CFA Institute
The Equity Premium: Stock and Bond Returns since 1802
Author(s): Jeremy J. Siegel
Source: Financial Analysts Journal, Vol. 48, No. 1 (Jan. – Feb., 1992), pp. 28-38+46
Published by: CFA Institute
Stable URL: http://www.jstor.org/stable/4479502
Accessed: 30/03/2010 21:52
Your use of the JSTOR archive indicates your acceptance of JSTOR’s Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR’s Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=cfa.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed
page of such transmission.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact support@jstor.org.
CFA Institute is collaborating with JSTOR to digitize, preserve and extend access to Financial Analysts
Journal.
http://www.jstor.org
r14
en C,
😀
LLU LL~
😀
z
z
😀
0
LI,
-J
z
u
z
z
L2
28
Jeremy J. Siegel
Over the period from 1802
through 1990, equity has
provided returns superior
to those on fixed income
investments, gold or commodities.
Most strikingly,
the real rate of return on
equity held remarkably
constant over this period,
while the real return on
fixed income assets declined
dramatically. Over
the subperiods 1802-70,
1871-1925 and 1926-90,
the real compound annual
returns on equity were 5. 7,
6.6 and 6.4 per cent, but
the real returns on shortterm
government bonds
dropped from 5.1 to 3.1
and, finally, 0.5 per cent.
The magnitude of the excess
return on equity, especially
during this century,
appears excessive relative to
the behavior of other macroeconomic
variables. In
the future, the real return
on fixed income assets may
be closer to the historical
norm of 3 to 4 per cent.
While stock returns will
probably continue to dominate
bond returns, they will
not do so by nearly as wide
a margin as they have over
the past 65 years.
Since 1926, the compound real
value-weighted return on all
stocks listed on the New York
The Equity Premium: Stock and Bond Returns Since
1802
Stock Exchange has averaged 6.4
per cent per year, while the real
return on Treasury bills has averaged
only 0.5 per cent.1 This
means that the purchasing power
of a given sum of money invested
(and reinvested) in stocks from
1926 to 1990 would have increased
over 50 times, while reinvestment
in bills would have
increased one’s real wealth by
about one-third. Using these historical
returns, it would take 139
years of investing in Treasury bills
to double one’s real wealth while
it would take only 11 years of
stock investment. Money managers
often use these figures persuasively
to convince investors
that, over long periods of time,
equity has no match as a wealth
builder.
The return on stocks in excess of
the return on short-term bonds is
called the equity premium. Because
stocks are generally riskier
than fixed income investments, it
is to be expected that the return
on stocks would exceed that on
bonds. However, in 1985 Rajnish
Mehra and Edward Prescott demonstrated
that stocks, despite
their risk, appear to offer investors
excessive returns, while
bonds offer puzzlingly low returns.2
The excessive return on
equity is termed the “equity premium
puzzle.” Investors would
have to be extraordinarily riskaverse,
given the documented
growth and variability of the
economy, to accept such low returns
on bonds while equity offered
such superior returns. Such
extreme risk-aversion appears to
be inconsistent with data that reveal
investor choice under uncertainty.
Many theories have been offered
to explain the equity premium
puzzle.3 The data that Mehra and
Prescott analyzed covered a sufficiently
long period of time and
were derived from well documented
sources. Thus no one
questioned the validity of their
return data.
I extended the time period analyzed
by Mehra and Prescott back
to 1802, while updating the returns
on stocks and bonds to
1990. My analysis demonstrates
that the returns from bonds during
most of the 19th century and
after 1980 were far higher than in
the period analyzed by Mehra and
Prescott. The equity premium is
not nearly as large when viewed
over this extended time span as it
is in the post-1926 period. These
data suggest that the excess return
of stocks over bonds may be
significantly smaller in the future
than it has been over the past 65
years.
Long-Term Asset
Returns
William Schwert has developed
historical stock price series dating
back to 1802; there are also some
fragmentary data on stock returns
dating to 1789.4 In order to analyze
asset returns since 1802, 1
divided the data into three subperiods.
The first period, running
from 1802 through 1870, contains
stocks of financial firms and, later,
railroads. The second period,
running from 1871 through 1925,
comprises the period studied by
the Cowles Foundation.5 The last
subperiod, from 1926 to the
present, coincides with the development
of the S&P 500 stock index
and contains the most comprehensive
data on stock prices
and other economic variables.6 I
use the Schwert data for the first
subperiod and a capitalizationweighted
index of all NYSE stocks
Glossary
*Equity Premium:
The expected return (dividends
plus capital gains) on
equity in excess of the return
on safe assets such as government
bonds.
*’ Total Return Index:
An index that measures the
increase in wealth generated
by assuming that all cash
flows and capital gains are
reinvested in the same asset
or class of assets.
* Capital Appreciation
Index:
An index that measures the
increase in wealth assuming
that just the capital gain, and
not any income generated, is
reinvested in the asset (or
class of assets).
*Geometric Return:
Compound return, or the nth
root of the n single-year returns.
*Synthetic Short-Term
Government Series:
A series of what short-term,
risk-free interest rates would
be, based on removing the
default premium on similar
risky assets. Computed in the
absence of actual government
interest rates.
for the second and third subperiods.
The early stock indexes were not
as comprehensive as those constructed
today. From 1802 to
1820, the stock index consisted of
an equally weighted portfolio of
stocks of several banks in Boston,
New York and Philadelphia. An
insurance company was added
later, and in 1834 the portfolio
became heavily weighted toward
railroad stocks. The Cowles index
consisted of all stocks listed on
the New York Stock Exchange
and recorded, for the first time,
dividend payments. The Cowles
index is spliced to modern indexes,
which calculate averages
for all classes of common stock.
Stock Returns
Figure A displays what one dollar
invested in various asset classes in
1802 would have accumulated to
by the end of 1990. These series
are referred to as total return
indexes, because they assume
that all cash flows, including interest
and dividends as well as
any capital gains, are continually
reinvested in the relevant asset.
