(10 pt.) There are three possible states of the world - bad, normal, and good - which occur with probability 0.25, 0.5 and 0.25 respectively. There are two assets, A and B, which give returns according to the following table Bad Normal Good A 5% 10% 12% B 4% 2% 0% (a) Suppose an investor invests fraction x of her wealth in A and the rest, 1 - x, in B. Write the expected return E(r) and the standard deviation of this return as a function of x. (3 pt.) (b) Write a formula for the combinations of (E(r), (r)) possibly achievable, assum- ing that short-selling is not possible in either asset. (I.e. Write E(r) as a function of the corresponding standard deviation o) (5 pt.) (c) The investor's preferences are such that if the expected return rises by 0.5% for every unit increase in the standard deviation of the return, then her utility remains unchanged. Assume that short selling is not allowed. Find the investor's optimal portfolio. Calculate it and round it off to after three decimal places. (2 pt.) (10 pt.) There are three possible states of the world - bad, normal, and good - which occur with probability 0.25, 0.5 and 0.25 respectively. There are two assets, A and B, which give returns according to the following table Bad Normal Good A 5% 10% 12% B 4% 2% 0% (a) Suppose an investor invests fraction x of her wealth in A and the rest, 1 - x, in B. Write the expected return E(r) and the standard deviation of this return as a function of x. (3 pt.) (b) Write a formula for the combinations of (E(r), (r)) possibly achievable, assum- ing that short-selling is not possible in either asset. (I.e. Write E(r) as a function of the corresponding standard deviation o) (5 pt.) (c) The investor's preferences are such that if the expected return rises by 0.5% for every unit increase in the standard deviation of the return, then her utility remains unchanged. Assume that short selling is not allowed. Find the investor's optimal portfolio. Calculate it and round it off to after three decimal places. (2 pt.)