The Crack Spread: A Gauge of Demand Strength and the Negative-Correlation Theorem

The crack spread (product price minus feedstock price) is a representation of demand strength. In bulk process industries, the crack spreads of multiple products derived from the same feedstock exhibit a stable negative correlation — this is not a coincidental empirical regularity but a linear relationship (ax+by=0) derivable from the financial-balance identity under the assumption of mass conservation; the criterion for distinguishing primary from by-products is “whether the product’s functional use can be replaced by the feedstock” rather than yield, which in refining translates to light oil (primary) vs. heavy oil (by-product); and the diesel crack spread is the anchor most closely tied to crude oil prices.

The Framework As It Stands

This section is organized from the compiled research draft: the original framework’s structure, terminology, and key formulations are preserved, including editorial bridging and external factual annotations; diagrams are drawn by the compiler following the original text’s structure.

Core Mainline

Of the three major spread studies (inter-regional spreads / crack spreads / calendar spreads), the crack spread — “product price minus feedstock price” — is the representation of demand strength. Using soybean crushing as the entry point, the framework establishes four core judgments:

The crack spread is the price adhesive between product and feedstock; its essence is a representation of demand strength
In bulk process industries, the crack spreads of multiple products from the same feedstock exhibit a stable negative correlation — derivable from the financial-balance identity + mass conservation assumption as a linear relationship (ax+by=0)
The criterion for distinguishing primary from by-products is not yield but “whether the product’s functional use can be replaced by the feedstock”; in refining this translates to light oil (primary) / heavy oil (by-product), with primary crack spread and by-product crack spread negatively correlated
The landing point — in the refining industry, the crack spread most closely tied to crude oil prices is the diesel crack spread; “only when diesel does well can crude do well”; the gasoline crack spread decouples from oil prices due to three compounding differences: demand nature, process pathway, and process reversibility

Three threads run through the framework:

Thread A — Crack Spread = Price Adhesive Between Product and Feedstock / Representation of Demand Strength

The crack spread is defined as product price minus feedstock price, and is a representation of demand strength. The inter-regional spread is the adhesive between global benchmark crudes (Shanghai crude futures linked to Dubai, Dubai linked to Brent, Brent linked to WTI); the crack spread is the price adhesive between product and feedstock. This adhesion only exists in bulk process industries — where feedstock and product prices in the supply chain are strongly correlated — whereas in assembly / manufacturing (e.g., smartphones) there is no such correlation between component prices and finished-product prices.

Thread B — The Mathematical Root of the Negative Correlation: Financial-Balance Identity + Mass Conservation

The soybean oil crack spread and the soybean meal crack spread show a pronounced negative correlation; this has held in historical data over long periods and is not coincidental. Its root is not an empirical fluke but the bulk process industry’s financial-balance formula (total value of all products − feedstock cost − expenses = gross profit), which, under the mass conservation assumption (100 tonnes of soybeans in, 100 tonnes of products out, commodity yield 97–98% or above), when expanded and like terms are collected, yields “soybean oil yield × soybean oil crack spread + soybean meal yield × soybean meal crack spread = expenses + gross profit.” Since expenses + gross profit account for an extremely small and relatively stable share (crude oil cost accounts for 95%+ of refinery costs), this approximates the linear relationship ax+by=0 (simplified to x+y=0), and negative correlation is therefore inevitable. Black-metal industries are inapplicable because mass is not conserved (oxygen combines with coke to form CO₂, a non-commodity); manufacturing is inapplicable because expenses and gross profit account for too large a share.

