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bear41 · 2020年03月01日

问一道题:NO.PZ2019103001000041 [ CFA III ]

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.

Donaldson suggests they also consider altering the portfolio’s convexity to enhance expected return given McLaughlin’s interest rate expectations.

Given McLaughlin’s interest rate expectations over the next 12 months, one way that Donaldson and McLaughlin could alter convexity to enhance expected return would be to:

选项:

A.

sell call options on bonds held in the portfolio.

B.

buy call options on long-maturity government bond futures.

C.

sell put options on bonds they would be willing to own in the portfolio.

解释:

B is correct.

McLaughlin expects interest rate volatility to be high and the yield curve to experience an increase in the butterfly spread, with the 30-year yield remaining unchanged. To increase the portfolio’s expected return, Donaldson and McLaughlin should buy call options on long-maturity government bond futures to increase convexity.

老师:您好!我一直搞不懂convexity和curvature在图形上的差异,比如这道题;我知道10年期利率上涨幅度高于短期和长期,但是这个变动到底是convexity还是curvature?烦请画图告知差异。谢谢!
1 个答案

发亮_品职助教 · 2020年03月02日

嗨,努力学习的PZer你好:


“我一直搞不懂convexity和curvature在图形上的差异,比如这道题;我知道10年期利率上涨幅度高于短期和长期,但是这个变动到底是convexity还是curvature?”


Convexity描述的是债券价格与Yield之间的关系,横轴是利率、纵轴是债券价格:

红线是切线代表Duration,反映出来的关系是:利率变化时,债券的价格呈线性变动;

债券价格与Yield的关系引入Convexity之后,反映出来的就是弯曲、凸向原点的曲线,如下图蓝线,相比用线性Duration衡量利率变动、债券价格的涨跌,引入Convexity之后,利率跌债券价格涨得更多,利率涨的时候,债券价格跌的更少。

所以引入Convexity后,这条凸向原点、债券价格与收益率关系的曲线,就能反映出Convexity涨多跌少的性质。




Cuvature衡量的是收益率曲线上,中期利率相对于短期、长期利率的大小关系;横轴是时间,纵轴是利率,反映的是利率与时间之间的关系:

中期利率相对于长期、短期利率上升,收益率曲线变得更弯曲,所以是More cuvature。


所以回复一下提问里的问题:

10年期利率相对于短期、长期利率的上升,描述的是利率与时间之间的关系,代表的是收益率曲线更加Cuvature、利率曲线更弯曲。


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NO.PZ2019103001000041 “因为题干预测的利率信息是利率波动加大 She expects interest rate volatility to high anthe yielcurve to experienincrease in the 2s/10s/30s butterfly sprea with the 30-yeyielremaining unchange所以B说的Buy options,就会增加组合的Convexity,于是组合获得“涨多跌少”的优势,策略会增强收益。” 怎么理解increase in the 2s/10s/30s butterfly spreasprea加利率增加,债券价格下跌幅度再有限,但那也是跌啊哪来的enhanreturn?为啥不能直接卖了option赚期权费 收益的更多?

2021-05-24 20:51 1 · 回答

NO.PZ2019103001000041 buy call options on long-maturity government bonfutures. sell put options on bon they woulwilling to own in the portfolio. B is correct. McLaughlin expects interest rate volatility to high anthe yielcurve to experienincrease in the butterfly sprea with the 30-yeyielremaining unchange To increase the portfolio’s expectereturn, nalon anMcLaughlin shoulbuy call options on long-maturity government bonfutures to increase convexity. 题干有错误吧?butterfly那里

2021-04-28 22:16 3 · 回答

NO.PZ2019103001000041 这道题为什么不选short put option,是因为可能接不到货吗?

2021-03-14 16:33 2 · 回答

请问,题干中已经说明30年期收益率不变,那么即便买入长期国债期货是不是也不会增加收益呢?毕竟convexity特性是涨多涨多跌少,可30年长期利率不变啊。

2021-02-04 12:13 2 · 回答

不好意思老师还是没有看懂,如果说利率上升,债券价格降低,为啥要买看涨期权呢?增加了convexity但是又额外付出了成本呀

2020-11-04 09:48 1 · 回答