It is not uncommon to find oneself fighting against the grain—sometimes literally!—when trading commodity futures.
Relative-value trades that seem obvious at first, such as going long an expensive commodity and short a cheaper, related commodity, require more than just the usual patience to wait for valuation spreads to compress. In fact, they often lose money even when the spreads move in an investor’s favor.
When that happens, the main reason is usually “carry,” or the cost of “rolling” commodity futures contracts. This is a feature of all commodity futures trading, but it can be especially prevalent and persistent in agricultural commodities. In this article, we aim to show that one can still “harvest” relative value opportunities by adjusting them for the cost of going “against the grain” of carry.
Cobweb Cycles
In the 1930s, the economist Nicholas Kaldor introduced the idea of “cobweb cycles” in his analysis of agricultural commodity pricing.¹ The economics of grain markets naturally result in temporal disequilibria in supply and demand. At the end of each winter, farmers need to decide how much soybeans and corn they should plant. Many factors inform the decision, but it ultimately boils down to relative prices: a shortage of soybeans inventory, and therefore high soybean prices, is an incentive to plant more soybeans versus corn. But that means at the next harvest there is likely to be a shortage of corn rather than soybeans, raising the price of corn relative to the price of soybeans. So goes the production and price cycle.
When you plot these evolutions of quantity and price on a classic supply-and-demand curve chart, you get a line that spirals toward or away from the point of equilibrium, creating a cobweb-like pattern. That cobweb is usually visible; because of the time lag between planting and harvesting, grain prices are rarely in equilibrium. But there is also a limit to how wide the cobweb gets, precisely because once one crop becomes very expensive relative to another, farmers grow less of it. We can see that not only in the widening and contrasting of the cobweb pattern, but also in the log ratio between historical soybean and corn prices, which has always reverted to its long-term mean within one or two crop cycles.
So when we saw record prices for soybeans relative to corn in 1973, we could have safely predicted that cattle farmers would put more corn in their feed mix at the same time as farmers were planting more soybeans. It would have seemed like a no brainer to go long corn and short soybeans… wouldn’t it?
A Spot Price-Based Mean Reversion Strategy
Let’s test the theory by applying a mean-reversion trading strategy to soybean and corn spot prices between 1989 and today. Starting in 1989 gives us 20 years of market data before that date with which to study equilibrium pricing for our model. The spot price is the price you pay for a physical commodity today.
We take the log ratio between soybean and corn spot prices over time and subtract its one-week rolling average from its five-year rolling average to give us a signal as to which grain is expensive and which is cheap. The wider the spread between the one-week and five-year averages, the bigger the bet we make on one grain versus the other. Specifically, we lag the signal by two business days and use a hyperbolic tangent transformation to arrive at daily weights between -100% and +100% for each commodity. There are numerous other ways of mapping signals to allocations, but for our simple analysis let’s stick with this relatively transparent method.
Figure 1 shows the cumulative log excess return to this trading strategy.
Figure 1. Have We Discovered A Truly Idiosyncratic Alpha Source?
Cumulative log (excess) return of a spot-based soybeans-versus-corn relative value strategy
Source: Bloomberg, Neuberger Berman.
The trading methodology is described in the text. Spot price growths are based on SPGSCI spot series. Bloomberg tickers SPGSCN Index and SPGSSO Index are used for corn and soybeans, respectively. The performance figures and numbers are transaction cost adjusted: daily rebalanced strategies described here have annual turnovers of 400%, on average; we assume a very conservative 5 basis points of proportional transaction costs, resulting in an annual drag on these strategies of around 20 basis points. For illustrative purposes only. Past performance is no guarantee of future results.
This chart suggests that, were we able to receive payoffs based on spot prices we would have discovered a truly idiosyncratic alpha source that would have made money even during recessions. It has a Sharpe ratio of 0.57 and an excess return of 4.5%, annualized.
Alas, except for a few precious metals that are simple and cheap to store and trade physically, payoffs based on commodity spot prices are impossible to engineer. Still, we can implement the same trade via commodity futures. How different could the results be?
Figure 2. In the Real World, the Alpha Disappears
Cumulative log (excess) return of both spot-based and futures-based soybeans-versus-corn relative value strategies
Source: Bloomberg, Neuberger Berman.
The trading methodology is described in the text. Futures excess returns are based on SPGSCI nearby contract excess return series. Bloomberg tickers SPGSCNP Index and SPGSSOP Index are used for corn and soybeans nearby futures, respectively. Spot price growths are based on SPGSCI spot series. Bloomberg tickers SPGSCN Index and SPGSSO Index are used for corn and soybeans, respectively. The performance figures and numbers are transaction cost adjusted: daily rebalanced strategies described here have annual turnovers of 400%, on average; we assume a very conservative 5 basis points of proportional transaction costs, resulting in an annual drag on these strategies of around 20 basis points. For illustrative purposes only. Past performance is no guarantee of future results.
Figure 2 gives us the answer; Unfortunately, it’s not encouraging. Futures-based pair trading of soybean and corn results in a meager Sharpe ratio of 0.24 and an average excess return of 1.5%, annualized, with long periods of inconsistent returns. What accounts for that yawning performance gap? The cost of carry.
