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魏丽aa · 2019年11月15日

问一道题:NO.PZ2019103001000025

问题如下:

Mowery informs Compton that DFC has a single $500 million liability due in nine years, and she wants SD&R to construct a bond portfolio that earns a rate of return sufficient to pay off the obligation. Mowery expresses concern about the risks associated with an immunization strategy for this obligation. In response, Compton makes the following statements about liability-driven investing:

Statement 1:Although the amount and date of SD&R’s liability is known with certainty, measurement errors associated with key parameters relative to interest rate changes may adversely affect the bond portfolios.

Statement 2:A cash flow matching strategy will mitigate the risk from non-parallel shifts in the yield curve.

Which of Compton’s statements about liability-driven investing is (are) correct?

选项:

A.

Statement 1 only.

B.

Statement 2 only

C.

Both Statement 1 and Statement 2

解释:

C is correct.

Compton is correct that measurement error can arise even in immunization strategies for Type 1 cash flows, which have set amounts and set dates. Also, a parallel shift in yield curves is a sufficient but not a necessary condition to achieve the desired outcome. Non-parallel shifts as well as twists in the yield curve can change the cash flow yield on the immunizing portfolio; however, minimizing the dispersion of cash flows in the asset portfolio mitigates this risk. As a result, both statements are correct.

老师 我想问问statement1 是啥意思呀 没读懂 谢谢哈

3 个答案

120555137 · 2020年08月26日

好厉害老师,说的好清楚,点个赞

发亮_品职助教 · 2019年11月19日

看了你的解释其实这种measurement error就是讲义中提到的model risk对不对?


对。参考原版书原句:

发亮_品职助教 · 2019年11月15日

嗨,努力学习的PZer你好:


由题干:DFC has a single $500 million liability due in nine years, and she wants SD&R to construct a bond portfolio that earns a rate of return sufficient to pay off the obligation.

知道DFC这家公司有一笔9年后到期的负债,负债金额为500million,然后想要让SD&R帮忙对这笔负债做Match。


然后Statement 1是说:即便我们能准确地知道SD&R要匹配的这笔负债的金额、以及负债的到期日,(构建好的匹配组合)也会受到Measurement errors的影响,而Measurement errors产生的原因是:衡量利率风险的相关指标。


具体理解如下:

由题干知道SD&R这笔Liability是Type 1 liability,也就是到期金额已知,到期日已知的Liability;按理说Type 1 liability很好做匹配策略,但仍然会存在Errors。

在做资产负债匹配时,匹配的就是资产、负债的利率敏感度,所以衡量资产、负债利率敏感的数据很重要:如Duration数据,Convexity数据,BPV等等。

所以这些数据如果不准确的话,会影响到资产负债的匹配效果;

这里的Measurement errors就指:由于衡量资产、负债特征,尤其是利率特征的数据误差,造成的匹配误差。

即便对于这种到期日、到期金额已知的Type 1 liability,在用Duration等数据衡量这种负债特征进行匹配时,也可能会有误差产生;


例如,已知一个负债由多个Type 1 Liability组成,如果要匹配这个负债,首先就是要计算这个Liability portfolio的Duration数据。

常见的错误计算方法就是直接对各个成份Liability的Duration做简单的加权平均,计算出来的加权平均Duration当成负债组合的Duration数据。

然后以这样的Duration数据为基础进行Duration-matching匹配。但是这样算是不合理的、有误差存在。

合理的算法就是将这个Liability portfolio当成一个大的债券,然后用Duration的定义去计算这支“大债券的”Duration。

只有这样计算出来的衡量指标,然后以此做匹配策略,才会尽量减少误差。(基础班视频例题有讲到)


此外,如果只考虑Duration,忽略Convexity以及更高阶的影响,也会有Measurement errors。

因为衡量利率敏感度的指标除了Duration,还有其他的。


总之,在匹配时,衡量资产、负债利率敏感度的指标很重要。即便是Type 1 liability,由于计算Duration时错误的方法,或者是忽略Convexity等更高阶的影响,在匹配这种Type 1 liability时,也会难以避免Measurement error.

Statement 1就是说对SD&R这种金额、日期已知的负债,匹配时也会存在由利率敏感度指标误差带来的Measurement errors.

Statement 1是原版书的结论,记住即可:

Measurement error can arise even in immunization strategies for Type 1 cash flows, which have set amounts and set dates.


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he123456 · 2019年11月19日

看了你的解释其实这种measurement error就是讲义中提到的model risk对不对?

Shafengler · 2022年02月02日

能总结成这样也是要加鸡腿的~

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NO.PZ2019103001000025问题如下Mowery informs Compton thC ha single $500 million liability e in nine years, anshe wants SR to construa bonportfolio thearns a rate of return sufficient to poff the obligation. Mowery expresses concern about the risks associatewith immunization strategy for this obligation. In response, Compton makes the following statements about liability-iven investing:Statement 1Although the amount ante of SR’s liability is known with certainty, measurement errors associatewith key parameters relative to interest rate changes maersely affethe bonportfolios.Statement 2A cash flow matching strategy will mitigate the risk from non-parallel shifts in the yielcurve.Whiof Compton’s statements about liability-iven investing is (are) correct? A.Statement 1 only. B.Statement 2 only C.Both Statement 1 anStatement 2 C is correct. Compton is correthmeasurement error carise even in immunization strategies for Type 1 cash flows, whihave set amounts anset tes. Also, a parallel shift in yielcurves is a sufficient but not a necessary contion to achieve the sireoutcome. Non-parallel shifts well twists in the yielcurve cchange the cash flow yielon the immunizing portfolio; however, minimizing the spersion of cash flows in the asset portfolio mitigates this risk. a result, both statements are correct.measurement errors这里是指mol risk吗?

2022-03-27 17:28 1 · 回答

NO.PZ2019103001000025 Statement 1Although the amount ante of SR’s liability is known with certainty, measurement errors associatewith key parameters relative to interest rate changes maersely affethe bonportfolios. Statement 1中的“measurement errors associatewith key parameters” 是不是在说macaulration和 spersion anconvexity计算错误的情况?比如不是站在portfolio整体的角度,而是通过加权平均求出来的。。。

2021-08-10 07:10 1 · 回答

NO.PZ2019103001000025 Statement 2 only Both Statement 1 anStatement 2 C is correct. Compton is correthmeasurement error carise even in immunization strategies for Type 1 cash flows, whihave set amounts anset tes. Also, a parallel shift in yielcurves is a sufficient but not a necessary contion to achieve the sireoutcome. Non-parallel shifts well twists in the yielcurve cchange the cash flow yielon the immunizing portfolio; however, minimizing the spersion of cash flows in the asset portfolio mitigates this risk. a result, both statements are correct. 这是一个single liability,cash flow matching不是只适用于multiple liability吗?

2021-02-25 21:55 1 · 回答

Although the amount ante of SR’s liability is known with certainty, measurement errors associatewith key parameters relative to interest rate changes maersely affethe bonportfolios. 请教下老师,请问statement 1 针对题干来说应该是错的吧,题目中提到是single liabilty,那么我通过Mration相同的零息债券match就完全避免mol risk了,不会因为interest rate的变化而影响其match的效果。老师,我的理解是否正确,多谢!

2020-01-31 21:07 1 · 回答

请教老师,statement 2 是错在哪里,如何修改就是正确的论述了啊?

2019-12-18 16:11 1 · 回答