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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

I. Introduction

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

of Management.

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

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. Mills

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 Mills 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 Clarks 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 1920s 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. Knights 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

manner, and he was completely silent on the issue of how one might quantify the equity

risk premium.

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 Dows 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 Smiths 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

4 For an excellent discussion of the development of early equity indices, see Hautcoeur,

Pierre-Cyrille and Muriel Petit-Koczyk (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.

Smiths book was not only widely read by investors but also closely studied by scholars.

It was immediately cited by Yales Irving Fisher as an argument for investing in a

diversified portfolio of equities over bonds.5 Based on Smiths findings, Fisher theorized

that the trend towards investment in diversified portfolios of common stock had actually

changed the equity premium in the 1920s. 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

time it has tended to decrease the demand for, and to lower the price of,

bonds.6

Smiths 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 Smiths 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 Bowlands 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 Smiths 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.

220-221.

7 Bowland, Chelcie, 1937, The Common Stock Theory of Investment. The Ronald Press

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 Smiths

earlier study, the Cowles analysis was silent on the relative performance of stocks and

bonds.

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

present conditions.

In sum, by the end of the 1930s, 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

1920s, 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 companys capitalization is. (p.72).

11 Ibid. p. 387.

to new levels in the 1920s 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 Stocks12 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 1950s and 1960s 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 1960s 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 investors 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