Question

Consider the following information on a portfolio of three stocks: Probability of State of Economy State of Economy Boom Normal Bust Stock A Stock B Stock C Rate of Return Rate of Return Rate of Return 47 .25 .23 -24 - 38 .05 .35 .52 34 25 23 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 4.4 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 return Variance Standard deviation Expected risk premium

Answer 1

a. Expected return
Boom = 0.42 x 0.05 + 0.42 x 0.35 + 0.16 x 0.47 = 0.2432
Normal = 0.42 x 0.13 + 0.42 x 0.25 + 0.16 x 0.23 = 0.1964
Bust = 0.42 x 0.19 + 0.42 x -0.24 + 0.16 x -0.38 = -0.0818

Expected return of portfolio = 0.14 x 0.2432 + 0.52 x 0.1964 + 0.34 x -0.0818 = 0.108364 or 10.84%

Variance = 0.42 x (0.2432-0.108364)² + 0.42 x (0.1964-0.108364)² + 0.42 x (-0.0818-0.108364)² = 2.61(%)²

Standard Deviation is square root of Variance = 1.62%

b. Expected Risk Premium = Expected Return - Risk free rate
= 10.84% - 4.40% = 6.44%