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little_back · 2021年03月28日

请问A为什么正确?

NO.PZ2019103001000054

问题如下:

Abram and Edgarton recently attended an investment committee meeting where interest rate expectations for the next 12 months were discussed. The Fund’s mandate allows its duration to fluctuate ±0.30 per year from the benchmark duration. The Fund’s duration is currently equal to its benchmark. Although the Fund is presently invested entirely in annual coupon
sovereign bonds, its investment policy also allows investments in mortgage-backed securities (MBS) and call options on government bond futures. The Fund’s current holdings of on-the-run bonds are presented in Exhibit 1

Abram’s supervisor disagrees with Abram’s yield curve outlook. The supervisor develops two alternative portfolio scenarios based on her own yield curve outlook:

Scenario 1:Sell all bonds in the Fund except the 2-year and 30-year bonds, and increase positions in these two bonds while keeping duration neutral to the benchmark.

Scenario 2:Construct a condor to benefit from less curvature in the 5-year to 10-year area of the yield curve. The condor will utilize the same 1-year, 5-year, 10-year, and 30-year bonds held in the Fund. The maximum allowable position in the 30-year bond in the condor is $17 million, and the bonds must have equal (absolute value) money duration.

The yield curve expectation that Abram’s supervisor targets with Scenario 1 is most likely a:

选项:

A.

flattening yield curve

B.

reduction in yield curve curvature.

C.

100 bps parallel shift downward of the yield curve

解释:

A is correct.

Scenario 1 is an extreme barbell and is typically used when the yield curve flattens. In this case, the 30-year bond has larger price gains because of its longer duration and higher convexity relative to other maturities. If the yield curve flattens through rising short-term interest rates, portfolio losses are limited by the lower price sensitivity to the change in yields at the short end of the curve while the benchmark’s middle securities will perform poorly.

请问老师:买2年期和30年期的债券,应该是2年期YTM和30年期YTM均下降比5、10年更多的时候采用的策略,也即在more curvature的时候采用的策略。当more curvature的时候,怎么会是flatten呢?



1 个答案
已采纳答案

发亮_品职助教 · 2021年03月29日

嗨,爱思考的PZer你好:


请问老师:买2年期和30年期的债券,应该是2年期YTM和30年期YTM均下降比5、10年更多的时候采用的策略,也即在more curvature的时候采用的策略。当more curvature的时候,怎么会是flatten呢?


这道题Scenario 1的策略其实也适用于More curvature。只不过选项里面没有这个选择。

当然,Scenario 1的策略也适用于A选项的Flattening yield curve。


所有的策略都是为了实现更多收益率的,所以,我们在判断题目为啥采用这个策略时,其实是判断在哪样的利率预期下,题目的新策略会有更高的收益。


Scenario 1的新策略是:卖出组合的所有期限,只买入2-year与30-year,并且保持了策略前后组合的Duration没变(keeping duration neutral to the benchmark)


既然没有改变组合的Duration,那直接排除C选项,因为如果是利率下降的预期,我们应该增加组合的Duration才对,不应该是题干里的Keeping duration neutral。


由于只保留了2-year与30-year,那显然是保留2-year、30-year的债券有好处。由于2-year的Duration太小了,利率变动对他的价格影响相对更小,因此这里我们就只讨论30-year即可。


哪种情况的利率变动,对30-year的头寸有好处呢?

其实就是30-year的利率下降,那我们30-year的债券头寸会产生很大的Capital gain,执行Scenario 1的策略会有更高的收益。


那什么样的收益率曲线变动,会使得30-year的利率相对下降呢?其实有2种情形:


(1)如果是收益率曲线斜率改变的话,也就是收益率曲线只分成了短期和长期利率,30-year的利率相对下降,就体现出收益率曲线变得更加平缓了,即长期利率相对下降(30s相对下降),短期利率相对上升,这就是收益率曲线的Flattening,;选项A符合要求。


(2)如果是收益率曲线弯曲度改变的话,也就是收益率曲线分成了短期、中期、长期;30-year的利率相对下降(长期利率相对下降),剩下的就是中期利率相对上升,短期利率相对下降,即收益率需求变得More curvature;


所以,以上2个情景,都能实现30s的利率相对下降,本题的策略在Flattening or more curvature的2个情境下,均能收益。但选项只有Flattening,因此直接选A。


反过我们也可以验证一下,Flattening时,卖出所有期限的债券,只保留短期2s与长期30s能否有盈利。显然是一定能盈利的,因为Flattening,长期利率相对下降,30s有巨大的Capital gain。


More curvature时,卖出其他所有期限的债券,只保留短期2s与长期30s能否有盈利。显然也是一定有盈利的,因为已经卖出了中期债券,避免了中期利率相对上升时产生的Capital loss;同时,买入了短期、长期债券,可以享受短期、长期利率相对下降带来的Capital gain。

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