Question

Rate of Return If State Occurs State of Probability of State of Economy Economy Stock A Stock B Stock C .55 .06 14 Boom Bust .45 .34 -.07 10 .02 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the variance of a portfolio invested 22 percent each in A and B and 56 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 161616.)

Answer 1

state of economy rate of return if state occurs Stock A stock B Stock C 0.06 0.14 0.34 0.10 0.02 -0.70 weighted return (weight x return) Stock A Stock B Stock C 2.000% 4.667% 11.333% 3.333% 0.667% -23.333% Boom Bust weighted sum probability expected return (sum of weighted return) 18.000% 0.55 9.90% -19.333% 0.45 -8.70% 1.20% Weight 33.33% 33.33% 33.33% Answer: Expected return = 1.20% [if equally weighted]

state of economy deviation “2x probability rate of return if state occurs Stock A Stock B Stock C 0.06 0.14 0.34 0.10 0.02 -0.70 weighted return (weight x return) weighted sum probability expected return Stock A Stock B Stock C l(sum of weighted return) 1.320% 3.080% 19.040% 23.440% 0.55 12.89% 2.200% 0.440% -39.200% -36.560% 0.45 -16.45% -3.56% deviation (weighted return- deviation^2 expected return) 27.000% 7.290000% -33.000% 10.890000% Boom Bust 0.040095000 0.04900500 Weight 22.00% 22.00% 56.00% Variance Standard deviation = variance10.5 0.08910 29.85% Answer: Variance 0.089100 [weighted not equally]