Measuring Hedging Effectivenew With R edging replaces exposure to the risk of cash price changes with exposure to the H risk of changes in the basis, where basis is defined as the difference between the cash p n e of a commodity and the hhms price on that commodity. Hedging is traditionally viewed as a risk duction strategy and the effectiveness of a hedge is usually judged by the ability of the futures position to reduce the variance inherent in the unhedged or cash position.
The most popular measure of hedging effectiveness is commonly called R2, referring to the coefficient of detemimtion of a regression of futures price changes (the independent variable) on cash price changes (the dependent variable).' The RZ statistic is an indication of the maximum risk reduction potential of a hedge. Specifically, R2 represents the percent reduction in the variance of the unhedged or cash position at the point of minimum variance and is defined by equstion (1):2
(1)
where:
Var(R*) = the minimum variance of the cash, futures portfolio Var(v) = the variance of the unhedged or cash position If perfect correlation exists between spot and futures price changes, R2 equals 1. A deficiency of the R 2 measure, however, is that expected price changes are not separated from unexpected price changes in the ordinary least squares regression. Working (1953) explained that because of the systematic tendency for the basis to narrow over time, a perfect R Z of 1 is not possible over any but the shortest time inter~al.~ Working (1962) also substantiated the fact that hedging is not done only to reduce risk. Despite these deficiencies, the R 2 risk reduction statistic continues to be the most often used measure of hedging effectiveness. Because R 2 has been used so extensively in the literature, higher R 2s have become practically synonymous with greater risk reduction and increased hedging effectiveness. While this reasoning is valid for certain comparisons,
The author expresses appreciation to two anonymous Journal reviewers for comments on an earlier draft of R 's are sometimes calculated using price levels instead of price changes, but this metfiod is less popular.
*See
Merington (1979) for a more detailed derivation of equation (1). 'See Working (1953 p. 544) and Bmwn (1985 p. 510) for a more complete discussion. this paper.
Unless otherwise identified, R2 refers to a regression of price changes.