Question

Consider the following information:

				Rate of Return If State Occurs
State of Economy	Probability of State of Economy			Stock A			Stock B
Recession		.18			.07			−.18
Normal		.55			.10			.11
Boom		.27			.15			.28

Calculate the expected return for the two stocks. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	Expected return
Stock A	%
Stock B	%

Calculate the standard deviation for the two stocks. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	Standard deviation
Stock A	%
Stock B	%

Answer 1

Stock A:

Expected Return = 0.18 * 0.07 + 0.55 * 0.10 + 0.27 * 0.15
Expected Return = 0.1081 or 10.81%

Variance = 0.18 * (0.07 - 0.1081)^2 + 0.55 * (0.10 - 0.1081)^2 + 0.27 * (0.15 - 0.1081)^2
Variance = 0.00077139

Standard Deviation = (0.00077139)^(1/2)
Standard Deviation = 0.0278 or 2.78%

Stock B:

Expected Return = 0.18 * (-0.18) + 0.55 * 0.11 + 0.27 * 0.28
Expected Return = 0.1037 or 10.37%

Variance = 0.18 * (-0.18 - 0.1037)^2 + 0.55 * (0.11 - 0.1037)^2 + 0.27 * (0.28 - 0.1037)^2
Variance = 0.02290131

Standard Deviation = (0.02290131)^(1/2)
Standard Deviation = 0.1513 or 15.13%