Contango Backwardation Explained: $6 Swing on $80 Oil

Oil sits at $80 a barrel and does not move for a year. A futures contract is a deal to buy oil on a set future date, at a price fixed today. Each expiry date has its own price. The list of those prices is the futures curve. A holder who wants to keep oil exposure must replace each contract as it expires. That replacement is the roll. When later contracts cost more than today's price, the curve slopes up (contango). The roll then costs $6 a barrel over the year. When later contracts cost less, the curve slopes down (backwardation). The roll then earns $6.

Every price in this article is an assumption we chose. Nothing here is a market quote. We build one made-up oil curve, tilt it each way, then follow the same position through both. All figures are per barrel, before fees, margin (the cash deposit a futures position needs) and tax.

A futures contract is an agreement to buy or sell an asset at a fixed price on a set future date. That date is the expiry. The spot price is the price for immediate delivery. Our spot price is $80 a barrel.

Plot those prices against the months left to expiry and you get the futures curve. Our curve covers expiries from 0 to 12 months away. Its slope decides whether the roll costs money or earns it.

Contango is an upward-sloping curve. Each later contract costs more than the one before it. All of them cost more than spot.

We build ours from two assumed costs of holding a barrel for a month.

Financing costs 3% a year on $80, which is $0.20 a month. Storage and insurance cost $0.30 a month. Together they add $0.50 a month. A contract one month out therefore costs $80.50. One 12 months out costs $86.

Backwardation is a downward-sloping curve. Each later contract costs less than the one before it. All of them cost less than spot.

We assume buyers pay a premium of $0.50 a month for oil in hand over oil later, the same size as the contango step with the sign reversed. A contract one month out costs $79.50. One 12 months out costs $74.

Chart 1 shows the two curves meeting at $80 at month 0. The contango line rises to $86 at month 12. The backwardation line falls to $74. The table gives both curves at five expiries.

Price per barrel, made-up oil with a spot price of $80. Source: YX Insights

The 12-month contract sits $6 above spot in contango, which is 7.5% of $80. In backwardation it sits $6 below spot, also 7.5%. The two 12-month contracts are $12 apart.

In our example, each contract calls for immediate delivery on its expiry day, so its price equals spot on that day. The 0-month row of the table shows it, where both curves meet at $80.

This is why the curve's slope matters.

If spot stays put, a contract bought above spot loses that gap by expiry. A contract bought below spot gains it. The gap closes through the contract's price. The holder receives it as a roll loss or a roll gain.

A holder who wants to keep oil exposure beyond one contract's expiry must close that contract and open the next one. We assume a holder who owns the one-month contract and rolls it each month for 12 months, with exposure to one barrel.

In contango, the holder buys at $80.50 each month. If spot is unchanged at $80, the contract is worth $80 at expiry. That is a $0.50 loss on each roll. Twelve rolls lose $6, which is 7.5% of $80.

In backwardation, the holder buys at $79.50 each month and the contract is worth $80 at expiry. That is a $0.50 gain on each roll. Twelve rolls gain $6. Chart 2 shows the running total, with the oil price unchanged for the whole 12 months.

The two lines are mirror images. The spot price never moved. The roll moved the holder's result by $6 in each direction.

Spot moves too. Over 12 months, the holder's result equals the change in spot plus the roll result (a roll loss in contango, a roll gain in backwardation). We keep the $0.50 monthly step on the curve in every case, which is an assumption. We also move spot in equal monthly steps to its end level.

Chart 3 shows three end levels: $72 (down 10%), $80 (unchanged) and $88 (up 10%).

If spot falls to $72, the spot change is an $8 loss. Contango adds a $6 roll loss for a $14 total loss. Backwardation adds a $6 roll gain, which cuts the total loss to $2.

If spot rises to $88, the spot change is an $8 gain. Contango adds a $6 roll loss and leaves a $2 gain. Backwardation adds a $6 roll gain and leaves a $14 gain. In the contango case the roll took three-quarters of the spot gain.

The spot result and the roll result add together. At $88, the contango roll cut the gain from $8 to $2. If the oil price rose by less than 7.5%, the $6 roll loss would leave the contango holder with a net loss.

The contango curve slopes up because we assumed storage and financing costs of $0.50 a month. The backwardation curve slopes down because we assumed a premium of $0.50 a month for oil in hand. We make no claim about what drives a real oil curve, or which shape one will take.

Our curve is a straight line with a flat $0.50 step. We chose that to keep the arithmetic clear. We left out margin, interest earned on the cash backing a position, fees and tax.

We also kept the curve's slope fixed while the spot price moved. If the slope changed as well, the roll result would change.

Our guide to how the oil market works sets the curve in the wider market for real oil.

Contango and backwardation are the two slopes of the futures curve. In our example, a monthly roll cost $6 a barrel in one and paid $6 in the other, while the oil price did not move.

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Contango is a futures curve where later contracts cost more than spot, the price for immediate delivery. Backwardation is the opposite, with later contracts costing less. In our example, the 12-month contract costs $86 in contango and $74 in backwardation, against a spot price of $80.

In our example, it costs a holder who rolls: each new contract is bought $0.50 above the spot price it reaches at expiry. Rolling monthly for 12 months with spot unchanged loses $6 a barrel.

A roll is the replacement of an expiring futures contract with one that expires later. It keeps exposure to the asset going. In our example, each monthly roll in contango costs $0.50 a barrel, while each roll in backwardation pays $0.50, with spot unchanged.

In our example, a futures price equals spot on its expiry day, because each contract calls for immediate delivery then. The one-month contract bought at $80.50 in contango is worth $80 at expiry if spot is unchanged.

DISCLAIMER: This article is intended for educational purposes only. Any information or analysis in this note does not constitute an offer to sell or a solicitation of an offer to buy any securities. Nothing in this note is intended to be investment advice, nor should it be relied upon to make investment decisions. Any opinions, analyses, or probabilities expressed in this note are those of the author as of the note's date of publication and are subject to change without notice.