Samuelson's Dictum and the Stock Market
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SAMUELSON’S DICTUM AND THE STOCK MARKET BY JEEMAN JUNG and ROBERT J. SHILLER COWLES FOUNDATION PAPER NO. 1183 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven, Connecticut 06520-8281 2006 http://cowles.econ.yale.edu/ SAMUELSON’S DICTUM AND THE STOCK MARKET JEEMAN JUNG and ROBERT J. SHILLER* Samuelson has offered the dictum that the stock market is ‘‘micro efficient’’ but ‘‘macro inefficient.’’ That is, the efficient markets hypothesis works much better for individual stocks than it does for the aggregate stock market. In this article, we review a strand of evidence in recent literature that supports Samuelson’s dictum and present one simple test, based on a regression and a simple scatter diagram, that vividly illus- trates the truth in Samuelson’s dictum for the U.S. stock market data since 1926. (JEL G14) I. INTRODUCTION dividends or earnings or cash flows) of indi- vidual firms than there is about future changes Paul A. Samuelson has argued that one would expect that the efficient markets hy- in the fundamentals of the aggregate stock market. Individual firms’ activities are highly pothesis should work better for individual diverse: Some have breakthrough discoveries stocks than for the stock market as a whole: or important new patents; others are in declin- Modern markets show considerable micro ing industries or have fundamental structural efficiency (for the reason that the minority who spot aberrations from micro efficiency can make problems. Hence some firms at some times money from those occurrences and, in doing so, may be well known to the market to have they tend to wipe out any persistent inefficiencies). a highly positive expected growth of funda- In no contradiction to the previous sentence, I had mental value, whereas different firms or the hypothesized considerable macro inefficiency, in the sense of long waves in the time series of aggre- same firms at different times may be well gate indexes of security prices below and above known to the market to have a highly negative 1 various definitions of fundamental values. expected growth of fundamental value. If We shall see in this article that there is now there is enough variation in information that substantial evidence supporting Samuelson’s the market has about future fundamental dictum where market inefficiency is defined growth of individual firms, then these varia- as predictability of future (excess) returns. tions might then be big enough to swamp We will also present a new test and scatter di- out the effect on price of time variation in agram that clarifies the truth in this dictum. other factors, such as speculative booms and Samuelson’s dictum is plausible if there is busts, making the simple efficient markets much more information available to the mar- model work fairly well as an approximation ket about future changes in fundamentals (the for individual firms. In contrast, there would seem not to be the same kind of clarity in the market about *We are indebted to John Y. Campbell, Erik Hjal- changes in the aggregate dividend or earnings marsson, Paul A. Samuelson, and Tuomo Vuolteenaho flow for the stock market of a country. for comments. Ana Fostel provided research assistance. Changes in these flows for the aggregate stock Jung: Associate Professor, Division of Economics and InternationalTrade,SangmyungUniversity,Seoul110- are less dramatic than for individual firms, 743 Korea. Phone 822-2287-5189, Fax 822-3965-702, because the aggregate averages out the indi- E-mail [email protected] vidual stories of the firms and the reasons Shiller: Professor, Cowles Foundation for Research in for changes in the aggregate are more subtle Economics, International Center for Finance,Yale University. 30 Hillhouse Ave., New Haven, CT and harder for the investing public to under- 06520. Phone 1-203-432-3708, Fax 1-203-432-6167, stand, having to do with national economic E-mail [email protected] 1. This quote is from a private letter from Paul Samuelson to John Campbell and Robert Shiller. The ABBREVIATIONS quote appears and is discussed in Shiller (2001, p. 243). Samuelson has been making this point for many years; CRSP: Center for Research on Security Prices it is also made in Samuelson (1998). 