开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

孙际尧 · 2021年04月14日

hedge

* 问题详情,请 查看题干

NO.PZ201902210100000105

问题如下:

If Winslow is limited to unhedged positions or hedging into each portfolio’s base currency, she can obtain the highest expected returns by

选项:

A.

buying the Mexican 5-year in each of the portfolios and hedging it into the base currency of the portfolio.

B.

buying the Greek 5-year in each of the portfolios, hedging the currency in the GBP-based portfolio, and leaving the currency unhedged in the dollar-based portfolio.

C.

buying the Greek 5-year in the Euro-denominated portfolio, buying the Mexican 5-year in the GBP and USD-denominated portfolios, and leaving the currency unhedged in each case.

解释:

B is correct.

Winston should buy the Greek 5-year bond for each portfolio. In the US dollar portfolio, she should leave the currency unhedged, accepting the exposure to the Euro, which is projected to appreciate by 1% against the USD. In the UK portfolio, she should hedge the bond’s EUR exposure into GBP. In the Euro-based portfolio there is no hedging decision to be made because the Greek bond is denominated in EUR.

Because yields are projected to remain unchanged in the US, UK, Euro, and Greek markets, the 5-year Greek bonds will still be priced at par in six months and the US, UK, and Euro bonds will realize a negligible price appreciation when they have 4.5 years to maturity.

Hence, the local market return for each of these bonds will equal half of the coupon: 0.975%, 0.55%, 0.30%, and 2.85%, respectively. The Mexican 5-year will be priced to yield 7.0% at the end of the period. Its price will be

t=1 9 7.25 2 (1+ 0.07 2 ) t + 100 (1+ 0.07 2 ) 9 =100.9501

Its local market return is therefore 4.576% = (100.9501 + 7.25/2)/100. By covered interest parity, the cost of hedging a bond into a particular currency is the short-term (six months here) rate for the currency into which the bond is hedged minus the short-term rate for the currency in which the bond is denominated. For hedging US, UK, and Mexican bonds into Euros for six months the calculation is: USD into EUR: (0.15% – 1.40%)/2 = –0.625% GBP into EUR: (0.15% –0.50%)/2 = –0.175% MXN into EUR: (0.15% – 7.10%)/2 = –3.475%

(Note that a negative number is a cost while a positive number would be a benefit.)

Combining these hedging costs with each bond’s local market return, the returns hedged into EUR, which can now be validly compared, are: US: 0.975% + (–0.625%) = 0.350% UK: 0.550% + (–0.175%) = 0.375% MX: 4.576% + (–3.475%) = 1.101% GR: 2.850% + 0 = 2.850% EU: 0.300% + 0 = 0.300%

The Greek bond is by far the most attractive investment. This would still be true if returns were hedged into USD or GBP. So, the Greek 5-year should be purchased for each portfolio. Whether or not to actually hedge the currency exposure depends on if the cost/benefit of hedging is greater than the projected change in the spot exchange rate. For the dollar-denominated portfolio, hedging the Greek bond into USD would "pick up" 0.625% (the opposite of hedging USD into EUR). But EUR is expected to appreciate by 1.0% against the dollar, so it is better to leave the bond unhedged in the USD-denominated portfolio. Hedging EUR into GBP picks up 0.175% of return. Since EUR is projected to remain unchanged against GBP, it is better (from an expected return perspective) to hedge the Greek bond into GBP.

A is incorrect because it can be seen from the explanation for B above that the Greek 5-year bond is by far the most attractive investment, returning 2.85% compared to the Mexican 5-year bond’s return of 1.101%. If the returns for these bonds were hedged into USD or GBP (instead of EUR), in each case the return on the Mexican 5-year bond would still be inferior to that of the Greek 5-year bond.

