144 CHAPTER 3 Risk and Return
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 cal-
culated 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 1997 because you do not have 1996 data.)
b.Calculate the standard deviations of the returns for Bartman, Reynolds, and the Market In-
dex. (Hint: Use the sample standard deviation formula given in the chapter, which corre-
sponds 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’ returns on the verti-
cal axis and the Market Index’s returns on the horizontal axis.
e.Estimate Bartman’s and Reynolds’ 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 equa-
tion 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 Bart-
man, 15 percent of Stock A, 40 percent of Stock B, and 20 percent of Stock C.
Assume that you recently graduated with a major in finance, and you just landed a job as a fi-
nancial planner with Merrill Finch Inc., a large financial services corporation. Your first assign-
ment is to invest $100,000 for a client. Because the funds are to be invested in a business at the
end of 1 year, you have been instructed to plan for a 1-year holding period. Further, your boss
has restricted you to the following investment alternatives, shown with their probabilities and
associated outcomes. (Disregard for now the items at the bottom of the data; you will fill in the
blanks later.)
Returns on Alternative Investments
Estimated Rate of Return
State of High U.S. Market 2-Stock
the Economy Probability T-Bills Tech Collections Rubber Portfolio Portfolio
Recession 0.1 8.0% (22.0%) 28.0% 10.0%* (13.0%) 3.0%
Below average 0.2 8.0 (2.0) 14.7 (10.0) 1.0
Average 0.4 8.0 20.0 0.0 7.0 15.0 10.0
Above average 0.2 8.0 35.0 (10.0) 45.0 29.0
Boom 0.1 8.0 50.0 (20.0) 30.0 43.0 15.0
rˆ 1.7% 13.8% 15.0%
0.0 13.4 18.8 15.3
CV 7.9 1.4 1.0
b 0.86 0.68
*Note that the estimated returns of U.S. Rubber do not always move in the same direction as the overall economy. For example, when the econ-
omy is below average, consumers purchase fewer tires than they would if the economy was stronger. However, if the economy is in a flat-out re-
cession, a large number of consumers who were planning to purchase a new car may choose to wait and instead purchase new tires for the car
they currently own. Under these circumstances, we would expect U.S. Rubber’s stock price to be higher if there is a recession than if the econ-
omy was just below average.
See Ch 03 Show.pptand
Ch 03 Mini Case.xls.
142 Risk and Return
