Question

State of Economy	Probability of State of Economy	Stock A	Stock B	TSX
Boom	.30	30%	-9%	18%
Normal	.40	16%	12%	10%
Recession	.30	-10%	20%	-10%

1. Calculate the risk for stock B.

2. Calculate the risk for the TSX.

3. Calculate the covariance and correlation of the returns for stock A and stock B.

4. Calculate the covariance and correlation of the returns for stock A and the TSX.

Answer 1

Expected Return (Mean) = [E(P*X)] Standard Deviation (risk) = V[3(P*(X-X)^2)] Where X is the Return of Asset X is the Mean P is the probability STOCKA: Return State of Squared Product Probability(P) Return(A) Deviation Deviation Economy (PA) (A-A) [(A-A)^2] Boom 0.30 0.30 0.0900 0.1760 0.030976 Normal 0.40 0.16 0.0640 0.0360 0.001296 Recession 0.30 -0.10 -0.0300 -0.2240 0.050176 TOTAL 0.1240 Expected Return A = 12.40% Standard Deviation(Risk) = V0.02486 = 0.1577 or 15.77% Product P*[(A-A)^2] 0.009293 0.000518 0.015053 0.024864 Product P*[(B-B)^2] STOCKB: Return Squared State of Product Probability(P) Return(B) Deviation Deviation Economy (PB) (B-B ) [(B-B)^2] Boom 0.30 -0.09 -0.0270 -0.1710 0.029241 Normal 0.40 0.12 0.0480 0.0390 0.001521 Recession 0.30 0.20 0.0600 0.1190 0.014161 TOTAL 0.0810 Expected Return B = 8.10% Standard Deviation(Risk) = V0.013628 = 0.1167 or 11.67% 0.008772 0.000608 0.004248 0.013628 Product P*[(x-x)^2] TSX(X) State of Return Product Squared Economy Probability(P) Return(X) Deviation Deviation (P*x) (X-X [(X-X)^2] Boom 0.30 0.18 0.0540 0.1160 0.013456 Normal 0.40 0.10 0.0400 0.0360 0.001296 Recession 0.30 -0.10 -0.0300 -0.1640 0.026896 TOTAL 0.0640 Expected Return B = 6.40% Standard Deviation(Risk) = V0.012624 = 0.1123 or 11.23% 0.004037 0.000518 0.008069 0.012624 Probability(P) A-A B-B 0.3 0.1760 Boom Normal Recession TOTAL P*(A- A)*(B-B) 0.01156 0.00459 -0.01472 0.00144 0.40 0.30 0.2190 0.3190 0.2190 0.0360 -0.2240 Covaraince = E(P*(A-A7*(B-B) 0.00144 Correlation coefficient ('') = Cov.(A,B)/(0A*B) = 0.00144/(15.7% 11.67%) = 0.0784 Probability(P) AA X-X Boom Normal Recession TOTAL 0.3 0.40 0.30 0.1760 0.0360 -0.2240 0.1160 0.0360 -0.1640 P*(A- A)*(X-X 0.00612 0.00052 0.01102 0.01766 Covaraince = (P*A-A7*X-X) 0.01766 Correlation coefficient(') = Cov.(A,x)/(0A*ox) = 0.01766 / (15.77% * 11.23%) = 0.997 Risk of Stock B = 11.67% Risk of TSX = 11.23% Covariance and Correlation between A and B is 0.00144 and 0.0784 Covariance and Correlation between A and TSX is 0.01766 and 0.997