C is incorrect because it can be seen from the explanation for B above that the Greek 5-year bond is by far the most attractive investment, returning 2.85% compared to the Mexican 5-year bond’s return of 1.101%. If the returns for these bonds were hedged into USD or GBP (instead of EUR), in each case the return on the Mexican 5-year bond would still be inferior to that of the Greek 5-year bond. Moreover, over the 6-month investment horizon the Mexican Peso is expected to depreciate against both the GBP and USD, further impairing the unhedged returns on the Mexican 5-year bond in GBP and USD terms.

base currency 和denominated currency的意思是base currency是基础货币,denominated currency是所买的外国债券吗

怎么讲denominated currency hedge成可比较的,这道题完全不明白

1 个答案

发亮_品职助教 · 2021年04月15日

嗨,爱思考的PZer你好:


base currency 和denominated currency的意思是base currency是基础货币,denominated currency是所买的外国债券吗


Base currency是指Portfolio base currency;组合的核算货币。


例如,我们现在是USD portfolio,那意思我们这个投资组合,他的本币就是美元;


当然,我们这个组合可以投资美元债券,也可以投资欧元债券,也可以投资英镑债券。但因为Portfolio的本币是USD,所以在投资这些所有海外债券时,期末核算收益要把欧元债、英镑债的收益换回美元。


这就是把投资收益换回Portfolio base currency


Denonimated currency就是指这个债券的计价货币。例如,GBP债券的计价货币就是GBP;人民币债券的计价货币就是人民币。


所以,我们碰到的题目就会有这种情形:


我们是一个USD-Portfolio,于是Portfolio的Base currency是USD,但我们投资了EUR债券;所以对于这个USD Portfolio来说,最终在核算收益时,需要将EUR债券收益换回USD,这就是把EUR Denominated Bond的收益换成Portfolio base currency USD的收益。


怎么讲denominated currency hedge成可比较的,这道题完全不明白


比如,我们现在是一个USD base portfolio,Portfolio的计价货币是USD(Base currency = usd );


现在我们去国际市场投资,备选的标的有USD-denominated bond收益率5%、GBP-Denominated bond收益率3%、EUR-denominated bond收益率6%;

因为这些债券的计价货币不同,这几个收益其实没有可比性


为了让这些债券实现可比,我们首先要做到的就是将所有的债券收益换成一个Common currency,这一步的目的是统一标准,方便比较。


怎么统一标准呢,就是将这些债券的收益都用Forward hedge成一个Common currency,例如,都Hedge成USD。


所以,我们使用Forward,将GBP 5%的收益,换成了USD收益;将EUR 6%的收益,通过Forward换成了USD收益。


现在这3个债券都以统一的货币计价了,在同一个比较标准上了,所以他们的收益可比,因此,我们可以选出一个收益最高的债券进行投资。


注意,这是投资海外债券这种题型中,第一步必须要做的。就是将所有的收益都Hedge成一个Common currency。


那为什么要使用Forward进行Hedge成Common currency进行比较,而不使用市场上的即期汇率换成Common currency呢?


这是因为,Forward里面的汇率是一个确定的数,不存在变数,用它将所有的外币收益换成Common currency非常的公平,不具有变数。


总结一下:

(1)所有的海外债券,都先需要Hedge成Common currency,然后再比较收益。本题就是将所有的债券收益都Hedge成了EUR进行比较,发现Greek bond是最优债券。

(2)债券的本币收益,加上Forward Hedge收益,就是Hedge成Common currency之后的收益。例如,MXN以本币计价的收益是4.576%,利用Forward将MXN换成EUR,这个Forward带来的收益是,–3.475%,所以,MXN债券以EUR货币计价的收益是:4.576% - 3.475%,其他债券收益同理,Hedge成Common currency之后,我们可以选出来收益最高的一个债券。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

玛卡巴卡 · 2021年09月15日

请问下:(1)这道理哪里有提到“将所有的债券收益都Hedge成了EUR进行比较”,是exhibit1里的数本身就已经是hedge成EUR之后的数了么? (2)题目里好像没有说greek相比其他币种的Rfx收益

  • 1

    回答
  • 2

    关注
  • 641

    浏览
相关问题

NO.PZ201902210100000105 老师,为什么计算半年的收益率?

2021-11-10 12:32 1 · 回答

NO.PZ201902210100000105 就这道题我反反复复听了何老师讲的和有问必答您的,但是有两个问题一直没搞明白 1.希腊债券半年的收益率直接用5.7%除以2,背后的逻辑是因为收益率曲线stable还是因为这些债券都是平价发行?有这个困惑是因为看书后的答案和您的都了半天coupon和4年跟5年之间收益率差别不大的问题。 2.为什么希腊债券半年的收益率可以直接用5.7%除以2,而墨西哥债券半年的收益率不能用改变后的7%直接除以2来计算。何老师视频里面也只是说了一句因为墨西哥债券收益率改变了,所以就要算现金流倒推收益率,也没说明白背后的具体逻辑是什么?

