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What Risk Premium is 'Normal'?

AbstractWe are in an industry that thrives on the expedient of forecasting the future by extrapolating the past. As a consequence, investors have grown accustomed to the idea that stocks "normally" produce an 8% real return and a 5% risk premium over bonds, compounded annually over many decades. Why? Because long-term historical returns have been in this range, with impressive consistency. Because investors see these same long-term historical numbers, year after year, these expectations are now embedded into the collective psyche of the investment community. Both figures are unrealistic from current market levels. Few have acknowledged that an important part of the lofty real returns of the past has stemmed from rising valuation levels and from high dividend yields which have since diminished. As this article will demonstrate, the long-term forward-looking risk premium is nowhere near the 5% of the past; indeed, it may well be near-zero today, perhaps even negative. Credible studies, in the US and overseas, are now challenging this flawed conventional view, in well-researched studies by Claus and Thomas [2001] and Fama and French [2000, Working Paper], to name just two. Similarly, the long-term forward-looking real return from stocks is nowhere near history's 8%. Our argument will show that, barring unprecedented economic growth or unprecedented growth in earnings as a percentage of the economy, real stock returns will probably be roughly 2-4%, similar to bonds. Indeed, even this low real return 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 returns lower still. Furthermore, if we examine the historical record, neither the 8% real return nor the 5% risk premium for stocks relative to government bonds has ever been a realistic expectation (except from major market bottoms or at times of crisis, such as wartime). Should investors require an 8% real return, or should a 5% risk premium be necessary to induce an investor to bear stock market risk? These returns and risk premiums are so grand that investors should perhaps have bid them away a long time ago - indeed, they may have done so in the immense bull market of 1982-1999. Intuition suggests that investors should not require such outsize returns, and the historical evidence supports this view. This is a topic meriting careful exploration. After all, according to the Ibbotson data, investors earned 8% real returns over the past 75 years, and stocks have outpaced bonds by nearly 5% over the past 75 years. So, why shouldn't investors have expected these returns in the past and why shouldn't they continue to do so? Expressed in a slightly different way, we examine two questions. First, can we derive an objective estimate of what investors should have had good reasons to have expected in the past? And, why should we expect less in the future than we've earned in the past? The answers to both questions lie in the difference between the observed excess return and the prospective risk premium, two fundamentally different concepts that unfortunately carry the same label, "risk premium." If we distinguish between past excess returns and future expected risk premiums, it is not at all unreasonable that the future risk premiums should be different from past excess returns. This is a complex topic, requiring several careful steps to evaluate correctly. 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, in reverse order, to form the building blocks for the final goal: an estimate of the objective, forward-looking equity risk premium, relative to bonds, through history.

Topics: Equity premium puzzle (64%), Volatility risk premium (62%), Risk premium (62%), Liquidity premium (61%), Stock market (55%)

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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 historyspecifically, 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®

Citations
More filters

Journal Article
Abstract: Stocks for the Long Run Jeremy J. Siegel McGraw Hill, 1998 Jeremy Siegel has written a book that could have a great effect on the reader's wealth while challenging conventional academic views. It is written at the popular level but references the underlying academic articles (i.e. it is footnoted). Siegel is a finance professor at the University of Pennsylvania's Wharton School, so he is well qualified to draw on the academic literature. The basic message of the book is that stocks have been a wonderful long run investment, and can be expected to continue to be so. The emphasis is on the long run, because there is no doubt that stocks can be exceedingly risky in the short run. As an illustration of stocks' short-run risk, consider October 19, 1987, when the stock market dropped by 22.6% in one day (see Miller 1999 for a review of a book focusing on this episode). Because of the short-run riskiness of stocks, one who is saving for an event in the near future (such as the next vacation), runs a considerable risk of losing money. However, most saving is done not for such short-run purposes but for long-run purposes such as retirement, or to leave money to descendants. Siegel makes a convincing case that stocks are much better for such long-run purposes than either bonds or money market instruments. Bank deposits usually earn even less than money market instruments, and hence are also dominated by stocks. The textbooks I use in teaching finance present evidence that stocks have, on average, outperformed bonds since 1926. Siegel carries this evidence back to 1802, presenting data on the returns from stocks and bonds from 1802 to 1997. Over this long period stocks have had an average return of 8.4%, composed of price increases averaging 3.0%, and dividends averaging 5.4%. In contrast, long-term US government bonds have averaged 4.7%, and short-term US governments, 4.3%. This superiority of stocks held true for major subdivisions of the period studied also. Economists talk about the equity risk premium, the differential between stocks and bonds, which is usually interpreted as the reward to bearing the risks of equity. This of course varies tremendously year to year. Siegel plots a thirty-year running average of the equity risk premium. It is striking that it is virtually always well above 0% (the exceptions appear to be around 1841 and 1861, which are well over a century ago). Thus, for someone investing for the long run, it appears stocks virtually always exceed bonds in return. The riskiness of having stocks underperform bonds turns out to depend very much on the holding period. A fascinating graph (showing data from 1802 to 1997) shows the maximum and minimum real (i.e., inflation adjusted) annualized returns for various holding periods (p. 27). For short holding periods, there is the expected result that one can lose more money on stocks than on either bonds or T-bills, frighteningly more. The worst one-year return on stocks is -30.6% (the best is 66.6%). Incidentally, bonds prove to have appreciable risk over short periods also, with the worse bond performance being -21.9%, and the worst Treasury bill performance -15.6%. The bond and Treasury bill losses occur when high inflation lowers their real purchasing power. Bonds have this risk. In addition, they can experience large losses when interest rates rise unexpectedly, reducing their risk. That stocks are riskier than bonds, and bonds riskier than treasury bills (and bank deposits and other money market instruments) is standard textbook material. It is usually explained by investors disliking risk and being willing to incur higher risk only if rewarded with greater returns. Thus, investors should be willing to hold stocks only if promised much higher returns than bonds. However, most investors (especially those with large sums of money) have longer horizons than one year. However, the equity risk premium appears to shrink with holding periods. …

