One measure of the risk or volatility of an individual stock is the standard deviation of the
total return (capital appreciation plus dividends) over several periods of time. Although
the standard deviation is easy to compute, it does not take into account the extent to which
the price of a given stock varies as a function of a standard market index, such as the S&P
500. As a result, many financial analysts prefer to use another measure of risk referred to
Betas for individual stocks are determined by simple linear regression. The dependent
variable is the total return for the stock and the independent variable is the total return for
the stock market.* For this case problem we will use the S&P 500 index as the measure of
the total return for the stock market, and an estimated regression equation will be developed using monthly data. The beta for the stock is the slope of the estimated regression equation (b1). The data contained in the DATAfile named Beta provides the total return
(capital appreciation plus dividends) over 36 months for eight widely traded common
stocks and the S&P 500.
The value of beta for the stock market will always be 1; thus, stocks that tend to
rise and fall with the stock market will also have a beta close to 1. Betas greater than 1
indicate that the stock is more volatile than the market, and betas less than 1 indicate
that the stock isless volatile than the market. For instance, if a stock has a beta of 1.4,
it is 40% more volatile than the market, and if a stock has a beta of .4, it is 60% less
volatile than the market.
You have been assigned to analyze the risk characteristics of these stocks. Prepare a report
that includes but is not limited to the following items.
a. Compute descriptive statistics for each stock and the S&P 500. Comment on your
results. Which stocks are the most volatile?
b. Compute the value of beta for each stock. Which of these stocks would you expect to perform
best in an up market? Which would you expect to hold their value best in a down market?
c. Comment on how much of the return for the individual stocks is explained by the