Question

HW #6

1. Use the following information to answer the questions.

State	Probability	Stock A return	Stock B return
Good Normal Bad	0.3 0.6 0.1	8% 2% -3%	5% 1% -1%

(a). Given that you form a portfolio by investing $4,000 in Stock A and $1,000 in Stock B, what is the expected return on your portfolio?

(b).What is the variance and standard deviation of your portfolio?

(c). Suppose that Stock A has a beta of 1.5 and Stock B has a beta of 0.8. What is the beta for your portfolio?

2.

	Beta	Expected return
S&P 500 Risk-free security Stock C Stock D	1.0 0.0 0.6 (     )	10.0% 5.0% (    )% 12.5%

(a). Figure out the market risk premium.

(b). What is the expected return on stock C?

(c). What is the beta for stock D?

(d). Total risk consists of systematic risk and unsystematic risk.

i.Which risk could be eliminated by diversification strategy? Total risk, systematic or unsystematic risk?

ii.Which risk will be priced? In other words, which risk will be important for your investment decision? Total risk, systematic or unsystematic risk?

iii.Expected return = risk-free interest rate + (         )* market risk premium.

Answer 1

Answer to Question 1:

Answer a.

Weight of Stock A = $4,000/$5,000 = 0.8
Weight of Stock B = $1,000/$5,000 = 0.2

Good:

Expected Return = 0.80 * 8% + 0.20 * 5%
Expected Return = 7.40%

Normal:

Expected Return = 0.80 * 2% + 0.20 * 1%
Expected Return = 1.80%

Bad:

Expected Return = 0.80 * (-3%) + 0.20 * (-1%)
Expected Return = -2.60%

Expected Return on Portfolio = 0.30 * 7.40% + 0.60 * 1.80% + 0.10 * (-2.60%)
Expected Return on Portfolio = 3.04%

Answer b.

Variance = 0.30 * (7.40% - 3.04%)^2 + 0.60 * (1.80% - 3.04%)^2 + 0.10 * (-2.60% - 3.04%)^2
Variance = 0.000981

Standard Deviation = (0.000981)^(1/2)
Standard Deviation = 0.0313
Standard Deviation = 3.13%

Answer c.

Portfolio Beta = Weight of Stock A*Beta of Stock A + Weight of Stock B*Beta of Stock B
Portfolio Beta = 0.80 * 1.50 + 0.20 * 0.80
Portfolio Beta = 1.36