Thread C — Primary/By-Product Criterion Goes Beyond Yield: Look at Whether Functional Use Can Be Replaced by the Feedstock

The core rule in bulk process industries is that the primary product crack spread and the by-product crack spread are negatively correlated. Distinguishing primary from by-products is not based on yield but on whether the product’s functional use can be replaced by the feedstock — a by-product’s functional use can be replaced by the feedstock (soybean meal feeds pigs, so can soybeans; fuel oil can be burned, so can crude oil), while a primary product’s functional use cannot be replaced by the feedstock (soybean oil cooks food, but raw soybeans cannot; cars run on gasoline but not on crude oil). In refinery terminology, primary products are called light oil and by-products heavy oil; light oil crack spread and heavy oil crack spread are negatively correlated. The ratio of crack spreads is inversely proportional to yield: the lower the yield of a product, the more its crack spread can fluctuate (C4 fractions can surge to tens of thousands of yuan per tonne; gasoline exceeding one thousand yuan/tonne is already extreme).

Argument Synthesis

Definition and essence of the crack spread. The crack spread is a representation of demand strength; first observed in oil products, but soybean crushing is used here to reveal the underlying regularity. Definition: the spread between product price and feedstock price.
Soybean crushing case — cross-product price adhesion mechanism. Soybean crushing is a continuous bulk process industry, yielding soybean oil and soybean meal; the absolute prices of the feedstock (soybeans) and the two products are highly correlated. Analogy: inter-regional spreads are the adhesive between global benchmark crudes; crack spreads are the price adhesive between product and feedstock. Bulk process industries are characterized by extremely strong feedstock-product price linkages; assembly/manufacturing (e.g., smartphones) has no such linkage between component prices and finished-product prices. Deductive reasoning also requires confirming the derivation conditions (bulk process industry applicability) before applying this regularity.
Empirical regularity of the negative correlation in crack spreads. Constructing the soybean oil crack spread (soybean oil price − soybean price) and the soybean meal crack spread (soybean meal price − soybean price), the two crack spreads show a pronounced negative correlation; this is not coincidental, and historical data has borne it out over extended periods.
Mathematical derivation of the negative correlation. Financial-balance formula for bulk process industries: total value of all products − feedstock cost − expenses = gross profit; total product value = Σ(product price × yield). Prerequisite assumption: mass conservation (100 tonnes of soybeans in, 100 tonnes of products out; commodity yield in soybean and crude processing reaches 97–98% or above, with minimal losses); black-metal industries are a counter-example because oxygen combines with coke to form CO₂ (not a commodity), violating conservation. Expanding and collecting like terms yields “soybean oil yield × soybean oil crack spread + soybean meal yield × soybean meal crack spread = expenses + gross profit” — this is the linear relationship ax+by=0 (simplified to x+y=0), making negative correlation inevitable. Because expenses and gross profit account for an extremely small and stable share (crude cost at refineries is 95%+), the regularity holds; in manufacturing (e.g., consumer electronics) expenses and gross profit account for a large share, so it does not apply. Bulk process industry economics: thin margins, volume-driven.
Crack spread ratio is inversely proportional to yield. The ratio of the two crack spreads is inversely proportional to their respective yields; corollary: the lower the yield of a product, the greater its allowed crack spread volatility — small-volume products have higher price volatility, while large-volume products (e.g., diesel) are more constrained. Example: in the petrochemical industry, C4 prices can surge to tens of thousands of yuan/tonne, while gasoline swings exceeding one thousand yuan/tonne are already extreme.
Empirical validation in the refining industry. European refinery products (gasoline, diesel, high-sulfur fuel oil) are highly correlated with Brent crude prices; subtracting Brent from each product yields crack spreads — the diesel crack spread and the high-sulfur fuel oil crack spread show a pronounced negative correlation, while the gasoline crack spread shows weaker regularity.
Definition of primary and by-products. Core rule in bulk process industries: primary product crack spread and by-product crack spread are negatively correlated. Criterion is not yield but whether the product’s functional use can be replaced by the feedstock — a by-product’s functional use can be replaced by the feedstock; a primary product’s functional use cannot. Soybean case: soybean meal is a by-product (feeds pigs, as do soybeans), soybean oil is a primary product (cooking oil, which soybeans cannot directly replace). Refining case: gasoline and diesel are primary products, fuel oil is a by-product (ships burn fuel oil, but can also burn crude oil). Refinery terminology: primary products = light oil, by-products = heavy oil; light oil crack spread and heavy oil crack spread are negatively correlated. In the data, diesel (representative primary product) and fuel oil (by-product) fit the regularity; gasoline as primary product representative shows anomalous behavior.
Special characteristics of the gasoline crack spread. Empirical: the gasoline crack spread (U.S. gasoline futures − WTI crude) has weak correlation with WTI crude prices; the diesel crack spread has strong, clearly synchronized correlation with crude prices; conclusion: “only when diesel does well can crude do well.” Three causes: ① Demand-nature difference — diesel consumption is more tied to heavy machinery and more closely linked to the economy; gasoline consumption more reflects a country’s living standards/level of development and is used in passenger vehicles; ② Process-pathway difference — diesel is closer to crude (crude → distillation → diesel hydrotreating → diesel), while gasoline is blended (components include catalytic gasoline, reformed gasoline, naphtha, methyl tert-butyl ether, etc., further from crude); ③ Process reversibility — excess diesel can be cracked into naphtha for gasoline production, but gasoline cannot be reverse-converted into diesel.
Conclusion — the central position of the diesel crack spread (+ yield data + warning). Standard refinery product yields: gasoline and diesel account for 60%+; at an 85% commodity rate, gasoline and diesel amount to approximately 75%, with chemical naphtha around 10%. In the refining industry, the crack spread most closely tied to crude oil prices is the diesel crack spread; diesel market anomalies have stronger correlation with oil prices. Warning (as of the December 2019 lecture): high-sulfur fuel oil (starting next year) cannot be used without exhaust gas cleaning; the market will see a major disruption. (Compiler’s note: this refers to IMO 2020, the low-sulfur bunker fuel regulation, effective January 1, 2020.)

