Question

Instructor-created question Expected return and standard deviation. Use the following information to answer the questions Return on Asset S in State Return on Probability Return on Asset R in State of Economy Boom Growth Stagnant Recession Asset T in of State State State 0.28 0.39 0.22 0.11 0.040 0.040 0.040 0.040 0.250 0.140 0.180 - 0.030 0.440 0.300 0.010 -0.165 a. What is the expected return of a portfolio with equal investment in all three assets? b. What is the portfolio's variance and standard deviation? a. What is the expected return of a portfolio with equal investment in all three assets? (Round to four decimal places.) b. What is the portfolio's variance? (Round to four decimal places.) What is the portfolio's standard? (Round to four decimal places.)

Answer 1

Asset R
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.28	4	1.12	0	0
Growth	0.39	4	1.56	0	0
Stagnant	0.22	4	0.88	0	0
Recession	0.11	4	0.44	0	0
	Expected return %=	sum of weighted return =	4	Sum=Variance Asset R=	0
			Standard deviation of Asset R%	=(Variance)^(1/2)	0
Asset S
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.28	25	7	8.91	0.002222867
Growth	0.39	14	5.46	-2.09	0.000170356
Stagnant	0.22	18	3.96	1.91	8.02582E-05
Recession	0.11	-3	-0.33	-19.09	0.004008709
	Expected return %=	sum of weighted return =	16.09	Sum=Variance Asset S=	0.00648
			Standard deviation of Asset S%	=(Variance)^(1/2)	8.05
Asset T
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Boom	0.28	44	12.32	21.575	0.013033458
Growth	0.39	30	11.7	7.575	0.002237844
Stagnant	0.22	1	0.22	-21.425	0.010098674
Recession	0.11	-16.5	-1.815	-38.925	0.016666712
	Expected return %=	sum of weighted return =	22.43	Sum=Variance Asset T=	0.04204
			Standard deviation of Asset T%	=(Variance)^(1/2)	20.5
Covariance Asset R Asset S:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Boom	0.28	0.0000	8.91	0
Growth	0.39	0	-2.09	0
Stagnant	0.22	0.00	1.91	0
Recession	0.11	0.00%	-19.09	0
			Covariance=sum=	0
		Correlation A&B=	Covariance/(std devA*std devB)=	0
Covariance Asset R Asset T:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
Boom	0.28	0	21.575	0
Growth	0.39	0	7.575	0
Stagnant	0.22	0.00%	-21.425	0
Recession	0.11	0	-38.925	0
			Covariance=sum=	0
		Correlation A&C=	Covariance/(std devA*std devC)=	0
Covariance Asset S Asset T:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
Boom	0.28	8.91	21.575	0.005382531
Growth	0.39	-2.09	7.575	-0.000617438
Stagnant	0.22	1.91	-21.425	-0.000900278
Recession	0.11	-19.09	-38.925	0.008173861
			Covariance=sum=	0.012038675
		Correlation B&C=	Covariance/(std devB*std devC)=	0.729295559
	a. Expected return%=	Wt Asset R*Return Asset R+Wt Asset S*Return Asset S+Wt Asset T*Return Asset T
	Expected return%=	0.3333*4+0.3333*16.09+0.3333*22.43
	Expected return%=	14.17
	b. Variance	=w2A*σ2(RA) + w2B*σ2(RB) + w2C*σ2(RC)+ 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB) + 2*(wA)*(wC)*Cor(RA, RC)*σ(RA)*σ(RC) + 2*(wC)*(wB)*Cor(RC, RB)*σ(RC)*σ(RB)
	Variance	=0.3333^2*0^2+0.3333^2*0.08051^2+0.3333^2*0.20503^2+2*(0.3333*0.3333*0*0.08051*0+0.3333*0.3333*0.08051*0.20503*0.7293+0.3333*0.3333*0*0*0.20503)
	Variance	0.00806
	c. Standard deviation=	(variance)^0.5
	Standard deviation=	8.98%