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 Probability of State of Economy Stock B Stock A 12 69 .31 27 -.07 06 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 retum b. What is the variance of a portfolio invested 24 percent each in A and B and 52 percent in C? Dnot round intermediate calculations and round your answer to 5 decimal places, eg. 32.16161.) Variance of a portfolio

Explanation / Answer

a.

Expected return is the weighted average of individual returns

Expected return in Boom = 1/3*0.12 + 1/3*0.06 +1/3*0.27 = 0.15 = 15%

Expected return in Bust = 1/3*0.16+1/3*0.22+1/3*-0.07 = 0.1033 = 10.33%

Expected return = 0.69*0.15 + 0.31*0.1033 = 0.1355 = 13.55%

b.

Find the expected return of the portfolio:

Expected return in Boom = 0.24*0.12+0.24*0.06 + 0.52*0.27 = 0.1836

Expected return in Bust = 0.24*0.16 + 0.24*0.22 + 0.52*-0.07 = 0.0548

Expected return = 0.69*0.1836 + 0.31*0.0548 = 0.1437 = 14.37%

Variance is the sum of squared deviations from the mean times the probability:

Variance = 0.69*(0.1437-0.1836)^2 + 0.31*(0.1437-0.0548)^2 = 0.00355

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