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Sample Final Exam—FINC
Multiple Choice Use the expected returns and standard deviations described below to answer questions 1 and 2.
Security
Expected Return
Standard Deviation A 15.0% 4.00% B 12.0% 10.00% C 14.0% 6.25%
- You wish to create a portfolio by combining one of the risky securities above with the risk- free security. The return on the risk-free security is 5.0%. Which of the securities listed would be the best security to combine with the risk-free security?
a) security A b) security B c) security C d) The answer cannot be determined from the information given
- Suppose an investor with a risk-aversion level of A=2 wishes to hold just a single security. The investor’s utility function equals: U = E(R) – ½ Aσ^2. Which of the three securities listed above would be the optimal security for this investor?
a) security A b) security B c) security C d) The answer cannot be determined from the information given
- Consider the two securities listed below:
Security
Expected Return
Standard Deviation Risk-free 8.0% 0.0% X 16.0% 12.0%
Based on this information, which of the following investments would provide an expected return of 22.0%?
a) Invest 25% of your money is security X and 75% in the risk-free security b) Invest 75% of your money is security X and 25% in the risk-free security c) Borrow 25% at the risk-free rate and take a margin position of 125% in security X d) Borrow 75% at the risk-free rate and take a margin position of 175% in security X
- Diversification is most effective when the correlation between securities is:
a) Negative b) Positive c) Zero d) Diversification is unrelated to the correlation between securities
- The risk-free rate is 6.0% and the risk-premium on the market is 12.0%. Based on CAPM, what is the expected return on a security with a beta of 1.3?
a) 12.0% b) 13.8% c) 18.0% d) 21.6%
- Your portfolio has an initial value of $575,000 and a final value of $630,000. What is your After-tax Real return if you are in the 28% tax bracket and the inflation rate is 4%?
a) 9.57% b) 6.89% c) 4.01% d) 2.89%
- Assume that your broker requires an initial margin rate of 60% and a maintenance margin rate of 45%. Using the full amount of margin allowed, you purchase 500 shares of IBM stock on margin at the current market price of $125 per share. At what price will you receive a margin call?
a) $90. b) $118. c) $137. d) $112.
- The optimal combination of the risky portfolio and the risk-free security is designated by:
a) The point of tangency between the investor’s indifference curve and the capital allocation line b) The point of tangency between the investor’s indifference curve and the minimum variance portfolio c) The point of tangency between the investor’s indifference curve and the efficient frontier d) The point of tangency between the efficient frontier and the capital allocation line
- The expected return on a GM stock is 13.0%, the expected return on the market is 16.0%, and the risk-free rate is 5.0%. What would be the revised expected return on GM stock if the beta of
- If security returns follow a random walk with positive drift, which of the following statements is true?
a) Security returns have zero autocorrelation. b) Security returns have positive autocorrelation. c) Security returns have negative autocorrelation.
Problems
- Portfolio Theory Consider the security information and correlation listed below.
Security
Expected Return
Standard Deviation Risk-free 4.0% 0.0% Intel 19.5% 22.3% GM 14.0% 16.1%
ρGM,Intel = 0.
a) Calculate the expected return of a portfolio that invests 65% in Intel and 35% in GM.
b) Calculate the standard deviation of the portfolio described in part (a).
c) Calculate the reward-to-variability ratios for each of the risky securities.
2. Short Sales You believe Amazon.com stock is overvalued and you hope to profit from this by short selling the stock. The current stock price is $75 per share. Your broker informs you that they require an initial margin rate of 55% and a maintenance margin rate of 40%. Answer the questions below based on this information.
a) What is the maximum number of shares your broker will allow you to short sell if you place $25,000 in your margin account?
b) Suppose you place the $25,000 in your margin account, but decide to short sell only 400 shares. What will be the return on your position if the stock price drops to $66 per share?
c) Again, assume you enter into the short sale position described in part (b). At what price would you receive a margin call from your broker?
3. Portfolio Theory and the Capital Asset Pricing Model Use the security information below to answer questions (a) through (e)
Expected Return Std.Deviation Risk-Free 3.0% 0.0% Market 18.0% 21.0% Security 1 24.0% 29.5% Security 2 11.5% 13.2%
a) Assuming CAPM holds, calculate the β for each of the four securities.
b) Consider an additional security, X , with an expected return of 22.5%, a standard deviation of 31.0%, and a beta of 1.3. Given the information above, is the existence of security X consistent with CAPM in equilibrium? Explain your answer.
c) You would like to create a portfolio that earns an expected return of 21.0% by combining the market portfolio and the risk-free security. Calculate the positions (weights) in the market and the risk-free that would be required in order to achieve this objective? Interpret these weights.
d) The correlation between Securities 1 and 2 is ρ=0.03. Calculate the expected return
AND standard deviation of a portfolio that invests 40% in Security 1 and 60% in Security 2.
e) Plot securities 1 and 2 on the expected return – standard deviation graph to the right. Add the security described in question (e) to the graph. Based on these points, draw the approximately investment opportunity set that is created by all realizable combinations of Securities 1 and 2.
E(R)
Std. Dev.
6. Options and Futures
- The spot market price for gold is $425 per oz. If the annual rate of interest in the economy is 5%, what should be the market price of a futures contract on 10 oz. of gold that expires in 6 months?
- Blue Chip Investment Fund is a fund that invests in large U.S. companies. The fund’s portfolio manager is worried about a short-term market dip coming soon after the holiday season. However, she does not wish to sell off stock since that action will generate a tax liability for
- Describe a strategy using S&P 500 futures contracts that will address her needs.
- Plot the following combination of options on the payoff diagram below. Explain who might be interested in this portfolio of options (what do they expect about the future value of the stock?):
Long 1 $55 put Long 1 $50 put Short 1 $45 put Short 1 $60 put
