Double-sort strategies

Today I’m going to draw on a May 2008 EDHEC paper entitled “Tactical Allocation in Commodity Futures Markets: Combining Momentum and Term Structure Signals” by Ana-Maria Fuertes, Joëlle Miffre, and Georgios Rallis. It’s a double-sort strategy that in its very broadest terms I think could serve as a model for traders and investors trying to gain an edge.

The individual strategies are simple. The momentum strategy sorts commodity futures contracts into quintiles at the end of each month based on their average return over the previous R months—that is, the ranking period. For purposes of the study it is assumed that the futures contracts in each quintile are equally weighted. The investor then buys the top quintile, shorts the bottom quintile, and holds the long-short position for H months—that is, the holding period. The authors focus on thirteen permutations that did well in a 2007 relative strength study: four with a 1-month ranking period (1-1, 1-3, 1-6, 1-12), four with a 3-month ranking period (3-1, 3-3, 3-6, 3-12), three with a 6-month ranking period (6-1, 6-3, 6-6) and two with a 12-month ranking period (12-1, 12-3).

The authors then explore various term-structure strategies. The most basic buys the quintile of commodities with the highest positive roll-returns, shorts the quintile with the most negative roll-returns and holds the positions for a month. For our purposes here it’s not important to explore the variations, especially since the basic strategy tweaked just a tad performs better than strategies with more frequent rebalancing.

The results of the authors’ studies are as follows. “On average, the trend-following strategies and the term-structure strategies that are profitable at the 5% level earn, respectively, annualized alpha of 10.14% and 12.66% whereas over the same period, a passive long-only portfolio yields alpha of only 2.48%. Second, with net returns above 13.5% a year, three momentum strategies (1-1, 3-1 and 12-1) and one term structure strategy [the basic] stand out as conveying the best signals for tactical allocation.”

Now comes the task of combining the strategies. First, it is important to ascertain whether there is enough difference in the strategy signals to make a combination worthwhile. “Term structure trading strategies in commodity futures select, by definition, the most backwardated and contangoed contracts. Even though momentum strategies are not designed per se to overtly shortlist the commodities with the steepest term structures, it has been show that their long portfolios tend to contain backwardated contracts, while their short portfolios are heavily tilted towards contangoed commodities.” Although the correlations between the returns from the two strategies are positive, they vary between 10.92% and 56.96%, with the mean correlation being 31.26%.

Since the correlations are low, a double-sort approach makes sense. Here’s how it works. “First, we compute the roll-returns at the end of each month and their 1/3 breakpoints to split the cross-section of futures contracts into 3 portfolios, labeled Low, Med, and High. We then sort the commodities in the High portfolio into 2 sub-portfolios (High-Winner and High-Loser) based on the mean return of the commodities over the past R months. In effect, the High-Winner and High-Loser portfolios contain 50% of the cross-section that was selected with the first term-structure sort or 50% x 33.3% of the initial cross-section that was available at the end of a given month. Intuitively, High-Winner is thus made of the commodities that have both the highest roll-returns at the time of portfolio construction and the best past performance. Similarly, we sort the commodities in the Low portfolio into 2 sub-portfolios (Low-Winner and Low-Loser) based on their mean return over the past R months. Low-Loser contains therefore commodities that have both the lowest roll-returns at the time of portfolio construction and the worst past performance. The combined strategy buys the High-Winner portfolio, shorts the Low-Loser portfolio, and holds this position for one month.”

The authors analyze six double-sort strategies—three that are sorted first on time-structure with ranking periods set to 1, 3, and 12 months and three that are sorted first on momentum with the same ranking periods. The most profitable strategy sorts first on time-structure and has a ranking period of one month (average return of 23.55% a year); the least profitable again sorts first on time-structure but has a ranking period of twelve months (18.81%).

The double-sort strategies are much riskier than the passive benchmark, but their reward-to-risk ratios and Sortino ratios are consistently higher. So “the higher risk of the double-sort strategies is more than rewarded by the market.” The authors go through the standard statistical checklist for robustness and conclude that “the abnormal returns uncovered are not an artifact of liquidity risk, data snooping, additional non-investable macroeconomic risk factors or time-variation in risks.”

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I have only skimmed the surface of this paper, but I wanted to give some idea of how one might develop a double-sort strategy. It doesn’t have to be a long-short strategy, it doesn’t have to focus on commodities. In place of term structure one could substitute a whole host of measurable variables. For instance, one could develop strategies incorporating volatility or open interest. Another idea, shamelessly stolen from David Varadi at CSS Analytics, is to include an element of cognitive dissonance. Let your informed imagination soar and see what you come up with. (Of course, if you want to share your wildly successful double-sort strategy with this humble blogger she would be very grateful!)