On the numerical dimension of Calabi-Yau 3-folds of Picard number 2

We show that for any smooth Calabi-Yau threefold $X$ of Picard number $2$ with infinite birational automorphism group, the numerical dimension ${\kappa }_{\sigma }$ of the extremal rays of the movable cone of $X$ is $\frac{3}{2}$. Furthermore, we provide new examples of Calabi-Yau threefolds of Picard number $2$ with infinite birational automorphism group.