Chapter 8 Risk and Rates of Return 245reasons. First, high administrative costs and commissions would more than offset
the bene" ts for individual investors. Second, index funds can diversify for inves-
tors, and many individuals can and do get broad diversi" cation through these
funds. Third, some people think that they can pick stocks that will “beat the mar-
ket”; so they buy them rather than the broad market. And fourth, some people
can, through superior analysis, beat the market; so they " nd and buy underval-
ued stocks and sell overvalued ones and, in the process, cause most stocks to be
properly valued, with their expected returns consistent with their risks.- One key question remains: How should the risk of an individual stock be mea-
sured? The standard deviation of expected returns, #, is not appropriate
because it includes risk that can be eliminated by holding the stock in a portfo-
lio. How then should we measure a stock’s risk in a world where most people
hold portfolios? That’s the subject of the next section.
8-3c Risk in a Portfolio Context: The Beta Coefficient
When a stock is held by itself, its risk can be measured by the standard deviation
of its expected returns. However, # is not appropriate when the stock is held in a
portfolio, as stocks generally are. So how do we measure a stock’s relevant risk in
a portfolio context?
First, note that all risk except that related to broad market movements can and
will be diversi" ed away by most investors—rational investors will hold enough
stocks to move down the risk curve in Figure 8-6 to the point where only market
risk remains in their portfolios.
The risk that remains once a stock is in a diversi! ed portfolio is its contribution
to the portfolio’s market risk, and that risk can be measured by the extent to
which the stock moves up or down with the market.
The tendency of a stock to move with the market is measured by its
beta coef! cient, b. Ideally, when estimating a stock’s beta, we would like to have
a crystal ball that tells us how the stock is going to move relative to the overall
stock market in the future. But since we can’t look into the future, we often use
historical data and assume that the stock’s historical beta will give us a reasonable
estimate of how the stock will move relative to the market in the future.
To illustrate the use of historical data, consider Figure 8-7, which shows the
historical returns on three stocks and a market index. In Year 1, “the market,” as
de" ned by a portfolio containing all stocks, had a total return (dividend yield plus
capital gains yield) of 10%, as did the three individual stocks. In Year 2, the market
went up sharply and its return was 20%. Stocks H (for high) soared by 30%; A (for
average) returned 20%, the same as the market; and L (for low) returned 15%. In
Year 3, the market dropped sharply; its return was !10%. The three stocks’ returns
also fell—H’s return was !30%, A’s was !10%, and L broke even with a 0% return.
In Years 4 and 5, the market returned 0% and 5%, respectively, and the three stocks’
returns were as shown in the " gure.
A plot of the data shows that the three stocks moved up or down with the
market but that H was twice as volatile as the market, A was exactly as volatile as
the market, and L had only half the market’s volatility. It is apparent that the
steeper a stock’s line, the greater its volatility and thus the larger its loss in a
down market. The slopes of the lines are the stocks’ beta coef! cients. We see in the
" gure that the slope coef" cient for H is 2.0; for A, it is 1.0; and for L, it is 0.5.^20
Thus, beta measures a given stock’s volatility relative to the market, and an
average stock’s beta, bA $ 1.0.
Relevant Risk
The risk that remains once
a stock is in a diversified
portfolio is its contribution
to the portfolio’s market
risk. It is measured by the
extent to which the stock
moves up or down with
the market.Relevant Risk
The risk that remains once
a stock is in a diversified
portfolio is its contribution
to the portfolio’s market
risk. It is measured by the
extent to which the stock
moves up or down with
the market.Beta Coefficient, b
A metric that shows the
extent to which a given
stock’s returns move up
and down with the stock
market. Beta thus
measures market risk.Beta Coefficient, b
A metric that shows the
extent to which a given
stock’s returns move up
and down with the stock
market. Beta thus
measures market risk.Average Stock’s
Beta, bA
By definition, bA = 1
because an average-risk
stock is one that tends to
move up and down in step
with the general market.Average Stock’s
Beta, bA
By definition, bA = 1
because an average-risk
stock is one that tends to
move up and down in step
with the general market.(^20) For more on calculating betas, see Brigham and Daves, Intermediate Financial Management, 9th ed.,
(Mason, OH: Thomson/South-Western, 2007), pp. 55–58 and pp. 89–94.