The Dynamics of Equity Prices in Fallible Markets

In an efficient securities market, prices correctly re ect news about future payoffs. This paper argues that there are two aspects to correctness: (i) correct updating of beliefs from news, (ii) correct prior beliefs. Traditionally, empirical research has implicitly insisted on both. Lucas' rational expectations equilibrium theory also assumes both, explicitly. Nevertheless, rationality requires only the former, but not the latter. This paper develops restrictions on the random behavior of prices of equity-like contracts when (i) is maintained, but the market may have mistaken priors about the likelihood of the bankruptcy state, in violation of (ii). The restrictions are cast in the form of familiar martingale difference results. They do not necessarily restrict returns as traditionally computed, however. Most importantly, the restrictions appear only when the empiricist deliberately imposes a selection bias. In particular, the price histories of securities that are in the money at the terminal date are to be separated from those of securities that end out of the money (i.e., in the bankruptcy state). As a result, this paper also demonstrates that something can be learned about market efficiency from samples subject to survivorship bias or the Peso problem.