The capital asset pricing model with non-homogeneous expectations: theory and evidence on systematic risks to the beta

This paper introduces non-homogeneity of expectations(NHE) among. investors on the parameters of the probability distribution of assets rates of return and derives an equilibrium return-risk relationship which is non-linear. This relationship shows a new and additional form of risk called theta risks I and II which are the systematic biases to the beta risk arising from NHE among investors on the mean and variance (covariance) respectively of the rates of return. The beta is no longer a complete measure of risk. Under the traditional homogeneous expectations(HE) assumption, or if the theta risks vanish, the CAPM of Sharpe and Lintner is a special case. An errors-in-variables model _sused to provide an indirect test and the results are explained within the framework of the model. It appears that the empirical anomalles on the CAPM are due to attempts to fit a linear model on a fundamentally non-linear return-risk relationship.