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little_back · 2021年03月28日

请问老师, increase in the 2s/10s/30s butterfly spread, with the 30-year yield remaining unchanged这句话的理解

NO.PZ2019103001000039

问题如下:

McLaughlin and Michaela Donaldson, a junior analyst at Delphi, are now discussing how to reposition the portfolio in light of McLaughlin’s expectations about interest rates over the next 12 months. She expects interest rate volatility to be high and the yield curve to experience an increase in the 2s/10s/30s butterfly spread, with the 30-year yield remaining unchanged. Selected yields on the Treasury yield curve, and McLaughlin’s expected changes in yields over the next 12 months, are presented in Exhibit 1.

Based on these interest rate expectations, McLaughlin asks Donaldson to recommend a portfolio strategy. Donaldson considers the following three options.

Bullet portfolio: Invest solely in 10-year Treasury government bonds

Barbell portfolio: Invest solely in 2-year and 30-year Treasury government bonds

Laddered portfolio: Invest equally in 2-year, 5-year, 10-year, and 30-year Treasury government bonds

Which of Donaldson’s statements is correct?

Using the yield curve forecast shown in Exhibit 1, which portfolio strategy should Donaldson recommend for the year ahead?

选项:

A.

The bullet portfolio

B.

The barbell portfolio

C.

The laddered portfolio

解释:

B is correct.

McLaughlin expects the yield curve to experience an increase in the butterfly spread, with the 30-year yield remaining unchanged, which implies that the yield curve will increase its curvature, pinned at the 30-year yield, as shown in Exhibit 1. The barbell portfolio, consisting of 2-year and 30-year bonds, would be expected to perform best. Although the two-year rate is expected to increase, the effective duration of two-year bonds is quite small, resulting in minimal price impact. Similarly, the 30-year yield is expected to remain constant, resulting in minimal price impact as well. Relative to the barbell portfolio, the laddered portfolio has greater exposure to the expected increases in the 5-year and 10-year yields, and the bullet portfolio has greater exposure to the expected increase in the 10-year yield. Therefore, the barbell portfolio would be expected to perform best given McLaughlin’s interest rate expectations.

老师,我理解这句话是30年yield 不变,但2s/10s/30s 均增加,收益率曲线应该是绕着30年的点向下转动,是steepening,哪里提到curvature了?

1 个答案

发亮_品职助教 · 2021年03月29日

嗨,爱思考的PZer你好:


老师,我理解这句话是30年yield 不变,但2s/10s/30s 均增加,收益率曲线应该是绕着30年的点向下转动,是steepening,哪里提到curvature了?


不是的,这句话的字眼在Butterfly spread上。

这个其实描述的是收益率曲线的弯曲度上升;他的弯曲度是用:2年期、10年期、30年期的3个利率来衡量的。

其中,2-year利率代表短期利率;10-year利率代表中期利率;30-year利率代表长期利率。

题干里面的Butterfly spread实际上说的就是收益率曲线Curvature的改变。Butterfly spread上升,就是Curvature上升,就是中期利率相对上升,曲线变得更加弯曲了。


the yield curve to experience an increase in the 2s/10s/30s butterfly spread, with the 30-year yield remaining unchanged.


这句是说,Yield curve的Butterfly spread会上升(Increase in...butterfly spread);


是什么样的Butterfly spread呢?是2s、10s、30s,这3个利率算出来的Butterfly spread。


我们有学到过一个Butterfly spread,他的计算公式等于:


Butterfly spread = 2 × Mid-rate - long-term rate - short-term rate;

即,2×中期利率 - 长期利率 - 短期利率。

所以,Butterfly spread衡量的就是中期利率相对于短期、长期利率的位置。Butterfy spread越大,就代表中期利率越大,即收益率曲线越弯曲。如果Butterfly spread越小,则代表收益率曲线越接近于直线;尤其是当Butterfly spread = 0时,就代表他是一条直线,Mid rate刚好是短期、长期利率的平均数。


用本题的3个利率衡量的话,就是:Butterfly spread = 2×10-year 减去 2-year 减去 30-year

题干说Butterfly spread上升,即10年期利率相对上升,也就是收益率曲线变得更加弯曲了。


针对本题的情况,Butterfly spread上升(中期利率相对上升),且30年的利率不变(with the 30-year yield remaining unchanged),我们可以认为是:中期利率10s上升引起的;或者是短期利率2s下降引起的;或者是中期利率10s上升、短期利率2s同时下降引起的等等。


不过我们也不用管这个Butterfly spread是具体咋发生的,提到Butterfly spread上升,就直接可以判断是Curvature上升,利率本题3个利率,知道是中期利率10s相对上升,收益率曲线更加弯曲了。

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