Total return indexes differ from
standard stock market indexes
such as the S&P 500, which do not
include the reinvestment of cash
flows. These standard indexes are
called capital appreciation indexes.’
Figure A indicates that, in terms of
total return, stocks have dominated
all other asset classes since
1802. Over the entire period, equities
achieved a compound annual
nominal rate of return of 7.6
per cent per year; at this rate, the
nominal value of equity approximately
doubles every 9.5 years.
Figure A also demonstrates that
nominal stock returns have also
increased over time. The average
compound rate of return on
stocks was 5.8 per cent from 1802
through 1870, 7.2 per cent from
1871 through 1925 and 9.8 per
cent from 1926 through 1990.8
Table I gives the stock returns in
each subperiod.
The average nominal arithmetic
(or mean) return on stocks is 9.0
per cent per year over the entire
period. Although this can be interpreted
as the expected return
on stocks over a 12-month period,
it cannot be converted into a
compound annual rate of return
over periods longer than one
year. Because of the mathematical
properties of return calculations,
the compound rate of return to a
buy-and-hold strategy is measured
by the geometric, rather
than the arithmetic, return.9
The power of compound returns
is clearly evident in the stock
market. One dollar invested in
1802, with all dividends reinvested,
would have accumulated
to nearly $1 million by the end of
1990. Hypothetically, this means
that $3 million, invested and reinvested
over these past 188 years,
would have grown to the incredible
sum of $3 trillion-nearly
equal to the entire capitalization
of the U.S. stock market in 1990!
Figure A Total Nominal Return Indexes, Before Taxes, 1802 – 1990
10,000,000-
-Stocks $5,0
1,000,000 Short-Term Governments $955,000
Governments
-Gold
100,000 –CP
10,000 5,770
-2,680
2 1,000 –
……………
4-J 100-
o
E 15.8
10-
0.1- lI Sub Period I Sub Period Sub Period III
I IIII 111 I II11-
–
I I I I I I I
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Year
r4
D
z
m
LLJ
LLw
D
z
z
cc:
D
0
H- <1:
z
-J
4
z
z
29
Table I Stock Market Returns (standard deviations in parentheses)*
Nominal
Total Capital Real Capital Total Real
Nominal Total Real Appreciation Appreciation Average After-Tax
Return (%lo) Return (%/6) (%) (%) Dividend Tax Return (%/6)
Income Rate
Period A G A G A G A G (%/6) A (%lo) A A G
1802-1990 9.0 7.6 7.8 6.2 4.0 2.5 2.8 1.2 5.0 6.8 7.3 5.8
(17.8) (18.4) (17.6) (18.1) (1.0) (18.1)
1871-1990 10.3 8.6 8.3 6.5 5.3 3.6 3.3 1.6 5.0 10.8 7.6 5.9
(18.9) (19.3) (18.6) (19.0) (1.3) (18.9)
1802-1870 6.8 5.8 6.9 5.7 1.8 0.7 1.9 0.6 5.0 0.0 6.9 5.7
(15.4) (16.6) (15.4) (16.5) (0.0) (16.6)
1871-1925 8.4 7.2 7.9 6.6 3.1 1.9 2.7 1.3 5.2 0.7 7.9 6.6
(15.6) (16.6) (15.9) (16.9) (1.1) (16.6)
1926-1990 11.9 9.8 8.6 6.4 7.1 5.0 3.9 1.8 4.8 19.3 7.4 5.3
(21.1) (21.2) (20.4) (20.5) (1.4) (20.7)
1946-1990 12.0 11.1 7.4 6.2 7.4 6.5 3.0 1.9 4.6 24.4 6.0 4.9
(14.6) (15.6) (13.8) (14.8) (1.4) (14.8)
1966-1981 7.3 6.2 0.4 -0.7 3.1 2.1 -3.5 -4.6 4.2 26.4 -0.9 -1.8
(15.1) (14.3) (14.3) (13.8) (1.3) (13.5)
1966-1990 10.7 9.6 4.6 3.5 6.3 5.3 0.6 -0.6 4.3 25.9 3.3 2.2
(15.1) (15.2) (14.4) (14.6) (1.2) (14.3)
1982-1990 16.7 15.9 12.3 11.4 12.1 11.3 7.9 7.0 4.6 25.1 10.5 9.8
(13.1) (13.5) (12.7) (13.0) (1.0) (12.7)
* A = arithmetic mean; G = geometric mean.
cD
mr
u-
D
z
z
Z
30
Three million 1802 dollarsequivalent
to about $35 million in
today’s purchasing power-was a
large-but certainly not overwhelming-sum
of money to the
industrialists and landholders of
the early 19th century.10
Long-Term Bonds
In comparing past with future
bond returns, it is important to
choose securities whose risk
characteristics match closely.
There was an active market for
long-term U.S. government bonds
over most of the 19th century
except for the years 1835 through
1841, when prior budget surpluses
eliminated all federal government
debt outstanding. Sidney
Homer presented a series of
long-term government yields in
his classic work, A History of Interest
Rates. 11 Long-term government
bond issues were not numerous
during the 19th century;
maturities generally ranged from
three to 20 years, although some
bonds had no fixed duration.12
Figure B displays the interest
rates on long-term U.S. government
bonds, joining the Homer
series with the Ibbotson and Sinquefield
series, which begins in
1926.13
Despite the good data on federal
government bond yields, there
are persuasive reasons why highgrade
municipal bonds may be
more representative of highquality
bonds during much of the
19th and early 20th centuries.
