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410140980 · 2022年03月04日

组合的variance是怎么计算的

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2016070202000020

问题如下：

You are given the following information about the returns of stock P and stock Q: variance of return of stock P=100； variance of return of stock Q=225; covariance between the return of stock P and the return of stock Q=53.2. At the end of 1999, you are holding USD 4 million in stock P. You are considering a strategy of shifting USD 1 million into stock Q and keeping USD 3 million in stock P. What percentage of risk, as measured by standard deviation of return, can be reduced by this strategy?

选项：

A.

0.5%

B.

5.0%

C.

7.4%

D.

9.7%

解释：

The variance of the original portfolio is 1,600, implying a volatility of 40. The new portfolio has variance of ;32×100+12×225+2×53.2×3×1=1,444;3^2\times100+1^2\times225+2\times53.2\times3\times1=1,444. This gives a volatility of 38, which is a reduction of 5%.

老师不理解组合的variance为什么算出来是1600，以及调整过后为什么是1440，P的头寸挪走了1m，剩下3m，3 就可以直接平方代替权重吗？

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1 个答案

DD仔_品职助教 · 2022年03月04日

嗨，努力学习的PZer你好：


同学你好，

因为原本的头寸只有4m的P，p的方差是100，标准差就是10，p的dollar形式的variance就是（4*10）^2=1600

这里利用权重法或者是直接用数值的σ计算都是可以的，答案是一样的：

下图蓝色方框是利用权重计算出来的答案，答案一样的都是下降5%


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NO.PZ2016070202000020 问题如下 You are given the following information about the returns of stoP anstoQ: varianof return of stoP=100； varianof return of stoQ=225; covarianbetween the return of stoP anthe return of stoQ=53.2. the enof 1999, you are holng US4 million in stoP. You are consiring a strategy of shifting US1 million into stoQ ankeeping US3 million in stoP. Whpercentage of risk, measurestanrviation of return, crecethis strategy? A.0.5% B.5.0% C.7.4% 9.7% The varianof the originportfolio is 1,600, implying a volatility of 40. The new portfolio hvarianof 32 ×100+12 ×225+2×53.2×3×1=1,444. This gives a volatility of 38, whiis a rection of 5%. 我直接用权重，算出组合1的标准差是10，组合2的标准差是9.5，然后就（10-9.5）/10=5%这样吗

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NO.PZ2016070202000020

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NO.PZ2016070202000020 5.0% 7.4% 9.7% The varianof the originportfolio is 1,600, implying a volatility of 40. The new portfolio hvarianof ;32×100+12×225+2×53.2×3×1=1,444;3^2\times100+1^2\times225+2\times53.2\times3\times1=1,444;32×100+12×225+2×53.2×3×1=1,444. This gives a volatility of 38, whiis a rection of 5%. 是直接资产价值4的平方×100吗

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NO.PZ2016070202000020 老师你好，这样算出的结果选D

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