Heterogeneous Beliefs Recovery

We show that, in a continuous time economy with heterogeneous expectations, equilibrium prices entirely reveal the wealth weighted distribution of beliefs among market participants. Specifically, our recovery theorem shows that the paths of the dividend rate, the stock price and the interest rate are enough to pin down the exact distribution of beliefs and its time evolution. Motivated by this novel finding, we develop an efficient methodology to approximate the implied distribution of beliefs given discrete time series of prices and dividends. The accuracy of our method is confirmed on simulated data and we illustrate its results by using daily S&P500 data to construct the distribution of beliefs in the U.S. stock market.