Question

21. Covariance and Correlation Based on the following information, calculate the expected return and standard deviation of each of the following stocks. Assume each state of the economy is equally likely to happen. What are the covariance and correlation between the returns of the two stocks?

STATE OF ECONOMY	RETURN ON STOCK A	RETURN ON STOCK B
Bear Normal Bull	-.032 .124 .193	-.103 -.025 .469

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Bear	0.15	-3.2	-0.48	-13.745	0.002833875
Good	0.5	12.4	6.2	1.855	0.000172051
Bull	0.25	19.3	4.825	8.755	0.001916251
	Expected return %=	sum of weighted return =	10.55	Sum=Variance Stock A=	0.00492
			Standard deviation of Stock A%	=(Variance)^(1/2)	7.02
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Bear	0.15	-10.3	-1.545	-19.23	0.005546894
Good	0.5	-2.5	-1.25	-11.43	0.006532245
Bull	0.25	46.9	11.725	37.97	0.036043023
	Expected return %=	sum of weighted return =	8.93	Sum=Variance Stock B=	0.04812
			Standard deviation of Stock B%	=(Variance)^(1/2)	21.94
Covariance Stock A Stock B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Bear	0.15	-13.745	-19.23	0.003964745
Good	0.5	1.855	-11.43	-0.001060133
Bull	0.25	8.755	37.97	0.008310684
			Covariance=sum=	0.011215297
		Correlation A&B=	Covariance/(std devA*std devB)=	0.728718129