Reasoning Chain

flowchart TD
    A[Crack Spread Regularity<br/>Demand strength representation · Primary/by-product negative correlation · Diesel anchor]

    A --> B[Thread A: Crack spread = price adhesive between product and feedstock]
    B --> B1[Definition = product price − feedstock price<br/>Representation of demand strength]
    B1 --> B2[Inter-regional spread adhesive for benchmark crudes<br/>Crack spread adhesive for product and feedstock]
    B --> B3[Holds only in bulk process industries<br/>Assembly/manufacturing (smartphones) has no such linkage]

    A --> C[Thread B: Mathematical root of negative correlation]
    C --> C1[Financial balance: total output value − feedstock − expenses = gross profit<br/>Mass conservation (commodity yield 97-98%)]
    C1 --> C2[Collect like terms<br/>Sum of yield × crack spread = expenses + gross profit]
    C2 --> C3[Expenses+profit share extremely small (crude cost 95%+)<br/>→ linear ax+by=0 → inevitable negative correlation]
    C3 --> C4[Counter-examples: black metals not conserved<br/>Manufacturing: large expense/profit share → inapplicable]

    A --> D[Thread C: Primary/by-product criterion goes beyond yield]
    D --> D1[Criterion = can functional use be replaced by feedstock?<br/>Not yield]
    D1 --> D2[By-product: replaceable by feedstock (soybean meal/fuel oil)<br/>Primary: not replaceable (soybean oil/gasoline+diesel)]
    D2 --> D3[Refinery terms: primary = light oil; by-product = heavy oil<br/>Light oil crack spread negatively correlated with heavy oil]
    D --> D4[Ratio inversely proportional to yield<br/>Small-volume products (C4) highly volatile; large-volume (diesel) constrained]

    C3 --> E[Landing point: diesel crack spread = closest anchor to crude prices]
    D3 --> E
    E --> E1[Gasoline crack spread anomaly: three causes<br/>Demand nature / process pathway / process reversibility]
    E --> E2[Diesel leads crude<br/>Gasoline+diesel yield 60%+ · diesel market anomalies track oil prices more closely]

Key Data Anchors (as of the December 2019 Lecture)

