<s> Patterns in Three Centuries of Stock Market Prices
 
William N. GoetzmannThe Journal of Business, Volume 66, Issue 2 (Apr., 1993), 249-270.
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http://www.jstor.org/Fri Jun 21 23:24:37 2002William N. Goetzmann
Columbia University
Patterns in Three Centuries ofStock Market Prices*
I. Introduction
Tests about the temporal behavior of long-ho-rizon stock returns by Fama and French (1988)have suggested the possibility of mean reversionin stock prices and breathed new life into theDow theory (see Rhea 1932), which claims thatthe stock market follows an alternating patternof bull and bear markets. The importance of theFama and French research lies not in the identi-fication of a particular stochastic model of stockreturn behavior but in the implication exploredby, among others, Poterba and Summers (1988)and Shiller (1989) that financial markets may besubject to temporary ‘‘fads’’ or at least periodi-cally time-varying expected returns. The Famaand French research has motivated several meth-odological studies of mean reversion tests. Boot-strapping tests by Kim, Nelson, and Startz(1988), Goetzmann (1990), McQueen (1992), andRichardson (in press) have explicitly modeled se-rial independence of monthly and annual stockreturns and have tended to reject mean reversionof long-term stock returns in favor of the moreparsimonious random-walk model of multipleyear stock returns.
* T wish to thank Roger Ibbotson, Stephen Ross, JonathanIngersoll, Jr., Robert Shiller, the editor, John Huizinga, andKenneth R. French, the referee, for their comments. Thanksare also due to Christopher Musto for his research assistanceand to Ibbotson Associates of Chicago for making their dataavailable. I am solely responsible for all errors.
(Journal of Business, 1993, vol. 66, no. 2)© 1993 by The University of Chicago. All rights reserved.0021-9398/93/6602-0004$01.50
249
 
This article appliesautoregression and re-scaled range statisticsto very long stock mar-ket series to test the hy-pothesis that long-termtemporal dependenciesare present in financialdata. For the annualcapital appreciation re-turns to the LondonStock Exchange, evi-dence of persistence inraw returns greaterthan 5 years and ofmean reversion in devi-ations from rolling 20-year averages is found.Similar patterns are ob-served for the NewYork Stock Exchange;however, they are notsignificant at traditionalconfidence levels.250 Journal of Business
Poterba and Summers (1988) observe that the failure to distinguishbetween low-frequency mean reversion and complete unpredictabilityof returns lies in the power of the tests used to examine them. Forinstance, a test of mean reversion in 5-year stock market returns basedon the data available from the Center for Research in Security Prices(CRSP) monthly files has only 11 independent observations—hardlyenough to draw convincing conclusions about repeated temporal pat-terns.
This lack of data has led to ingenious attempts to extract more infor-mation from the existing series. Fama and French (1988) use overlap-ping observations rather than temporally independent returns and cor-rect for the lack of independence in the errors by the method proposedby Hansen and Hodrick (1980). They find that 4- and 5-year returns tothe equal-weighted New York Stock Exchange (NYSE) over the 1926-87 period are negatively autocorrelated. Richardson and Stock (1989)derive the distribution of the Fama and French regression coefficientsand demonstrate that overlapping observations may contain more in-formation than independent observations; however, they cannot rejectthe random walk model.
Another solution for increasing the power of the test is to collectmore data. In tests of long-run price dependency, Poterba and Sum-mers (1988) and Lo (1991) use the annual Cowles (1938) U.S. stockindex extending back to 1872. Lo uses the rescaled range (R/S) statisticto test for aperiodic reversals and finds no evidence of them. Poterbaand Summers use a variance ratio test and find marginal evidence ofmean reversion, although the results are not strong enough to rejectthe random walk model at traditional confidence levels.
