Why is Long-Horizon Equity Less Risky? A Duration-Based Explanation of the Value Premium

This paper proposes a dynamic risk-based model that captures the high expected returns on value stocks relative to growth stocks, and the failure of the capital asset pricing model to explain these expected returns. To model the difference between value and growth stocks, we introduce a cross-section of long-lived firms distinguished by the timing of their cash flows. Firms with cash flows weighted more to the future have high price ratios, while firms with cash flows weighted more to the present have low price ratios. We model how investors perceive the risks of these cash flows by specifying a stochastic discount factor for the economy. The stochastic discount factor implies that shocks to aggregate dividends are priced, but that shocks to the time-varying price of risk are not. As long-horizon equity, growth stocks covary more with this time-varying price of risk than value stocks, which covary more with shocks to cash flows. When the model is calibrated to explain aggregate stock market behavior, we find that it can also account for the observed value premium, the high Sharpe ratios on value stocks relative to growth stocks, and the outperformance of value (and underperformance of growth) relative to the CAPM.

Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption

Both textbook economics and common sense teach us that the value of household wealth should be related to consumer spending. At the same time, movements in asset values often seem disassociated with important movements in consumer spending, as episodes such as the 1987 stock market crash and the contraction in equity values that occurred in the fall of 1998 suggest. An important first step in understanding the consumption-wealth linkage is determining how closely the two variables are actually correlated, and whether there exist important movements in asset values that are not associated with changes in consumption. This paper provides evidence that a surprisingly small fraction of the variation in household net worth is related to variation in aggregate consumer spending. We use empirical techniques that allow us to quantify the relative importance of permanent and transitory innovations in the variation of consumer spending and wealth and find that transitory shocks dominate post-war variation in wealth, while permanent shocks dominate variation in aggregate consumption. Although transitory innovations are found to have little influence on consumer spending, they have long-lasting effects on wealth , exhibiting a half-life of a little over two years. The findings suggest that most macro models which make no allowance for transitory variation in wealth that is orthogonal to consumption are likely to misstate both the timing and magnitude of the consumption-wealth linkage.

Expected Returns and Expected Dividend Growth

We investigate a consumption-based present value relation that is a function of future dividend growth. Using data on aggregate consumption and measures of the dividend payments from aggregate wealth, we show that changing forecasts of dividend growth make an important contribution to fluctuations in the U.S. stock market, despite the failure of the dividend-price ratio to uncover such variation. In addition, these dividend forecasts are found to covary with changing forecasts of excess stock returns. The variation in expected dividend growth we uncover is positively correlated with changing forecasts of excess returns and occurs at business cycle frequencies, those ranging from one to six years. Because positively correlated fluctuations in expected dividend growth and expected returns have offsetting affects on the log dividend-price ratio, the results imply that both the market risk-premium and expected dividend growth vary considerably more than what can be revealed using the log dividend-price ratio alone as a predictive variable.

Euler Equation Errors

The standard, representative agent, consumption-based asset pricing theory based on CRRA utility fails to explain the average returns of risky assets. When evaluated on cross- sections of stock returns, the model generates economically large unconditional Euler equation errors. Unlike the equity premium puzzle, these large Euler equation errors cannot be resolved with high values of risk aversion. To explain why the standard model fails, we need to develop alternative models that can rationalize its large pricing errors. We evaluate whether four newer theories at the vanguard of consumption-based asset pricing can explain the large Euler equation errors of the standard consumption-based model. In each case, we find that the alternative theory counterfactually implies that the standard model has negligible Euler equation errors. We show that the models miss on this dimension because they mischaracterize the joint behavior of consumption and asset returns in recessions, when aggregate consumption is falling. By contrast, a simple model in which aggregate consumption growth and stockholder consumption growth are highly correlated most of the time, but have low or negative correlation in severe recessions, produces violations of the standard model's Euler equations and departures from joint lognormality that are remarkably similar to those found in the data.

The Declining Equity Premium: What Role Does Macroeconomic Risk Play?

