# 07%20risk%20and%20return%20extra%20problems.doc

## Finance 491 with Pilofo at George Mason University *

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Hassaan K.

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FNAN 301 Extra problems – risk and return 1. Amazon has never paid any dividends. Eleven years ago, the firm’s stock was selling for $7.88 per share. Today the stock is priced at $78.96. What was the compound return over the past 11 years? 2. Fargo stock had the following returns over the eight-year period between January 1, 2000, and December 31, 2007: geometric average annual rate of return of 9 percent and arithmetic average annual rate of return of 10 percent. If the market value of an investor’s shares at the beginning of 2000 was $1,000,000 and the stock paid no dividends over the period, then what was the market value of the shares at the end of 2007? If there is insufficient information to answer the question, write “insufficient information” as your answer. Assume that the investor did not buy or sell any shares during the relevant period. 3. Twenty years ago, you bought stock in 3 companies: $1,000 worth of Murphy Corporation; $1,000 worth of Brown Corporation, and $1,000 worth of Jackson Corporation. None of the stocks has ever paid a dividend. Based on the information in the question and table, which assertion is true regarding the values of the three investments? Murphy Brown Jackson Average annual return 15.5% 14.7% 15.1% Compound return 12.7% 13.6% 11.5% Standard deviation of returns 20.0% 23.7% 29.4% A. Today, the value of your investment in Murphy would be worth the most of the three B. Today, the value of your investment in Brown would be worth the most of the three C. Today, the value of your investment in Jackson would be worth the most of the three D. At least two of the three investments would be tied for being worth the most today E. It is not clear which of the three investments would be worth the most today 4. A stock had returns of 9.0%, 3.0%, -7.0%, and 7.0% over the past four years. a. What was the arithmetic mean return? b. What was the compound return? c. What was the variance of returns? d. What was the standard deviation of returns? 5. A stock had returns of 5%, 8%, -3%, 10%, and 7% over the past five years. a. What was its arithmetic average return? b. What was its geometric return? c. What was its variance of returns? d. What was its standard deviation of returns? 6. Shares of the Barclo Company are currently priced at $30 per share. The following table indicates what could happen with the economy and Barclo stock over the next year State of Economy Probability Price of Barclo Dividend paid by Barclo Boom .2 $87 $3 Normal .4 $30 $0 Recession .4 $0 $0 a. What is the expected return of Barclo stock? b. What is the standard deviation of Barclo stock’s returns? 7. What are the portfolio weights for a portfolio that has 60 shares of Stock A that sell for $30 per share and 40 shares of Stock B that sell for $50 per share? 8. You own a portfolio that has $1,500 invested in Stock A and $2,000 invested in Stock B. If the expected returns on these stocks are 12% and 15%, respectively, what is the expected return on the portfolio? 9. Consider the following information: State of economy Probability Stock A return Stock B return Boom .3 .20 .35 Normal .5 .15 .12 Bust .2 .01 -.25 a. What is the expected return of stock A? b. What is the standard deviation of stock A’s returns? c. What is the expected return of stock B? d. What is the standard deviation of stock B’s returns? e. What is the expected return on a portfolio of these two stocks if you invested $20,000 in Stock A and $50,000 in Stock B? f. What is the standard deviation of the portfolio? 10. Melanie Murdock owns 100 shares of Arnot Industries, 200 shares of Beehive Technology, and 400 shares of Crown Software. The current share price is $30 for Arnot is $20 for Beehive, and $2.50 for Crown. There are two possible outcomes that could take place over the next year. There is a 60 percent chance of a boom and a 40 percent chance of a bust. The following table presents the returns for each of Melanie’s stocks in each of the possible outcomes. State of Economy Arnot Return Beehive Return Crown Return Boom 30% 20% 0% Bust -10% 10% 20% a. What is the expected return of Melanie’s portfolio? b. What is the standard deviation of the returns of Melanie’s portfolio? 11. Your portfolio is valued at $20,000 and has an expected return of 15.0 percent. You own some of stock A and some of stock B. If stock A has an expected return of 18.0 percent and stock B has an expected return of 13.4 percent, then what are the values of your holdings of stocks A and B? 12. Marge Simpson’s investment portfolio has 2 stocks: $13,000 worth of Duff Beer, which has an expected return of 16.0 percent and $19,000 worth of Kwik-E-Mart Corporation. If Marge’s portfolio has an expected return of 14.0 percent, then what is the expected return on Kwik-E-Mart stock? 13. Homer Simpson’s investment portfolio has 2 stocks: Duff Beer, which has an expected return of 16.0 percent and Springfield Nuclear Power (SNP) Corporation, which has an expected return of 10.5 percent. If Homer’s portfolio has an expected return of 14.2 percent, then what is the weight in his portfolio for SNP stock? 14. If Treasury Bills have a return of 2.9% and the required rate of return for Marcus stock is 15.8%, what is the risk premium on Marcus stock? 15. If the risk premium for Label-Fair stock is 4.2% and the expected return on a Label-Fair stock is 7.5%, what is the rate being offered on Treasury Bills? 16. If Treasury Bills have a return of 1.1% and the risk premium for Landly stock is 28.0%, what is the expected return Landly stock? 17. If Treasury Bills have a return of 5.1% and the risk premium for a collection of all common stocks is 8.4%, what is the required rate of return for a collection of all common stocks? 18. If Treasury Bills have a return of 7.7% and the required rate of return for a collection of all common stocks is 18.8%, what is the risk premium for a collection of all common stocks? 19. If the risk premium for a collection of all common stocks is 9.5% and the expected return on a collection of all common stocks is 15.2%, what is the rate being offered on Treasury Bills? 