Estimating the Real Rate of Return on Stocks Over the Long Term

Estimating the Real Rate
of Return on Stocks
Over the Long Term
Papers by
John Y. Campbell
Peter A. Diamond
John B. Shoven
Presented to the
Social Security Advisory Board
August 2001

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Social Security Advisory Board
An independent, bipartisan Board created by Congress and appointed by the
President and the Congress to advise the President, the Congress, and the Commissioner
of Social Security on matters related to the Social Security and Supplemental Security Income programs.

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TABLE OF CONTENTS
Introduction .......................................................................................................... 1
Forecasting U.S. Equity Returns in the 21st Century ........................................ 3
John Y. Campbell
I.
Methods for Forcasting Returns ..................................................... 3
II.
Current Market Conditions ............................................................. 6
III.
Implications for Future Returns ...................................................... 6
What Stock Market Returns to Expect for the
Future: An Update ....................................................... ............11
What Stock Market Returns to Expect for the Future?.................................. 17
Peter A. Diamond
I.
Summary ....................................................................................... 17
II.
Introduction .................................................................................. 18
III.
Historical Record .......................................................................... 19
IV.
Why Future Returns May Differ From Past Returns ................... 20
V.
Other Issues .................................................................................. 31
VI.
Conclusion .................................................................................... 33
What Are Reasonable Long-Run Rates of Return
To Expect on Equities? ................................................................47
John B. Shoven
I.
Introduction .................................................................................. 47
II.
Dividends Are Obsolete ................................................................ 47
III.
The Model..................................................................................... 48
IV.
Steady State Returns ..................................................................... 49
V.
The Big Question: Future P-E Ratios .......................................... 49
VI.
The Long-Run Outlook for Equity Rates of Return ..................... 50
VII.
Why Won’t Equity Returns Be As Good
In the 21st Century? ........................................................... 51
VIII. The Equity Premium Will Be Lower Because
Real Interest Rates Are Higher ......................................... 51
IX.
Which Rate to Use for Projections? .............................................. 52
X.
Conclusions ................................................................................... 52
Biographies of Authors............................................................................................54
Appendix: Equity Yield Assumptions Used by the Office of the
Chief Actuary, Social Security Administration, to Develop
Estimates for Proposals with Trust Fund and/or Individual
Account Investments.................................................................55
Stephen C. Goss
Social Security Advisory Board........................................................................59

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INTRODUCTION
In recent years there have been a variety of proposals that would change the current
Social Security system to include some form of investment of funds in private equities. These
proposals include allowing or requiring individuals to use a portion of the payroll tax to fund
individual investment accounts, either as part of the Social Security system or as an addition
to it. They also include proposals to require the government to invest a portion of the Social
Security Trust Funds in equities.
A key element in evaluating these proposals is the rate of return that can be expected
on such investments. The members of the 1994-1996 Advisory Council on Social Security
agreed to use a real annual rate of 7 percent (the average for the period 1900-1995) to
compare the three plans put forward by the Council. The Office of the Chief Actuary
(OCACT) of the Social Security Administration has continued to use 7 percent to evaluate
proposals for investment in stocks. However, there is a question as to whether the historical
rate for the last century should be used to make long-term projections over the coming
decades or whether an alternative rate or range of rates is more appropriate.
This document includes papers by three distinguished economists that examine this
important question, including the issue of how to reflect the higher risk inherent in stock
investment relative to investment in U.S. Treasury securities. The papers are by John
Campbell, Otto Eckstein Professor of Applied Economics at Harvard University; Peter
Diamond, Institute Professor at the Massachusetts Institute of Technology; and John Shoven,
Charles Schwab Professor of Economics at Stanford University. The Board is publishing
them in order to make them available to policy makers and members of the public who are
interested in the issue of how to ensure the long-term solvency of the Social Security system.
The papers (which have been updated for purposes of this document) were the basis
for a discussion sponsored by the Social Security Advisory Board on May 31, 2001. The
purpose of the discussion was to enable individuals from OCACT who have the responsibility
of estimating the effects of changes in the Social Security system to hear a range of views on
the likely real yields on equities over the long term. Participants in the discussion from
OCACT included Stephen Goss, Chief Actuary; Alice Wade, Deputy Chief Actuary; Patrick
Skirvin, Lead Economist; and Anthony Cheng, Economist.
Participants also included three other distinguished economists who were on the 1999
Technical Panel on Assumptions and Methods: Eugene Steuerle, Senior Fellow, The Urban
Institute; Deborah Lucas, Professor of Finance, Northwestern University and currently Chief
Economist, Congressional Budget Office; and Andrew Samwick, Assistant Professor of
Economics, Dartmouth College. The 1999 Technical Panel, which was sponsored by the
Advisory Board, was charged with reviewing the assumptions and methods used in the long-
term projections of the Social Security Trust Funds. The Panel also examined the question of
how to evaluate the returns and risks involved in stock market investments. The Panel’s
report was published by the Board in November 1999 and is available on the Board’s Web site
(www.ssab.gov).
