Soybean Futures Crush Spread Arbitrage: Trading Strategies and Market Efficiency

This paper revisits the soybean crush spread arbitrage work of Simon (1999) by studying a longer time period, wider variety of entry and exit limits, and the risk-return relationship between entry and exit limits. The lengths of winning and losing trades are found to differ systematically, with winning trades significantly shorter on average than losing trades. Exiting trades near the 5-day moving average is shown to improve trade performance relative to a reversal of sign and magnitude from the entry spread. These results lead to trading rules designed to prevent lengthy trades; however, the profitability of trading rules is found to be unstable.


Soybean (S), soybean meal (SM), and soy oil (BO) futures contracts are traded on the Chicago
Board of Trade (CBOT). This paper explores the relationship between these three contracts, commonly referred to as the crush spread. The soybean crush spread provides an interesting opportunity for exploring market efficiency. The relatively stable relationship between soybeans and the amount of meal and oil that are produced when the beans are crushed results in predictable value relationships between the relevant futures contracts.
The crush spread is employed both by speculators betting on a widening or narrowing of the relationship between the contracts and by other market participants, such as soybean crushing mill owners, with an economic stake in the relative prices of the three commodities. A long crush refers to buying the meal and oil and selling the beans. Speculators would employ this trade when the spread is narrow relative to normal levels and the value of meal and oil is expected to rise relative to the value of beans. This trade minimizes the risk associated with general price movements of the three contracts and allows speculators to focus on the relationship between the contracts. Similarly, a wide spread could be exploited by selling the meal and oil and buying the beans.
Owners of crushing mills can employ the same trades to lock in profit margins by guaranteeing the relative value of their final products (meal and oil) relative to their principal input (beans). Mill owners would, for example, sell the spread (sell meal and oil and buy beans) when the spread is large.
The crush spread is calculated here based on a naïve 1:1:1 relationship, consistent with earlier studies.
Crush Spread = (SM x 100) + (BO x 600) -(S x 50) (1) Where SM is the price of Soybean Meal in dollars per ton, BO is the price of Soybean Oil in dollars per 100 pounds, and S is the price of Soybeans in dollars per 100 bushels. The Holmes (2002). Dunis et al., (2006) find that a moving average model outperforms a fair value model for petroleum inter-market spreads from 1995-2004. They find annualized returns as high as 26.15% using a correlation filter and including transaction costs. Similarly, Haigh and Holt (2002) find that a multivariate GARCH model increases the effectiveness of crack spread hedging.
The interest in the risk reduction and arbitrage opportunities in spread trading is exemplified by the recent introduction of spread futures on the Chicago Board of Trade. This development is chronicled by Cuny (2006). The CBOT introduced Soybean Crush Options, further emphasizing the need existing in the market for understanding the behavior of the soybean crush spread.

MOTIVATION FOR STUDY
This study differs from earlier research in the five ways. First, this study reverses trades at, or near, its 5-day moving average rather than at a spread of equal but opposite sign as the opening limit. Simon (1999) finds mean reversion. However, mean reversion does not necessarily imply that the spread will continue beyond equilibrium in an oscillating manner. By choosing closing limits short of equilibrium, this study attempts to increase the percentage of profitable trades and reduce the standard deviation of profit; albeit at the possible expense of reduced profit.

METHODOLOGY
Trades are opened when the crush spread deviates from its most recent 5-day moving average by amounts ranging from $200 to $400. If the crush spread exceeds the specified amount, sell the spread i.e., sell oil and meal and buy soybeans. Similarly, if the crush spread falls below the 5-day moving average by the specified amount, buy the spread i.e., buy oil and meal and sell soybeans.
Transactions are reversed (closed) if the deviation from the 5-day moving average becomes less than specified amounts ranging from zero to $200. This trade reversal rule differs from the rule employed by Simon. Simon tests for movement beyond the 5-day moving average.
Mean reversion does not necessarily imply that the spread will do anything more than revert towards the mean. There is no reason to expect that the spread will continue in an oscillating manner beyond the 5-day moving average. Once exceeding its recent average there should be immediate pressure to move back toward that average. Therefore, it is unreasonable to expect, and indeed count upon, continued movement away from the 5-day average. Closing limits short of reverting to the 5-day moving average are tested to determine if stopping short of the average improves the percentage of profitable trades and other trade characteristics.
Closing transactions on rollover dates are triggered based on the previous contracts while opening transactions on those dates are triggered based on the new contracts. Therefore, the 5day moving average is always calculated based on the previous 5 days for the same contract expiration month being employed to trigger a transaction.
Only one trade is allowed to exist at any given point in time. New positions are not created until existing trades have been reversed to isolate the effects of particular opening limits.
Secondly, the use of symmetric (+/-) opening limits combined with smaller closing limits precludes the establishment of long positions while short positions, or vice versa, are outstanding.

