Pure martingale and joint normality tests for energy futures contracts*

- Perform pure martingale hypothesis on logarithm of futures prices for crude oil, heating oil and natural gas.
- Perform joint normality tests on spot and futures returns for crude oil, heating oil and natural gas.
- Both hypothesis tests are performed for 1-day, 1-week, 4-week, 8-week and 12-week hedging horizons.
- Draw some conclusions.

In this study, we empirically analyze to see if the pure martingale hypothesis holds for three energy-related commodities: crude oil, heating oil and natural gas. We also test this hypothesis for five different hedging horizons: 1-day, 1-week, 4-week, 8-week and 12-week. Our empirical results show that the pure martingale hypothesis holds for all three commodities and all five horizons. This implies that the expected return on futures contract can be ignored in determining the optimal hedge ratio. We also test to see if the joint normality between futures and spot returns holds for the same three commodities and five hedging horizons. We reject the joint normality hypothesis for all three commodities and five hedging horizons. This implies that hedgers with different utility function have different optimal hedge ratios. Thus, in general, one needs to take into account of hedger's utility function when deriving optimal hedge ratio. Our results are robust to pre- and post-financial crisis as well as some other specifications considered in the paper.