Chapter 9 Stocks and Their Valuation 303(^1) A price change of this magnitude is by no means rare. The prices of many stocks double or halve during a year.
For example, during 2007, Amazon.com, a large online retailer of books, music, and videos, increased in value by
134.8%. On the other hand, ETrade Financial, a discount brokerage! rm, fell in value by 84.2%.
(^2) It should be obvious by now that actual realized rates of return are not necessarily equal to expected and
required returns. Thus, an investor might have expected to receive a return of 15% if he or she had bought
Amazon.com or ETrade Financial stock in 2007; but after the fact, the realized return on Amazon.com was far
above 15%, whereas the return on E*Trade Financial was far below.
Using these values, together with the new g, we! nd that Pˆ 0 rises from $27.27 to
$75.71, or by 178%:^1
Original Pˆ 0! $2.8571(1.05)____0.16 $ (^) 0.05! $3.00_0.11! $27.27
New Pˆ 0! $2.8571(1.06)____0.10$ (^) 0.06! $3.0285___0.04! $75.71
Note too that at the new price, the expected and required rates of return will
be equal:^2
rˆX! $3.0285___
$75.71
" 6%! 10%! rX
Evidence suggests that stocks, especially those of large companies, adjust
rapidly when their fundamental positions change. Such stocks are followed
closely by a number of security analysts; so as soon as things change, so does the
stock price. Consequently, equilibrium ordinarily exists for any given stock, and
required and expected returns are generally close to equal. Stock prices certainly
change, sometimes violently and rapidly; but this simply re" ects changing condi-
tions and expectations. There are, of course, times when a stock will continue to
react for several months to unfolding favorable or unfavorable developments.
However, this does not signify a long adjustment period; rather, it simply indi-
cates that as more new information about the situation becomes available, the
market adjusts to it.
For a stock to be in equilibrium, what two conditions must hold?
If a stock is not in equilibrium, explain how financial markets adjust to bring it into
equilibrium.
RATES OF RETURN AND EQUILIBRIUM Stock C’s beta coefficient is bC " 0.4, while Stock
D’s is bD " #0.5. (Stock D’s beta is negative, indicating that its return rises when returns
on most other stocks fall. There are very few negative beta stocks, although collection
agency stocks are sometimes cited as an example.)
a. If the risk-free rate is 7% and the expected rate of return on an average stock is 11%,
what are the required rates of return on Stocks C and D?
b. For Stock C, suppose the current price, P 0 , is $25.00; the next expected dividend, D 1 , is
$1.50; and the stock’s expected constant growth rate is 4%. Is the stock in equilibrium?
Explain and describe what will happen if the stock is not in equilibrium.