a) Consider an economy with two types of firms, S and I. Type S firms always move together, but type I firms move independently of each other. For both types of firms, the expected return of an individual firm is given by 5%, and the return volatility of an individual firm is given by 25%.

i) (10 points) There is an equally-weighted portfolio made of 10 type S firms and 10 type I firms. What is the expected return and the return volatility of the portfolio?

ii) (7 points) Now, suppose that there are 15 type S firms and 5 type I firms in an equally-weighted portfolio. What is the expected return and the volatility of the portfolio? Compare your result with that in (a). Briefly explain the intuition behind your findings.