Results with Transaction Costs
Results are presented with the same $103.50 transaction costs employed by Simon for both short and long trades for each combination of trade limits. Although brokerage fees fell over the study period, the bid-ask spread, which is the largest component of the transaction cost, was relatively stable. For ease of reporting the trade limits are symmetric. Long and short trades use the same limit with opposite sign, and limits are reported as opening/closing. Results consist of the number of trades, average profit, standard deviation of profit, coefficient of variation, percentage of profitable trades, maximum profit and loss, average length of trade, average length of profitable and unprofitable trades, maximum length of profitable and minimum length of unprofitable trades, and maximum trade length.

Number of Trades
The number of trades over the 20-year study, Table 1, varies from a low of 70 in the case of 400/0 thru 40 (an opening trade limit of 400 and a closing limit of anywhere between 0 and 40) to a high of 994 for 100/80. The effects of increasing the closing limit are relatively modest. For example, at an opening limit of 400, raising the closing limit from 0 to 200 only increases the number of trades by 6% (from 70 to 74) while at an opening limit of 220, raising the closing limit to 200 increases the number of trades by 20% (from 285 to 341). Closing limits of half the size of opening limits (e.g., 400/200) result in a 6 -13% increase in trades relative to a return to the 5-day moving average (e.g., 400/0). The effect is less at higher opening limits. The increase in the number of trades as the closing limit is increased is a result of completing transactions more rapidly and therefore clearing the way for additional trades.
The number of trades is more sensitive to the opening limit. An increase of 20 in the opening limit results, on average, in a 15% reduction in the number of trades when the closing limit is zero. It is important to note that the reported results are for a 20-year period. Even the maximum number of 994 trades amounts to no more than one trade every 7 days; and at the highest limits only one trade every 104 days. Unless trades prove very profitable, only an automated trading system could prove economically worthwhile.
The maximum profit for each opening limit generally occurs at, or near, a closing limit of zero.
Closing limits half as large as opening limits, result in a 24 -65% decrease in average profit relative to a closing limit of zero at opening limits above 240, where such a comparison becomes meaningful. Increasing the opening limit increases average profit most rapidly between 140 and 320 with more modest increases at each end of the range.

. Standard Deviation of Profit
The standard deviation of profit, Table 3, ranges from a low of $219 at 100/80 to a high of $595 at 400/0. The standard deviation increases as the opening limit is increased and as the closing limit is decreased. The standard deviation is less sensitive to changes in the closing limit, at least at low levels of the closing limit, when the opening limit is large. This suggests that closing limits near zero may result in more advantageous risk-return relationships and is explored later by examining the coefficient of variation.

Coefficient Variation
The coefficient of variation, Table 4, ranges from a low of 4.28 at 380/80 to extremely high levels where the average profit is near zero. The coefficient of variation decreases in an irregular manner as the opening limit increases to 320 and then rises at higher levels of the opening limit.
The lowest value for the coefficient of variation occurs at opening limit levels of 320 to 380. At opening limits below 380 the minimum coefficient of variation occurs at a closing limit of zero.
At opening limits of 380 and 400 the minimum shifts to a closing limit of 80. For opening limits of 280 and greater the coefficient is fairly steady over a wide range of limits suggesting a consistent risk-return relationship.

Percentage of Profitable Trades
The percentage of profitable trades, Table 5, ranges from 35% at 100/80 to 73% at opening limits of 380 and 400 at mostly low closing limits. The percentage increases in a fairly steady manner as the opening limit increases and is generally greatest at or near a closing limit of zero. If the level of profit is normally distributed, which it is not, a coefficient of variation of 4.28 (the best possible combination as noted above) would signify approximately a 55% probability of gain.
The fact that the probability of gain is somewhat higher (72% again at 380/80) is a result of skewness in the distribution of profit.

Maximum Profit and Maximum Loss
The maximum profit is $1,210 at all limits. This is caused by the same outlier trade in each case.
The maximum loss is -$3,089 at all closing limits of 120 or lower, -

Average Trade Length
The average trade length, Table 6, ranges from 1.79 days at 220/200 to 4.34 days at 200/0. At low closing limit levels the average trade length generally increases slightly with the opening limit up to an opening limit of 200, and then generally declines slightly. However, at closing limit levels of 60 or higher the average trade length continues to increase as the opening limit increases. Higher closing limits in general tend to reduce average trade length since the trade does not need to return as far towards the recent average spread. Overall, average trade length exhibits relative stability.

