Financial Markets and Investments: Stock Splits, Dividends, and Portfolio Optimization, Assignments of Finance

Download Financial Markets and Investments: Stock Splits, Dividends, and Portfolio Optimization and more Assignments Finance in PDF only on Docsity! 1 Name _______Answer Key______________ Homework #1 FIN 4504 Equity and Capital Markets Karceski Fall 2005 Due date: Thursday, October 6th at the beginning of class Answer all questions. I will check to make sure that you make an honest attempt to answer all of the questions, and then I will formally grade five of the multiple choice questions and a few of the remaining problems. Multiple Choice (Circle the best answer) 1. Four stocks have the following properties: Stock Total Shares Outstanding Price Per Share A 10 million $47.50 B 15 million $57.00 C 18 million $24.25 D 32 million $55.00 Currently, the market index is a price-weighted index that includes only stocks A, B, and C. The current divisor is 0.14. Which of the following changes would NOT require the divisor to change (and be recalculated)? (a) Stock C does a 1-for-20 reverse stock split (b) Stock A does a 2-for-1 stock split (c) Stock B is replaced in the index by stock D (d) Stock B declares a 15 percent stock dividend (e) All of the above would require the divisor to change. 2. Mutual funds that hold both stocks and bonds in relatively stable proportions are called __________. (a) growth and income funds (b) asset allocation funds (c) balanced funds (d) safe funds (e) hedge funds 3. You purchased 100 shares of Wal-Mart stock on margin for $70 per share (you put in the minimum amount of cash allowed). The initial margin is 50% and the maintenance margin is 30%. Below the stock price of __________, you would get a margin call. Assume the stock pays no dividends and ignore interest on margin. (a) $21 (b) $27 (c) $49 (d) $50 (e) $60 / .50 / 7000 3500, 3500 100 100 3500 100 3500 / .30 100 30 100 3500 50 E A E E D Assets P Equity P Debt P Equity Assets P P P P = =
= = = = − = −= = = − = 2 4. . __________ is the rate at which an investor is willing to trade risk for return. (a) The insurance premium (b) The indifference curve (c) The concavity of the utility function (d) The utility function (e) Risk aversion 5. The market price of risk is given by __________ . (a) the first derivative of the capital allocation line (b) the second derivative of the investor's indifference curve (c) the second derivative of the capital allocation line (d) the expected return of the optimal complete portfolio (e) the point at which the investor's indifference curve is tangent to the capital allocation line 6. Which of the following statements is (are) true? (circle all that are true) (a) Risk averse investors reject investments that are fair games. (b) Risk neutral investors judge risky investments only by their expected returns. (c) Risk averse investors judge investments only by their standard deviations. (d) Risk seeking investors reject investments that are fair games. 7. Firms which specialize in helping companies raise capital by selling securities are called __________ . (a) investment banks (b) credit unions (c) commercial banks (d) CMOs (e) Bowie bonds 8. A 1986 study by Brinson, Beebower and Singer identified the three main components that determine the success of investment portfolios. Their study analyzed portfolios held by institutional pension funds, but their results presumably apply to most people’s portfolios. Of these three components, __________ was the primary determinant of portfolio returns, accounting for 94% of the return variation of portfolios. (a) security selection (b) the expense ratio (c) the investment objective (d) market timing (e) asset allocation 9. Suppose your wealth is $500,000, half of which is in a tax-deferred IRA and half of which is in a normal taxable account. You wish to have half of your wealth invested in the stock market and half invested in the bond market. How much of your IRA money should you invest in stocks? (a) 0% (b) 50% (c) 100% (d) It doesn't matter--anywhere between 0% and 100% 10. A passive asset allocation strategy involves __________ . (a) maintaining approximately the same proportions of a portfolio in each asset class over time (b) not buying or selling securities which allows the proportions of a portfolio in each asset class to change over time (c) investing in the stocks of companies that are neither over- or under-priced (d) varying the proportions of a portfolio in each asset class in response to changing market conditions 5 15. Why are current insider trading laws made purposefully vague? If the laws were very detailed, insiders would try to find loopholes in the law and engage in legal but unethical behavior. By keeping the law vague, the SEC has the ability to examine a wide range of behavior and activities. A vague law supposedly encourages insiders to not profit through questionable behavior. 16. (a) How did Jeff Vinik lose his job as portfolio manager at Fidelity Magellan? Vinik thought that stocks would underperform bonds, so he put about 30% of Fidelity Magellan’s money into bonds. When the market continued going up in late 1996 and early 1997, Magellan underperformed. (b) What did Vinik stand to gain if the market went down and his strategy proved successful? Vinik would have been a hero and lots of new cash flows would have poured into Magellan. (c) Does his story imply that it is easy or difficult to successfully “time the market”? It is very difficult to time the market. (d) How has Jeff Vinik done since being fired by Fidelity? Vinik started his own hedge fund after getting fired. His fund was very successful, and Vinik made more money with his hedge fund than he ever did at Fidelity. 6 17. (a) Describe what we mean by the fundamental tradeoff between risk and return. The only way to get higher expected returns is to accept more risk. (b) Jeremy Siegel, author of Stocks for the Long Run, says that this fundamental tradeoff between risk and return does not hold. What empirical evidence does Siegel present in the article we read in class to support his position? Siegel shows that for 20 year holding periods between 1926 and 1995, stock outperformed bonds 98% of the time. Also, stocks had much higher returns on average than bonds over that period, so that stocks have high expected returns and low risk. (c) What counter-argument could you make that would question the validity of Siegel's conclusions (see the same article from class)? He said that Siegel’s results suffer from survivorship bias. The US market has been very successful over the last 100 years, but what about Russia and Germany? So the history of the US market could be a very misleading example to use to determine the long term risk return tradeoff for stocks. 7 Numerical Problems (show all work since partial credit will be given) 18. Nat-T-Cat Enterprises has decided to go public. After getting feedback from some experts in the kitty litter business, the firm's underwriter decides that the true value of the Nat-T-Cat's equity will be $100 million with probability 0.35 and $200 million with probability 0.65. The underwriter has decided to sell 4 million shares, and it needs to compute the appropriate offer price. There is a group of uninformed investors willing to submit bids for 6 million shares as long as their expected profit is not negative. These uninformed investors know the probability distribution of firm values at given above, but do not know the true value of Nat-T-Cat as informed investors do. These informed investors are willing to order 10 million shares of the IPO if the offer price is lower than the true value. (a) Compute the equilibrium offer price that the underwriter should charge for each share so that uninformed investors are willing to participate in the offering. Prob True Value .35 $25 .65 $50 Expected profit to uniformed = 0 6 6 0 .35 (4 million)(25 ) .65 (4 million)(50 ) 6 6 10 0 35 1.4 48.75 .975 0 83.75 2.375 2.375 83.75 $35.26 OP OP OP OP OP OP OP    = − + −   +    = − + − = − = = (b) What is the total expected profit in dollars to the informed investors if the investment bank sets the offer price at the value computed in part (a)? 