Pricing Two Trees When Trees and Investors are Heterogeneous

Abstract

We consider an exchange economy with two heterogeneous stocks and two groups of investors. Dividends follow diffusion processes, with a constant expected growth rate for one stock and a stochastic drift for the other. 'Rational investors' can either observe this stochastic drift without error or are at least able to use a noisy signal about it, while 'irrational investors' base their inference only on dividend observations. In an economy with homogeneous investors, uncertainty about the drift increases the volatilities of both stocks and the expected return of the smaller stock. Differences between the two types of stocks are mainly caused by learning, which increases both the volatility and the expected return of the stock with the stochastic drift. When both groups of investor are present, differences in portfolio holdings and thus trading mainly depend on differences in beliefs. In the long run, the irrational investors will be driven out of the market, and for realistic parameter scenarios, they can loose on average half of their wealth within twenty years.