FRBSF Economic Letter
2002-16; May 24, 2002
Searching for Value in the U.S. Stock Market
The Standard & Poor's (S&P) 500 stock index closed at an all-time
high of 1527 on March 24, 2000. Since then, the index has declined by
about 28% to 1097 as of May 14, 2002, roughly where it was four years
ago. Falling stock prices have been accompanied by even larger percentage
declines in corporate earnings. In 2001, the reported (GAAP-based) earnings
of S&P 500 companies totaled $24.69 per share—the lowest earnings
figure since 1993 and a whopping 50% drop from 2000 earnings of $50 per
share. The collapse in corporate earnings caused the price-earnings (P/E)
ratio of the S&P 500 index to increase sharply to a year-end 2001
value of 46. This figure exceeds the P/E ratio of 28 that prevailed at
the market peak in March 2000 and is three times higher than the average
P/E ratio of 15.2 going back to 1926.
This Economic Letter examines the long-run behavior of the P/E
ratio and describes how it might be used to assess the fundamental value
of the stock market.
the rising P/E ratio
According to Ibbotson Associates (2002), the average compound annual
return on the S&P 500 (including dividends) was 10.7% from 1926 to
2001. The corresponding return on long-term U.S. government bonds (with
a maturity near 20 years) was 5.3%. Hence stocks delivered an annual excess
return over bonds of 5.4% during this period.
Ibbotson and Chen (2002) show that the increase in the P/E ratio since
1926 accounts for about one-fourth of the historical excess return on
stocks over bonds. This result takes on greater significance when we recognize
that the bulk of the net increase in the P/E ratio occurred during the
last two decades. Since 1982, there has been a sixfold expansion (from
7.5 to 46) in the "multiple" that investors assign to each dollar
of reported earnings. This expansion helped to produce an extraordinary
compound annual return on stocks of 15.2% over the period. Given this
record, future movements in the P/E ratio (or lack thereof) will likely
play an important role in determining how well stocks perform in the coming
for the rising P/E ratio?
Why would investors be willing to pay more for each dollar of corporate
earnings than they have in the past? There are several candidate explanations.
These include: (1) higher expected future earnings growth, (2) lower perceptions
of the risks of holding stocks, and (3) irrational exuberance. Over long
periods, corporate earnings growth has tracked the economy's trend growth
rate of productivity. Starting around 1995, the U.S. economy saw a pickup
in measured productivity growth that is thought by some to represent a
permanent structural change. Improved growth prospects associated with
the so-called "new economy" have been cited as justification
for the unprecedented valuations assigned to stocks in recent years.
Diminished risk perceptions can also justify higher valuations. All else
equal, investors would be willing to pay more for a claim on future earnings
if they thought that the risk of suffering a bad outcome was smaller than
in the past. Institutional and regulatory developments during the past
century and an improved understanding of the economy on the part of policymakers
have been cited as factors contributing to a safer environment for stocks.
Campbell and Shiller (2001) mention (but do not necessarily endorse) the
idea that baby boomers may be more risk-tolerant than earlier generations
because memories of the depressed economic conditions of the 1930s have
faded. Moreover, baby boomers may view stocks more favorably than bonds
because they recall the poor performance of bonds during the high-inflation
decade of the 1970s.
The third possible explanation for the rising P/E ratio, advocated by
Shiller (2000), is that investors have irrationally bid up stock prices
to levels that bear no relationship to the intrinsic values of the underlying
businesses (as measured by the expected discounted value of their future
earnings streams). Shiller notes that, throughout history, occurrences
of major speculative bubbles have generally coincided with the emergence
of some superficially plausible "new era" theory. Even with
a pickup in trend productivity growth, investors may have overreacted
by heedlessly extrapolating the temporary surge in earnings growth of
the late 1990s far into the future. Some recent studies provide support
for this idea. Chan, et al. (2001) show that equity analysts' forecasts
of long-term earnings growth rates have been consistently too optimistic
and have exhibited low predictive power for the actual earnings growth
rates subsequently achieved. Sharpe (2002) shows that the dramatic increase
in equity analysts' long-term growth forecasts in the latter half of the
1990s may explain as much as one-half of the rise in the P/E ratio during
A simple valuation
model: stock as a "disguised bond"
To gauge the relative merits of fundamental versus bubble explanations
for the rise in the P/E ratio, we must apply a valuation model to the
aggregate stock market. One simple valuation model compares the earnings
yield on stocks—defined as the inverse of the P/E ratio—to the yield
on a long-term bond. The logic behind this comparison is nicely summarized
by the following quote from famed investor Warren Buffett who describes
a stock as a type of "disguised bond" (Loomis, 2001):
A stock...is a financial instrument that has claim on future distributions
made by a given business, whether they are paid out as dividends or
to repurchase stock or to settle up after sale or liquidation. These
payments are in effect "coupons." The set of owners getting
them will change as shareholders come and go. But the financial outcome
for the business' owners as a whole will be determined by the size and
timing of these coupons. Estimating those particulars is what investment
analysis is all about.
