Soaring stock prices continue to pit those who claim that investors are paying too much against those who believe stocks are worth even more. Prices of stocks are determined by people's perceptions of worth, which are themselves based on expectations for the future Although we cannot be sure whether the market is over- or undervalued, we can clarify the factors that determine stock prices and discover the assumptions underlying our expectations. Assessing the consistency of these assumptions may help keep our exuberance in check.Stock - Prices ; Economic conditions - United States

John B. Carlson

English

Research Papers in Economics

“…how do we know when irrational
exuberance has unduly escalated asset
values, which then become subject to
unexpected and  prolonged contrac-
tions? …We have not been able, as yet,
to provide a satisfying answer to this
question, but there are reasons in the
current environment to keep the question
on the table.”
—Chairman Alan Greenspan
It has been almost three years since
Chairman Greenspan posed the foregoing
question and thereby launched the phrase
“irrational exuberance” into the eco-
nomic idiom. Since then, of course, some
stock-price indexes have doubled, and
the question still remains unanswered.
Over the same period, favorable U.S.
economic performance continued to sur-
prise even some of the more optimistic
prognosticators. Because stock prices are
presumably forward looking, earlier exu-
berance appears, at least up to this point,
to have been validated by experience.
Some analysts insist that the party will
continue. Among the most ardent are
James K. Glassman and Kevin A.
Hassett, who argue that the market is
rationally exuberant. Their assessment
hinges on two key assumptions: first,
that future earnings growth will continue
at a pace comparable to the post–World
War II experience, and second, that
investors are demanding a smaller pre-
mium for stock returns relative to other
financial instruments.1  Glassman and
Hassett assert this premium has perma-
nently declined because investors have
become “calmer and smarter.” More-
over, they argue that the premium should
be zero. This suggests that as investors
become even calmer and smarter, stock
prices could increase—not just moder-
ately but by threefold or more! 
Whether one agrees with Glassman and
Hassett or not, their perspective illus-
trates how sensitive stock prices are to
key investor judgments. To appreciate
this sensitivity, it is useful to review
briefly the fundamentals of stock price
determination. This is done in the fol-
lowing section. Each of the assumptions
made by Glassman and Hassett will then
be discussed in turn. We shall see that
given their assumptions, their conclu-
sions are not unreasonable. This is, of
course, no endorsement for their as-
sumptions. I will offer an array of valua-
tions for the S&P500 index given alter-
native sets of assumptions. Readers are
left to make their own judgments.
 The Fundamentals
Investors purchase stocks because they
expect to receive some future income
stream—either in the form of dividends
and/or the proceeds from the eventual
sale of the shares of stock.2 The stan-
dard model of stock valuation posits that
a stock’s price equals the discounted pre-
sent value of this income stream.3  Be-
cause the amount of income ultimately
depends on the firm’s potential to gener-
ate earnings, a key fundamental determi-
nant of the stock’s value will be expected
earnings growth.4  The more a firm is
expected to earn, the more investors will
pay for its stock.
Future income from stocks must be dis-
counted to compensate investors for
assuming inherent risks and associated
costs. The discount rate is the rate of
return the investor demands as compen-
sation. The higher the discount rate, the
lower the price the investor is willing to
August 15, 1999
Federal Reserve Bank of Cleveland
The Recent Ascent in Stock Prices:
How Exuberant Are You?
by John B. Carlson
Stock prices have soared in the last
few years, and the debate between
those who claim that investors are
paying too much and those who
believe stocks are worth even more
continues unabated. Because stock
prices are determined by people’s
perceptions of their worth, and these,
in turn, are based on their predictions
for the future, the possibility that
expectations will exceed reality always
exists. While we cannot know for cer-
tain whether the market is over- 
or undervalued, we can clarify the
factors that determine stock prices
and discover the assumptions which
underly our expectations. Assessing
the consistency of our assumptions
may keep our exuberance in check.
ISSN 0428-1276
pay for the stock. The discount rate is
commonly called the expected return be-
cause it is the return the investor earns if
the income stream is realized as expected.
