Multiple Priors and Asset Pricing

The asset pricing implications of a statistical model consistent with multiple priors, or beliefs about return distributions, are developed. It is shown that quite generally equilibrium differences in mean returns across priors are to be explained in terms of perceived risk differences between these priors. Advances in filtering theory are employed on time series data to filter all the multiple state conditional components of risks and rewards. It is then observed that excess return differentials across priors are broadly consistent with required risk compensations under these priors, though the sharp hypothesis of zero intercept and unit slope is rejected. The filtered results also deliver numerous other interesting statistics. Here we focus on the construction of long horizon return distributions from data on daily returns using a Markov chain approach to incorporate stochasticity in elementary risk characterizations like volatility, skewness and kurtosis.