Average Length of Profitable Trades
The average length of profitable trades, Table 7, ranges from 1.27 days at 220/200 to 2.63 days at 220/0. The average length of profitable trades behaves much the same as the average length of all trades; as might be expected given the high percentage of profitable trades. However, the average length of profitable trades is lower at all levels, typically by approximately 1 day. This is the first indication that profitable and unprofitable trades differ systematically in length. In general, higher closing limits reduce average profitable trade length and higher opening limits increase average profitable trade length, as least to opening limits of 220. Above opening limits of 220 the values fluctuate but are relatively stable.

. Average Length of Unprofitable Trades
The average length of unprofitable trades,

Maximum Trade Length
Maximum trade length, Table 9, ranges from 13 days at various combinations of opening limits above 240 and closing limits of 180 or greater to a high of 24 for opening limits of 100 to 180 with closing limits of 40 or less. In general, low opening and closing limits produce high maximum trade lengths. Closing limits near the opening limit slightly decrease the maximum length. This suggests that high opening limits signal situations where there is intense pressure to return toward zero while low opening limits (especially very low opening limits not reported in this paper) may capture situations where the current trend is away from zero.

Maximum Length of Profitable Trades
The maximum length of profitable trades, Table 10, ranges from 5 days at high opening and closing limits to 9 days at combinations of low opening and closing limits. This parameter is, of course, determined by some individual trade.

Minimum Length of Unprofitable Trades
The minimum length of unprofitable trades, Table 11, ranges from 1 to 3 days. Highest values are at opening limits of 220 to 280 and closing limits of 20 or less. As with the maximum length of profitable trades, this parameter is potentially affected by some outlier trade. The obvious implication of some unprofitable trades being shorter than some profitable trades is that it may not be profitable to truncate trade length in an attempt to avoid the worst trades.

Time Segment Characteristics
Crush spread results are compiled for four equal non-overlapping time segments in Table 12.
Results vary systematically over the time segments. The first segment has, on average, a negative crush spread while the mean crush spread over the remaining three segments is 1,716. Although the fourth segment has the lowest standard deviation of the spread, it has the highest kurtosis and the most positive skewness. This increased incidence of extreme changes potentially leads to incorrect buy and sell signals.

Trade Results by Segment
The four time segments are analyzed for differences in trade results in Table 13. In general, the fourth time segment gives negative average profit results, a higher standard deviation of profit, a lower percentage of profitable trades, and longer trade length. These results demonstrate that even should a profitable set of opening and closing limits be found, in general, specific time periods may yield negative results. Traders need be aware of changing spread characteristics due to heteroskedasticty. The problem during the fourth time period was that spread deviations large enough to trigger trades were sometimes followed by further movement away from the 5-day moving average. Reversal of that movement away from the average was sometimes rapid enough to trigger the closing trade based on the updated moving average, but at a price disadvantageous to the initial position.
The soybean crush spread must be evaluated in the context of worldwide production of numerous crops of varying substitution opportunity in an industry with regulation of production, price supports, and trade quotas. Soybean meal and oil are just one source of protein and oil for animal feed, human consumption, and industrial use. Corn is the typical alternative for animal feed, the overwhelming use of soy meal. Canola is a major alternative to soy oil. Changes in the supply and demand conditions, including crushing capacity, may render the crush spread unstable. Goodwin, Schnepf, and Dohlman (2005) find that the pricing relationships for soybeans change over time with major structural breaks. Kruse (2003) reports that while meal demand is highly price elastic, oil demand is more inelastic, and that the elasticities change over time. Further econometric research beyond the scope of this study is needed to better understand the changing nature of the process which determines the crush spread.

Ignoring Transaction Costs
When transaction costs are ignored, the percentage of profitable trades increases from the range of 31% -74% to the range of 72% -80%. Additionally, the systematic difference between the length of winning and losing trades is increased. For example, at 380/140 the percentage of profitable trades increases from 71% to 80%, while the average length of winning trades increases from 1.71 to 1.91 days, and the average length of losing trades increases from 5.17 to 6.00 days. It is interesting that BOTH the overall (un-weighted) average length of profitable trades (increases by .23 days) and the average length of losing trades (increases by 1.17 days) increase as some of the relatively short losing trades with transaction costs become relatively longer profitable trades without transaction costs. Consistent with this, the maximum length of profitable trades increases by 1 to a length of 4 days in most events at closing limits of 100 or less. Similarly, the minimum loss length increases by 1 day at most combinations of limits.
Meanwhile, the coefficient of variation of course falls, as profit has been increased by $103.5 while the standard deviation is unchanged. In the case of 380/140, the coefficient of variation falls from 5.22 to 2.56 when transaction costs are ignored. It is this change in coefficient of variation as a measure of the risk-return relationship which potentially creates differential arbitrage opportunities. Traders with lower transaction costs face better risk-return relationships. The transaction costs of the most efficient traders that will dictate market behavior.

