Financial management(BSM-410) problem solving 6
8-1 EXPECTED RETURN A stock’s returns have the following distribution: Assume the risk-free rate is 2%. Calculate the stock’s expected return, standard deviation, coefficient of variation, and Sharpe ratio 8-4 EXPECTED AND REQUIRED RATES OF RETURN Assume that the risk-free rate is 3.5% and the market risk premium is 4%. What is the required return for the overall stock market? What is the required rate of return on a stock with a beta of 0.8? 8-7 PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4.82 million investment fund. The fund consists of four stocks with the following investments and betas: If the market’s required rate of return is 8% and the risk-free rate is 4%, what is the fund’s required rate of return? 8-17 PORTFOLIO BETA A mutual fund manager has a $20 million portfolio with a beta of 1.7. The risk-free rate is 4.5%, and the market risk premium is 7%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund’s required return to be 15%. What should be the average beta of the new stocks added to the portfolio? 8-22 EVALUATING RISK AND RETURN Bartman Industries’s and Reynolds Inc.’s stock prices and dividends, along with the Winslow 5000 Index, are shown here for the period 2015–2020. The Winslow 5000 data are adjusted to include dividends. A. Use the data to calculate annual rates of return for Bartman, Reynolds, and the Winslow 5000 Index. Then calculate each entity’s average return over the 5-year period. (Hint: Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and dividing the result by the beginning price. Assume that dividends are already included in the index. Also, you cannot calculate the rate of return for 2015 because you do not have 2014 data.) B. Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000. (Hint: Use the sample standard deviation formula) C. Calculate the coefficients of variation for Bartman, Reynolds, and the Winslow 5000. D. Assume the risk-free rate during this time was 3%. Calculate the Sharpe ratios for Bartman, Reynolds, and the Index over this period using their average returns. E. construct a scatter diagram that shows Bartman’s and Reynolds’s returns on the vertical axis and the Winslow 5000 Index’s returns on the horizontal axis. F. Estimate Bartman’s and Reynolds’s betas by running regressions of their returns against the index’s returns. (Hint: Refer to Web Appendix 8A.) Are these betas consistent with your graph? G. Assume that the risk-free rate on long-term Treasury bonds is 4.5%. Assume also that the average annual return on the Winslow 5000 is not a good estimate of the market’s required return—it is too high. So use 10% as the expected return on the market. Use the SML equation to calculate the two companies’ required returns. H. If you formed a portfolio that consisted of 50% Bartman and 50% Reynolds, what would the portfolio’s beta and required return be? I. Suppose an investor wants to include Bartman Industries’s stock in his portfolio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio’s required return if it consists of 25% of Bartman, 15% of Stock A, 40% of Stock B, and 20% of Stock C. Source: Eugene F. Brigham; Joel F. Houston (2022). Fundamentals of Financial Management: Concise (11th Edition). Cengage Learning
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