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Abstract:
This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962-97 there has been a noticeable increase in firm-level volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, while the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested.

Abstract:
This paper explores the ability of theoretically based asset pricing models such as the CAPM and the consumption CAPM-referred to jointly as the (C)CAPM-to explain the cross-section of average stock returns. Unlike many previous empirical tests of the (C)CAPM, we specify the pricing kernel as a conditional linear factor model, as would be expected if risk premia vary over time. Central to our approach is the use of a conditioning variable which proxies for fluctuations in the log consumption-aggregate wealth ratio and is likely to be important for summarizing conditional expectations of excess returns. We demonstrate that such conditional factor models are able to explain a substantial fraction of the cross-sectional variation in portfolio returns. These models perform much better than unconditional (C)CAPM specifications, and about as well as the three-factor Fama-French model on portfolios sorted by size and book-to-market ratios. This specification of the linear conditional consumption CAPM, using aggregate consumption data, is able to account for the difference in returns between low book-to-market and high book-to-market firms and exhibits little evidence of residual size or book-to-market effects.

Abstract:
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.

Abstract:
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. Empirically, we find a strong correlation between low-frequency movements in macroeconomic volatility and low-frequency movements in the stock market. To model this phenomenon, 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 use these estimates from postwar data to calibrate a rational asset pricing model with regime switches in both the mean and standard deviation of consumption growth. Plausible parameterizations of the model are found to account for a significant portion of the run-up in asset valuation ratios observed in the late 1990s.

G12

Abstract:
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. Empirically, we find a strong correlation between low frequency movements in macroeconomic volatility and low frequency movements in the stock market. To model this phenomenon, 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 use these estimates from post-war data to calibrate a rational asset pricing model with regime switches in both the mean and standard deviation of consumption growth. Plausible parameterizations of the model are found to account for a significant portion of the run-up in asset valuation ratios observed in the late 1990s.

Equity premium, macroeconomic volatility, stock market boom, regime shifts

Abstract:
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. Empirically, we find a strong correlation between low frequency movements in macroeconomic volatility and low frequency movements in the stock market. To model this phenomenon, 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 use these estimates from post-war data to calibrate a rational asset pricing model with regime switches in both the mean and standard deviation of consumption growth. Plausible parameterizations of the model are found to account for a significant portion of the run-up in asset valuation ratios observed in the late 1990s.

Abstract:
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.

Abstract:
This paper studies the role of detrended wealth in predicting stock returns. We call a transitory movement in wealth one that produces a deviation from its shared trend with consumption and labor income. Using U.S. quarterly stock market data, we find that these trend deviations in wealth are strong predictors of both real stock returns and excess returns over a Treasury bill rate. We also find that this variable is a better forecaster of future returns at short and intermediate horizons than is the dividend yield, the earnings yield, the dividend payout ratio, and several other popular forecasting variables. Why should wealth, detrended in this way, forecast asset returns? We show that a wide class of optimal models of consumer behavior imply that the log consumption-aggregate (human and nonhuman) wealth ratio forecasts the expected return on aggregate wealth, or the market portfolio. Although this ratio is not observable, we demonstrate that its important predictive components may be expressed in terms of observable variables, namely in terms of consumption, nonhuman wealth, and labor income. The framework implies that these variables are cointegrated, and that deviations from this shared trend summarize agents' expectations of future returns on the market portfolio.

Abstract:
This paper studies the role of detrended wealth in predicting stock returns. We call a transitory movement in wealth one that produces a deviation from its shared trend with consumption and labor income. Using U.S. quarterly stock market data, we find that these trend deviations in wealth are strong predictors of both real stock returns and excess returns over a Treasury bill rate. We also find that this variable is a better forecaster of future returns at short and intermediate horizons than is the dividend yield, the earnings yield, the dividend payout ratio, and several other popular forecasting variables.

Why should wealth, detrended in this way, forecast asset returns? We show that a wide class of optimal models of consumer behavior imply that the log consumption-aggregate (human and nonhuman) wealth ratio forecasts the expected return on aggregate wealth, or the market portfolio. Although this ratio is not observable, we demonstrate that its important predictive components may be expressed in terms of observable variables, namely in terms of consumption, nonhuman wealth, and labor income. The framework implies that these variables are cointegrated, and that deviations from this shared trend summarize agents' expectations of future returns on the market portfolio.

