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 an 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. (a) What are the expectation and variance of my annual return if I invest all my money in fund A? (b) What are the expectation and variance of my annual return if I invest all my money in fund B? (c) What are the expectation and variance of my total annual return if I invest half.

EBK CONTEMPORARY FINANCIAL MANAGEMENT
14th Edition
ISBN:9781337514835
Author:MOYER
Publisher:MOYER
Chapter8: Analysis Of Risk And Return
Section: Chapter Questions
Problem 6P
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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 an 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. (a) What are the expectation and variance of my annual return if I invest all my money in fund A? (b) What are the expectation and variance of my annual return if I invest all my money in fund B? (c) What are the expectation and variance of my total annual return if I invest half. 

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