Problem Set 10 QRM 3001 PDF

Problem Set 10 QRM 3001 (Fall 2024) Due: November 15, 2024 at 0:00 AM (Thursday midnight) Problem 1. Answer the following questions. (a) Describe the similarities between computing average return and expected return. Also, describe the similari...

Problem Set 10 QRM 3001 (Fall 2024) Due: November 15, 2024 at 0:00 AM (Thursday midnight) Problem 1. Answer the following questions. (a) Describe the similarities between computing average return and expected return. Also, describe the similarities between expected return risk and historical risk. (b) Why would people take risk by investing their hard-earned money? Answer: (a) Average return is computed using the simple average of historical returns. The expected return is a forward-looking return. However, it is computed using a weighted average (the probabilities) of returns. The returns used in the various economic stages are usually chosen from historical knowledge of how the firm performs in each stage. Thus, both measures use an average of historical returns in one way or another. The historical risk and expected risk are both measured using standard deviation and historical knowledge of returns as well. (b) Many people are willing to take market risk because over time they expect to earn a risk premium. This risk premium allows them to build their wealth significantly more than just investing in the risk-free asset. However, because risk is involved, these people should have a long-term focus and recognize that they can lose money in the short term. Problem 2. Answer the following questions. (a) Explain why portfolios that lie on the capital market line offer better risk-return trade-offs than those that lie on the efficient frontier. (b) Examine betas in the table in the lecture slide 10-13. Which seem about right to you and which seem to indicate too much or too little risk for that firm? Answer: (a) For every point on the efficient frontier (except the market portfolio), you can form a portfolio that has the same level of risk but a higher expected return through a combination of the market portfolio and the risk-free asset. Thus, the capital market line has a better risk-return trade-off because it has a higher return at every level of risk. (b) Procter & Gamble and Johnson & Johnson are diversified firms selling consumer goods that are purchased in good economies and bad. Therefore, their low betas of 0.38 and 0.70 seem reasonable. Nike is an apparel firm that is in a market share battle with Under Armor and Adidas, so its beta of 0.84 seems too low. Financial firm Goldman Sachs’ beta is 1.50. That seems high in comparison to competitor JPMorgan Chase’s beta of 1.22 1 Problem 3. Answer the following questions. (a) Can the market be semi-strong-form efficient but not week-form efficient? Explain. (b) If the market usually overreacts to bad news announcements, what would your return be like if you brought after you heard the bad news? Answer: (a) No. Weak-form efficiency is a subset of semi-strong-form efficiency. Information about market prices and volumes is public and is thus included in the broader definition of public information in the semi-strong-form efficiency hypothesis. Therefore, if a market is semi-strong-form efficient, it is also weak-form efficient, by definition. (b) Consider a case when the market consistently overreacted to bad news announcements. This means that prices would fall too far after the announcement and eventually partially rebound. If this scenario was predictable, an investor could make money by buying stocks after bad news and cap- turing the price bounce. Problem 4. Why is the shareholders’ required return important to corporate managers? Answer: Consider that you obtained money from the bank and had to pay an 8 percent interest rate. If you invested that money in a project that returned 5 percent to you, then you would not be earning enough to pay back the bank. You need to earn more than 8 percent on your business project in order to be successful. Corporate managers are using the shareholders’ equity capital and need to know what return they require. This return is more difficult to estimate than a bank loan, but it