Question

Problem 13-9 Returns and Variances (L01, 2) Consider the following information: State of Economy Boom Bust Probability of State of Economy 0.58 0.42 Rate of Return if State Occurs Stock A Stock B Stock C 0.07 0.15 0.33 0.15 0.05 -0.07 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Round the final answer to 2 decimal places.) Expected return % b. What is the variance of a portfolio invested 20% each in A and B and 60% in C? (Do not round intermediate calculations. Round the final answer to 6 decimal places.) Variance

Answer 1

a) Expected return :

Expected return A= 0.58*0.07+0.42*0.15= 0.1036

Expected return B = 0.58*0.15+0.42*0.05= 0.108

Expected return C = 0.58*0.33+0.42*(-0.07)=0.162

Expected return of portfolio :

Probability (1)	Return (2)	Expected return (3) (1*2)
1/3	0.1036	0.035
1/3	0.108	0.036
1/3	0.162	0.054
	Expected return	0.125

Expected return of portfolio = 0.125 or 12.5%

b) Calculation of Variance of portfolio:

Expected return of portfolio:

Probability (1)	Return (2)	Expected return (3) (1*2)
0.2	0.1036	0.0207
0.2	0.108	0.0216
0.6	0.162	0.0972
	Expected return	0.1395

Expected return = 0.1395 or 13.95%

Calculation of Variance:

Probability (1)	Return-Expected return (2)	Square of Return-Expected return (3)	Variance (4) (1*3)
0.2	0.1036-0.1395=-0.0359	(-0.0359)^2=0.00128	0.000256
0.2	0.108-0.1395=-0.0315	(-0.0315)^2=0.00099	0.000198
0.6	0.162-0.1395=0.0225	(0.0225)^2=0.00051	0.000306
		Variance	0.00076

Variance = 0.00076