Exam 2 - Sample Solution

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Michigan State University *

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Jan 9, 2024

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Exam II – Sample (Solution) Section 1 - Multiple Choice Questions (each is worth 5 points): Circle only 1 answer 1. Company A’s dividends are expected to grow at a constant rate of g=0.04. This year’s dividend has just been paid. If next year’s expected dividend per share is $5 and r=0.08, then according to the constant growth dividend discount model what would we expect the current stock price to be? a) $62.50 b) $100.00 c) $110.00 d) $125.00 e) $130.00 2. Firm A and Firm B are both expected to have the same earnings next year and investors in both firms use the same discount rate r=10%. However, Firm A’s earnings are expected to grow very slowly in the future, while Firm B’s earnings are expected to grow very rapidly in the future. Given our class discussion of price-earnings ratios, which firm should have a higher P/E ratio? a) Firm A b) Firm B 3. In the Snap Inc. IPO, the stock price of Snap _________ during the first day of trading. a) decreased sharply b) decreased moderately c) increased sharply d) increased moderately 4. In the Snap IPO, we predicted that the cash flows of Snap would be ____________ for several years following the IPO. a) large and positive b) large and negative c) approximately zero 5. Historically, the arithmetic average annual return on U.S. stocks has been: a) above 10% b) between 5% and 10% c) below 5%

6. Kids Toy Co. has had annual returns over the past five years of 3%, 7%, -2%, 10%, and 12%. Based on these data, what is your estimate of this firm’s expected return? a) 6.5% b) 6.0% c) 6.8% 7. 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 unsystematic risk while standard deviation is a measure of total risk c) beta measures only systematic 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 8. Suppose I form a portfolio by placing ½ my money in security A and ½ my money in security B. If the standard deviation of A and B remain fixed, but the correlation between A and B becomes more negative (i.e., it decreases), then my portfolio’s standard deviation will: a) increase b) decrease 9. The set of points in risk-return space (that is in σ/E(r) space) that lie on the northwest boundary of the investment opportunity set is known as ____________. a) the last frontier b) the inefficient frontier c) an accountant’s nightmare d) the efficient frontier 10. Which of the following is true of the optimal risky portfolio? a) it is the portfolio in risk-return space that forms the steepest line when combined with the risk-free security b) it is always the same as the market portfolio according to the CAPM theory c) it is the same for all investors d) a and b e) b and c f) a and b and c

11. A firm’s stock has a beta of 2.0. The market risk premium is 6% and the risk-free rate is 2%. According to the CAPM, what is the expected return for this stock? a) 6% b) 10% c) 12% d) 14% e) 16% 12. You create Firm ABC. This firm raises money from investors and hires professional gamblers to go to Las Vegas each month and gamble all of the firm's cash. The beta on this firm's stock will be ______________. We would expect this stock to have a high level of _________ risk. a) a very large positive number, systematic b) a very large positive number, unsystematic c) a very large negative number, systematic d) a very large negative number, unsystematic e) zero, systematic f) zero, unsystematic 13. Consider the following data: Expected return on stock A = 15%, standard deviation of returns = 10% Expected return on stock B = 20%, standard deviation of returns = 15% Correlation of stock A's return and stock B's return is -0.2 Given these data, what is the covariance between these two stocks? a) -0.003 b) -0.015 c) 0 d) +0.003 e) +0.015 f) none of the above 14. You notice that Stock A tends to increase a great deal when the overall stock market goes up and it decreases a great deal when the overall stock market goes down. The return on Stock B appears to be much less related to how the market is performing. Which stock would you expect to have a higher beta? a) Stock A b) Stock B

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15. There is 40% chance of a boom next year in the economy and a 60% chance of a bust. Stock A is expected to yield a 30% return in a boom and a 10% return in a bust. Stock B is expected to yield a 20% return in a boom and a 10% return in a bust. You invest $1000 in Stock A and $2000 in Stock B. What is the expected return on your portfolio? a) 10.67% b) 12.33% c) 16.00% d) 15.33% e) 17.33% 16. Consider the same data as in the previous problem. What is the covariance of the returns of Stock A and Stock B? a) -0.0048 b) -0.0024 c) 0 d) +0.0024 e) +0.0048 17. Suppose a portfolio P has an expected return of 12% and a standard deviation of 16%. The risk-free interest rate is 6%. If your client requests that you construct a portfolio from portfolio P and risk-free securities with a standard deviation of 8% what will your client’s expected return be? a) 6% b) 8% c) 9% d) 12% e) none of the above 18. The market’s expected return next year is 16% and a stock with a beta of 0.5 has an expected return of 10%. What must the risk-free rate be? a) 2% b) 4% c) 6% d) 8% 19. Suppose a stock has a beta of -0.5. According to the CAPM, the expected return on this stock would be _________. a) greater than the risk-free rate b) equal to the risk-free rate c) less than the risk-free rate

