Risk and Return, Build a Model
Ch 06-15 Build a Model12/7/12Chapter:6Problem:15
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 2008 because you do not have 2007
data.)
Data as given in the problem are shown below:Goodman
IndustriesLandry IncorporatedMarket IndexYearStock
PriceDividendStock PriceDividendIncludes
Divs.2013$25.88$1.73$73.13$4.5017,495.972012$22.13$1.59$78.45$4.3513,178.552011$24.75$1.50$73.13$4.1313,019.972010$16.13$1.43$85.88$3.759,651.052009$17.06$1.35$90.00$3.388,403.422008$11.44$1.28$83.63$3.007,058.96
We now calculate the rates of return for the two companies and
the index:
GoodmanLandryIndex2013
Kenneth D. Jackson: Change in stock price plus any dividends,
divided by the previous stock price2012201120102009
Average
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 Goodman and then copy the cell
for the other items.
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 function in Excel.)
Use the function wizard to calculate the standard
deviations.
GoodmanLandryIndexStandard deviation of returns
c. Construct a scatter diagram graph that shows Goodmans and
Landry returns on the vertical axis and the Market Indexs 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.
YearIndexGoodmanLandry20130.0%0.0%0.0%20120.0%0.0%0.0%20110.0%0.0%0.0%20100.0%0.0%0.0%20090.0%0.0%0.0%
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.
beta and Landry a negative one.
d. Estimate Goodmans and Landrys 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
Excels SLOPE function.) Are these betas consistent with your
graph?
Goodman's beta =
Landry' beta =
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.
Market risk premium (RPM) =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=x
Goodman:Required return==
Landry:Required return=x=
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?
The beta of a portfolio is simply a weighted average of the
betas of the stocks in the portfolio, so this portfolio's betawould
be:
Portfolio beta =
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 portfolios required return if it
consists of 25% of Goodman, 15% of Stock A, 40% of Stock B, and 20%
of Stock C.
BetaPortfolio WeightGoodman25% Stock A0.76915% Stock B0.98540%
Stock C1.42320%100%Portfolio Beta =
Required return on portfolio:= Risk-free rate +Market Risk
Premium * * Beta==
