Question

Consider the following information: Rate of Return If State Occurs State of Economy Boom Probability of State of Economy .15 Good .55 Stock A .33 11 .02 -12 Stock B 45 10 .02 -.25 Stock C 33 17 -05 -09 .20 Poor Bust 10 a. Your portfolio is invested 25 percent each in A and C and 50 percent in B. What the expected return of the portfolio? (Do not round intermediate calculations an enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b-1. What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g. 16161.) b-2. What is the standard deviation of this portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

state of economy deviation ^2x probability Boom Good rate of return if state occurs Stock A Stock B Stock C 0.33 0.45 0.33 0.11 0.10 10.17 0.02 0.02 -0.05 -0.12 -0.25 weighted return (weight x return) weighted sum probability expected return Stock A Stock B Stock C l(sum of weighted return) 8.250% 22.500% 8.250% 39.000% 0.15 5.85% 2.750% 5.000% 4.250% 12.000% 0.55 6.60% 0.500% 1.000% -1.250% 0.250% 0.20 0.05% -3.000% -12.500% -2.250% -17.750% 0.10 -1.78% 10.73% deviation (weighted return- deviation^2 expected return) 28.275% 7.994756% 1.275% 0.016256% -10.475% 1.097256% -28.475% 8.108256% Poor Bust 0.011992134 0.00008941 0.00219451 0.00810826 Weight 25.00% 50.00% 25.00% Variance Standard deviation = variance10.5 0.02238 14.96% Expected return = 10.73% b-1) Variance = 0.02238 b-2) Standard deviation = 14.96%