Investor Expectations and Fundamentals:
John B. Carlson and Eduard A. Pelz
The average annual return of the S&P 500 index since 1994
has exceeded 25 percent. Confidence is high and investors are
looking forward to continued above-average returns. In this Economic Commentary,
we attempt to reconcile investors expectations with
a decline in the equity premium, using a standard approach to
Although the stock market
got off to a choppy start this year and investor confidence has
fallen of late, recent surveys reveal that investors still expect
stocks to yield returns of around 15 percent.1
Accounting for expected inflation of about 2 to 3 percent, such
anticipated returns remain significantly higher than historical
average real returns of 7 percent.2 What could
explain such optimistic expectations?
One possibility is that survey
respondents are following so-called momentum investment strategies.
Momentum investors base their investment decisions on recent
movements of stock prices, which, as measured by various indices,
were trending upward until recently. Near-term optimism might
represent an extrapolation of the high returns of recent years.3
Another explanation for survey
respondents optimism is that they expect fundamentalsexpected
earnings growth and the rate of return required by investorsto
support a continued rise in stock prices. For example, respondents
may expect the extraordinary earnings growth of recent years
to continue indefinitely, fueling further stock-price appreciation.
Stock prices may also be expected to appreciate if investors
require lower returns. While it may seem paradoxical, lower required
returns initially generate higher realized returns for those
who already own stock, but this is a transitory (though perhaps
persistent) state. If investors assess the path of future earnings
correctly, their actual return would be expected to equal the
rate at which they discount those earnings, that is, their required
return. Discounting future cash flows from equities using a lower
required return implies that investors are willing to pay more
for stocks, pushing up current returns. Higher current returns
would thus be associated with lower expected (future)
returns, contrary to the expectations of those investors surveyed.
Some advocates of the view that
required returns are falling maintain that investors are becoming
calmer and smarter. They argue that investors have
come to recognize that when held over long horizons, a
diversified portfolio of equities produces returns that are no
more variable (hence no more risky) than those of any other safe
market security.4 Consequently, investors now require
a smaller premium to induce them to hold equities over essentially
riskless alternatives such as U.S. Treasury securities. This
is often called the equity premium.5
Their required rate of return on equities is smaller, reflecting
the shrinking equity premium.
In this Economic Commentary,
we focus on some implications of a shrinking equity premium in
standard models of stock-price valuation. We examine the conditions
under which the survey results can be reconciled with the view
that the equity premium is falling. Our analysis illustrates
a potential hazard of extrapolating recent returns indefinitely
into the futurethose who do so are likely to be disappointed.
Discounting Future Returns
The standard approach to valuing
equities is straightforward and involves two basic elementsearnings
growth and discounting. To appreciate the role of these elements,
it is useful to ask why investors hold stocks. The answer, of
course, is that they expect some future income, either in the
form of dividends or through stock-price appreciation, that is,
capital gains. Income depends clearly on the firms ability
to grow earnings. The higher its earnings growth, the greater
its potential to pay dividends and the greater its stock-price
appreciation. This all seems quite clear.
Central to the valuation problem,
however, is the fact that an investors income from holding
stock accrues in the future and is uncertain. Given a choice,
individuals would prefer to receive income sooner rather than
later. To give up a dollars worth of current income, investors
demand more than a dollar in the future. The more impatient the
investor, the less he is willing to pay for a stock with a given
level of future income, that is, the higher his required return.6
Given a choice, individuals also
prefer less uncertainty. Investors discount risky investments
more than safe onesequivalently, the more risk associated
with a stock, the higher the attendant required return. Naturally,
the equity premium is also affected by the degree to which an
investors portfolio is diversified. Individuals can reduce
their overall exposure to risk by holding a portfolio of stocks
in which risks are offsetting. Moreover, individuals will discount
a stock less if they can add it to a portfolio that offsets the
risk associated with that particular stock (idiosyncratic risk)
and thereby reduce their total risk.
