This paper introduces the concept of non-homogeneity of expectations (NHE) among investors on the parameters of the probability distribution of assets’ rates of return and derives a non-linear equilibrium return-risk relationship. 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 respectively of the rates of return. Under the traditional homogenous expectations assumption, or if the theta risks vanish, the CAPM of Sharpe and Lintner is a special case. Using an error-in-variable model to provide an indirect test and explaining the result within the framework of the model, analysis indicates that the empirical anomaly on the CAPM are due to the attempts to fit a linear model to a fundamentally non-linear return-risk relationship.