Some of the municipal bonds isFigure
B Long-Term Interest Rates, 1800 – 1990
17
16
1 5 – U.S. High-Grade Bonds
14
……….. U.S Govt Bonds
13 Prime Corp Bonds
12
_ New England Musnis
10 –U.K. Consols
9
6
4
2
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Year
Table II Fixed Income Returns (standard deviations in parentheses)*
Long-Term Governments Short-Term Governments
Nominal Real Return Real After-Tax Real Return Real After-Tax
Coupon Return (%/6) (%/0) Return (?%/)
Rae (%) Return (%/)
Period (%/6) AA G A G A G A A G A G
1802-1990 4.7 4.8 4.7 3.7 3.4 3.2 2.9 4.3 3.1 2.9 2.8 2.6
(1.8) (5.4) (8.5) (8.4) (2.2) (6.2) (6.3)
1871-1990 4.5 4.7 4.5 2.8 2.5 2.1 1.8 3.7 1.8 1.7 1.4 1.2
(2.3) (6.5) (8.5) (8.3) (2.5) (4.7) (4.8)
1802-1870 4.9 5.1 5.0 5.2 4.9 5.1 4.8 5.2 5.4 5.1 5.4 5.1
(0.4) (2.7) (8.3) (8.2) (1.1) (7.6) (7.6)
1871-1925 4.0 4.5 4.4 4.0 3.8 3.9 3.7 3.8 3.3 3.1 3.2 3.1
(0.6) (2.9) (6.3) (6.3) (0.9) (4.8) (4.8)
1926-1990 5.0 4.9 4.6 1.8 1.4 0.6 0.2 3.7 0.6 0.5 -0.2 -0.3
(2.9) (8.4) (9.9) (9.4) (3.4) (4.3) (4.2)
1946-1990 5.9 4.9 4.5 0.5 -0.1 -1.1 -1.6 4.9 0.4 0.3 -0.8 -0.9
(3.1) (9.6) (10.5) (9.5) (3.3) (3.6) (3.3)
1966-1981 7.2 2.8 2.5 -3.9 -4.2 -5.6 -5.9 6.9 -0.1 -0.2 -1.9 -1.9
(1.8) (6.9) (7.9) (7.5) (2.9) (2.0) (2.0)
1966-1990 8.2 7.4 6.8 1.6 0.9 -0.7 -1.3 7.2 1.3 1.2 -0.5 -0.6
(2.2) (11.5) (12.5) (11.3) (2.5) (2.7) (2.5)
1982-1990 10.0 15.7 14.9 11.3 10.5 7.9 7.3 7.9 3.7 3.7 1.8 1.8
(13A3) (1.8) (13.2) (11.7) (1 6) (1.8) (1.4)
A = arithmetic mean; G =geometric mean.
sued during the early 19th century,
particularly those of the
Commonwealth of Massachusetts
and the City of Boston, were considered
of higher quality than
those of the federal government
and thus traded at lower yields.14
Risk of default on federal government
bonds increased during
both the War of 1812 and the Civil
War, hence yields on federal debt
rose above the yields on comparable
high-grade municipals. 15
Furthermore, these high-grade
municipals promised to pay interest
and principal only in gold,
thereby avoiding the “bimetal”
option, which gave the federal
government the right to redeem
the principal in either gold or
silver. This option may have biased
the yields on federal government
bonds upward.16
There is another reason why municipal
bond yields should sometimes
be substituted for federal
government bonds. From the
Civil War to 1920, the yields on
federal government bonds were
biased downward because banks
were permitted to issue circulating
bank notes against government
bonds held as reserves.
These rights, called “circulation
privileges,” motivated banks to
bid the prices of federal bonds up
above the prices of comparable
high-grade securities. The effect
of this bias is evident in Figure B.
In 1920, circulation privileges
were abolished, and the yield on
federal government bonds
jumped to the level of high-grade
municipals.17
To avoid the noted problems with
federal government bond yields, I
constructed a high-grade series
that uses the minimum yield on
Treasury bonds and high-grade
municipal bond yields from 1800
to 1865 and high-grade municipal
yields from 1865 to 1917. This is
the high-grade bond series depicted
in Figure A. Table II summarizes
the statistics.
Short-Term Bonds
Treasury bills, or short-term governments,
did not exist before
1920. Data on commercial paper
rates dating back to the 1830s are
available from Macaulay, but during
the 19th century commercial
paper was subject to a high and
variable risk premium, as Figure
C shows.18 These premiums often
developed during or just prior to
liquidity and financial crises
(marked by NBER-designated recessions).
There were also defaults
on this paper, but there is
insufficient information to correct
the yield series for these defaults.
Despite the obvious shortcomings
of the data, there are few
other short-term rates available
for the early 19th century, and
those that are available cover very
short periods.
To remedy this deficiency, I constructed
a synthetic short-term
government series that removes
the risk premium on commercial
paper.1 I did so by using
the relation between short and
long-term interest rates that prevailed
in Britain during the 19th
century, where the yields for long
and short-term bonds were more
representative of high-grade securities.
The construction of the
U.S. series assumes that the term
structure of high-grade interest
al
LL
Z
3
z
I-
z
..
31
Figure C Short-Term Interest Rates, 1800 – 1990
19
18 I
U.S . Risk-Free Rate
17 U.S. Com. Paper
16 U.K. Risk-Feee Rate
15-
14-
13-
12-
11-
a 9-
8-
7-
6-
5-
4i
0-U1 1 I 1 V I 1 1 I I
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Year
Figure D Price Indexes, 1800 – 1990
2.0-
1.9- -CPI
1.8 -_
….. WPI
GNP Deflator |..
1.7 – Consumption Deflator
16- 1945=1.0
15-
14-
7~ 13-
045 1.2
1.0
0.9
0.8
0.7
0.6
0.5-
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Year
am
D
z
z
D
0)
Q-
z
z
LLJ
z
32
rates was the same over concurrent
five-year periods in the U.S.
and in the U.K. Figure C shows
the short-term, risk-free series,
along with other available shortterm
rates.
It is clear from Figure A that the
total return indexes for fixed income
assets fall far short of that
for equity. With reinvestment of
coupons, an initial investment of
$1 in long-term bonds in 1802
would have yielded $5,770 in
1990; the same investment in riskfree,
short-term assets would
have yielded $2,680. Both these
returns are less than 1 per cent of
the sum accumulated in stocks
over the entire period.