 Expected Returns 
In competitive financial markets, ex-
pected returns on stocks are linked 
to returns on alternative assets, includ-
ing Treasury bonds and bills. Because
stock returns are generally perceived as
being riskier than those on “safer” in-
struments such as Treasury bonds and
bills, investors typically exact a higher
return. This extra return is called the
“equity premium.”
When thinking about stock returns, it is
important to keep in mind the distinction
between historical returns and expected
returns. Historically, returns in stockshave been quite stable over long hori-
zons. Using U.S. data from 1802–1998,
Jeremy Siegel computes returns for equi-
ty and alternative assets (see table 1).5
While real (inflation-adjusted) equity re-
turns have been consistently around 7
percent for long horizons, returns on 
U.S. Treasury securities have varied
substantially. 
To those who view the stock market as
relatively volatile, the stability of these
measured historical returns is perhaps
surprising.6 They clearly illustrate that a
buy-and-hold strategy in stocks has paid
off handsomely relative to “safer” alter-
natives. Since 1926, the equity premium
has averaged around 6 percent.7
Optimists like Glassman and Hassett
argue that for long-horizon investors,
stocks are no more risky than the re-
cently issued 10-year Treasury inflation
protected security (TIPS), which cur-
rently yields around 4 percent. Thus,
they view this yield as the appropriate
(that is, rational) required return for a
sufficiently diversified portfolio of
stocks, such as an index fund.8 That is,
they argue that there should be no equity
premium. This view implies that the
stock market has been historically under-
valued. Thus, the recent bull market is
seen as evidence that investors are be-
coming calmer and smarter. 
One need not solely rely on the argument
that investors are becoming calmer and
smarter to explain why expected returns
may have fallen. Siegel offers an alterna-
tive explanation. While he believes that 
7 percent does approximate the real long-
term return on equity indexes, it does not
represent the realized return to the equity
holder after expenses—such as transac-
tions and management fees. Once one
accounts for such costs, Siegel argues,
realized returns were more like 5 percent
for the typical investor.
Siegel notes that recent innovations in
financial instruments, such as the advent
of index funds, have sharply reduced the
costs of investing in diversified portfo-
lios.9  Some index funds, for example,
charge less than ¼ percent of asset value
per year. Fees associated with standard
mutual funds, on the other hand, often
amount to more than 2 percent per year.
Because lower investment costs allow
investors to realize a greater portion of
the income flows from holding stocks,
one would expect measured stock returns
(which are not net of costs) to fall. Siegel
believes that current expected return on
stocks is more in line with the historical
“realized” return of 5 percent.
 Earnings Growth
Even if the expected return were 5 per-
cent, current market values of U.S. stock
indexes would imply that equity holders
expect earnings growth to exceed histor-
ical averages. Since 1871, earnings per
share have increased at an average
annual rate of 1.7 percent for S&Pcom-
panies.10  Since the World War II era,
earnings per share have grown at an
average rate of over 3 percent. Figure 1
illustrates just how favorable earnings
growth has been in recent years for S&P
500 companies. After declining over
much of the 1970s and 1980s, earnings
accelerated sharply in the 1990s.
As figure 1 illustrates, neither earnings
nor dividends grow at constant rates.
Rather, we observe that variations in the
growth rates of both are quite persistent.
Thus, it is plausible to argue that recent
above-trend rates in earnings growth
will persist for some time before settling
down to a rate more commensurable
with historical averages.
Siegel makes a strong case for persis-
tently (though not permanently) higher
earnings growth. He notes that the United
States has emerged as the leader in the
fastest growing segments of the world
economy, particularly in information
technology and pharmaceuticals. He also
notes that U.S. brand names such as Coca
Cola, Procter and Gamble, Disney, and
others have quite successfully penetrated
the global market. Together, these factors
could justify temporarily but persistently
higher earnings growth for U.S. firms. It
is clearly possible, though by no means
certain, for earnings levels to double from
current levels before resuming longer-
term trend rates.11
 Putting It All Together
There are many reasonable explanations
for why stock market indices should
have accelerated in the 1990s. However,
depending on one’s own assumptions,
current index levels could be viewed as
FIGURE 1 S&P 500 EARNINGS AND DIVIDENDS
SOURCE: Standard & Poor’s Corporation. 
