B 1 08problem F G H 3/9/22 23:19 9/14/15 3 Problem 8-22 NO SE 5 Bartman Industries' and Reynolds Inc.'s stock prices and dividends, along with the Winslow 5000 Index, are shown 6 here for the period 2010-2015. The Winslow 5000 data are adjusted to indude dividends. 7 8 a. Use the data to calculate annual rates of return for Bartman, Reynolds, and the Winslow 5000 Index. Then 9 calculate each entity's average return over the 5-year period. (Hint: Remember, returns are calculated by 10 subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the 11 capital gain or loss, and dividing the result by the beginning price. Assume that dividends are already included 12 in the index. Also, you cannot calculate the rate of return for 2010 because you do not have 2009 data.) 13 14 Data as given in the problem are shown below: 15 Bartman Industries Reynolds Inc. 16 Winslow 5000 Year Stock Price Dividend Stock Price 17 Dividend Includes Divs. 2015 $17.25 $1.15 18 $48.75 $3.00 $11,663.98 2014 14.75 1.06 19 52.30 2.90 2013 8,785.70 16.50 1.00 20 48.75 2.75 2012 8,679.98 10.75 21 0.95 57.25 2.50 2011 11.37 6,434.03 22 0.90 60.00 2.25 2010 5,602.28 7.62 0.85 23 55.75 2.00 4,705.97 24 We now calculate the rates of return for the two companies and the index for 2011-2015: 25 26 Bartman Reynolds 27 Index 2015 24.7% -1.1% 28 32.8% 2014 4.2% 13.2% 1.2% 2013 62.8% 30 -10.0% 34.9% 2012 2.9% -0.4% 31 14.8% 61.0% 11.7% 32 19.0% 33 Avg Returns 34 29 2011 35 Note: To get the average, you could get the column sum and divide by 5, but you could also use the function wizard, . 36 Click the Formulas tab, fx, then statistical, then Average, and then use the mouse to select the proper range. Do this for Bartman 37 and then copy this cell to put the formula in the other 2 cels. 38 39 b. Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000. (Hint: Use the 40 sample standard deviation formala, Equation 8.2a in this chapter, which corresponds to the STDEV function in Exod.) 41 42 43 44 Bartman 45 Standard deviation of retur Reynolds Index 08problem + 161 x fx D E A B Index Bartman Reynolds 45 44 45 Standard deviation of return 46 47 48 49 c Calculate the coefficients of variation for Bartman, Reynolds, and the Wiinslow 5000. 50 51 52 53 Bartman Reynolds Index 54 Coefficient of Variation 55 56 57 58 d. Construct a scatter diagram that shows Bartman's and Reynolds retums on the vertical axis and the 59 Winslow 5000 Index's retums on the horizontal axis. 60 61 62 63 64 65 e Estimate Bartman's and Reynolds' betas by running regressions of their returns against the index's 66 returns. (Hint: Refer to Web Appendix 8A.) Are these betas consistent with your graph? 67 6B 69 Assume the risk-free rate on long-term Treasury bonds is 4.5%. Assume also that the average annual return on the 70 Winslow 5000 is not a good estimate of the market's required return-It is too high. So use 10% as the expected return 71 on the market. Use the SML equation to calculate the two companies' required retums. 72 73 74 75 R. If you formed a portfolio that consisted of 50% Bartman and 50% Reynolds, what would the portfolio's beta and required 76 return be? 77 78 79 h. Suppose an investor wants to indude Bartman Industries' stock in his portfolio Stocks A, B, and Care currently in the portfolio; and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio's 81 required return if it consists of 25% of Bartman, 15% of Stock A, 40% of Stock B, and 20% of Stock C. 80 82 83 84
