There have been many studies concerning the relationships between stock returns and volatilities. Their positive relationship is well known from the theoretical point of view, but not empirically shown. Franch, Schwert and Stambaugh [11] has empirically provided the indirect evidence of the positive relationship betwen expected stock return and expected volatility. However, their study lacks some statistical validity. This study reexamines the relationship using regression diagnostics and GARCH model from an international point of view. The empirical results fall to show the positive relationship between expected stock return and expected volaiility, which contradicts those of France, Schwert and Stambangh [1].