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很不酷 · 2020年08月29日

问一道题：NO.PZ2020011303000049

  1. FRM I
  2. Valuation And Risk Models

问题如下：

An investment has probabilities of 0.1, 0.3, 0.2, 0.3, and 0.1 of giving one-year returns equal to 30%, 20%,10%, 0%, and -10%.

Suppose that there are two investments with the same probability distribution of returns as above. What is the total mean and standard deviation of returns if the correlation between them is 0.2?

选项：

解释：

The total mean return is 10%.

The expected squared return is 0.024 so that the standard deviation of the return is 0.024−0.12=0.014=0.118\sqrt{0.024-0.1^2}=\sqrt{0.014}=0.118 or 11.8%

standard deviation of returns is 0.52×0.1182+0.52×0.1182+2×0.5×0.5×0.118×0.118×0.2=0.0914\sqrt{0.5^2\times0.118^2+0.5^2\times0.118^2+2\times0.5\times0.5\times0.118\times0.118\times0.2}=0.0914 or 9.14%

数学太差，这个expected squared return is 0.024是怎么来的？ 这个求标准差的公式 \sqrt{0.024-0.1^2}=\sqrt{0.014}=0.118也不明白。

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1 个答案

小刘_品职助教 · 2020年08月29日

同学你好，

expected squared return is 0.024 是这么算的

E(R^2) = 0.1*(30%)^2+0.3*(20%)^2+0.2*(10%)^2+0.3*(0%)^2+0.1*(-10%)^2=0.024

下面标准差的公式就是直接套用就行 前面那个值是0.024，后面那个值是0.1

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NO.PZ2020011303000049问题如下 investment hprobabilities of 0.1, 0.3, 0.2, 0.3, an0.1 of giving one-yereturns equto 30%, 20%,10%, 0%, an-10%.Suppose ththere are two investments with the same probability stribution of returns above. Whis the totmeanstanrviation of returns if the correlation between them is 0.2? The totmereturn is 10%. The expectesquarereturn is 0.024 so ththe stanrviation of the return is 0.024−0.12=0.014=0.118\sqrt{0.024-0.1^2}=\sqrt{0.014}=0.1180.024−0.12​=0.014​=0.118 or 11.8% stanrviation of returns is 0.52×0.1182+0.52×0.1182+2×0.5×0.5×0.118×0.118×0.2=0.0914\sqrt{0.5^2\times0.118^2+0.5^2\times0.118^2+2\times0.5\times0.5\times0.118\times0.118\times0.2}=0.09140.52×0.1182+0.52×0.1182+2×0.5×0.5×0.118×0.118×0.2​=0.0914 or 9.14% 有一个投资产品获得30%回报率的可能性是0.1，20%回报率的可能性是0.3，10%回报率的可能性是0.2，0%回报率的可能性是0.3，-10%回报率的可能性是0.1。假设有两个投资具有与上述相同的收益概率分布。如果它们之间的相关性为 0.2，则回报的总均值和标准差是多少？expectesquareeturn=0.1*(30%)^2+0.3*(20%)^2+0.2*(10%)^2+0.3*(0%)^2+0.1*(-10%)^2=0.024stanrviation ofreturn=(0.5^2×0.118^2+0.5^2×0.118^2+2×0.5×0.5×0.118×0.118×0.2)^0.5=0.0914 or 9.14% 还是不懂tot10咋求出来的 还有那个0.5和0.118怎么得的

2024-04-11 03:29 1 · 回答

NO.PZ2020011303000049 为什么总的variance不是2*（1+correlation coefficient）*单个的variance？

2021-07-05 17:35 1 · 回答

0.5，0.118怎么来的呢，老师

2020-04-25 14:30 1 · 回答