helps managers to know what return they must achieve when using the capital to fund business opportunities. Problem 5. If the risk-free rate is 3 percent and the risk premium is 5 percent, what is the required return? Answer: Required return = 3% + 5% = 8% Problem 6. Hastings Entertainment has a beta of 0.65. If the market return is expected to be 11 percent and the risk-free rate is 4 percent, what is Hastings’ required return? Answer: Hastings’ required return = 4% + 0.65 × (11% - 4%) = 8.55% 2 Problem 7. You have a portfolio with a beta of 1.35. What will be the new portfolio beta if you keep 85 percent of your money in the old portfolio and 5 percent in a stock with a beta of 0.78? Answer: New portfolio beta = (0.85 × 1.35) + (0.15 × 0.78) = 1.26 Problem 8. Paccar’s current stock price is $48.20 and it is likely to pay a $0.80 dividend next year. Since analysts estimate Paccar will have an 8.8% growth rate, what is its required return? Answer: D1 $0.80 Use the equation in slide 10-31: i = P1 +g = $48.20 + 0.088 = 0.1046 or 10.46% Problem 9. For the same economic state probability distribution described below, determine the stan- dard deviation of the expected return Economic State Probability Return Fast growth 0.3 40% Slow growth 0.4 10% Recession 0.3 -25% Answer: Expected return = (0.3 × 40%) + (0.4 × 10%) + (0.3 × -25%) = 8.5% Standard q deviation 2 2 2 = 0.3 × (40% − 8.5%) + 0.4 × (10% − 8.5%) + 0.3 × (−25% − 8.5%) √ = 297.7 + 0.9 + 336.7 = 25.21% Problem 10. You own $10,000 of Olympic Steel stock that has a beta of 2.2. You also own $7,000 of Rent-a-Center (beta = 1.5) and $8,000 of Lincoln Educational (beta = 0.5). What is the beta of your portfolio? Answer: First determine the total value of the portfolio and the weights of each stock in the portfolio: Total value = $10,000 + $7,000 + $8,000 = $25,000 Olympic Steel weight = $10,000 / $25,000 = 40% Rent-a-Center weight = $7,000 / $25,000 = 28% Lincoln Educational weight = $8,000 / $25,000 = 32% Now compute the portfolio beta: (0.40 × 2.2) + (0.28 × 1.5) + (0.32 × 0.5) = 1.46 Problem 11. You own $10,000 of Denny’s Corp stock that has a beta of 2.9. You also own $15,000 of Qwest Communications (beta = 1.5) and $5,000 of Southwest Airlines (beta = 0.7). Assume that 3 the market return will be 11.5 percent and the risk-free rate is 4.5 percent. What is the market risk premium? What is the risk premium of each stock? What is the risk premium of the portfolio? Answer: Market risk premium = 11.5% - 4.5% = 7% Denny’s risk premium = 2.9 × (11.5% - 4.5%) = 20.30% Qwest’s risk premium = 1.5 × (11.5% - 4.5%) = 10.50% Southwest Airlines’ risk premium = 0.7 × (11.5% - 4.5%) = 4.9% For the portfolio, determine the total value of the portfolio and the weights of each stock in the portfolio: Total value = $10,000 + $15,000 + $5,000 = $30,000 Now compute the portfolio beta: (0.3333 × 2.9) + (0.5 × 1.5) + (0.1667 × 0.7) = 1.833 So, the portfolio’s risk premium = 1.833 × (11.5% - 4.5%) = 12.83% Problem 12. Using the information in the table, compute the required return for each company using both CAPM and the constant growth model. Compare and discuss the results. Assume that the market portfolio will earn 12 percent and the risk-free rate is 3.5 percent. Company Price Upcoming Dividend Growth Beta US Bancorp $36.55 $1.60 10.0% 1.8 Praxair $64.75 $1.12 11.0% 2.4 Eastman Kodak $24.95 $1.00 4.5% 0.5 Answer: First, use CAPM to determine each firm’s required return: US Bancorp required return = 3.5% + 1.8 × (12% - 3.5%) = 18.8% Praxair required return = 3.5% + 2.4 × (12% - 3.5%) = 23.9% Eastman Kodak required return = 3.5% + 0.5 × (12% - 3.5%) = 7.75% Now, compute the required return using the constant growth rate model: US Bancorp required return = $1.60 / $36.55 + 0.10 = 14.38% Praxair required return = $1.12 / $64.75 + 0.11= 12.73% Eastman Kodak required return = $1.00 / $24.95 + 0.045 = 8.51% The US Bancorp CAPM estimate of 18.8 percent is too high compared to the 14.38 percent constant growth rate model estimate. The CAPM estimate for Praxair is far different than the constant growth rate model estimate. The CAPM estimate for Eastman Kodak is similar to that of the constant growth rate model. 4