Module Categories and Cocontinuity of Hom

Question

Let ${}_BM_A$ be a $B$-$A$ bimodule and let ${}_BX$ be a $B$-module. We know that the functor $\operatorname{Hom}({}_BM_A,-)$ produces an $A$ module out of a $B$ module. The fact that the adjoint functor ${}_BM_A\otimes (-)$ takes $A$ modules to $B$ modules makes the last statement clear. Now given that $\operatorname{Hom}({}_BM_A,{}_BX)$ is an $A$-Module and that module categories are cocomplete, can we conclude that the $\operatorname{Hom}$ functor (EDIT: the functor $\operatorname{Hom}({}_BM_A,-)$ to be specific) is concontinuous when acting on modules?