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xujii · 2021年08月13日

到底hedge不hedge?

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).

本题是选出一个最高的retrun 本例下里面那问是也是选一个最高return 最后选的是买5年Greek。问:为什么本题不用hedge去比较retrun 而后面那个题需要先用hedge锁定再比较,都是比较retrun,什么时候要hedge去比?什么时候不hedge去比?

2 个答案

pzqa015 · 2021年09月01日

嗨,努力学习的PZer你好:


表中已知的利率是年化利率(比如USD 6M是1.4%,代表投资半年期美元资产的年化利率是1.4%,那么投资这半年实际收益是0.7%。),我们投资期是半年,所以只要hedge半年后的汇率就可以,所以IRP公式中的利率要用半年的投资收益。

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加油吧,让我们一起遇见更好的自己!

pzqa015 · 2021年08月14日

嗨,从没放弃的小努力你好:


同学你好。

本题也是要比较hedge return和unhedge return。

只不过本题的hedge return<unhedged return,所以答案没展示。具体求解见下图。


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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!

翁旸勤 · 2021年09月01日

为什么hedged的部分也要除以2呢? 不应该直接是 r_x - r_y 么?