Complexity and the character of stock returns: Empirical evidence and a model of asset prices based upon complex investor learning

Abstract

Empirical evidence on the distributional characteristics of common stock returns indicates: 1) A power-law with exponent > 2 describes the positive tail behavior of the survivor function of returns ( pr(r > x ) – x-u ) (Gopikrishnan et al., 1999; Plerou et al., 1999), 2) The time-series return process is characterised by autoregressive conditional heteroskedasticity (Bollerslev, Chou and Kroner, 1992; Glosten, Jaggannathan and Rankle, 1993: Engle, 2004). and, 3) General nonlinear dependencies exist in the time-series of returns (Scheinkrnan and LeBaron, 1989; Hsieh, 1991; Brock, Hsieh and LeBaron, 1991). We propose a model of complex, self-referential learning and reasoning amongst economic agents that jointly produces security returns consistent with these general observed facts and which are supported here by empirical. results presented for a benchmark sample of 50 stocks traded on the New York Stock Exchange, The market we postulate is populated by traders who reason inductively while compressing information into a few fuzzy notions which they can in turn process and analyze with fuzzy logic. We analyze the implications of such behavior for the returns on risky securities within the context of an artificial stock market model. Dynamic simulation experiments of the market arc conducted from two such market-clearing prices emerge, allowing us then to compute realized returns. The results indicate that the model proposed in this paper can jointly account for the presence of a power-law characterization of the positive tail of the survivor function of returns with exponent on the order of 3, for autoregressive conditional heteroskedasticity and for general nonlinear dependencies in returns. The appeal of the model is its close ties to evidence on how individuals actually reason and provides an alternative view of the influence of nontraditional learning and reasoning in complex, ill-defined capital market settings.