50%组成。所以，barbell的convexity=（85.2+4.9）/2=45.05

equal weights由2年、4.5年和9年各1/3组成，所以equal weights的convexity=(4.9+22.1+85.2)/3=37.4

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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