We reformulate the zero-dimensional Hermitian one-matrix model as a (nonlocal) collective field theory, for finite N. The Jacobian arising as a result of changing variables from matrix eigenvalues to their density distribution is treated exactly. The semiclassical loop expansion turns out not to coincide with the (topological) [Formula: see text] expansion, because the classical background has a nontrivial N dependence. We derive a simple integral equation for the classical eigenvalue density, which displays strong nonperturbative behavior around N=∞. This leads to IR singularities in the large-N expansion, but UV divergencies appear as well, despite remarkable cancelations among the Feynman diagrams. We evaluate the free energy at the two-loop level and discuss its regularization. A simple example serves to illustrate the problems and admits explicit comparison with orthogonal-polynomial results.