John Y. Campbell

Understanding Risk and Return

This paper uses an equilibrium multifactor model to interpret the cross-sectional pattern of postwar U.S. stock and bond returns. Priced factors include the return on a stock index, revisions in forecasts of future stock returns (to capture intertemporal hedging effects), and revisions in forecasts of future labor income growth (proxies for the return on human capital). Aggregate stock market risk is the main factor determining excess returns; but in the presence of human capital or stock market mean reversion, the coefficient of relative risk aversion is much higher than the price of stock market risk.

Asset Pricing At The Millennium

This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work, and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor (SDF) that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, while patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and cross-sectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance.

Valuation Ratios and the Long-Run Stock Market Outlook

The use of price–earnings ratios and dividend-price ratios as forecasting variables for the stock market is examined using aggregate annual US data 1871 to 2000 and aggregate quarterly data for twelve countries since 1970. Various simple efficient-markets models of financial markets imply that these ratios should be useful in forecasting future dividend growth, future earnings growth, or future productivity growth. We conclude that, overall, the ratios do poorly in forecasting any of these. Rather, the ratios appear to be useful primarily in forecasting future stock price changes, contrary to the simple efficient-markets models. This paper is an update of our earlier paper (1998), to take account of the remarkable behavior of the stock market in the closing years of the twentieth century.

Who Should Buy Long-Term Bonds?

According to conventional wisdom, long-term bonds are appropriate for long-term investors who value stability of income. We develop a model of optimal consumption and portfolio choice for infinitely-lived investors facing stochastic interest rates, solve it using an approximate analytical method, and evaluate the conventional wisdom. We show that the demand for long-term bonds has both a myopic component and an intertemporal hedging component. As risk aversion increases, the myopic component shrinks to zero but the hedging component does not. An infinitely risk-averse investor who is infinitely unwilling to substitute consumption intertemporally should hold a portfolio of long-term indexed bonds that is equivalent to an indexed perpetuity. This portfolio finances a riskless consumption stream and in this sense provides a stable income. We calibrate our model to postwar US data and compare consumption and portfolio rules with and without bond indexation, portfolio constraints, and the possibility of investment in equities. We find that when indexed bonds are not available, inflation risk leads investors to shorten their bond portfolios and increase their precautionary savings. This has serious welfare costs for conservative investors, who are much better off when they have the opportunity to buy indexed bonds. We also find that the ratio of bonds to equities in the optimal portfolio increases with the coefficient of relative risk aversion, which is consistent with conventional portfolio advice but inconsistent with the mutual fund theorem of static portfolio analysis. Our results illustrate the general point that static portfolio choice models should not be used to study the dynamic problems facing long-term investors.

The response of consumption to income: A cross-country investigation

Abstract In previous work we have argued that aggregate, post-war. United States data on consumption and income are well described by a model in which a fraction of income accrues to individuals who consume their current income rather than their permanent income. This fraction is estimated to be about 50%, indicating a substantial departure from the permanent income hypothesis. In this paper we ask whether the same model fits quarterly data from the United Kingdom over the period 1957–1988 and from Canada, France, Japan, and Sweden over the period 1972–1988. We also explore several generalizations of the basic model.

Why is Consumption So Smooth

For thirty years it has been accepted that consumption is smooth because permanent income is smoother than measured income. This paper considers the evidence for the contrary position, that permanent income is in fact less smooth than measured income, so that the smoothness of consumption cannot be straightforwardly explained by permanent income theory. The paper argues that in postwar U.S. quarterly data, consumption is smooth because it responds with a lag to changes in income.

International Evidence on the Persistence of Economic Fluctuations

This paper presents new evidence on the persistence of fluctuations in real GNP. Two measures of persistence are estimated non-parametrically using post-war quarterly data from Canada, France, Germany, Italy, Japan, the United Kingdom. and the United States. These estimates are compared with Monte Carlo results from various AR(2) processes. For six out of seven countries, the results indicate that a 1 percent shock to output should change the long-run univariate forecast of output by well over I percent. Low-order ARM models for output growth are also estimated, and yield similar conclusions. Finally, the persistence in relative outputs of different countries is examined.

