Question

Given the returns and probabilities for the three possible states listed below, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 11.75 percent and 18 percent, respectively. Probability Return on Stock A Return on Stock B Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 −0.25 −0.30

Answer 1

Stock A
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(A)	(A)^2* probability
Good	0.35	0.3	0.105	-0.0175	0.000107188
OK	0.5	0.5	0.25	0.1825	0.016653125
Poor	0.15	-0.25	-0.0375	-0.5675	0.048308438
	Expected return =	sum of weighted return =	0.3175	Sum=	0.06506875
			Standard deviation of Stock A	=(sum)^(1/2)	0.25508577
Stock B
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(B)	(B)^2* probability
Good	0.35	0.5	0.175	0.365	0.04662875
OK	0.5	0.01	0.005	-0.125	0.0078125
Poor	0.15	-0.3	-0.045	-0.435	0.02838375
	Expected return =	sum of weighted return =	0.135	Sum=	0.082825
			Standard deviation of Stock B	=(sum)^(1/2)	0.287793329
Covariance Stock A Stock B:
Scenario	Probability	Actual return -expected return(A)	Actual return -expected return(B)	(A)*(B)*probability
Good	0.35	-0.0175	0.365	-0.002235625
OK	0.5	0.1825	-0.125	-0.01140625
Poor	0.15	-0.5675	-0.435	0.037029375
			Covariance=sum=	0.0233875
		Correlation A&B=	Covariance/(std devA*std devB)=	0.318578781