Question

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	0.3333	-3.2	-1.06656	-12.69905	0.005374991
Normal	0.3333	12.4	4.13292	2.90095	0.000280489
Bull	0.3333	19.3	6.43269	9.80095	0.003201634
	Expected return %=	sum of weighted return =	9.5	Sum=Variance Stock A=	0.00886
			Standard deviation of Stock A%	=(Variance)^(1/2)	9.41
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Bear	0.3333	-10.3	-3.43299	-7.596937	0.001923589
Normal	0.3333	-2.5	-0.83325	0.203063	1.37435E-06
Bull	0.3333	4.69	1.563177	7.393063	0.00182173
	Expected return %=	sum of weighted return =	-2.7	Sum=Variance Stock B=	0.00375
			Standard deviation of Stock B%	=(Variance)^(1/2)	6.12
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	0.3333	-12.69905	-7.596937	0.003215475
Normal	0.3333	2.90095	0.203063	1.96339E-05
Bull	0.3333	9.80095	7.393063	0.00241506
			Covariance=sum=	0.005650168
		Correlation A&B=	Covariance/(std devA*std devB)=	0.980824107