Learning from Prices: Information Aggregation and Accumulation in an Asset Price Model

Can prices convey information about the fundamental value of an asset? This paper considers this problem in relation to the dynamic properties of the fundamental (whether it is constant or time-varying) and the structure of information available to agents. Risk averse traders receive two potential signals each period: one exogenous and private and the other, prices, endogenous and public. Prices aggregate private information, but include aggregate noise. Information can accumulate over time both through endogenous and exogenous signals. With a constant fundamental, the precision of both private and public cumulative information increases over time but agents put progressively more weight on the endogenous signals, asymptotically disregarding private ones. If the fundamental is time-varying, the use of past private signals complicates the role of prices as a sources of information, since it introduces endogenous serial correlation in the price signal and cross correlation between it and innovations in the fundamental. A modified version of the Kalman filter can still be used to extract information from prices and results show that the precision of the endogenous signals converges to a constant, with both private and public information used at all times.