Asset pricing theory predicts high expected returns are a compensation for risk. However, high expected returns might also represent anomalies due to frictions or behavioral biases. We propose two complementary tests to assess whether risk alone can explain differences in expected returns, provide general-equilibrium foundations, and study their properties in simulations. The tests account for any risk disliked by risk-averse individuals, including high-order moments and tail risks. The tests do not rely on the validity of a factor model or other parametric statistical models. Empirically, we find risk cannot explain a large majority of differences in expected returns of characteristic-sorted portfolios.

We propose a method to estimate latent asset-pricing factors that incorporates economically motivated targets for both cross-sectional and time-series properties of the factors. Cross-sectional targets may capture the shape of loadings (monotonicity of expected returns across characteristic-sorted portfolios) or the pricing span of exogenous state variables (macroeconomic innovations or intermediary-based risk factors). Time-series targets may capture overall expected returns or mispricing relative to a benchmark reduced-form model. Using a large-scale set of assets, we show that these targets nudge risk factors to better span the pricing kernel, leading to substantially higher Sharpe ratios and lower pricing errors than conventional approaches.

U.S. stocks' response to inflation surprises is, on average, robustly negative. Stocks' response to positive inflation surprises shows much more pronounced time-series variability than their response to negative inflation surprises. In our sample, stocks react significantly to positive inflation surprises only when there is a contemporaneous change in monetary policy expectations. In the cross-section, firms with low net leverage, large market capitalization, high market beta, low book-to-market, and low market power (i.e. low markups) are especially susceptible to inflation surprises.