350 citations



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Journal ArticleDOI
TL;DR: A theoretical expression is derived that links forward-looking risk premium to investors' risk aversion and forward- looking volatility, skewness, and kurtosis of the corresponding cumulative return, and the model adopted is the generalized autoregressive conditional heteroskedasticity model for the physical return process.
Abstract: A method for computing forward-looking market risk premium is developed in this paper. We first derive a theoretical expression that links forward-looking risk premium to investors' risk aversion and cumulative return's forward-looking volatility, skewness and kurtosis. In addition, investor's risk aversion is theoretically linked to volatility spread defined as the gap between the risk-neutral volatility deduced from option data and the physical return volatility exhibited by return data. The volatility spread formula serves as the basis for using the GMM method to estimate investor's risk aversion. We adopt the GARCH model for the physical return process, and estimate the model using the S&P500 daily index returns and then deduce the corresponding cumulative return's forward-looking variance, skewness and kurtosis. The forward-looking risk premiums are estimated monthly over the sample period of 2001-2010 and found to be all positive. The forward-looking risk premium was higher during volatile market periods (such as September 2001 and October 2008) and lower when the market was calm. Furthermore, two asset pricing tests are conducted. First, change in forward-looking risk premiums is negatively related to the S&P500 holding period return, reflecting that an increase in discount rate reduces current stock price. Second, market illiquidity positively affects forward-looking risk premium, indicating that forward-looking risk premium contains an illiquidity risk premium component.

34 citations


Journal ArticleDOI
Abstract: Many market observers point to the very high fraction of earnings retained (or low dividend payout ratio) among companies today as a sign that future earnings growth will be well above historical norms. This view is sometimes interpreted as an extension of the work of Miller and Modigliani. They proved that, given certain assumptions about market efficiency, dividend policy should not matter to the value of a firm. Extending this concept intertemporally, and to the market as a whole, as many do, whenever market-wide dividend payout ratios are low, higher reinvestment of earnings should lead to faster future aggregate growth. However, in the real world, many complications exist that could confound the expected inverse relationship between current payouts and future earnings growth. For instance, dividends might signals managers' private information about future earnings prospects, with low payout ratios indicating fear that the current earnings may not be sustainable. Alternatively, earnings might be retained for the purpose of "empire-building," which itself can negatively impact future earnings growth. We test whether dividend policy, as we observe in the payout ratio of the market portfolio, forecasts future aggregate earnings growth. This is, in a sense, one test of whether dividend policy "matters." The historical evidence strongly suggests that expected future earnings growth is fastest when current payout ratios are high and slowest when payout ratios are low. This relationship is not subsumed by other factors such as simple mean reversion in earnings. Our evidence contradicts the views of many who believe that substantial reinvestment of retained earnings will fuel faster future earnings growth. Rather, it is fully consistent with anecdotal tales about managers signaling their earnings expectations through dividends, or engaging in inefficient empire building, at times; either of these phenomena will conform with a positive link between payout ratios and subsequent earnings growth. Our findings offer a challenge to optimistic market observers who see recent low dividend payouts as a sign of high future earnings growth to come. These observers may prove to be correct, but history provides scant support for their thesis. This challenge is potentially all the more serious, as recent stock prices, relative to earnings, dividends and book values, rely heavily upon this expectation of superior future real earnings growth.

33 citations


References
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Journal ArticleDOI
Abstract: One of the problems which has plagued thouse attempting to predict the behavior of capital marcets is the absence of a body of positive of microeconomic theory dealing with conditions of risk/ Althuogh many usefull insights can be obtaine from the traditional model of investment under conditions of certainty, the pervasive influense of risk in finansial transactions has forced those working in this area to adobt models of price behavior which are little more than assertions. A typical classroom explanation of the determinationof capital asset prices, for example, usually begins with a carefull and relatively rigorous description of the process through which individuals preferences and phisical relationship to determine an equilibrium pure interest rate. This is generally followed by the assertion that somehow a market risk-premium is also determined, with the prices of asset adjusting accordingly to account for differences of their risk.

