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皓月 · 2024年11月04日

这题解析没懂

  1. CFA III
  2. Fixed Income

NO.PZ2021120102000002

问题如下：

An analyst manages an active fixed-income fund that is benchmarked to the Bloomberg Barclays US Treasury Index.

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

选项：

A.

Purchasing a 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 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.

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 zero equals its maturity, and ModDur = MacDur/(1+r) versus 7.25 for the index.

Under c.), the manager introduces leverage by purchasing a long-term bond and financing it at a lower short-term repo rate.

我蒙对的，但是没看懂为什么选择这个

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1 个答案

发亮_品职助教 · 2024年11月05日

这道题考的是stable yield curve下的策略。

已知是stable yield curve，benchmark投资的债券是8.5 years，其duration是7.25

现在问，对于组合而言，哪个策略是least attractive的一项。

在stable yield curve下，组合可以增强收益的策略有：

  • buy-and-hold（extend duration增加组合duration/Maturity）
  • roll down the yield curve
  • leverage

buy-and-hold时，买入期限比benchmark更长的债券，因为是Upward sloping的yield curve，长期债券的收益率更高，这可以获得比Benchmark更高的收益。债券的期限更长其实就是duration更大，所以这个增强收益的策略也叫extend duration。

选项A说买入期限为10年期的零息债券。

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

该债券的期限是10年，大于benchmark的8.5年，且因为是零息债券，所以其Macaulay duration=maturity=10年。其Modified duration=10/(1+2%) = 9.80，这个duration和maturity确实比benchmark要大，所以选项A可以增强收益，是extend duration。

 

选项B是进入一个30年期的Pay fixed receive floating swap：

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

30年期Pay-fixed swap，要支付30年的fixed coupon，这相当于就是发行了一个30年期的固定利率债券。发行债券是short duration，所以获得short 30-year债券duration头寸

在swap里面的receive floating，是收到浮动利率cash flow，相当于是买入了浮动利率债券，这获得浮动利率债券的正duration。

于是该swap的duration是：

short 30-year债券的duration + 获得浮动利率债券的正duration

由于浮动利率债券的duration极小，所以这个swap是会获得negative duration。这会降低组合的duration。不符合在stable yield curve时，extend duration的策略。

且，本题是upward sloping yield curve，长期利率更大，30年期利率要远远大于floating rate，所以Pay 30-year fixed，receive floating，支付30year利率，收到短期浮动利率，我们会有negative cash flow。这也不是一个最佳的策略。所以本题B不是stable yield curve下的最佳策略。

 

选项C：

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

买入一个20年期的债券，这个债券的期限明显大于benchmark的8.5 years，是extend duration，且选项C还额外用repo策略融资了。所以选项C是一个加杠杆的策略。在stable yield curve下这会进一步加大收益。所以本题C也是一个最佳的策略。

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