Do the pure martingale and joint normality hypotheses hold for futures contracts?. Implications for the optimal hedge ratios

Sheng Syan Chen, Cheng few Lee, Keshab Shrestha

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12 Citations (Scopus)


It is well known that the optimal hedge ratios derived based on the mean-variance approach, the expected utility maximizing approach, the mean extended-Gini approach, and the generalized semivariance approach will all converge to the minimum-variance hedge ratio if the futures price follows a pure martingale process and if the spot and futures returns are jointly normal. In this paper, we perform empirical tests to see if the pure martingale and joint normality hypotheses hold using 25 different futures contracts and five different hedging horizons. Our results indicate that the pure martingale hypothesis holds for all commodities and all hedging horizons except for three stock index futures contracts. As for joint normality, we propose two new tests based on the generalized method of moments, which allow for calculating multivariate test statistics that take account of the contemporaneous correlation across spot and futures returns. Our findings show that the joint normality hypothesis generally does not hold except for a few contracts and relatively long hedging horizons.

Original languageEnglish
Pages (from-to)153-174
Number of pages22
JournalQuarterly Review of Economics and Finance
Issue number1
Publication statusPublished - Feb 2008
Externally publishedYes


  • Hedge ratio
  • Joint normality hypothesis
  • Pure martingale hypothesis

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