An of Intertemporal Measure Hedging Effectiveness
Jack S.K. Chang Hsing Fang edging effectiveness is measured to determine the effectiveness of adding a given H futures contract to a hedger's cash portfolio. It is determined by comparing the combined futures-cash position with the cash position alone according to certain criteria. The traditional measure developed by Johnson (1960) and Ederington (1979) has the single objective of minimizing a hedger's risk, which is proper when risk-reduction is his only concern. A second measure pioneered by Howard and D'Antonio (HD) (1984, 1987), and Chang and Shanker (CS) (1987) has the objective of maximizing a hedger's risk-return tradeoff, which is proper when both risk and return are important.' These two measures have been tested empirically by Chang and Shanker (1986), Chen, Sears, and Tzang (1987), Howard and D'Antonio (1986), and Overdahl and Starleaf (1986).
These hedging effectiveness measures suffer from a major deficiency: they are derived in a one-period setting. This setting imposes rather restrictive conditions on a hedger's behavior. For example, a hedger is assumed to ignore any new information and, therefore, adjusts neither consumption behavior nor hedging positions to his changing consumptiodinvestment opportunity set during the hedge period. This is inconsistent with evidence in the literature which suggests that an optimum hedge ratio should be time-varying, and tends to be unstable when the market is volatile.' These hedging effectiveness measures are accurate only when the market is stable and tend to be noticeably biased when applied to recent market data. This bias problem, however, can be corrected using an intertemporal measure of hedging effectiveness.
The authors would like to thank two anonymous reviewers of the journal and the editor, Mark J. Powers, for very constructive comments.
'Strictly speaking, the HDICS measures assume a given long-spot position. In contrast, Levy (1987) derives an alternative measure with a variable spot position. However, as shown in Chang and Shanker (1986). the HDlCS measures can be easily modified to a variable spot position with short-sale constraints, margin requirements, and other transaction costs. Gjerde (1987) also has derived alternative risk-return hedging effectiveness measures that assume a hedger's loss function is based upon dollar-return but not percentage returns. For a discussion of alternative performance models, see Yau, Savanayana, and Schneeweis (1988).
'For empirical investigations of the properties of the time-varying hedge ratio, see Lee, Bubnys, and Lin (1986), and Grammatikos andSaunders (1983). For the derivation of a stochastic hedge ratio, see Geske and Pieptea (1987). Evidence of this is also seen in the daily movements of trading volume. Initial low volume of a futures contract tends to rise over time, reaches a peak near the contract's termination, and drops off as its maturity nears. 'Fortin and Khoury (1988) derived an intertemporal measure of hedging effectiveness based upon a constant consumptionlinvestment opportunity set. Thus, their measure suffers from the bias problem.