Pricing Futures Contracts Part 2: What the Data Shows
Book: Commodities: Markets, Performance, and Strategies
Editors: H. Kent Baker, Greg Filbeck, Jeffrey H. Harris
Publisher: Oxford University Press, 2018
ISBN: 9780190656010
From Theory to Spread Trading
In Part 1, we covered the theoretical framework for pricing futures contracts. Now we get into the more practical side of Chapter 15 by Timothy Krause: spread trading relationships between related commodities and the use of statistical models to forecast energy prices.
This is where the chapter shifts from “here is how pricing should work in theory” to “here is what traders actually do with these pricing relationships.”
The Crack Spread: Oil Refining in Futures Form
One of the most practical applications of futures pricing theory is spread trading. A spread trade takes advantage of the price relationship between related commodities.
The most famous example is the crack spread in energy markets. Three barrels of crude oil can be refined (“cracked”) into roughly two barrels of gasoline and one barrel of heating oil. This is called the 3:2:1 spread.
Krause walks through a concrete example from January 2017. March crude oil futures were at $53.20 per barrel. RBOB gasoline futures were $1.522 per gallon, and heating oil futures were $1.620 per gallon. Running the math:
- Two-thirds of the gasoline revenue per barrel of oil: $42.64
- One-third of the heating oil revenue per barrel of oil: $22.65
- Total revenue from products: $65.29 per barrel
- Minus crude oil cost: $53.20
- Gross crack spread: $12.09 per barrel
If your refining costs are $8 per barrel, that leaves a net profit of about $4.09 per barrel. An oil refiner can lock this in by selling the appropriate gasoline and heating oil futures while simultaneously buying crude oil futures.
This is not just a trading strategy. It is how real refineries hedge their business. They know their costs, and they can use futures to guarantee a profit margin regardless of where absolute price levels go.
Other Important Commodity Spreads
Krause covers several other spread relationships beyond the crack spread:
The spark spread captures the relationship between natural gas prices and electricity prices. Power plants burn natural gas to produce electricity, so these prices are linked through something called the heat rate, which measures how efficiently a plant converts fuel into power.
The dark spread is similar but uses coal instead of natural gas as the input for electricity production.
The frac spread looks at the relationship between natural gas and natural gas liquids (NGLs) like propane and ethylene. Refiners break down raw natural gas into these usable products.
In agricultural markets, the crush spread mirrors the crack spread but for soybeans. Soybeans get “crushed” into soybean meal and soybean oil. All three trade as futures, so you can lock in the processing margin.
The cattle crush replicates feedlot operations. The inputs are feeder cattle and corn. The output is live cattle. Again, all tradeable as futures.
These spread relationships exist because the commodities are physically connected through production processes. They give producers and consumers real tools to manage their business risk.
Forecasting Energy Prices with GARCH
The second major empirical section of the chapter tackles a different question: can statistical models predict commodity futures prices?
Krause uses an EGARCH-t model (a type of GARCH model) to analyze crude oil and natural gas futures between 2010 and 2016. The data comes from NYMEX daily futures and spot prices.
A quick explanation of what GARCH does: it models the changing volatility of price movements over time. Regular models assume volatility stays constant. GARCH recognizes that in financial markets, volatility clusters. High volatility periods tend to be followed by more high volatility. Calm periods tend to stay calm. The EGARCH version also accounts for the fact that prices tend to be more volatile after drops than after gains (the leverage effect).
Here is what the model found for crude oil futures:
- The mean daily price change was -$0.018 with a standard deviation of $1.446
- Price changes ranged from -$9.44 to +$7.37
- Kurtosis was 5.618, meaning fat tails (extreme moves happen more than a normal distribution would predict)
- The asymmetric volatility coefficient was positive and significant, confirming that prices are more volatile after declines
For natural gas, the picture was similar but with even fatter tails (kurtosis of 7.683) and evidence of stronger mean-reverting behavior.
The Forecasting Results: Honest but Humbling
Here is the thing about the GARCH forecasting results. The model produces forecasts that look pretty close to actual prices on a chart. But Krause is honest about why.
Most of the forecasting “power” comes from the fact that the one-day-ahead forecasts get updated daily with new price information. The actual predicted changes are much smaller than real price changes. The median absolute daily change in the forecast was only 0.201, while the median absolute actual price change was 0.610.
Even more telling: out of 19 out-of-sample forecast observations for November 2016, the model predicted the correct direction of the next day’s price change only 9 times. That is barely better than flipping a coin.
Krause is straightforward about this. Statistically significant forecasting ability does not necessarily translate into economically significant profits. The models are interesting academically, but whether you can trade on them profitably is a different question entirely. And Krause says the answer is “uncertain” and “seems unlikely without further refinement.”
This is a refreshing level of honesty for an academic chapter. Many researchers show their statistically significant results and stop there. Krause goes the extra step to say: look, statistical significance and economic significance are not the same thing.
Seasonality Matters
One interesting observation from the natural gas analysis is the role of seasonality. Natural gas futures showed a clear uptrend in late November as winter months approached, because natural gas is a primary heating fuel. The GARCH model used in the chapter does not account for this seasonality, which probably hurts its performance.
This makes sense intuitively. Energy markets have strong seasonal patterns. Heating oil demand rises in winter. Gasoline demand peaks in summer driving season. Any model that ignores these patterns is leaving predictive power on the table.
What Krause Concludes
The chapter wraps up with several key points:
The no-arbitrage pricing framework works very well for financial assets like stock indices. For commodities, the results vary because of supply and demand dynamics in the physical markets.
Spread trading provides useful information to commodity producers and consumers. The crack spread, spark spread, crush spread, and others are real tools that businesses use every day.
The cost of carry model is generally accepted by both academics and practitioners as the correct framework for thinking about futures pricing.
GARCH models can produce statistically significant forecasts of commodity futures prices, but they are probably not useful for implementing profitable trading strategies.
My Take
The spread trading section is the most practically useful part of this chapter. Understanding that crude oil, gasoline, and heating oil prices are linked through the refining process is not just academic knowledge. It explains why these prices move together and how real businesses manage their risk.
The GARCH forecasting section is valuable for a different reason: it shows the limits of quantitative models. You can build a sophisticated model that passes every statistical test, but if it only predicts the direction of price changes half the time, it is not going to make you money after trading costs.
The broader lesson is that commodity markets are harder to model than equity markets. The physical nature of commodities, the storage constraints, the seasonality, and the supply and demand shocks all create complexity that clean mathematical models struggle to capture.
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