4 - A Simple Asset Pricing Model Featuring Representativeness

Abstract

This chapter describes a very simple complete market asset pricing model to illustrate the impact of representativeness described in Grether's experiment. It develops a model to identify the channel through which representativeness operates. The discussion proceeds in two stages. In the first stage, a non-signal-based framework is presented and equilibrium asset prices derived. In the second stage, the framework is reinterpreted to bring out the signal-based features. The impact of representativeness on equilibrium prices in a simple asset pricing model is illustrated. In the model, state prices are proportional to subjective probability beliefs. Therefore, errors in probability beliefs are directly transmitted to equilibrium prices. Bayesian-based beliefs are error-free. Therefore, state prices associated with Bayesian-based beliefs can be viewed as corresponding to fundamental value. The discussion in this chapter demonstrates how representativeness can lead prices to deviate from fundamental values and a simple model is also described that provides a foretaste of the key ideas. Here, the log-ratio probability columns describe the percentage probability errors induced by representativeness relative to the Bayesian case. Technically, these log-ratio probabilities constitute a log-change of measure. In behavioral finance, errors in judgment associated with market outcomes are called “sentiment.” The Bayesian-based model represents the situation when information is processed efficiently. As a result, the state prices associated with the Bayesian-based model can be termed efficient. In contrast, the state prices associated with the representativeness-based model can be termed inefficient.