Rothschild–Stiglitz's definition of increasing risk and the relationship between volatility and risk premium

This paper analyzes the relationship between volatility and risk premium under the capital asset pricing model and Rothschild and Stiglitz's [Rothschild, M. and J.E. Stiglitz. (1970) Increasing risk I: a definition. Journal of Economic Theory, 2, 225–243.] definition of increasing risk. Especially examined are the conditions of the widely used assumption of constant correlation, which results in a linear relationship. Though both the above model and definition are widely known and accepted, their compatibility has remained unclear in the literature. According to this paper, they are in harmony with the linear relationship, if the correlation between a stock and the market portfolio is less than 0.7. Otherwise a conflict may arise.