If $x is invested in mutual fund A. the annual return has an expectation of $0.lx and a standard deviation of S0.02.V. If $x is invested in mutual fund B. the annual return has an expectation of $0.lx and a standard deviation of $0.03.1x. 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 of my money in fund A and half in fund B?
(d) Suppose I invest $x in fund A and the rest of my money in fund B. What value of x minimizes the variance of my total annual return?
Explain why your answers illustrate the importance of diversity in an investment strategy.