An important element of the equity
premium often overlooked is shareholder cost.7
Investing in stock incurs time and money. What matters to the
investor is income received after accounting for coststhe
net return. The greater the costs, the higher the return required
to maintain a given level of net return. For the small investor
holding mutual funds, such costs historically accounted for more
than two percentage points of returns (although there is evidence
that this is declining).8 The historical
average return of 7 percent on stocks is a gross real return.
Hence, the net return for a typical mutual fund investor would
have been less than 5 percent.
Implications of a Permanent Decline
in the Equity Premium
Anyone exposed to U.S. television
commercials must surely be aware of dramatic declines in the
costs of trading stocks. We have witnessed a barrage of advertisements
by dot-com brokers, stressing the low cost and convenience of
making trades on the Internet. Moreover, the availability of
new investment products such as low-cost index funds has increased
the small investors access to highly diversified portfolios.9
These trends, a result of technological
innovations in information and communications technologies, clearly
justify lower required returns. Whats more, because these
technologies are irreversible, the effect is permanent. The only
issue is the size of the decline. Jeremy Siegel of the Wharton
School estimates that lower shareholder costs and increased diversification
have reduced the equity premium and hence required returnsas
much as two percentage points.10 If we
assume that investors earnings forecasts are correct on
average, actual returns will equal required returns. Siegel believes
that, looking forward, we might reasonably expect gross returns
of 5 percent, down two percentage points from historical averages.
Figure 1 illustrates the implications of a smooth
change in required returns from 7 percent to 5 percent over a
period of 15 years. Panel A shows the assumed
path for required returns. Panel B illustrates
the corresponding impact on the level of the stock-price index
under the assumption that dividend growth remains unchanged at
an expected rate of 3 percent annuallythe actual trend
rate for earnings in the postWorld War II period. Panel
C shows the path of gross returns implied by this path of
stock-price appreciation and 3 percent annual dividend growth.11
In panel B we see how the estimated
value of stocks would change if required returns drop, relative
to a path assuming no change. A two-percentage-point decline
in required returns yields a doubling of the index value. Since
our hypothetical example assumes that the bulk of the change
takes place over 15 years, average annualized gross returns over
the period would be approximately 4.7 percentage points higher
than they would have been otherwise.
Note that the increase in gross
(realized) returns (panel C) occurs when required returns begin
to fall. This reflects the fact that a decline in required returns
implies investors are willing to pay more for equities than they
were previously. Hence, in competitive markets, the price of
the stock would be bid up.
The appreciation in stock prices
is essentially a windfall return for current equity owners.12 That is, gains from reduced required
returns accrue to holders of equities as above-average returns.
The extra returns that result from the fall in required returns
persist only as long as required returns continue to decline.
It is important to note that when required returns stop falling,
the windfall ceases and realized returns end up at 5 percent,
the new required return (barring, of course, surprises to earnings
Reconciling High Expected Returns
This brings us back to the puzzle
posed in the introduction. If recent high stock returns can be
at least partly attributed to a decline in required returns,
then we might expect future long-term returns to ultimately fall
below their historical average, as in figure 1. Thus, at some
point, rational investors should expect returns that are lower
than the historical average. Yet we find that investor surveys
reveal just the opposite. What can explain this discrepancy?
One possibility is that the equity
premium continues to fall. The fact that the new transactions
technology has been readily available does not imply that the
benefits are currently enjoyed by all. We may still be in the
midst of diffusing its benefits.
Another reason the equity premium
may be continuing to fall is that, as weve noted, investors
are increasingly taking the long view. That is, they are buying
stocks and holding onto them to diversify risks across time.
