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Zachary · 2020年06月25日

问一道题:NO.PZ2019103001000061

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.

Winslow thinks the Mexican and Greek markets may offer attractive opportunities to enhance returns. Yields in these markets are given in Exhibit 1, along with those for the base currencies of her portfolios. The Greek rates are for euro-denominated government bonds priced at par. In the other markets, the yields apply to par sovereign bonds as well as to the fixed side of swaps versus six-month Libor (i.e., swap spreads are zero in each market). The six-month Libor rates also represent the rates at which investors can borrow or lend in each currency. Winslow observes that the five-year Treasury-note and the five-year German government note are the cheapest to deliver against their respective futures contracts expiring in six months.

Winslow expects yields in the US, Euro, UK, and Greek markets to remain stable over the next six months. She expects Mexican yields to decline to 7.0% at all maturities. Meanwhile, she projects that the Mexican Peso will depreciate by 2% against the Euro, the US Dollar will depreciate by 1% against the Euro, and the British Pound will remain stable versus the Euro. Winslow believes bonds of the same maturity may be viewed as having the same duration for purposes of identifying the most attractive positions.

Based on these views, Winslow is considering three types of trades. First, she is looking at carry trades, with or without taking currency exposure, among her three base currency markets. Each such trade will involve extending duration (e.g., lend long/borrow short) in no more than one market. Second, assuming the legal department confirms her interpretation of permissible currency hedging, she wants to identify the most attractive five-year bond and currency exposure for each of her three portfolios from among the five markets shown in Exhibit 1. Third, she wants to identify the most attractive five-year bond and hedging decision for each portfolio if she is only allowed to hedge into the portfolio’s base currency.

Among the carry trades available in the US, Euro, and UK markets, the highest expected return for the USD-denominated portfolio over the next 6 months is closest to:

选项:

A.

0.275%

B.

0.85%

C.

0.90%.

解释:

B is correct.

The highest potential return, 0.85%, reflects borrowing USD for 6 months and buying the UK 5-year bond. The carry component of the expected return is actually a loss of 0.15% [= (1.10% – 1.40%)/2], but this is more than offset by the 1% expected appreciation of GBP versus USD. A much higher carry component +0.90% = (1.95% – 0.15%)/2 could be obtained by borrowing for 6 months in EUR to buy the US 5-year note, but that advantage would be more than offset by the expected 1% loss from depreciation of the USD (long) against the Euro (short).

A is incorrect because a higher expected return of 0.85% can be obtained. This answer, +0.275% [= (1.95% – 1.40%)/2], is the highest carry available over the next 6 months within the US market itself (an intra-market carry trade).

C is incorrect. This answer (+0.90%) is the highest potential carry component of return but ignores the impact of currency exposure (being long the depreciating USD and short the appreciating Euro).

请问解析中的= (1.10% – 1.40%)/2这个是计算持有收益吗?为什么是这个公式?在强化班哪里有讲到这个?

2 个答案

发亮_品职助教 · 2020年07月16日

"为什么Susan Winslow这题,算6个月carry trade收益,直接用的yield,但是基础班里simon millsap这题,要先用total return拆分的方式把yield return,rolling return,cm yields都加在一起。Susan这边为啥不考虑rolling return?"


算Carry trade,就是投资获得的收益,减去借款的成本;理论上,债券的投资收益,确实包括Yield return,Roll-down return等等。

所以比较复杂的题目,算Carry trade投资收益时,首先就需要老老实实地算投资债券的Total return,以及“借款成本”Short债券的Total return。相减才能得到Carry trade收益

具体的算法就和讲义里面那个millsap Case一样;或者不用拆开算,直接算债券持有期Total return即可。


但是我们这道题给的利率比较特殊:


他这里给的利率是Par rate,也就是使得债券价格等于面值的折现率;我们知道当债券的价格等于面值时,其Coupon rate等于折现率;

所以这个表里的利率即是债券的折现率(收益率),也是债券的Coupon rate;

由于5年期利率和4年期利率在这个表里比较接近,我们可以用线性插值法,大概算出来4.5年期利率是多少;

比如,对于EUR,5年期利率是0.6%,所以我们期初投资的5年期债券、他的Coupon rate是0.6%;

4年期利率是0.50%,5年期利率是0.6%,我们知道4.5年期利率是0.55%;这个0.55%的债券收益率和Coupon rate的0.6%很接近了,我们就知道投资半年之后,这支5年期债券变成了4.5年期债券,他的期末债券价格仍然是Par value;因为折现率0.55%离Coupon rate很近

那这样的话,在投资期内,债券的价格基本没变化,我们只收到一笔债券的Coupon,5年期EUR债券投资半年的收益就是0.5%/2,这里的0.5%代表的是债券的Coupon rate。

这样的话,看起来这道题我们算投资债券的收益率使用的是表格里的债券Yield,但实际上他代表的是我们获得的Coupon。


因为债券的收益率包括债券价格变动与Coupon,由于本题债券价格一直等于Par、投资半年债券价格没有变化,只有一笔Coupon,所以本题债券的投资收益就是债券Coupon rate,又因为本题的表格是Par rate,他既是债券的Yield、又是债券的Coupon rate,所以看起来这道题在算债券投资收益时使用了债券Yield,但其实代表的意思是Coupon收益。


这是这道题的简化之处,但其实算出来的收益不完整,因为从表格的数据看,确确实实债券投资半年之后,折现率会发生一点变化,债券的价格会偏离Par value一点,但因为这个数太小了,可以忽略,债券的收益只用Coupon代表即可。

在其他题目中,如果碰到了一般情况,算债券的投资收益就需要算两部分:Coupon + Price变化

发亮_品职助教 · 2020年06月28日

嗨,从没放弃的小努力你好:


“请问解析中的= (1.10% – 1.40%)/2这个是计算持有收益吗?为什么是这个公式?”


这个就是第一种Inter-market carry trade的方式:在A国低利率借钱,换成B国货币,投资B国高利率,赚取息差。

提问里(1.10% – 1.40%)/2对应的就是在US借钱(借6-month,借钱成本1.40%),在UK投资(投5-Year,投资收益1.10%)。

我们表里的利率都是年利率数据,所以在US借钱的年利率就是6-month LIBOR 1.40%,因为题干有说LIBOR利率就是直接的借贷利率:The six-month Libor rates also represent the rates at which investors can borrow or lend in each currency;

那这样的话,借US 6-month LIBOR的年利率是1.40%,我们借了6个月,对应借钱成本是:1.40%/2


1.10%就是在UK投资的收益;现在表里的利率,他既是债券的收益率,又是债券的Coupon rate,因为题干有说这些利率是Par rates:

the yields apply to par sovereign bonds;

因为我们投资了5-Year UK bond,持有了6个月,收到的Coupon收益就是1.10%/2;

那这样的话,投资收益是1.10%/2,支付的成本是1.40%/2。

Carry trade不考虑汇率,只看息差的收益为:(1.10%/2 -  1.40%/2) = (1.10% - 1.40%) / 2

 


"在强化班哪里有讲到这个?"


对应知识点是强化班Reading 20,Stable Yield Curve Strategies-Inter-Market Carry trade 

在经典题也有讲这道题,对应经典题Reading 20 Strategies under a Stable Yield Curve: Carry Trade


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!


leslie_cheng · 2020年07月16日

为什么Susan Winslow这题,算6个月carry trade收益,直接用的yield,但是基础班里simon millsap这题,要先用total return拆分的方式把yield return,rolling return,cm yields都加在一起。Susan这边为啥不考虑rolling return?

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