Risk in a Portfolio Context 123cannot be eliminated by diversification—those risks related to broad, systematic
changes in the stock market will remain.
Are all stocks equally risky in the sense that adding them to a well-diversified port-
folio would have the same effect on the portfolio’s riskiness? The answer is no. Differ-
ent stocks will affect the portfolio differently, so different securities have different
degrees of relevant risk. How can the relevant risk of an individual stock be measured?
As we have seen, all risk except that related to broad market movements can, and pre-
sumably will, be diversified away. After all, why accept risk that can be easily elimi-
nated? The risk that remains after diversifying is market risk, or the risk that is inherent in
the market, and it can be measured by the degree to which a given stock tends to move up or
down with the market.In the next section, we develop a measure of a stock’s market risk,
and then, in a later section, we introduce an equation for determining the required
rate of return on a stock, given its market risk.The Concept of Beta
As we noted above, the primary conclusion of the CAPM is that the relevant risk of an
individual stock is the amount of risk the stock contributes to a well-diversified port-
folio. The benchmark for a well-diversified stock portfolio is the market portfolio,
which is a portfolio containing all stocks. Therefore, the relevant risk of an individual
stock, which is called its beta coefficient, is defined under the CAPM as the amountof risk that the stock contributes to the market portfolio. In CAPM terminology, (^) iM
is the correlation between the ith stock’s expected return and the expected return on
the market, iis the standard deviation of the ith stock’s expected return, and Mis the
standard deviation of the market’s expected return. In the literature on the CAPM, it is
proved that the beta coefficient of the ith stock, denoted by bi, can be found as follows:
(3-6)
This tells us that a stock with a high standard deviation, i, will tend to have a high
beta. This makes sense, because if all other things are equal, a stock with high stand-
alone risk will contribute a lot of risk to the portfolio. Note too that a stock with a high
correlation with the market, (^) iM, will also have a large beta, hence be risky. This also
makes sense, because a high correlation means that diversification is not helping
much, hence the stock contributes a lot of risk to the portfolio.
Calculators and spreadsheets use Equation 3-6 to calculate beta, but there is an-
other way. Suppose you plotted the stock’s returns on the y-axis of a graph and the
market portfolio’s returns on the x-axis, as shown in Figure 3-9. The tendency of a
stock to move up and down with the market is reflected in its beta coefficient. An
average-risk stockis definedas one that tends to move up and down in step with the gen-
eral market as measured by some index such as the Dow Jones Industrials, the S&P
500, or the New York Stock Exchange Index. Such a stock will, by definition,be as-
signed a beta, b, of 1.0, which indicates that, in general, if the market moves up by 10
percent, the stock will also move up by 10 percent, while if the market falls by 10 per-
cent, the stock will likewise fall by 10 percent. A portfolio of such b 1.0 stocks will
move up and down with the broad market indexes, and it will be just as risky as the in-
dexes. If b 0.5, the stock is only half as volatile as the market—it will rise and fall
only half as much—and a portfolio of such stocks will be half as risky as a portfolio of
b 1.0 stocks. On the other hand, if b 2.0, the stock is twice as volatile as an aver-
age stock, so a portfolio of such stocks will be twice as risky as an average portfolio.
The value of such a portfolio could double—or halve—in a short time, and if you held
such a portfolio, you could quickly go from millionaire to pauper.
bia
i
M
b (^) iM.