November 2016 Page 1 of (6) Multiple Choice Questions (3 points per question) For each of the questions 1-6, check one of the response alternatives A, B, C, D, E with a cross in the table below: Question A B C D E 1 2 3 4 5 6 Question 1. Which of the following orders instructs the broker to buy at the current market price? A. Market order B. Discretionary order C. Limit-loss order D. Stop-buy order E. Limit order Answer A. Market orders are to be executed immediately at the best prevailing price. Question 2. Researchers have found that most of the small firm effect occurs A. during the spring months B. during the summer months C. in December D. January E. randomly Answer D. Much of the so-called small firm effect simply may be the tax effect as investors sell stocks on which they have losses in December and reinvest the funds in January. As small firms are especially volatile, these actions affect small firms in a more dramatic fashion 1
November 2016 Page 2 of (6) Question 3. bias means that investors are too slow in updating their beliefs in response to evidence. A. Framing B. Conservatism C. Regret avoidance D. Overconfidence E. None of these is correct Answer B. Conservatism bias means that investors are too slow in updating their beliefs in response to evidence Page 390. Question 4. According to the mean-variance criterion, which one of the following investments dominates all others? A. E(r) = 0.15; Variance = 0.25 B. E(r) = 0.10; Variance = 0.20 C. E(r) = 0.10; Variance = 0.25 D. E(r) = 0.15; Variance = 0.20 E. None of these options dominates the other alternatives. Answer D see page 173 Question 5. A European spread can be exercised A. only at the expiration date. B. only after the expiration date. C. at any date in the indefinite future. D. at any date up until and including the maturity date. E. None of these is correct. Answer A. A European spread is a portfolio of European options. Question 6. Standard deviation and beta both measure risk, but they are different in that A. beta measures both systematic and unsystematic risk. B. beta measures only systematic risk while standard deviation is a measure of total risk. C. beta measures only unsystematic risk while standard deviation is a measure of total risk. D. beta measures both systematic and unsystematic risk while standard deviation measures only systematic risk. E. beta measures total risk while standard deviation measures only nonsystematic risk. B. Standard deviation and beta both measure risk, but they are different in that beta measures only systematic risk while standard deviation is a measure of total risk. Remember to mark your answers in the table above question 1! 2
November 2016 Page 3 of (6) Essay Question (28 points) Question 7. Anna and Rosie are two utility maximizing risk averse investors. Anna s utility function is given by E[r]-σ 2 and Rosie s utility function is given by E[r]-2σ 2. Carefully sketch one indifference curve for Anna and one indifference curve for Rosie on the same graph for a given utility level (for example for utility level U=0.08), clearly illustrating how the curves relate to one another. In the graph, let E[r] be the unit on the y-axis and clearly state what should be the unit on the x-axis. (10 points) Anna has risk aversion coefficient A=2 and Rosie has A=4 so Rosie is more risk averse. The curves may or may not intersect within the range of the graph. Rosies curve will have a steeper slope than Annah's. The levels of risk aversion can be illustrated by examining the curves' slopes over a fixed range. Because Rosies curve is steeper than Annah's, for a fixed change in standard deviation on the horizontal axis, he will have a greater change in expected return on the vertical axis. It takes more compensation in the form of expected return to allow Rosie to maintain his level of utility than it takes for Anna. Standard deviation (sigma) is on the x-axis. See for instance figure 6.7 on page 185 with either U=0.09 or for U=0.05. Question 8. Theoretically, the standard deviation of a portfolio can be reduced to what level? Explain. Realistically, is it possible to reduce the standard deviation to this level? Explain. (9 points) Chapter 7, see figure 7.4. Theoretically, if one could find two risky securities with perfectly negatively correlated returns (correlation coefficient = -1), one could solve for the weights of these securities that would produce the minimum variance portfolio of these two securities. The standard deviation of the resulting portfolio would be equal to zero. In reality, securities with perfect negative correlations do not exist so unless the portfolio consists of the riskfree asset only, there will be positive amount of standard deviation left (In reality it is not possible to diversify away all risk ). Question 9. State and explain three major differences between hedge funds and mutual funds. (9 points) The five major categories of differences are transparency, investors, investment strategies, liquidity, and compensation structure. Mutual funds are more highly regulated by the SEC and thus are required to be far more transparent. Hedge funds provide only minimal information about portfolio composition or strategy. Investors in hedge funds differ in that investment minimums were traditionally set at $250,000 to $1,000,000. This minimum is outside the reach of many mutual fund investors. Mutual funds must provide an investment strategy and are restricted in the use of leverage, short selling, and in their use of derivatives. However, hedge funds are less restricted and frequently make large bets that can result in large losses over the short term. Mutual funds are liquid and investors can redeem shares at NAV and have proceeds within seven business days. Conversely, hedge funds often impose lock-up periods as long as several years and require redemption notices of several months even after the lock-up period is over. Thus, hedge funds are far less liquid. While mutual funds charge a management fee, hedge funds add an incentive fee as well. 3
