Question

Consider the following information on a portfolio of three stocks Probability of State of State of Stock A Stock B Stock C Economy Rate of Return Rate of Return Rate of Return Economy 14 Boom 03 .33 .59 Normal 54 11 13 21 Bust .32 17 -12 -36 a. If your portfolio is invested 38 percent each in A and B and 24 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 3.8 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.) a. Expected return Variance Standard deviation b. Expected risk premium % %

Answer 1

weighted return state of economy rate of return if state occurs (weight x return) Expected return Stock A Stock B Stock C Stock A Stock Stock Cl(sum of weighted return) Boom 0.03 0.33 0.59 0.01 0.13 0.14 27.84% Normal 0.11 0.13 0.21 0.04 0.05 0.05 14.16% Bust 0.17 -0.12 -0.36 0.06 -0.05 -0.09 -6.74% deviation probability expected return | (weighted return- deviation^2 deviation ^2x probability expected return) 0.14 3.90% 18.45% 3.41% 0.004767082 0.54 7.65% 4.77% 0.23% 0.00123010 0.32 -2.16% -16.13% 2.60% 0.00832277 9.39% Variance 0.0143 Weight 38.00% 38.00% 24.00% al Portfolio expected return = 9.39% Variance = 0.01432 Standard deviation = variance^0.5 = 11.97% 5.59%