Short versus Long Trades
Results are compiled separately for short and long trades in Table 14. Long trades are more profitable on average and have a higher likelihood of profitability but have a higher standard deviation of profit. Consistent with this are higher maximum gains and losses for long trades.
Some combinations of limits do have a lower coefficient of variation for long trades. Statistics for trade lengths are very similar for short and long trades.

Higher Limits
Higher opening limits (up to 800/400) are also studied with transaction costs. The number of trades drops precipitously. While average profit fails to increase, the percentage of profitable trades hovers in the 60-70% range. Probability of gain as high as 77% exists (560/0 and 560/40), but the coefficient of variation is 5.95 and 7.24 respectively with average profit of $142.82 and $115.23. In general the coefficient of variation at higher opening limits deteriorates, although it is as low as 2.24 at 800/400. Unfortunately only 8 trades exist over the 20-year study period at this level and waiting for them is likely not justified by the $242 average profit.

Reversal Strategy
The strategy of reversing trades only when the spread has reached a level equal but of opposite sign to the opening limit, as employed by Simon, reduces the number of trades and increases average profit, the standard deviation of returns, and the coefficient of variation.

Summary of Analysis
A risk-return tradeoff (coefficient of variation) indicates that contrary to the symmetric limits studied by Simon (e.g., short the crush if the spread is greater than $100 above the 5-day moving average and reverse the trade if the spread is $100 less than the 5-day moving average), traders can benefit by reversing trades near the 5-day moving average. Average profit increases, the standard deviation of profit decreases, and the percentage of winning trades increases.
Traders also may benefit from establishing trade length limits (i.e., truncating trades).
Losing trades are, on average, significantly longer than winning trades. Artificial trade length limits may help to reduce the incidence and severity of the worst losing trades.

Truncation of Trade Length
Because the average length of profitable trades is lower than the average length of losing trades, and because the maximum length of profitable trades is relatively short; it may be profitable to truncate trade length. For example, no trade at any set of limits up to 400/200 produces a profitable trade in excess of 9 days and almost no profitable trades over 7 days exist at opening limits over 200. See Table 10. Truncating trades may or may not avoid losing trades, and could exacerbate losses if trades are closed before a reversal (closing) signal is produced by the spread.
Three trade truncation limits are studied. In general, the coefficient of variation is improved as the trade truncation limit is reduced to 10 or 8 days. At a truncation limit of 6 days the coefficient of variation begins to increase. This is demonstrated with un-weighted averages of all coefficients of variation at opening limits of 300 and higher. The region of 300 and higher is chosen due to negative and extremely high coefficient of variations at lower opening limits which indicate unlikely opportunities for arbitrage attempts. The average coefficient of variation falls from 5.72 to 5.60 to 5.30 and then rises to 6.56 for unlimited trade length, 10-day, 8-day and 6-day limits respectively. These same trade truncation limits have minimal effect on the probability of profitable trades. The shortened trades avoid few losses and free up the trading account for additional trades in the same unfavorable environment that caused the original trade to lose money. Therefore, the trade truncation limits are judged non-beneficial.
Trade truncation if a contract roll-over occurred during the trade failed to improve results.
Results for that variation are not reported here.

RESEARCH
Unless further research demonstrates arbitrage limits (filters) with more appealing risk-return characteristics, the soybean crush spread should be considered an efficient market. Although the risk-return relationships are not consistent, they do not provide profitable arbitrage opportunities using a variety of opening and closing limits.
In contrast to previous work by Simon, profitable trades are significantly shorter than losing trades. However, truncating trade lengths in an attempt to segregate gains from losses does not significantly improve results.
The averaging period employed to determine significant deviations should be explored to ascertain if a longer (shorter) period better identifies significant deviations. Similarly, other more sophisticated arbitrage identification techniques such as Simon's "Fair Value", regression techniques, and neural networks may still yield arbitrage opportunities. In October, 1992 the CBOT changed the soymeal contract specifications from 44% protein to 48% protein. A more exact representation of the spread as it is now commonly traded of 10 soybean, 9 soyoil, and 11 soymeal contracts, for all contracts expirations after October, 1992, may better track prices.
The persistence of those arbitrage opportunities that do exist could also be investigated.