Question

2) What is the expected return and standard deviation of a portfolio that is invested in stocks A, B, and C? Twenty five percent of the portfolio is invested in stock A, 40 percent is invested in stock C, and the remaining is invested in stock B. (20 pts) Probability of State of Economy State of Economy Boom Normal Recession 5% Returns if State Occurs Stock A Stock B Stock C 17% 6% 22% 8% 10% 15% -3% 19% -25% 55% 40%

Answer 1

Weight of Stock A = 25%
Weight of Stock B = 35%
Weight of Stock C = 40%

Boom:

Expected Return = 0.25 * 0.17 + 0.35 * 0.06 + 0.40 * 0.22
Expected Return = 0.1515

Normal:

Expected Return = 0.25 * 0.08 + 0.35 * 0.10 + 0.40 * 0.15
Expected Return = 0.1150

Recession:

Expected Return = 0.25 * (-0.03) + 0.35 * 0.19 + 0.40 * (-0.25)
Expected Return = -0.0410

Expected Return of Portfolio = 0.05 * 0.1515 + 0.55 * 0.1150 + 0.40 * (-0.0410)
Expected Return of Portfolio = 0.0544 or 5.44%

Variance of Portfolio = 0.05 * (0.1515 - 0.0544)^2 + 0.55 * (0.1150 - 0.0544)^2 + 0.40 * (-0.0410 - 0.0544)^2
Variance of Portfolio = 0.0061316825

Standard Deviation of Portfolio = (0.0061316825)^(1/2)
Standard Deviation of Portfolio = 0.0783 or 7.83%