Question

refer to the table of data below and answer the questions that follow

economic state probability of economic state return on stock J return on stock K

bear 0.25 -0.02 0.034

normal 0.60 0.138 0.062

bull 0.15 0.218 0.092

calculate the expected return of each stock

if a portfolio was created with from 30% of stock j and 70% of stock k what is the expected return of the portfolio?

calculate the standard deviation of each stock?

calculate the covariance between the two stocks

calculate the correlation coefficient between the two stocks

what is the portfolio standard deviation?

Answer 1

Stock J
Scenario	Probability	Return%	=rate of return% * probability
Bear	0.25	-2	-0.5
Normal	0.6	13.8	8.28
Bull	0.15	6.2	0.93
	Expected return %=	sum of weighted return =	8.71
			Standard deviation of Stock J%
Stock K
Scenario	Probability	Return%	=rate of return% * probability
Bear	0.25	3.4	0.85
Normal	0.6	6.2	3.72
Bull	0.15	9.2	1.38
	Expected return %=	sum of weighted return =	5.95

Expected return%=	Wt Stock J*Return Stock J+Wt Stock K*Return Stock K
Expected return%=	0.3*8.71+0.7*5.95
Expected return portfolio%=	6.78

Stock J
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Bear	0.25	-2	-0.5	-10.71	0.002867603
Normal	0.6	13.8	8.28	5.09	0.001554486
Bull	0.15	6.2	0.93	-2.51	9.45015E-05
	Expected return %=	sum of weighted return =	8.71	Sum=Variance Stock J=	0.00452
			Standard deviation of Stock J%	=(Variance)^(1/2)	6.72
Stock K
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Bear	0.25	3.4	0.85	-2.55	0.000162563
Normal	0.6	6.2	3.72	0.25	0.00000375
Bull	0.15	9.2	1.38	3.25	0.000158438
	Expected return %=	sum of weighted return =	5.95	Sum=Variance Stock K=	0.00032
			Standard deviation of Stock K%	=(Variance)^(1/2)	1.8

Covariance Stock J Stock K:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Bear	0.25	-10.71	-2.55	0.000682763
Normal	0.6	5.09	0.25	0.00007635
Bull	0.15	-2.51	3.25	-0.000122363
			Covariance=sum=	0.00063675
		Correlation A&B=	Covariance/(std devA*std devB)=	0.525761813

Portfolio std dev

Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.3^2*0.06721^2+0.7^2*0.01802^2+2*0.3*0.7*0.06721*0.01802*0.52576
Variance	0.00083
Standard deviation=	(variance)^0.5
Standard deviation=	2.88%