Integrated Operational and Financial Hedging Across Multiple Markets: A Value-at-Risk Approach

Abstract

We study the optimal integrated capacity and financial hedging strategies for a downside risk-averse global firm that faces multiple demand and foreign exchange rate risks. The firm seeks to maximize its expected profit while controlling its profit risk through a Value-at-Risk (VaR) constraint, which ensures the probability of profit falling below a reservation level is within tolerance. We introduce a tractable approach to resolving the well-known challenging VaR constraint, enabling analysis of multiple foreign markets -- a significant advancement over the usual single foreign market focus in the literature under other risk measures. We characterize efficient financial hedging under any given capacity in a general form with continuous strike price and general stochastic distribution that can be replicated with vanilla derivatives, making the profit reservation level and tolerance level interchangeable. Our findings reveal that the optimal capacity choice is either the risk-neutral solution or on the boundary of the feasible region, differing from the mean-variance framework where multiple solutions may occur for multi-markets. Furthermore, we demonstrate that while operational hedging boosts expected profits directly, financial hedging lowers the chance of incurring risks. These strategies can substitute or complement each other in managing downside risks, serving distinct purposes in risk control.

Keywords: capacity investment, financial hedging, value-at-risk, integrated risk management, global supply chain