The investor can calculate Stock i’s expected rate of returnas follows:
ˆri
D
P 0
1
g
$
$
3
3
0
5% 15%.
This value is plotted on Figure 5-4 as Point i, which is below the SML. Because the
expected rate of return is less than the required return, this marginal investor would
want to sell the stock, as would most other holders. However, few people would want
to buy at the $30 price, so the present owners would be unable to find buyers unless
they cut the price of the stock. Thus, the price would decline, and this decline would
continue until the price reached $27.27, at which point the stock would be in
equilibrium,defined as the price at which the expected rate of return, 16 percent, is
equal to the required rate of return:
ˆri
$2
$
7
3
.27
5% 11% 5% 16% ri.
Had the stock initially sold for less than $27.27, say, at $25, events would have
been reversed. Investors would have wanted to buy the stock because its expected rate
of return would have exceeded its required rate of return, and buy orders would have
driven the stock’s price up to $27.27.
To summarize, in equilibrium two related conditions must hold:
- A stock’s expected rate of return as seen by the marginal investor must equal its re-
quired rate of return: ˆriri.
- The actual market price of the stock must equal its intrinsic value as estimated by
the marginal investor: P 0 Pˆ 0.
Of course, some individual investors may believe that ˆrir andPˆ 0 P 0 , hence
they would invest most of their funds in the stock, while other investors may have
an opposite view and would sell all of their shares. However, it is the marginal
investor who establishes the actual market price, and for this investor, we must
have ˆririand P 0 Pˆ 0. If these conditions do not hold, trading will occur until
they do.
206 CHAPTER 5 Stocks and Their Valuation
FIGURE 5-4 Expected and Required Returns on Stock i
Rate of Return
(%)
r = 16
r = 15
r = 12
r = 8RF
M
i
i
0 1.0 2.0 Risk, bi
SML: ri = rRF + (rM– rRF) bi
>
i
202 Stocks and Their Valuation
