  Let $X$ be a Calabi--Yau variety of Picard number two with infinite
birational automorphism group. We show that the numerical dimension
$\kappa^{\mathbb{R}}_{\sigma}$ of the extremal rays of the closed movable cone
of $X$ is $\dim X/2$. More generally, we investigate the relation between the
two numerical dimensions $\kappa^{\mathbb{R}}_{\sigma}$ and
$\kappa^{\mathbb{R}}_{\mathrm{vol}}$ for Calabi--Yau varieties. We also compute
$\kappa^{\mathbb{R}}_{\sigma}$ for non-big divisors in the closed movable cone
of a projective hyperk\"{a}hler manifold.
