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Gwen博 · 2021年09月03日

老师,这道题的解题思路能用中文解答一遍么?

NO.PZ2019103001000064

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.

If Winslow is allowed to hedge into any of the currencies, she can obtain the highest expected returns by

选项:

A.

buying the Greek 5-year in each portfolio and hedging it into Pesos

B.

buying the Greek 5-year in each portfolio and hedging it into USD.

C.

buying the Mexican 5-year in each portfolio and not hedging the currency

解释:

A is correct.

As shown in the previous question, the Greek bond is the most attractive. Although the Peso is expected to depreciate by 2% against the EUR and the GBP and by 1% against the USD, this is less than the benefit of hedging EUR into MXN (+3.475%). The net currency component of the expected return is +1.475% = (3.475% – 2.0%) for the EUR and GBP portfolios and +2.475% = (3.475% – 1.0%) for the USD-denominated portfolio. Hedging into GBP would add only 0.175% for any of the portfolios. Hedging into USD would reduce expected return for any of the portfolios because the pick up on the hedge (+0.625%) is less than the expected depreciation (–1.0%) of the USD against the Euro and GBP.

B is incorrect. Hedging the Euro-denominated Greek bond into USD would reduce expected return for any of the portfolios because the pick on the hedge (+0.625%) is less than the expected depreciation of the USD against the Euro and GBP.

C is incorrect. As shown above, the Greek bond is more attractive than the Mexican bond.

老师,这道题的解题思路能用中文解答一遍么?

1 个答案

发亮_品职助教 · 2021年09月06日

嗨,努力学习的PZer你好:


这道题是让在多国债券里,找到一个收益最高的,所以需要选择买Greek bond还是买MXN bond(选项里只出现了这两个债券,因此只需比较这两个债券)。

但因为我们买入的是国外债券,Portfolio的本币分别为EUR,USD,GBP(本题有3个Portfolio,本币分别是EUR/USD/GBP)。

那这样的话,投资了外国债券,就需要将外国债券收益换回Portfolio本币(base currency),即对于EUR Portfolio,需要将外国债券收益换回EUR;对于USD Portfolio,需要将外国债券收益换回USD,对于GBP Portfolio,需要将外国债券收益换成GBP。


这道题,对汇率的限制是:hedge into any of the currencies,也就是说,投资了外国债券,将外国债券收益换回本币收益时,可以用Forward将汇率Hedge成任意货币。

Hedge的意思就是期初签订Forward合约,锁定换汇汇率,注意本题是Hedge into any of the currencies,其实就是利用Currency Forward寻找换汇能够获得的最高收益。

这样的话,投资外国债券的总收益是:

外国债券的收益 + Forward hedge的收益


所以这种题目,有两个步骤,第一步先找所有债券中哪个债券的收益最高。

在确定了债券之后,第二步再考虑用Forward hedge成哪种货币的换汇收益最高。


步骤一:多国债券收益率比较,选一个收益最大的债券进行投资;

步骤二:上步我们已经选好了收益最大的债券、已经为USD-Portfolio、UK-Portfolio、EUR-portfolio买了该债券,但是最终核算收益还是要按各个Portfolio的Base currency,所以第二步就需要将外国债券收益换回Portfolio Base currency,因为本题是Hedge into any currency,所以可以换成任意货币,于是需要判断用Forward先hedge成哪个货币,然后再用期末的预期即期汇率将外汇换回Portfolio base currency。判断标准就是,Hedge成哪个货币的收益最高,就Hedge成该货币。


步骤一,因为是多国收益率比,我们没法直接比较债券收益,所以先统一把不同国家的收益Hedge成一个Common currency,这一步的目的只是为了统一比较基础;


例如,在本题中,我们已经算出来了MXN债券与Greek债券的本国收益,但是这两个本国收益不可比,所以我们统一将这两个债券的收益Hedge成EUR收益,这样就统一了比较基准。

比较之后发现,在多国的债券中Greek bond的收益最高,于是我们给所有的Portfolio都买了Greek bond,也就是给UK/US/EUR这三个Portfolio都买了Greek bond。


此时,对于UK/US的组合,他们的核算货币分别是GBP与USD,而Greek债券的收益为EUR,所以在投资期结束时,我们还要考虑把EUR收益换成GBP/USD;


但注意,题目说可以Hedge into any currencies,所以,我们可以把EUR换成其他任意货币,先用Forward赚取一个外汇收益。然后再用期末的预期即期汇率,将外汇再换成Portfolio base currency。这样做的目的就是用Forward与预期汇率之间的差异,赚取一个换汇差。


例如,使用Forward将EUR换成GBP的收益是:(0.50% –0.15%)/2 = 0.175%;

对于USD-Portfolio来讲,核算收益的货币是USD,我们先用Forward将EUR换成了GBP,获得额外收益+0.175%,但最终还需要将GBP换成本币USD,此时需要用预期的汇率来换,预期USD相对GBP贬值1%,所以将GBP换成USD能额外收到+1%的收益。

那这样的话,对于USD-Portfolio,我们先使用Forward将EUR hedge成GBP,收益增加+0.175%,再用预期即期汇率将GBP换成USD,收益增加+1%,一来一回,仅仅是换汇获得额外收益:

1%+0.175= 1.175%


对于GBP Portfolio来讲,将EUR用Forward hedge成GBP带来的收益是0.175%。


再考虑使用Forward将EUR换成MXN的收益是:(7.10%-0.15%)/2= 3.475%

对于USD-Portfolio来讲,核算收益的货币是USD,我们先用Forward将EUR换成了MXN,收益增加+3.475%,最终还需要将MXN换成本币USD,此时需要用预期的汇率来换,预期MXN相对USD贬值2%,所以将MXN换成USD会亏损2%。

对于USD-Portfolio,EUR收益先用Forward hedge成MXN,收益+3.475%,再用预期即期汇率换成USD,汇率损失-2%,一来一回仅仅是换汇获得的净收益是:

3.475%- 2% =1.475%


发现,用Forward hedge成MXN,再将MXN换成USD,给USD-Portfolio带来的净收益是:1.475%(3.475%-2%)

用Forward hedge成GBP,再将GBP换成USD,给USD-Portfolio带来的净收益是:1.175%


显然,给USD-Portfolio买入了Greek bond,我们应该Hedge成MXN。


同理,用以上的判断思路,我们可以确定对于UK-Portfolio,EUR-portfolio,都是买入Greek bond,然后将Greek bond的EUR收益先Hedge成MXN,再用期末对应的预期汇率换成本币,这样做的收益是最高的。

于是,这道题选A选项:给3个Portfolio都买入Greek bond,然后都Hedge成MXN。

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Meixf · 2021年10月22日

为什么MXN depreciate by 2% against EUR,US Dollar will depreciate by 1% against the Euro, 所以MXN depreciate against USD by 2%呢?不是1%吗

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