Gold and Commodities
The gold series represents the
value of gold measured at the
market price. Until the mid-1960s,
this price was controlled by the
government; furthermore, U.S.
citizens were not allowed to hold
gold in monetary form between
1933 and 1970. Gold has nonetheless
been a key asset in world
monetary history and many investors
still consider it an important
hedge asset. One dollar of gold
bullion purchased in 1802 would
have been worth $15.80 by the
end of 1990.
The Consumer Price Index (CPI),
provided for comparison, represents
the value of a basket of
widely diversified goods that
could be stored costlessly, with
20 no depreciation. Consumer
prices increased about 11-fold
from 1802 to 1990, almost all of
the appreciation coming in the
last subperiod. Table III summarizes
the returns for gold and
commodities over the various
time periods.
Note that, by the end of the first
subperiod, 1802-70, the accumulations
in government bonds,
bills and stocks were virtually
identical. It is in the second and
especially the third subperiods
that stocks clearly dominated
fixed income assets. The return
on gold is clearly dominated by
bonds and stocks over the entire
period, but its appreciation did
surpass bonds (but not stocks)
over the past 65 years.
The Price Level and
Asset Returns
The behavior of price levels is
critical to any interpretation of
asset price movements over time.
Figure D displays various U.S.
price indexes. They all tell the
same story. Before World War IL,
the price level displayed no over-
Table III Economic Variables (standard deviations in parentheses)*
Prices Output S&P 500 (per share)
GNP Industrial Real
Deflator Real GNP Production Real Earnings Dividends
CPI (%/0) WPI (/0) (/) Gold (0/) (%0/) (/0) (0/)
Period A G A G A G A A G A G A G A G
1802-1990 1.5 1.3 1.4 1.0 2.3 – – – –
(6.1) (9.0) (14.8)
1871-1990 2.1 2.0 2.0 1.6 2.3 2.2 3.3 3.5 3.3 5.5 4.0 6.0 3.0 3.9 3.1
(5.0) (8.1) (5.3) (17.7) (5.6) (17.7) (25.7) (12.8)
1802-1870 0.4 0.1 0.4 -0.1 0.5 – – – –
(7.5) (10.3) (7.0)
1871-1925 0.7 0.6 0.7 0.2 0.9 0.7 -0.2 3.8 3.7 5.6 4.1 6.5 2.1 2.5 1.6
(5.1) (9.6) (5.5) (1.2) (4.9) (18.2) (31.9) (13.4)
1926-1990 3.2 3.1 3.1 2.9 3.5 3.4 6.2 3.2 3.0 5.4 4.0 5.6 3.7 5.2 4.4
(4.7) (6.4) (4.7) (23.6) (6.1) (17.4) (19.1) (12.1)
1946-1990 4.6 4.5 4.3 4.1 4.9 4.9 7.4 2.6 2.5 3.7 3.5 7.1 6.1 6.4 6.2
(3.9) (5.3) (4.0) (26.5) (4.3) (6.1) (14.9) (5.9)
1966-1981 7.0 7.0 6.8 6.7 6.6 6.6 22.0 2.8 2.8 3.4 3.3 7.6 7.0 5.8 5.7
(3.3) (4.2) (2.1) (39.2) (2.3) (5.1) (10.8) (4.5)
1966-1990 6.0 5.9 5.2 5.2 5.6 5.6 13.4 2.8 2.8 3.2 3.1 4.7 3.9 5.4 5.3
(3.1) (4.1) (2.2) (34.4) (2.3) (4.9) (12.7) (3.7)
1982-1990 4.0 4.0 2.5 2.5 3.9 3.9 -2.0 2.8 2.8 2.8 2.7 -0.4 -1.4 4.6 4.6
(1.2) (2.1) (1.0) (13.4) (2.4) (4.6) (14.3) (1.6)
* A = arithmetic mean; G = geometric mean.
Figure E Total Real Return Indexes, Before Taxes, 1802 – 1990
1,000,000-
– Stocks
Short-Term Governments
100,000 – | Governments _ _
____ $86,100
Gold
10,000 – Money _ – –
5)~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~5
1,000 52
Ht 10. 7: A -1.42
0.1
_ _ _ _ _ — – — >- 0 .0 9
0.01-
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Year
all trend. Since the war, the price
level has increased steadily.
Prices accelerated until the 1980s,
when the rate of inflation slowed.
The CPI in 1990 was nearly seven
times- its 1945 value. Over the
entire period, prices increased at
an average compound annual rate
of 1.3 per cent. Inflation averaged
0.1 per cent per year in the first
subperiod and 0.6 and 3.1 per
cent in the second and third subperiods.
Table III gives the statistics.
Over long periods of time, increases
in the price level are
strongly associated with increases
in the money supply. Throughout
the 19th and the early part of the
20th centuries, the money stock
was closely tied to the amount of
gold held by the Treasury and
central bank. The abandonment
of the gold standard, a process
that started in 1933 but gained
momentum in the post-World
War II period, reduced constraints
on the monetary authority’s
issuance of money. Chronic
inflation, which cannot occur under
a gold standard, became the
norm in the postwar period.
