Consumption-Based Asset Pricing John Y.Campbelll First draft:July 2001 This version:July 2002 Harvard University and NBER.Department of Economics,Littauer Center,Harvard Univer- sity,Cambridge MA 02138,USA.617-496-6448.Email john_campbell@harvard.edu.Web page http://post.economics.harvard.edu/faculty/campbell/campbell.html. This paper has been prepared for the Handbook of the Economics of Finance,edited by George Constan- tinides,Milton Harris,and Rene Stulz.The paper is a revised and updated version of John Y.Campbell, "Asset Prices,Consumption,and the Business Cycle",Chapter 19 in John Taylor and Michael Woodford eds.Handbook of Macroeconomics Vol.1,1999,pp.1231-1303.All the acknowledgements in that chapter continue to apply.In addition,I am grateful to the National Science Foundation for financial support,to the Faculty of Economics and Politics at the University of Cambridge for the invitation to deliver the 2001 Marshall Lectures,where I presented some of the ideas in this chapter,to Andrew Abel,Sydney Ludvigson, and Rajnish Mehra for helpful comments,and to Samit Dasgupta,Stephen Shore,Daniel Waldman,and Motohiro Yogo for able research assistance
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Abstract This chapter reviews the behavior of financial asset prices in relation to consumption. The chapter lists some important stylized facts that characterize US data,and relates them to recent developments in equilibrium asset pricing theory.Data from other countries are examined to see which features of the US experience apply more generally.The chapter argues that to make sense of asset market behavior one needs a model in which the market price of risk is high,time-varying,and correlated with the state of the economy.Models that have this feature,including models with habit-formation in utility,heterogeneous investors, and irrational expectations,are discussed.The main focus is on stock returns and short-term real interest rates,but bond returns are also considered. JEL classification:G12
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1 Introduction The behavior of aggregate stock prices is a subject of enduring fascination to investors,pol- icymakers,and economists.In recent years stock markets have continued to show some fa- miliar patterns,including high average returns and volatile and procyclical price movements. Economists have struggled to understand these patterns.If stock prices are determined by fundamentals,then what exactly are these fundamentals and what is the mechanism by which they move prices? Researchers,working primarily with US data,have documented a host of interesting styl- ized facts about the stock market and its relation to short-term interest rates and aggregate consumption. 1.The average real return on stock is high.In quarterly US data over the period 1947.2 to 1998.4,a standard data set that is used throughout this chapter,the average real stock return has been 8.1%at an annual rate.2 2.The average riskless real interest rate is low.3-month Treasury bills deliver a return that is riskless in nominal terms and close to riskless in real terms because there is only modest uncertainty about inflation at a 3-month horizon.In the postwar quarterly US data,the average real return on 3-month Treasury bills has been 0.9%per year. 3.Real stock returns are volatile,with an annualized standard deviation of 15.6%in the US data. 4.The real interest rate is much less volatile.The annualized standard deviation of the ex post real return on US Treasury bills is 1.7%,and much of this is due to short-run inflation risk.Less than half the variance of the real bill return is forecastable,so the standard deviation of the ex ante real interest rate is considerably smaller than 1.7%. 2Here and throughout the chapter,the word return is used to mean a log or continuously compounded return unless otherwise stated.Thus the average return corresponds to a geometric average,which is lower than the arithmetic average of simple returns. 1
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5.Real consumption growth is very smooth.The annualized standard deviation of the growth rate of seasonally adjusted real consumption of nondurables and services is 1.1%in the US data. 6.Real dividend growth is extremely volatile at short horizons because dividend data are not adjusted to remove seasonality in dividend payments.The annualized quarterly standard deviation of real dividend growth is 28.3%in the US data.At longer horizons, however,the volatility of dividend growth is intermediate between the volatility of stock returns and the volatility of consumption growth.At an annual frequency,for example, the volatility of real dividend growth is only 6%in the US data. 7.Quarterly real consumption growth and real dividend growth have a very weak corre- lation of 0.05 in the US data,but the correlation increases at lower frequencies to 0.25 at a 4-year horizon. 8.Real consumption growth and real stock returns have a quarterly correlation of 0.23 in the US data.The correlation increases to 0.34 at a 1-year horizon,and declines at longer horizons. 