Abstract We characterize and measure a long-run risk return tradeoff for the valuation of cash flows exposed to fluctuations in macroeconomic growth. This tradeoff features the risk prices of cash flows that are realized far into the future but are reflected in asset values. We apply this analysis to a claims on aggregate cash flows, as well as to the cash flows from value and growth portfolios. Based on vector autoregressions, we characterize the dynamic response of cash flows to macroeconomic shocks and document that there are important differences in the long-run responses. We isolate those features of a recursive utility model and the consumption dynamics needed for the long run valuation differences among these portfolios to be sizable. Finally, we show how the resulting measurements vary when we alter the statistical specifications of cash flows and consumption growth.

Motivated by the implications from a stylized self-contained general equilibrium model incorporating the effects of time-varying economic uncertainty, we show that the difference between implied and realized variation, or the variance risk premium, is able to explain a non-trivial fraction of the time series variation in post 1990 aggregate stock market returns, with high (low) premia predicting high (low) future returns. Our empirical results depend crucially on the use of “model-free, ” as opposed to Black-Scholes, options implied volatilities, along with accurate realized variation measures constructed from high-frequency intraday, as opposed to daily, data. The magnitude of the predictability is particularly striking at the intermediate quarterly return horizon, where it easily dominates that afforded by other popular predictor variables, like the P/E ratio, the default spread, and the consumption-wealth ratio (CAY).

Not necessarily. The fundamental value of a firm increases with uncertainty about average future profitability, and this uncertainty was unusually high in the late 1990s. We calibrate a stock valuation model that includes this uncertainty, and compute the level of uncertainty that is needed to match the observed Nasdaq valuations at their peak. This uncertainty seems plausible because it matches not only the high level but also the high volatility of Nasdaq stock prices. We also show that uncertainty about average profitability has the biggest effect on stock prices when the equity premium is low.

Existing empirical literature on the risk-return relation uses a relatively small amount of conditioning information to model the conditional mean and conditional volatility of excess stock market returns. We use dynamic factor analysis for large datasets to summarize a large amount of economic information by few estimated factors, and find that three new factors- termed “volatility,” “risk premium,” and “real” factors- contain important information about one-quarter-ahead excess returns and volatility not contained in commonly used predictor variables. Our specifications predict 16-20 % of the one-quarter-ahead variation in excess stock market returns, and exhibit stable and statistically significant out-of-sample forecasting power. We also find a positive conditional risk-return correlation.

Evidence of stock-return predictability by financial ratios is still controversial, as docu-mented by inconsistent results for in-sample and out-of-sample regressions and by substan-tial 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. (JEL 12, 14) 1.

Uncertainty plays a key role in economics, finance, and decision sciences. Financial markets, in particular derivative markets, provide fertile ground for understanding how perceptions of economic uncertainty and cashflow risk manifest themselves in asset prices. We demonstrate that the variance premium, defined as the difference between the squared VIX index and expected realized variance, captures attitudes toward uncertainty. We show conditions under which the variance premium displays significant time variation and return predictability. A calibrated, generalized Long-Run Risks model generates a variance premium with time variation and return predictability that is consistent with the data, while simultaneously matching the levels and volatilities of the market return and risk free rate. Our evidence indicates an important role for transient non-Gaussian shocks to fundamentals that affect agents ’ views of economic uncertainty and prices. We thank seminar participants at Wharton, the CREATES workshop ‘New Hope for the C-CAPM?’,

We study the economic sources of stock–bond return comovements and their time variation using a dynamic factor model. We identify the economic factors employing a semistruc-tural regime-switching model for state variables such as interest rates, inflation, the output gap, and cash flow growth. We also view risk aversion, uncertainty about inflation and output, and liquidity proxies as additional potential factors. We find that macroeconomic fundamentals contribute little to explaining stock and bond return correlations but that other factors, especially liquidity proxies, play a more important role. The macro factors are still important in fitting bond return volatility, whereas the “variance premium ” is criti-cal in explaining stock return volatility. However, the factor model primarily fails in fitting covariances. (JEL G11, G12, G14, E43, E44) Stock and bond returns in the United States display an average correlation of about 19 % during the post-1968 period. Shiller and Beltratti (1992) un-derestimate the empirical correlation using a present value with constant dis-count rates, whereas Bekaert, Engstrom, and Grenadier (2005) overestimate it in a consumption-based asset pricing model with stochastic risk aversion. Yet,

A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date-stamping the origination and collapse of economic exuberance, and providing valid confidence intervals for explosive growth rates. The method involves the recursive implementation of a right-side unit root test and a sup test, both of which are easy to use in practical applications, and some new limit theory for mildly explosive processes. The test procedure is shown to have discriminatory power in detecting periodically collapsing bubbles, thereby overcoming a weakness in earlier applications of unit root tests for economic bubbles. An empirical application to Nasdaq stock price index in the 1990s provides confirmation of explosiveness and date-stamps the origination of financial exuberance to mid-1995, prior to the famous remark in December 1996 by Alan Greenspan about irrational exuberance in financial

Brandt, Cochrane, and Santa-Clara (2004) pointed out that the implicit stochastic discount factors computed using prices, on the one hand, and con-sumption growth, on the other hand, have very different implications for their cross country correlation. They leave this as an unresolved puzzle. We ex-plain it by combining Epstein and Zin (1989) preferences with a model of predictable returns and by positing a very correlated long run component. We also assume that the intertemporal elasticity of substitution is larger than one. This setup brings the stochastic discount factors computed using prices and quantities close together, by keeping the volatility of the depreciation rate in the order of 12 % and the cross country correlation of consumption growth around 30%.

We provide a user’s guide to “exotic ” preferences: nonlinear time aggregators, departures from expected utility, preferences over time with known and unknown probabilities, risksensitive and robust control, “hyperbolic ” discounting, and preferences over sets (“temptations”). We apply each to a number of classic problems in macroeconomics and finance, including consumption and saving, portfolio choice, asset pricing, and Pareto optimal allocations.