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鱼豆腐 · 2022年12月22日

老师想问下那个只能抵消一次非平行移动的策略是哪一个呀

  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.

老师想问下那个只能抵消一次非平行移动的策略是哪一个呀

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3 个答案

pzqa015 · 2023年06月05日

嗨，爱思考的PZer你好：


比如资产端是3年期的coupon bear bond，coupon=2%，期初ytm=2%，则债券价格为100元。

第一笔现金流的现值为2/(1+2%)=1.96，第二笔现金流的现值为102/(1+2%)^2=98.04

则这只债的mac D=1.96/100*1+(98.04/100)*2=1.9804。假设single负债的剩余到期日就是1.98，那么此时，这只债是可以duration match的，也就是mac D=investment horizon。

如收益率曲线变化，ytm由2%变为3%，则此时债券价格为2/(1+3%)+102/(1+3%)^2=98.09

第一笔现金流的现值为2/（1+3%）=1.94，第二笔现金流的限制为102/(1+3%）^2=96.14。

此时mac D=1.94/98.09+(96.14/98.09)*2=1.9800。

而由于负债是single liability，无论收益率如何变，剩余到期日（Investment horizon）都是不变的，也就是仍未1.9804，此时，mac D≠ investment horizon，此时，免疫策略就不再成立了。

由于利率变动一次后，免疫策略不再成立，所以需要做rebalance，让mac重新等于investment horizon。

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treize_oz · 2023年06月04日

呃老师好 为何说"duration matching策略只可以免疫一次利率变动，利率变动一次后要对portfolio做rebalance"？  如何理解呢

pzqa015 · 2022年12月24日

嗨，从没放弃的小努力你好：


duration matching策略只可以免疫一次利率变动，利率变动一次后要对portfolio做rebalance，让免疫条件重新成立，否则，免疫策略就失效了。

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