An investor can invest in two assets, X and Y. Asset X has the expected return of 0.06 and the variance of 0.0004, and asset Y has the expected return of 0.08 and the variance of 0.0025. The correlation coefficient of the rate of return of the two assets, , is 0.5. The investor is assumed to have the following expected utility function: [] = [ ] () where is a positive constant. a) Determine, as a function of , the portfolio that maximizes the expected utility. b) Show that, as increases, the investor selects an increasing proportion of Asset X and explain why the relationship holds