In this article, I extend market history even further back in time.Joint-stock shares have traded in London for 300 years and in NewYork for 200 years. If cycles of periodicity greater than a year areconsistently present in British or American stock prices, one wouldexpect to find them in the longest indices of all. These long series offeran opportunity to identify patterns that shorter time series cannot. Forinstance, tests of 5-year serial dependence in London and New Yorkstock price indices using the available published data may employ 57and 39 observations, respectively. In autocorrelation tests of meanreversion and persistence of multiple horizon capital appreciation re-turns, I apply the bootstrapping methodology to two stock price indi-ces that extend back to the eighteenth century. I perform separate aswell as joint significance tests with respect to models that hypothesizelong-term periodic behavior. In addition, I measure the R/S statisticproposed by Mandelbrot (1972) and modified by Lo (1991) as a test oflong-term dependency in prices. Contrary to the results from testson the last 120 years of U.S. stock market data, the longer-term per-spective suggests that the random walk model does not correctly de-Patterns of Stock Market Prices 251
scribe the behavior of U.S. stock prices. I find evidence of long-termstructural changes in stock price appreciation. Once these structuralchanges are incorporated in the tests, I find some evidence of a persis-tent mean-reverting component in stock market prices of the sort dis-cussed by Fama and French (1988) and Poterba and Summers (1988).Although autocorrelation tests on the long-term NYSE capital appreci-ation index yield test statistics consistent with mean reversion, the nullhypothesis of temporal independence cannot be rejected at traditionalconfidence levels. The R/S tests, however, provide some evidence thatthe detrended London Stock Exchange (LSE) and NYSE prices mayexhibit long-term memory.
This article is organized as follows: Section II describes the sourcesof the data and discusses the possible errors and biases in each series.Section III reports the methodology and results of autoregression tests.Section IV reports the methodology and results of the rescaled rangetests. Section V concludes.
Il. Data Sources
Shares of the Bank of England were traded on the Royal Exchange inthe seventeenth century, and British publications such as John Cas-taing’s The Course of the Exchange regularly reported share prices ofat least six joint stock companies, beginning in the eighteenth century.!According to Mirowski (1981), who compiled an equal-weighted aver-age of British share prices through the eighteenth century, the Londonmarket for shares was active and fully functional by 1700, althoughthe frequency of trades and price quotations fluctuated considerably.In this article, I analyze an annual share price index for the LSEcompiled from seven different sources, beginning with the Mirowski(1981) index. These sources are reported and described in table 1.Gayer, Rostow, and Schwartz (1953) provide a broad-based index ofshares through the first half of the nineteenth century and report theHaekel index that extends the LSE index to 1866. Several economistshave constructed indices for periods of the late nineteenth and earlytwentieth centuries—I use Bowley, Schwartz, and Smith (1931) andSmith and Horne (1934). Two financial periodicals provide index mea-sures of equity price appreciation through the early and middle twenti-eth century: the Bankers Magazine (1915-27) and the Economist (to1970), which prints the Financial Times Index. Data on the capitalappreciation of the LSE since 1970 are collected by the Financial
1. See Neal (1990) for a discussion of The Course of the Exchange. It was publishedsemiannually, with daily price quotes for major stocks, over the period from 1698 to1810. These are available in electronic form from Inter-University Consortium for Politi-cal and Social Research, P.O. Box 1248, Ann Arbor, MI 48106. 
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Times in their Financial Times Actuaries Index and by Morgan StanleyCapital International. Both of these are available from Ibbotson Asso-ciates, Inc. Because the LSE index is spliced from many sources, itdoes not necessarily reflect the continuous performance of an in-vestable portfolio through time, although it is probably a fair approxi-mation. The existence of overlapping observations at each splice in-sures that there is no abrupt change in the composition of the indexthat could be misinterpreted as an actual return.
