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🍥火火🍥 · 2021年07月26日

关于effective duration和empirical duration

NO.PZ2019103001000070

问题如下:

Gerber explains the concept of empirical duration to Petit and makes the following points.

Point 1: A common way to calculate a bond’s empirical duration is to run a regression of its price returns on changes in a benchmark interest rate.

Point 2: A bond’s empirical duration tends to be larger than its effective duration.

Point 3: The price sensitivity of high-yield bonds to interest rate changes is typically higher than that of investment-grade bonds.

Which of Gerber’s points about empirical duration is correct?

选项:

A.

Point 1

B.

Point 2

C.

Point 3

解释:

A is correct.

A bond’s empirical duration is often estimated by running a regression of its price returns on changes in a benchmark interest rate.

A bond’s empirical duration tends to be larger than its effective duration

为什么是错的呢

有什么解题思路呢

1 个答案

pzqa015 · 2021年07月27日

嗨,爱思考的PZer你好:


B选项说反了。

Empirical duration tends to be smaller than its effective duration。原因在于,根据yC=yB+spread公式,我们计算effective时假设基准利率的变动对spread无影响,那么基准利率的变动可以完全传导至公司债折现率,即△yc=△yB,基于△P/P=-Effective duration*△yc,可以计算出effective duration。

Empirical duration通常用债券价格变动率对△yB进行回归得到,反映债券价格对基准利率的敏感程度;实务中,我们观察到spread与yB变化负相关这样一个现象,这种现象使得yB的变化不能完全传导至yC,使得△yc<△yB

那么由于△P/P=-effective duration*△yc=-empirical duration*△yB且△yc<△yB,effective duration>empirical duration。

C选项也说反了。

HYB have lower price sensitivity to interest rate changes than IG bond。原理如下:

根据yC=yB+spread,实务中我们观察到spread与yB变化负相关,yB下降,表明经济衰退,央行采取扩张的货币政策,衰退时公司经营恶化,公司债风险比变大,所以spread变大,正是由于spread与基准利率的负相关,导致spread对基准利率有抵消作用,这种现象在HYB身上尤为明显,因为经济衰退时,HYB的信用风险更大,spread上涨的更多,所以抵消作用更大,故yb上涨带来的yC上涨更少,也就是yc对基准利率的变化less sensitivity。Price是根据yc求出来的,所以price对基准利率的变化less sensitivity。


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