Start with the partial model in the file IFM9 Ch02 P14 Build a Model.xls from the ThomsonNOW Web site. Bartman Industries' and Reynolds Incorporated's stock prices and dividends, along with the Market Index, are shown below. Stock prices are reported for December 31 of each year, and dividends reflect those paid during the year. The market data are adjusted to include dividends.
| |
BARTMAN INDUSTRIES |
REYNOLDS INCORPORATED |
Market Index |
| Year |
Stock Price |
Dividend |
Stock Price |
Dividend |
Includes Divs. |
|
2006
|
$17.250
|
$1.15
|
$48.750
|
$3.00
|
11,663.98
|
|
2005
|
14.750
|
1.06
|
52.300
|
2.90
|
8,785.70
|
|
2004
|
16.500
|
1.00
|
48.750
|
2.75
|
8,679.98
|
|
2003
|
10.750
|
0.95
|
57.250
|
2.50
|
6,434.03
|
|
2002
|
11.375
|
0.90
|
60.000
|
2.25
|
5,602.28
|
|
2001
|
7.625
|
0.85
|
55.750
|
2.00
|
4,705.97
|
a. Use the data given to calculate annual returns for Bartman, Reynolds, and the Market Index, and then calculate average returns 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 2001 because you do not have 2000 data.)
b. Calculate the standard deviations of the returns for Bartman, Reynolds, and the Market Index. (Hint: Use the sample standard deviation formula given in the chapter, which corresponds to the STDEV function in Excel.)
c. Now calculate the coefficients of variation for Bartman, Reynolds, and the Market Index.
d. Construct a scatter diagram graph that shows Bartman's and Reynolds's returns on the vertical axis and the Market Index's returns on the horizontal axis.
e. Estimate Bartman's and Reynolds's betas by running regressions of their returns against the Index's returns. Are these betas consistent with your graph?
f. The risk-free rate on long-term Treasury bonds is 6.04 percent. Assume that the market risk premium is 5 percent. What is the expected return on the market? Now use the SML equation to calculate the two companies' required returns.
g. If you formed a portfolio that consisted of 50 percent of Bartman stock and 50 percent of Reynolds stock, what would be its beta and its required return?
h. Suppose an investor wants to include Bartman Industries' stock in his or her 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 percent of Bartman, 15 percent of Stock A, 40 percent of Stock B, and 20 percent of Stock C.