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fanfan · 2021年02月28日

请问c选项在讲义哪里有?

NO.PZ2019103001000059

问题如下:

Susan Winslow manages bond funds denominated in US Dollars, Euros, and British Pounds. Each fund invests in sovereign bonds and related derivatives. Each fund can invest a portion of its assets outside its base currency market with or without hedging the currency exposure, but to date Winslow has not utilized this capacity. She believes she can also hedge bonds into currencies other than a portfolio’s base currency when she expects doing so will add value. However, the legal department has not yet confirmed this interpretation. If the lawyers disagree, Winslow will be limited to either unhedged positions or hedging into each portfolio’s base currency.

Given the historically low rates available in the US, Euro, and UK markets, Winslow has decided to look for inter-market opportunities. With that in mind, she gathered observations about such trades from various sources. Winslow’s notes with respect to carry trades include these statements:

I. Carry trades may or may not involve a maturity mismatch.

II. Carry trades require two yield curves with substantially different slopes.

III. Inter-market carry trades just break even if both yield curves move to the forward rates.

Which of Winslow’s statements about carry trades is correct?

选项:

A.

Statement I

B.

Statement II

C.

Statement III

解释:

A is correct.

Carry trades may or may not involve maturity mis-matches. Intra-market carry trades typically do involve different maturities, but inter-market carry trades frequently do not, especially if the currency is not hedged.

B is incorrect. Carry trades may involve only one yield curve, as is the case for intra-market trades. In addition, if two curves are involved they need not have different slopes provided there is a difference in the level of yields between markets.

C is incorrect. Inter-market carry trades do not, in general, break even if each yield curve goes to its forward rates. Intra-market trades will break even if the curve goes to the forward rates because, by construction of the forward rates, all points on the curve will earn the “first-period” rate (that is, the rate for the holding period being considered). Inter-market trades need not break even unless the “first-period” rate is the same in the two markets. If the currency exposure is not hedged, then breaking even also requires that there be no change in the currency exchange rate.

请问c选项在讲义哪里有?谢谢
1 个答案
已采纳答案

发亮_品职助教 · 2021年03月01日

嗨,爱思考的PZer你好:


“请问c选项在讲义哪里有?"


讲义正文内容没有出现C的这条结论。在讲义第288页,刚好就是这道例题里面有出现。

关于C的这句话,他描述是错误的。

C选项是错误的结论,把它改成Intra-market就正确了。


下面就解释一下为什么改成Intra-market之后是正确的结论,以及解释一下为什么C选项Inter-market是错误的结论。


C选项这句话改成这样是正确的:

"Intra-market carry trades just break even if both yield curves move to the forward rates"

注意是:Intra-market

也就是说,对于一国内部的Carry trade,如果未来的利率曲线实现了期初的Forward rates,那么Carry trade实现盈亏平衡(Breakeven),这句话正确,记住这句结论即可。

C选项就是把Intra-market carry trade的结论引申到Inter-market来混淆题目、做干扰信息的,对于Inter-market carry trade,没有这一个结论。


下面做一个简单的解释帮助理解,考试的话只要记住这句结论即可:

Intra-market carry trades just break even if yield curve moves to forward rates

对于Intra-market carry trade,如果收益率曲线实现了期初Spot rate隐含的Implied forward rate,那么Intra-market carry trade实现盈亏平衡。

关于这个结论,其实是来自2级的一个结论:

If forward rates are realized, then all bonds, regardless of maturity, will have the same one-period realized return, which is the first-period spot rate.

也就是说,如果利率实现了期初的implied Forward rates,那所有债券投资,无论是什么期限的债券,投资这一年实现的收益都一样,都是第一期的Spot rate收益。


下面做一个简单的证明,假设:

1-year Spot rate = 2%

2-year spot rate = 3%

3-year spot rate = 4%

这个Spot rate隐含的forward rate为:

f(1,1) = 4.01%

f(1,2) = 5.015%

假设一年过去了,利率实现了当初Spot rate隐含的Forward rate,即站在1年后的时间点看,one-year spot rate = 4.01%;2-year spot rate = 5.015%;