Abstract:
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 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 "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.

Abstract:
This study examines the out-of-sample predictive power of fluctuations in the aggregate consumption wealth ratio in one-quarter-ahead forecasts of excess stock returns. We find that observations of the aggregate consumption wealth ratio would have consistently improved forecasts of excess stock returns in post-war data relative to a variety of alternative forecasting models. Furthermore, this improvement in out-of-sample predictive is found to be statistically significant according to a variety of statistical tests.

Abstract:
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 adjustedprice 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 thanthe 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.

Abstract:
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 article 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 forecastability 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.

12, 14

Abstract:
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 forecasting relationship of adjusted price ratios and future returns is statistically significant and stable over time. We also show that shifts in the steady-state are responsible for the parameter instability and poor out-of-sample performance of unadjusted price ratios that are found in the data. 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.

Abstract:
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 forecasting relationship of adjusted price ratios and future returns is statistically significant and stable over time. We also show that shifts in the steady-state are responsible for the parameter instability and poor out-of-sample performance of unadjusted price ratios that are found in the data. 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.

return predictability, structural breaks

Abstract:
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 co-vary more with this time-varying price of risk than value stocks, which co-vary 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 out-performance of value (and underperformance of growth) relative to the CAPM.

Value, growth, duration, habit formation

Abstract:
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.

Abstract:
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 much of 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.

Value, Growth, duration, habit formation

Abstract:
Among the most important pieces of empirical evidence against the standard representative agent, consumption-based asset pricing paradigm are the formidable unconditional Euler equation errors the model produces for cross-sections of asset returns. Here we ask whether calibrated leading asset pricing models- specifically developed to address empirical puzzles associated with the standard paradigm- explain the mispricing of the standard consumption-based model when evaluated on cross-sections of asset returns. We find that, in many cases, they do not. We present several results. First, we show that if the true pricing kernel that sets the unconditional Euler equation errors to zero is jointly lognormally distributed with aggregate consumption and returns, such a kernel will not rationalize the magnitude of the pricing errors generated by the standard model, particularly when the curvature of utility is high. Second, we show that leading asset pricing models also do not explain the significant mispricing of the standard paradigm for plausibly calibrated sets of asset returns, even though in those models the pricing kernel, returns, and consumption are not jointly lognormally distributed. Third, in contrast to the above results, we provide one example of a limited participation/incomplete markets model capable of explaining larger pricing errors for the standard model; but we also find many examples of such models, in which the consumption of marginal assetholders behaves quite differently from per capita aggregate consumption, that do not explain the large Euler equation errors of the standard representative agent model.

Abstract:
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 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 log normality that are remarkably similar to those found in the data.

Abstract:
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.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
Among the most important pieces of empirical evidence against the standard representative agent, consumption-based asset pricing paradigm are the formidable unconditional Euler equation errors the model produces for cross-sections of asset returns. Here we ask whether calibrated leading asset pricing models - specifically developed to address empirical puzzles associated with the standard paradigm - explain the mispricing of the standard consumption-based model when evaluated on cross-sections of asset returns. We find that, in many cases, they do not. We present several results. First, we show that if the true pricing kernel that sets the unconditional Euler equation errors to zero is jointly lognormally distributed with aggregate consumption and returns, such a kernel will not rationalize the magnitude of the pricing errors generated by the standard model, particularly when the curvature of utility is high. Second, we show that leading asset pricing models also do not explain the significant mispricing of the standard paradigm for plausibly calibrated sets of asset returns, even though in those models the pricing kernel, returns, and consumption are not jointly lognormally distributed. Third, in contrast to the above results, we provide one example of a limited participation/incomplete markets model capable of explaining larger pricing errors for the standard model; but we also find many examples of such models, in which the consumption of marginal assetholders behaves quite differently from per capita aggregate consumption, that do not explain the large Euler equation errors of the standard representative agent model.

