Cross and Delta-Hedges : Regression Versus Price-Based Hedge Ratios

In implementing a variance-minimizing cross or delta hedge, the regression coefficient is often estimated using data from the past, but one could also use estimators that are suggested by the random-walk or unbiased-expectations models and require just a single price. We compare the performances of various hedge ratios for three-month currency exposures, and find that the price-based hedge ratios generally perform better than the regression-based ones. Specifically, all our regressions do systematically worse in the case of a delta hedge, and seem to beat the price-based hedge ratios only in the case of cross- or cross-and-delta problems where the two currencies are so distantly related-like, e.g., hedging ITL/USD using JPY/USD-that no risk manager would even consider them as hedges of each other. The poor performance of the regressions is all the more surprising as we correct the futures prices for errors-in-variables (synchronization noise, bid-ask bounce, and changing time to maturity). The results are robust to observation frequency in the regressions, sample period, percentage vs. dollar returns, and OLS versus IV. One reason that price-based methods do better is that they provide immediate adjustment to breaks in the data (like EMS realignments, which get incorporated into rolling regression coefficients only very slowly, as time elapses) or other events that change the relationship between the regressor and regressand. For cross or cross-and-delta hedges between European currencies, regressions also have difficulties in capturing cross-correlations between exchange rates