What Risk Premium Is "Normal"?
Robert D. Arnott and Peter L. Bernstein
The
goal
oftJiis article is an estimate of the objective forward-looking U.S.
equity risk premium relative to bonds through history—specifically, since
1802.
For correct
evaluation, such a complex topic
requires several careful
steps:
To
gauge the risk premium for stocks relative to bonds, we need an
expected
real
stock return and an expected
real
bond return.
To
gauge the
expected real bond return, we need both bond yields and an estimate of
expected inflation through history.
To
gauge the
expected real
stock return,
we
need both
stock dividend yields and
an
estimate of expected
real
dividend
growth. Accordingly, we go through each of
these
steps. We demonstrate
that the long-term forzoard-looking risk premium is
noivhere
near the
level
oftfie past; today, it may well be near
zero,
perhaps
even negative.
f
he investment management industry
I M thrives on the expedient of forecasting the
/ future by extrapolating the past. As a con-
^^ sequence, U.S. investors have grown
accustomed to the idea that stocks "normally" pro-
duce an 8 percent real return and a 5 percent (that
is,
500 basis point) risk premium over bonds, com-
pounded annually over many decades. Why?
Because long-term historical returns have been in
this range with impressive consistency. And
because investors see these same long-term histor-
ical numbers year after year, these expectations are
now embedded in the collective psyche of the
investment community.^
Both the return and the risk premium assump-
tions are unrealistic when viewed from current
market levels. Few have acknowledged that an
important part of the lofty real retums of the past
stemmed from rising valuation levels and from
high dividend yields, which have since dimin-
ished. As we will demonstrate, the long-term
forward-looking risk premium is nowhere near the
5 percent level of the past; indeed, today, it may
well be near zero, perhaps even negative. Credible
studies in and outside the United States are chal-
lenging the flawed conventional view. Well-
researched studies by Claus and Thomas (2001)
and Fama and French (2000) are just two (see also
Arnott and Ryan 2001). Similarly, the long-term
forward-looking real return from stocks
is
nowhere
near history's 8 percent. We argue that, barring
unprecedented economic growth or unprece-
Robert D. Arnott is managing partner at First
Quad-
rant, L.P., Pasadena, California. Peter L. Bernstein is
president of Peter L. Bernstein, Inc., New
York.
dented growth in earnings as a percentage of the
economy, real stock returns will probably be
roughly 2—4 percent, similar to bond retums. In
fact, even this low real retum figure assumes that
current near-record valuation levels are "fair" and
likely to remain this high in the years ahead.
"Reversion to the mean" would push future real
retums lower still.
Furthermore, if we examine the historical
record, neither the 8 percent real retum nor the 5
percent risk premium for stocks relative to govern-
ment bonds has ever been a realistic
expectation,
except from major market bottoms or at times of
crisis,
such as wartime. But this topic merits careful
exploration. After all, according to the Ibbotson
Associates data, equity investors earned 8 percent
real returns and stocks have outpaced bonds by
more than 5 percent over the past
75
years.
Intuition
suggests that investors should not require such
outsized returns
in
order to bear equity market risk.
Should investors have expected these returns in the
past, and why shouldn't they continue
to
do
so?
We
examine these questions expressed in a slightly
different way. First, can we derive an objective
estimate of what investors had good reasons to
expect in the past? Second, why should we expect
less in the future than we have earned in the past?
The answers
to
both questions lie in the differ-
ence between the
observed
excess retum and the
prospective
risk premium, two fundamentally dif-
ferent concepts that, unfortunately, carry the same
label—risk premium. If we distinguish between
past excess returns and future expected risk pre-
miums, the idea that future risk premiums should
be different from past excess retums is not at all
unreasonable.
©2002,
AIMR®
What Risk Premium Is "Normal"?
