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松松 · 2021年10月17日

请问这里的cancelling out是指资产和负债的麦考利久期相等,还是指资产/负债的久期和investment horizon相等?

NO.PZ2019103001000032

问题如下:

Doug Kepler, the newly hired chief financial officer for the City of Radford, asks the deputy financial manager, Hui Ng, to prepare an analysis of the current investment portfolio and the city’s current and future obligations. The city has multiple liabilities of different amounts and maturities relating to the pension fund, infrastructure repairs, and various other obligations.

Ng observes that the current fixed-income portfolio is structured to match the duration of each liability. Previously, this structure caused the city to access a line of credit for temporary mismatches resulting from changes in the term structure of interest rates.

Kepler asks Ng for different strategies to manage the interest rate risk of the city’s fixed-income investment portfolio against one-time shifts in the yield curve. Ng considers two different strategies:

Strategy 1: Immunization of the single liabilities using zero-coupon bonds held to maturity

Strategy 2: Immunization of the single liabilities using coupon-bearing bonds while continuously matching duration.

An upward shift in the yield curve on Strategy 2 will most likely result in the:

选项:

A.

price effect cancelling the coupon reinvestment effect.

B.

price effect being greater than the coupon reinvestment effect.

C.

coupon reinvestment effect being greater than the price effect.

解释:

A is correct.

An upward shift in the yield curve reduces the bond’s value but increases the reinvestment rate, with these two effects offsetting one another. The price effect and the coupon reinvestment effect cancel each other in the case of an upward shift in the yield curve for an immunized liability.

请问这里的cancelling out是指资产和负债的麦考利久期相等,还是指资产/负债的久期和investment horizon相等?

虽然在本题中似乎是一个意思,但是我比较困惑的是这个问题的要点是麦考利久期等于investment horizon,还是资产和负债的麦考利久期相等?

3 个答案

pzqa015 · 2022年02月08日

嗨,努力学习的PZer你好:


不好意思,我没听明白。您解释的是asset的 Mac D 么? 我没明白,资产的investment horizon为什么是大于资产的mac D的。付息和不付息债券,做到single liab immunization, 不是都要满足investment horizon=mac D 嘛? 麻烦再解释一下。谢谢

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不好意思,之前描述的不太准确

应该是:

零息债:maturity=mac D,也就是零息债的到期时间等于mac D,比如,2年期零息债的mac D=2

付息债:maturity>mac D,也就是付息债的到期时间是大于mac D,比如,2年期付息债的mac D<2.


至于你的提问资产investment horizon大于mac D,这个investment horizon是指maturity,也就是资产的正常到期期限,付息债的资产正常到期期限大于付息债的mac D。这个结论要记一下

举个例子给你证明一下:

2年期付息债,coupon=2,ytm=1.5%,P=100.98

PVCF1=(2/(1+1.5%))/100.98=1.95%; PVCF2=((100+2)/(1+1.5%)^2)/100.98=98.05%

mac D=1.95%*1+98.05%*2=1.9805<2.


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

pzqa015 · 2022年02月07日

嗨,从没放弃的小努力你好:


零息债的investment horizon=mac D

付息债的investment horizon>mac D

mac D=∑(PVCFi/P)*t,是时间的加权平均值,它小于∑(1/n)*t,后者代表的是investment horizon。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

mario · 2022年02月07日

不好意思,我没听明白。您解释的是asset的 Mac D 么? 我没明白,资产的investment horizon为什么是大于资产的mac D的。付息和不付息债券,做到single liab immunization, 不是都要满足investment horizon=mac D 嘛? 麻烦再解释一下。谢谢

pzqa015 · 2021年10月18日

嗨,努力学习的PZer你好:


cancelling是指price effect与coupon reinvestment effect相互抵消,cancel 相互抵消之意。

资产的mac D=负债的time horizon=负债的mac D(single liability的mac D与time horizon相等哈),但是它们不等于资产的investment horizon哈。

资产的investment horizon是大于资产的mac D的。



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虽然现在很辛苦,但努力过的感觉真的很好,加油!

松松 · 2021年10月19日

很清晰谢谢!

mario · 2022年02月06日

可以解释一下资产的investment horizon是大于资产的mac D的?