9.Quarterly real dividend growth and real stock returns have a very weak correlation of 0.03 in the US data,but the correlation increases dramatically at lower frequencies to reach 0.47 at a 4-year horizon. 10.Real US consumption growth is not well forecast by its own history or by the stock market.The first-order autocorrelation of the quarterly growth rate of real nondurables and services consumption is a modest 0.2,and the log price-dividend ratio forecasts less than 4%of the variation of real consumption growth at horizons of 1 to 4 years. 11.Real US dividend growth has some short-run forecastability arising from the seasonality of dividend payments.But it is not well forecast by the stock market.The log price- dividend ratio forecasts no more than 8%of the variation of real dividend growth at horizons of 1 to 4 years. 2
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12.The real interest rate has some positive serial correlation;its first-order autocorrelation in postwar quarterly US data is 0.5.However the real interest rate is not well forecast by the stock market,since the log price-dividend ratio forecasts less than 1%of the variation of the real interest rate at horizons of 1 to 4 years. 13.Excess returns on US stock over Treasury bills are highly forecastable.The log price- dividend ratio forecasts 10%of the variance of the excess return at a 1-year horizon, 22%at a 2-year horizon,and 38%at a 4-year horizon. These facts raise two important questions for students of macroeconomics and finance. Why is the average real stock return so high in relation to the average short-term real interest rate? Why is the volatility of real stock returns so high in relation to the volatility of the short-term real interest rate? Mehra and Prescott(1985)call the first question the "equity premium puzzle".3 Finance theory explains the expected excess return on any risky asset over the riskless interest rate as the quantity of risk times the price of risk.In a standard consumption-based asset pricing model of the type studied by Rubinstein (1976),Lucas(1978),Grossman and Shiller (1981) and Hansen and Singleton (1983),the quantity of stock market risk is measured by the covariance of the excess stock return with consumption growth,while the price of risk is the coefficient of relative risk aversion of a representative investor.The high average stock return and low riskless interest rate (stylized facts 1 and 2)imply that the expected excess return on stock,the equity premium,is high.But the smoothness of consumption (stylized fact 5) makes the covariance of stock returns with consumption low;hence the equity premium can only be explained by a very high coefficient of risk aversion. Shiller(1982),Hansen and Jagannathan (1991),and Cochrane and Hansen (1992),build- ing on the work of Rubinstein(1976),have related the equity premium puzzle to the volatility 3For excellent recent surveys,see Kocherlakota(1996)or Cochrane(2001). 3
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of the stochastic discount factor,or equivalently the volatility of the intertemporal marginal rate of substitution of a representative investor.Expressed in these terms,the equity pre- mium puzzle is that an extremely volatile stochastic discount factor is required to match the ratio of the equity premium to the standard deviation of stock returns (the Sharpe ratio of the stock market). Some authors,such as Kandel and Stambaugh (1991),have responded to the equity pre- mium puzzle by arguing that risk aversion is indeed much higher than traditionally thought. However this can lead to the "riskfree rate puzzle"of Weil(1989).If investors are very risk averse,then they have a strong desire to transfer wealth from periods with high consump- tion to periods with low consumption.Since consumption has tended to grow steadily over time,high risk aversion makes investors want to borrow to reduce the discrepancy between future consumption and present consumption.To reconcile this with the low real interest rate we observe,we must postulate that investors are extremely patient;their preferences give future consumption almost as much weight as current consumption,or even greater weight than current consumption.In other words they have a low or even negative rate of time preference. I will call the second question the "equity volatility puzzle".To understand the puzzle, it is helpful to classify the possible sources of stock market volatility.Recall first that prices, dividends,and returns are not independent but are linked by an accounting identity.If an asset's price is high today,then either its dividend must be high tomorrow,or its return must be low between today and tomorrow,or its price must be even higher tomorrow.If one excludes the possibility that an asset price can grow explosively forever in a "rational bubble",then it follows that an asset with a high price today must have some combination of high dividends over the indefinite future and low returns over the indefinite future.Investors must recognize this fact in forming their expectations,so when an asset price is high investors expect some combination of high future dividends and low future returns.Movements in prices must then be associated with some combination of changing expectations ("news") about future dividends and changing expectations about future returns;the latter can in 4