This complex topic requires several careful
steps if it is to be evaluated correctly. To gauge the
risk premium for stocks relative to bonds, we need
an expected real bond retum and an expected real
stock retum. To gauge the expected real bond
retum, we need both bond yields and an estimate
of expected inflation through history. To gauge the
expected real stock return, we need both stock div-
idend yields and an estimate of expected real divi-
dend growth. Accordingly, we go through each of
these steps, in reverse order, to form the building
blocks for the final goal—an estimate of the objec-
tive forward-looking equity risk premium relative
to bonds through history.
Has the Risk Premium Natural
Limits?
For equities to have a zero or negative risk premium
relative to bonds would be uiinatural because
stocks
are,
on average over time, more volatile than
bonds. Even if volatility were not an issue, stocks
are a secondary call on the resources of
a
company;
bondholders have the first call. Because the risk
premium is usually measured for corporate stocks
as compared with government debt obligations
(U.S.
T-bonds or T-bills), the comparison is even
more stark. Stocks should be priced to offer
a
supe-
rior retum relative to corporate
bonds,
which should
offer a premium yield (because of default risk and
tax differences) relative to T-bonds, which should
typically offer a premium yield (because of yield-
curve risk) relative to T-bills. After all, long bonds
have greater duration—hence, greater volatility of
price in response to yield changes—so
a
capital loss
is easier on a T-bond than on a T-bill.
In other words, the current circumstance, in
which stocks appear to have a near-zero (or nega-
tive) risk premium relative to government bonds,
is abnormal in the extreme. Even if we add
100
bps
to the risk premium
to
allow for the impact of stock
buybacks, today's risk premium relative to the
more relevant corporate bond alternatives is still
negligible or negative. This facet was demon-
strated in Arnott and Ryan and
is
explored further
in this article.
If zero is the natural minimum risk premium,
is there a natural maximum? Not really. In times of
financial distress, in which the collapse of a
nation's economy, hyperinflation, war, or revolu-
tion threatens the capital base, expecting a large
reward for exposing capital to risk is not unreason-
able.
Our analysis suggests that the
U.S.
equity risk
premium approached or exceeded 10 percent dur-
ing the Civil War, during the Great Depression,
and in the wake of World Wars
I
and II. Tliat said.
however, it is difficult to see how one might objec-
tively measure the forward-looking risk premium
in such conditions.
A
5
percent excess return on stocks over bonds
compounds so mightily over long spans that most
serious fiduciaries, if they believed stocks were
going to earn a 5 percent risk premium, would not
even consider including bonds in a portfolio with a
horizon of more than a few years: The probabilities
of stocks outperforming bonds would be too high to
resist. Hence, under so-called normal conditions—
encompassing booms and recessions, bull and bear
markets,
and "ordinary" economic stresses—a good
explanation is hard to find for why expected long-
term real retums should ever reach double digits or
why the expected long-term risk premium of stocks
over bonds should ever exceed about 5 percent.
These upper bounds for expected real returns or for
the risk premium, unlike the lower bound of zero,
are "soft"
limits;
in times of real crisis or distress, the
sky's the limit.
Expected versus "Hoped-For"
Returns
Throughout this article, we deal with
expected
retums and
expected
risk premivims. This concept is
rooted in objective data and defensible expectations
for portfolio returns, rather than in the retiuns that
an investor might
hope
to earn. The distinction is
subtle; both represent expectations, but one
is
objec-
tive and the other subjective. Even at times in the
past when valuation levels were high and when
stockholders would have had no objective reason to
expect any growth in real dividends over the long
run, hopes of better-than-market short-term profits
have always been the primary lure into the game.^
When we refer to expected retums or expected
risk premiums, we are referring to the estimated
future retums and risk premiums that an objective
evaluation—based on past rates of growth of the
economy, past and prospective rates of inflation,
current stock and bond yields, and so forth—might
have supported at the time. We explicitly do not
include any extrapolation of past returns per se,
because past retums are driven largely by changes
in valuation levels (e.g., changes in yields), which
in an efficient market, investors should not expect
to continue into the indefinite future. By the same
token, we explicitly do not presume any reversion
to the mean, iji which high yields or low yields are
presumed to revert toward historical norms. We
presume that the current yield is "fair" and is an
unbiased estimator of future yields, both for stocks
and bonds.
