Ch 06 P14 Build a Model

a. Use the data given to calculate annual returns for Bartman, Reynolds, and the Market Index, and then calculate average returns over the five-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 2005 because you do not have 2004 data.)

b. Calculate the standard deviation 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 Bartman, Reynolds, and the Market Index.

d. Construct a scatter diagram graph that shows Bartman’s and Reynolds’ returns on the vertical axis and the Market Index’s returns on the horizontal axis.

e. Estimate Bartman’s and Reynolds’s betas as the slopes of regression lines with stock returns on the vertical axis (y-axis) and market return on the horizontal axis (x-axis). (Hint: use Excel’s SLOPE function.) Are these betas consistent with your graph?

f. The risk-free rate on long-term Treasury bonds is 6.04%. Assume that the market risk premium is 5%. 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% Bartman stock and 50% 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 1.223, 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.