Question

State of Economy	Probability of State of Economy	Return of Stock A if State Occurs	Return of Stock B if State Occurs
Recession	0.20	-0.20	0.05
Normal	?	0.20	0.22
Boom	0.25	0.30	0.25

7. What is the expected return for Stock A?

8. What is the standard deviation for Stock A?

9. Suppose you have $50,000 total. If you put $10,000 in Stock A and the remainder in Stock B, what are the portfolio returns in each state?

10. Suppose you have $50,000 total. If you put $10,000 in Stock A and the remainder in Stock B, what will be the expected return of your portfolio?

11. Suppose you have $50,000 total. If you put $10,000 in Stock A and the remainder in Stock B, what will be the standard deviation of your portfolio?

Answer 1

Answer a.

Stock A:

Expected Return = 0.20 * (-0.20) + 0.55 * 0.20 + 0.25 * 0.30
Expected Return = 0.1450 or 14.50%

Answer b.

Stock A:

Variance = 0.20 * (-0.20 - 0.145)^2 + 0.55 * (0.20 - 0.145)^2 + 0.25 * (0.30 - 0.145)^2
Variance = 0.031475

Standard Deviation = (0.031475)^(1/2)
Standard Deviation = 0.1774 or 17.74%

Answer c.

Weight of Stock A = Investment in Stock A / Total Investment
Weight of Stock A = $10,000 / $50,000
Weight of Stock A = 0.20

Weight of Stock B = Investment in Stock B / Total Investment
Weight of Stock B = $40,000 / $50,000
Weight of Stock B = 0.80

Recession:

Expected Return = 0.20 * (-0.20) + 0.80 * 0.05
Expected Return = 0.00

Normal:

Expected Return = 0.20 * 0.20 + 0.80 * 0.22
Expected Return = 0.2160 or 21.60%

Boom:

Expected Return = 0.20 * 0.30 + 0.80 * 0.25
Expected Return = 0.2600 or 26.00%

Answer d.

Expected Return of Portfolio = 0.20 * 0.00 + 0.55 * 0.2160 + 0.25 * 0.2600
Expected Return of Portfolio = 0.1838 or 18.38%

Answer e.

Variance of Portfolio = 0.20 * (0.00 - 0.1838)^2 + 0.55 * (0.2160 - 0.1838)^2 + 0.25 * (0.2600 - 0.1838)^2
Variance of Portfolio = 0.008778

Standard Deviation of Portfolio = (0.008778)^(1/2)
Standard Deviation of Portfolio = 0.0937 or 9.37%