Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

V. Risk and Return 13. Return, Risk, and the

Security Market Line

(^444) © The McGraw−Hill
Companies, 2002
returns on individual assets. In particular, it is the basis for a famous relationship between
risk and return called the security market line, or SML. To develop the SML, we introduce
the equally famous “beta” coefficient, one of the centerpieces of modern finance. Beta and
the SML are key concepts because they supply us with at least part of the answer to the
question of how to go about determining the required return on an investment.
EXPECTED RETURNS AND VARIANCES
In our previous chapter, we discussed how to calculate average returns and variances us-
ing historical data. We now begin to discuss how to analyze returns and variances when
the information we have concerns future possible returns and their probabilities.
Expected Return
We start with a straightforward case. Consider a single period of time, say, a year. We
have two stocks, L and U, which have the following characteristics: Stock L is expected
to have a return of 25 percent in the coming year. Stock U is expected to have a return
of 20 percent for the same period.
In a situation like this, if all investors agreed on the expected returns, why would
anyone want to hold Stock U? After all, why invest in one stock when the expectation is
that another will do better? Clearly, the answer must depend on the risk of the two in-
vestments. The return on Stock L, although it is expectedto be 25 percent, could actu-
ally turn out to be higher or lower.
For example, suppose the economy booms. In this case, we think Stock L will have
a 70 percentreturn. If the economy enters a recession, we think the return will be
20
percent. In this case, we say that there are two states of the economy,which means that
these are the only two possible situations. This setup is oversimplified, of course, but it
allows us to illustrate some key ideas without a lot of computation.
Suppose we think a boom and a recession are equally likely to happen, for a 50–50
chance of each. Table 13.1 illustrates the basic information we have described and some
additional information about Stock U. Notice that Stock U earns 30 percent if there is a
recession and 10 percent if there is a boom.
Obviously, if you buy one of these stocks, say Stock U, what you earn in any partic-
ular year depends on what the economy does during that year. However, suppose the
probabilities stay the same through time. If you hold U for a number of years, you’ll
earn 30 percentabout half the time and 10 percentthe other half. In this case, we say
that your expected returnon Stock U, E(RU), is 20 percent:
416 PART FIVE Risk and Return

TABLE 13.1

States of the Economy

and Stock Returns State of Probability of

Economy State of Economy Stock L Stock U

Recession .50 
20% 30%

Boom .50 70% 10

1.00

Rate of Return if

State Occurs

13.1

expected return
The return on a risky
asset expected in the
future.