标准差什么时候是百分比的形式，什么时候不是百分比的形式呢？

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：

0.5%

5.0%

7.4%

9.7%

解释：

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

标准差什么时候是百分比的形式，什么时候不是百分比的形式呢？这两种形式组合标准差计算的公式是不是有差别？

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品职答疑小助手雍 · 2021年06月13日

嗨，爱思考的PZer你好：

这种情况有时候题目里会写的~比如这题写了“What percentage of risk,”

不过我觉得看选项就就好啦~选项写的是百分比的就用百分比的，写的是绝对数值就用数值

然后，公式都是一样的，σA方+σB方+2*ρ*σA*σB，只不过这里面的sigma可能是数值或者百分比。

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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

2022-03-04 17:03 1 · 回答

NO.PZ2016070202000020 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？

2022-03-04 16:50 1 · 回答

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

2021-11-06 17:53 1 · 回答

NO.PZ2016070202000020 老师你好，这样算出的结果选D

2021-09-27 11:17 4 · 回答

标准差什么时候是百分比的形式，什么时候不是百分比的形式呢？

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