Question 1: Consider two assets with the following:

1 = 0.10, 1 = 0.40

1 = 0.03; 2 = 0

Calculate the weights of the portfolio, (w1,w2) such that the expected return, w = 16. Calculate the variance of this portfolio. (15 marks)

Question 2: Consider a security with the stock prices with probabilitywith probabilitywith probabilitywith probability

(a) What is the current price of the stock for which the expected returnwould be 12%?

(b) What is the current price of the stock for which the standard deviationwould be 18% (25 marks)

Question 3: Assume that S(0) = 100, the current price of the stock, and that the ex dividend price is:with probabilitywith probabilitywith probability

110 with probability

The company will pay out a constant dividend D (independent of the future stock price). Compute D for which the expected return on stock would be 18%. (10 marks)

1

Question 4: Consider two risky assets with prices S1(0) = 100, S2(0) = 150 the price is:

(80,250) with probability

S1(1),S2(1) = (90,150) with probability

(120,200) with probability

(a) Compute mean and standard deviations (1,1) and (2,2) for the two assets (10 marks)

(b) Compute the correlation coe cient between the two assets (5 marks)

(c) Assuming :w1 0.5 and w2 0.5. On the (,)-plane, plot all the portfolios attainable by investing in the risky assets. Highlight the two risky assets on the plot. (10 marks)

(d) Assume we allow for borrowing and investment with the risk free rater = 3%. Compute the Sharp ratio with some arbitrary weights satisfying the conditions set on the weights in (c). (5 marks)

(e) Following the assumptions in (d), maximise the Sharp ratio and on the(,)-plane plot the e cient portfolios. (10 marks)

(f) Derive the Capial Market Line (CML) and plot this on the e cient (,)plane of part (d). (10 marks)