Question

You are given the following information: State of Return on Economy Bear Normal Bull Stock A 104 113 .075 Return on Return Stock B -.047 .150 235 Assume each state of the economy is equally likely to happen. a. Calculate the expected return of each stock. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. Calculate the standard deviation of each stock. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c. What is the covariance between the returns of the two stocks? (A negative answer should be indicated by a minus sign, Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 161616.) d. What is the correlation between the returns of the two stocks? (A negative answer should be indicated by a minus sign, Do not round intermediate calculations and round your answer to 4 decimal places, e.g., .1616.) Stock A Stock B Stock A Stock B Covariance Correlation

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Bear	0.3333	10.4	3.46632	0.66764	1.48566E-05
Normal	0.3333	11.3	3.76629	1.56764	8.19083E-05
Bull	0.3333	7.5	2.49975	-2.23236	0.000166098
	a. Expected return %=	sum of weighted return =	9.73	Sum=Variance Stock A=	0.00026
			b. Standard deviation of Stock A%	=(Variance)^(1/2)	1.62
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Bear	0.3333	-4.7	-1.56651	-15.96554	0.008495766
Normal	0.3333	15	4.9995	3.73446	0.000464827
Bull	0.3333	23.5	7.83255	12.23446	0.004988901
	a. Expected return %=	sum of weighted return =	11.27	Sum=Variance Stock B=	0.01395
			b. Standard deviation of Stock B%	=(Variance)^(1/2)	11.81
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	0.66764	-15.96554	-0.000355272
Normal	0.3333	1.56764	3.73446	0.000195123
Bull	0.3333	-2.23236	12.23446	-0.0009103
			c. Covariance=sum=	-0.001071
		d. Correlation A&B=	Covariance/(std devA*std devB)=	-0.5590