(3-9)
rirRF(rMrRF)bi
rRF(RPM)bi
The required return for Stock i can be written as follows:
ri6% (11% 6%)(0.5)
6% 5%(0.5)
8.5%.
If some other Stock j were riskier than Stock i and had bj2.0, then its required
rate of return would be 16 percent:
rj6% (5%)2.0 16%.
An average stock, with b 1.0, would have a required return of 11 percent, the same
as the market return:
rA6% (5%)1.0 11% rM.
As noted above, Equation 3-9 is called the Security Market Line (SML) equation,
and it is often expressed in graph form, as in Figure 3-12, which shows the SML when
rRF6% and rM11%. Note the following points:
- Required rates of return are shown on the vertical axis, while risk as measured by
beta is shown on the horizontal axis. This graph is quite different from the one
shown in Figure 3-9, where the returns on individual stocks were plotted on the
SML Equation:
Required return
on Stock i
Risk-free
rate
¢
Market risk
premium
≤ ¢
Stock i’s
beta
≤
The Relationship between Risk and Rates of Return 133
FIGURE 3-12 The Security Market Line (SML)
Relatively
Risky Stock’s
Risk Premium: 10%
Market Risk
Premium: 5%.
Applies Also to
an Average Stock,
and Is the Slope
Coefficient in the
SML Equation
Safe Stock’s
Risk
Premium: 2.5%
Risk-Free
Rate, rRF
0 0.5 1.0 1.5 2.0 Risk, b i
Required Rate
of Return (%) SML: r
i^ = rRF + (RPM ) bi
= 6% + (5%) bi
rM = rA = 11
rL = 8.5
rH = 16
rRF = 6
Risk and Return 131