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turn be broken into news about future riskless real interest rates and news about future excess returns on stocks over short-term debt. Until the early 1980's,most financial economists believed that there was very little pre- dictable variation in stock returns and that dividend news was by far the most important factor driving stock market fluctuations.LeRoy and Porter (1981)and Shiller (1981)chal- lenged this orthodoxy by pointing out that plausible measures of expected future dividends are far less volatile than real stock prices.Their work is related to stylized facts 6,9,and 11. Later in the 1980's Campbell and Shiller (1988a,b),Fama and French (1988a,b,1989), Poterba and Summers (1988)and others showed that there appears to be a forecastable component of stock returns that is important when returns are measured over long horizons. The variables that predict returns are ratios of stock prices to scale factors such as dividends, earnings,moving averages of earnings,or the book value of equity.When stock prices are high relative to these scale factors,subsequent long-horizon real stock returns tend to be low.This predictable variation in stock returns is not matched by any equivalent variation in long-term real interest rates,which are comparatively stable and do not seem to move with the stock market.In the late 1970's,for example,real interest rates were unusually low yet stock prices were depressed,implying high forecast stock returns;the 1980's saw much higher real interest rates along with buoyant stock prices,implying low forecast stock returns.Thus excess returns on stock over Treasury bills are just as forecastable as real returns on stock.This work is related to stylized facts 12 and 13.Campbell(1991)used this evidence to show that much of stock market volatility is associated with changing forecasts of excess stock returns.Changing forecasts of dividend growth and real interest rates are less important empirically. The equity volatility puzzle is closely related to the equity premium puzzle.A complete model of stock market behavior must explain both the average level of stock prices and their movements over time.One strand of work on the equity premium puzzle makes this explicit by studying not the consumption covariance of measured stock returns,but the 5
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consumption covariance of returns on hypothetical assets whose dividends are determined by consumption.The same model is used to generate both the volatility of stock prices and the implied equity premium.This was the approach of Mehra and Prescott (1985),and many subsequent authors have followed their lead. Unfortunately,it is not easy to construct a general equilibrium model that fits all the stylized facts given above.The standard model of Mehra and Prescott (1985)gets variation in stock prices relative to dividends only from predictable variation in consumption growth which moves the expected dividend growth rate and the riskless real interest rate.The model is not consistent with the empirical evidence for predictable variation in excess stock returns.Bond market data pose a further challenge to this standard model of stock returns. In the model,stocks behave very much like long-term real bonds;both assets are driven by long-term movements in the riskless real interest rate.Thus parameter values that produce a large equity premium tend also to produce a large term premium on real bonds.While there is no direct evidence on real bond premia,nominal bond premia have historically been much smaller than equity premia. Since the data suggest that predictable variation in excess returns is an important source of stock market volatility,researchers have begun to develop models in which the quantity of stock market risk or the price of risk change through time.ARCH models and other econo- metric methods show that the conditional variance of stock returns is highly variable.If this conditional variance is an adequate proxy for the quantity of stock market risk,then perhaps it can explain the predictability of excess stock returns.There are several problems with this approach.First,changes in conditional variance are most dramatic in daily or monthly data and are much weaker at lower frequencies.There is some business-cycle variation in volatility,but it does not seem strong enough to explain large movements in aggregate stock prices (Bollerslev,Chou,and Kroner 1992,Schwert 1989).Second,forecasts of excess stock returns do not move proportionally with estimates of conditional variance(Harvey 1989, 1991,Chou,Engle,and Kane 1992).Finally,one would like to derive stock market volatility endogenously within a model rather than treating it as an exogenous variable.There is little 6
