Why do asset prices not follow random walks?

This paper analyzes the effect of non-constant elasticity of the pricing kernel on asset return characteristics in a rational expectations model. It is shown that declining elasticity of the pricing kernel can lead to predictability of asset returns and high and persistent volatility. Also, declining elasticity helps to motivate technical analysis and to explain stock market crashes. Moreover, based on a general characterization of the pricing kernel, we propose analytical asset price processes which can be tested empirically. The numerical analysis reveals strong deviations from the geometric Brownian motion which are caused by declining elasticity of the pricing kernel.