March/April 2002
65
Financial Analysts Journal
Few investors subjectively expect retums as
low as the objective returns produced by this sort
of analysis. In a recent study by Welch (2000), 236
financial economists projected, on average, a 7.2
percent risk premium for stocks relative to T-bills
over the next 30 years. If we assume that T-bUls
offer the same 0.7 percent real return in the future
that they have offered over the past 75 years, then
stocks must be expected to offer a compounded
geometric average real retum of about 6.6 percent.^
Given a dividend yield of roughly 1.5 percent in
1998-1999, when the survey was being carried out,
the 236 economists in the survey were clearly pre-
suming that dividend and eamings growth will be
at least 5 percent a year above inflation, a rate of
real growth three to five times the long-term histor-
ical norm and substantially faster than plausible
long-term economic growth.
Indeed, even if ir vestors take seriously the real
return estimates and risk premiums produced by
the sort of objective analysis we propose, many of
them will continue
to
believe that their own invest-
ments cannot fail to do better. Suppose they agree
with us that stocks and bonds are priced to deliver
2—1 percent real returns before taxes. Do they
believe that their investments will produce such
uninspired pretax real returns? Doubtful. If these
kinds of projections were taken seriously, markets
would be at far different levels from where they
are.
Consequently, if these objective expectations
are correct, most investors will be wrong in their
(our?) subjective expectations.
What Were investors Expecting in
1926
Are we being reasonable to suggest that, after a
75-year span with 8 percent real stock returns and
a 5 percent excess retum over bonds (the Ibbotson
findings), an
8
percent real retum or
a 5
percent risk
premium is abnormal? Absolutely. The relevant
question is whether the investors of 1926 would
have had reason to expect these extraordinary
retums. In fact, they would not. What they got was
different from what they should have expected,
which is a normal result in a world of uncertainty.
At the start of
1926,
the beginning of the returns
covered in the Ibbotson data, investors had no rea-
son to expect the 8 percent real retums that have
been earned over the past 75 years nor that these
retums would provide a 5 percent excess return
over bonds. As we will describe, these outcomes
were the consequence of a series of historical acci-
dents that uniformly helped stocks and/or helped
the risk premium.
Consider what investors might objectively have
expected at the start of 1926 from their long-term
investments in stocks and bonds, In January that
year, government bonds were yielding 3.7 percent.
The United States was on a gold standard, govern-
ment was small relative to the economy as a whole,
and the price level of consumer goods, although
volatile, had been trendless throughout most of
U.S.
history up to that moment; thus, inflation expecta-
tions were
nil.
It was a time of relative stability and
prosperity, so investors would have had no reason
to
expect to receive less than this 3.7 percent govem-
ment bond yield. Accordingly, the
real
retum that
investors would have expected on their government
bonds was 3.7 percent, plain and simple.
Meanwhile, the dividend yield on stocks was
5.1 percent.
We
can take that number as the starting
point to apply the sound theoretical notion that the
real retum on stocks is equal to
• the dividend yield
• plus (or minus) any change in the real dividend
(now viewed as participation in economic
growth)
• plus (or minus) any change in valuation levels,
as measured by P/F multiples or dividend
yields.
What did the investors expect of stocks in early
1926?
The time was the tail end of the era of "robber
baron" capitalism. As Chancellor (1999) observed,
investors were accustomed to the fact that company
managers would often dilute shareholders' retums
if an enterprise was successful but that the share-
holder was a full partner in any business decline.
More important was the fact that the long-run his-
tory of the market was trendless. Thoughts of long-
term economic growth, or long-run capital appreci-
ation in equity holdings, were simply not part of the
tool kit for retum calculations in those days.
