Question

Consider the following information: Rate of Return if State Occurs Probability of State of Economy State of Economy Boom Stock A Stock B Stock C 66 09 03 .34 Bust 34 23 29 -14 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 21 percent each in A and B and 58 percent in C? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) a. Expected return b. Variance of portfolio

Answer 1

state of economy rate of return if state occurs Stock A Stock B Stock 0.09 0.03 0.34 0.23 0.29 -0.14 weighted return (weight x return) weighted sum probability expected return Stock A Stock B Stock C l(sum of weighted return) 3.000% 1.000% 11.333% 15.333% 0.66 7.667% 9.667% -4.667% 12.667% 0.34 4.31% 14.43% 10.12% Boom Bust Weight 33.33% 33.33% 33.33% Answer: Expected return = 14.43% [if equally weighted]

deviation ^2x probability state of economy rate of return if state occurs Stock A Stock B Stock C Boom 0.09 0.03 0.34 Bust 0.23 0.29 -0.14 weighted return (weight x return) weighted sum probability expected return Stock A Stock B Stock C l(sum of weighted return) | 1.890% 0.630% 19.720% 22.240% 0.66 14.68% 4.830% 6.090% -8.120% 2.800% 0.34 0.95% 15.63% deviation (weighted return- deviation^2 expected return) 6.610% 0.436868% -12.830% 1.646192% 0.002883330 0.00559705 Weight 21.00% 21.00% 58.00% Variance Standard deviation = variance10.5 0.00848 9.21% Answer: Variance 0.00848 [weighted not equally]