Consider the following information on a portfolio of three stocks: a. If your po

Question

Consider the following information on a portfolio of three stocks:

a. If your portfolio is invested 42 percent each in A and B and 16 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places, e.g., 32.16161. Enter your other answers as a percent rounded to 2 decimal places, e.g., 32.16.)

b. If the expected T-bill rate is 4.15 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected risk premium             

State of Probability of Stock A Stock B Stock C Economy State of Economy Rate of Return Rate of Return Rate of Return Boom .15 .10 .35 .52 Normal .52 .18 .20 .28 Bust .33 .19 .19 .38

Explanation / Answer

a.

Expected return of portfolio in each state is the weighted average of individual probabilities

Expected return in Boom = 0.42*0.1 + 0.42*0.35 + 0.16*0.52 = 0.2722

Expected return of B = 0.42*0.35+0.42*0.2+0.16*-0.19 = 0.2044

Expected return of C = 0.42*0.52+0.42*0.28+0.16*-0.38 = -0.0608

Expected return of the portfolio = 0.15*0.2722+0.52*0.2044+0.33*-0.0608 = 0.1271 = 12.71%

Variance is the sum of squared deviations form the mean times the probability

Vairance = 0.15*(0.1271-0.2722)^2 + 0.52*(0.1271-0.2044)^2 + 0.33*(0.1271-(-0.0608))^2 = 0.0179

Std dev = sqrt(Variance) = 0.0179^(1/2) = 0.13385 = 13.385%

b.

Expected risk premium = expected return - risk free rate

= 12.71%-4.15% = 8.56%

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