Consumption CAPM and pricing errors

Abstract:
The standard, representative agent, consumption-based asset pricing theory based on CRRA utility fails to explain the average returns of risky assets. This is evident from the large unconditional Euler equation errors, or pricing errors (terms we use interchangeably), that the model generates when evaluated on cross-sections of stock returns. To understand why the standard model fails, we need alternative models that explain its mispricing. We ask whether four alternative models at the vanguard of consumption-based asset pricing theory explain the standard model's large pricing errors. We find that, in each case, the alternative theories counterfactually imply that the standard model generates negligible asset pricing errors when evaluated on empirically plausible cross-sections of stock returns. In contrast to these results, we provide a stylized example of a limited participation/incomplete markets model capable of rationalizing the pricing errors of the standard consumption-based model; but we also find many examples of such models, in which the consumption of marginal assetholders behaves quite differently from per capita aggregate consumption, that do not explain the large Euler equation errors of the standard representative agent model.

Pricing errors, consumption-based asset pricing, CRRA utility

Abstract:
A paper presented at the April 2001 conference "Financial Innovation and Monetary Transmission," sponsored by the Federal Reserve Bank of New York.

monetary policy transmission

Abstract:
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 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 "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.

Abstract:
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 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 "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.

Abstract:
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.

Risk premia, dividend growth, cash-flow predictability, return predictability

Abstract:
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 co-vary 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 haveno 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 co-vary 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.

Abstract:
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.

Abstract:
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 fluctuations in the US stock market, despite the failure of the dividend-price ratio to uncover such variation. In addition, these dividend forecasts are found to co-vary 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 co-vary 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.

Dividend growth, consumption, cointegration

Abstract:
This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962-97 there has been a noticeable increase in firm-level volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, while the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested.

Abstract:
This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962-97 there has been a noticeable increase in firm-level volatility relative to market volatility. Accordingly correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, while the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested.

Abstract:
This paper explores the ability of theoretically based asset pricing models such as the CAPM and the consumption CAPM-referred to jointly as the (C)CAPM - to explain the cross-section of average stock returns. Unlike many previous empirical tests of the (C)CAPM, we specify the pricing kernel as a conditional linear factor model, as would be expected if risk premia vary over time. Central to our approach is the use of a conditioning variable which proxies for fluctuations in the log consumption-aggregate wealth ratio and is likely to be important for summarizing conditional expectations of excess returns. We demonstrate that such conditional factor models are able to explain a substantial fraction of the cross-sectional variation in portfolio returns. These models perform much better than unconditional (C)CAPM specifications, and about as well as the three-factor Fama-French model on portfolios sorted by size and book-to-market ratios. This specification of the linear conditional consumption CAPM, using aggregate consumption data, is able to account for the difference in returns between low book-to-market and high book-to-market firms and exhibits little evidence of residual size or book-to-market effects.

Abstract:
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.

Abstract:
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 forecasting relationships of adjusted price ratios and future returns is statistically significant, stable over time, and present in out-of-sample tests. We also show that shifts in the steady-state are responsible for the parameter instability and poor out-of sample performance of unadjusted price ratios that are found in the data. 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.

Abstract:
This paper uses Hansen and Jagannathan's (1991) volatility bounds to evaluate models with idiosyncratic consumption risk. I show that idiosyncratic risk does not change the volatility bounds at all when consumers have CRRA preferences and the distribution of the idiosyncratic shock is independent of the aggregate state. Following Mankiw (1986), I then show that idiosyncratic risk can help to enter the bounds when idiosyncratic uncertainty depends on the aggregate state of the economy. Since individual consumption data are not reliable, I compute an upper bound of the volatility bounds using individual income data and assume that agents have to consume their endowment. I find that the model does not pass the Hansen and Jagannathan test even for very volatile idiosyncratic income data.

equity premium, incomplete markets, volatility bounds

Abstract:
We study the role of information in asset pricing models with long-run cash flow risk. To illustrate the importance of the information structure, we show how the implications of the long-run risk paradigm for the cross-sectional properties of stock returns and cash flow duration are affected by information. When investors can fully distinguish short- and long-run consumption risk components of dividend growth innovations (full information), only exposure to long-run consumption risk generates significant risk premia, implying that high-return value stocks are long-duration assets, contrary to the historical data. By contrast, when investors observe the change in consumption and dividends each period but not the individual components of that change (limited information), exposure to short-run risk can generate large risk premia, so that high-return value stocks are short-duration assets while low-return growth stocks are long-duration assets, as in the data. We also show that, in order to explain empirical finding that long-horizon equity is less risky than short-horizon equity, the properties of the cash flow model and the values of primitive preference parameters must be quite different from those emphasized in the existing long-run risk literature.

