Use the following data in answering questions 1 through 3:
Investment (options) Expected Return E(r) Standard Deviation
1 12% 30%
2 15% 50%
3 21% 16%
4 24% 21%
U = E(r) -0.5*A*σ2, where A = 4.0.
1. Based on the utility function above, which investment would you select?
2. Which investment would you select if you were risk neutral?
3. What does the variable, A, in the utility function represent?
Use the following information to answer questions 4 through 8.
Consider the following probability distribution for stocks A and B:
State Probability Return on Stock A Return on Stock B
1 0.30 10% 8%
2 0.30 13% 7%
3 0.40 12% 6%
4. What are the expected rates of return of stocks A and B?
5. What are the standard deviations of stocks A and B?
6. What is the coefficient of correlation between A and B if the covariance is -0.000063?
7. If you were to use only the two risky funds and still require an expected return of 10%, what would be the investment proportions of your portfolio?
8. What is the standard deviation of this risky portfolio?
Use the following information to answer questions 9 through 12:
You write a call option with X=60 and buy a call with X= 70. The options are on the same stock and have the same maturity date. One of the calls sells for $3; the other sells for $9.
9. Write out the payoff and profit function for this strategy at the option maturity date
10. Draw the payoff graph for this strategy at the option maturity date.
11. Draw the profit graph for this strategy.
12. What is the break-even point for this strategy? Is the investor bullish or bearish on the stock?