Figure 3. Explanatory power of risk measures in long term.

Note: The four panels show the relationship between risk premium and risk (standard deviation, CAPM beta, Shannon- and Rényi entropy) of 150 randomly selected securities by using different estimation methods. Both types of entropy functions are calculated by histogram based density function estimation, with 175 bins for Shannon entropy and 50 bins for Rényi entropy. The equation and the explanatory power (R ²) of the linear regressions are presented using expected risk premium as target variable and risk as explanatory variable. Under the OLS regression equations in brackets the p-values can be seen for each parameter estimations. The R²s of the models applying entropy based risk measures are significantly different form standard deviation and CAPM beta at 1% level.