Question

Problem 13-9 Returns and Variances [LO1] Consider the following information: Rate of Return If State Occurs State of Probability of - State of State of Economy Economy Stock B Boom Stock A .11 12 .65 35 .19 Stock C 37 -05 Bust .06 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return 16.03% b. What is the variance of a portfolio invested 16 percent each in A and B and 68 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) Variance

Answer 1

state of economy rate of return if state occurs Stock A Stock B Stock 0.11 0.19 0.37 0.12 | 0.06 -0.05 weighted return (weight x return) Stock A Stock B Stock C 3.667% 6.333% 12.333% 4.000% 2.000% -1.667% Boom Bust weighted sum probability expected return (sum of weighted return) 22.333% 0.65 14.52% 4.333% 0.35 1.52% 16.03% Weight 33.33% 33.33% 33.33% Answer: Expected return = 16.03% [if equally weighted]

deviation 2x probability state of economy rate of return if state occurs Stock A Stock B Stock C Boom 0.11 0.19 0.37 Bust 0.12 0.06 -0.05 weighted return (weight x return) weighted sum probability expected return Stock A Stock B Stock C l(sum of weighted return) 1.760% 3.040% 25.160% 29.960% 0.65 19.47% 1.920% 0.960% -3.400% -0.520% 0.35 -0.18% 19.29% deviation (weighted return- deviation^2 expected return) 10.668% 1.138062% -19.812% 3.925153% 0.007397405 0.01373804 Weight 16.00% 16.00% 68.00% Variance Standard deviation = variance10.5 0.02114 14.54% Answer: Variance 0.021135] [weighted not equally]