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.