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The optimal number of contracts in cross- or delta-hedges.

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Abstract

When hedging in futures markets, the hedge instruments typically fail to match the exposed asset or portfolio by expiration date and/or underlying asset. The theoretical variance-minimizing hedge is given by the slope coefficient of the conditional (forward-looking) regression of the spot-price that one is exposed to on the futures price used as a hedge. We explore the hedging performance of simple rules of thumb and of unconditional regressions on past data, focusing on the effect of the choice of observation frequency, sample period, percentage vs. dollar returns, and lead/lag effects. Our findings are the following : (a) the effects of varying the observation frequency, sample period, etc., are much larger than the effects of using GARCH instead of OLS. (b) Regardless of sample size and estimation technique, the exposure is best estimated using percentage returns rather than (dollar) first differences. © In the case of delta hedges, and also a cross-hedges among closely related currencies, regressions are systematically beaten by naïve rules of thumb. (d) This relatively poor performance of regression-based hedges is not just due to errors in data. (e) The optimal estimation technique depends on the situation. For cross-hedges involving two European currencies, high-frequency OLS estimates is flawed by EMS-induced leads and lags among exchange rate changes, and the best regressions are those using monthly data from longish sample periods. For delta-hedges the dominant source of estimation problems seems to be a time-varying relationship between the regression variables, and the best regressions use daily data from short sample periods.

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