Question

Suppose an investor can invest in two stocks, whose returns are random variables X and Y, respectively. Both are assumed to have the same mean returns E(X) = E(Y) = μ; and they both have the same variance Var(X) = Var(Y) = σ2. The correlation between X and Y is some valueρ.

The investor is considering two invesment portfolios: (1) Purchase 5 shares of the first stock (each with return X ) and 1 of the second (each with return Y ). (2) Purchase 3 shares of the first stock (each with return X ) and 3 of the second (each with return Y ).

Assuming that the investor prefers higher mean and lower variance of the total return on the portfolio, for which values of μ, σ2, and ρ would the investor prefer plan 2 to plan 1?

Answer 1