TABLE 1 COMPOUND ANNUALREALRETURNS
(PERCENT) U.S. DATA, 1802–1998
Stocks Bonds Bills
1802–1998 7.0 3.5 2.9
1802–1870 7.0 4.8 5.1
1871–1925 6.6 3.7 3.2
1926–1998 7.4 2.2 0.7
1946–1998 7.8 1.3 0.6
SOURCE: Siegel (1999).undervalued or overvalued. Table 2 pro-
vides alternative valuations of the S&P
index that correspond to different as-
sumptions about earnings growth and
expected returns. Each valuation has
been calculated using the present-value
formulation for the levels given for each
of the fundamentals. These computa-
tions build in an assumption that earn-
ings decelerate smoothly from the recent
five-year average rates to corresponding
trend-rate assumptions.12
The table is intended to provide a simple
consistency check between recent levels
of stock prices and a level warranted by
one’s assumptions about earnings
growth and expected returns. If, for
example, one agrees with Glassman and
Hassett that the appropriate expected
return is 4 percent (recent yield on the
10-year TIPS), and if one assumes trend
earnings growth of 3 percent, then the
warranted value of the S&Pindex is
2085. This is well above recent levels of
around 1300. On the other hand, if one
believes that stocks are somewhat more
risky than the TIPS and hence demands
an expected return of 5 percent (1 per-
cent equity premium), then the market is
clearly overvalued under the assumption
of 3 percent earnings growth. How exu-
berant are you?
Readers may also use the table to inter-
polate what approximate return they
might expect from an S&P500 index
fund given their assumption about earn-
ings growth. For example, if one be-
lieves that trend earnings growth is 
3 percent, then this valuation exercise in-
dicates that the current level of the S&P
500 is consistent with an expected return
of between 4½ percent and 5 percent. An
expected return of 5 percent would im-
ply a modest equity premium of 1 per-
cent as measured against the TIPS yield.
It should be evident from this exercise
that it is difficult to justify expected re-
turns above 5 percent unless one is ex-
tremely optimistic about trend earnings
growth. Thus, the historical return of 
7 percent on stocks is not a good pro-
jection for future returns.
 Concluding Thoughts
We have seen how sensitive stock-index
valuations are to key assumptions about
earnings growth and expected return.
Standard economic theory provides little
guidance for pinning down precise val-
ues. One’s assumptions must ultimately
be based on judgment. This is why some
readers undoubtedly will be exuberant
while others will be leery. One inescap-
able conclusion, however, is that at to-
day’s prices, future long-term returns of 
7 percent seem extremely unlikely. 
Further, recent stock-price levels undeni-
ably reflect a high degree of investor con-
fidence. History reveals that sharp drops
in stock prices occur spontaneously with
no apparent change in fundamentals. The
experiences of October 1987 and October
1997 offer two recent examples. Such
events are viewed as unpredictable col-
lapses in investor confidence. They are
evident only in retrospect.
For buy-and-hold investors, such swings
may be of little consequence. For in-
vestors with short horizons, on the other
hand, it would appear unwise to count all
recent paper gains as permanent until
they are realized. Just as one cannot
know if investors are irrationally exuber-
ant, one cannot know if a sudden drop in
investor confidence is around the corner.
 Footnotes
1. For a concise presentation of their argu-
ments, see James K. Glassman and Kevin A.
Hassett, “Stock Prices Are Still Far Too
Low,” On the Issues,American Enterprise
Institute for Public Policy Research, April
1999. These arguments are developed in their
book titled, Dow 36,000: A New Strategy for
Profiting from the Coming Rise in the Stock
Market, Washington, D.C.: American Enter-
prise Institute, 1999. 
2. For the mathematically minded reader:
Rt +1 = (Dt +1 + P t +1)/P t –1, where Rt +1is a
one-period return, Dt +1 is the dividend paid
during the period, and P t and P t + 1 are the
prices of the equity at the beginning and end
of the period.
