Question

What is the standard deviation of the returns on a portfolio that is invested in Stocks A, B, and C? Twenty percent of the portfolio is invested in Stock A and 35 percent is invested in Stock C. Probability of State of Rate of Return State of Economy Economy if State Occurs Stock Stock A Stock B Boom 04 .17 .09 .09 Normal .81 .08 .06 Recession .15 - 24 .02 - a. 3.28% O b. 4.91% OC 5.65% O d. 7.22%

Answer 1

Answer is 5.65%

Weight of Stock A = 0.20
Weight of Stock B = 0.45
Weight of Stock C = 0.35

Boom:

Expected Return = 0.20 * 0.17 + 0.45 * 0.09 + 0.35 * 0.09
Expected Return = 0.1060

Normal:

Expected Return = 0.20 * 0.08 + 0.45 * 0.06 + 0.35 * 0.08
Expected Return = 0.0710

Recession:

Expected Return = 0.20 * (-0.240 + 0.45 * 0.02 + 0.35 * (-0.13)
Expected Return = -0.0845

Expected Return of Portfolio = 0.04 * 0.1060 + 0.81 * 0.0710 + 0.15 * (-0.0845)
Expected Return of Portfolio = 0.049075

Variance of Portfolio = 0.04 * (0.1060 - 0.049075)^2 + 0.81 * (0.0710 - 0.049075)^2 + 0.15 * (-0.0845 - 0.049075)^2
Variance of Portfolio = 0.00319533

Standard Deviation of Portfolio = (0.00319533)^(1/2)
Standard Deviation of Portfolio = 0.0565 or 5.65%