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fresh · 2023年10月27日

 30-year pay- fixed swap 为啥是negative carry  

NO.PZ2021120102000002

问题如下:

An analyst manages an activefixed-income fund that is benchmarked to the Bloomberg Barclays US TreasuryIndex.

This index of US government bonds currently has a modifiedportfolio duration of 7.25 and an average maturity of 8.5 years. The yieldcurve is upward-sloping and expected to remain unchanged. Which of thefollowing is the least attractive portfolio positioning strategy in astatic curve environment?

选项:

A.

Purchasinga 10-year zero-coupon bond with a yield of 2% and a price of 82.035

B.

Entering a pay-fixed, 30-year USD interest rate swap

C.

Purchasing a 20-year Treasury and financing it in the repo market

解释:

B is correct.

The 30-year pay-fixed swap is a “short”duration position and also results innegative carry (that is, the fixed rate paid would exceed MRR received) in anupward-sloping yield curve environment; therefore, it is the leastattractive static curvestrategy.

In the case of a.), the manager enters a “buy-and-hold”strategy by purchasing the 10-year zero-coupon bond and extends duration,which is equal to 9.80 = 10/1.02 since the Macaulay duration of a zeroequals its maturity,and ModDur = MacDur/(1+r) versus 7.25 for the index.

Under c.), the manager introduces leverage bypurchasing a long-term bond and financing it at a lowershort-term repo rate.

The 30-year pay-fixed swap is a “short” duration position and also results in negative carry (that is, the fixed rate paid would exceed MRR received) in an upward-sloping yield curve environment; therefore, it is the least attractive static curve strategy. 不理解为啥the fixed rate paid would exceed MRR received?谢谢老师

2 个答案
已采纳答案

pzqa31 · 2023年11月07日

嗨,从没放弃的小努力你好:


30-year swap的fixed-rate是30年期的长期利率,floating rate是短期利率。


这是swap的特点决定的,就是swap里面,Fixed rate是相对的长期利率,Floating rate会根据市场调整,所以是相对短期的利率。比如,5年期的swap,半年交换一次利息现金流,里面的fixed rate就是5年期的利率(swap rate),floating rate就是半年浮动一次的短期利率。


分析Swap时,floating rate就当成短期利率,fixed rate就当成相对长期利率。


pay 30-year fixed, receive floating,就是支付长期30-year利率(fixed),收到短期利率(floating),在upward sloping的曲线下,这是一个负的收益,所以是negative carry。通常讨论carry的话,可以从利息角度来分析。

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努力的时光都是限量版,加油!

pzqa31 · 2023年10月27日

嗨,从没放弃的小努力你好:


这道题考察的是static yield curve下的策略

我们应该增加duration

pay fixed swap是降低duration,所以不正确

第一项与第三项,都会增加duration,所以attractive。


这句话其实就是想说payer-fixed swap会降低久期,在这种收益率曲线形状的预期下,整体是会赔钱的,因为是付固定收浮动,所以这里又说了一下支出会大于收入,得到negative carry,同学理解这个意思就行,咱们还是从久期的角度理解更好,不用太纠结这个解释。

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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!

fresh · 2023年10月27日

久期理解容易,但这个利率上升情况下,fixed rate 超过MMR negative carry 结论是怎么来的?

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