Investments
Practice Problems for Exam
1. You own a 7.5 percent, semiannual coupon bond that matures in 8 years. The par value is $1,000 and the current yield to maturity is 7.6 percent. What will the percentage change in the price of your bond be if the yield to maturity suddenly increases by 75 basis points?
2. Blue Water Homes has 8 percent bonds outstanding that mature in 13 years. The bonds pay interest semiannually. These bonds have a par value of $1,000 and are callable in 2 years at a premium of $75. What is the yield to call if the current price is equal to 103.5 percent of par?
3. A bond has a modified duration of 6.13 and a yield to maturity of 8.9 percent. If interest rates increase by 75 basis points, the bond's price will decrease by _____ percent.
4. A portfolio consists of the following securities. What is the portfolio weight of stock X?
|
Stock
|
Number of Shares
|
Price per Share
|
|
X
|
600
|
$17
|
|
Y
|
900
|
$23
|
|
Z
|
400
|
$46
|
5. You have a portfolio which is comprised of 70 percent of stock A and 30 percent of stock B. What is the expected rate of return on this portfolio?
|
State of Economy
|
Probability of State of Economy
|
Rate of Return if State Occurs
|
|
Stock A
|
Stock B
|
|
Boom
|
0.1
|
17%
|
9%
|
|
Normal
|
0.9
|
8%
|
22%
|
6. Stock A has a standard deviation of 12 percent per year and stock B has a standard deviation of 16 percent per year. The correlation between stock A and stock B is .47. You have a portfolio of these two stocks wherein stock B has a portfolio weight of 35 percent. What is your portfolio variance?
7. A stock fund has a standard deviation of 18 percent and a bond fund has a standard deviation of 11 percent. The correlation of the two funds is .24. What is the approximate weight of the stock fund in the minimum variance portfolio?
8. Of the following, Stock _____ has the greatest level of total risk and Stock _____ has the highest risk premium.
|
Stock
|
Beta
|
Standard deviation
|
|
A
|
1.09
|
11%
|
|
B
|
0.96
|
13%
|
|
C
|
1.24
|
18%
|
|
D
|
1.13
|
26%
|
|
E
|
0.87
|
9%
|
9. A portfolio consists of two stocks and has a beta of 1.07. The first stock has a beta of 1.48 and comprises 38 percent of the portfolio. What is the beta of the second stock?
10. The following portfolio has an expected return of _____ percent and a beta of _____.
|
Security
|
Amount Invested
|
Expected Return
|
Beta
|
|
J
|
$36,000
|
16.20%
|
1.47
|
|
K
|
24,000
|
10.5
|
1.38
|
|
L
|
20,000
|
11.8
|
1.29
|
11. A risky asset has a beta of .88 and an expected return of 7.4 percent. What is the reward-to-risk ratio if the risk-free rate is 2.8 percent?
12. Wilson Farms' stock has a beta of .79 and an expected return of 7.8 percent. The risk-free rate is 2.6 percent and the market risk premium is 6 percent. This stock is ____ because the CAPM return for the stock is _____ percent.
A. undervalued; 7.34
B. undervalued; 7.49
C. undervalued; 7.59
D. overvalued; 7.34
E. overvalued; 7.49
13. The market has a standard deviation of 11.7 percent while a risky security has a standard deviation of 23.7 percent. The covariance of the stock with the market is .0149. What is the beta of the stock?
14. The U.S. Treasury bill is yielding 3.1 percent and the market has an expected return of 11.2 percent. What is the Sharpe ratio of a portfolio that has a beta of 1.32 and a variance of .027556?
15. What is the Treynor ratio of a portfolio comprised of 50 percent portfolio A and 50 percent portfolio B? (The risk-free rate is 3.3 percent and the market risk premium is 8.5 percent)
|
Portfolio
|
Average Return
|
Standard Deviation
|
Beta
|
|
A
|
13.60%
|
17.20%
|
1.38
|
|
B
|
8.4
|
6.4
|
0.87
|
16. A portfolio has a beta of 1.52 and an actual return of 13.7 percent. The risk-free rate is 2.7 percent and the market risk premium is 7.8 percent. What is the value of Jensen's alpha?
17. A stock has an annual standard deviation of 14.1 percent and an expected annual return of 11.5 percent. What is the smallest expected loss for the next 6 months given a probability of 2.5 percent?
18. Southern Fuel has an inventory of 714,000 gallons of heating oil. The futures contracts on heating oil are based on 42,000 gallons. If the firm wishes to fully hedge its inventory, it should take which one of the following positions in heating oil futures contracts?
A. long on 15
B. long on 17
C. short on 15
D. short on 16
E. short on 17
19. You purchased five September wheat futures contracts at the open today and sold those contracts at the close. What is your total profit or loss on these contracts?
|
Contract
|
Open
|
High
|
Low
|
Close
|
|
Sep, Corn, 5,000 Ims, cents/bu
|
615.5
|
618.25
|
608
|
612.5
|
|
Sep, Wheat, 5,000 bu, cents/ bu
|
814
|
820
|
808.5
|
811
|
20. Which one of the following options is out-of-the-money?
A. call with a $20 strike and a stock price of $21
B. put with a $35 strike and a stock price of $33
C. call with a $45 strike and stock price of $46
D. put with a $75 strike and a stock price of $70
E. call with a $50 strike and a stock price of $49
21. Josh owns 2 call options on Foster Glass stock. The exercise price is $47.50 and the stock price at expiration is $49.01. What is the total payoff on the option contracts?
22. A stock is valued at $26 a share. A European 6-month call option has a strike price of $25 and an option premium of $1.40. The market rate is 9.5 percent and the risk-free rate is 2.5 percent. What is the price of a European 6-month put option with a $25 strike price?