Futures Cross-Hedging with a Stationary Basis

When managing risk, frequently only imperfect hedging instruments are at hand. We show how to optimally <italic>cross-hedge</italic> risk when the spread between the hedging instrument and the risk is <italic>stationary</italic>. For linear risk positions we derive explicit formulas for the hedge error, and for nonlinear positions we show how to obtain numerically efficient estimates. Finally, we demonstrate that even in cases with no clear-cut decision concerning the stationarity of the spread, it is better to allow for <italic>mean reversion of the spread</italic> rather than to neglect it.