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evidence of cyclical variation in consumption or dividend volatility that could explain the variation in stock market volatility. A more promising possibility is that the price of risk varies over time.Time-variation in the price of risk arises naturally in a model with a representative agent whose utility displays habit-formation.Campbell and Cochrane (1999),building on the work of Abel (1990), Constantinides (1990),and others,have proposed a simple asset pricing model of this sort. Campbell and Cochrane suggest that assets are priced as if there were a representative agent whose utility is a power function of the difference between consumption and "habit",where habit is a slow-moving nonlinear average of past aggregate consumption.This utility function makes the agent more risk-averse in bad times,when consumption is low relative to its past history,than in good times,when consumption is high relative to its past history.Stock market volatility is explained by a small amount of underlying consumption(dividend)risk, amplified by variable risk aversion;the equity premium is explained by high stock market volatility,together with a high average level of risk aversion. Similar ideas have been put forward in the recent literature on behavioral finance.Kah- neman and Tversky(1979)used experimental evidence to argue that agents behave as if their utility function is kinked at a reference point which is close to the current level of wealth Benartzi and Thaler (1995)argued that Kahneman and Tversky's "prospect theory"could explain the equity premium puzzle if agents frequently evaluate their utility and reset their reference points,so that the kink in utility increases their effective risk aversion.Barberis, Huang,and Santos(2001),building on behavioral evidence of Thaler and Johnson (1990), argue that prospect theory should be extended to make agents effectively less risk averse if their wealth has recently risen,very much in the spirit of a habit-formation model. Time-variation in the price of risk can also arise from the interaction of heterogeneous agents.Constantinides and Duffie(1996)develop a simple framework with many agents who have identical utility functions but heterogeneous streams of labor income;they show how changes in the cross-sectional distribution of income can generate any desired behavior of the market price of risk.Dumas (1989),Grossman and Zhou (1996),Wang (1996),Sandroni 7
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(1999)and Chan and Kogan(2001)move in a somewhat different direction by exploring the interactions of agents who have different levels of risk aversion. Some aspects of asset market behavior could also be explained by irrational expectations of investors.If investors are excessively pessimistic about economic growth,for example,they will overprice short-term bills and underprice stocks;this would help to explain the equity premium and riskfree rate puzzles.If investors overestimate the persistence of variations in economic growth,they will overprice stocks when growth has been high and underprice them when growth has been low,producing time-variation in the price of risk(Barsky and De Long 1993,Barberis,Shleifer,and Vishny 1998). This chapter has three objectives.First,it tries to summarize recent work on stock price behavior,much of which is highly technical,in a way that is accessible to a broader pro- fessional audience.Second,the chapter summarizes stock market data from other countries and asks which of the US stylized facts hold true more generally.The recent theoretical literature is used to guide the exploration of the international data.Third,the chapter systematically compares stock market data with bond market data.This is an important discipline because some popular models of stock prices are difficult to reconcile with the behavior of bond prices. The organization of the chapter is as follows.Section 2 introduces the international data and reviews stylized facts 1-9 to see which of them apply outside the United States. (Additional details are given in a Data Appendix available on the author's web page.)Section 3 discusses the equity premium puzzle,taking the volatility of stock returns as given.Section 4 discusses the stock market volatility puzzle.This section also reviews stylized facts 10-13 in the international data. Sections 3 and 4 drive one towards the conclusion that the price of risk is both high and time-varying.It must be high to explain the equity premium puzzle,and it must be time- varying to explain the predictable variation in stock returns that seems to be responsible for the volatility of stock returns.Section 5 discusses models which produce this result,including models with habit-formation in utility,heterogeneous investors,and irrational expectations. 8
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