Asymmetric information in fads models

Fads models were introduced by Shiller (Am Econ Rev 71:421-436, 1981) and Summers (J Finance 41:591-601, 1986) as plausible alternatives to the efficient markets/constant expected returns assumptions. Under these models, logarithms of asset prices embody both a martingale component, with permanent shocks, and a stationary component, with temporary shocks. We study a continuous-time version of these models both from the point of view of informed agents, who observe both fundamental and market values, and from that of uninformed agents, who only observe market prices. We specify the asset price in the larger filtration of the informed agent, and then derive its decomposition in the smaller filtration of the uninformed agent using the Hitsuda representation of Gaussian processes. For uninformed agents we obtain a non-Markovian dynamics, which justifies the use of technical analysis in optimal trading strategies. For both types of agents, we solve the problem of maximization of expected logarithmic utility from terminal wealth, and obtain an explicit formula for the additional logarithmic utility of informed agents. Finally, we apply the decomposition result to the problem of testing the presence of fads from market data. An application to the NYSE-AMEX indices from the CRSP database shows that, if the fads component prevails, then the mean-reversion speed must be slow.