20. Many firms in the U.S. automobile sector are currently experiencing severe financial difficulties. Yesterday, the Wall Street Journal reported that market experts and investors expected General Motors to report a loss of $2 billion for their most recent fiscal year. This morning, General Motors announced that it is experiencing severe financial difficulties and that it suffered a very large loss in the most recent fiscal year of $1.5 billion. The amount of the loss was not known before the announcement, so the announcement can be considered the release of new information. Which of the following assertions do you think best describes what most likely happened with GM stock today? No other news was released except for earnings and risk is expected to remain unchanged. Assume past returns are a good predictor of future returns. A. The actual return was greater than the expected return B. The actual return was less than the expected return C. The actual return was equal to the expected return 21. Gable Electronics has increased its dividends by 2 percent a year for each of the past 28 years. Recently, it has been experiencing very high levels of growth, so market experts and investors anticipated that the firm would announce that it expects dividends to increase by 5 percent a year forever. This morning, Gable announced that it expects dividends to increase by 4 percent a year forever, which would be higher than any annual dividend increase in the company’s history. The amount of the expected dividend increase was not known before the announcement, so the announcement can be considered the release of new information. Which of the following assertions do you think best describes what most likely happened with Gable stock today? No other news was released except the expected dividend increase and risk is expected to remain unchanged. A. The actual return was greater than the expected return B. The actual return was less than the expected return C. The actual return was equal to the expected return 22. Eleanor Rigby owns 3 stocks. Her portfolio has a beta of 1.29. Given the information on in the following table, what is the beta of Advisicon? Shares Share price Beta Advisicon 2,000 $30.00 ? Cornerium 5,000 $14.00 1.40 Ventico 3,500 $20.00 1.60 23. Barney Rubble owns a portfolio worth $12,000 that consists of 2 stocks: Barbicon Enterprises, which has a beta of 1.40, and Center Stage Productions, which has a beta of 0.50. How much is his Center Stage stock worth if his portfolio has a beta of 0.85? 24. Suppose the expected return on the market is 18.0 percent and the risk-free rate is 6.0 percent. According to the CAPM: a. What is the expected return on Southwest Air stock if its beta is 1.5? b. What is the expected return on Caterpillar stock if its beta is 1.2? c. What is the expected return on McDonald’s stock if its beta is 0.9? d. What is the expected return on Lightbulb Edison stock if its beta is 0.4? e. What is the expected return on Rainy Day Fun stock if its beta is -0.7? 25. Juan Pablo Montoya has a portfolio that consists of 600 shares of GlaxoSmithKline (GSK) common stock, which are priced at $29.00, and 4,000 shares of General Motors (GM) common stock priced at $1.50 each. The beta for GSK is 0.75 and the beta for GM is 1.65. a. What is the beta of Juan Pablo’s portfolio? b. If the risk-free rate is 2.0 percent and the market risk premium is 8.5 percent, then what is the expected return on Juan Pablo’s portfolio? c. If the risk-free rate is 2.0 percent and the market risk premium is 8.5 percent, then what is the reward-to-risk ratio for Juan Pablo’s portfolio? 26. Barry has $15,000 invested in a stock A, which has a beta of 1.60; $20,000 invested in stock B, which has a beta of 1.20; and $25,000 invested in stock C, which has a beta of -0.60. a. What is the beta of Barry’s portfolio? b. What is the expected return of Barry’s portfolio if the expected return on the market is 11.6 percent and the risk-free return is 2.8 percent? c. What is the reward-to-risk ratio of Barry’s portfolio if the expected return on the market is 11.6 percent and the risk-free return is 2.8 percent? 27. If the expected return on the market is 16.0 percent, the risk-free rate is 4.0 percent, and Telestration Corporation common stock has an expected return of 14.8 percent, then what is the beta for Telestration Corporation according to the CAPM? 28. If the expected return on Pluppinatti Corporation stock is 8.6 percent, the risk-free rate is 2.0 percent, and Pluppinatti stock has a beta of 0.60, then what is the expected return on the market if the CAPM holds? 29. If the expected return on Lois Lane’s portfolio is 17.8 percent, the expected return on the market is 16.0 percent, and Lois’ portfolio has a beta of 1.25, then what is the risk-free rate according to the CAPM? 30. Based on the information in the table on the stocks of 4 companies, which of the assertions is true? Company Johnson Whitman Blair Einstein Average annual return over the past 5 years 12% 13% 14% 15% Compound return over the past 5 years 10% 9% 8% 7% Standard deviation of returns over the past 5 years 10% 12% 14% 13% Beta 1.3 1.4 1.2 1.1 A. Johnson stock has a higher expected return than the other three stocks B. Whitman stock has a higher expected return than the other three stocks C. Blair stock has a higher expected return than the other three stocks D. Einstein stock has a higher expected return than the other three stocks The following questions are very similar to question asked previously in this document. They provide opportunities for additional practice. 31. A stock had returns of -25%, -18%, 30%, and 9% over the past four years. a. What was its arithmetic average return? b. What was its geometric return? c. What was the variance of its returns? d. What was the standard deviation of its returns? 32. Consider the following information: State of economy Probability Stock A return Stock B return Boom .75 .320 .160 Bust .25 -.200 .000 a. What is the expected return on a portfolio of these two stocks if you have $3,000 in Stock A and $5,000 in Stock B? b. What is the standard deviation of the portfolio? 33. An individual has $35,000 invested in a stock which has a beta of 0.8 and $40,000 invested in a stock with a beta of 1.4. a. If these are the only two investments in her portfolio, what is her portfolio’s beta? b. If the risk-free rate is 3.0 percent and the expected return on the market is 12.0 percent, then what is the expected return on her portfolio? c. If the risk-free rate is 3.0 percent and the expected return on the market is 12.0 percent, then what is the reward-to-risk ratio for her portfolio? PAGE \* MERGEFORMAT 5

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