Aggregate stock prices, relative to virtually any indicator of fundamental value, soared to unprecedented levels in the 1990s. Even today, after the market declines since 2000, they remain well above historical norms. Why? We consider one particular explanation: a fall in macroeconomic risk, or the volatility of the aggregate economy. We estimate a two-state regime switching model for the volatility and mean of consumption growth, and find evidence of a shift to substantially lower consumption volatility at the beginning of the 1990s. We then show that there is a strong and statistically robust correlation between low macroeconomic volatility and high asset prices: the estimated posterior probability of being in a low volatility state explains 30 to 60 percent of the post-war variation in the log price-dividend ratio, depending on the measure of consumption analyzed. Next, we study a rational asset pricing model with regime switches in both the mean and standard deviation of consumption growth, where the probabilities of a regime change are calibrated to match estimates from post-war data. Plausible parameterizations of the model are found to account for a significant fraction of the run-up in asset valuation ratios observed in the late 1990s.Equity Premium, Macro Volatility

Dispersion and Volatility in Stock Returns: An Empirical Investigation

This paper studies three different measures of monthly stock market volatility: the time-series volatility of daily market returns within the month; the cross-sectional volatility or 'dispersion' of daily returns on industry portfolios, relative to the market, within the month; and the dispersion of daily returns on individual firms, relative to their industries, within the month. Over the period 1962-97 there has been a noticeable increase in firm-level volatility relative to market volatility. All the volatility measures move together in a countercyclical fashion. While market volatility tends to lead the other volatility series, industry-level volatility is a particularly important leading indicator for the business cycle.

Investor Information, Long-Run Risk, and the Term Structure of Equity

We study the role of information in asset pricing models with long-run cash flow risk. When investors can distinguish short- from long-run consumption risks (full information), the model generates a sizable equity risk premium only if the equity term structure slopes up, contrary to the data. In general, the short- and long-run components are unidentified. We propose a sparsity-based bounded rationality model of long-run risk that is both parsimonious and fully identified from historical data. In contrast to full information, the model generates a sizable market risk premium simultaneously with a downward sloping equity term structure, as in the data.

Expected Returns and Expected Dividend Growth

We investigate a consumption-based present value relation that is a function of future dividend growth. Using data on aggregate consumption and measures of the dividend payments from aggregate wealth, we show that changing forecasts of dividend growth are an important feature of the post-war U.S. stock market, despite the failure of the dividend-price ratio to uncover such variation. In addition, these dividend forecasts are found to covary with changing forecasts of excess stock returns. The variation in expected dividend growth we uncover is positively correlated with changing forecasts of excess returns and occurs at business cycle frequencies, those ranging from one to six years. This covariation is important because positively correlated fluctuations in expected dividend growth and expected returns have offsetting affects on the log dividend-price ratio. The results therefore imply that both the market risk-premium and expected dividend growth vary considerably more than what can be revealed using the log dividend-price ratio alone as a predictive variable

Reconciling the Return Predictability Evidence

Evidence of stock return predictability by financial ratios is still controversial, as documented by inconsistent results for in-sample and out-of-sample regressions and by substantial parameter instability. This paper shows that these seemingly incompatible results can be reconciled if the assumption of a fixed steady-state mean of the economy is relaxed. We find strong empirical evidence in support of shifts in the steady-state and propose simple methods to adjust financial ratios for such shifts. The in-sample forecasting relationship of adjusted price ratios and future returns is statistically significant and stable over time. In real-time,however, changes in the steady-state make the in-sample return forecast ability hard to exploit out-of-sample. The uncertainty of estimating the size of steady-state shifts rather than the estimation of their dates is responsible for the difficulty of forecasting stock returns in real-time. Our conclusions hold for a variety of financial ratios and are robust to changes in the econometric technique used to estimate shifts in the steady-state

Expected Returns and Expected Dividend Growth

We develop a consumption-based present value relation that is a function of future dividend growth. Using data on aggregate consumption and measures of the dividend payments from aggregate wealth, we show that changing forecasts of dividend growth make an important contribution to fluctuation's in the U.S. stock market, despite the failure of the dividend price ratio to uncover such variation. In addition, these dividend forecasts are found to covary with changing forecasts of excess stock returns. The variation in expected dividend growth we uncover is positively correlated with business cycle variation in expected returns, and the results suggest that a substantial fraction of the variation in expected dividend growth is common to variation in expected excess returns. Movements in expected dividend growth that are entirely common to movements in expected returns have no effect on the log dividend-price ratio. An implication of these findings is that the log dividend-price ratio will have difficulty predicting both dividend growth and excess returns at business cycle frequencies. Such a failure of predictive power is not an indication that risk-premia are constant, however. On the contrary, the results presented here imply that the log dividend-price ratio will have difficulty revealing business cycle variation in both the equity risk-premium and expected dividend growth precisely because expected returns fluctuate at those frequencies, and covary with changing forecasts of dividend growth. The findings imply that both the market risk premium and expected dividend growth vary considerably more than what can be revealed using the log dividend-price ratio alone as a predictive variable