Question

You are given the following information:

State of Economy	Return on Stock A	Return on Stock B
Bear	.109	−	.052
Normal	.108		.155
Bull	.080		.240

Assume each state of the economy is equally likely to happen.

Calculate the expected return of each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	Expected return
Stock A	%
Stock B	%

  
Calculate the standard deviation of each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	Standard deviation
Stock A	%
Stock B	%

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., 32.161616.)

Covariance             

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., 32.1616.)

Correlation            

Answer 1

			STOCK A
		p	A	A*p	Da=A-0.099	Ea=(Da^2)	Ea*p
	State of Economy	Probability	Return of stock A	Return*Probability	Deviation from expected return	Deviation Squared	(Deviation Squared)*(Probability)
	Bear	(1/3)	0.109	0.036333	0.01	0.0001	0.0000333
	Normal	(1/3	0.108	0.036	0.009	0.000081	0.000027
	Bull	(1/3)	0.08	0.026667	-0.019	0.000361	0.000120333
			SUM	0.099		SUM	0.0001807
	Expected Return of stockA	0.099
	Variance of Stock A	0.0001807
	Standard Deviation =Square Root of Variance
	Standard Deviation of Stock A	0.01344123	(Square Root of 0.0001807)
			STOCK B
		p	B	B*p	Db=B-0.149	Eb=(Db^2)	Eb*p
	State of Economy	Probability	Return of stock B	Return*Probability	Deviation from expected return	Deviation Squared	(Deviation Squared)*(Probability)
	Bear	(1/3)	0.052	0.017333	-0.097	0.0094	0.0031363
	Normal	(1/3	0.155	0.051667	0.006	0.000036	0.000012
	Bull	(1/3)	0.240	0.08	0.091	0.008281	0.002760333
			SUM	0.149		SUM	0.0059087
	Expected Return of stockB	0.149
	Variance of Stock B	0.0059087
	Standard Deviation =Square Root of Variance
	Standard Deviation of Stock B	0.076867852	(Square Root of 0.0059087)
			Expected Return
		Stock A	9.90%
		Stock B	14.90%
			Standard Deviation
		Stock A	1.34%
		Stock B	7.69%
	CALCULATION OF COVARINCE
		p	Da	Db	F=Da*Db*p
	State of Economy	Probability	Deviation from expected return of StockA	Deviation from expected return of StockB	(Deviation of A)*(Deviation of B)* Probability
	Bear	(1/3)	0.01	-0.097	-0.0003233
	Normal	(1/3	0.009	0.006	0.000018
	Bull	(1/3)	-0.019	0.091	-0.0005763
				SUM	-0.0008817
	Covariance between return of A&B	-0.000881667
	Correlation between Stock A & Stock B=Covariance (a,b)/((Standard Deviation of A)*(Standard Deviation of B))
	Correlation between return of A&B	-0.853337165	(-0.0008817/(0.01344123*0.076867852)