We empirically analyze the pricing of political uncertainty, guided by a the-oretical model of government policy choice. To isolate political uncertainty, we exploit its variation around major political events, namely, national elections and global summits. We find that political uncertainty is priced in the equity option market in ways predicted by the theory. Options whose lives span political events tend to be more expensive. Such options provide valuable protection against the risk associated with political events, including not only price risk but also vari-ance and tail risks. This protection is more valuable in a weaker economy as well as amid higher political uncertainty.

We propose two performance measures for asset pricing models and apply them to representative agent models with recursive preferences, habits, and jumps. The measures describe the pricing kernel’s dispersion (the entropy of the title) and dynamics (horizon dependence, a measure of how entropy varies over different time horizons). We show how each model generates entropy and horizon dependence, and compare their magnitudes to estimates derived from asset returns. This exercise — and transparent loglinear approximations — clarify the mechanisms underlying these models. It also reveals, in some cases, tension between entropy, which should be large enough to account for observed excess returns, and horizon dependence, which should be small enough to account for mean yield spreads.

This paper studies the asset pricing implications of Bayesian learning about the parameters, states, and models determining aggregate consumption dynamics. Our approach is empirical and focuses on the quantitative implications of learning in real-time using post World War II consumption data. We characterize this learning process and provide empirical evidence that revisions in beliefs stemming from parameter and model uncertainty are signi…cantly related to realized aggregate equity returns. Further, we show that beliefs regarding the conditional moments of consumption growth are strongly time-varying and exhibit business cycle and/or long-run ‡uctuations. Much of the long-run behavior is unanticipated ex ante. We embed these subjective beliefs in a general equilibrium model and …nd that about half of the post World-War II observed equity market risk premium and much of the observed return predictability are due to unexpected revisions in beliefs about parameters and models governing consumption dynamics.

Abstract Standard macroeconomic models imply that credit spreads directly re ‡ect expected losses (the probability of default and the loss in the event of default). In contrast, in the data credit spreads are signi…cantly larger than expected losses, suggestive of an aggregate risk premium. Building on the idea that corporate debt, while safe in normal times, is exposed to economic depressions, this paper embeds a trade-o¤ theory of capital structure into a real business cycle model with a small, time-varying risk of economic disaster. The model replicates the level, volatility and cyclicality of credit spreads, and variation in the corporate bond premium ampli…es macroeconomic ‡uctuations in investment, employment and GDP. JEL: E32, E44, G12.

Abstract Theory suggests that the risk of infrequent yet extreme events has a large impact on asset prices. Testing models of this hypothesis remains a challenge due to the difficulty of measuring tail risk fluctuations over time. I propose a new measure of time-varying tail risk that is motivated by asset pricing theory and is directly estimable from the cross section of returns. My procedure applies

We present evidence that shocks to household consumption growth are negatively skewed, persistent, and countercyclical and play a major role in driving asset prices. We construct a parsimonious model with one state variable that drives the conditional cross-sectional moments of household consumption growth. The estimated model provides a good fit for the moments of the cross-sectional distribution of household consumption growth and the unconditional moments of the risk free rate, equity premium, market price-dividend ratio, and aggregate dividend and consumption growth. The explanatory power of the model does not derive from possible predictability of aggregate dividend and consumption growth as these are intentionally modeled as i.i.d. processes. Consistent with empirical evidence, the model implies that the risk free rate and price-dividend ratio are pro-cyclical while the expected market return and the variance of the market return and risk free rate are countercyclical. Household consumption risk also explains the cross-section of excess returns.

Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

a b s t r a c t In this paper, we develop lower bounds on the variance of the permanent component and the transitory component, and on the variance of the ratio of the permanent to the transitory components of SDFs. Exactly solved eigenfunction problems are then used to study the empirical attributes of asset pricing models that incorporate long-run risk, external habit persistence, and rare disasters. Specific quantitative implications are developed for the variance of the permanent and the transitory components, the return behavior of the long-term bond, and the comovement between the transitory and the permanent components of SDFs. Published by Elsevier B.V.

The average investor in the variance swap market is indifferent to news about future variance at horizons ranging from 1 month to 14 years. It is only purely transitory and unexpected realized variance that is priced. These results present a challenge to most structural models of the variance risk premium, such as the intertemporal CAPM, recent models with Epstein–Zin preferences and long-run risks, and models where institutional investors have value-at-risk constraints. The results also have strong implications for macro models where volatility affects investment decisions, suggesting that investors are not willing to pay to hedge shocks in expected economic uncertainty. 1

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