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黄路迦 · 2023年12月04日

immunization

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000025

问题如下：

Leah informs Molly 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. Leah expresses concern about the risks associated with an immunization strategy for this obligation. In response, Molly 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 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：

Correct Answer: C

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.

第二个statement怎么理解呢

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1 个答案

pzqa31 · 2023年12月05日

嗨，从没放弃的小努力你好：


利率的改变不会影响到Cash flow matching的匹配效果。


Cash flow matching的原理就是：

我们先分析负债现金流发生的日期与金额，这是我们需要满足的现金流流出。然后我们购买合适的债券组合，经过计算与设计，让债券的Coupon与本金现金流流入正正好等于负债的现金流流出，且Coupon以及本金现金流的发生日期也正正好等于负债现金流发生的日期。就是设计好资产现金流，让资产现金流严丝合缝地与负债现金流对上。


注意到，收到债券Coupon与本金的日期正正好是负债的到期日，所以Coupon现金流就发生在负债到期时，这样就不存在Coupon reinvestment risk。这样无论利率如何改变，都不影响Coupon现金流归还负债。

同时，又由于归还负债现金流还包含债券本金的自然到期，这是债券的自然到期，债券到期拿到的一定是本金面值，不存在Price risk。所以无论利率如何改变，也都不会影响本金现金流。


于是，设计好的Coupon现金流与本金现金流，都不受利率改变的影响，归还的金额也是我们提前计算好的，这样归还负债的现金流也就不受利率的影响了。这就导致Cash flow matching这种方法，可以消除利率的影响。


这就是statement2的结论：利率改变（Parallel shift也好，Non-parallel shift也好，都无所谓），都不影响Cash flow matching来偿还负债。


和Cash flow matching相对应的是Duration-matching。Duration-matching我们不管负债的现金流，我们匹配的原理是保证资产的收益不受利率的影响。

如何保证债券资产的收益不受利率的影响呢？

实际上是让利率改变时，债券的Coupon reinvestment risk与债券价格的Price risk相互抵消，即，利率改变对债券收益的影响途径就是Coupon reinvestment risk与Price risk，现在这两个风险抵消掉了，那么就意味着，利率改变不会影响到债券的投资收益，那么债券可以实现预期的增值，负债到期时，资产可以顺利实现增值偿还负债。

但要让Coupon reinvestment risk与Price risk相互抵消有一个前提，就是：只有利率的平行移动才能一定保证price risk与Coupon reinvestment risk完全抵消。

当发生非平行移动时，两个风险有可能会出现无法抵消的情况，如果这两个风险无法抵消，就会导致Duration-matching失效。

所以发生non-parallel shift时，Duration-matching相比就没那么保险了，于是Cash flow matching有更好的immunization效果。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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