Fall 2, 2012
Chapter 6.
Ch 06 P14 Build a Model
Except for charts and answers that must be written, only Excel formulas that use cell references or functions
Numeric answers in cells will not be accepted.
Data as given in the problem are shown below:
Bartman Industries
Reynolds Incorporated
Market Index
Year
Stock Price
Dividend
Stock Price
Dividend Includes Divs.
2010
$17.250
$1.150
$48.750
$3.000
11,663.98
2009
15.000
1.060
52.300
2.900
8,785.70
2008
16.500
1.000
48.750
2.750
8,679.98
2007
10.750
0.950
57.250
2.500
6,434.03
2006
11.375
0.900
60.000
2.250
5,602.28
2005
7.625
0.850
55.750
2.000
4,705.97
We now calculate the rates of return for the two companies and the index:
Bartman
Reynolds
Index
2010
2009
2008
2007
2006
Average
Use the function wizard to calculate the standard deviations.
Bartman
Reynolds
Index
Standard deviation of returns
No answer shou
c.
Now calculate the coefficients of variation Bartman, Reynolds, and the Market Index.
No answer shou
Bartman
Reynolds
Index
Coefficient of Variation
No answer shou
Year
Index
Bartman
Reynolds
2010
0.0%
0.0%
0.0%
2009
0.0%
0.0%
0.0%
2008
0.0%
0.0%
0.0%
2007
0.0%
0.0%
0.0%
2006
0.0%
0.0%
0.0%
Bartman's beta =
Reynolds' beta
=
5.000%
Risk-free rate
=
6.040%
Expected return on market =
Risk-free rate
+
Market risk premium
=
6.040%
+
5.000%
=
11.040%
Required return
=
Bartman:
Required return
=
=
Reynolds:
Required return
=
=
The beta of a portfolio is simply a weighted average of the betas of the stocks in the portfolio, so this portfolio's beta
would be:
Portfolio beta =
Beta
Portfolio Weight
Bartman
25%
Stock A
0.769
15%
Stock B
0.985
40%
Stock C
1.223
20%
100%
Portfolio Beta
=
Required return on portfolio:
=
Risk-free rate
+
Market Risk Premium
*
Beta
=
=
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.)
Note: To get the average, you could get the column sum and divide by 5, but you could also use the function wizard, fx.
Click fx, then statistical, then Average, and then use the mouse to select the proper range.
Do this for Bartman and then
copy the cell for the other items.
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.)
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.
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.
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 match the dots.
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.
Market risk premium (RP
M
) =
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.