Analytics Underlying the Ag Metallgesellschaft Hedge : Short Term Forwards in a Multi-Period Environment

In a highly publicized example, a marketing and refining subsidiary of AG Metallgesellschaft controlled short term forward positions reportedly equivalent to 160 million barrels of oil, 60 times the daily output of Kuwait. Presumably, the short term positions were taken to hedge oil contracts to customers over an extended period. This paper develops the analytics underlying the hedging of long term flow commitments with short term forward contracts. Its contributions include the determination of minimum variance hedging paths for multi-period flow portfolios and theevaluation of both period-by-period and end-of-horizon volatilities under various hedging schemes. The analysis allows for basis risk, non-zero cost-of-carry, and spot diffusion processes that have a non-zero market price of risk. The results are developed in the context of an efficient market and standard equilibrium pricing models