Investors generally did not yet consider stocks
to be "growth" investments, although a few people
were beginning to acknowledge the fuU import of
Smith's extraordinary study
Common Stocks as
Long-
Term Investments, which had appeared in 1924.
Smith demonstrated how stocks had outperformed
bonds over the 1901-22 period. His work became
the bible of the bulls as the bubble of the late 1920s
progressed. Prior to 1926, however, investors con-
tinued to follow
J.P.
Morgan's dictum that the mar-
ket would fluctuate, a traditional view hallowed by
more than
100
years of stock market
history.
In other
words, investors had no trend in mind. The effort
was to buy low and to sell high, period.
Assuming that markets were fairly priced in
early 1926, investors should have expected little or
no benefit from rising valuation levels. Accord-
ingly, the real long-term retum that stock investors
could reasonably have expected on average, or from
m
• ©2002, AIMR®
What Risk Premium
Is
"Normal"?
the market as
a
whole, was the
5.1
percent dividend
yield, give or take a little. Thus, stock investors
would have expected roughly a 1.4 percent risk
premium over
bonds,
not the
5
percent they actually
earned in the next 75 years. The market exceeded
objective expectations as a consequence of a series
of historical accidents:
• Historical accident
M:
Decoupling yields from
real
yields. The Great Depression (roughly 1929-
1939) introduced a revolutionary increase in
the role of government in peacetime economic
policy and, simultaneously, drove the United
States (and just about the rest of the world) off
the gold standard. As prosperity came back in
a big way after World War
II,
expected inflation
became a normal part of bond valuation. This
change created a one-time shock to bonds that
decoupled nominal yields from real yields and
drove nominal yields higher even as real yields
fell. Real yields at year-end 2001 were 3.4 per-
cent (the Treasury Inflation-Indexed Securities,
commonly called TIPS, yield ), but nominal
yields were 5.8 percent. This rise in nominal
yields (with real yields holding steady) has cost
bondholders 0.4 percent a year over 75 years.
That accident alone accounts for nearly one-
tenth of the 75-year excess retum for stocks
relative to bonds.
• Historical accident #2: Rising valuation multiples.
Between 1926 and 2001, stocks rose from a
valuation level of 18 times dividends to nearly
70 times dividends. This fourfold increase in
the value assigned to each dollar of dividends
contributed 180 bps to annual stock returns
over the past 75 years, even though the entire
increase occurred in the last 17 years of the
period (we last saw 5.1 percent yields in 1984).
This accident explains fully one-third of the
75-year excess retum.
• Historical accident #3: Survivor
bias.
Since
1926,
the United States has fought no wars on its own
soil, nor has it experienced revolution. Four of
the fifteen largest stock markets in the world in
1900 suffered a total loss of capital, a -100 per-
cent return, at some point in the past century.
The markets are China, Russia, Argentina, and
Egypt. Two others came close—Germany
(twice) and Japan. Note that war or revolution
can wipe out bonds as easily as stocks (which
makes the concept of "risk premium" less than
relevant).
U.S.
investors in early
1926
would
not
have considered this likelihood to be zero, nor
should today's true long-term investor.
• Historical accident #4; Regulatory reform. Stocks
have gone from passing relatively little eco-
nomic growth through to shareholders to
passing much of the economic growth through
to shareholders. This shift has led to 1.4 per-
cent a year growth in real dividend payments
and in real earnings since 1926. This acceler-
ated growth in real dividends and earnings,
which no one in 1926 could have anticipated,
explains roughly one-fourth of the 75-year
excess return.
In short, the equity investors of 1926 probably
expected to eam a real return little different from
their 5.1 percent yield and expected to earn little
more than the 140 bp yield differential over bonds.
Indeed, an objective investor might have expected
a notch iess because of the greater frequency with
which investors encountered dividend cuts in
those days.
