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sliang · 2024年10月20日

fixed income

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NO.PZ201812020100000405

问题如下:

Which of Molly’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. Molly 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.

这一题是match single liability。那么在portfolio里直接买9年到期的zero coupon bond就可以match single liability并且不会受利率风险的影响了。那么statement1就是错的了。但是答案说statement1是对的,请问这点怎么理解?

1 个答案
已采纳答案

发亮_品职助教 · 2024年10月21日

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 1里面的关键词是measurement error。Measurement error是指在计算债券的关键性指标时,如duration、convexity等,由于计算的误差导致的匹配失效。

 

statement 1是原版书原话哈,只不过是套用了SD&R的背景。这段是说,即便对于cash flow amount以及time明确的Liability,我们有可能在计算关键性指标(key parameters)时,会出现误差。这种误差会对免疫产生不利的影响。

例如,用债券组合资产去cover负债,债券组合由3个债券构成,3个债券都是type 1 cash flow,即,现金流金额和发生日都知道。于是3个债券都有明确的duration/convexity指标。我们需要利用3个债券的Duration和convexity计算出组合的duration/convexity。在算组合的数据时,一个常见的方法是利用加权平均,3个债券的指标加权平均就是组合的指标。但这种加权平均的数据其实有误差。

最严谨的应该是用duration和convexity的定义,从组合的现金流入手计算。利用加权平均算的数据和用定义算的数据有差异。

 

所以可见,即便对于type 1 cash flow,他们有明确的duration/convexity等风险指标,但是在计算时,我们多多少少都会算一点误差出来,进而会导致匹配的效果变差,产生measurement error.

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