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fanfan · 2021年03月04日

计算MXN收益率

* 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.

请问MXN持有期收益率的计算coupon rate如何从题目找到? MXN债券的P0=100, 半年后的FV=100这两个条件如何通过题干找到?谢谢!
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发亮_品职助教 · 2021年03月05日

嗨,从没放弃的小努力你好:


请问MXN持有期收益率的计算coupon rate如何从题目找到? MXN债券的P0=100, 半年后的FV=100这两个条件如何通过题干找到?谢谢!


Coupon rate的信息由下句可得:

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)

注意,在上句中,他说表格里的Yield,也是Par sovereign bonds的收益率。Par bonds是债券价格等于面值的债券,而当债券的价格等于面值时,其Coupon rate就等于他的折现率Yield。所以,这个表格里的利率,即是债券的折现率,又是债券的Coupon rate。所以5年期MXN债券的Coupon rate就等于7.25%。由于表格里都是Par sovereign bonds,所以我们可知表里的债券期初价格都等于面值。


MXN债券的期初价格P0=100面值,这点也是由上句Par sovereign bonds告诉我们的。由于表格里面的利率都是Par yields,所以债券的价格在期初的时候都等于其面值Par=100


注意,从表格里面,我们发现,MXN债券的5年期Yield=7.25%,4年期的Yield也等于7.25%,我们很容易知道,在4~5年这段内,MXN的利率曲线是水平的,即,我们知道4.5年期的利率也是7.25%。既然7.25%是使得该支债券价格等于面值时的折现率,我们就知道,如果MXN的利率曲线没变时,这支5年期债券在持有半年之后、在4.5年的价格也应该是面值。


但是注意,本题题干告诉了我们,Winslow预期MXN的利率会在未来6个月后下降:

She expects Mexican yields to decline to 7.0% at all maturities.


那这样的话,在4.5年时,债券的折现率就不是7.25%了,应该用最新的折现率7.0%。用计算器算的话应该为:

I/Y = 7.00%/2;PMT = 7.25%/2;FV = 100,N=9;CPT → PV;用这样的方法可以算出来MXN的期末价格。


同理,在本题中,由于预期Greek的利率不会发生改变,Greek的利率在4~5年期是水平的,我们知道Greek 5-year债券在期初时的价格为Par=100,在4.5年时,折现率没变,折现率依然等于Coupon rate,所以其在期末4.5年的价格依然为Par=100。

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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……

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