A Bayesian Estimate of the Pricing Kernel

The focus of this article is the Pricing Kernel (PK), the building-block of asset pricing theory. In the classical framework the shape of the PK is monotonically decreasing in the stock price, nevertheless empirical evidence suggests that the PK is locally increasing in the interval around the 0% return and has an irregular behaviour in the tails of the distribution. We argue that these deviations, known as pricing kernel puzzle, derive from a dis-homogeneity between the physical and the risk neutral (RN) measure and can be corrected by embedding some forward looking information into the physical measure. Our proposed methodology combines the information from historical returns with that coming from the RN measure through a non-parametric Poisson-Dirichlet process. As a result the irregular behaviour of the PK in the tails of the distribution is reduced and the monotonicity is ensured in almost all cases.