Active trading in shares in the United States dates from the end ofthe eighteenth century (see table 2). The New York Stock Exchangewas founded in 1792, and the Foundation for the Study of Cycles (seeIbbotson and Brinson 1987) has compiled an annual stock price seriesfrom 1790 to the present that combines a number of other studies.”Unfortunately, many of the component series suffer from biases dueto smoothing and survivorship. For the period from 1815 to 1859, abroad-based index of the New York Stock Exchange is available fromGoetzmann and Ibbotson (1992). It is an equal-weighted annual indexof all listed equity shares on the NYSE and is based on the pricequotes in the New York Shipping and Commercial (see New YorkShipping List [1815—1926]), which provided the official record of NYSEprice quotes and representative transactions prices for several decadesof the early nineteenth century. It deals with the problem of infrequenttrading through the use of the weighted repeat sales method proposedby Case and Shiller (1987) and studied by Goetzmann (1992). For theperiod from 1860 to 1871, I must again rely on the Foundation for theStudy of Cycles index, which is probably composed of the Cole-Frickey (1928) index of railroad shares over this period and is thus notbroad based. The index created by Cowles (1938) and adjusted for dataerrors by Wilson and Jones (1987) begins in 1872 and is constructedusing the average of the high and low prices of individual stocks ineach month. It is a capital-weighted index that is broad based, but itmay be subject to survivorship bias, and, as Working (1960) points out,the averaging procedure introduces monthly smoothing. After 1926, Iuse the capital appreciation return to the Standard and Poor’s index,reported by Ibbotson Associates (1991). For a complete discussion of
2. See Ibbotson and Brinson (1987). They explain that the index is composed of ‘‘aninternal index . . . the Cleveland Trust Company Index . . . the Clement-Burgess Indexand the Cowles Index’’ (p. 73). The Cleveland Trust Company Index includes indicescompiled from other sources—probably Cole and Frickey (1928), while the ClementBurgess Index is extremely narrow. As Cowles (1938) notes, it is ‘composed of fromfour to nine stocks, chiefly leading railroads’’ (p. 439). This narrow base, which coversperiods in the nineteenth century when the NYSE listed over one hundred frequentlytraded stocks, suggests that the index may have been created by using only companieswith data extending over the entire period of study, that is, 1854-83. Given this survivor-ship bias, the Foundation for the Study of Cycles NYSE index from 1790 to the latenineteenth century may be positively biased in the early years.Journal of Business
 
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the limitations and biases in the pre-CRSP U.S. stock return series,the reader is referred to Schwert (1990).
As noted, the problems associated with the spliced long-term ap-preciation series tend to bias estimates of both the long-term mean andthe standard deviation and to a lesser extent the annual autocorrela-tion. The long-term mean may be upwardly biased due to the selectionof frequently traded or surviving securities used to create the indicesover the early periods. The standard deviation may fluctuate since thenumber of stocks in each series also fluctuates—because of the effectof diversification, one would expect the standard deviation of the indi-ces to decline as the number of stocks increases. The direction of theautocorrelation bias at the annual horizon is not clear. While smooth-ing may be caused by averaging of high and low prices and by infre-quent price observations, some annual negative correlation in theNYSE series may be induced by the use of the repeat-sales method.For horizons greater than 1 year, both effects decline in importance;however, the question of dividend yield becomes significant. If totalreturns are independent, but dividend policy changes slowly throughtime, then one would observe long-term price dependency. Conse-quently, in the following tests, I allow for fixed as well as slowlychanging mean values. Unfortunately, there is no ready evidence fordividend yields from the early periods covered by the data.?
Perhaps more significant than the biases introduced by survivorship,recording methods, data splicing, and dividend policy changes is thefact that the economies of both countries changed profoundly over thecourse of the last 3 centuries. The LSE series, for instance, documentsshare prices through the entire industrial revolution, the nation’s colo-nial expansion, and centuries of development in the capital markets.Similarly, the NYSE documents the U.S. equity market over the pe-riod of westward expansion, the development of the U.S. rail transpor-tation system, and the evolution of the economy from agrarian to in-dustrial. Such broad historical changes are reflected in the compositionof both indices as different types of corporations financed growththrough the equity markets. Not only would some of these firms havedifferent expected returns, but they would also reflect different kindsof risks. These broad, evolutionary issues present problems in regres-sion tests of mean reversion since the tests assume stationarity of theparameters of the model to be estimated. Thus, by gathering more dataI have solved some problems, while introducing others.