November 2016 Page 4 of (6) Computational questions (6 points per question) Question 10. An investor decides to create a portfolio by investing 55% in a mutual fund and 45% in T-bills. The mutual fund has an expected rate of return of 18% and a standard deviation of 34%. The T-bill rate is 4%. a) What is the expected return on the investor's complete portfolio? b) What is the standard deviation of investor's complete portfolio? a) E(r C) =.55 * 18.00% +.45 * 4.00% =11,70% b) Std. Dev. of C =.55 * 34% = 18.70% Question 11. The risk-free rate and the expected market rate of return are 5 % and 15 %, respectively. a) What is the expected rate of return on security AB with a beta of 1.3 according to the capital asset pricing model (CAPM)? b) If an analyst believe that the expected rate of return on security AB was 17 %, would the analyst consider the security to be overpriced according to the capital asset pricing model (CAPM) given that everything else remains the same? : Chapter 9, page 299 a) E(r)=0.05+1.3*(0.15-0.05)=0.18 18 % b) Yes. Security AB is overpriced with a beta of 1.3 because the expected rate of return is lower 17% < 18 which is the return dictated by CAPM. Question 12. Consider a mutual fund with $100 million in assets at the start of the year and with 5 million shares outstanding. The fund invests in a stock portfolio that provides no dividend or other income, but that increases in value with 10%. The expense ratio is 2% per year on total assets under management in the beginning of the year. a) Calculate the NAV at the start of the year and the NAV at the end of the year. b) What is the rate of return for an investor in the mutual fund? a) Initial NAV=100/5=$20 per share. In absence of expenses fund assets grows to $110 million. However the expense rate is 2% on $100 million, i.e. $2 million, so end-year NAV is (110-2)/5=$21.6. b) Rate of return is=21.6/20-1=8%. 4
November 2016 Page 5 of (6) Question 13. Suppose a US Investor wishes to invest in a British company currently trading at 70 per share. The investor has $133 000 and the current exchange rate is 1.9 USD per pound i.e. $1.9/ 1. a) How many shares can the investor buy? b) One year later, the British company trades at a price of 77 per share and the exchange rate is 1.65 USD per pound i.e. $1.65/ 1. Calculate the British pound denominated return as well as the US-dollar denominated return. Answer a) 133000/(70*1.9)=1000 b) In pounds: (77*1000-70*1000)/70*1000=10% In dollars: (77*1.65*1000-70*1.9*1000)/70*1.9*1000=-4.47% Question 14. Assume that the risk free rate of interest is 5% per annum and the expected rate of return on the market portfolio is 15% per annum. A share of stock sells for $70 today. It will pay out a dividend of 4$ per share at the end of the year. The stocks beta is 1.3. a) According to the Capital Asset Pricing Model (CAPM), what is the annual expected return? b) What do CAPM believers expect about the stock price at the end of the year? a).05 + [1.3 * (.14.05)] = 18.00% D1 + P1 P0 P1 $70 + $4 b) ) E ( r) = 0.18 = P1 = $78. 60 P $70 0 Question 15. Consider an at-the-money European call option on Apple Inc. with one month left to maturity, and an atthe-money European put option on Apple Inc. with one month left to maturity. Apple Inc. Currently trades at $110, the call option currently trades at $1.6, the put option currently trades at $1.40 and the interest rate is zero. Create a portfolio by going long in one unit of the call option and by going long one unit of the put option. a) If Apple Inc. at maturity date trades at $100. What is the payoff of your portfolio? b) If Apple Inc. at maturity date trades at $100. What is the profit of your portfolio? a) Max(100-110,0)+max(110-100,0)=0+10=10 b) 10-1.6-1.4=7 5
November 2016 Page 6 of (6) Question 16. Consider the following weekly price data. Each observation represent the closing price of the Dow Jones Industrial Average (DJIA) on the last trading day of the week. The 5 week moving average each week is the average of the DJIA over the previous 5 weeks. 5-week Moving Week DJI Average 1 13 620 2 13 590 3 13 652 4 13 625 5 13 657 13 629 6 13 710 13 647 7 13 651 13 659 8 13 610 13 651 9 13 595 X 10 13 499 13 613 a) Calculate the missing 5-week moving average at week 9. b) At what week is there a trade signal, and is this a buy or sell signal? Answer. See ch 12. At week 9 the 5 weeks moving average is: a) (13657+13710+13651+13610+13595)/5=13645. b) There is a sell signal at week 7 since the DJI cross the Moving average from above at this point. Question 17 You are evaluating two investment alternatives. One is a passive market portfolio with an expected return of 10% and a standard deviation of 16%. The other is a fund that is actively managed by your broker. This fund has an expected return of 15% and a standard deviation of 20%. The risk-free rate is currently 7%. Answer the questions below based on this information. a) What is the intercept and the slope of the capital market line (CML)? b) What is the intercept and slope of the capital allocation line (CAL) offered by your broker's fund? c) What is the maximum fee your broker could charge and still leave you as well off as if you had invested in the passive market fund? (Assume that the fee would be a percentage of the investment in the broker's fund and would be deducted at the end of the year.) a) Intercept is 0.07. The slope of the CML is (10-7)/16 = 0.1875. b) Intercept is 0.07. The slope of the CAL is (15-7)/20 = 0.40. c) To find the maximum fee the broker can charge, the equation (15-7 - fee)/20 = 0.1875 is solved for "fee." The resulting fee is 4.25%. 6
November 2016 Page 7 of (6) Question 18 You want to evaluate four mutual funds using the Jensen measure and the Sharpe measure for performance evaluation. The risk free return during the sample period is 5%. The average return on the market portfolio is 22 %. The information on the four funds are given in the table below. Average return Residual standard deviation Beta Standard deviation Fund A 23.0% 5.0% 0.7 16.0% Fund B 22.5% 1.0% 0.8 14.0% Fund C 23.0% 2.0% 0.6 11.0% Fund D 23.0% 2.0% 1.5 19.0% a) Which fund has the highest Sharpe ratio? b) Which funds outperformed the market portfolio according to the Jensen measure? a) Fund C has the highest Sharpe ratio: (0.23-0.05)/0.11=1.64 b) Use the Jensen measure Fund A, Fund B and Fund C A alpha=0.23-0.05 0.7*(0.22-0.05)=0.061 B alpha = 0.039 C alpha = 0.078 D alpha = -0.075 7