FRBSF Economic Letter
2004-30; October 29, 2004
Inflation-Induced Valuation Errors in the Stock Market
A recent front-page article in
the Wall Street Journal documented an increasing tendency among
economists to move away from theories of efficient stock market
valuation in favor of "behavioral" models that emphasize
the role of irrational investors (see Hilsenrath 2004). The long-run
rate of return on stocks is ultimately determined by the stream
of corporate earnings distributions (cash flows) that accrue to
shareholders. In assigning prices to stocks, efficient valuation
theory says that rational investors should discount real cash flows
using real interest rates or discount nominal cash flows using
nominal interest rates. Twenty-five years ago, Modigliani and Cohn
(1979) put forth the hypothesis that investors may irrationally
discount real cash flows using nominal interest rates—a behavioral
trait that would lead to inflation-induced valuation errors. This
Economic Letter examines some recent research that finds support
for the Modigliani-Cohn hypothesis. In particular, studies show
that the Standard & Poor's (S&P) 500 stock index tends
to be undervalued during periods of high expected inflation (such
as the late 1970s and early 1980s) and overvalued during periods
of low expected inflation (such as the late 1990s and early 2000s).
This result implies that the long bull market that began in 1982
can be partially attributed to the stock market's shift from a
state of undervaluation to one of overvaluation. Going forward,
the return on stocks could be influenced by a shift in the opposite
direction.
Stock as a "disguised bond"
Famed
investor Warren Buffett has described a stock as a type of "disguised
bond." A stock represents a claim to a stream of earnings
distributions, whereas a bond represents a claim to a stream of
coupon payments. Given that stocks and bonds can be viewed as competing
assets in a portfolio, investors may wish to compare the valuations
of these two asset classes in some quantitative way. Wall Street
practitioners typically compare the earnings yield on stocks (denoted
here by the E/P ratio, the inverse of the price-earnings ratio)
with the nominal yield on a long-term U.S. Treasury bond. Stocks
are supposedly undervalued relative to bonds when the E/P ratio
exceeds the nominal bond yield and supposedly overvalued relative
to bonds when the E/P ratio is below the nominal bond yield. This
valuation technique is often referred to as the "Fed model," but
it is important to note that the Federal Reserve neither uses nor
endorses it. Many authors, including Ritter and Warr (2002) and
Asness (2003), have pointed out that the practice of comparing
a real number like the E/P ratio to a nominal yield does not make
sense. While it would be more correct to compare the E/P ratio
to a real bond yield, that comparison still ignores the different
risk characteristics of stocks versus bonds and the reality that,
over the past four decades, cash distributions to shareholders
in the form of dividends have averaged only about 50% of earnings.
Long-run yield comparison
 Wall Street practitioners often argue that comparing the E/P ratio
to a nominal bond yield is justified by the observed comovement
of the two series in the data. Figure 1 plots the E/P ratio of
the S&P 500 index (based on 12-month trailing reported earnings)
together with the nominal and real yields on a long-term U.S. Treasury
bond (with a maturity near 20 years). The figure uses monthly data
from December 1945 to June 2004. The real yield is obtained by
subtracting expected inflation from the nominal yield. Expected
inflation is constructed as an exponentially weighted moving average
of past (12-month) CPI inflation, where the weighting scheme is
set to approximate the time-series behavior of the one-year-ahead
inflation forecast from the Survey of Professional Forecasters.
The
figure shows that the E/P ratio is more strongly correlated with
movements in the nominal yield than with the real yield, particularly
since the mid-1960s. This result is a puzzle from the perspective
of efficient valuation theory. Observed movements in the nominal
yield can be largely attributed to changes in expected inflation
which, in turn, have been driven by changes in actual inflation.
If investors were rationally discounting future nominal cash flows
using nominal interest rates, they would understand that inflation-induced
changes in the nominal bond yield are accompanied by inflation-induced
changes in the magnitude of future nominal cash flows. Indeed,
Asness (2003) shows that low-frequency movements in the U.S. inflation
rate are almost entirely passed through to changes in the growth
rate of nominal earnings for the S&P 500 index. Thus, to a
first approximation, a real valuation number like the E/P ratio
(or its inverse, the P/E ratio) should not move at all in response
to changes in the nominal bond yield. Similar logic applies to
the residential housing market; the ratio of house prices to rents
(a real valuation number) should not be affected by inflation-induced
changes in mortgage interest rates. Nevertheless, the data show
that the ratio of house prices to rents in the U.S. economy has
been trending up since the mid-1980s as inflation and mortgage
interest rates have been trending down.
The observation that real
valuation ratios are correlated with movements in nominal interest
rates lends credence to the Modigliani-Cohn
hypothesis. Investors and homebuyers appear to be adjusting their
discount rates to match the prevailing nominal interest rate.
However, for some unexplained reason, they do not simultaneously
adjust
their forecasts of future nominal cash flows, i.e., earnings
distributions or imputed rents. The failure to take into account
the influence
of inflation on future nominal cash flows is an expectational
error that is equivalent to discounting real cash flows using a
nominal
interest rate.
