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jianghaiyang · 2020年02月24日

问一道题:NO.PZ201902210100000104

* 问题详情,请 查看题干

问题如下:

Considering only the US, UK, and Euro markets, the most attractive duration-neutral, currency-neutral carry trade could be implemented as:

选项:

A.

Buy 3-year UK Gilts, Sell 3-year German notes, and enter a 6-month FX forward contract to pay EUR/receive GBP.

B.

Receive fixed/pay floating on a 3-year GBP interest rate swap and receive floating/pay fixed on a 3-year EUR interest rate swap.

C.

Buy the T-note futures contract and sell the German note futures contract for delivery in six months.

解释:

B is correct.

In order to be duration-neutral and currency-neutral, the trade must lend long/borrow short in one market and do the opposite (lend short/borrow long), with the same maturities, in another market. The best carry is obtained by lending long/borrowing short on the steepest curve and lending short/borrowing long on the flattest curve. The GBP curve is the steepest and the EUR curve is the flattest. The largest yield spread between these markets is 0.55% at the 3-year maturity, and the narrowest spread is 0.35% at the 6-month maturity. Hence, the best trade is to go long the GBP 3-year/short the EUR 3-year and long the EUR 6-month/short the GBP 6-month. This can be implemented in the swaps market by receiving 3-year fixed/paying 6-month floating in GBP and doing the opposite in EUR (receiving 6-month floating/paying 3-year fixed). The net carry is +0.10% = [(0.95% – 0.50%) + (0.15% – 0.40%)]/2 for six months.

A is incorrect. The FX forward position as stated (pay EUR/receive GBP) corresponds to implicitly borrowing EUR for six months and lending GBP for six months. Correct execution of the trade would require the opposite, receiving EUR and delivering GBP 6 months forward.

C is incorrect. This combination of futures positions does create a duration-neutral, currency neutral carry trade, but it is not the highest available carry. Since the T-note futures price reflects the pricing of the 5-year note as cheapest to deliver, the long position in this contract is equivalent to buying the 5-year Treasury and financing it for 6 months. This generates net carry of 0.275% = (1.95% – 1.40%)/2. Similarly, the short position in the German note futures is equivalent to being short the 5-year German note and lending the proceeds for 6 months, generating net carry of –0.225% = (0.15% – 0.60%)/2. The combined carry is 0.05%, half of what is available on the position in B.

您好,能解释一下选项C吗?为啥用5年期利率与6个月利率?

1 个答案

发亮_品职助教 · 2020年02月25日

嗨,爱思考的PZer你好:


"能解释一下选项C吗?为啥用5年期利率与6个月利率?"


C选项就是用Futures来构建duration-neutral, currency-neutral的Carry trade的策略。

因为Bond futures自带两个利率头寸,一个利率头寸是标的物债券对应的利率,一般Bond futures的标的物为长期债券,所以对应的利率为长期利率;

第二个利率头寸是Futures合约定价的利率,Futures合约是短期合约,所以为Futures定价的利率为短期利率;

这样的话,只要进入一个Futures,就能获得2个利率Exposure。

对于Long bond futures,我们获得标的物债券对应的利率头寸,如标的物债券是5年期债券,那获得的就是5年期利率;

同时,Long bond futures约定在期末支付一个价格,这个期末支付的价格是以短期利率定价的,所以支付的价格是短期利率,即:借短期;

于是,Long bond futures天然就是:借短期、投长期的Carry trade;

同理,Short bond futures天然就是:借长期、投短期的Carry trade。

Futures能天然获得Carry trade,就是因为Futures定价的利率与标的物债券的利率期限不一致导致的。

关于为啥Bond futures可以看成是Carry trade,可以参考前面的回复,有疑问的话继续追问:

http://class.pzacademy.com/qa/questions/49965



“为啥用5年期利率与6个月利率?”


前面提到过,Bond futures自带两个利率,一个是标的物债券的利率,第二个利率是与Future期限对应的短期利率;

这道题的题干信息中提到过Futures的标的物是5年期债券,且Futues的期限是6个月:

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

CTD标的物为:five-year Treasury-note、German government note;期货合约的期限为:contracts expiring in six months

所以,我们可以确定这道题的Bond Futures,对应的两个利率是5年期利率、与6个月利率。

于是这道题通过Futures获得的头寸为:

Long T-note futures,就相当于:借6-month US、投5-year US;

Short German futures,就相当于:借5-year EUR、投6-month EUR.

两个Futures对应的Duration一致,Long/Short实现Duration-neutral;通过Futures,实现了一国内部的借低利率、投高利率,所以实现了Currency-neutral;

第三点就是判断一下是否是Most attractive,即和B选项比一下净息差收益;所以第三点就算一个净息差(Net carry)是否是最大,C选项的净息差为:

(1.95% - 1.40%)/ 2    +  (0.15% - 0.60%)/2 = 0.05%

 


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