Prospect Theory and the Law of Small Numbers in the Evaluation of Asset Prices

We develop a model of one representative agent and one asset. The agent evaluates the earnings according to Prospect Theory and he does not know exactly the stochastic process generating earnings. While the earnings are generated by a random walk process, the agent considers a Markovian process, according to which firm's earnings move between two regimes, represented by a mean-reverting process and a trend process, as in Barberis, Shleifer and Vishny (1998). We study how an agent who is loss averse evaluates the price of a stock when she takes into account the wrong stochastic process. This twofold departure from rationality determines permanent effects on stock prices, even in long run. First, the model shows that agent who evaluates the asset according to Prospect Theory consistently underestimates the asset, due to loss aversion bias. This is shown under two different assumption regarding the functional form of utility. A kinked linear utility function (as in Bernatzi and Thaler, 1985) and the original and more general specification of Kahneman and Tversky (1979) are used. The model allows to explain observed phenomenon in the cross-section earnings return distribution. We solve this model and according to Barberis et all (1998), we evaluate the framework by using artificial data sets of earnings and prices simulated from the model. For plausible range of parameter values, it generates the empirical predictions of overreaction and underreaction observed in the data are explained.