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SUN · 2020年06月04日

问一道题:NO.PZ201902210100000104 第4小题 [ CFA III ]

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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.

C项最终的盈利不考虑美元的贬值吗?何老师的讲解没有提这一点,但是感觉在比较最终收益的时候,比如和B比较,这种贬值会影响最终的收益吧?

2 个答案
已采纳答案

发亮_品职助教 · 2020年06月04日

嗨,努力学习的PZer你好:


“C项最终的盈利不考虑美元的贬值吗?何老师的讲解没有提这一点,但是感觉在比较最终收益的时候,比如和B比较,这种贬值会影响最终的收益吧?”


不考虑。

在三个要求的Carry trade里(1、Duration-neutral;2、Currency-neutral;3、Most attractive)。

这种特殊的Carry trade,我们不需要考虑汇率的升贬值问题。

可以参考这道题目的答案,其实就非常严谨,在找最优的策略时,比较的只是Net carry,也就是只比较净息差的大小,没有考虑任何汇率问题。

这种题目不会要求计算题,但是在筛选哪个选项收益率更大时,可以按照答案的方法来。



A选项因为不符合Duration-neutral、Currency-neutral,所以直接排除。

B、C选项符合Duration-neutral、Currency-neutral,所以进入备选。

注意,这里面的Currency-neutral,是指赚取息差没有汇率风险,比如Carry trade的借贷都在UK市场上发生,赚息差的过程没有汇率风险。

但实际上B、C两个选项里,这种策略始终还是涉及到2个市场,最终核算最后收益时,还会涉及到汇率问题。好在我们原版书这里不要求计算最后收益,只要能筛选出最优的策略即可。

我们以B选项为例,Receive fixed/pay floating on a 3-year GBP,这就相当于在UK市场上:

借:6-month利率;投资3-year利率;所以赚取的是3年和6个月利率之间的息差。

息差收益是:(0.95% – 0.50%)/2

为了构建Duration-neutral,在German市场上,构建了receive floating/pay fixed on a 3-year EUR,这就相当于在EUR市场上:

借:3年期利率;投资6个月利率;产生的收益是:(0.15% – 0.40%)/2

注意,如果要核算策略的最终净收益的话,UK市场的息差收益和EUR市场的息差收益并不能直接相加,因为一个是GBP计价,一个是EUR计价,最终一定会涉及到一个汇率转换问题。

但是,我们这种题目只需要考虑到净息差收益(Net carry)即可,所以答案只计算了B选项的Net carry(只是息差收益,不考虑汇率):

B策略产生的Net carry是:+0.10% = [(0.95% – 0.50%) + (0.15% – 0.40%)]/2


同理,C选项的策略,也是Duration-neutral、Currency-neutral的策略,但因为他的Net carry低于B选项,所以排除。

Buy the T-note futures contract,相当于在美国市场上借6-month,Buy 5-year(因为Futures的标的物是5年期债券)

这样的话,美国市场上Carry trade赚取的收益是5年期利率与6个月利率的差异:

0.275% = (1.95% – 1.40%)/2

为了构建Duration-neutral,我们在德国市场上sell the German note futures,因为Futures的标的物是5年期债券,这就相当于做空5年期利率,做多6个月利率,所以德国市场的收益是:

 –0.225% = (0.15% – 0.60%)/2

但是注意,如果要算最终总收益的话US的收益和EUR的收益并不能直接相加,好在这种题目我们只要算到Net carry即可,那C选项产生的Net carry是:

[(1.95% – 1.40%) + (0.15% – 0.60%) ] / 2 = 0.05%

最终排除C选项。

发现,答案在计算策略收益大小时,是UK内部的息差,和EUR内部的息差直接相加,算的是Net carry收益,不考虑汇率变化。


所以,在碰到这种3个要求的Carry trade时,我们不考虑任何汇率问题,在比较哪个策略的收益最大时,只用考虑息差大小即可。


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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!


SUN · 2020年06月08日

其实还是没太理解。因为题目如果不提贬值,那就利率差肯定是没问题的。但是这道题明确说了美元贬值1%,客观存在如果不考虑肯定和实际收益比较有差异呀。 或者换句话问,就是只考虑利率差是因为出题人压根没考虑这一点,以后出题也不可能考虑这么复杂,所以不用考虑的角度,还是说实际计算确实不需要考虑汇率问题,感觉如果是后者,和实际情况不符合呀

发亮_品职助教 · 2020年06月08日

“其实还是没太理解。因为题目如果不提贬值,那就利率差肯定是没问题的。但是这道题明确说了美元贬值1%,客观存在如果不考虑肯定和实际收益比较有差异呀。 或者换句话问,就是只考虑利率差是因为出题人压根没考虑这一点,以后出题也不可能考虑这么复杂,所以不用考虑的角度,还是说实际计算确实不需要考虑汇率问题,感觉如果是后者,和实际情况不符合呀”


这道题的汇率变动实际上是针对这个Case其他题目的。

Duration-neutral/Currency-neutral/Most attractive Carry trade这种题目来看的话,不需要考虑汇率升贬值的问题。直接考虑利率差,算到Net carry比较即可。

针对这类三个要求的Carry trade题目,原版书以及题目也只考虑到了息差,不考虑汇率。但是如果考虑实际情况的话,因为涉及两个市场,的确需要考虑汇率。我们原版书没有进一步展开讲解,就以这道题的计算方法为准即可。

SUN · 2020年06月08日

谢谢