Advances in Cointegration and Subset Correlation Hedging Methods

Abstract

We divide hedging methods between single-period and multi-period. After reviewing some well-known hedging algorithms, two new procedures are introduced, called Dickey-Fuller Optimal (DFO), Mini-Max Subset Correlation (MMSC). The former is a multi-period, cointegration-based hedging method that estimates the holdings that are most likely to deliver a hedging error absent of 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 DFO produces estimates similar to the Error Correction Method, but more stable. Likewise, MMSC estimates are similar to Principal Component Analysis but more stable. Finally, a generalized Box-Tiao Canonical Decomposition (BTCD) method is proposed, which is of the multi-period class. BTCD estimates are also very stable, and cannot be related to any of the aforementioned methodologies. Finally, we find that all three advanced hedging methods (MMSC, BTCD, DFO) perform well.

Keywords: Hedging portfolios, robustness, portfolio theory, stationarity, subset corrrelations, Maeloc spread, ECM, ADF, KPSS, PCA, BTCD, MMSC

JEL Classification: C01, C02, C61, D53, G11