Solution 7/16/2015
Chapter: 6
Problem: 15
Data as given in the problem are shown below:
Market Index
Year Stock Price Dividend Stock Price Dividend Includes Divs.
2016 $25.88 $1.73 $73.13 $4.50 17,495.97
2015 $22.13 $1.59 $78.45 $4.35 13,178.55
2014 $24.75 $1.50 $73.13 $4.13 13,019.97
2013 $16.13 $1.43 $85.88 $3.75 9,651.05
2012 $17.06 $1.35 $90.00 $3.38 8,403.42
2011 $11.44 $1.28 $83.63 $3.00 7,058.96
We now calculate the rates of return for the two companies and the index:
Goodman Landry Index
2016 24.8% -1.0% 32.8%
2015 -4.2% 13.2% 1.2%
2014 62.7% -10.0% 34.9%
2013 2.9% -0.4% 14.8%
2012 60.9% 11.7% 19.0%
Average 29.4% 2.7% 20.6%
b. Calculate the standard deviation of the returns for Goodman, Landry, and the Market Index. (Hint:
Use the sample standard deviation formula given in the chapter, which corresponds to the STDEV
wizard, fx. Click fx, then statistical, then Average, and then use the mouse to select the proper range. Do this
for Goodman and then copy the cell for the other items.
Landry Incorporated
Goodman Industries
a. Use the data given to calculate annual returns for Goodman, Landry, 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 2010
because you do not have 2009 data.)
It is easiest to make scatter diagrams with a data set that has the X-axis variable in the left
column, so we reformat the returns data calculated above and show it just below.
Year Index Goodman Landry
2016 32.8% 24.8% -1.0%
2015 1.2% -4.2% 13.2%
2014 34.9% 62.7% -10.0%
2013 14.8% 2.9% -0.4%
2012 19.0% 60.9% 11.7%
It is clear that Goodman moves with the market and Landry moves counter to the market. So, Goodman has a positive
beta and Landry a negative one.
expected return on the market? Now use the SML equation to calculate the two companies’ required returns.
Risk-free rate = 6.040%
Expected return on market = Risk-free rate + Market risk premium
=11.040%
To make the graph, we first selected the range with the returns and the column heads, then clicked the chart
wizard, then choose the scatter diagram without connected lines. That gave us the data points. We then used
the drawing toolbar to make free-hand (“by eye”) regression lines, and changed the lines color and weights to
d. Estimate Goodman’s and Landry’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?
-20.0%
-10.0%
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
0.0% 10.0% 20.0% 30.0% 40.0%
Stocks’ Returns
Index Returns
Goodman
Landry
Required return = Risk-free rate +
x
Goodman:
Required return = 6.040% 5.000%
=
13.728%
Landry:
Required return = 6.040% 5.000% x
=
3.240%
This suggests that Landry’ stock is like an insurance policy that has a low expected return, but it will pay off in the
event of a market decline. Actually, it is hard to find negative beta stocks, so we would not be inclined to believe the
Landry data.
The beta of a portfolio is simply a weighted average of the betas of the stocks in the portfolio, so this portfolio’s beta
Portfolio beta =
0.49
Required return on portfolio: = Risk-free rate +
* Beta
=6.04% 5.00% 1.178
=
11.93%
f. If you formed a portfolio that consisted of 50% Goodman stock and 50% Landry stock, what would be
its beta and its required return?
g. Suppose an investor wants to include Goodman 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% of Goodman, 15% of Stock A, 40% of Stock B,
and 20% of Stock C.
It is clear that Goodman moves with the market and Landry moves counter to the market. So, Goodman has a positive
Note that these betas are consistent with the scatter diagrams we constructed earlier. Landry‘ beta suggests that it
e. 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.
Beta
1.538
-0.560
event of a market decline. Actually, it is hard to find negative beta stocks, so we would not be inclined to believe the
The beta of a portfolio is simply a weighted average of the betas of the stocks in the portfolio, so this portfolio’s beta