Question

Consider the following information on a portfolio of three stocks: State of Probability of State of Economy Economy .13 Stock A Stock B Stock C Rate of Return Rate of Return Rate of Return .50 .20 .16 -21 Boom Normal .32 .02 10 .55 .32 Bust -35 a. If your portfolio is invested 40 percent each in A and B and 20 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 4.25 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.)

Answer 1

Answer a.

Weight of Stock A = 40%
Weight of Stock B = 40%
Weight of Stock C = 20%

Boom:

Expected Return = 0.40 * 0.02 + 0.40 * 0.32 + 0.20 * 0.50
Expected Return = 0.2360

Normal:

Expected Return = 0.40 * 0.10 + 0.40 * 0.22 + 0.20 * 0.20
Expected Return = 0.1680

Bust:

Expected Return = 0.40 * 0.16 + 0.40 * (-0.21) + 0.20 * (-0.35)
Expected Return = -0.0900

Expected Return of Portfolio = 0.13 * 0.2360 + 0.55 * 0.1680 + 0.32 * (-0.0900)
Expected Return of Portfolio = 0.0943 or 9.43%

Variance of Portfolio = 0.13 * (0.2360 - 0.0943)^2 + 0.55 * (0.1680 - 0.0943)^2 + 0.32 * (-0.0900 - 0.0943)^2
Variance of Portfolio = 0.01647

Standard Deviation of Portfolio = (0.01647)^(1/2)
Standard Deviation of Portfolio = 0.1283 or 12.83%

Answer b.

Expected Risk Premium of Portfolio = Expected Return of Portfolio - Risk-free Rate
Expected Risk Premium of Portfolio = 9.43% - 4.25%
Expected Risk Premium of Portfolio = 5.18%