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Arnie · 2023年07月15日

这道题目为啥不能定性的判断

  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)].

这道题目0.5%上升是level的，根据性质判断：barbell 表现最好，convexity最大，涨多跌少的性质最好，为了验证：且我计算出来了bullet 、 barbell、还有laddered 的 portfolio convexity， 是barbell的convexity最大，直接判断涨多跌少，在这道题目中为啥不适用？

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2 个答案

pzqa31 · 2023年07月17日

嗨，努力学习的PZer你好：


可以加权平均的，这是简便的算法，这种算法也比较常见，是最简单高效的算法，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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加油吧，让我们一起遇见更好的自己！

pzqa31 · 2023年07月15日

嗨，爱思考的PZer你好：


只有duration相同，才可以直接用convexity来判断。这道题的duration并不相同，所以要具体计算duration和convexity的影响。

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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！

Kiyo · 2023年07月16日

convexity也是用加权平均计算吗？

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