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sliang · 2024年10月27日

fixed income

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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。

1 个答案
已采纳答案

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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