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Forecasting U.S. Equity Returns in the 21st Century
John Y. Campbell, Professor of Economics
Harvard University
July 2001
What returns should investors expect the U.S. stock market to deliver on average during the
next century? Does the experience of the last century provide a reliable guide to the future? In
this short note I first discuss alternative methodologies for forecasting average future equity
returns, then discuss current market conditions, and finally draw conclusions for long-term return
forecasts. Throughout I work in real, that is inflation-adjusted, terms.
I. Methods for Forecasting Returns
1. Average past returns
Perhaps the simplest way to forecast future returns is to use some average of past returns.
Very naturally, this method has been favored by many investors and analysts. However there are
several difficulties with it.
a) Geometric average or arithmetic average? The geometric average return is the
cumulative past return on U.S. equities, annualized. Siegel (1998) studies long-term historical
data on value-weighted U.S. share indexes. He reports a geometric average of 7.0% over two
different sample periods, 1802-1997 and 1871-1997. The arithmetic average return is the average
of one-year past returns on U.S. equities. It is considerably higher than the geometric average
return, 8.5% over 1802-1997 and 8.7% over 1871-1997.1
When returns are serially uncorrelated, the arithmetic average represents the best forecast of
future return in any randomly selected future year. For long holding periods, the best forecast is
the arithmetic average compounded up appropriately. If one is making a 75-year forecast, for
example, one should forecast a cumulative return of 1.08575 based on 1802-1997 data.
When returns are negatively serially correlated, however, the arithmetic average is not
necessarily superior as a forecast of long-term future returns. To understand this, consider an
extreme example in which prices alternate deterministically between 100 and 150. The return is
50% when prices rise, and -33% when prices fall. Over any even number of periods, the
geometric average return is zero, but the arithmetic average return is 8.5%. In this case the
arithmetic average return is misleading because it fails to take account of the fact that high returns
always multiply a low initial price of 100, while low returns always multiply a high initial price of
1 When returns are lognormally distributed, the difference between the two averages is approximately one-half
the variance of returns. Since stock returns have an annual standard deviation of about 18% over these long
periods, the predicted difference is 0.182/2=0.016 or 1.6%. This closely matches the difference in the data.
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150. The geometric average is a better indication of long-term future prospects in this
example.2
This point is not just a theoretical curiosity, because in the historical data summarized by
Siegel, there is strong evidence that the stock market is mean-reverting. That is, periods of
high returns tend to be followed by periods of lower returns. This suggests that the arithmetic
average return probably overstates expected future returns over long periods.
b) Returns are very noisy. The randomness in stock returns is extreme. With an annual
standard deviation of real return of 18%, and 100 years of past data, a single year’s stock
return that is only one standard deviation above average increases the average return by 18
basis points. A lucky year that is two standard deviations above average increases the average
return by 36 basis points. Even when a century or more of past data is used, forecasts based
on historical average returns are likely to change substantially from one year to the next.
c) Realized returns rise when expected returns fall. To the extent that expected future
equity returns are not constant, but change over time, they can have perverse effects on
realized returns. Suppose for example that investors become more risk-tolerant and reduce
the future return that they demand from equities. If expected future cash flows are
unchanged, this drives up prices and realized returns. Thus an estimate of future returns
based on average past realized returns will tend to increase just as expected future returns are
declining.
Something like this probably occurred in the late 1990’s. A single good year can have a
major effect on historical average returns, and several successive good years have an even
larger effect. But it would be a mistake to react to the spectacular returns of 1995-99 by
increasing estimates of 21st Century returns.
d) Unpalatable implications. Fama and French (2000) point out that average past U.S.
stock returns are so high that they exceed estimates of the return to equity (ROE) calculated
for U.S. corporations from accounting data. Thus if one uses average past stock returns to
estimate the cost of capital, the implication is that U.S. corporate investments have destroyed
value; corporations should instead have been paying all their earnings out to stockholders.
This conclusion is so hard to believe that it further undermines confidence in the average-
return methodology.
One variation of the average-past-returns approach is worth discussing. One might take
the view that average past equity returns in other countries provide relevant evidence about
U.S. equity returns. Standard international data from Morgan Stanley Capital International,
2 One crude way to handle this problem is to measure the annualized variance of returns over a period
such as 20 years that is long enough for returns to be approximately serially uncorrelated, and then to adjust
the geometric average up by one-half the annualized 20-year variance as would be appropriate if returns are
lognormally distributed. Campbell and Viceira (2001, Figure 4.2) report an annualized 20-year standard
deviation of about 14% in long-term annual U.S. data, which would imply an adjustment of
0.142/2=0.010 or 1.0%.