What Expectations Were Realistic
in
the
Past?
To gauge what risk premium an investor might
have objectively expected in the longer run past, we
need to (1) estimate the real retum that investors
might reasonably have expected from stocks, (2)
estimate the real return that investors might reason-
ably have expected from bonds, and (3) take the
difference. From this exercise, we can gauge what
risk premium an investor might reasonably have
expected at any point in history, not simply an
isolated snapshot of early 1926. A brief review of
the sources of stock returns over the past tw^o cen-
turies should help lay
a
foundation for our work on
retum expectations and shatter a few widespread
misconceptions in the process. The sources of the
data are given in Appendix A.^^
Step
I:
How Well Does Economic Growth
Flow into Dividend Growth? Over the past
131 years, since reliable eamings data became
available in 1870, the average eamings yield has
been 7.6 percent and the average real return for
stocks has been 7.2 percent; this close match has
persuaded many observers to the view (which is
wholly consistent with finance theory) that the best
estimate for real retums is, quite simply, the earn-
ings yield. On careful examination, this hypothesis
tums out to be wrong. In the absence of changing
valuation levels, real retums are systematically
lower
than eamings yields.
Figure
1
shows stock market retums since 1802
in a fashion somewhat different from that shown in
most of the literature. The solid line in Figure 1
shows the familiar cumulative total return for U.S.
equities since 1802, in which each $100 invested
grows, with reinvestment of dividends, to alm^ost
$700 million in 200 years. To be sure, some of this
growth came from inflation; as the line "Real Stock
Retum" shows, $700 million will not buy what it
March/April 2002
67
Financial Atialysts Journal
Figure 1. Return from Inflation and Dividends: Growth of $100,1801-2001
U.S.
DoUar
1,000,000,000
1802
1820 1840 1860 1880 1900 1920 1940 1960 1980
2000
would have in 1802, when one could have pur-
chased the entire
U.S.
GNP for less than that sum.^^
By removing inflation, we show in the "Real Stock
Retum" line that the $100 investment grew to
"only"
$37
million. Thus, adjusted for inflation, our
fortune is much diminished but still impressive.
Few portfolios are constructed without some plans
for future spending, and the dividends that stocks
pay are often spent.
So,
the "Real Stock Price Index"
line shows the wealth accumulation from price
appreciation alone, net of inflation and dividends.
This bottom line (literally and figuratively) reveals
that stocks have risen just 20-fold from 1802 levels.
Put another way, if an investor had placed $100 in
stocks in 1802 and received and spent the average
dividend yield of
4.9
percent for the next 200 years,
his or her descendants would today have
a
portfolio
worth $2,099, net of inflation. So much for our $700
million portfolio!
Worse, the lion's share of the growth from $100
to $2,099 occurred in the massive bull market from
1982 to date. In the 180 years from 1802 to the start
of 1982, the real value of the $100 portfolio had
grown to a mere $400. If stocks were priced today
at the same dividend yields as they were in 1802
and 1982, a yield of 5.4 percent, the $100 portfolio
would be worth today, net of inflation and divi-
dends,
just
$550.
These data put the lie to the con-
ventional view that equities derive most of their
returns from capital appreciation, that income
is
far
less important, if not irrelevant.
Figure 2 allows
a
closer lookat the link between
equity price appreciation and economic growth. It
shows that the growth in share prices is much more
closely tied to ^e growth in real
per
capita
GDP (or
GNP) than to growth in real GDP per se. The solid
line shows that, compounding at about
4
percent in
the 1800s and 3 percent in the 1900s, the economy
itself delivered an impressive
1,000-fold
growth.
Figure 2. The Link between Stock Prices and Economic Growth, 1802-2001
U.S.
DoUar
100,000
10,000
1,000
100
10
Real GDP Growth
Real Per Capita GDP Growai
Real Stock Price Index
1802 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000
68
©2002,
AIMR®