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Betty · 2024年07月19日

想确认思路

NO.PZ2023032703000021

问题如下:

Beatriz Maestre is a fixed-income consultant who has been retained by Filipe Ruelas, the CFO of Cávado Produtos Agricolas, SA (Cávado). Cávado is a manufacturer of prepared foods headquartered in Braga, Portugal.

Maestre discusses an example of a single liability owed by Cávado, a EUR 2.3 million balloon payment due to the former CEO of the company in approximately six and a half years as a part of her deferred compensation package.

Maestre tells the group, “Suppose you wanted to immunize this liability. One way to do so would be to purchase zero-coupon bonds with essentially zero credit risk that mature in six-and-a-half years and have a face value of EUR 2.3 million. Unfortunately, no zero-coupon bonds are available with this maturity. Therefore, a portfolio of high-quality government bonds with a duration of approximately six-and-a-half years could be used, although this portfolio might have to be adjusted over time to maintain a matched duration with the liability.” She proposes to select one of the three portfolios shown in Exhibit 2.


Which of the portfolios described in Exhibit 2 would most likely be recommended by Maestre?

选项:

A.

Portfolio A

B.

Portfolio B

C.

Portfolio C

解释:

B is correct. The three portfolios have essentially the same cash flow yield. They also have Macaulay durations very close to the horizon for the liability (i.e., 6.5 years). Therefore, the question is one of convexity, and the differences in convexity are meaningful. Although more (positive) convexity is generally desired by fixed-income investors, the goal of ALM is to minimize the dispersion of cash flows around the Macaulay duration and make the portfolio more like the zero-coupon liability it is attempting to immunize. Therefore, Portfolio B should be recommended because it has the lowest convexity. Minimizing the portfolio convexity (i.e., the dispersion of cash flows around the Macaulay duration) makes the portfolio closer to the zero-coupon bond that would provide perfect immunization.

这道题之前做对了,但是这次错了,想问的就是,这道题是因为虽然没有提到liability convexity的数值,但是因为需要minimize convexity, 所以在macaulay duration差不多的情况下,就选minimum convexity的portfolio。思路是这样的吗?

另外,想问一下是不是没有任何情况会通过cash flow yield判断?如果有,会是什么样的问题&设定?

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已采纳答案

发亮_品职助教 · 2024年07月21日

这道题是因为虽然没有提到liability convexity的数值,但是因为需要minimize convexity, 所以在macaulay duration差不多的情况下,就选minimum convexity的portfolio。思路是这样的吗?


是的,做Duration-matching,第一筛选条件是Macaulay duration/BPV以及PV。

先找duration-matching相等的or差不多相等的,如果差不多相等,就进入第2轮convexity的筛选,如果不满足条件,就直接排除。


像这道题,负债的Macaulay duration=6.5,组合A是6.5,组合B是6.52,组合C是6.47,其中组合B和组合C的数据与负债的Macaulay duration很接近,差距只有0.02,这个差距是可以接受的。假设组合C的Macaulay duration是6.7,这个差距太大了,直接排除。


另外需要注意的是,基本上单期负债匹配不给PV数据,所以默认满足。如果给了的话,PV和Macaulay duration一样,属于第一筛选条件,直接排除资产PV小于负债PV的。而多期负债考虑的是BPV,已经涵盖PV的影响了,所以多期负债匹配不看PV。


回到原题,通过第一筛选条件macaulay duration,没办法做排除。三个组合都进入第二轮的筛选,第二轮用convexity筛。

单期负债就是找资产convexity最小的;多期负债就是找资产convexity大于负债convexity的基础上,再找资产convexity最小的。


想问一下是不是没有任何情况会通过cash flow yield判断?如果有,会是什么样的问题&设定?


不会用Cash flow yield判断。

因为资产的cash flow yield可大可小,并没有明确的约束。理论上来讲,做匹配就是让资产的数据匹配负债的数据。理论上应该让资产的Cash flow yield等于负债的cash flow yield,但是,在做匹配的时候,是已知资产的折现率/收益率cash flow yield,然后用这个折现率给负债折现,充当负债的cash flow yield,所以不用讨论,资产与负债的cash flow yield是相等的。


题干之所以要给出cash flow yield,只是为了严谨。因为备选的3个组合,在cash flow yield差不多大的情况下,债券组合的现金流分散程度dispersion,可以用convexity这个指标衡量。保证cash flow yield差不多大,就保证了dispersion的大小完全体现在convexity的大小上,此时convexity指标可以用来衡量现金流分散程度。


这样保证了题目的严谨性,为了保证convexity不受cash flow yield差异的影响。所以可以发现,即便题目给了cash flow yield,三个备选组合的cash flow yield也是差不多大的,不会有太大的差异。

发亮_品职助教 · 2024年07月22日

不用客气哈!一般提到duration默认是modified duration。如果是portfolio duration,那默认是weighted average modified duration。所以针对匹配的题目,要考查duration选择这个考点,会做说明是macaulay duration,or portfolio weighted average macaulay duration or portfolio macaulay duration(按定义算的组合Macaulay duration)

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