Figure E depicts total real return
indexes-total (nominal) return
indexes deflated by the price
level. Because of inflation, real
returns are much more modest
than nominal returns, especially
in the final subperiod. One dollar
invested in equities in 1802
would have accumulated to
$86,100 of constant purchasing
power, or real dollars, by 1990.
r14
crD
m
LU
LLD
z
-J
V)
z
-i
u
z
z
33
D
z
J
z
H-
-J
34
Figure F Total Real Return Indexes, After Taxes, 1802 – 1990
100,000- :
– Stocks $43,10(
Short-Term Governments
10,000 Governments
Gold
—Money /
1)~~~~~~~~~~~~~~~~~~1 tCa 100- – -:–LL 138
_0 10
0.1 ___ — 0.09
0.01- I I 1
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Year
Figure G Real Returns on Stocks and Bonds, 1806 – 1900
(30-year centered geometric moving average)
11-*
10-
9-
7-
6-
~ 5-
4 –
3-
2 – U..Sok
……..U.S. Long Bonds
1 – –[—U.S. hort onds J
-2-
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Year
Over the same period, one dollar
would have accumulated to $520
in real dollars if invested in longterm
governments, to $242 in real
dollars if invested in short-term
governments, and to only $1.42 if
invested in gold. A dollar of
hoarded currency, which pays no
return and whose value is eroded
by inflation, would have left an
investor with only 9 cents of purchasing
power in 1990.21
Taxes and Returns
Figure F displays the total return
index corrected for both federal
taxes and inflation. Average federal
income tax rates were taken
from studies by Robert Barro and
Chaipat Sahasakul and are reported
in Table 1.22 Because no
state or local taxes are considered,
tax rates before 1913, when
the federal income tax was instituted,
are set at zero. It is assumed
that dividends and interest
income are taxed at the average
marginal tax rate prevailing in the
year they were earned and that
capital gains are taxed (and losses
remitted) at one-fifth the prevailing
average marginal tax rate.23
The reduced tax rate on capital
gains arises primarily from the
deferment of taxes on gains accrued
but not realized and secondarily
from the lower tax rate
on realized gains.
Because a significant part of the
returns on equity has been
earned through capital gains,
while virtually all the returns on
bonds are in the form of taxable
interest, the returns on equity are
taxed at a lower effective rate than
those on fixed income securities.
In the third subperiod, 1926-90,
when taxes became significant,
the compound after-tax real return
on stocks is reduced by 1.1
percentage points, to 5.3 per cent;
the after-tax real return on shortterm
bonds is reduced by 0.8
percentage points, to -0.3 per
cent, while the return on longterm
government bonds falls 1.2
percentage points, to 0.2 per cent.
These results indicate that, on an
after-tax basis, investors rolling
over long-term bonds in the third
subperiod have barely kept up
with inflation, while those rolling
over short-term bonds have fallen
behind inflation. In fact, investors
in short-term bonds have earned
no after-tax real return from 1900
through 1990. Over the same period,
the after-tax real return index
for equities increased 90-
fold!
Trends in Returns
Figure G displays 30-year centered
moving averages of compound
real rates of return on
stocks, short and long-term government
bonds.24 One of the
Table IV Holding-Period Returns on Stocks, Long Bonds and Short
Bonds
Holding Stock Return > Stock Return > Long Bond >
Period Time Long Bond (%/6) Short Bond (%lo) Short Bond (%/6)
1802-1870 49.3 49.3 34.8
1871-1925 56.4 60.0 65.5
1 Year 1926-1990 67.7 69.2 86.2
1802-1990 57.7 59.3 61.4
1871-1990 62.5 64.7 76.5
1802-1870 52.9 48.5 44.1
1871-1925 58.2 61.8 56.4
2 Years 1926-1990 75.4 69.2 60.0
1802-1990 62.2 59.6 53.2
1871-1990 67.5 65.8 58.3
1802-1870 47.7 49.2 43.1
1871-1925 67.3 67.3 60.0
5 Years 1926-1990 78.5 80.0 61.5
1802-1990 64.3 65.4 54.6
1871-1990 73.3 74.2 60.8
1802-1870 46.7 43.3 46.7
1871-1925 83.6 83.6 60.0
10 Years 1926-1990 83.1 83.1 56.9
1802-1990 71.1 70.0 54.4
1871-1990 83.3 83.3 58.3
1802-1870 54.0 60.0 46.0
1871-1925 94.5 100.0 52.7
20 Years 1926-1990 95.4 98.5 64.6
1802-1990 82.9 87.6 55.3
1871-1990 95.0 99.2 59.2
1802-1870 55.0 52.5 40.0
1871-1925 100.0 100.0 60.0
30 Years 1926-1990 100.0 100.0 63.1
1802-1990 88.8 88.1 56.3
1871-1990 100.0 100.0 61.7
striking aspects of these data is
the relative constancy of the real
returns on equity across all the
subperiods. In the first subperiod,
the average geometric real
return on equity is 5.7 per cent; it
is 6.6 per cent in the second
subperiod and 6.4 per cent in the
third.25 These figures imply that,
although inflation increased substantially
in the third subperiod,
the nominal return on equity increased
by an almost identical
amount, so the return after inflation
remained essentially unchanged.
To the extent that stocks
are claims on real assets, they
might be expected to be good
hedges against inflation over the
long run.
As noted, the average real compound
rate of return on stocks
over the entire period has been
6.2 per cent. Over every 30-year
period from 1802 through 1990,
there have been only two when
the compound real annual rate of
return on stocks fell below 3.5
per cent, and those occurred in
the depths of the Depression, in
1931 and 1932. The periods of the
highest real returns on stock
ended in the early 1960s, when
the real compound annual return
exceeded 10 per cent.
The most striking pattern in Figure
G is the decline in the average
real return on fixed income
assets. In all 30-year periods beginning
with 1888, the year that
Mehra and Prescott began their
analysis, the real rate of return on
short-term government securities
has exceeded 2 per cent in only
three periods, ending in the Depression
years 1932-34. Since the
late 19th century, the real return
on bonds and bills over any 30-
year horizon has almost never
matched the average return of 4.5
to 5 per cent reached during the
first 70 years of our sample period.
Since 1878, the real return
on long-term bonds has never
reached 4 per cent over any 30-
year period; it exceeded 3 per
cent in only six years. One has to
go back to the 1831-61 period to
find any 30-year period where the
return on either long or shortterm
bonds exceeded that on equities.
The dominance of stocks
over fixed income securities, so
evident from Figures A, E and F, is
borne out by examining longterm
holding-period returns.
