Production with Risk Hedging Optimal Policy and Efficient Frontier

Abstract

Demand for many products may depend on the price of a tradable asset or on the economy in general. For instance, demand for equipment that plants or harvests corns correlates with the fluctuations of the corn price on the commodity market; and discount stores experienced increased sales revenue during the last recession. Thus, we model demand as a stochastic process with two components: in addition to the usual Gaussian component due to forecast errors, there is a drift component taking the form of a function of a tradable asset price. (In the case of dependence on the general economy, the asset price can be a broad market index, such as the S&P500 index.) With this demand model, we study the one-time production quantity decision along with a real-time risk-hedging strategy over a given planning horizon (the production cycle). Pursuing a mean-variance formulation, we derive the optimal solution to both production and hedging decisions. In addition, we give a complete characterization of the efficient frontier, and quantify the improvement in risk-return tradeoff achieved by the hedging strategy.