Assume that there are two shares, called A and B. Investors decide what share of the money which is to be invested in the two different shares (no other investment objects are available, and shorting is not possible.). Share A has an expected value of 2 and a variance of 1, while share B has an expected value of 1 and a variance at 2. The shares are independent. Investor Ola dislikes risk so much that he is willing to do everything he can to minimize the variance of his portfolio, while investor Kari does not care about variance at all, and will only create a portfolio for to maximize the expected return. What would an optimal portfolio look like for Ola and Kari respectively? Hint 1: If you invest a share s of your money in share A and a share 1 s in share B, then the variance of this portfolio (when the stocks are independent) given by

²_p(s) = ²_As² + ²_B(1 s)_²

Here is ²_A and ²_B the variance of share A and share B respectively.

Hint 2: How do you go about minimizing ²_p(s) with regard to s? Looks like how we wanted set out to maximize the same expression?