# Designing a Proper Hedge: Theory versus Practice

**Publication: **The Journal of Financial Research, Volume 39, Issue 2

Authors: Chao Jiang, Ira Kawaller, and Paul Koch

Determining the hedge ratio based on the slope coefficient of a regression on price changes suffers from several critical shortcomings. First, it is difficult to assemble a properly constructed data set. Second, results vary depending on the length of the change interval. Third, the resulting ex post effective prices realized under this approach are wholly uncertain, ex ante. We show that when the hedge ratio is determined with reference to a regression on the respective price levels, rather than price changes, the resulting hedge ratio solution is superior in that none of these shortcomings apply.

**You can find the full paper at the Wiley Online Library:**
http://onlinelibrary.wiley.com/doi/10.1111/jfir.12091/abstract

For many hedgers, determining the size of the hedging position may be trivial. For example, when hedging a foreign exchange exposure of €20 million, the hedger would naturally apply a €20 million notional-size derivative. Similarly, hedging 10 million MMBTUs of natural gas would normally require a derivative having a notional of 10 million MMBTUs. Such intuition applies, however, only when the underlying to the derivative is identical to the hedged item. In a cross hedge, where the respective assets are distinct, an analytical solution is required. For example, when no viable jet fuel derivative contract is available, hedgers seek to identify a closely correlated oil-based commodity for which a derivative is available, but in this situation a one-to-one hedge construction would likely be inappropriate. Typically, the size of a cross hedge of this nature would be determined using regression analysis; but in performing this exercise, the design of that regression is critical.

In fact, because of hedge accounting requirements, this issue is central to the sizing of virtually any commodity hedge for which hedge accounting is intended. Under FASB’s hedge accounting rules, hedges should be engineered to offset the exposure’s entire price change for any commodity exposure – not just the price changes associated with some industry-standard price. This requirement should motivate the hedger to view their hedges as cross hedges and assess whether one-to-one hedge ratios should still be applied.

The article challenges conventional wisdom as to the form of the regression. Specifically, the traditional text book solution performs a regression using price change series for the hedged item and the hedging derivative, respectively. We argue that that price change specification has some serious problems and that in the vast majority of hedging situations a regression performed using price levels will have superior properties.

**Ira Kawaller, Managing Director**

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