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临江仙 · 2022年10月24日

这题用YTM的公式,如何解释

NO.PZ2016031001000059

问题如下:

Which bond will most likely experience the smallest percent change in price if the market discount rates for all three bonds increase by 100 basis points?

选项:

A.

Bond A

B.

Bond B

C.

Bond C

解释:

B is correct.

Bond B will most likely experience the smallest percent change in price if market discount rates increase by 100 basis points. A higher-coupon bond has a smaller percentage price change than a lower-coupon bond when their market discount rates change by the same amount (the coupon effect). Also, a shorter-term bond generally has a smaller percentage price change than a longer-term bond when their market discount rates change by the same amount (the maturity effect). Bond B will experience a smaller percent change in price than Bond A because of the coupon effect. Bond B will also experience a smaller percent change in price than Bond C because of the coupon effect and the maturity effect.

考点:maturity effect & coupon effect

解析:maturity effect表明,对于coupon rate一样的债券,maturity较大的债券,其价格改变较大,在债券A和C中,我们排除C。coupon effect表明,对于maturity一样的债券,coupon rate较小的债券,其价格改变较大,在债券A和B中,排除A。故选项B正确。

请教如何用YTM的公式,判断coupon rate的影响

1 个答案

吴昊_品职助教 · 2022年10月25日

嗨,爱思考的PZer你好:


这道题有两种理解思路,一个是maturity effect角度,另一个是duration角度,没有从YTM公式去理解的角度。

1、maturity effect表明,对于coupon rate一样的债券,maturity较大的债券,其价格改变较大,在A和C中,我们排除C。coupon effect表明,对于maturity一样的债券,coupon rate较小的债券,其价格改变较大,在A和B中,排除A。因此,选项B正确。

2、这个题目也可以从duration的角度来思考。题目问的是当利率上涨100bp,哪一只债券价格改变最小。换句话说,是问哪一只债券的duration最小。首先排除债券C,maturity最长。在A和B中,coupon rate越大的债券,期间现金流越大,还款时间更短,duration更小。因此,bond B的duration最小。选项B正确。等到学到duration那一块再回过头来做就简单了。

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