221 Economic Inquiry (ISSN 0095-2583) doi:10.1093/ei/cbi015 Vol. 43, No. 2, April 2005, 221–228 Ó Western Economic Association International 222 ECONOMIC INQUIRY growth, stabilizing monetary policy, and the analysis, that about 75% of the variance of (un- like. If changes in aggregate dividends are expected) annual firm stock excess returns can harder to predict, we might then expect that be justified in terms of the efficient market factors other than information about funda- component. mentals, factors such as stock market booms Vuolteenaho also estimated the standard and busts, would swamp out the effect of in- deviation of the ‘‘atypical discount’’ (the dif- formation about future dividends in determin- ference between the log stock price and the ing price and make the simple efficient log value that is justified by fundamentals as markets model a bad approximation for the he measures them) to be about 25%. Vuoltee- aggregate stock market. naho concludes that even though he found that most of the variance of returns can be jus- II. EVIDENCE IN THE LITERATURE FOR tified in terms of fundamentals, the inefficient SAMUELSON’S DICTUM component of stock price variation that gener- ates predictable movements in future returns There is now substantial evidence in the ‘‘still has an economically significant impact published literature for Samuelson’s dictum. on firm-level stock prices’’ (p. 246). Samuel- One of us (Shiller 1981) presented evidence son’s dictum asserts that individual-firm stock that was interpreted as finding evidence of price variations are dominated by genuine in- ‘‘excess volatility’’ in the stock market relative formation about future cash flows of the firm, to the efficient markets model using U.S. data but they are not perfect indicators of these 1871–1979 (see also LeRoy and Porter 1981; cash flows either. Campbell 1991). The same methods did not Cohen et al. (2001) used a method similar find much evidence of inefficiency in other to that in Vuolteenaho (2002) to derive a de- principal components of industry stock mar- composition of the cross-portfolio variance ket indexes over the same time interval (Shiller of the log ratio of book value to market value 1989, ch. 11). In this sense, the aggregate mar- into three components: a component that ket was found to be inefficient and the indus- could be justified in terms of information try deviations from the aggregate market were about future cash flow, a component related not found to be inefficient. to the persistence of the value spread, and To deal with criticisms that these early what we might call an ‘‘inefficiency compo- efforts to detect excess volatility made inap- nent’’ that generates predictable future propriate assumptions about stationarity returns.2 They also used a longer sample pe- around trend, Campbell and Shiller (1988 riod, an international data set, and some a,b) derived a cointegrated model for divi- improvements in method. Their conclusions dend, price, and earnings, a model that was with U.S. data 1937–97 and 192,661 firm- then recast as a vector autoregression in the years were that 80% of the cross-sectional var- log dividend-price ratio, the change in log div- iance in the log ratio of book value to market idends, and the log earnings-price ratio. Ap- value can be justified by the first few compo- plying this model to the aggregate U.S. stock nents, only 20% by the inefficiency component market 1871–1987, they concluded that only that explains 15-year returns. Their conclu- about 7% of the variance of annual stock mar- sion with international data on 22 countries ket returns can be justified in terms of new in- 1982–98 and 27,913 firm-years was that 82% formation about future dividends. of the cross-sectional variance of book- Vuolteenaho (2002) extended the Campbell– to-market values was explained by the first Shiller framework in such a way that it could be two components, and only 18% by the ineffi- used to produce a decomposition of unex- ciency component that explains five-year pected excess returns of a firm into a compo- returns. nent due to information about future cash flows of the firm (what we will call the efficient 2. Cohen et al. (2001) assembled firms into portfolios market component) and a component due to and looked at cross-portfolio variance rather than cross- information about future returns (what we will firm variance. They did this because their (logarithmic) call the inefficient market component of model does not allow zero or negative book values, but returns). Vuolteenaho studied 36,791 firm- individual firms sometimes have these. In this article, we would have a similar problem with zero dividends, years of data for the United States 1954–96. for which a log is not defined, but we do not use a logarith- He found, based on a vector-autoregressive mic model. JUNG & SHILLER: SAMUELSON’S DICTUM 223 The Campbell–Shiller results, the Vuoltee- factor used in the present value formula for naho results, and the Cohen et al. results to- stock prices, and Et denotes expectation gether make a case for Samuelson’s dictum: conditional on information at time t.4 D; Campbell and Shiller found that little of the Note that in the equation gt representing variability of aggregate stock market returns a dividend growth rate, is expressed as the are explained by fundamentals, whereas sum of discounted amounts of future dividend Cohen and colleagues found that much of changes from a $1 investment at time t.5 In the variability of individual stock returns or other words, the growth rates are computed ratios of book value to market value are relative to price P rather than D, and this is explained by fundamentals.