  We prove that the almost sure Lyapunov exponent \lambda(\kappa) of the
continuous space Parabolic Anderson Model is bounded above by $c_u
\kappa^{1/3}$ as $\kappa\downarrow0$ under mild regularity conditions. This
bound of the same order of the previously proven lower bound, $\lambda(\kappa)
\ge c_l \kappa^{1/3}$.
