The empirical evidence on initial returns in IPOs reveals average overpricing as well as underpricing, depending on the type of security offered for sale. Consistent with this evidence, the present paper develops a model in which an IPO may be overpriced in equilibrium relative to its expected (or average) aftermarket price. Overpricing disappears, however, once the offer price is compared to a ‘float-weighted’ expectation, where the weights are given by the extent to which the number of securities that are floated in the offering (at the posted price) is positively related to the demand for allocations. Empirically, the model implies that equally-weighted returns underestimate initial returns in IPOs, and hence that inferences based on equally-weighted returns may be misleading.