Fundamentals of Corporate Finance
11th Edition
ISBN: 9780077861704
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Chapter 12, Problem 15QP
Arithmetic and Geometric Returns [LO1] A stock has had returns of 9 percent, 21 percent, 32 percent, −18 percent, 27 percent, and −12 percent over the last six years. What are the arithmetic and geometric returns for the stock?
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Arithmetic and Geometric Returns (LO1) A stock has had returns of 9%,21%,32%,-18%,27%, and -12% over the last six years. What are the arithmetic and geometric returns for the stock?
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Chapter 12 Solutions
Fundamentals of Corporate Finance
Ch. 12.1 - Prob. 12.1ACQCh. 12.1 - Why are unrealized capital gains or losses...Ch. 12.1 - What is the difference between a dollar return and...Ch. 12.2 - Prob. 12.2ACQCh. 12.2 - Why doesnt everyone just buy small stocks as...Ch. 12.2 - What was the smallest return observed over the 88...Ch. 12.2 - About how many times did large-company stocks...Ch. 12.2 - What was the longest winning streak (years without...Ch. 12.2 - How often did the T-bill portfolio have a negative...Ch. 12.3 - Prob. 12.3ACQ
Ch. 12.3 - What was the real (as opposed to nominal) risk...Ch. 12.3 - Prob. 12.3CCQCh. 12.3 - What is the first lesson from capital market...Ch. 12.4 - In words, how do we calculate a variance? A...Ch. 12.4 - With a normal distribution, what is the...Ch. 12.4 - Prob. 12.4CCQCh. 12.4 - What is the second lesson from capital market...Ch. 12.5 - Prob. 12.5ACQCh. 12.5 - Prob. 12.5BCQCh. 12.6 - What is an efficient market?Ch. 12.6 - Prob. 12.6BCQCh. 12 - Chase Bank pays an annual dividend of 1.05 per...Ch. 12 - The risk premium is computed as the excess return...Ch. 12 - Prob. 12.4CTFCh. 12 - Prob. 12.5CTFCh. 12 - Prob. 12.6CTFCh. 12 - Investment Selection [LO4] Given that Fannie Mae...Ch. 12 - Prob. 2CRCTCh. 12 - Risk and Return [LO2, 3] We have seen that over...Ch. 12 - Market Efficiency Implications [LO4] Explain why a...Ch. 12 - Efficient Markets Hypothesis [LO4] A stock market...Ch. 12 - Semistrong Efficiency [LO4] If a market is...Ch. 12 - Efficient Markets Hypothesis [LO4] What are the...Ch. 12 - Stocks versus Gambling [LO4] Critically evaluate...Ch. 12 - Efficient Markets Hypothesis [LO4] Several...Ch. 12 - Efficient Markets Hypothesis [LO4] For each of the...Ch. 12 - Calculating Returns [LO1] Suppose a stock had an...Ch. 12 - Calculating Yields [LO1] In Problem 1, what was...Ch. 12 - Prob. 3QPCh. 12 - Prob. 4QPCh. 12 - Nominal versus Real Returns [LO2] What was the...Ch. 12 - Bond Returns [LO2] What is the historical real...Ch. 12 - Prob. 7QPCh. 12 - Risk Premiums [LO2, 3] Refer to Table 12.1 in the...Ch. 12 - Calculating Returns and Variability [LO1] Youve...Ch. 12 - Calculating Real Returns and Risk Premiums [LO1]...Ch. 12 - Calculating Real Rates [LO1] Given the information...Ch. 12 - Prob. 12QPCh. 12 - Prob. 13QPCh. 12 - Calculating Returns and Variability [LO1] You find...Ch. 12 - Arithmetic and Geometric Returns [LO1] A stock has...Ch. 12 - Arithmetic and Geometric Returns [LO1] A stock has...Ch. 12 - Using Return Distributions [LO3] Suppose the...Ch. 12 - Prob. 18QPCh. 12 - Distributions [LO3] In Problem 18, what is the...Ch. 12 - Blumes Formula [LO1] Over a 40-year period an...Ch. 12 - Prob. 21QPCh. 12 - Calculating Returns [LO2, 3] Refer to Table 12.1...Ch. 12 - Using Probability Distributions [LO3] Suppose the...Ch. 12 - Using Probability Distributions [LO3] Suppose the...Ch. 12 - Prob. 1MCh. 12 - Prob. 2MCh. 12 - Prob. 3MCh. 12 - Prob. 4MCh. 12 - A measure of risk-adjusted performance that is...Ch. 12 - Prob. 6M
