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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