What has to be true for December oil to cost less than today's oil?

Something quite specific. Go back to the identity:

F = S + financing + storage + insurance − convenience yield

For F < S, the convenience yield must exceed everything else combined. Not "sentiment is bullish", not "traders expect a decline" — a hard arithmetic condition:

convenience yield > financing + storage + insurance

Somebody, somewhere, is willing to pay more than the full cost of carry for the privilege of having the physical commodity now rather than later. That is what a downward-sloping commodity curve means, and it is essentially the only thing it means.

Putting a number on it

Spot $78.00, full carry over six months $4.55, and the six-month contract quoted at $74.50:

c = 78.00 + 4.55 − 74.50 = $8.05 a barrel over six months

As a rate: 8.05 ÷ 78.00 = 10.3% over six months, roughly 20.6% a year.

Sit with that figure. The market is saying that the option to have a barrel today rather than in June is worth about a fifth of the barrel's value on an annualised basis. That is not a mood. It is a price, paid in cash, by people who need the commodity to run a business.

The inventory relationship

Convenience yield is not random — it is a decreasing, convex function of inventory. Plenty in store, and the marginal barrel confers almost no operational benefit, because you were never going to run out. Stocks near the operational minimum, and the marginal barrel is the difference between running and stopping, so its convenience value climbs steeply.

That gives you a clean mapping from stocks to curve shape:

• Inventories high → convenience yield near zero → curve at or near full carry (contango).
• Inventories normal → partial-carry contango.
• Inventories low → convenience yield exceeds carry → backwardation.
• Inventories critically low → steep backwardation, and it steepens fast, because the function is convex.

This is why the same commodity can flip from contango to backwardation and back inside a single year without anything strange happening. Nothing about the market's structure changed. The tanks emptied, then refilled.

Two roads to backwardation

Inventory draw. Demand has been outrunning supply for long enough that stocks have fallen. This is the slow, structural version, and it usually shows up first as a shallow backwardation at the very front of the curve.

Disruption risk. A pipeline outage, a strike, a sanctioned exporter, a drought in a growing region. Here the market may be adequately supplied today but frightened about tomorrow, and holders will not part with inventory at any normal price. This version can appear overnight and can unwind just as fast.

You cannot tell them apart from the curve alone. You can tell them apart by looking at published inventory statistics next to the curve, which is exactly what Unit 4 does.

Backwardation is self-correcting too

A steeply backwardated curve pays a holder of inventory to sell it now and buy it back forward at a discount. That is a genuine incentive to liquidate stocks — which relieves the immediate tightness that caused the backwardation, and draws inventories down further. So backwardation both signals scarcity and helps resolve it, right up until stocks reach the level below which operations break, at which point holders stop responding to the incentive entirely.

That last clause is important. Below a certain inventory level, the arithmetic stops being about profit and starts being about whether the plant runs. Convenience yield becomes, in effect, unbounded — which is exactly the asymmetry from Unit 1.

Try it now

1. Five years of front-month natural gas is below. Measure the three sharpest rallies you can find, and drop a Level at the top of each so you can find them again.

2. For two or three of those dates, find the exchange's settlement strip as it stood then and check whether the curve was backwardated at the time. In tight markets the price and the shape move together, and the shape usually moves first.
3. Now look up the published inventory series for the same weeks (for natural gas, the US Energy Information Administration's Weekly Natural Gas Storage Report, free on eia.gov, every Thursday), and describe the relationship in one sentence — as a description, not a rule.