17,152 citations


Journal Article
Abstract: The potential advantages of the market-value approach have long been appreciated; yet analytical results have been meager. What appears to be keeping this line of development from achieving its promise is largely the lack of an adequate theory of the effect of financial structure on market valuations, and of how these effects can be inferred from objective market data. It is with the development of such a theory and of its implications for the cost-of-capital problem that we shall be concerned in this paper. Our procedure will be to develop in Section I the basic theory itself and to give some brief account of its empirical relevance. In Section II we show how the theory can be used to answer the cost-of-capital questions and how it permits us to develop a theory of investment of the firm under conditions of uncertainty. Throughout these sections the approach is essentially a partial-equilibrium one focusing on the firm and "industry". Accordingly, the "prices" of certain income streams will be treated as constant and given from outside the model, just as in the standard Marshallian analysis of the firm and industry the prices of all inputs and of all other products are taken as given. We have chosen to focus at this level rather than on the economy as a whole because it is at firm and the industry that the interests of the various specialists concerned with the cost-of-capital problem come most closely together. Although the emphasis has thus been placed on partial-equilibrium analysis, the results obtained also provide the essential building block for a general equilibrium model which shows how those prices which are here taken as given, are themselves determined. For reasons of space, however, and because the material is of interest in its own right, the presentation of the general equilibrium model which rounds out the analysis must be deferred to a subsequent paper.

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Book
01 Jan 1936
Abstract: Part I. Introduction: 1. The general theory 2. The postulates of the classical economics 3. The principle of effective demand Part II. Definitions and Ideas: 4. The choice of units 5. Expectation as determining output and employment 6. The definition of income, saving and investment 7. The meaning of saving and investment further considered Part III. The Propensity to Consume: 8. The propensity to consume - i. The objective factors 9. The propensity to consume - ii. The subjective factors 10. The marginal propensity to consume and the multiplier Part IV. The Inducement to Invest: 11. The marginal efficiency of capital 12. The state of long-term expectation 13. The general theory of the rate of interest 14. The classical theory of the rate of interest 15. The psychological and business incentives to liquidity 16. Sundry observations on the nature of capital 17. The essential properties of interest and money 18. The general theory of employment re-stated Part V. Money-wages and Prices: 19. Changes in money-wages 20. The employment function 21. The theory of prices Part VI. Short Notes Suggested by the General Theory: 22. Notes on the trade cycle 23. Notes on mercantilism, the usury laws, stamped money and theories of under-consumption 24. Concluding notes on the social philosophy towards which the general theory might lead.

15,140 citations


Journal ArticleDOI
Abstract: Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market 3, size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the tests allow for variation in 3 that is unrelated to size, the relation between market /3 and average return is flat, even when 3 is the only explanatory variable. THE ASSET-PRICING MODEL OF Sharpe (1964), Lintner (1965), and Black (1972) has long shaped the way academics and practitioners think about average returns and risk. The central prediction of the model is that the market portfolio of invested wealth is mean-variance efficient in the sense of Markowitz (1959). The efficiency of the market portfolio implies that (a) expected returns on securities are a positive linear function of their market O3s (the slope in the regression of a security's return on the market's return), and (b) market O3s suffice to describe the cross-section of expected returns. There are several empirical contradictions of the Sharpe-Lintner-Black (SLB) model. The most prominent is the size effect of Banz (1981). He finds that market equity, ME (a stock's price times shares outstanding), adds to the explanation of the cross-section of average returns provided by market Os. Average returns on small (low ME) stocks are too high given their f estimates, and average returns on large stocks are too low. Another contradiction of the SLB model is the positive relation between leverage and average return documented by Bhandari (1988). It is plausible that leverage is associated with risk and expected return, but in the SLB model, leverage risk should be captured by market S. Bhandari finds, howev er, that leverage helps explain the cross-section of average stock returns in tests that include size (ME) as well as A. Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) find that average returns on U.S. stocks are positively related to the ratio of a firm's book value of common equity, BE, to its market value, ME. Chan, Hamao, and Lakonishok (1991) find that book-to-market equity, BE/ME, also has a strong role in explaining the cross-section of average returns on Japanese stocks.

13,618 citations


Journal ArticleDOI
Abstract: In the hope that it may help to overcome these obstacles to effective empirical testing, this paper will attempt to fill the existing gap in the theoretical literature on valuation. We shall begin, in Section I , by examining the effects the effects of differences in dividend policy on the current price of shares in an ideal economy characterized by perfect capital markets, rational behavior, and perfect certainty. Still within this convenient analytical framework we shall go on in Section II and III to consider certain closely related issues that appear to have been responsible for considerable misunderstanding of the role of dividend policy. In particular, Section II will focus on the longstanding debate about what investors "really" capitalize when they buy shares; and Section III on the much mooted relations between price, the rate of growth of profits, and the rate of dividends per share. Once these fundamentals have been established, we shall proceed in Section IV to drop the assumption of certainty and to see the extent to which the earlier conclusions about dividend policy must be modified. Finally, in Section V , we shall briefly examine the implications for the dividend policy problem of certain kinds of market imperfections.

5,969 citations