Table 3 reports summary statistics for the NYSE and the LSE over
3. Indirect evidence for the NYSE stocks is implicit in the manner in which stockprices were quoted on the exchange. Prices were quoted with respect to a par value of100, with prices rarely deviating above 200, and splits were practically nonexistent inthe early nineteenth century. This suggests that investors expected earnings to be paidout rather than retained.Journal of Business
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the entire period for which I have data and also breaks the resultsdown by centuries. These summary figures are interesting in their ownright. The long-term annual geometric capital appreciation return ofthe LSE, based on 290 years of data, is 2.1%. The long-term annualgeometric capital appreciation return of the NYSE, based on 197 yearsof data, is 3.9%. The annual standard deviation of returns to the LSEand NYSE is 15.7% and 18.4%, respectively. The mean return in eachcountry differs significantly over the nineteenth century but not soover the twentieth century. This may reflect the economic return ofthe underlying assets themselves, or it may reflect international differ-ences in dividend yields. When logged, neither distribution is dramati-cally skewed, while both are leptokurtotic when compared to normaldistribution. Despite the kurtosis, however, a Kolmogorov-Smirnovtest rejects normality for the LSE but not the NYSE.*
Figure 1 plots the LSE and NYSE capital appreciation indices. It isclear that the variance of the LSE is not stable over time; note thehigh variance periods in the 1720s and in the 1950s through the 1980s,with a long stretch of relative calm in between. The NYSE varianceis more stable, although the Great Depression stands out as a periodof relatively high volatility, along with occasional dramatic outliers inthe first 50 years of the series. Note also that the appreciation rate ofthe LSE increases dramatically over time. It exhibits practically noincrease through the eighteenth century and appears to increase at alower rate than the NYSE through the nineteenth century and the firsthalf of the twentieth century. After 1950, it appears to increase at agreater rate than the NYSE.
III. Methodology
A. Autocorrelation Tests
Following Fama and French (1988), I use an autoregression of multipleyear capital appreciation returns to test for long-term serial depen-dency in stock market prices. Without an ex ante hypothesis regardingthe number of years to include in the compound returns, I test theserial dependency of 1-10-year horizon returns. That is,
r(it,t + T) = a(T) + B(T)r(t — T, 1) + e(t,t + T), qd)
fort = 0, T, 2T,...,nT, where T= 1,..., 10.Unlike Fama and French (1988), I use only nonoverlapping returns,so that I do not need to correct for serial dependency in the residuals;>
4. The probability associated with rejection of the null hypothesis that the series isdrawn from a normal distribution is .997 for the LSE and .1872 for the NYSE.
5. Fama and French (1988) employ the Hansen and Hodrick (1980) correction foroverlapping returns. Richardson and Smith (1991) have analyzed the behavior of statis-258 Journal of Business
10000:
| #
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
100
10 pl—
1700 1750 1800 1850 1900 1950
— LSE —— NYSE
Fic. 1.—London and New York Stock Exchanges Capital Appreciation In-dices, 1790-1989. The dotted line (begins ca. 1800) indicates the annual capitalappreciation of the NYSE; the solid line (begins ca. 1700) indicates the annualcapital appreciation of the LSE; the X-axis indicates the time period from 1790to 1989; the Y-axis indicates the growth of an invested dollar or pound overthe period. Sources for both indices are described in the text.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
however, I correct for the bias in the autoregression coefficient notedby Kendall (1954) by bootstrapping the autoregression coefficient, un-der the null hypothesis that successive annual capital appreciation re-turns to the stock market are independent and identically distributed.The bootstrap is performed by drawing r*, a bootstrapped pseudohis-tory of market returns with replacement from the empirical distributionof r(t). The multiple year returns are formed by compounding r