Table IV compares the compound
returns on stocks, long and shortterm
bonds. Over the entire period,
stocks outperformed shortterm
bonds 57.7 per cent of the
time on a year-to-year basis but
88.8 per cent of the time over
30-year horizons. Since 1871,
over horizons of 20 years or
longer, stocks have underperformed
short-term assets only
once and have outperformed
long-term bonds 95 per cent of
the time. Even with holding periods
as short as five years, stocks
have outperformed long and
short-term bonds by a four-to-one
margin since 1926 and a three-toone
margin since 1872. In contrast,
in 1802-71, stocks outperformed
short or long-term bonds
only about one-half the time over
any holding period.
Trends in the U.K.
In the 19th century, as London
emerged as the world’s financial
center, capital markets in Great
Britain were far more developed
than in the U.S. The British consol,
depicted in Figure B, is a
security that pays interest only; it
was first floated in 1729. The consol
has long been used by economists
to construct a continuous
and homogeneous long-term interest
rate series stretching over
250 years. British short-term in-
0)1
::
LL.
CK 4
z
3
z
w
0
V-
z
-j
u
z 4
z
–
35
Figure H Real Returns on U.K. Bonds, 1806 – 1900
(30-year moving average)
7-.. .
6-
5-
4 –
3-
2-Il
U.K Bonds
——U.K. Short Rate
0 – — —–
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Yea r
eN
z
z
H-
-J
z
-J
U
z
36
terest rates are represented, with
some exceptions, by the openmarket
rate at which high-quality
commercial paper is discounted.27
Figure H shows the 30-year
average real returns on U.K. short
and long-term bonds.
There is remarkable similarity in
the yield trends in the U.K. and
the U.S. The sharp decline in the
real yields on fixed income securities
in the U.S. was closely mirrored
in the U.K. Statistical tests
cannot reject the hypothesis that
the return process was identical
for both long and short-term real
interest rates in the U.S. and the
U.K. over the entire period.
Explanations of Trends
Although the data demonstrate
that returns on equities have
compensated investors for increased
inflation over the postwar
period, the returns on fixed income
securities have not. One
possible explanation is that lenders
did not anticipate inflation
during much of the period.
One could argue that a large part
of the increase in the price level
since World War II, especially
since 1970, was unanticipated,
hence bondholders did not have
a chance to adjust their required
returns. The progressive abandonment
of the gold standard
only slowly reduced investors’
convictions about the stability of
the long-run price level.
Unanticipated inflation certainly
lowered the real return on longterm
bonds. Buyers of such instruments
in the 1960s and early
1970s could scarcely have imagined
the double-digit inflation
that followed. But unanticipated
inflation is less important for
short-term bonds. The inflationary
process, although increasingly
subject to long-term uncertainty,
has been quite persistent
and inertial in the short run.
Short-term investors thus have a
better opportunity to capture the
inflation premium in the rate of
interest as they roll over their
investments. Short-term bonds
should therefore provide better
protection against unanticipated
inflation than longer-term bonds.
Of course, this protection is not
perfect; unanticipated inflation
may account for up to one percentage
point of the decline in
the real yield on short-term
bonds over the sample period.28
Other Factors
Other factors influence the real
rate of interest. Slower or more
variable economic growth, for example,
will generally lower the
real rate investors demand to
hold fixed income assets. Slower
growth may have depressed real
yields over short periods of time,
including the 1970s, when real
returns on short-term Treasury
bills were negative. Economic
growth in general, however, has
been as high in the 20th as in the
19th century.
There is no evidence that the
economy has become more volatile.
In fact, Table III suggests that
the real economy has actually
been more stable since World
War II, but real rates have been
very low in this period. Intuition
would suggest that the yield differential
between risky assets
such as stocks and less risky assets
such as bonds would be smaller,
the less risky the economy. If the
real return on stocks has remained
constant (and this is what
the data suggest), then the real
return on fixed income should
have risen. The decline in the real
yields on bonds suggests that
changing variability of the real
economy can not adequately explain
the decline in real returns.
Perhaps the low real interest rates
during much of this century can
be explained by a combination of
historical and institutional factors.
The 1929-32 stock market crash
and the Depression left a legacy
of fear; most investors clung to
government securities and insured
deposits, driving their
yields down. Redistribution policies
undertaken by the government
subsequent to the Depression
may also have lowered real
rates by shifting wealth to more
risk-averse segments of the population.
Furthermore, during
World War II and the early postwar
years, interest rates were kept
low by the Federal Reserve. Because
of its inflationary conse-
Figure I Equity Risk Premium, 1806 – 1900
(30-year centered geometric moving average)
12-
– -fi _ Stocks Minus U.S. Short Rate
8 i| L _ Stocks Minus U.S. Long Rate
10-
9-
7-
1-4
3
-1-
-2-
1800 10 20 30 40 50 60 70 80 90 1900 10 20 30 40 50 60 70 80 90
Year
quences, this policy was abandoned
in 1951, but interest rate
controls, particularly on deposits,
lasted much longer.
Finally, one cannot ignore the
development of the capital markets,
which transformed a highly
segmented market for short-term
instruments in the 19th century
into one of the world’s most liquid
markets in this century.
The Equity Premium
The decline in the real return on
fixed income investments has
meant that the advantage of holding
equities, which have experienced
a remarkably steady real
return, has increased over time.
The equity premium, plotted in
Figure I, has trended up over the
last 200 years and was particularly
high in the middle of this century.
The premium, computed from
real geometric returns, averaged
0.6 per cent in the first subperiod,
3.5 per cent in the second, and 5.9
per cent in the third.
The primary source of this equity
premium has been the fall in the
real return on bonds, not the rise
in the return on equity. Nonetheless,
it is not unreasonable to
believe that the low real rates on
bonds may, on occasion, have fueled
higher equity returns, because
the costs of obtaining leverage
were so low. The highest
30-year average equity return occurred
in 1931-61, a period that
also experienced very low real
returns on bonds.
