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让我爱你 · 2021年02月24日

题干中描述的第一个目标,不理解 in no more than one market 的意思

* 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.

“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. ”


其中 in no more than one market是什么意思,是不是写错了?题目中实际做的策略都是在两个市场中操作的,不满足这个in no more than one market的要求啊?

1 个答案

发亮_品职助教 · 2021年02月25日

嗨,爱思考的PZer你好:


这个In no more than one market是限制Carry trade那道小题的。对应的这道题题干为:

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......


他这里是这样,这道题让我们找到对于USD-Denominated portfolio来说,收益最高的一组Carry trade。可选的利率市场为UK、EUR、US利率市场。如果不对市场加以限制的话,那其实Carry trade的可能性非常多。例如,我们可以在EUR市场上借0.5年期,在UK市场上投资5年期,这样赚取Carry trade收益,然后再换回USD;这样做也是可以做到更优的Carry trade收益的。3个市场的利率可以任意两两组合,可能性会很多。


不加以限制,就会出现很多的Carry trade的可能,于是他说了:Each such trade will involve extending duration (e.g., lend long/borrow short) in no more than one market/

这种Carry trade,最多只能在一个市场上引入Duration头寸(extending duration in no more than one market)。

那Carry trade必须要有2个利率头寸,他说只能再额外引入1个利率头寸,那言下之意就是这个Carry trade里,必须有一个头寸是USD利率头寸。因为对于USD的Portfolio来说,他本身就已经有USD Duration了,所以Carry trade里用USD头寸不算是额外引入Duration。

那另外一个利率头寸就可以是USD利率,可以是UK/EUR的利率。

观察这道题的答案我们也发现,他的几个Carry trade,都是有一个USD的利率头寸,所以也刚好符合本题的这个要求。


但其实这道题还是有一点Bug的,有一个Carry trade他的收益比答案的3种都高,也符合In no more than one market的要求。我们可以在UK市场上借0.5年、投5年,这对于USD-portfolio里面也是只引入了一个市场的Duration,最终再换成USD,那对USD-Portfolio来说,这个Carry trade的收益比3个选项里的收益都更高。


所以本题的In no more than one market,在出题的角度看实际上是用来限制在Carry trade里面有一个是USD头寸,从答案的3个选项看,也是这个意思。但他忽略了上面我们说的UK那种情况。所以这道题有点小Bug。不过先以答案的思路做即可,后期看协会是否有勘误。

这个In no more than one market只对这道USD-portfolio的Carry trade有用,对其他题属于无用信息。

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