History and the Equity Risk Premium1
William N. Goetzmann and Roger G. Ibbotson
Yale School of Management
First Draft: February 26, 2005
Current Draft: October 18, 2005
Abstract: We summarize some of our own past findings and place them in the context of
the historical development of the idea of the equity risk premium and its empirical
measurement by financial economists. In particular, we focus on how the theory of
compensation for investment risk developed in the 20th century in tandem with the
empirical analysis of historical investment performance. Finally, we update our study of
the historical performance of the New York Stock Exchange over the period 1792 to the
present, and include a measure of the U.S. equity risk premium over more than two
centuries. This last section is based upon indices constructed from individual stock and
dividend data collected over a decade of research at the Yale School of Management, and
contributions of other scholars.
JEL: N2, G11
1 This is a draft of a chapter intended for a collection of essays on the equity risk
premium edited by Rajnish Mehra . It summarizes our past research related to the equity
premium, and places it in historical context. We thank Mehra for the opportunity to
contribute, and for his feedback on the research. Please direct all correspondence to about
the paper to firstname.lastname@example.org.
The equity premium puzzle posed in Mehra and Prescott (1985) was, in part, motivated
by historical evidence on the return of U.S. stocks in excess of the riskless rate. Much of
our own research has focused on estimating the equity risk premium using long-term
historical data, and examining how historical accident may relate to the classic puzzle.
While the equity premium is a fascinating topic for scholarship it is also one of the most
important economic topics in modern finance. The equity risk premium is widely used to
forecast the growth of investment portfolios over the long term. It is also used as an input
to the cost of capital in project choice, and employed as a factor in the expected rate of
return to stocks. Given its prevalence in practice and its importance to academic thought,
it is interesting to discover that the calculation of the equity risk premium is a fairly new
phenomenon. Reliable data to estimate the historical premium of stocks over bonds were
only collected in the mid 20th Century, and precise econometric estimates of the equity
premium only came after the development of the theory that uses it as a central input –
the Capital Asset Pricing Model, or CAPM.
The chapter in part is intended to review our own contributions to the literature on the
equity risk premium. Working both separately and together on a series of empirical
research studies conducted with colleagues through the years, we have looked at the
equity risk premium from a few different perspectives. First, research by Roger
Ibbotson and Rex Sinquefield provided some of the first accurate calculations of the
annual rate of return on U.S. asset classes over long investment horizons with specific
measures of the equity and other risk premiums. These calculations have come into
widespread academic and industrial use as inputs to research and investment decision-
making through numerous works that Ibbotson has produced. Second, Will Goetzmann
and co-authors Stephen Brown and Stephen Ross proposed and examined the hypothesis
that the equity premium estimated from U.S. financial data alone is subject to a bias due
to analysis of a winning market rather than losing ones. Third, both of us together with
our co-author Liang Peng have constructed one of the most complete long-term databases
of U.S. financial returns yet developed and have used it to study the variations in the
equity risk premium through nearly 200 years. Finally, both of us have them contributed
to the literature on other ways of measuring the equity risk premium and on various ways
of applying the concept. This chapter will summarize this past work and place it the
historical context of the evolution of the concept of the equity premium.
The chapter is structured as follows. We first review the historical development of the
idea of the equity risk premium in financial economics as the theory of compensation for
investment risk developed in tandem with the empirical analysis of historical investment
performance. Next we summarize some of our past findings about the historical equity
risk premium and present further analysis on potential survival biases. Finally, we update
our analysis of the historical performance of the New York Stock Exchange over the
period 1792 to the present, and include a measure of the U.S. equity risk premium over
more than two centuries. This last section is based upon indices constructed from
individual stock and dividend data collected over a decade of research at the Yale School
II. Historical Conception and Measurement of the Equity Risk Premium
One of the earliest and must succinct expressions of the concept of the equity risk
premium came from John Stuart Mill in his 1848 classic Principles of Political Economy.