One might take an even broader
view of the superior returns on
equity. Certainly investors in 1802
(or even 1872) did not universally
expect the United States to become
the greatest economic
power in the next century. This
was not the case in many other
countries. What if one had owned
stock in Japanese or German
firms before World War II? Or
consider Argentina, which, at the
turn of the century, was one of
the great economic powers. In
some sense, the returns on U.S.
stocks might not be representative
of the broader international
context.29
Conclusions
The high real interest rates in the
19th century may have reflected
the possibility that the U.S. would
default on its bonds or abandon
the gold standard. Since the inflation
shocks of the 1970s, fear of
outright default has been replaced
by an inflationary premium
in nominal interest rates.
Future inflation may be caused by
growing U.S. government deficits
or by inflationary policies pursued
by the Federal Reserve in
response to political pressures or
economic crises.
The last 10 years represent only
about 5 per cent of the total time
examined in this study, but the
period since 1980 contains the
highest real long-term bond returns
during any consecutive 10-
year period since 1884 and the
highest real short-term bond returns
since the 19th century (excepting
the sharp deflationary periods
of the Depression). It is not
unreasonable to assume that the
current higher real rates will turn
out to be more characteristic of
future returns than the unusually
low real rates of the earlier part of
this century. If they do, then the
advantage of holding equities
over bonds will shrink from the
levels reached over the past several
generations. The holders of
fixed income investments should
enjoy enhanced real returns in
the future. Equities, however, still
appear to be the best route to
long-term wealth accumulation.30
Footnotes
1. The average compound real return
on the S&P 500 has been 6 7 per
cent over the same period Very
small stocks (bottom quartile of
capitalization) have performed better,
averaging 8.2 per cent compound
real return since 1926
2. R. Mehra and E Prescott, “The Equity
Premium: A Puzzle,” Journal of
Monetary Economics 15 (1985), pp.
145-61. The time period covered by
Mehra and Prescott was 1889-
1978. The returns on stocks and
bonds were very similar to the returns
since 1926
3. Some rely on non-standard preference
functions; see, for example,
G. M Constantinides, “Habit Formation:
A Resolution of the Equity
Premium Puzzle,” Journal of Political
Economy 98:3 (1990), pp. 519-
43; A. Abel, “Asset Prices under
r4
L)
4
D
z
co
4
LU
z
3
z 4
0
z
37
0.)
uJ
()
z
z
:
m
F-
Z)
z
J
z
‘:1
z
38
Habit Formation and Catching up
with the Joneses,” American Economic
Review 2:80 (1990), pp. 38-
43; S Benninga and A. Protopapadakis,
“Time Preference and the
‘Equity Premium Puzzle’,” Journal
of Monetary Economics, January
1990; and P. Weil, “The Equity Premium
Puzzle and the Risk-free Rate
Puzzle,'” Journal of Monetary Economics,
November 1989. Others rely
on individual stocks and segmented
asset holdings; see N. G. Mankiw,
“The Equity Premium and the Concentration
of Aggregate Shocks,”
Journal of Financial Economics 17
(1986), pp. 211-19 and N G.
Mankiw and S. P. Zeldes, “The Consumption
of Stockholders and NonStockholders,”
Journal of Financial
Economics 29 (1991), pp. 97-112.
See A. Abel, “The Equity Premium
Puzzle,” Federal Reserve Bank of
Philadelphia Business Review, September-October
1991, for a summary.
4 G. William Schwert, “Indexes of
United States Stock Prices from
1802 to 1987,” Journal of Business
63:3 (1990), pp. 399-426 R. Ibbotson
and G. Brinson (Investment
Markets: Gaining the Performance
Advantage (New York: McGraw Hill,
1987), p. 73) report that the Foundation
for the Study of Cycles, in
Pittsburgh, has published data from
an internal stock index entitled
“Historical Record: Stock Prices
1 789-Present, ” Data Bulletin
1975-1. However, attempts to obtain
documentation for this series
have not been successful.
5. A. Cowles, Common Stock Indexes,
1871-1937 (Bloomington, IN: Principia
Press, 1938).
6. In the 1970s and 1980s, Roger Ibbotson
and Rex Sinquefield analyzed
data on inflation, stock and
bond returns since 1926 (see
Stocks, Bonds, Bills, and Inflation,
1991 Yearbook (Chicago: Ibbotson
Associates, 1991)). Several authors
(see for example J W Wilson and
C P. Jones, “A Comparison of Annual
Common Stock Returns:
1871-1925 with 1926-85,” Journal
of Business, April 1987, and “Stock,
Bonds, Paper, and Inflation, 1870-
1985,” Journal of Portfolio Management,
Fall 1987) have extended
much of the data back to 1872.
7. Standard stock indexes do, however,
reflect increases in the value
of shares resulting from reinvestment
of retained earnings and
changes in the capitalization of
expected earnings.
8. The data from the Foundation for
the Study of Cycles (found in Ibbotson
and Brinson, Ivestment Markets,
op. cit) show a compound
return of 7.95 per cent from 1802
through 1870 and 7.92 per cent
from 1789 through 1870.
9. The geometric, or compound, return
is the nth root of the one-year
returns; it is always less than the
average or mean arithmetic return,
except when all yearly returns are
equal. The geometric return can be
approximated by the arithmetic
mean minus one-half the variance
of the individual yearly returns.
10. S. Blodget, Jr. (A Statistical Manual
for the United States of America,
1806 ed, p. 68) estimated that
wealth in the US. was $2.45 billion
in 1802. Total wealth today is estimated
at nearly $15 trillion, of
which about $4 trillion is in the
stock market.
11. S. Homer, A History of Interest
Rates (New Brunswick, NJ Rutgers
University Press, 1963).
12. The first federal government debt
was the Hamilton refunding 6s of
1790, “redeemable at the pleasure
of the government at 100 in an
amount not exceeding 2% a year.”