Abstract:
In a recent paper ("A Primer on the Economics and Time Series Econometrics of Wealth Effects," 2001), Davis and Palumbo investigate the empirical relation between three cointegrated variables: aggregate consumption, asset wealth, and labor income. Although cointegration implies that an equilibrium relation ties these variables together in the long run, the authors focus on the following structural question about the short-run dynamics: "How quickly does consumption adjust to changes in income and wealth? Is the adjustment rapid, occurring within a quarter, or more sluggish, taking place over many quarters?" The authors claim that their findings answer this question, and imply that spending adjusts only gradually after gains or losses in income or wealth have been realized. We argue here, however, that a statistical methodology different from that used by Davis and Palumbo is required to address these questions, and that once it has been employed, the resulting empirical evidence weighs considerably against their interpretation of the data.

wealth effect, cointegretion, permanent income

Abstract:
This Paper uses restrictions implied by cointegration to identify the permanent and transitory elements (the 'trend' and 'cycle') of household asset wealth. Our empirical analysis yields answers to the following questions: 1. Is there a large transitory component in household net worth or is wealth close to a random walk? Our point estimates imply that a striking 85% of the post-war variation in the growth of household net worth is transitory, attributable to fluctuations in the stock market component of wealth. Transitory wealth shocks are quite persistent, affecting asset values for a number of years. This transitory element picks out the 'bull markets' of the late 1960s and 1990s, and the 'bear' markets of the 1970s. If markets are efficient, these transitory fluctuations must be attributable to time-variation in the required rate of return on assets (discount rates). 2. How is transitory variation in household net worth related to consumer spending? Does consumption adapt with a lag to permanent movements in wealth? Despite their quantitative importance, transitory fluctuations in asset values are found to be unrelated to aggregate consumer spending. Instead, aggregate consumption can be well described as a function of the trend components in wealth and income. We find no evidence that consumption adapts with a long lag to fluctuations in wealth. 3. What kinds of shocks govern the dynamic behaviour of consumption, asset wealth and labour income? We characterize three: a permanent income shock that affects consumption, asset wealth and labour earnings without distorting their long-run equilibrium relation; an income redistributive shock that shifts the composition of income between labour and capital; and a discount rate shock that generates transitory variation in asset values.

Wealth effect, cointegration, consumption, asset values

Abstract:
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.

Abstract:
Are excess stock market returns predictable over time and, if so, at what horizons and with which economic indicators? Can stock return predictability be explained by changes in stock market volatility? How does the mean return per unit risk change over time? This chapter reviews what is known about the time-series evolution of the risk-return tradeoff for stock market investment, and presents some new empirical evidence using a proxy for the log consumption-aggregate wealth ratio as a predictor of both the mean and volatility of excess stock market returns. We characterize the risk-return tradeoff as the conditional expected excess return on a broad stock market index divided by its conditional standard deviation, a quantity commonly known as the Sharpe ratio. Our own investigation suggests that variation in the equity risk-premium is strongly negatively linked to variation in market volatility, at odds with leading asset pricing models. Since the conditional volatility and conditional mean move in opposite directions, the degree of countercyclicality in the Sharpe ratio that we document here is far more dramatic than that produced by existing equilibrium models of financial market behaviour, which completely miss the sheer magnitude of variation in the price of stock market risk.

Sharpe ratio, expected returns, volatility, consumption

Abstract:
We study the role of information in asset pricing models with long-run cash flow risk. To illustrate the importance of the information structure, we show how the implications of the long run risk paradigm for the cross-sectional properties of stock returns and cash flow duration are affected by information. When investors can fully distinguish short- and long-run consumption risk components of dividend growth innovations (full information), only exposure to long-run consumption risk generates significant risk premia, implying that high return value stocks are long-duration assets, contrary to the historical data. By contrast, when investors observe the change in consumption and dividends each period but not the individual components of that change (limited information), exposure to short-run risk can generate large risk premia, so that high-return value stocks are short-duration assets while low-return growth stocks are long-duration assets, as in the data. We also show that, in order to explain empirical finding that long-horizon equity is less risky than short-horizon equity, the properties of the cash flow model and the values of primitive preference parameters must be quite different from those emphasized in the existing long-run risk literature.

