Summary: This paper gives a new proof of the index formula established by T. Momi [J. Math. Econ. 39, No. 3–4, 273–297 (2003; Zbl 1049.91116)] for an economy with incomplete asset markets where the difference between the number of states \((S)\) and the number of assets \((J)\) is an even number. The proof uses a single globally defined homotopy function on the asset pseudo-equilibrium manifold connecting the excess demand of a given economy to the individual excess demand of the unconstrained agent. We show that the asset pseudo-equilibrium manifold is orientable if the number \(S - J\) is even and deduce the index formula from the homotopy invariance theorem for the degree of a map.