Changing risk perceptions
 Asness
(2000) shows that movements in the E/P ratio also appear to be
driven by changes in investors' risk perceptions. Monthly
stock return volatility has declined relative to monthly bond return
volatility, regardless of whether returns are measured in nominal
or real terms. If investors' risk perceptions are based on their
own generation's volatility experience, then stocks will appear
to have become less risky relative to bonds over time. Following
Asness, a statistical model of investor behavior can be constructed
by regressing the E/P ratio on a constant term and three nominal
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. It turns out that this simple behavioral model
can account for 70% of the variance in the observed E/P ratio from
December 1945 to June 2004. In contrast, an otherwise identical
model that employs real explanatory variables can account for only
26% of the variance in the observed E/P ratio. In Figure 2, the
fitted E/P ratios from both the nominal and real models are inverted
for comparison with the observed P/E ratio of the S&P 500 index.
The nominal model does a much better job of matching the level
and volatility of the observed P/E ratio. The real model, in contrast,
predicts a relatively stable P/E ratio—one that remains close
to its long-run average over much of the sample period, particularly
during the so-called "new economy" years of the late
1990s and beyond. At the end of the sample period in June 2004,
the observed P/E ratio is 20.2. The predicted P/E ratio from the
nominal model is 24.1 while that from the real model is 14.8.
Inflation-induced
valuation errors
 The predicted P/E ratio from the real model can be interpreted
as an estimate of the rational (or fundamentals-based) P/E ratio
because the model assumes that investors discount real cash flows
using real interest rates. In this case, the difference between
the observed P/E ratio and the real-model prediction can be viewed
as a measure of overvaluation. Figure 3 shows that overvaluation
(measured as a percent of fundamental value) is negatively correlated
with the level of expected inflation; overvaluation tends to be
high when expected inflation is low, and vice versa. According
to the analysis, overvaluation was highest during the late 1990s
and early 2000s—a period when expected and actual inflation were
quite low. The late 1990s witnessed the emergence of the biggest
bubble in history. The bubble burst in March 2000, setting off
a chain of events that eventually dragged the U.S. economy into
a recession in 2001. The recession-induced collapse in corporate
earnings caused the market P/E ratio to spike above 45, thereby
exceeding the previous high that had prevailed near the bubble
peak. In contrast, the high inflation era of the late 1970s and
early 1980s was characterized by substantial undervaluation, as
the market P/E ratio languished below its long-run average for
more than a decade. The results plotted in Figure 3 reinforce those
of Ritter and Warr (2002) and Campbell and Vuolteenaho (2004),
who find strong support for the Modigliani-Cohn hypothesis using
more sophisticated empirical methods.
Conclusion
In recent years, contributors to the rapidly growing field of
behavioral finance have been refining a new class of asset pricing
models. These models are motivated by a variety of empirical and
laboratory evidence which shows that people's decisions and forecasts
are often less than fully rational. Simple behavioral models can
account for many observed features of real-world stock market data
including: excess volatility of stock prices, time-varying volatility
of returns, long-horizon predictability of returns, bubbles driven
by optimism about the future, and market crashes that restore attention
to fundamentals (see, for example, Lansing 2004 and the references
cited therein).
Twenty-five years ago, Modigliani and Cohn (1979),
put forth a behavioral model that predicted mispricing of stocks
in the presence
of changing inflation. The comovement of the stock market E/P
ratio with the nominal bond yield observed since the mid-1960s
(when
U.S. inflation started rising) is consistent with the Modigliani-Cohn
hypothesis. A regression model that includes a constant term
and three nominal variables can account for 70% of the variance
in
the observed E/P ratio over the past four decades. However, as
noted by Asness (2003), the success of this model in describing
investor behavior should not be confused with the model's ability
to forecast what investors should really care about, namely,
long-run real returns. Investors of the early 1980s probably did
not anticipate
the 20-year declining trend of inflation and nominal interest
rates that helped produce above-average real returns as stocks
moved
from a state of undervaluation to one of overvaluation in the
manner by described by Modigliani and Cohn (1979). Today's investors
may
suffer the opposite fate if a secular trend of rising inflation
and nominal interest rates causes the stock market to move back
towards a state of undervaluation.
Kevin J. Lansing
Senior Economist
References
Asness, C.S. 2003. "Fight the Fed Model." Journal
of Portfolio Management 30(1) (Fall) pp. 11-24.
Asness, C.S. 2000. "Stocks
versus Bonds: Explaining the Equity Risk Premium." Financial
Analysts Journal 56(2) pp. 96-113.
Campbell, J.Y., and T. Vuolteenaho.
2004. "Inflation Illusion
and Stock Prices." American Economic Review, Papers and
Proceedings 94, pp. 19-23.
Hilsenrath, J.E. 2004. "Stock Characters:
As Two Economists Debate Markets, the Tide Shifts." Wall
Street Journal, October 18, p. A1.
Lansing, K.J. 2004. "Lock-in of
Extrapolative Expectations in an Asset Pricing Model." FRBSF
Working Paper 2004-06.
http://www.frbsf.org/publications/economics/papers/2004/wp04-06bk.pdf
Modigliani,
F., and R.A. Cohn. 1979. "Inflation, Rational
Valuation and the Market." Financial Analysts Journal 35,
pp. 24-44.
Ritter, J.R., and R.S. Warr. 2002. "The
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of Financial and Quantitative Analysis 37(1) pp. 29-61.
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Ibbotson Associates.
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