10 .35(0) .65(50 35.26) 4 Informed Expected Profit 6 10 0 23.95 23.95 million  + − = +  + = (c) How much money will the firm raise in this IPO? 4 million shares * $35.26/share = $141.04 million (d) What is the expected true value of Nat-T-Cat? ETV=.35(100)+.65(200) 35 + 130 $165 million (e) Why are the answers to parts (c) and (d) different (i.e., who pockets the difference)? The difference is the answer for (b), so the firm loses $23.95 million to the informed investors. 10 21. You have $100 to invest. The riskfree rate is 5%, and there are three mutual funds that you can choose from. However, you are only allowed to choose one of the three mutual funds. After you select a mutual fund, you are allowed to split your $100 however you would like across the riskfree asset and that mutual fund. Short selling both the riskfree asset or your mutual fund is permitted. The expected return and standard deviation of each mutual fund is given in the table below. Fund Expected Return Standard Deviation Mutual Fund A 15% 25% Mutual Fund B 2% 8% Mutual Fund C 10% 20% Your utility function is 2 ( ) ( ( ), ) . 7 0.2 E r U E r σ σ = + What is your optimal portfolio (in other words, which mutual fund do you select, how much of your $100 do you invest in that mutual fund, and how much money do you invest in the riskfree asset)? .15 .05 ( ) .05 This is the equation for the CAL for fund A .25 .05 .4 .02 .05 ( ) .05 This is the equation for the CAL for fund B .08 .05 .375 .10 .05 ( ) .05 .20 A B C E r E r E r σ σ σ σ σ − = + ←    = + − = + ←    = − − = +     2 2 This is the equation for the CAL for fund C .05 .25 The slope of CAL is highest for Mutual Fund A (slope = .4), so the investor will choose this fund (.05 .4 ) : 7 .2 .4(7 .2) 14 (.05 .4) 0 (7 Max σ σ σ σ σ σ σ ← = + + + + − += 2 2 2 2 2 2 .2) 0 2.8 .08 .7 5.6 0 2.8 .7 .08 .7 ( .7) 4( 2.8)(.08) .7 1.177 0 .3352, .0852 2( 2.8) 5.6 Choose the positive solution since it is not possible for to be negative. let y = the weight on Mut σ σ σ σ σ σ + = + − − = − − + ± − − − ±= = = − − − ual Fund A, so 1-y is the weight on the riskfree asset. The standard deviation of the complete portfolio equals y times the standard deviation of the risky portfolio. So, .0852 (.25) .3408 1 .6592 Fi y y so y = = − = nal answer: You will invest in Mutual Fund A, $34.08 will be invested in Mutual Fund A, and $65.92 will be invested in the riskfree asset. 11 22. Consider the four stocks in the following table. Pt represents closing price on day t, and Qt represents the total shares outstanding at the market close of day t. Stock C splits three-for-one just before the market opens on day 2. stock P0 Q0 P1 Q1 P2 Q2 A 92 137 87 137 89 137 B 23.25 58 24.25 58 23.25 58 C 145 102 153 102 54 306 D 90 70 85 70 65 70 (a) Initially, set the divisor equal to 4. What is the initial value of the price-weighted index (at the end of day 0)? 0 92 23.25 145 90 87.56 4index t PW = + + += = (b) Calculate the rate of return on a price-weighted index of the four stocks for day 1. 1 87 24.25 153 85 87.31 4 87.31 87.56 0.29% 87.31 index t return PW PW = + + += = −= = − (c) What is the value of the divisor just after stock C does a three-for-one stock split (right before the market opens on day 2)? 87 24.25 51 85 87.31 2.832 d d + + += = (d) Calculate the rate of return on a value-weighted index of the four stocks for the two-day period that includes day 1 and day 2. 89 92 12604 3.26% 92(137) 12604 .3597 92 35042.5 23.25 23.25 1348.5 0% 23.25(58) 1348.5 .0385 23.25 35042.5 54(3) 145 14790 11.72% 145(102) 14790 .4221 145 35042.5 65 90 27.78% 90 A A A B B B C C C D r MC W r MC W r MC W r MC −= = − = = = = −= = = = = = −= = = = = = −= = − 630090(70) 6300 .1798 35042.5 35042.5 .3597( 3.26%) .0385(0%) .4221(11.72%) .1798( 27.78%) 1.22% D D VW W MC R = = = = Σ = = − + + + − = − (e) If the initial value of the equally-weighted index of the four stocks was 317 at the beginning of day 1 (i.e. at the end of day 0), what is the value of the equally-weighted index at the end of day 1? 87 92 5.43% ending = beginning(1 ) 92 24.25 23.25 4.30% ending 317(1 .0029) 23.25 153 145 5.52% ending 316.08 145 85 90 5.55% 90 5.43% 4.30% 5.52% 5.55% .29% 4 A EW B C D EW r r r r r r −= = − + −= = = − −= = = −= = − − + + −= = −