Writing about a farmer considering investment in the land, Mill argues that:
…he will probably be willing to expend capital on it (for an immediate
return) in any manner which will afford him a surplus profit, however
small, beyond the value of the risk, and the interest which he must pay for
the capital if borrowed, or can get for it elsewhere if it is his own.2
2 Book 2, Chapter 16, The Principles of Political Economy, 1848. See also J. S. Mill,
Essays on Some Unsettled Questions of Political Economy Essay IV: On Profits, And
Interest. “ The profits of stock are the surplus which remains to the capitalist after
replacing his capital: and the ratio which that surplus bears to the capital itself, is the rate
of profit. The gross profits from capital, the gains returned to those who supply the funds
for production, must suffice for these three purposes. They must afford a sufficient
Mill thus separates profit into three parts: first, the interest that must be paid for the
capital borrowed, determined in terms of alternative opportunity cost of money. This is
equivalent to the riskless rate. The second component is the “value of the risk”
associated with the investment. This is equivalent to the equity risk premium. Mill’s
third component is a surplus profit, no matter how small. In modern parlance, the
“alpha” – a portion of compensation expected to be small in a competitive market.
Despite Mill’s early formulation of the idea, the concept of equity profit as compensation
for risk did not develop quickly. Economists at the turn of the century tended to focus
instead on the apparent paradox of profit and perfect competition rather than risk and
return. Columbia University professor John Bates Clark, for example, asserted that
returns in excess of the riskless rate were due to monopolistic advantage, rather than
compensation for insurable risk. In his view, innovation led to a comparative advantage
which was in turn rewarded by excess return.3
Chicago economist Frank Knight responded to Clark’s formulation by asserting the
importance of risk. In his famous 1921 work Risk, Uncertainty and Profit, he noted the
lack of useful models of risk and return in economic research. Knight reviewed the role
of risk in the economic theory of profit up to the 1920’s and took exception to the lack of
distinction in previous analyses between quantifiable and unquantifiable risk – the latter
he termed uncertainty, but both of which he asserted should command an investment
premium. Knight’s philosophical treatise did little, however, to clarify how the different
roles of risk and uncertainty would affect prices and business ventures in a practical
equivalent for abstinence, indemnity for risk, and remuneration for the labour and skill
required for superintendence.” It is somewhat unclear whether he is referring only to a
return that covers a probability of expected loss instead of the equity risk premium's
increase of expected return to cover systematic risk.
3 Clark, J. B., 1892, “Insurance and Business Profit,” The Quarterly Journal of
Economics, 7(1) 40-54. See a response to Clark by Fredrick B. Hawley, 1893, “The
Risk Theory of Profit,” The Quarterly Journal of Economics, 7(4) 459-479.
manner, and he was completely silent on the issue of how one might quantify the equity
As theorists debated the role of risk in the expected return to investment, empirical
researchers in the early 20th century began to collect historical performance data from the
markets. The earliest attempts to construct stock price indices were motivated by the
need for a “barometer” of current market trends, or as an indicator of fluctuating
macroeconomic conditions. Charles Henry Dow’s famous index of 30 stocks was not
originally intended as a measure of long term investment performance, but rather as a
daily measure of the market. A number of macroeconomists began to create stock price
indexes in the early 20th Century. Mitchell (1910, 1916), Persons (1916, 1919), Cole and
Frickey (1928) are among the number of scholars who collected U.S equity prices and
constructed indices as a means to study the interaction between economic cycles and the
financial markets. Likewise, Smith and Horne (1934) and Bowley, Schwartz and Smith
(1931) built similar indices for Great Britain. None of them addressed the obvious
question – at least from our modern perspective -- of long-term investment returns.4
Edgar Lawrence Smith’s 1924 book Common Stocks as Long Term Investments is the
first significant attempt to advocate equity investing as a means to achieve higher
investment returns. Smith collected historical price and dividend data for stocks and
corporate bonds over the period 1866 through 1923 from the Boston and New York Stock
Exchanges. He formed stock and bond investment portfolios of ten securities each as the
basis for simulating investor performance over four different time periods. He studied
the relative appreciation returns and income returns from both asset classes and
documented fairly convincingly that over a variety of sub-periods equities yielded higher
income than bonds and also provided significant capital appreciation.
4 For an excellent discussion of the development of early equity indices, see Hautcoeur,
Pierre-Cyrille and Muriel Petit-Koñczyk (2005). For a complete list of indices developed
before Cowles (1938), see Cowles own discussion and notes in his volume.
