Hedging methods are divided into single-period and multiperiod forms. After reviewing some well-known hedging algorithms, two new procedures called the Dickey-Fuller optimal (DFO) method and the minimax subset correlation (MMSC) method are introduced. The former is a multiperiod, cointegration- based hedging method that estimates the holdings that are most likely to deliver a hedging error with no unit root. The latter is a single-period method that studies the geometry of the hedging errors and estimates a hedging vector such that subsets of its components are as orthogonal as possible to the error. We test each method for stability and robustness of the derived hedged portfolio. Results indicate that the DFO method produces estimates that are similar to those for the error correction method, but more stable. Likewise, MMSC estimates are similar to principal component analysis, but more stable. A generalized Box-Tiao canonical decomposition (BTCD) method, which is of the multiperiod class, is proposed. The BTCD estimates are also very stable, and cannot be related to any of the aforementioned methodologies. Finally, it is found that all three advanced hedging methods (MMSC, BTCD and DFO) perform well.