More precisely, if one buys a portfolio of stocks and holds it
for, say, 40 years, then one might expect cyclical effects to
be averaged outgood times will offset bad. James K. Glassman
and Kevin Hassett take this view when they argue that the stock
market continues to be undervalued.13
So far, we have largely ignored
earnings growth, the other fundamental of stock valuation. In
fact, our analysis assumes that earnings increase at some constant
long-run rate.14 In a more general setting, it is reasonable
to expect the required rate of return to rise when productivity
(the engine of earnings growth) increases, as it has in recent
years. Improved productivity creates more profitable investment
opportunities, and these must compete for limited resources,
a process which pushes up the real interest rate. Higher real
interest rates raise the return on all investments (including
risk-free Treasury bills) and hence the required rate of return
on equities. Increased productivity can push up the price of
a single stock, or even an entire sector, but broad-based increases
in productivity will eventually affect required returns (through
interest rates) and ease stock-price appreciation.
Is there evidence that improved
productivity is stimulating higher required returns? Productivity
has been rising, and real interest rates also seem to be higher
than their historical averages. Yields on 10-year Treasury inflation-protected
securities (TIPs), which Seigel argues are an appropriate benchmark
for a risk-free return,15 are currently around 4 percent. What does all this
mean for the equity premium? If we assume a required return of
5 percent for the reasons given earlier, the equity premium becomes
only 1 percent.
A good case can be made that
permanent declines in shareholder costs and increased diversification
have worked together to produce a substantial permanent increase
in stock values. This, in turn, could explain why recent returns
on equities have far exceeded their historical average. Whether
this process justifies current stock prices or whether the market
has overreacted, one cannot know. Equity prices could correctly
reflect expectations of persistently high future earnings growth.
What concerns us is the possibility
that momentum strategies could bid up the general level of stock
prices beyond that supported by fundamentals. The financial literature
establishes clearly that it is possible to earn higher returns
than the market by investing in stocks whose values have recently
increased faster than the market, but only over short horizons.16 In brief, it makes sense to jump on the bandwagonat
least in the near term. It is unclear to what extent this applies
to the market in its entirety; recent empirical evidence suggests
that the profitability of momentum strategies decreases with
firm size.17 However, an unanticipated, permanent
drop in the equity premium could lead individually rational momentum
investors to overreactthat is, to bid stock values past
levels justified by the new fundamentals. Recent market movements,
especially in technology-laden indexes like the Nasdaq, may reflect
such an overreaction.
An important lesson of our analysis
is that the extra returns generated by a drop in the equity premium
disappear when required returns stop falling. Thus, even if investors
correctly forecast higher-than-average cash flows from stocks,
they should expect a lower-than-average historical returnreflecting
a lower equity premium. To the extent that the recent surge in
stock prices is the transitory result of a shrinking equity premium,
investors expecting higher-than-average returns based solely
on momentum will likely be disappointedif they havent
A: REQUIRED RATE OF RETURNa
FIGURE 1 THE
EFFECT OF A DECLINING EQUITY PREMIUM
B: SIMULATED STOCK VALUES
C: GROSS RETURN
a. The dashed
lines indicate the time period over which the equity premium
SOURCE: Authors' calculations.
1. See for example, Dennis J. Jacobe and
David W. Moore, Investor Optimism Falls, The Gallup
Organization, Poll Releases, March 29, 2000, <http://www.gallup.com/
2. For a comparison of long-term returns
equities versus returns on U.S. Treasury bills and bonds, see
Jeremy J. Siegel, The Shrinking Equity Premium, Journal
of Portfolio Management, vol. 26, no. 1 (Fall 1999), pp.
3. Over short time horizons, stock-price
increases tend to persist, and investment strategies designed
to exploit this fact can be lucrative. Over extended horizons,
momentum investing will be profitable only if supported by fundamentals.
A theoretical justification for momentum-investment strategies
is provided by Harrison Hong and Jeremy C. Stein, A Unified
Theory of Underreaction, Momentum Trading, and Overreaction in
Asset Markets, Journal of Finance, vol. 54, no.
6 (December 1999), pp. 214384. A key assumption is that
investors are boundedly rational, that is, rational, but with
limits on how much they can know. This creates a tendency for
prices to underreact in the short run, making trend-chasing profitable.
