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chch · 2021年07月26日

平行移动的话没有影响吗？

  1. CFA III
  2. Fixed Income

NO.PZ2019103001000033

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.

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：

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.

平行移动的话没有影响吗？对duration和凸度有没有影响？

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2 个答案

pzqa015 · 2021年08月02日

嗨，爱思考的PZer你好：


duration 和 convexity 不是衡量收益率曲线平行移动的吗？Key duration才是非平行移动吧

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是的同学，你说的没错，duration和convexity衡量收益率曲线的平行移动，KRD衡量收益率曲线的非平行移动。这两条结论的内在含义是这样的。

之所以可以用duration来衡量平行移动，是因为平行移动情况下，所有时间点利率的变化相同的，因此portfolio duration这一个值，就可以衡量portfolio value受利率变动的影响。

而在非平行移动下，不同时间点的利率变化是不一样的，因此无法用portfolio duration这一个值来衡量portfolio value受利率变化的影响。所以要分别考察不同时间点利率变动，对Portfolio value的影响，引入了KRD这个概念，portfolio中所有KRD加总之后就是portfolio duration。

本题问的是免疫过程中如何减少收益率曲线非平行移动的影响，也即降低structural risk，我们通常是通过降低portfolio的convexity来降低sturcutral risk。

根据convexity=(mac D+mac D^2+dispersion)/(1+y)^2，我们降低convexity也就是降低dispersion，让现金流尽可能集中，降低现金流分散程度，从而规避多个时间点利率变化对portfolio value的影响。

比如，单笔负债是t=4年到期，我们通过调整portfolio 的convexity，让现金流也集中在t=4周围，那么即使收益率曲线发生非平行移动，t=2、3时间点的利率变化不同，对portfolio value也没有影响呀，所以，这就可以降低structural risk了。


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加油吧，让我们一起遇见更好的自己！

pzqa015 · 2021年07月27日

嗨，努力学习的PZer你好：


同学你好

Strategy 2是用coupon bear bond来对多笔现流金负债做免疫。题干问如何降低收益率曲线非平行移动对多笔现金流负债免疫策略的影响，


我们先回顾一下多笔现金流负债免疫的条件：

PVA≥PVL

BPVA=BPVL

ConvexityA＞ConvexityL，且Minimize

第三个条件最小化portfolio凸度，就是为了降低structural risk，structural risk是指收益率曲线非平行移动导致△asset value≠△liab value，通过设定凸度条件，使得收益率曲线非平行移动时，△asset value尽量与△liab value相等，从而可以实现免疫。


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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！

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NO.PZ2019103001000033 maximizing the cash flow yielof the bonportfolio. minimizing the fferenbetween liability ration anbonportfolio ration. A is correct. Minimizing the convexity of the bonportfolio minimizes the spersion of the bonportfolio. A non-parallel shift in the yielcurve mresult in changes in the bonportfolio’s cash flow yiel In summary, the characteristiof a bonportfolio structureto immunize a single liability are thit (1) hinitimarket value thequals or excee the present value of the liability, (2) ha portfolio Macaulration thmatches the liability’s e te, an(3) minimizes the portfolio convexity statisti​为了降低Structurrisk（Non-parallel时，资产不匹配负债的风险），我们就要选择Convexity最小的债券但是这应该是在ration匹配的基础上再选convexity最小啊

2022-01-14 17:49 1 · 回答

NO.PZ2019103001000033 No.PZ2019103001000033 (选择题) 来源: 原版书 ug Kepler, the newly hirechief financiofficer for the City of Raor asks the puty financimanager, Hui Ng, to prepare analysis of the current investment portfolio anthe city’s current anfuture obligations. The city hmultiple liabilities of fferent amounts anmaturities relating to the pension fun infrastructure repairs, anvarious other obligations. Ng observes ththe current fixeincome portfolio is structureto matthe ration of ealiability. Previously, this structure causethe city to access a line of cret for temporary mismatches resulting from changes in the term structure of interest rates Kepler asks Ng for fferent strategies to manage the interest rate risk of the city’s fixeincome investment portfolio against one-time shifts in the yielcurve. Ng consirs two fferent strategies: Strategy 1: Immunization of the single liabilities using zero-coupon bon helto maturity Strategy 2: Immunization of the single liabilities using coupon-bearing bon while continuously matching ration. The effects of a non-parallel shift in the yielcurve on Strategy 2 creceby: 您的回答正确答案是: A A 正确minimizing the convexity of the bonportfolio. B maximizing the cash flow yielof the bonportfolio. C minimizing the fferenbetween liability ration anbonportfolio ration. A能选，为啥B不能选，根据convexity的公式，当CFY增加的时候convexity 减小，最大化CFY也可以是认为最小化convexity啊

2022-01-09 00:02 1 · 回答

请问题目中不是说针对multiple liabilities吗？那么为何是选择convexity最小的状况呢？

2020-03-12 21:16 1 · 回答

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2020-02-20 18:58 2 · 回答