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If a particular stock is highly susceptible to market or systematic risk, during good economic
conditions the stock will earn larger than average positive returns, and during poor economic
conditions the stock will earn larger than average negative returns. This type of stock is risky to
include in a portfolio, since it increases the standard deviation of returns of the portfolio by making
good years even better and poor years even worse. Stocks that are not very susceptible to market or
systematic risk, in contrast, are not risky when held in a portfolio. They do not go up much in good
years, and they do not go down much in poor years, reducing the standard deviation of returns of the
portfolio.
The CAPM measure of the risk of any stock when held in a portfolio is called a beta coefficient, and
is calculated with this formula:
This formula says the beta coefficient for any stock, i, is calculated as the covariance between the
stock, i, and the overall stock market, m, divided by the variance of the overall stock market, m. Beta
coefficients are published by many information sources, and they can be easily calculated with a time
series of returns for an individual stock and the overall stock market. We will not go into the detail of
how to calculate beta coefficients, but we will discuss in detail what a beta coefficient tells us about
the risk of a stock when held in a portfolio.
The covariance of returns between a stock and the overall stock market is the multiplication of three
terms; the correlation between the returns of the stock and the returns of the market, the standard
deviation of returns of the stock, and the standard deviation of returns of the market. If the numerator
in the beta calculation is larger than the denominator, it means the correlation between the stock and
the market is high and the stock is highly volatile, having a large standard deviation of returns. This
tells us the stock tends to move in the same direction as the overall market and these movements are of
greater magnitude. From our previous discussion, this tells us the stock has greater than average risk
when held in a portfolio, which results in a beta coefficient for the stock greater than 1.0.
If the numerator in the beta calculation is equal to the denominator, the covariance between the
returns of the stock and the returns of the overall market is equal to the variance of returns of the
overall market. This tells us the stock tends to move in the same direction as the overall market, and
these movements are of the same magnitude. A stock that behaves in this manner is exactly as volatile
as the overall market, and it is therefore of average risk when held in a portfolio, which results in a
beta coefficient of 1.0.
Exhibit 5.5 Beta coefficients.
Source: Value Line Survey pages, Value Line Publishing, Inc., 2008.