Question

9. Returns and Standard Deviations. Consider the following information: 101 State of Economy Probability of State of Economy Rate of Return If State Occurs Stock A Stock B Stock C .02 Boom Bust .60 .40 .15 .03 .34 -.08 .16 a. What is the expected return on an equally weighted portfolio of these three stocks? b. What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? c ider the following information:

Answer 1

Answer to Question 9:

Part a:

Weight of Stock A = 1/3
Weight of Stock B = 1/3
Weight of Stock C = 1/3

Boom:

Expected Return = (1/3) * 0.15 + (1/3) * 0.02 + (1/3) *0.34
Expected Return = 0.1700

Bust:

Expected Return = (1/3) * 0.03 + (1/3) * 0.16 + (1/3) * (-0.08)
Expected Return = 0.0367

Expected Return of Portfolio = 0.60 * 0.1700 + 0.40 * 0.0367
Expected Return of Portfolio = 0.1167 or 11.67%

Part b:

Weight of Stock A = 0.20
Weight of Stock B = 0.20
Weight of Stock C = 0.60

Boom:

Expected Return = 0.20 * 0.15 + 0.20 * 0.02 + 0.60 *0.34
Expected Return = 0.2380

Bust:

Expected Return = 0.20 * 0.03 + 0.20 * 0.16 + 0.60 * (-0.08)
Expected Return = -0.0100

Expected Return of Portfolio = 0.60 * 0.2380 + 0.40 * (-0.0100)
Expected Return of Portfolio = 0.1388 or 13.88%

Variance of Portfolio = 0.60 * (0.2380 - 0.1388)^2 + 0.40 * (-0.0100 - 0.1388)^2
Variance of Portfolio = 0.01476