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sliang · 2024年10月27日

fixed income

  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)].

这题答案还用公式算出了每个portfolio的price change是多少. 我是直接看A的duration最小，就选了A. 请问我的方法有什么问题么?谢谢。

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发亮_品职助教 · 2024年10月28日

直接看A的duration也可以，这是定性判断。因为这道题是利率上升，债券的价格下降，Duration越小价格下降的幅度越少。

大体上判断因为A的duration最小，所以A的market value可能是最小幅度的下降。

但这种定性判断不一定准确！

因为有可能A,B,C三个组合的duration差不多，duration的差距可以忽略不计。这时候三个组合convexity的影响就占主导了。所以还得额外考虑convexity。

这道题因为3个组合的duration差异太大了，convexity的差异起不到多大的影响。duration就直接决定了A的价格下降幅度是最小的。所以可以通过duration最小判断选A。

一般定性判断不太有把握，建议还是按照答案的方法计算一下！

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