Carry That Weight
When we buy or sell commodity futures, we are contracting to deliver or take delivery of that commodity on the day the contract expires. If all we want is financial exposure and we don’t have the commodity to deliver or the facilities to receive it, we need to sell the contract before it expires and buy a longer-dated one. This is known as “rolling.”
Long-dated contracts do exist, and holding them would make rolling unnecessary. They are less liquid, however, and if we go too far out on the curve the price may be more correlated with expected spot prices for the next crop cycle than with expected spot prices for the current cycle—it is not uncommon for spot and long-dated futures pricing to move in opposite directions. For that reason, investors tend to hold near-dated contracts, and there are five new corn futures each year and seven new soybean futures. Holding a relative value trading position between these two crops for a year is therefore likely to require rolling 12 contracts—and as we know, it usually takes one or more crop cycles for relative pricing to mean-revert.
It is not the cost of trading those contracts that eats into the return, as these are liquid markets and the costs are low. The issue is that the contracts do not trade at the same price. Corn for delivery next month may not command the same price as corn for delivery in six months’ time.
When we roll from one futures contract to another, the difference in the price we receive for selling and the price we pay for buying is known as the “roll yield,” and it can be positive or negative. It stands to reason that a commodity we perceive to be trading cheaply today and whose price we expect to mean-revert over time is more likely to have a futures price curve that is upward-sloping—what is known as “in contango.” By the same token, an expensive commodity is more likely to have a downward-sloping, or “backwardated” curve.
This means that, if we are long the cheap commodity we will likely have to pay more for the new contract every time we roll, and if we are short the expensive commodity we get paid less for the new contract every time we roll—a double-whammy negative roll yield for a relative-value trade. And it gets worse if we are long corn and short soybeans: some commodity futures curves tend to be in contango more than others, and corn is one of them due to its relatively high storage costs and generally large inventories.
Basically, going long a cheap commodity and short an expensive one is likely to incur a negative roll yield. These trades therefore require high conviction.
Building Conviction: Carry-Adjusted Trading Signals
One simple way to build that conviction is to estimate the cost of carrying a relative-value trade and then use that estimate to adjust our relative-value trading signal.
To estimate the ongoing cost of carry, we calculate the cumulative roll yield incurred by going long one commodity and short another over the past 12 months, by subtracting the spot spread return from the futures spread return. We then blend that roll yield with our relative-value signal in proportions of 25% and 75%, respectively—we want to adjust the relative value signal but not override it completely—before applying the hyperbolic tangent transformation to arrive at our trade weights. When we did this for soybeans and corn between 1989 and today, the resulting weights did tend to move in favor of soybeans, as we would expect given the contango bias in corn futures curves, but only by an average of around 10 percentage points. What the carry adjustment did is to slightly raise the bar for going long corn versus soybeans when corn is perceived as relatively cheap.
Figure 3 shows how a relative-value strategy using these carry-adjusted weights in corn and soybean futures would have fared, relative to the theoretical spot-based return and the non-adjusted futures-based return.
Figure 3. The Impact of Adjusting for the Cost of Carry
Cumulative log (excess) return of spot-based, futures-based and carry-adjusted futures-based soybeans-versus-corn relative value strategies
Source: Bloomberg, Neuberger Berman.
The trading methodology is described in the text. Futures excess returns are based on SPGSCI nearby contract excess return series. Bloomberg tickers SPGSCNP Index and SPGSSOP Index are used for corn and soybeans nearby futures, respectively. Spot price growths are based on SPGSCI spot series. Bloomberg tickers SPGSCN Index and SPGSSO Index are used for corn and soybeans, respectively. The performance figures and numbers are transaction cost adjusted: daily rebalanced strategies described here have annual turnovers of 400%, on average; we assume a very conservative 5 basis points of proportional transaction costs, resulting in an annual drag on these strategies of around 20 basis points. For illustrative purposes only. Past performance is no guarantee of future results.
The result suggests that it would have been desirable to accept the additional bias of the carry adjustment in order to achieve substantially higher risk-adjusted returns. Indeed, with the exception of a false signal from the estimate of carrying costs during the drought of 1996, which caused an initial performance drag, our carry adjustments would have brought the implementable performance using futures much closer to the non-implementable spot-based performance. It almost doubled the Sharpe ratio of the non-adjusted futures-based strategy with very similar volatility.
Going With the Grain
Commodities offer opportunities to harvest relative valuation dislocations, but those opportunities are often not tradable without adjusting for the cost of carry or roll yield in futures markets.
We have focused on corn and soybeans here, but there are many other pairs of related commodities where one leg tends to have a similarly persistent carry advantage: examples include but are not limited to oil versus natural gas, Kansas wheat versus Chicago wheat, cattle spreads, location spreads (between Brent crude and WTI, for example) and “crush spreads” (between soybean, soybean meal and soybean oil futures, or between crude oil and refined products).
In this article, we have presented a simple way to adjust for carry costs, and by going with the grain of carry rather than against it we believe it becomes feasible to implement effective relative-value strategies for a broader commodity futures portfolio. Given their non-financial and truly idiosyncratic nature, a blend of commodity relative-value strategies has the potential to be used as a great portable alpha source.