Mean–variance trade-offs in supply contracts

We study the trade-offs faced by a manufacturer signing a portfolio of long-term contracts with its suppliers and having access to a spot market. The manufacturer incurs inventory risk when purchasing too many contracts and spot price risk when buying too few. We quantify these risks for a single selling period by studying the profit mean and variance for a given portfolio of option contracts. We characterize the set of efficient portfolios that the manufacturer must hold in order to obtain dominating mean–variance pairs. Among these, we emphasize the maximum expectation portfolio, obtained by solving the classical newsvendor problem, and the corresponding minimum variance portfolio. We show that the upper-level sets of a mean–variance utility function are connected. Hence, a greedy method will find the portfolios on the efficient frontier. Finally, we provide a comparison with standard hedging strategies and show that the approximation associated with financial hedging can be relatively inaccurate.