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Sample Final Exam—FINC
Multiple Choice Use the expected returns and standard deviations described below to answer question 1.
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
- 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 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 GM doubled?
a) 21.0% b) 31.0% c) 29.0% d) 26.0%
- Which of the following portfolios would result in a portfolio Beta of 0.75?
a) 50% in the market and 50% in the risk-free security b) 25% in the market and 75% in the risk-free security c) 75% in the market and 25% in the risk-free security d) 125% in the market and -25% in the risk-free security
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 the market at Security 1.
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.
4. Relative Valuation
Some economists argue that relative valuation models have no theoretical basis. Explain briefly how market-to-book (P/B) ratios might be related to stock prices using basic finance theory.
You run a regression of some fundamental stock characteristics on past retail stock characteristics and get the following relationship:
P / E = 2. 0 + 2. 6 * Beta + 3. 6 * g − 0. 5 * b
where P/E is the price to earnings ratio using trailing 12-month earnings, beta is the CAPM beta, g is the consensus analyst forecast of growth and b is the earnings retention ratio (the amount of earnings reinvested in the company). You collect the following data on retail stocks that you are considering purchasing before the busy holiday shopping season. Firm Beta g b Viking Velcro and Velour 1.5 6.0 1. Eagle Earmuffs 0.5 8.0 0.
a) Calculate the expected P/E ratio of Viking and Eagle.
b) Calculate the PEG ratio of both Viking and Eagle.
c) Using the PEG ratios, make a recommendation for each stock and explain your logic.
5. Portfolio Evaluation An analyst wants to evaluate the performance of Random Walk Mutual Fund, which consists entirely of U.S. common stocks and seeks to mimic the performance of the S&P 500. The analyst computes the following summary statistics for the fund, the market (represented by the S&P 500), and the risk-free security (represented by the U.S. Treasury Bills).
Average Standard Deviation Beta
Answers:
Multiple Choice 1-a 2-d 3-a 4-d 5-d 6-a 7-a 8-c 9-b 10-e 11-b 12-a
Problems
1a) E(r) = 0.65 (19.5%) + 0.35(14%) = 17.575%
b) Variance = (0.65)^2 (0.223)^2 + (0.35)^2 (0.161)^2 +2 (0.65)(0.35)(0.25)(0.223)(0.161)
= 0.
Std. dev = square root of variance = .168136226 or 16.81%
c) reward-to-variability for Intel = (19.5 – 4)/22.3 = 0.
reward-to-variability for GM = (14 – 4)/16.1 = 0.
- a) Required margin =100% (sale proceeds) + 55% (cash added) = 155% total
Here cash added is $25,000, so sale proceeds = $25,000/.55 = $45,454.
Number of shares = $45,454.55/$75 = 606 shares
b) Assuming price drops immediately, the return is (75 - 66)/75 = 12%
c) 0.40 = [(75*400) + 25,000 – 400P]/ 400P
Solving for P, we get P= $98.
3. a) β = 1.
b) Yes, security X is consistent with the CAPM since 22.5 = 3 + 1.3(18 – 3)
c) 21 = w(18) + (1-w)(3) so w = 1.2 We need to buy the market with margin, borrowing 20% at the risk-free rate and investing 120% in the market.
d) E(r) = 0.4 (24) + 0.6 (11.5) = 16.5 %
Variance = (0.4)^2 (0.295)^2 + (0.6)^2 (0.132)^2 +2 (0.4)(0.6)(0.295)(0.132)(0.03)
= 0.
Std. dev = square root of variance = 0.144074203 or 14.4%
- Relative Valuation
For discussion of market-to-book (P/B) ratios in theory, see notes and textbook. The idea is that price (P) reflects the present value of future cash flows in a basic perpetuity equation. We can divide prices by the book value (B) and show that this ratio is then a function of the riskiness of the cash flows, the expected growth of the cash flows, the dividend payout ratio and the ROE of the firm.
a) The expected PE for Viking = 2.0 + 2.61.5 + 3.66 – 0.5*1 = 27
The expected PE for Eagle = 2.0 + 2.60.5 + 3.68 – 0.5*0.98 = 31.
b) The PEG for Viking = 27/6 = 4.5 and for Eagle = 31.61/8 = 3.
c) Based on the PEG cutoffs touted by the Motley Fools, both of these stocks are overvalued. The PEG accounts for the expected growth of the stock and in both of these cases, it looks like the expected growth that is impounded in the PE ratio far exceeds the growth forecasts. Therefore, by this measure, both stocks are overvalued at current prices.
- a) Sharpe Jensen Treynor Random Walk Fund 0.22 0.4 6. S&P 500 0.46 0.0 6.
b) The rankings are not consistent across the three performance measures. This is because the Sharpe measure examines excess returns per unit of risk measured by the standard deviation of the portfolio. Conversely, Jensen and Treynor measures use the portfolio beta as the measure of risk (and so these two measures are indeed consistent). Since beta measures only market risk and standard deviation measures total risk, it isn’t unusual to see inconsistent rankings.
