The Capital Asset Pricing Model (CAPM) has received tremendous attention since 1964. One of the main aspects of the model is a linear relationship between the coefficient of systematic risk, beta, and expected stock returns. This linear relationship is tested with non-parametric estimation. While the linear relationship is sustainable, the parabolic relationship is rejected significantly. The result is a strong support for the CAPM. Linear non-parametric estimation produces better predictions, which can benefit professionals.