Questions and Problems
1. What is the difference between systematic and unsystematic risk?
2. What is beta? What type of risk does it represent?
3. What effect will diversifying your portfolio have on your returns and risk?
4. What is the security market line? What does it represent?
5. How do you measure the beta of a portfolio?
6. If a stock has a beta greater than 1, what can you say about its riskiness? What if it has a beta smaller than 1?
1-You have $100,000 invested in a 2-stock portfolio. $30,000 is invested in A and the remainder is invested in B. A' beta is 1.60 and B' beta is 0.60. What is the portfolio's beta?
2-A Company's stock has a beta of 1.40, the risk-free rate is 4.25%, and the market risk premium is 5.50%. What is its required rate of return?
3-A stock has an expected return of 12.60%. Its beta is 1.49 and the risk-free rate is 5.00%. What is the market risk premium?
4-A stock has a beta of 1.23, its required return is 11.25%, and the risk-free rate is 4.30%. What is the required rate of return on the stock market?
5-The market return based on a broad market index is calculated as 15%. Calculate a company's expected return if the risk free rate is 4% and the stock's beta is 1.35.
6-A company's stock had a required return of 11.50% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Now suppose there is a shift in investor risk aversion, and the market risk premium increases by 2%. The risk-free rate and the beta remain unchanged. What is this company's new required return?
7- Vera Paper's stock has a beta of 1.40, and its required return is 12.00%. Dell Dairy's stock has a beta of 0.80. If the risk-free rate is 4.75%, what is the required rate of return on Dell's stock?
8- You hold a diversified portfolio consisting of a $5,000 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. You have decided to sell a lead mining stock (b = 1.00) at $5,000 net and use the proceeds to buy a like amount of a steel company stock (b = 2.00). What is the new beta of the portfolio?
9- For the information given below find the following:
|
Stock
|
Percentage of Portfolio
|
Beta
|
Expected Return
|
|
1
|
20%
|
1
|
16%
|
|
2
|
30%
|
0.85
|
14%
|
|
3
|
15%
|
1.2
|
20%
|
|
4
|
25%
|
0.6
|
12%
|
|
5
|
10%
|
1.6
|
24%
|
Calculate the expected return on your portfolio. Calculate the portfolio's beta.
Suppose you drop stock # 2 from your portfolio and replace it with another stock that has a beta of 1.35 and an expected return of 25%, how your portfolio's return and beta would be affected by this change? Answer the question intuitively and then calculate the new return and beta.
10-A company's stock has a 50% chance of producing a 25% return, a 30% chance of producing a 10% return, and a 20% chance of producing a -28% return. What is the firm's expected rate of return? What is the standard deviation?
11-A company's stock has a 25% chance of producing a 30% return, a 50% chance of producing a 12% return, and a 25% chance of producing a -18% return. What is the firm's expected rate of return? What is the standard deviation?
12-A company is considering a capital budgeting project that has an expected return of 25% and a standard deviation of 30%. What is the project's coefficient of variation?
13-A company is considering an investment that has an expected return of 15% and a standard deviation of 10%. What is the investment's coefficient of variation?
14-A company believes the following probability distribution exists for its stock. What is the coefficient of variation on the company's stock?
|
State of the Economy
|
Probability of State Occurring
|
Stock's Expected Return
|
|
Boom
|
0.45
|
25%
|
|
Normal
|
0.50
|
15%
|
|
Recession
|
0.05
|
5%
|
15-You hold the following portfolio:
|
Stock
|
Investment
|
Beta
|
|
A
|
$150,000
|
1.40
|
|
B
|
50,000
|
0.80
|
|
C
|
100,000
|
1.00
|
|
D
|
75,000
|
1.20
|
|
Total
|
$375,000
|
|
What is the portfolio's beta?