Do prices of commodity futures contract series reliably exhibit reversal and/or momentum? In their October 2018 paper entitled “Do Momentum and Reversal Strategies Work in Commodity Futures? A Comprehensive Study”, Andrew Urquhart and Hanxiong Zhang investigate the performance of four momentum/reversal trading strategies as applied to excess return indexes for 29 commodity futures contract series. Excess return indexes invest continuously in nearest S&P GSCI futures, rolling forward during the fifth to ninth business day of each month. The four strategies are:

- Pairs reversal trading – At the end of each formation interval, identify the five pairs of indexes (with equal capital commitments) that track most closely based on sum of squared deviations of normalized price differences. During the ensuing trading interval, when the normalized prices of any pairs diverge by at least two standard deviations of formation period differences, go long (short) the member of the pair that is undervalued (overvalued). Close all pair trades when prices re-converge at a daily close or at the end of the trading interval.
- Pairs momentum trading – The inverse of pairs reversal trading, wherein the long (short) position is the pair member exhibiting relative strength (weakness) during the trading interval.
- Conventional momentum – At the end of each month, rank all indexes by cumulative return over the formation interval. Go long (short) the equal-weighted 30% of assets with the highest (lowest) past returns during the ensuing holding interval.
- Nearness to high momentum – At the end of each month, rank all indexes based on nearness to respective formation interval highs. Go long (short) the equal-weighted 30% of assets that are nearest/at (farthest below) past highs during the ensuing holding interval.

They consider nine formation intervals (1, 3, 6, 9, 12, 24, 36, 48 and 60 months) and 21 holding intervals (1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57 and 60 months).They assume that long-short strategies are about 50% collateralized, with capital therefore available to handle holding interval margin calls. They also test effects of 0.69% per year (0.06% per month) transaction costs. Using daily levels of six energy, 10 metal and 13 agriculture and live stock commodity futures excess return indexes during January 1979 through October 2017, *they find that:*

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