我们投资一个1-year zero-coupon bond,那实现的收益就是1-year spot rate = 2%,因为到期100,期初定价是2%定的,所以实现2%的收益率。

假设我们投资的是一个2-year zero-coupon bond,投资这一年实现的收益率计算为:

期初买债券的价格:100/(1+3%)^2=94.26

1年过去后,这支2年期债券变成了1年期债券,如果利率实现了期初的Implied forward rate,那1年期利率为:4.01%;按照新的Spot rate定价卖出债券的价格为:

100/(1+4.01%)=96.145

所以投资一年的收益率为:(96.145-94.26)/(94.26)=1.9998%,考虑计算的时候是近似的,所以理论值应该是2%

这样发现,如果收益率曲线实现了期初Spot rate隐含的Implied forward rate,投资1年期债券的收益是2%,投资2年的期债券的收益也是2%。这一年实现的投资收益率一样,都是第一期的Spot rate 2%。

这就是上面这个结论说的:

If forward rates are realized, then all bonds, regardless of maturity, will have the same one-period realized return, which is the first-period spot rate.


同理,如果我们投资的是3年期的债券,期初价格为:100/(1+4%)^3=88.90

1年的投资期,1年后这支债券变成了2年期ZCB,如果利率实现了期初的Implied forward rate,那新的两年期利率是5.015%,那期末债券的卖出价格为:

100/(1+5.015%)^2=90.68

所以这一年的投资收益为:(90.68 - 88.90)/88.90 = 2%

发现投资3年期债券1年,实现的收益率也是2%。


因为Carry trade是借短期利率、投长期利率,在这个期间内实现利差。

而如果利率实现了期初Spot rate隐含的Implied forward rate,那么无论是何种期限的债券,期间实现的投资收益率都一样,都是第一期的Spot rate,那这样的话,在这个投资期内,Carry trade即便是借短期、投长期,借钱的利率和投资实现的收益,都是第一期的Spot rate,那就刚好盈亏平衡。

比如,我们借1年期利率,投资三年期利率,从上面的计算可以看到,如果实现了Implied forward rates,那借钱(1年期)的成本是2%,投资3年期债券1年实现的收益也是2%。这样,借钱的成本等于投资的收益,一国内部的Carry trade实现盈亏平衡。

所以做Intra-market Carry trade的投资者都是认为将来实现的利率不等于期初隐含的Implied forward rate。

回忆Carry trade的收益率预测是Stable,收益率曲线今天长啥样明天还是啥样,所以按Stable的要求,明年的1-year spot rate应该还是2%,2-year还是3%,显然没有实现期初预测的4.01%与5.015%,这样其实Stable也是说利率没有实现期初的Implied forward rate。


然后,这道题是想把上面那个结论引申到Inter-market carry trade。在Inter-market carry trade里,这个结论不成立。

首先对于Inter-market carry trade,即便两国的利率曲线实现了期初预测的Implied forward rate也无所谓,因为是两个市场,大家都有各自自己市场内部的First-period spot rate rate,first-period rate也不一定相等。

我们是在一个市场上借钱、另一个市场上投资,即便两个市场各自实现了First-period spot rate也无所谓,因为两个市场上First-period spot rate不一定相等,所以借钱利率和投资收益不一定相等。Carry trade不一定会Breakeven。

然后就是即便两国的First-period rate相等,因为两国还涉及汇率的变动,Carry trade也不一定Breakeven。

综上:

Intra-market carry trades just break even if both yield curves move to the forward rates,正确

Inter-market carry trades just break even if both yield curves move to the forward rates,错误

该结论推广到Inter-market carry trade不成立。

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Yaq7 · 2021年11月21日

发亮老师,想补充问个问题,关于汇率变动的表述。 :the US Dollar will depreciate by 1% against Euro, and the British Pound will remain stable versus the Euro 在计算Q1里,算hedged return。题目没选借Euro投美元是因为考虑了美元贬值1%后,R很小了。于是选了借USD投GBP,我没理解的是为啥这里直接可以等价于GBP相对于USD升值了1%呢?不是应相当于the US Dollar will depreciate by 1% against GBP吗?GBP升值幅度应倒数一下?