beta is about half the 1.0 average beta. Thus, Wal-Mart moves up and down by
roughly half the percent as the market. Note, however, that the points are not clus-
tered very tightly around the regression line. Sometimes Wal-Mart does much better
than the market, while at other times it does much worse. The R^2 value shown in the
chart measures the degree of dispersion about the regression line. Statistically speak-
ing, it measures the percentage of the variance that is explained by the regression equa-
tion. An R^2 of 1.0 indicates that all points lie exactly on the line, hence that all of the
variance of the y-variable is explained by the x-variable. Wal-Mart’s R^2 is about 0.08,
which is a little lower than most individual stocks. This indicates that about 8 percent
of the variance in Wal-Mart’s returns is explained by the market returns. If we had
done a similar analysis for portfolios of 50 randomly selected stocks, then the points
would on average have been clustered tightly around the regression line, and the R^2
would have averaged over 0.9.
Finally, note that the intercept shown in the regression equation on the chart is
about 2 percent. Since the regression equation is based on monthly data, this means
that over this period Wal-Mart’s stock earned 2 percent more per month than an aver-
age stock as a result of factors other than a general increase in stock prices.
What types of data are needed to calculate a beta coefficient for an actual
company?
What does the R^2 measure? What is the R^2 for a typical company?
The Relationship between Risk and Rates of Return
In the preceding section, we saw that under the CAPM theory, beta is the appropriate
measure of a stock’s relevant risk. Now we must specify the relationship between risk
and return: For a given level of risk as measured by beta, what rate of return should
130 CHAPTER 3 Risk and Return
TABLE 3-5 Stock Return Data for Wal-Mart Stores
Market Level Wal-Mart Adjusted
(S&P 500 Market Stock Wal-Mart
Date Index) Return Pricea Return
August 2001 1,294.0 –3.5% 47.976 –14.0%
July 2001 1,341.0 –3.3 55.814 14.5
June 2001 1,386.8 –2.6 48.725 –5.6
May 2001 1,424.2 –13.9 51.596 0.0
... ... ... ... ...
... ... ... ... ...
October 1997 994.0 6.0 17.153 –4.4
September 1997 1,057.3 0.8 17.950 3.4
August 1997 1,049.4 NA 17.368 NA
Average (annual) 6.9% 31.4%
Standard deviation (annual) 18.7% 34.5%
Correlation between
Wal-Mart and the
market 27.4%
aYahoo actually adjusts the stock prices to reflect any stock splits or dividend payments.
Check out http://finance.
yahoo.com for Wal-Mart
using its ticker symbol of
WMT. You can also down-
load data for the S&P 500
index using its symbol of
^SPI.
128 Risk and Return
