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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年07月25日

请讲讲解题思路(题目把duration和VaR结合起来)

NO.PZ2016082402000054

问题如下:

A portfolio consists of two zero-coupon bonds, each with a current value of $10. The first bond has a modified duration of one year and the second has a modified duration of nine years. The yield curve is flat, and all yields are 5%. Assume all moves of the yield curve are parallel shifts. Given that the daily volatility of the yield is 1%, which of the following is the best estimate of the portfolio’s daily value at risk (VAR) at the 95% confidence level?

选项:

A.

USD 1.65

B.

USD 2.33

C.

USD 1.16

D.

USD 0.82

解释:

ANSWER: A

The dollar duration of the portfolio is 1×$10+9×$10=$100\times\$10+9\times\$10=\$100 . Multiplied by 0.01 and 1.65, this gives $1.65.

一个组合包含两个零息债券,每一个债券价格10,第一个债券的MD=1,第二个MD=9,利率全部是5%。假设利率都是平行移动,每日的波动率为1%,请问95%置信区间下的dailyVaR是多少?

VARσ*Z(0.95)=1%*1.65

95%z=1.65

组合的Dollar Duration=1*10+9*10=100

VaR=100*1.65*1%=1.65

助教你好:


这题把duration和VaR结合起来之后让我不知从何下手。


我首先想到dollar VaR这个式子,z=1.65,sigma=0.01,asset value=20,可是这样算的话就没答案。


题干给出了两只债券各自的duration,要怎么用上这个条件?


我还看见这同学问到了讲义上没有的dollar duration: https://class.pzacademy.com/qa/97506。


所以我想了解,拿到这道题之后,我首先该往哪个方向去思考?谢谢。


1 个答案

李坏_品职助教 · 2023年07月25日

嗨,爱思考的PZer你好:


题目最后问的是VaR,传统的daily VaR计算公式是: VaR=value * |μ-Z*σ|,Z是1.65,σ是1%,μ是收益率,题目没说,可以默认为是0.


注意题目给的1%这个条件是“volatility of the yield is 1%”,也就是债券的到期收益率的波动率为1%,到期收益率的波动率是通过duration进而影响资产价值变动的,所以公式最前面的value要改为duration * value,也就是dollar duration,是100.


你说的用asset value直接乘以Z和σ,那个σ是资产的波动率,而不是到期收益率的波动率。


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