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薛真 · 2020年04月25日

问一道题:NO.PZ2020011303000049

问题如下:

Previous question:

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 in the previous question. 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 standard deviation of returns is [(0.5 × 0.118)^2 + (0.5 × 0.118)^2+ 2 × 0.5 × 0.5 × 0.118 × 0.118 × 0.2]^0.5 = 0.0914 or 9.14%.

0.5,0.118怎么来的呢,老师

1 个答案
已采纳答案

小刘_品职助教 · 2020年04月26日

同学你好,

0.118是根据上一问算来的,0.5是权重,题目中说有两个相同的收益概率分布。

这道题可以等价于一个组合有两个资产,A、B,A和B的均值及标准差都相同,投资权重各为0.5,A和B的相关系数为0.2,求组合的均值及方差。

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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

数学太差,这个expectesquarereturn 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。

2020-08-29 10:36 1 · 回答