A note on imperfect hedging: a method for testing stability of the hedge ratio

Abstract

Companies producing, processing and consuming commodities in the production process often hedge their commodity expositions using derivative strategies based on different, highly correlated underlying commodities. Once the open position in a commodity is hedged using a derivative position with another underlying commodity, the appropriate hedge ratio must be determined in order the hedge relationship be as effective as possible. However, it is questionable whether the hedge ratio determined at the inception of the risk management strategy remains stable over the whole period for which the hedging strategy exists. Usually it is assumed that in the short run, the relationship (say, correlation) between the two commodities remains stable, while in the long run it may vary. We propose a method, based on statistical theory of stability, for on-line detection whether market movements of prices of the commodities involved in the hedge relationship indicate that the hedge ratio may have been subject to a recent change. The change in the hedge ratio decreases the effectiveness of the original hedge relationship and creates a new open position. The method proposed should inform the risk manager that it could be reasonable to adjust the derivative strategy in a way reflecting the market conditions after the change in the hedge ratio.

Keywords

• stability analysis
• imperfect hedging
• changepoint detection