2021-10-01 13:34 2 · 回答

buying the Greek 5-yein eaof the portfolios, heing the currenin the GBP-baseportfolio, anleaving the currenunheein the llar-baseportfolio. buying the Greek 5-yein the Euro-nominateportfolio, buying the Mexic5-yein the GanUSnominateportfolios, anleaving the currenunheein eacase. B is correct. Winston shoulbuy the Greek 5-yebonfor eaportfolio. In the US llportfolio, she shoulleave the currenunhee accepting the exposure to the Euro, whiis projecteto appreciate 1% against the US In the UK portfolio, she shoulhee the bons EUR exposure into GBP. In the Euro-baseportfolio there is no heing cision to ma because the Greek bonis nominatein EUR. Because yiel are projecteto remain unchangein the US, UK, Euro, anGreek markets, the 5-yeGreek bon will still pricepin six months anthe US, UK, anEuro bon will realize a negligible priappreciation when they have 4.5 years to maturity. Hence, the locmarket return for eaof these bon will equhalf of the coupon: 0.975%, 0.55%, 0.30%, an2.85%, respectively. The Mexic5-yewill priceto yiel7.0% the enof the perio Its priwill ∑ t=1 9 7.25 2 (1+ 0.07 2 ) t + 100 (1+ 0.07 2 ) 9 =100.9501 Its locmarket return is therefore 4.576% = (100.9501 + 7.25/2)/100. covereinterest parity, the cost of heing a boninto a particulcurrenis the short-term (six months here) rate for the curreninto whithe bonis heeminus the short-term rate for the currenin whithe bonis nominate For heing US, UK, anMexicbon into Euros for six months the calculation is: USinto EUR: (0.15% – 1.40%)/2 = –0.625% Ginto EUR: (0.15% –0.50%)/2 = –0.175% MXN into EUR: (0.15% – 7.10%)/2 = –3.475% (Note tha negative number is a cost while a positive number woula benefit.) Combining these heing costs with eabons locmarket return, the returns heeinto EUR, whicnow valiy compare are: US: 0.975% + (–0.625%) = 0.350% UK: 0.550% + (–0.175%) = 0.375% MX: 4.576% + (–3.475%) = 1.101% GR: 2.850% + 0 = 2.850% EU: 0.300% + 0 = 0.300% The Greek bonis fthe most attractive investment. This woulstill true if returns were heeinto USor GBP. So, the Greek 5-yeshoulpurchasefor eaportfolio. Whether or not to actually hee the currenexposure pen on if the cost/benefit of heing is greater ththe projectechange in the spot exchange rate. For the llar-nominateportfolio, heing the Greek boninto USwoul\"piup\" 0.625% (the opposite of heing USinto EUR). But EUR is expecteto appreciate 1.0% against the llar, so it is better to leave the bonunheein the USnominateportfolio. Heing EUR into Gpicks up 0.175% of return. SinEUR is projecteto remain unchangeagainst GBP, it is better (from expectereturn perspective) to hee the Greek boninto GBP. A is incorrebecause it cseen from the explanation for B above ththe Greek 5-yebonis fthe most attractive investment, returning 2.85% compareto the Mexic5-yebons return of 1.101%. If the returns for these bon were heeinto USor G(insteof EUR), in eacase the return on the Mexic5-yebonwoulstill inferior to thof the Greek 5-yebon C is incorrebecause it cseen from the explanation for B above ththe Greek 5-yebonis fthe most attractive investment, returning 2.85% compareto the Mexic5-yebons return of 1.101%. If the returns for these bon were heeinto USor G(insteof EUR), in eacase the return on the Mexic5-yebonwoulstill inferior to thof the Greek 5-yebon Moreover, over the 6-month investment horizon the MexicPeso is expecteto preciate against both the GanUS further impairing the unheereturns on the Mexic5-yebonin GanUSterms. 请问Limiteto unhee or hegng into是什么意思……

2021-05-12 21:05 1 · 回答

NO.PZ201902210100000105 这题Mexic5-yeprice怎么算出的100.9501?? 我算的是30.9988 + 73.373, 哪里错了?

2021-04-24 18:55 2 · 回答