Does the pricing kernel anomaly reflect forward looking beliefs?

We propose a nonparametric Bayesian approach for the estimation of the pricing kernel. Historical stock returns and option market data are combined through the Dirichlet Process (DP) to construct an option-adjusted physical measure. The precision parameter of the DP process is calibrated to the amount of trading activity in deep-out-of-the-money options. We use the option-adjusted physical measure to construct an option-adjusted pricing kernel. An empirical investigation on the S&P 500 Index from 2002 to 2015 shows that the option-adjusted pricing kernel is consistently monotonically decreasing, regardless of the level of volatility, thus providing an explanation to the well known U-shaped pricing kernel puzzle