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- Consider the rate of return of stocks ABC and XYZ. Year rABC rXYZ 1 20 % 28 % 2 8 11 3 16 19 4 4 1 5 2 −9 a. Calculate the arithmetic average return on these stocks over the sample period. b. Which stock has greater dispersion around the mean return? A. ABC B. XYZ c. Calculate the geometric average returns of each stock. What do you conclude? (Do not round intermediate calculations. Round your answers to 2 decimal places.) d. If you were equally likely to earn a return of 20%, 8%, 16%, 4%, or 2%, in each year (these are the five annual returns for stock ABC), what would be your expected rate of return? (Do not round intermediate calculations.) e. What if the five possible outcomes were those of stock XYZ? f. Given your answers to (d) and (e), which measure of average return, arithmetic or geometric, appears more useful for predicting future performance? A. Arithmetic B. Geometricarrow_forward5."A stock has yielded 15.3%, 10.8%, 5.2%, -3.4%, and 14% over the past five years, respectively. What is the geometric average return? " Please use excel to answerarrow_forwardNow assume that the stock is currently selling at $30.29. What is its expected rate of return?arrow_forward
- Consider the rate of return of stocks ABC and XYZ. Year rABC rXYZ 1 20 % 28 % 2 8 11 3 16 19 4 4 1 5 2 −9 (PLEASE SKIP THE FIRST THREE QUESTIONS) a. Calculate the arithmetic average return on these stocks over the sample period. b. Which stock has greater dispersion around the mean return? multiple choice A. ABC B. XYZ c. Calculate the geometric average returns of each stock. What do you conclude? (Do not round intermediate calculations. Round your answers to 2 decimal places.) d. If you were equally likely to earn a return of 20%, 8%, 16%, 4%, or 2%, in each year (these are the five annual returns for stock ABC), what would be your expected rate of return? (Do not round intermediate calculations.) e. What if the five possible outcomes were those of stock XYZ? f. Given your answers to (d) and (e), which measure of average return, arithmetic or geometric, appears more useful for predicting future…arrow_forwardProblem 2 . Suppose your expectations regarding the stock price are as follows: State of the Market Probability Ending Price Boom 0.35 Normal growth 0.30 Recession 0.35 $140 110 80 HPR (including dividends) 44.5% 14.0 -16.5 Use Equations 5.11 and 5.12 to compute the mean and standard deviation of the HPR on stocks.arrow_forwardWhat is the standard deviation of returns on a stock priced today at $10 that has a 25.0% probability of increasing to $13, a 50.0% probability of increasing to $12, a 15.0% probability of increasing by 5.0%, and a 10.0% probability of decreasing to $ 7? 0.0286 0.0968 0.1692 0.0094arrow_forward
- . You have observed the following returns over time: Stock X Stock Y Year Price Div Price Div Market Returns 2005 20 0 11 0 0 2006 24 1.2 13 1.6 0.25 2007 26 0.5 17 0.5 0.18 2008 31 1 20 0.9 0.11 2009 33 1.5 23 1.2 0.12 2010 40 2 27 1.5 0.15 a. Calculate the annual returns for each stock (2006-2010) b. Calculate the average returns for each of the stocks and the market c. Calculate the covariance between the stocks d. Compute the portfolio return and portfolio risk if the Stock A and Stock B are combined equally in a portfolio.arrow_forwardQ.Which of the following statements are true/false: I: The implied volatility of a stock can be calculated by deternining the standard deviation of stock returns over the last one year. II: The implied volatility of a stock can be calculated by deternining the standard deviation of stock returns over the last six months. A. I is true, II is false B. I is false, II is true C. I and II are both false D. I and II are both truearrow_forwardWhat is the standard deviation of the returns on a stock given the following information? Could you please show the work? State of Economy Probability of state of Economy Rate of return if state occurs Boom 0.3000 0.1500 Normal 0.6500 0.1200 Recession 0.0500 0.0600 Average 0.3333 0.1100arrow_forward
- A stock has had returns of −19 percent, 29 percent, 24 percent, −10.1 percent, 34.8 percent, and 27 percent over the last six years. What is the geometric return for the stock?arrow_forward5. Given the following expectations for the next year, what is the expected return, standard deviation, and beta of Stock A? Use the excel sheet we covered to find the answer. Returns Probability Stock A Market 0.10 0.05 0.02 0.25 0.09 0.08 0.30 0.13 0.12 0.25 0.19 0.15 0.10 0.21 0.16arrow_forwardWhat is the standard deviation of the returns on a stock given the following information? State of Economy Probability of State of Economy Rate of Return if State Occurs Boom .08 .171 Normal .70 .076 Recession .22 .017arrow_forward
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