Data Item	Value/Ratio	Meaning
Bulk process industry commodity yield	97–98% or above	Basis for mass conservation assumption
Refinery crude cost share	95% or above	Expenses + profit very small; negative correlation regularity holds
Gasoline + diesel yield	60% or above	At 85% commodity rate, gasoline + diesel ~75%
Chemical naphtha yield	~10%	Standard refinery product structure
C4 extreme volatility	Can reach tens of thousands of yuan/tonne	Low yield → allows very large crack spread swings
Gasoline extreme volatility	Exceeding 1,000 yuan/tonne is already extreme	High yield → swings are constrained

Mathematical root of negative correlation: ax+by=0 (simplified x+y=0), where x = soybean oil / light oil crack spread, y = soybean meal / fuel oil crack spread, a/b = respective yields; the yield-weighted sum approximates a constant (expenses + gross profit).

Key concepts: crack spread (product price − feedstock price; representation of demand strength); bulk process industry (continuous process, feedstock and product prices strongly linked, high commodity yield and mass conservation); primary/by-product criterion (can functional use be replaced by feedstock? not yield); light oil / heavy oil (refinery terms for primary / by-product; crack spreads of the two are negatively correlated); diesel crack spread (the anchor in the refining industry most closely tied to crude oil prices).

Relationship with the inventory cycle: diesel demand directly maps to the intensity of economic activity (heavy machinery, freight), so the diesel crack spread has an intrinsic resonance with the restocking/destocking phases of the general inventory cycle — in an expansion phase, restocking requires diesel-driven activity, and the diesel crack spread strengthens ahead of crude prices.

Compiler’s Perspective

Coordinates: Category = Energy and Commodities · axis_h = Fa (Method) · axis_v = Why It Is So

Its Place in the Whole

The specific error in the old approach: upon seeing the soybean oil/soybean meal crack spread chart showing a negative correlation, treating it as a “market empirical regularity” and memorizing it; when encountering a period of divergence (e.g., high-protein meal prices pushing up the soybean meal crack spread but the soybean oil crack spread not declining simultaneously), feeling confused and thinking the regularity had failed — in reality, the “contingent empirical rule” framework was being misapplied instead of the “necessary theorem” framework. Without understanding the mathematical root of the regularity, it is impossible to judge in which circumstances deviations are ignorable and in which circumstances they indicate that the original assumption (mass conservation) no longer holds.

The more common error on the gasoline side: seeing that gasoline is a “primary product (light oil)” → inferring that the gasoline crack spread should be most correlated with crude prices → treating as “data anomaly” when the actual data shows weak correlation. The correct reasoning path requires working through three compounding differences (demand nature / process pathway / process reversibility); gasoline is “the light oil furthest from crude” and the light/heavy-oil negative-correlation regularity cannot be used to predict the relative movements of gasoline and diesel.

Proprietary Increment: This framework’s standard for the “primary/by-product criterion” is asymmetric — the condition for designating a by-product is “functional use can be replaced by feedstock,” and “can be replaced” requires two conditions to hold simultaneously: the functional use is the same (both can serve as some form of fuel/feed) and the price differential is not extreme (otherwise the market would not actually substitute). Fuel oil and crude oil can both be burned, but under the IMO 2020 high-sulfur fuel oil regulatory constraint, fuel oil’s “substitutability” underwent a structural shift (it could not be used for shipping without a cleaning device), causing its by-product character to be weakened under a specific regulatory backdrop — this is an extension that can only be derived by someone who understands the substance of the “functional substitutability” criterion.

Relationship with Three Modes of Macro Research Thinking and the Primacy of Empirical Regularity: This framework provides a demonstration of upgrading from “empirical regularity” to “logically derivable theorem” — the soybean oil/soybean meal negative correlation was initially only an empirical regularity, but the financial identity derivation elevated it to “as long as mass conservation holds and expenses + gross profit are sufficiently small, the regularity must hold,” thus achieving greater predictive strength than a pure empirical regularity. This is a methodological cognitive difference: the former starts doubting the regularity at the first sign of divergence; the latter first checks whether the prerequisite conditions still hold.

Sources

“Compiled draft: z-0171 · collected July 2026”
“Public course audio transcription (2019-12)”

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