  In this work, we study the deformed Hermitian-Yang-Mills equation on compact
K\"ahler manifold. We introduce the notions of coerciveness and properness of
the $\mathcal{J}$-functional on the space of almost calibrated $(1,1)$-forms
and show that they are both equivalent to the existence of solutions to the
hypercritical deformed Hermitian-Yang-Mills equation.
