Question

11.09 Returns and Standard Deviations Consider the following information:

Main Page
State of Economy	Probability of State of Economy	Rate of Return if State Occurs
		Stock A	Stock B	Stock C	Portfolio
Boom	0.25	25.00%	45.00%	33.00%
Good	0.4	9.00%	10.00%	15.00%
Poor	0.3	3.00%	-10.00%	-5.00%
Bust	0.05	-5.00%	-25.00%	-9.00%
	Expected Value
	Variance
	Standard Deviation
a. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? b. What is the variance of this portfolio? The standard deviation?

Answer 1

Weight of Stock A = 30%
Weight of Stock B = 40%
Weight of Stock C = 30%

Boom:

Expected Return = 30% * 0.25 + 40% * 0.45 + 30% * 0.33
Expected Return = 0.3540

Good:

Expected Return = 30% * 0.09 + 40% * 0.10 + 30% * 0.15
Expected Return = 0.1120

Poor:

Expected Return = 30% * 0.03 + 40% * (-0.10) + 30% * (-0.05)
Expected Return = -0.0460

Bust:

Expected Return = 30% * (-0.05) + 40% * (-0.25) + 30% * (-0.09)
Expected Return = -0.1420

Answer a.

Expected Return of Portfolio = 0.25 * 0.3540 + 0.40 * 0.1120 + 0.30 * (-0.0460) + 0.05 * (-0.1420)
Expected Return of Portfolio = 0.1124 or 11.24%

Answer b.

Variance of Portfolio = 0.25 * (0.3540 - 0.1124)^2 + 0.40 * (0.1120 - 0.1124)^2 + 0.30 * (-0.0460 - 0.1124)^2 + 0.05 * (-0.1420 - 0.1124)^2
Variance of Portfolio = 0.025356

Standard Deviation of Portfolio = (0.025356)^(1/2)
Standard Deviation of Portfolio = 0.1592 or 15.92%