Survival of Noise Traders and the Implications for Asset Prices

This paper shows that in financial markets with endogenous asset supply and demand, both rational and noise traders do co–exist in the long run. The finding implies that financial markets are neither informationally nor allocationally efficient. While rational traders have a consistently higher cash inflow from dividends, noise trader are able to speculate successfully on capital gains. Thus, investors who need a regular cash inflow should invest rationally, i.e., hold a portfolio proportional to the expected relative dividends of its assets. Investors interested in maximum capital gains may try and realize the alpha opportunities in the market. To succeed, their timing must be optimal, however. The worst strategy is ’buy and hold’: Neither does it lead to a cash inflow like the rational strategy, nor does it open the chance to realize capital gains. We would like to mention that our evolutionary model does not face problems of common interactive agent models such as infinite supply of riskless assets or the lack of modelling the evolution of the investor’s wealth. Moreover, we investigate the two most prominent puzzles related to low-frequency stock prices: The conditional volatility of price returns, and the price forecasting power of dividend yields. Using the indirect inference methodology, we estimate an version of the evolutionary stock market model with endogenous asset supply and demand. We find that our economically well founded model is able to approximate the conditional volatility, quantified with a GARCH(1,1) process, that is observed in empirical price data. To investigate the price forecasting power of dividend yields, we derive for rational markets a close form of linking dividend yields to future prices, inherently de-trending the price process. Based on this result, we show that the prices of roughly two third of the considered assets depend on the dividend yields. The prices of the other assets deviate from the rational values due to the presence of noise traders in the market, whose speculative activities leads to price bubbles. Finally, recurring to the Lyapunov characteristic exponents of the relative wealth evolution, we show that none of the traders is able to marginalize the others in the long run, i.e., to take over all wealth in the market. JEL Classification Codes: C15, C32, C52, G11, G12