Since the "coupon" payments from stocks are typically viewed
as more risky than those associated with bonds, one might expect the earnings
yield on stocks to exceed the yield on, say, a long-term government bond
which is considered safe from default. On the other hand, the coupon payments
from stocks will tend to grow over time with the earnings of the underlying
businesses, whereas the coupon payments from bonds are fixed. If the expected
earnings growth from stocks exactly compensated shareholders for the extra
risk, then a direct comparison between the earnings yield on stocks and
the yield on a long-term government bond could be justified.
with changing risk perceptions
One drawback of the simple valuation model described above is that it
does not allow for changes in investors' perceptions of the risks of holding
stocks versus bonds. Asness (2000) develops a valuation model that addresses
this issue. In one version, the earnings yield on the S&P 500 is regressed
on a constant term and the following three explanatory variables: (1)
the yield on a long-term government bond, (2) the volatility of monthly
stock returns over the preceding 20 years, and (3) the volatility of monthly
bond returns over the preceding 20 years. The long-term bond yield captures
expectations of future economic growth as well as expectations of future
inflation. The other two variables capture the slowly changing risk perceptions
of successive generations of investors, where risk perceptions are based
on each generation's volatility experience. According to these volatility
measures, stocks have become less risky over time while bonds have become
more risky (Figure 1). Asness shows that the inclusion of these volatility
measures significantly improves the model's ability to explain movements
in the earnings yield and, by extension, the P/E ratio.
Figure 2 plots a variant of Asness's model where the P/E ratio itself
(rather than the earnings yield) is regressed on a constant term and the
logarithms of the same three explanatory variables. For comparison, the
figure also plots the inverse yield on a long-term government bond. The
fitted P/E ratio from the model captures 70% of the variance in the observed
P/E ratio over the sample period 1946 to 2001 (monthly data from 1926-1945
are used to compute the initial volatility measures). In contrast, the
inverse bond yield alone does a poor job of capturing movements in the
observed P/E ratio. These results confirm Asness's finding of a strong
empirical link between valuation ratios and the return volatilities experienced
In Figure 2, the observed P/E ratio lies above the fitted P/E ratio from
November 1998 until the end of the data sample in December 2001. One interpretation
of this result is that the stock market has been overvalued for the past
several years, i.e., the observed value has consistently exceeded the
"fundamental value" implied by the long-standing relationship
between the P/E ratio, the bond yield, and the volatility measures. Alternatively,
one could argue that the market is properly priced but the valuation model
is missing some crucial elements.
Making predictions about the stock market can be a humbling experience.
Still, it may be worthwhile to consider the model's predictions for the
year-end 2002 level of the S&P 500 index. Given a current 20-year
government bond yield of about 5.5% and employing the end-of-sample volatility
measures for stocks and bonds, the model predicts a P/E ratio of 24.1.
Applying this multiple to the S&P's estimate of $36.34 for reported
earnings in 2002 yields a predicted value of 876 for the index—about
20% below the current level. Different predictions would be obtained if
any of the model inputs (for example, the bond yield or the earnings forecast)
were to change significantly over the coming year. Also note that the
market has deviated from the model's predictions for sustained periods
in the past.
Over the long history of the stock market, high P/E ratios have been
transitory phenomena. Campbell and Shiller (2001) show that, sooner or
later, the P/E ratio has tended to adjust back towards its long-run average.
These adjustments have taken place mainly through changes in stock prices
(P) rather than through changes in earnings (E). While Campbell and Shiller
do not expect a complete return of the P/E ratio to its long-run average,
they predict poor returns from stocks in the coming years. The valuation
model described here says something similar: we would not expect the P/E
ratio to return to its long-run average because the bond yield and the
volatility measures are now different from the past. Nevertheless, given
the current earnings forecast, the model predicts a downward adjustment
in stock prices.
Finally, investors should recognize that the extraordinary returns on
stocks recorded over the last 20 years have been driven in large measure
by a rising P/E ratio. A believer in efficient markets would not expect
the P/E ratio to continue its upward trend because the current market
price supposedly already reflects investor risk perceptions and expectations
about the future trajectory of earnings. Absent further changes in the
P/E ratio, stock prices can rise only as fast as earnings. Since 1926,
earnings have grown by an average compound rate of 5.8%. If we add to
this figure the current dividend yield on stocks of about 1.2%, we obtain
a forecasted total return on stocks of 7% per year—only about one-half
the average compound return since 1982.
Kevin J. Lansing
[URLs accessed in May 2002.]
Asness, Clifford S. 2000. "Stocks
versus Bonds: Explaining the Equity Risk Premium." Financial
Analysts Journal 56(2), pp. 96-113.
Campbell, John, and Robert J. Shiller. 2001. "Valuation
Ratios and the Long-Run Stock Market Outlook: An Update." NBER
Working Paper 8221.
Chan, Louis K.C., Jason Karceski, and Joseph Lakonishok.
2001. "The Level and
Persistence of Growth Rates." NBER Working Paper 8282.
Ibbotson, Roger G., and Pend Chen. 2002. "Stock
Market Returns in the Long Run: Participating in the Real Economy."
Yale University, International Center for Finance, Working Paper No. 00-44.
Loomis, Carol. 2001. "Warren
Buffett on the Stock Market." Fortune Magazine (December 10).
Shiller, Robert J. 2000. Irrational Exuberance. Princeton:
Princeton University Press.
Stocks, Bonds, Bills, and Inflation, 2002 Yearbook.
Chicago: Ibbotson Associates.
Sharpe, Steven A. 2002. "How
Does the Market Interpret Analysts' Long-Term Growth Forecasts?"
Federal Reserve Board, Finance and Economics Discussion Series Paper 2002-7.