We show that investors price short-term stock market outcomes very different from outcomes that occur further into the future. To this end, we introduce the expected forward pricing kernel and decompose long-term pricing kernels into short-term and expected forward pricing kernels. Using index options, we find that kernels with maturities of up to 12 months are U-shaped and show that this results from the shape of the 1-month pricing kernel. Once we remove the impact of the 1-month kernel, the expected forward kernels are in line with standard long-run risk models in terms of their shape, level, and time-series variation.

This paper shows that belief differences have strong effects on asset prices in consumption-based asset-pricing models with long-run risks. Belief heterogeneity leads to time-varying consumption and wealth shares of the agents. This time variation can resolve several asset-pricing puzzles, including the large countercyclical variation of expected risk premia, the volatility of the price-dividend ratio, the predictability of cash flows and returns, and the large predictability of returns in recessions. These findings show that belief differences, a widely observed attribute of investors, significantly improve the explanatory power of long-run risk asset-pricing models.

Modern asset pricing models combine recursive preferences with complex dynamics for the underlying consumption process. The existence of solutions is for many of these models an unsettled question. This paper introduces a novel technique to prove existence and nonexistence, as well as uniqueness for models with recursive preferences. The approach applies to many models of interest, including those with long-run consumption risks, with stochastic volatility and jumps, with time-varying consumption disasters, and with smooth ambiguity aversion and learning. Collectively, the proven results settle the existence question for many of today’s leading asset pricing models.

We build a novel data set of time-stamped corporate decarbonization commitments—green pledges—for U.S. public firms by classifying news articles with large language models and human validation. Firms announcing green pledges tend to be larger and browner than other firms, both within and across industries. Green pledges significantly raise stock prices, consistent with a reduction in the carbon premium, and predict sizable declines in future carbon emissions and emission intensities. These effects tend to be strongest for firms in brown industries. Green pledges thus appear credible, convey relevant new information to investors, and provide meaningful financial incentives to decarbonize.

This paper shows that the latest generation of asset pricing models with long‐run risk exhibit economically significant nonlinearities, and thus the ubiquitous Campbell‐Shiller log‐linearization can generate large numerical errors. These errors translate in turn to considerable errors in the model predictions, for example, for the magnitude of the equity premium or return predictability. We demonstrate that these nonlinearities arise from the presence of multiple highly persistent processes, which cause the exogenous states to attain values far away from their long‐run means with nonnegligible probability. These extreme values have a significant impact on asset price dynamics.