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Luhunlu · 2025年05月14日

和后面的知识点混淆了

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.

老师,这道题我有点跟后面的知识点混淆了,对于B我理解的角度是利率上升,价格下降,所以要降低duration,而payer fixed swap的duration是负的,我可能还是没有完全理解stable yield curve和dynamic yield curve

1 个答案

发亮_品职助教 · 2025年05月15日

老师,这道题我有点跟后面的知识点混淆了,对于B我理解的角度是利率上升,价格下降,所以要降低duration


B的理解不太对。利率上升是利率改变了,这属于dynamic yield curve,并不是这道题的stable yield curve。

B是dynamic yield curve下的策略,即,如果题目说,未来预测利率会下降,那我们可以使用B的策略,来故意降低组合的duration,避免过多的capital loss。

但这道题的stable yield curve,利率不会发生改变,所以不能从价格下降的角度思考。

注意,题目说的upward sloping yield curve,是说利率曲线向上倾斜,短期利率更低,长期利率更高,这是利率的形态,不是利率的改变。


这道题可以从多个角度解释为什么B不合适。下面先说一下stable yield curve和dynamic的大体概念:


stable yield curve,题目会说预测利率曲线remain stable, or unchanged。

dynamic yield curve,题目会说,预测利率上升or下降,预测利率发生非平行移动flattening or steepening,或者预测利率的波动加大volatility increase,这些都属于dynamic yield curve。

注意到,dynamic yield curve一定是会发生利率的动态改变。而stable yield curve一定是利率曲线在前后维持一致,并未发生改变。


在发生dynamic yield curve时,我们是会搭配着调整组合的duration or 组合的形态,目标就是在利率改变时可以盈利。

比如,题目说利率曲线上升,我们就应该降低组合的duration,防止组合duration过大会产生过大的capital loss

或者题目说利率曲线下降,应该增加duration,获得更多的capital gain。

或者题目说发生flattening,短期利率相对上升,长期利率相对下降,盈利的策略就是增加长期期限的duration,降低短期期限的duration

发生steepening,短期利率相对下降,长期利率相对上升,盈利的策略是增加短期期限的duration,降低长期期限的duration。

预测利率曲线波动加大,可以增加组合的convexity,等等。

以上策略的关键就是,先明确利率的改变方式,然后再专门针对这样的利率改变做策略,一般策略就是针对性调整duration or convexity。


在stable yield curve下,利率不会改变。意思我们投资的债券不需要考虑债券价格变动,我们投资债券的收益差不多就是债券的YTM。

所以这时候,我们可以买更长期的债券,因为期限越长,YTM更大,可以赚到更大的收益率。这是stable yield curve下的策略的一个核心理念:extend duraiton/maturity,即,增加组的债券期限maturity or duration来赚更到的债券收益率YTM。

这道题原本组合的duration=7.25,maturity=8.5,选项A是买入一个10年期零息债券,新增的债券期限更长,duration更大,可以获得更大的YTM收益。


stable yield curve下的策略第二个核心理念:using leverage,即,本身利率曲线stable,利率不波动,不存在利率不确定的风险。在没风险的情况下,现在为了增加收益,我们可以使用杠杆放大收益。

如选项C,是利用repo市场借入资金,买入了长期的20年期债券。

这个策略不但是买入了更长期债券(20年期),可以赚取更大的收益率,而且买债券的钱也是借的,带有杠杆,会进一步放大收益率。


选项B的pay 30-year fixed, receive floating swap,这是一个支付30-year固定利率,收到浮动利率的swap。这个swap可以看成是:short 30-year fixed rate bond + long floating-rate bond

这个组合有一个极大的负duration,在stable yield curve下赚不到钱,因为stable yield curve下要extend duration/maturity,要增加组合的duration和期限,而选项B的策略会降低duration。这不符合stable yield curve的策略核心理念。


需要注意的是,在stable yield curve下,extend duration/maturity,增加组合的duraiton/maturity,只是因为长期债券的duration/maturity更大,在stable yield curve下我们是买更长期债券赚更大的YTM。买入长期债券自然会增加组合的duration/maturity。所以才把这个理念叫做extend/increase maturity or duration

这里的increase/extend duration并不是说为了赚到价格上升的收益,因为利率stable,没有发生利率改变,这块没有价格上升的收益。


选项B是short 30-year fixed rate + long floating,支付30-year利率,收到浮动利率。

在upward-sloping下,长期利率更大,短期利率更小,而且预测利率曲线stable,即这个利率大小关系稳定,那意思是这个头寸一直要支付更大的利率,收到更小的利率,这个头寸会亏损。所以不合适。


第二个角度是,这个头寸是short 30年期债券,这会降低组合的maturity与duration,与stable yield curve的核心理念extend duration/maturity相反。所以这个策略不适用。

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