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Kathy苏苏 · 2023年04月28日

dollar value

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

老师,为什么要乘以dollar value,而不是乘以各自的value10?

Kathy苏苏 · 2023年04月28日

老师,问题里不是 dollar value,是dollar duration

Kathy苏苏 · 2023年04月28日

我的问题:老师,为什么Z和西格玛的乘积要乘以dollar duration,而不是乘以各自的value10?

2 个答案

品职答疑小助手雍 · 2023年04月30日

section4 Risk Metrics and Hedges 里的 one factor Risk Metrics and Hedges很大篇幅都在讲duration还有它作为利率和债券价格的勾稽关系,讲义196页,Portfolio Duration and Convexity那部分里提到了dollar duration。

品职答疑小助手雍 · 2023年04月28日

同学你好,因为利率的波动要通过duration作为传导机制才能计算债券价格的变化,所以不能直接乘以债券的value,而是要乘以dollar duration。

Kathy苏苏 · 2023年04月28日

老师,对应讲义第几页?我想看下讲解和公式。

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