4. See James K. Glassman and Kevin A. Hassett,
Stock Prices Are Still Far Too Low, in American Enterprise
Institute for Public Policy Research, On the Issues, April
1999. The authors develop these arguments in their book, Dow
36,000: The New Strategy for Profiting from the Coming Rise in
the Stock Market, (New York: Times Business, 1999).
5. The equity premium over the last century
was higher than can easily be explained by the increased risk
associated with holding equities. See Rajnish Mehra and Edward
C. Prescott, The Equity Premium: A Puzzle, Journal
of Monetary Economics, vol. 15,
no. 2 (March 1985), pp. 14561.
6. Present value calculations define the
price of a stock in the current period (P0)
as the sum of the discounted values of all future dividends.
where D0 is the initial dividend, gt is the growth rate of dividends at time t,
is the required return at
time t. One can show that this simplifies to the well-known
Gordon growth model,
under the assumption of constant dividend growth (g) and
constant required returns (r).
7. For a thorough discussion of costs borne
by mutual fund investors, see John D. Rea and Brian K. Reid,
Trends in the Ownership Costs of Equity Mutual Funds,
Investment Company Institute, November 1998, pp. 112.
8. The most obvious cost is the commission
paid on the purchase of a stock. Less obvious (as well as difficult
to measure) are costs associated with tax liability, market research,
management, and loads. For a more detailed examination of the
components of required returns, see the companion Economic
Commentary by John B. Carlson and Eduard A. Pelz on the decline
in required returns, forthcoming.
9. John Heaton and Deborah Lucas, Stock
Prices and Fundamentals, NBER Macroeconomics Annual,
vol. 14 (1999), pp. 21342.
10. See footnote 2.
11. The simulated fall in required returns
from 7 to 5 percent is specified by the function
This particular function was chosen to accommodate a diffusion
process that first accelerates and then decelerates. The price
level is normalized to 1 in the first period.
12. It is, of course, implicitly assumed
that technological advances that reduce shareholder costs are
a surprise. Had they been anticipated, the windfall would have
occurred at an earlier date; that is, only the timing would have
been affected. Moreover, we are ignoring potential general equilibrium
effects on returns of other assets.
13. See footnote 4.
14. That is, we present a partial equilibrium
analysis of the standard valuation method. We implicitly assume
that in the long run, the required rate of return is greater
than earnings growth. There may be good reason to believe that
a firms earning potential may exceed the required return
in the near term, but this implies an infinite stock price. Clearly,
this cannot persist indefinitelymarket forces will work
to bring required returns and earnings growth back into line.
For general equilibrium approaches, see Nathan S. Balke and Mark
E. Wohar, Why are Stock Prices So High? Dividend Growth
or Discount Factor? Federal Reserve Bank of Dallas Working
Paper 00-01, and Michael T. Kiley, Stock Prices and Fundamentals
in a Production Economy, Finance and Economics Discussion
Series Working Paper 2000-5, Federal Reserve Board.
15. See footnote 2.
16. See, for example, Mark Grinblatt, Sheridan
Titman, and Russ Wermers, Momentum Investing Strategies,
Portfolio Performance, and Herding: A Study of Mutual Fund Performance,
American Economic Review, vol. 85, no. 5 (December 1995),
17. Harrison Hong, Terence Lim, and Jeremy
C. Stein, Bad News Travels Slowly: Size, Analyst Coverage,
and the Profitability of Momentum Strategies, Journal
of Finance, vol. 55, no. 1 (February 2000), pp. 26595.
B. Carlson is an economic advisor at the Federal Reserve Bank
of Cleveland, and Eduard A. Pelz is a senior research assistant
at the Bank.
The views stated herein are those of the authors and not necessarily
those of the Federal Reserve Bank of Cleveland or of the Board
of Governors of the Federal Reserve System.
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