3. The present value formulation, as it is
commonly known, is summarized by the fol-
lowing relationship: In its simplest form, a
stock’s price, P t, is determined by the expected
present value of future dividends, Dt +1, and 
of the expected present value of the terminal
price for the holding period K, P t + K :
Pt = Et 1 + R
i
Dt  + i+ Et 1 + R
K
PT+ k,
where R is the discount rate (expected
return), assumed here to be constant, and E is
an expectations operator. For a lucid treat-
ment of standard valuation approaches, see
John Campbell, Andrew Lo, and Craig
MacKinlay, The Econometrics of Financial
Markets, Princeton: Princeton University
Press, 1997, especially chapter 7.
4. Earnings are either distributed as divi-
dends or reinvested. Historically, firms have
paid out about half their earnings in the form
of dividends, although this payout ratio has
varied substantially. Given some norm for the
payout ratio, events that affect an investor’s
forecast of an earnings growth rate will also
affect her expected dividend growth rate by
the same amount.
5. These results are discussed in Jeremy
Siegel, “The Shrinking Equity Premium: His-
torical Facts and Future Projections,” in The
Equity Premium and Stock Market Valua-
tions, Conference Proceedings, April 30,
1999, Anderson School at UCLA. 
6. Moreover, for horizons of 15 years or
more, the S&P500 index has always yielded
a positive return. See Jagadeesh Gokhale and
Kevin Lansing, “Social Security: Are We
Getting Our Money’s Worth?” Federal
Reserve Bank of Cleveland, Economic Com-
mentary, January 1, 1996. 
TABLE 2  ALTERNATIVE VALUATIONS FOR S&P500 INDEX
Expected return (percent)
Earnings growth  4.0 4.5 5.0 5.5
(percent)
3.5 3912 2046 1384 1044
3.0 2085 1457 1119 871
2.5 1485 1111 887 737
SOURCE: Author’s calculations. Values are obtained from the following formula:
Pt =  Et 1 + R
i
Dt + i+Et1 + R
8
Pt + 7,
where Pt + 8 = Dt + 8 /(R–G), where D is the level of real dividends, R is the assumed
expected return, and G is the assumed growth rate of earnings per share. The path of
dividends is derived assuming that earnings growth decelerates uniformly from 10
percent to assumed rate over seven years, and that the dividend payout ratio increases
smoothly to 45 percent over the same period.
1 1
1 1
8
i = 1
K
i =17. Because standard economic theory can-
not satisfactorily explain why stock returns
have been so high relative to other instru-
ments, this fact has become known as the
equity premium puzzle.
8. Implicitly, Glassman and Hassett are
assuming that the buy-and-hold investor is the
marginal investor. 
9. Though we focus on reduced transactions
cost below, increased diversification also
offers an important channel for reducing
expected returns. For a general equilibrium
analysis of this issue, see John Heaton and
Deborah Lucas, “Stock Prices and Funda-
mentals,” presented at the 1999 Macroeco-
nomics Annual Conference, June 1999. 
10. Earnings are based on the “survivor”
companies. That is, firms that go out of busi-
ness are replaced in the index by new, pre-
sumably healthier, firms. Hence, earnings
(per share) growth rates for the index over-
state the earnings of a comparable constant
set of firms.
11. There are other explanations (related to
accounting practices) for expecting persistent
strength in measured earnings growth, but
these are beyond the scope of this article.
12. Thus, they incorporate persistently
higher earnings growth based on the case
made by Siegel. See the source note in table 2
for more detailed assumptions about the rela-
tionship between dividends and earnings.
John B. Carlson is an economist at the Fed-
eral Reserve Bank of Cleveland. The author
would like to thank Giuseppe Cinquemani 
for discovering a computational error in our
earlier version.
The views stated herein are those of the
author and not necessarily those of the Fed-
eral Reserve Bank of Cleveland or of the
Board of Governors of the Federal Reserve
System.
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The recent ascent in stock prices: how exuberant are you?

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