Equity Pricing and Risk Premium under Long-Run Risks and Incomplete Information

Abstract

In this paper we derive a pricing kernel for continuous-time long-run risks economy with the Epstein-Zin utility function, non-i.i.d. consumption growth, and incomplete information about fundamentals. In equilibrium, agents learn about latent conditional mean of consumption growth and price equity simultaneously. We demonstrate our analytical results by applying the model to a well-known complete information equity valuation model. Calibration of the model reveals that it can match price-earnings ratio of the market index, equity premium, and a short term interest rate in the data, which, as we show, we can only achieve for high levels of latent state variable persistence. There is a trade-off between the persistence necessary to fit the data and parameters controlling the inference process. The easier the inference is, the larger persistence is required to fit the data.