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 0.66 0.27 0.33 0.29 Bust 0.34 0.19 0.15 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

State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	66%	27%	33%	29%
Bust	34%	19%	15%	11%

Boom return = 66% * (27% + 33% + 29%)/ 3

Boom return = 19.58%

Bust return = 34% * (19% + 15% + 11%)/ 3

Bust return = 5.1%

Expected Return = 19.58% + 5.1%

Expected Return = 24.680%

Part B - Variance

Boom return = 0.1 * 27% + 0.1 * 33% + 0.8 * 29%

Boom return = 29.2%

Bust return = 0.1 * 19% + 0.1 * 15% + 0.8 * 11%

Bust return = 12.20%

Expected Return = 0.66 * 29.2% + 0.34 * 12.20%

Expected Return = 23.42%

Variance = 0.66 * (29.2% - 23.42%)² + 0.34 * (12.20%% - 23.42%)²

Variance = 0.006485