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
!"#$% & '#( )*' '))% + ,- ++.- / - 011 - 1+ 1 ++1 ++- + 2- - - 3 + & +4 2- 5- 6 ++ 7 8 - + 9 - #* 5- 2 + - + / :+ # #*** #"$#;#$!$ ++ - <=+ - - + > > + - + & ? @+ - ?+ 8+ - - + - "!!# -++ =- > - - - = + & , - - - ++ & & - &- + /+ - 6 + -
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
!" # $ % & ' !" ' % % ( ( ( ( %# ) %# * # % ) # % # ' # ( ) # +
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
%% % ( , % # ) ( # - ( ( ) # % % % . %% - ( # ' / 0 # (% !" # % ) ( ( ) %% % % ( % - $ !" 123 1142# % # % ( 45 % ( 6) ( ( 7 6) - $ !" # % 6) 15 6 0 ( # 895 !" 2 ' !" 35# ) 7 ( : # ' 35 - - - - - = + + + - = 2- - =-- += - - - +
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
8 0 % % , 5 !" 9 0 % ' , $ % 465 !" ; % # # % ( % ; $ # ' # % 95 !" 3 < % % ( ) 8 !" # $ 8 2) 4 0 % ( $ 6 !" 62 ) # % 1 < % ( ( 6 !" # $ 23 2) 0 !" % ( ( ) $ % # % ) 25 % 2 0 !" % ) % = ( ( % ) 45 % 2
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
> ) $ !" 8 ? ( ( # % ) 5 2 6 .' !" ( % % ) 5 ' ) # 5 ) # 645 2) $ * @ A148B $ C $ D ' ' ' ( ( $ ( ( - ) % 0 A139B# : A134B# + " A14B ? "% A146B# $ ( ( ( ' ( % # ( E ( % % ( ( A B ' ' (# $ # % = A 8B ( ( > $ ' % E ( " A14B# ? % A11B# ? A11B# ) % ( 0 A139B# $ ? A ++ B- +< C#**'D - C"!!#D 6