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 0.72 0.25 0.11 0.07 Bust 0.28 0.17 0.07 0.11 Requirement 1: What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.) Requirement 2: What is the variance of a portfolio invested 10 percent each in A and B and 80 percent in C? (Do not round your intermediate calculations.)

Answer 1

Answer 1.

Weight of each Stock = 1/3

Boom:

Expected Return = 1/3 * 0.25 + 1/3 * 0.11 + 1/3 * 0.07
Expected Return = 0.1433

Bust:

Expected Return = 1/3 * 0.17 + 1/3 * 0.07 + 1/3 * 0.11
Expected Return = 0.1167

Expected Return of Portfolio = 0.72 * 0.1433 + 0.28 * 0.1167
Expected Return of Portfolio = 0.1359
Expected Return of Portfolio = 13.59%

Answer 2.

Weight of Stock A = 0.10
Weight of Stock B = 0.10
Weight of Stock C = 0.80

Boom:

Expected Return = 0.10 * 0.25 + 0.10 * 0.11 + 0.80 * 0.07
Expected Return = 0.092

Bust:

Expected Return = 0.10 * 0.17 + 0.10 * 0.07 + 0.80 * 0.11
Expected Return = 0.112

Expected Return of Portfolio = 0.72 * 0.092 + 0.28 * 0.112
Expected Return of Portfolio = 0.0976

Variance = 0.72 * (0.092 - 0.0976)^2 + 0.28 * (0.112 - 0.0976)^2
Variance = 0.000081