A Dynamic Model of the Incorporation of New Information into Prices

A representative investor in a competitive financial market is uncertain about the true state of the economy. This uncertainty is reflected by a probability distribution of values which the investor forms subjectively based on information that is arriving randomly. The subjective distribution of values is updated by the investor's learning process, which systematically lowers the perceived probability of events economically different from the latest news and increases the believed likelihood of values consistent with this information. By following this learning process, the investor's subjective distribution becomes identical (in an expected sense) to the true distribution of values. The model shows that if there is a regime shift in the true world, the subjective distribution begins an adjustment process which ends again with the true and subjective distributions equal. In increase in real volatility causes no change in the expected subjective mean, but induces an increase in the volatility of the subjective probability function. An increase in the mean of the true world causes the subjective mean to increase, but also causes a temporary increase in the subjective volatility.