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菱秋秋 · 2021年06月13日

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？

  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%.

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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1 个答案

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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