8 - A Simple Asset Pricing Model with Heterogeneous Beliefs

Abstract

This chapter extends the asset pricing model in order to include heterogeneous beliefs. The model features two investors, each with logarithmic utility. In equilibrium, prices are set as if there is a representative investor whose probability density function is a wealth-weighted convex combination of the individual investors' density functions. The model can be structured to reflect the major empirical findings where one investor predicts continuation and the other investor predicts reversal. In this case, the representative investor's probability density function might well be bimodal in respect to long time horizons. In this chapter, the state price model is developed and then extended to develop the two-securities model. The simplest such model features two agents with different beliefs, trading over time in a market for two securities, a risk-free security and a risky security, which can be viewed as the market portfolio. The formal analysis focuses on underlying state prices. The equilibrium pricing equation involves the state price vector ν. The equation indicates that a state price is a ratio of a discounted probability to the cumulative consumption growth rate. Notably, the state price embodies heterogeneity through the discounted probability. The discounted probability is a relative wealth-weighted convex combination of the individual investors' probabilities.