Long-term commodity procurement risk management using futures contracts: a dynamic stack-and-rollapproach

Abstract

The procurement of commodity materials for production is an important issue in supply chain management. Effective procurement should consider both uncertain customer demand and fluctuating commodity price which, when act together, give rise to the procurement risk. To protect the bottom line, a manufacturer has to plan its procurement activities with special attention given to such procurement risk. Existing research has studied the use of exchange market-traded commodities in mitigating procurement risk. This study addresses the case of a manufacturer with long-term procurement commitments who wishes to hedge against the risk exposure by using long-dated futures contracts. In the commodities markets, however, long-dated futures are often illiquid or even unavailable, thus making the hedge ineffective. Alternatively, in a stack-and-roll hedge, the hedging positions are rolled forward in actively traded short-dated futures contracts of equal maturity until the procurement is executed. This in effect replicates the long-term futures contract in performing a hedge. This study therefore aims at developing a dynamic stack-and-roll approach that can effectively manage the long maturity procurement risk. The proposed dynamic stack-and-roll approach is inherently a discrete-time hedging strategy that divides the procurement planning horizon into multiple decision stages. The nearby futures are adopted as the short-dated futures as they are typically liquid. The hedging positions are adjusted periodically in response to the commodity price behaviour and updated information about the forward customer demand. For a manufacturer who wishes to mitigate the procurement risk as well as maximise the terminal revenue after the procurement, the mean-variance objective function is employed to model the manufacturer’s risk aversion behaviour. Then, a dynamic program formulation of the approach is presented for determining a closed-form expression of the optimal hedging positions. Notice that the hedging policy is a time-consistent mean-variance policy in discrete-time, in contrast to the existing discrete hedging approaches that employ minimum-variance policies. In this study, the commodity prices are modelled by a fractal nonlinear regression process that employs a recurrent wavelet neural network as the nonlinear function. The purpose of this arrangement is to incorporate the fractal properties discovered in commodity prices series. In the wavelet transform domain, fractal self-similarity and self-affinity information of the price series over a certain time scale can be extracted. The Extended Kalman Filter (EKF) algorithm is applied to train the neural network for its lower training error comparing with classical gradient descent algorithms. Monthly returns and volatility of commodity prices are estimated by daily returns data in order to increase the estimation accuracy and facilitate effective hedging. The demand information is updated stage by stage using Bayesian inference. The updating process are defined and adapted to a filtration, which can be regarded as the information received at the beginning of each decision stage. Numerical experiments are carried out to evaluate the performance of the proposed stack-and-roll approach. The results show that the proposed approach robustly outperforms other hedging strategies that employ minimum-variance or naïve policies, and effectively mitigate the procurement risk.