13. Ibbotson and Sinquefield, Stocks,
Bonds, Bills, op. cit.
14. See Homer (A History, op. cit., pp.
296 and 301) andJ G. Martin
(Boston Stock Market, 1871) for a
description of these municipals. The
lower yield for municipals was not
due to any tax advantage, because
tax considerations did not emerge
until the early 20th century.
15. The Greenback period, when the
government issued notes not redeemable
in specie, provides a fascinating
episode in monetary theory.
For further discussion, see R. Roll,
“Interest Rates and Price Expectations
During the Civil War,” Journal
of Economic History, June 1972.
16 For a discussion of the issues involved
in the bimetal standard and
the potential distortion in yields see
P. M Garber, “Nominal Contracts
in a Bimetallic Standard,” American
Economic Review, December
1986.
17. The magnitude of this distortion
can be seen by examining the yields
in 1917-20 on government bonds
issued with and without circulation
privileges (see Homer, A History, op.
cit., Table 46). The yield differential
between bonds with and without
circulation privileges ranged from
50 to 100 basis points.
18. F R. Macaulay (The Movements of
Interest Rates, Bond Yields, and
Stock Prices in the United States
since 1856 (New York: National
Bureau of Economic Research,
1938)) reported rates for choice 60
to 90-day commercial paper after
1856, while data from 1831
through 1856 were collected from
E B. Bigelow (The Tariff Question…,
(Boston, 1862)), which covers
“Street rates on First class paper
in Boston and New York, at the
beginning, middle, and end of the
month. ” The paper floated in Boston
is said to be of three to six
months in duration. See Macaulay,
p. A341, for a more detailed discussion
of these sources.
19. For details of the construction of
U.S. short-term rate series, see j j
Siegel, “The Real Rates of Interest
from 1800-1900: A Study of the
US. and UK,” Journal of Monetary
Economics, forthcoming.
20. The CPI includes services that cannot
be stored. Since World War II,
commodity prices have risen slower
and service prices faster than the
CPI. When futures markets exist,
investors can buy futures, putting
up margin in interest-bearing Treasury
bills. This may result in returns
higher than the CPI.
21. An investor would actually have
done far better hoarding paper
money than gold bullion. The first
US. currency, a one dollar US.
note issued in 1862, now catalogues
for $1000 in uncirculated
condition, while earlier colonial
paper goes for even more. Of
course, gold coins have also increased
in value far more than bullion.
22. R. J Barro and C Sahasakul, “Measuring
the Average Marginal Tax
Rate from the Individual Income
Tax,” Journal of Business 56
(1982), pp. 419-52 and “Average
Marginal Tax Rates from Social
Security and the Individual Income
Tax,” Journal of Business 59
(1986), pp. 555-6.
23. This adjustment is consistent with
research done by A. Protopapadakis,
“Some Indirect Evidence
on Effective Capital Gains Tax
Rates, ” Journal of Business 56
(1982), pp. 12 7-38.
24. The averaging period is progressively
shortened to 15 years at the
end points of these series.
25. If the stock data from the Foundation
for the Study of Cycles (see
footnote 4) are considered, the real
compound annual return in equity
from 1802 to 1870 is 6.8 per cent.
26 In the short run, stocks have proved
poor hedges against inflation. This
is particularly true if inflation is
induced by supply shocks, which
Footnotes concluded on page 46.
12. The more sophisticated method that
has been developed on Wall Street
to measure option cost can also be
applied to the holding-period return.
A project is now under way
at the Wharton School to develop
this methodology.
13. H. P. Wallace (“The Total Return
Calculation for Mortgage PassThroughs,”
in F j Fabozzi, ed., The
Handbook of Mortgage-Backed Securities
(Chicago: Probus, 1985))
refers to the four components of the
wealth increase shown in Equation
(3) as the market value return,
principal payment return, interest
return and reinvestment return,
respectively. The first two components,
however, defy any analyticallv
useful interpretation. The
market value return component
combines the change in price and
the change in balance, whereas we
want to know the impact of the
price change alone. Furthermore,
showing the return of principal as
a component of return is misleading,
because most of the principal
repaid during any period was in
fact part of the investor’s wealth at
the beginning. The only part that
was not is the recovery of the discount-the
difference between the
market value of the security and its
face value at the beginning of the
period. After this article was drafted,
Andrew Carron provided me with
some unpublished tabulations that
indicate that the First Boston Corporation
breaks down holding-period
yields in a way very similar to
that developed here.
14. The best way to do this is by multiplying
the total holding-period return
by the ratio of the dollar value
of the components to the total dollar
increase in wealth. This is no
more than an approximation, however.
The annual equivalent holding-period
return is not the sum of
the annual equivalents of the components
because the price change
component is realized only at the
end of the period, while the other
components are received during the
period.
15. 1 thank Andrew S. Carron, Allan
Redstone and Kenneth R. Scott for
their helpful suggestions.
Siegel footnotes concludedfrom page 38.
affect the productivity of capital. See
E F Fama, “Stock Returns, Real
Activity, Inflation and Money,” The
American Economic Review, September
1981.
27 These series can be found in Homer
(A History, op. cit., Table 23). He
describes the paper as of “nonuniform
maturity of afew months”
before 1855 and thereafter “three
month bills.” These series are based
on data compiled by the NBER
from British Parliamentary papers
andfrom various editions of The
Economist (1858-1900). Details
are contained in Siegel, “The Real
Rate of Interest,” op. cit.
28. This has been suggested to me by
some preliminary work done by
Charles Calomaris.
29. Of course, even on a worldwide
basis, who might have expected the
triumph of capitalism and marketoriented
economies 100 or even 50
years ago? We may be living in the
golden age of capitalism, the fortunes
of which may decline in the
next 100 years (or sooner)!
30. I thank Peter Scherer and Ashish
Shah for their research assistance.
46