Abstract:
Evidence suggests that expected excess stock market returns vary over time, and that this variation is much larger than that of expected real interest rates. It follows that a large fraction of the movement in the cost of capital in standard investment models must be attributable to movements in equity risk premia. In this Paper we emphasise that such movements in equity risk premia should have implications not merely for investment today, but also for future investment over long horizons. In this case, predictive variables for excess stock returns over long-horizons are also likely to forecast long-horizon fluctuations in the growth of marginal Q, and therefore investment. We test this implication directly by performing long-horizon forecasting regressions of aggregate investment growth using a variety of predictive variables shown elsewhere to have forecasting power for excess stock market returns.

Q-Theory, investment, risk premia

Abstract:
Evidence of stock return predictability by financial ratios is still controversial as documented by inconsistent results for in-sample and out-of-sample regressions as well as 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 forecasting relationship of adjusted price ratios and future returns is statistically significant, stable over time and present in out-of-sample tests. We also show that shifts in the steady state are responsible for parameter instability and poor out-of-sample performance of unadjusted price ratios that is found in the data. 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.

Predictibility, Stock returns, dividend price ratio, price ratios, out-of-sample test

Abstract:
We study the role of information in asset pricing models with long-run cash flow risk. To illustrate the importance of the information structure, we show how the implications of the long-run risk paradigm for the cross-sectional properties of stock returns and cash flow duration are affected by information. When investors can fully distinguish short- and long-run consumption risk components of dividend growth innovations (full information), only exposure to long-run consumption risk generates significant risk premia, implying that high-return value stocks are long-duration assets, contrary to the historical data. By contrast, when investors observe the change in consumption and dividends each period but not the individual components of that change (limited information), exposure to short-run risk can generate large risk premia, so that high-return value stocks are short-duration assets while low-return growth stocks are long-duration assets, as in the data. We also show that, in order to explain empirical finding that long-horizon equity is less risky than short-horizon equity, the properties of the cash flow model and the values of primitive preference parameters must be quite different from those emphasized in the existing long-run risk literature.

Abstract:
This paper proposes a dynamic risk-based model capable of jointly explaining the term structure of interest rates, returns on the aggregate market and the risk and return characteristics of value and growth stocks. Both the term structure of interest rates and returns on value and growth stocks convey information about how the representative investor values cash flows of different maturities. We model how the representative investor perceives risks of these cash flows by specifying a parsimonious stochastic discount factor for the economy. Shocks to dividend growth, the real interest rate, and expected inflation are priced, but shocks to the price of risk are not. Given reasonable assumptions for dividends and inflation, we show that the model can simultaneously account for the behavior of aggregate stock returns, an upward-sloping yield curve, the failure of the expectations hypothesis and the poor performance of the capital asset pricing model.

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Abstract:
Dynamic models in which agents' behaviour depends on expectations of future prices or other endogenous variables can have steady states that are stationary equilibria for a wide variety of expectations rules, including rational expectations. When there are multiple steady states, stability is a criterion for selecting predictions of long-run outcomes among them. The purpose of this Paper is to study how sensitive stability is to certain details of the expectations rules, in a simple OLG model with constant government debt that is financed through seigniorage. We compare simple recursive learning rules, learning rules with vanishing gain, and OLS learning, and also relate these to expectational stability. One finding is that two adaptive expectation rules that differ only in whether they use current information can have opposite stability properties.

Inflation, adaptive expectations, stability

Abstract:
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 forecasting relationship of adjusted price ratios and future returns is statistically significant, stable over time, and present in out-of-sample tests. We also show that shifts in the steady-state are responsible for theparameter instability and poor out-of-sample performance of unadjusted price ratios thatare found in the data. 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.

Abstract:
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 forecasting relationship of adjusted price ratios and future returns is statistically significant, stable over time, and present in out-of-sample tests. We also show that shifts in the steady-state are responsible for theparameter instability and poor out-of-sample performance of unadjusted price ratios thatare found in the data. 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.

Abstract:
We derive closed-form solutions for asset prices in an RBC economy. The equations are based on a log-linear solution of the RBC model and allow a clearer understanding of the determination of risk premia in models with production. We demonstrate not only why the premium of equity over the risk-free rate is small but also why the premium of equity over a real long-term bond is small and often negative. In particular, risk premia for equity and long real bonds are negative when technology shocks are permanent.