Smith simulated the performance of these portfolios in a number of ways. The simplest
was to treat the income and capital appreciation returns from the stock and bond
portfolios separately and show that stocks nearly always dominated in both measures. He
came close to developing a total return measure for the equity premium by the
mechanical process of taking the income return each year from stocks and “paying” out
of it the amount generated by the bond portfolio and then re-investing the residual back
into shares. The relative growth of the stock portfolio through this procedure can be
interpreted as a measure of the equity premium – at least with respect to corporate bonds.
Smith’s book was not only widely read by investors but also closely studied by scholars.
It was immediately cited by Yale’s Irving Fisher as an argument for investing in a
diversified portfolio of equities over bonds.5 Based on Smith’s findings, Fisher theorized
that the trend towards investment in diversified portfolios of common stock had actually
changed the equity premium in the 1920’s. His views on the factors influencing the
equity risk premium are worth quoting at length.
Studies of various writers, especially Edgar Smith and Kenneth Van Strum
have shown that in the long run stocks yield more than bonds. Economists
have pointed out that the safety of bonds is largely illusory since every
bondholder runs the risk of a fall in the purchasing power of money and
this risk does not attach to the same degree to common stock, while the
risks that do attach to them may be reduced, or insured against, by
It is in this way that investment trusts and investment council tend to
diminish the risk to the common stock investor. This new movement has
created a new demand for such stocks and raised their prices, at the same
5 Fisher, Irving, 1925, “Stocks vs. Bonds”, American Review of Reviews, July issue.
time it has tended to decrease the demand for, and to lower the price of,
Smith’s empirical approach to measuring the relative performance of the two asset
classes was widely imitated in later studies. In 1937, Brown University Professor
Chelcie Bowland published a synthesis of research following Smith’s book and showed
how the common stock investment strategy performed through the worst years of the
depression.7 Bowland concluded on considerable empirical evidence that the theory of
common stock investment survived the crash. An interesting feature of the studies cited
in Bowland’s book is that none of them produced what we now think of as a measure of
the equity premium – that is, the difference in total return between a portfolio of equities
and the riskless rate over the same period.
The most carefully crafted early empirical analysis of the long term performance of the
stock market was Common Stock Indices, by Alfred Cowles III, published in 1938. This
ambitious study, undertaken before the advent of computers, but assisted by the invention
of Holerith cards, collected individual stock prices (actually monthly highs and lows by
stock) and dividends from 1872 to 1937 for stocks on the NYSE. Its stated goal was to
“portray the average experience of those investing in this class of security in the United
States from 1871 to 1937” 8
Cowles improved upon Smith’s work by developing a methodology which reinvested the
dividend proceeds from stocks into the purchase of shares, thus avoiding the complexities
of comparing income and capital appreciation returns separately. Two other important
features of the Cowles study were that he collected data on virtually all of the stocks on
the New York Stock Exchange, and that he capital-weighted them, a procedure that
6 Fisher, Irving, 1930, The Theory of Interest, The Macmillan Company, New York, pp.
7 Bowland, Chelcie, 1937, The Common Stock Theory of Investment, The Ronald Press
Company, New York.
8 Cowles, Alfred, 1938, Common Stock Indices, Cowles Commission for Research in
Economics, Monograph number 3, Principia Press, Bloomington, p. 2.
allowed the index to simulate a passive buy and hold investment strategy. The one
serious limitation of the Cowles study is that it relied on the average of high and low
prices during the month as a proxy for end-of-month stock prices. This had a smoothing
effect on the returns, downward biasing the volatility and muddying up any econometric
analysis of the data.9 Oddly enough, given such widespread interest in Edgar Smith’s
earlier study, the Cowles analysis was silent on the relative performance of stocks and
The first book to explicitly define, model and estimate an equity risk premium was John
Burr Williams’ The Theory of Investment Value, also published in 1938. According to
Williams “The customary way to find the value of a risky security has always been to add
a ‘premium for risk’”.10 He provides a table of “Interest Rates, Past Present and Future”
which takes the riskless rate as the long-term government bond rate of 4% and the
expected return to “Good stocks” as 5 1/2%.11 Williams’ estimated the forward equity
premium from a dividend discount model, and he was careful to explain that historical
(i.e. past) estimates provide a good forecast of the future, even when they deviate from
In sum, by the end of the 1930’s, economists had developed a clear conception of the
equity risk premium, a means to measure rates of return on investments, and had
collected historical data extending back through American financial history for several
decades. The first empirical estimate of the equity premium by Smith is generally
regarded as a major factor in the rush by retail investors into the stock market in the
1920’s, and Irving Fisher is often taken to task for his theory that stock prices increased
9 Cowles, Alfred, 1960, “A Revision of Previous Conclusions Regarding Stock Price
Behavior,” Econometrica, Vol. 28, No. 4. pp. 909-915.
