Question

3) Consider information given in the following table.

State of the Economy	Probability	Return of Stock A	Return of Stock B
Recession	0.1	2%	-5%
Normal	0.3	10%	8%
Boom	0.6	20%	25%

a) Calculate the expected return, variance of each stock, and the covariance between the two stocks.

b) If the weights of both stocks are 55% in A and 45% in B, respectively, what are the expected return and variance of the sum of these two stocks?

Answer 1

(a) Expected Return = SUM of (Probability of each economic state x Return of Stock in that particular economic state)

Therefore,

Expected Return of Stock A = 0.1 x 2 + 0.3 x 10 + 0.6 x 20 = 15.2 %

Expected Return of Stock B = 0.1 x (-5) + 0.3 x 8 + 0.6 x 25 = 16.9%

(b)

Expected Return of Stock A = Ra= 15.2 %

Expected Return of Stock B = Rb = 16.9%

Weight of Stock A = Wa = 0.55 and Weight of Stock B = Wb = 0.45

Let Expected Return of Portfolio be Rp and Variance be V. Also let A's Variance be Va and that of B be Vb

Therefore, Rp = Wa x Ra + Wb x Rb = 0.55 x 15.2 + 0.45 x 16.9 = 15.965 %

V = (Wa)^(2) x Va + (Wb)^(2) xVb + 2 x Wa x Wb x Covariance = (0.55)^(2) x 54.22 + (0.45)^(2) x 150.89 + 2 x 0.55 x 0.45 x 90.44 = 91.73