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saimeiei · 2020年03月07日

问一道题: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.

老师你好。没太理解这道题,

1、如果已经做好了duration match,那么收益率不论怎样变动,只一次的变动都能够免疫吗?

2、structure risk是指非平行移动而带来的不能免疫的风险,那么是不是发生了非平行移动,很大概率是不能够完全免疫的,不论是不是首次变动?

1 个答案

WallE_品职答疑助手 · 2020年03月08日

1.因为我们在Match liability的时候会做到Macaulay Duration相等,利率变化一次,我们的确能让资产、负债实现Immunization. 一次的免疫之后,就得在做rebalance。匹配macaulay duration之后,只要资产的Convexity足够小,绝大多数非平行移动也能免疫。

2.Strucutral risk就是非平行移动时,资产不匹配负债的风险。匹配好之后,所有的平行移动都免疫;一些非平行移动也能免疫。

举个例子,负债是10年期,资产是8年期、12年期的组合构成,如果非平行移动时,只要8/10/12年期的利率没变,资产负债的价值就不会变,他俩仍然是匹配的。

所以为了降低Structural risk,就要降低Convexity,让资产的现金流足够的贴近负债的现金流,这样影响资产、负债的Key rate是非常接近、几乎一样的,这样资产、负债对非平行移动的反映也会差不多。所以在满足匹配的情况下,非平行移动就看Convexity数据,Convexity越小,非平行产生不匹配的风险就越小。

Convexity足够地小,代表资产、负债的现金流发生时间点很接近。如果资产的现金流发生时间点很近的话,那影响他们的Key rate就差不多,所以不论是啥非平行移动,既然影响资产、负债的Key rate一样,那非平行移动对资产、负债的影响也就一样了