Abstract:
This paper explores the ability of conditional versions of the CAPM and the consumption CAPM - jointly the (C)CAPM - to explain the cross section of average stock returns. Central to our approach is the use of the log consumption-wealth ratio as a conditioning variable. We demonstrate that such conditional models perform far better than unconditional specifications and about as well as the Fama-French three-factor model on portfolios sorted by size and book-to-market characteristics. The conditional consumption CAPM can account for the difference in returns between low-book-to-market and high-book-to-market portfolios and exhibits little evidence of residual size or book-to-market effects.

Abstract:
This paper estimates the parameters of a stochastic growth model with asset market and contrasts the model's moments with moments of the actual data. We solve the model through log-linearization along the line of Campbell (1994) [Journal of Monetary Economics 33(3), 463] and estimate the model without and with asset pricing restrictions. As asset pricing restrictions we employ the riskfree interest rate and the Sharpe-ratio. To estimate the parameters we employ, as in Semmler and Gong (1996a) [Journal of Economics Behavior and Organization 30, 301], a ML estimation. The estimation is conducted through the simulated annealing. We introduce a diagnostic procedure which is closely related to Watson (1993) [Journal of Political Economy 101(6), 1011] and Diebold et al. (1995) [Technical Working Paper No. 174, National Burea of Economic Research] to test whether the second moments of the actual macroeconomic time series data are matched by the model's time series. Several models are explored. The overall results are that sensible parameter estimates may be obtained when the actual and computed riskfree rate is included in the moments to be matched. The attempt, however, to include the Sharpe-ratio as restriction in the estimation does not produce sensible estimates. The paper thus shows, by employing statistical estimation techniques, that the baseline real business cycle (RBC) model is not likely to give correct predictions on asset market pricing when parameters are estimated from actual time series data.

JEL Classification: C13; C15; C61; E32; G1; G12

Keyword(s): Stochastic growth model, Sharpe-ratio, Maximum likelihood

Abstract:
This paper studies portfolio decisions of boundedly rational agents in a financial market. Learning is modelled via a genetic algorithm. Learning as modelled in this paper leads agents to hold too much risk as compared to the optimal portfolio of rational investors. Moreover, learning agent exhibit an asymmetric response after positve and negative returns where the portfolio adjustment is more pronounced after negative returns. It is demonstrated that investors in mutual funds show the same investment patterns as the learning agents in the model. A steady-state version of the model is able to match the mutual fund data closely.

Abstract:
In this paper, we derive closed-form solutions for a variety of prices for financial assets in an RBC economy. The equations are based on a loglinear solution of the RBC model and allow a clearer understanding of the determination of risk premia in models with production, e.g., we show that risk premia of long real bonds and equity are negative when technology shocks are permanent. Moreover, the wedge between the equity premium and the long bond premium is small and often negative. The closed-form solutions presented here are applicable to any RBC model that can be approximated in loglinear form.

Abstract:
Many asset pricing puzzles can be explained when habit formation is added to standard preferences. We show that utility functions with a habit then gives rise to a puzzle of consumption volatility in place of the asset pricing puzzles when agents can choose consumption and labor optimally in response to more fundamental shocks. We show that the consumption reaction to technology shocks are too small by an order of magnitude when a utility includes a habit. Alternative models with consistent and exogenous but stochastic labor input are considered. A model with persistent technology shocks and stochastic labor is shown to be potentially consistent with substantial consumption variability as well as procyclical labor input and labor productivity even when a habit is present.

Abstract:
This paper evaluates models with idiosyncratic consumption risk using Hansen and Jagannathan's (1991) volatility bounds. It is shown that idiosyncratic risk does not change the volatility bounds at all when consumers have constant relative risk aversion (CRRA) preferences and the distribution of the idiosyncratic shock is independent of the aggregate state. Following Mankiw (1986), I show that idiosyncratic risk can help to enter the bounds when idiosyncratic uncertainty depends on the aggregate state of the economy. Since individual consumption data is not reliable, I compute an upper bound of the volatility bounds using individual income data and assume that agents must consume their endowment. I find that the model does not pass the Hansen and Jagannathan test even for very volatile idiosyncratic income data.

Abstract:
Risk premia in the consumption capital asset pricing model depend on preferences and dividends. We develop a decomposition which allows for the separate treatment of both components. We show that preferences alone determine the risk-return trade-off measured by the Sharpe-ratio.