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逆流的鱼🐠🐠 · 2023年08月23日

convexity

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000033

问题如下：

Doug, the newly hired chief ­financial officer for the City of Radford, asks the deputy ­financial manager, Hui, 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.

Hui 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.

Doug asks Hui 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. Hui 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.
The effects of a non-parallel shift in the yield curve on Strategy 2 can be reduced by:

选项：

A.

minimizing the convexity of the bond portfolio.

B.

maximizing the cash flow yield of the bond portfolio.

C.

minimizing the difference between liability duration and bond-portfolio duration.

解释：

Correct Answer: A

A is correct. Minimizing the convexity of the bond portfolio minimizes the dispersion of the bond portfolio. A non-parallel shift in the yield curve may result in changes in the bond portfolio’s cash flow yield. In summary, the characteristics of a bond portfolio structured to immunize a single liability are that it (1) has an initial market value that equals or exceeds the present value of the liability, (2) has a portfolio Macaulay duration that matches the liability’s due date, and (3) minimizes the portfolio convexity statistic.

这道题使用coupon bearing bond和zero coupon bond结论一样吗？有没有区别点？

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1 个答案

pzqa015 · 2023年08月23日

嗨，努力学习的PZer你好：


如果用zero coupon bond，那么portfolio与liability都不受曲线任何移动的影响了。题目也就不会这么问了

题目这种问法只能是coupon bear bond。

另外，zero coupon bond本身的convexity就是0，因此，也符合minimize the convexity of the portfolio。

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努力的时光都是限量版，加油！

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