Consider the following information Rate of Return if State Occurs State of Econo

Question

Consider the following information Rate of Return if State Occurs State of Economy Boom Bust Probability of State of Economy Stock A 70 30 08 .27 Stock B 02 Stock C 38 18 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.) Expected return b. What is the variance of a portfolio invested 25 percent each in A and B and 50 percent in C? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance of a portfolio

Explanation / Answer

1.

a.

Expected return is the weighted average of individual returns

Expected return of A = 0.7*0.08 + 0.3*0.27 = 0.1370

Expected return of B = 0.7*0.02 + 0.3*0.33 = 0.1130

Expected return of C = 0.7*0.38 + 0.3*-0.18 = 0.2120

Expected return of portfolio = 1/3*0.137 + 1/3*0.113 + 1/3*0.212 = 0.1540 = 15.40%

b.

Expected return of portfolio = 0.25*0.137 + 0.25*0.113 + 0.5*0.2120 = 0.1685 = 16.85%

Expected return in Boom = 0.25*0.08 + 0.25*0.113 + 0.5*0.38 = 0.2150

Expected return in Bust = 0.25*0.27 + 0.25*0.33 + 0.5*-0.18 = 0.06

Vairance is the sum of squared deviations from the mean times the probability

Variance = 0.7*(0.1685-0.2150)^2 + 0.3*(0.1685-0.06)^2 = 0.50453%

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