Question

Joey Moss, a recent finance graduate, has just begun his job
with the investment firm of Covili and Wyatt. Paul Covili, one
of the firm’s founders, has been talking to Joey about the firm’s
investment portfolio.
As with any investment, Paul is concerned about the risk
of the investment as well as the potential return. More specifically, because the company holds a diversified portfolio, Paul
is concerned about the systematic risk of current and potential
investments. One such position the company currently holds
is stock in Colgate-Palmolive (CL). Colgate-Palmolive is the
well-known manufacturer of consumer products under brand
names such as Colgate, Palmolive, Softsoap, Irish Spring,
Ajax, and others.
Covili and Wyatt currently uses a commercial data vendor
for information about its positions. Because of this, Paul is
unsure exactly how the numbers provided are calculated. The
data provider considers its methods proprietary, and it will not
disclose how stock betas and other information are calculated.
Paul is uncomfortable with not knowing exactly how these
numbers are being computed and also believes that it could be
less expensive to calculate the necessary statistics in-house. To
explore this question, Paul has asked Joey to do the following
assignments.
QUESTIONS
1. Go to finance.yahoo.com and download the ending
monthly stock prices for Colgate-Palmolive for the last
60 months. Use the adjusted closing price, which adjusts
for dividend payments and stock splits. Next, download
the ending value of the S&P 500 index over the same
ros18955_ch13_420-457.indd 456 06/02/18 3:08 pm
Chapter 13 Return, Risk, and the Security Market Line 457
period. For the historical risk-free rate, go to the St.
Louis Federal Reserve website (www.stlouisfed.org) and
find the three-month Treasury bill secondary market
rate. Download this file. What are the monthly returns,
average monthly returns, and standard deviations for
Colgate-Palmolive stock, the three-month Treasury bill,
and the S&P 500 for this period?
2. Beta is often estimated by linear regression. A model commonly used is called the market model, which is:
R
t
− R
ft = αi + βi [RMt − Rft] + εt
In this regression, Rt is the return on the stock and Rft is
the risk-free rate for the same period. RMt is the return
on a stock market index such as the S&P 500 index; α
i is
the regression intercept; βi is the slope (and the stock’s
estimated beta); and ε
t represents the residuals for the
regression. What do you think is the motivation for this
particular regression? The intercept, α, is often called Jensen’s alpha. What does it measure? If an asset has a positive Jensen’s alpha, where would it plot with respect to the
SML? What is the financial interpretation of the residuals
in the regression?
3. Use the market model to estimate the beta for Colgate-Palmolive using the last 36 months of returns (the
regression procedure in Excel is one easy way to do this).
Plot the monthly returns on Colgate-Palmolive against the
index and also show the fitted line.
4. When the beta of a stock is calculated using monthly
returns, there is a debate over the number of months that
should be used in the calculation. Rework the previous
questions using the last 60 months of returns. How does
this answer compare to what you calculated previously?
What are some arguments for and against using shorter
versus longer periods? Also, you’ve used monthly data,
which is a common choice. You could have used daily,
weekly, quarterly, or even annual data. What do you think
are the issues here?
5. Compare your beta for Colgate-Palmolive to the beta you
find on finance.yahoo.com. How similar are they? Why
might they be differen