20. A portfolio has experienced the following returns over the past two years: Year -2: +50% Year -1: -50% What was the firm’s geometric average annual return over this two-year period? a) A negative number b) 0 c) A positive number 21. Over time in the U.S., stock returns have on average been _________ than the returns on corporate bonds, and the standard deviation of stock returns has been _____________ than the standard deviation of returns on bonds. a) higher, higher b) higher, lower c) lower, higher d) lower, lower 22. Are the following data consistent with the CAPM model? Portfolio Expected Return Standard Deviation Risk-free 0.10 0 Market 0.18 0.24 Portfolio A 0.14 0.20 a) Yes b) No 23. If an investor takes a negative position in a stock, this is known as __________ and if they invest more than 100% of their funds in a stock this is known as ________________. a) long selling, buying on margin b) short selling, buying on margin c) long selling, buying on option d) short selling, buying on option 24. In estimating Ameritrade's cost of capital, in our calculations we argued that it was best to use beta estimates from __________ in the ____________. a) a single firm, automobile industry b) a single firm, discount brokerage industry c) several other firms, automobile industry d) several other firms, discount brokerage industry

25. Ameritrade had a beta that was substantially __________1.0. a) above b) below

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Section 2 - Long Answer Problems (12.5 points each): Show your work clearly 1. Consider the return behavior of the following two stocks: State of Economy Probability of State Return on Stock A Return on Stock B Recession 0.5 -10.0% -5.0% Boom 0.5 +20.0% +15.0% An investor with $1 million plans to invest $400,000 in Stock A and $600,000 in Stock B. What will be the standard deviation of her portfolio? Note that the weights in A and B are: w A = 0.4 ∧ w B = 0.6 Method 1: State Return on Portfolio Recession w A R A + w B R B = 0.4 × − 0.1 + 0.6 × − 0.05 =− 0.07 Boom w A R A + w B R B = 0.4 × 0.2 + 0.6 × 0.15 = 0.17 Then: R P = Prob ( Rec ) × R P ( Rec ) + Prob ( Boom ) ×R P ( Boom ) ¿ 0.5 × − 0.07 + 0.5 × 0.17 = 0.05 And, σ P 2 = Prob ( Rec ) × [ R P ( Rec ) − R P ] 2 + Prob ( Boom ) × [ R P ( Boom ) − R P ] 2 = 0.5 ( − 0.07 − 0.05 ) 2 + 0.5 ( 0.17 − 0.05 ) 2 = 0.0144 So σ p = √ σ P 2 = √ 0.0144 = 0.12 or 12% Method 2: R A = Prob ( Rec ) ×R A ( Rec ) + Prob ( Boom ) ×R A ( Boom ) ¿ 0.5 × − 0.10 + 0.5 × 0.20 = 0.05 R B = Prob ( Rec ) ×R B ( Rec ) + Prob ( Boom ) ×R B ( Boom ) ¿ 0.5 × − 0.05 + 0.5 × 0.15 = 0.05 And, σ A 2 = Prob ( Rec ) × [ R A ( Rec ) − R A ] 2 + Prob ( Boom ) × [ R A ( Boom ) − R A ] 2 = 0.5 ( − 0.10 − 0.05 ) 2 + 0.5 ( 0.2 − 0.05 ) 2 = 0.0225 σ B 2 = Prob ( Rec ) × [ R B ( Rec ) − R B ] 2 + Prob ( Boom ) × [ R B ( Boom ) − R B ] 2 = 0.5 ( − 0.05 − 0.05 ) 2 + 0.5 ( 0.15 − 0.05 ) 2 = 0.01 σ AB = Prob ( Rec ) × [ R A ( Rec ) − R A ] [ R B ( Rec ) − R B ] + Prob ( Boom ) × [ R A ( Boom ) − R A ] [ R B ( Boom ) − R B ] ¿ 0.5 × [ − 0.10 − 0.05 ] [ − 0.05 − 0.05 ] + 0.5 × [ 0.20 − 0.05 ] [ 0.15 − 0.05 ] = 0.015

Now, we can apply Rule 2: σ P 2 = w A 2 σ A 2 + w B 2 σ B 2 + 2 w A w B σ AB ¿ 0.4 2 × 0.0225 + 0.6 2 × 0.01 + 2 × 0.4 × 0.6 × 0.015 = 0.0144 And, σ p = √ σ P 2 = √ 0.0144 = 0.12 or 12% 2. You are constructing an investment portfolio by buying Stock X and Stock Y. You have a total of $10,000 to invest. The expected return on Stock X is 10% with a standard deviation of 20%. The expected return on Stock Y is 12% with standard deviation of 24%. The correlation coefficient between Stock X and Stock Y is -0.3. a. If you invest $4,000 in Stock X and $6,000 in Stock Y, what is the expected return of your portfolio? R P = w X R X + w Y R Y = 0.4 × 0.1 + 0.6 × 0.12 = 0.112 b. If you invest $4,000 in Stock X and $6,000 in Stock Y, what is the standard deviation of your portfolio? Using Rule 2: σ P 2 = w X 2 σ X 2 + w Y 2 σ Y 2 + 2 w X w Y σ X σ Y ρ XY ¿ 0.4 2 × 0.2 2 + 0.6 2 × 0.24 2 + 2 × 0.4 × 0.6 × 0.2 × 0.24 × − 0.3 = 0.020224 And, σ p = √ σ P 2 = √ 0.020224 = 0.1422 or 14.22% c. Given you answers to (a) and (b), if the investor had a choice between: choice 1 of placing all $10,000 in Stock X and choice 2 of placing $4,000 in Stock X and $6,000 in Stock Y, which choice would the investor prefer. Explain your reasoning. Note that stock X has a lower expected return than the portfolio (10% vs 11.2%) yet has a higher standard deviation (20% vs 14.22%). Therefore, choice 2 is a better choice as it offers a better reward for less risk.