Question

2. Calculate the expected return, variance, and standard deviations of stock A, stock B, and obtain the expected return of an equally weighted portfolio of both (meaning 50% in A, and 50% in B). Please show all work and formulas used.

Scenario	Probability	A	B
Boom	1/3	-4%	9%
Normal	1/3	8%	4%
Recession	1/3	20%	-4%

Answer 1

Answer a.

Stock A:

Expected Return = (1/3) * (-0.04) + (1/3) * 0.08 + (1/3) * 0.20
Expected Return = 0.08 or 8.00%

Variance = (1/3) * (-0.04 - 0.08)^2 + (1/3) * (0.08 - 0.08)^2 + (1/3) * (0.20 - 0.08)^2
Variance = 0.0096

Standard Deviation = (0.0096)^(1/2)
Standard Deviation = 0.0980 or 9.80%

Answer b.

Stock B:

Expected Return = (1/3) * 0.09 + (1/3) * 0.04 + (1/3) * (-0.04)
Expected Return = 0.03 or 3.00%

Variance = (1/3) * (0.09 - 0.03)^2 + (1/3) * (0.04 - 0.03)^2 + (1/3) * (-0.04 - 0.03)^2
Variance = 0.002867

Standard Deviation = (0.002867)^(1/2)
Standard Deviation = 0.0535 or 5.35%

Answer c.

Boom:

Expected Return = 0.50 * (-0.04) + 0.50 * 0.09
Expected Return = 0.025

Normal:

Expected Return = 0.50 * 0.08 + 0.50 * 0.04
Expected Return = 0.06

Recession:

Expected Return = 0.50 * 0.20 + 0.50 * (-0.04)
Expected Return = 0.08

Expected Return of Portfolio = (1/3) * 0.025 + (1/3) * 0.06 + (1/3) * 0.08
Expected Return of Portfolio = 0.055 or 5.50%

Variance of Portfolio = (1/3) * (0.025 - 0.055)^2 + (1/3) * (0.06 - 0.055)^2 + (1/3) * (0.08 - 0.055)^2
Variance of Portfolio = 0.000517

Standard Deviation of Portfolio = (0.000517)^(1/2)
Standard Deviation of Portfolio = 0.0227 or 2.27%