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available since the early 1970’s, show that equity returns in most other industrialized countries
have been about as high as those in the U.S. The exceptions are the heavily commodity-
dependent markets of Australia and Canada, and the very small Italian market (Campbell 1999).
Jorion and Goetzmann (1999) argue that other countries’ returns were lower than U.S. returns in
the early 20th Century, but this conclusion appears to be sensitive to their omission of the dividend
component of return (Dimson, Marsh, and Staunton 2000). Thus the use of international data
does not change the basic message that the equity market has delivered high average returns in the
past.
2. Valuation ratios
An alternative approach is to use valuation ratios—ratios of stock prices to accounting
measures of value such as dividends or earnings—to forecast future returns. In a model with
constant valuation ratios and growth rates, the famous Gordon growth model says that the
dividend-price ratio
(1)
where R is the discount rate or expected equity return, and G is the growth rate of dividends
(equal to the growth rate of prices when the valuation ratio is constant). This formula can be
applied either to price per share and conventional dividends per share, or to the total value of the
firm and total cash paid out by the firm (including share repurchases). A less well-known but just
as useful formula says that in steady state, where earnings growth comes from reinvestment of
retained earnings which earn an accounting ROE equal to the discount rate R,
(2)
Over long periods of time summarized by Siegel (1998), these formulas give results consistent
with average realized returns. Over the period 1802-1997, for example, the average dividend-
price ratio was 5.4% while the geometric average growth rate of prices was 1.6%. These
numbers add to the geometric average return of 7.0%. Over the period 1871-1997 the average
dividend-price ratio was 4.9% while the geometric average growth rate of prices was 2.1%, again
adding to 7.0%. Similarly, Campbell and Shiller (2001) report that the average P/E ratio for S&P
500 shares over the period 1872-2000 was 14.5. The reciprocal of this is 6.9%, consistent with
average realized returns.
When valuation ratios and growth rates change over time, these formulas are no longer
exactly correct. Campbell and Shiller (1988) and Vuolteenaho (2000) derive dynamic versions of
the formulas that can be used in this context. Campbell and Shiller show, for example, that the
log dividend-price ratio is a discounted sum of expected future discount rates, less a discounted
sum of expected future dividend growth rates. In this note I will work with the simpler
deterministic formulas.
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II. Current Market Conditions
Current valuation ratios are wildly different from historical averages, reflecting the
unprecedented bull market of the last 20 years, and particularly the late 1990’s. The attached
figure, taken from Campbell and Shiller (2001), illustrates this point. (See p. 9) The bottom left
panel shows the dividend-price ratio D/P in January of each year from 1872-2000. The long-term
historical average is 4.7%, but D/P has fallen dramatically since 1982 to about 1.2% in January
2000 (and 1.4% today).
The dividend-price ratio may have fallen in part because of shifts in corporate financial policy.
An increased tendency for firms to repurchase shares rather than pay dividends increases the
growth rate of dividends per share, by shrinking the number of shares. Thus it increases G in the
Gordon growth formula and reduces conventionally measured D/P. One way to correct for this is
to add repurchases to conventional dividends. Recent estimates of this effect by Liang and Sharpe
(1999) suggest that it may be an upward adjustment of 75 to 100 basis points, and more in some
years. Of course, this is not nearly sufficient to explain the recent decline in D/P.
Alternatively, one can look at the price-earnings ratio. The top left panel of the figure shows
P/E over the same period. This has been high in recent years, but there are a number of earlier
peaks that are comparable. Close inspection of these peaks shows that they often occur in years
such as 1992, 1934, and 1922 when recessions caused temporary drops in (previous-year)
earnings. To smooth out this effect, Campbell and Shiller (2001), following Graham and Dodd
(1934), advocate averaging earnings over 10 years. The price-averaged earnings ratio is
illustrated in the top right panel of the figure. This peaked at 45 in January 2000; the previous
peak was 28 in 1929. The decline in the S&P 500 since January 2000 has only brought the ratio
down to the mid-30’s, still higher than any level seen before the late 1990’s.
The final panel in the figure, on the bottom right, shows the ratio of current to 10-year
average earnings. This ratio has been high in recent years, reflecting robust earnings growth
during the 1990’s, but it is not unprecedentedly high. The really unusual feature of the recent
stock market is the level of prices, not the growth of earnings.
III. Implications for Future Returns
The implications of current valuations for future returns depend on whether the market has
reached a new steady state, in which current valuations will persist, or whether these valuations
are the result of some transitory phenomenon.
If current valuations represent a new steady state, then they imply a substantial decline in the
equity returns that can be expected in the future. Using Campbell and Shiller’s (2001) data, the
unadjusted dividend-price ratio has declined by 3.3 percentage points from the historical average.
Even adjusting for share repurchases, the decline is at least 2.3 percentage points. Assuming
constant long-term growth of the economy, this would imply that the geometric average return on
equity is no longer 7%, but 3.7% or at most 4.7%. Looking at the price-averaged earnings ratio,
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