The Term Structure of the Risk–Return Trade-Off

Expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist for long periods. Changes in investment opportunities can alter the risk–return trade-off of bonds, stocks, and cash across investment horizons, thus creating a “term structure” of the risk–return trade-off. This term structure can be extracted from a parsimonious model of return dynamics, as is illustrated with data from the U.S. stock and bond markets. Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. One important implication of time variation in expected returns is that investors, particularly aggressive investors, may want to engage in market-timing (or tactical asset allocation), based on the predictions of their return forecasting model, in order to maximize short-term return. There is considerable uncertainty, however, about the degree of asset return predictability, which makes it hard to identify the optimal market-timing strategy. A second, less obvious implication of asset return predictability is that risk—defined as the conditional variances and covariances per period of asset returns—may be significantly different for different investment horizons, thus creating a “term structure of the risk–return trade-off.” This article characterizes this trade-off and explores its implications for the asset allocation decisions of long-horizon investors. We present an empirical model that captures the complex dynamics of expected returns and risk but is simple to apply. Specifically, we model interest rates and returns as a vector autoregressive (VAR) model. We show how to extract the term structure of risk using this parsimonious model of return dynamics, and we illustrate our approach with the use of quarterly data from the U.S. stock, T-bond, and T-bill markets for the period since World War II. In our empirical application, we use variables that have been identified as return predictors by past empirical research, such as the short-term interest rate, the dividend–price ratio, and the yield spread between long-term and short-term bonds. These variables enable us to capture horizon effects on stock market risk, inflation risk, and real interest rate risk. Among our findings are the following: Mean reversion in stock returns decreases the volatility per period of real stock returns at long horizons, whereas reinvestment risk increases the volatility per period of real T-bill returns. Inflation risk increases the volatility per period of the real return on long-term nominal bonds held to maturity. Stocks and bonds exhibit relatively low positive correlation at both ends of the term structure of risk, but they are highly positively correlated at intermediate investment horizons. Inflation is negatively correlated with the real returns on bonds and stocks at short horizons but positively correlated at long horizons. These patterns have important implications for the efficient mean–variance frontiers that investors face at different horizons and suggest that asset allocation recommendations based on short-term risk and return may not be adequate for long-horizon investors. For example, the composition of the global minimum variance (GMV) portfolio changes dramatically for different horizons. We calculated the GMV portfolio when predictor variables are at their unconditional means—that is, when market conditions are average—and found that at short horizons, the GMV portfolio consists almost exclusively of T-bills but at long horizons, reinvestment risk makes T-bills risky. Thus, long-term investors can achieve lower risk with a portfolio that consists predominantly of long-term bonds and stocks. We also found that the composition of the tangency portfolio of bonds and stocks (calculated under the counterfactual assumption that a riskless long-term asset exists with a return equal to the average T-bill return) becomes increasingly biased toward stocks as the horizon increases. The reason is the increasing positive correlation between stocks and bonds at intermediate investment horizons and the decrease of the volatility per period of stock returns at long horizons. To concentrate on horizon effects, we bypass several other considerations that may be important in practice—for example, changes in volatility through time—and, ignoring the possibility that investors care about other properties of the return distribution, we consider only the first two moments of returns. In addition, our results depend on the particular model of asset returns that we estimated. We treated the parameters of our VAR(1) model as known, whereas these parameters are highly uncertain, and investors should take this uncertainty into account in their portfolio decisions. Fortunately, our main conclusions hold up well when the model is estimated over subsamples or is extended to allow higher-order lags. The technical details of this study are provided in “Long-Horizon Mean–Variance Analysis: User Guide,” which is available in the supplemental material.

A Scorecard for Indexed Government Debt

Within the last five years, Canada, Sweden, and New Zealand have joined the ranks of the United Kingdom and other countries in issuing government bonds that are indexed to inflation. Some observers of the experience in these countries have argued that the United States should follow suit. This paper provides an overview of the issues surrounding debt indexation, and it tries to answer three empirical questions about indexed debt. First, how different would the returns on indexed bonds be from the returns on existing U.S. debt instruments? Second, how would indexed bonds affect the governments average financing costs? Third, how might the Federal Reserve be able to use the information contained in the prices of indexed bonds to help formulate monetary policy? The paper concludes with a more speculative discussion of the possible consequences of increased use of indexed debt contracts by the private sector.

The Dollar and Real Interest Rates

In this paper, we investigate the link between the real foreign exchange value of the dollar and real interest rates since 1979. We argue that it is important to consider the possibility that real exchange rate movements reflect movements of the long-run equilibrium exchange rate as well as real interest differentials. We use a state-space approach to estimate the importance of shifts in the long-run equilibrium exchange rate, the persistence of the ex ante short-term real interest differential, and the effect of this differential on the exchange rate. Using U.S., Canadian, British, German and Japanese data from October 1979 to March 1986, we find that movements in the dollar real exchange rate have been dominated by unanticipated shifts in the expected long-run real exchange rate. Ex ante real interest differentials have not been persistent or variable enough to account for a major part of exchange rate variation. We use Mussas (1984) rational expectations model of the real exchange rate and the current account to interpret our results.