3:2:1 Crack Spread: Formula and Worked Example

The formula

Let G be gasoline in dollars per gallon, D be ULSD in dollars per gallon and C be crude oil in dollars per barrel. The theoretical 3:2:1 crack quote per barrel of crude input is:

The division by three matters: the basket contains three crude units. Omitting it produces the basket difference rather than the comparable per-barrel quote. If your product feed is in cents per gallon, first divide that quote by 100.

Worked hypothetical example

Gasoline contributes 2 × 2.20 × 42 = $184.80. ULSD contributes 2.40 × 42 = $100.80. Three crude units cost $225. The basket difference is $60.60, and the crack quote is $60.60 ÷ 3 = $20.20 per barrel.

These are invented teaching inputs, not current prices. The quoted level is not the profit earned merely by opening a position.

Sensitivity of the basket

Holding the other legs fixed, a $1 rise in crude reduces the per-barrel crack by $1. A $0.01/gallon rise in gasoline increases it by $0.28; the same rise in ULSD increases it by $0.14. These arithmetic sensitivities follow from the basket weights.

To estimate position P&L, apply the change in the quote to the correctly sized exposure and include execution costs. Do not multiply by a generic contract value without checking the contracts and the number of baskets.

Document expiry choices

Record the exact months used for all three legs and use the same convention when comparing dates or platforms. A futures proxy does not reproduce every refinery’s timing or output mix. For the exchange’s explanation, see CME’s crack conversion calculator.

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