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Shawnxz · 2024年05月04日

请问这种equally weighted的convexity和MD可以直接加权平均吗？

  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)].

请问这种equally weighted的convexity和MD可以直接加权平均吗？获得新的组合MD和ConV. ,能解释一下原理吗？谢谢

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已采纳答案

pzqa31 · 2024年05月05日

嗨，爱思考的PZer你好：


Portfolio duration与Portfolio convexity都可以加权平均算，这是简单高效的算法，并没有什么原理，但是有误差，如果要精确地算的话，需要把Portfolio当成一个大债券，Portfolio内部各期现金流就是这个大债券的现金流，然后通过Duration与Convexity的定义去算，不过这种计算量太大了。

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