Starting from an information process governed by a geometric Brownian motion we show that asset returns are predictable if the elasticity of the pricing kernel is not constant. Declining [Increasing] elasticity of the pricing kernel leads to mean reversion and negatively autocorrelated asset returns [mean aversion and positively autocorrelated asset returns]. Under nonconstant elasticity of the pricing kernel financial ratios as the price-earnings ratio have predictive power for future asset returns. In addition, it is shown that asset prices will be governed by a time-homogeneous stochastic differential equation only under the constant elasticity pricing kernel. Hence, usually asset price processes do not satisfy the assumptions needed for empirical estimation.
Pricing kernel Diffusion processes Stationarity Predictability of asset returns Autocorrelation