Hedging under square loss

Abstract

The framework of minimum-variance hedging rests on a restrictive foundation. This study shows that the objective of variance minimization is only justifiable when variance coincides with expected squared forecast error. Nevertheless, the classical framework is routinely applied when the condition fails, giving rise to inaccurate risk assessments and suboptimal hedging decisions. This study proposes a new, improved framework of hedging which relaxes the condition at no tangible cost. It derives a new objective function, an optimal hedge ratio, and a measure of hedging effectiveness under square loss. Their superior performance is demonstrated from a theoretical standpoint and by applying them to hedging the price risk of oil and natural gas. Simple yet general, the new framework is well suited to replace the classical one and facilitates adequate risk measurement and improved hedging decisions. It also provides fundamental insight into dealing with uncertainty under square loss and beyond