10 Williams, John Burr, 1938, The Theory of Investment Value, Harvard University Press,
Cambridge, page 67. Of interest to those interested in financial history is that Williams
solves algebraically for the discount rate on the common stock of a firm as a function of
the discount rate for the all-equity firm and the firm debt – preceding Modigliani and
Miller in arguing that “The investment value of an enterprise … in no way depends
upon what the company’s capitalization is.” (p.72).
11 Ibid. p. 387.
to new levels in the 1920’s as a result of a decreasing equity risk premium. Alfred
Cowles created the first relatively accurate long-term index of total return to investing in
common stocks, and J.B. Williams provided the first numeric estimate of the forward-
looking equity risk premium. Their work provided a valuable foundation for the next
generation of financial research.
The next major attempt to empirically quantify the equity returns was undertaken at the
University of Chicago. Beginning in 1960, CRSP, the Chicago Center for Research on
Security Prices, headed by economists Lawrence Fisher and James H. Lorie,
systematically began to collect stock prices and dividends from U.S. capital market
history. Fisher and Lorie published the results of their study of returns to U.S. stocks in
1964, as “Rates of Return on Investments in Common Stocks”12 and in 1977 as a volume
including returns to U.S. government securities as well. 13 Like Cowles, they based their
analysis of individual share prices and re-investment of dividends of U.S. stocks.
The theoretical developments in financial economics in the 1950’s and 1960’s made these
empirical estimates of rates of return particularly interesting. In 1952, Harry Markowitz
published his famous model of portfolio selection which explicitly linked investment
return and risk. Markowitz proposed taking as inputs to his model the historical means,
variances and covariances of individual securities, although he regarded this as a method
which could be improved upon with better forecasting tools.
The Markowitz model, as it is now applied, identifies an optimal portfolio of assets in
expected return and standard deviation space by the point of tangency formed by a ray
extending from the expected return of the riskless (zero standard deviation) asset to the
continuous frontier of portfolios providing the highest return for each level of standard
deviation. The difference between the return of the riskless asset and the expected return
12 Fisher, Lawrence and James H. Lorie, 1964, “Rates of Return on Investments in
Common Stocks,” Journal of Business 37, 1-21, covered the period 1926-60 which in
1968 they updated through 1965.
13 Fisher and Lorie, 1977, “A Half Century of Returns on Stocks and Bonds,” University
of Chicago Graduate School of Business.
of the tangency portfolio in this model is the equity risk premium. 14 In the Markowitz
framework, the size of the equity risk premium is an empirical question. Later scholars
took a theoretical approach to its estimation.
The Sharpe-Lintner-Mossin Capital Asset Pricing Model [CAPM] was independently
developed in the 1960’s in part as a means to identify the optimal portfolio of risky assets
in the Markowitz framework. As such, the CAPM takes an analytical approach to the
equity risk premium. The theory endogenizes asset prices as a function of the risk
aversion of the representative investor and the variance-covariance structure of the
universe of assets. The shape of the representative investor’s utility function,
parameterized by a coefficient of risk aversion for the market as a whole is central to
identification of the equity premium.
In the framework of the CAPM, if the form of the utility function and the coefficient of
risk aversion are both known, then knowledge of the variance-covariance of the universe
of assets (or the variance of the portfolio of risky assets) is sufficient to identify the
spread between risky and riskless asset portfolios.
An important feature of the Markowitz model and the CAPM is that they provide a
theoretical foundation for estimating the magnitude of the equity risk premium directly
from investor preferences. It was not until Mehra and Prescott (1985), however that
anyone attempted to compare the equity premium implied by preferences with the
empirical measures provided by historical returns.
III. Stocks, Bonds, Bills and Inflation
In 1976, Ibbotson and Sinquefield published “Stocks, Bonds, Bills and Inflation: Year-
by Year Historical Returns (1926-1974).” The stock market returns were calculated as
14 The Markowitz framework is a single-period model. As such, the arithmetic return and
the geometric return are the same.