Question

Consider the following information:

  

Rate of Return If State Occurs

State of

Probability of

Economy

State of Economy

Stock A

Stock B

Stock C

Boom

.15

.31

.41

.21

Good

.60

.16

.12

.10

Poor

.20

−.03

−.06

−.04

Bust

.05

−.11

−.16

−.08

  

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?

Expected return

%

b-1	What is the variance of this portfolio?

Variance

b-2	What is the standard deviation?

Standard deviation

%

Answer 1

Weight of Stock A = 0.30
Weight of Stock B = 0.40
Weight of Stock C = 0.30

Boom:

Expected Return = 0.30 * 0.31 + 0.40 * 0.41 + 0.30 * 0.21
Expected Return = 0.3200

Good:

Expected Return = 0.30 * 0.16 + 0.40 * 0.12 + 0.30 * 0.10
Expected Return = 0.1260

Poor:

Expected Return = 0.30 * (-0.03) + 0.40 * (-0.06) + 0.30 * (-0.04)
Expected Return = -0.0450

Bust:

Expected Return = 0.30 * (-0.11) + 0.40 * (-0.16) + 0.30 * (-0.08)
Expected Return = -0.1210

Expected Return of Portfolio = 0.15 * 0.3200 + 0.60 * 0.1260 + 0.20 * (-0.0450) + 0.05 * (-0.1210)
Expected Return of Portfolio = 0.1086 or 10.86%

Variance of Portfolio = 0.15 * (0.3200 - 0.1086)^2 + 0.60 * (0.1260 - 0.1086)^2 + 0.20 * (-0.0450 - 0.1086)^2 + 0.05 * (-0.1210 - 0.1086)^2
Variance of Portfolio = 0.01424

Standard Deviation of Portfolio = (0.01424)^(1/2)
Standard Deviation of Portfolio = 0.1193 or 11.93%