If $x is invested in mutual fund A, the annual return has an expectation of $0.1x and a standard deviation of $0.02x. If $x is invested in mutual fund B, the annual return has expectation of $0.1x and a standard deviation of $0.03x. Suppose that the returns on the two funds are independent of each other and that I have $1000 to invest.
Then suppose I invest $x in fund A and the rest of my money in fund B. What value of of x minimizes the variance of my total annual return?
How to minimizes variance?
2013-05-17 8:08 pm
回答 (1)
2013-05-17 10:35 pm
✔ 最佳答案
Let say I invest $x in fund A and 1000 - x in fund BThen the total variance is f(x) = (0.02x)^2 + [0.03(1000 - x)]^2
f'(x) = 2(0.02x)(0.02) + 2[0.03(1000 - x)](-0.03)
= 0.0008x - 0.0018(1000 - x)
= 0.0026x - 1.8
Set f'(x) = 0 => x = 692.307692
So, when I invest $692.307692 in fund A and the rest of my money in fund B,the variance of my total annual return will be minimized
收錄日期: 2021-04-27 17:45:24
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130517000051KK00097