This paper investigates Euler equations involving security prices and household‐level consumption data. It provides a useful complement to many existing studies of consumption‐based asset pricing models that use a representative‐agent framework, because the Euler equations under investigation hold even if markets are incomplete. It also provides a useful complement to simulation‐based studies of market incompleteness. The empirical evidence indicates that the theory is rejected by the data along several dimensions. The results therefore indicate that some well‐documented asset‐pricing puzzles do not result from aggregation problems for the preferences under investigation.

This paper investigates Euler equations involving security prices and household‐level consumption data. It provides a useful complement to many existing studies of consumption‐based asset pricing models that use a representative‐agent framework, because the Euler equations under investigation hold even if markets are incomplete. It also provides a useful complement to simulation‐based studies of market incompleteness. The empirical evidence indicates that the theory is rejected by the data along several dimensions. The results therefore indicate that some well‐documented asset‐pricing puzzles do not result from aggregation problems for the preferences under investigation.

This paper investigates the importance of idiosyncratic consumption risk for the cross‐sectional variation in asset returns. We find that besides the rate of aggregate consumption growth, the cross‐sectional variance of consumption growth is also a priced factor. This suggests that consumers are not fully insured against idiosyncratic consumption risk, and that asset returns reflect their attempts to reduce their exposure to this risk. The resulting two‐factor consumption‐based asset pricing model significantly outperforms the CAPM, and its performance compares favorably with that of the Fama–French three‐factor model.

We propose a novel factor model for option returns. Option exposures are estimated nonparametrically, and factor risk premia can vary nonlinearly with states. The model is estimated using regressions with minimal assumptions on factor and option return dynamics. We estimate the model using index options to characterize the conditional risk premia for factors of interest, such as the market return, market variance, tail and intermediary risk factors, higher moments, and the VIX term structure slope. Together, market return and variance explain more than 90% of option return variation. Unconditionally, the magnitude of the variance risk premium is plausible. It displays pronounced time variation, spikes during crises, and always has the expected sign.

Building on theoretical asset pricing literature, we examine the role of market risk and the size, book‐to‐market (BTM), and volatility anomalies in the cross‐section of unlevered equity returns. Compared with levered (stock) returns, unlevered market beta plays a more important role in explaining the cross‐section of unlevered equity returns, even after controlling for size and BTM. The size effect is weakened, while the value premium and the volatility puzzle virtually disappear for unlevered returns. We show that leverage induces heteroskedasticity in returns. Unlevering returns removes this pattern, which is otherwise difficult to address by controlling for leverage in regressions.