Question

Consider the following information:

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	0.20	0.19	0.46	0.32
Good	0.40	0.12	0.19	0.14
Poor	0.10	0.04	–0.09	–0.05
Bust	0.30	–0.04	–0.30	–0.09

a. Your portfolio is invested 20 percent each in A and C and 60 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b-1. What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places.)

b-2. What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

   

Answer 1

Answer a.

Boom:

Expected Return = 0.20 * 0.19 + 0.60 * 0.46 + 0.20 * 0.32
Expected Return = 0.3780

Good:

Expected Return = 0.20 * 0.12 + 0.60 * 0.19 + 0.20 * 0.14
Expected Return = 0.1660

Poor:

Expected Return = 0.20 * 0.04 + 0.60 * (-0.09) + 0.20 * (-0.05)
Expected Return = -0.0560

Bust:

Expected Return = 0.20 * (-0.04) + 0.60 * (-0.30) + 0.20 * (-0.09)
Expected Return = -0.2060

Answer a.

Expected Return of Portfolio = 0.20 * 0.3780 + 0.40 * 0.1660 + 0.10 * (-0.0560) + 0.30 * (-0.2060)
Expected Return of Portfolio = 0.0746 or 7.46%

Answer b-1.

Variance of Portfolio = 0.20 * (0.3780 - 0.0746)^2 + 0.40 * (0.1660 - 0.0746)^2 + 0.10 * (-0.0560 - 0.0746)^2 + 0.30 * (-0.2060 - 0.0746)^2
Variance of Portfolio = 0.04708

Answer b-2.

Standard Deviation of Portfolio = (0.04708)^(1/2)
Standard Deviation of Portfolio = 0.2170 or 21.70%