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

S1(1), S2(1) =

(80, 250) with probability 2/8

(90, 150) with probability 4/8

(120, 200) with probability 2/8

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

(b) Compute the correlation coefficient between the two assets

(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.

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

(e) Following the assumptions in (d), maximize the Sharp ratio and on the (, )-plane plot the efficient portfolios.

(f) Derive the Capital Market Line (CML) and plot this on the efficient (, )- plane of part (d)