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Lulu1214 · 2021年01月12日

问一道题: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.

这个题看到老师的回答“同时买入2-year bond的原因是,我们买入了30年期债券,会大幅增加组合的Duration数据,这时候买入一部分2-year的债券,来降低整个Portfolio的Duration。”可是其他期限的债券是卖出啊,这样不就降低duration了吗?为什么买入2yr的可以降低Duration?只要是买入不都是增加了duration,卖出才降低duration不是吗?

1 个答案

发亮_品职助教 · 2021年01月12日

嗨,爱思考的PZer你好:


这里是这样,他把Portfolio里面所有期限的债券都卖掉了,然后去买了2年期、30年期债券。


我们可以分步来看:

他把Portfolio里面所有期限的债券都卖掉了,然后,先全部买了30年期债券。这样会使得组合的Duration大幅上升。

由于最初Portfolio的Duration是7.43,30年期债券的Duration要大很多,这么操作之后显然会大幅增加组合的Duration。那可知现在的Portfolio duration是19.69。

这显然与题目的要求:策略前后keeping duration neutral to the benchmarkPortfolio不符(策略前后保证组合的Duration和Benchmark一致,即Portfolio Duration没有发生改变)。

为了把现在组合19.69的Duration再降低到7.43,我们就需要卖出一部分30年期债券,同时买入一部分Duration比7.43小的债券,显然买2年期债券可以实现这个目标。

组合的Duration是2年期、30年期债券Duration的加权平均,因为2年期债券的Duration很小,加权平均之后组合的Duration可以从19.69降低到7.43。

如果组合全部是30年期债券,Duration是19.69;

如果加入一些2年期债券,30年期债券与2年期债券经过加权平均之后,可以让组合的Duration等于7.43。

这就是买入2年期债券的目的,是用来拉低平均数的,让组合的Duration平均数从19.69降低到7.43.


“只要是买入不都是增加了duration,卖出才降低duration不是吗?”


如果是买卖单支债券的,确实是这样。

如果是Bond Portfolio的话,不一定。

因为Bond portfolio的Duration是组合内所有债券Duration的加权平均。

我们如果买入的债券,他的Duration比组合平均Duration要小的话,买入这支债券,实际上是会拉低组合的加权平均Duration;因为我们给组合内加入了一个Duration比平均数还小的债券,这会进一步降低组合Duration这个平均数。

如果卖出的债券,他的Duration小于组合平均Duration的话,卖出之后,组合的Duration反而会上升。

只有买入Duration比组合Duration大的债券,才会提升组合的Duration数据,因为组合的Duration数据是所有债券Duration的平均数。

所以,在组合Duration分析时,需要看个体债券与组合Duration的大小关系,进而再判断买卖债券对组合Duration的影响。


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