Conditional risk and the pricing kernel

We propose a statistical methodology for jointly estimating the pricing kernel and conditional physical return densities from option prices. Pricing kernel estimates show that negative stock market returns are significantly more painful to investors in low-volatility periods. Density estimates reflect a significantly positive risk–return trade-off, suggest that Martin’s (2017) lower bound on the equity premium is violated in high-volatility periods, and provide new evidence on the variance premium’s predictive power for excess returns as well as the co-movement between higher return moments. Lastly, we show that leading macrofinance models are at odds with basic features of conditional stock market risks and risk pricing.