Initial Public Offerings: An Equilibrium Model of Price Determination

Abstract

We determine the optimal initial offering price for a new equity issue. Our model includes an entrepreneur, an underwriter, and investors, all belonging to a larger economic environment. The entrepreneur is willing to forgo some of his equity for investors' capital. We formulate the underwriter's pricing decision in the presence of signaling uncertainty as a minimax problem and show that underpricing follows from a specific set of loss functions. The more the underwriter wishes to avoid the consequences of overpricing relative to underpricing, the lower the optimal initial offering price and, all things being equal, the greater the underpricing. Also, when the optimal initial offering price is driven to its lower bound, it is, almost surely, less than the random equilibrium price, and the issue is underpriced. Consistency of our model with empirical evidence is discussed.