Question

Consider the following information on a portfolio of three stocks:

State of	Probability of			Stock A			Stock B			Stock C
Economy	State of Economy			Rate of Return			Rate of Return			Rate of Return
Boom		.12			.09			.34			.53
Normal		.53			.17			.19			.27
Bust		.35			.18		−	.18		−	.37

a. If your portfolio is invested 36 percent each in A and B and 28 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places, e.g., 32.16161. Enter your other answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return		%
Variance
Standard deviation		%

b. If the expected T-bill rate is 4.1 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected risk premium             %

Answer 1

a

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.12	9	1.08	-1.09	1.42572E-05
Normal	0.53	17	9.01	6.91	0.002530649
	Expected return %=	sum of weighted return =	10.09	Sum=Variance Stock A=	0.00254
			Standard deviation of Stock A%	=(Variance)^(1/2)	5.04
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.12	34	4.08	19.85	0.00472827
Normal	0.53	19	10.07	4.85	0.001246693
	Expected return %=	sum of weighted return =	14.15	Sum=Variance Stock B=	0.00597
			Standard deviation of Stock B%	=(Variance)^(1/2)	7.73
Covariance Stock A Stock B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Boom	0.12	-1.09	19.85	-0.000259638
Normal	0.53	6.91	4.85	0.001776216
			Covariance=sum=	0.001516578
		Correlation A&B=	Covariance/(std devA*std devB)=	0.388920738
	Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B
	Expected return%=	0.36*10.09+0.36*14.15
	Expected return%=	8.73
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.36^2*0.05045^2+0.36^2*0.0773^2+2*0.36*0.36*0.05045*0.0773*0.38892
	Variance	0.0015
	Standard deviation=	(variance)^0.5
	Standard deviation=	3.87%

b

expected risk premium = portfolio return-risk free rate = 8.73-4.1=4.63%