Backwardation

Under the cost-of-carry framework, the no-arbitrage futures price equals the spot price compounded at the risk-free rate, plus the present value of storage and insurance costs, minus the convenience yield earned by holding the physical asset. Financing and storage push the futures price above spot; convenience yield pulls it below. Backwardation is simply the outcome when that last term dominates the other two, so net carry is negative.

Convenience yield is the non-monetary benefit of having inventory on hand: a refiner that owns barrels can keep running when a pipeline fails, while a holder of a futures contract cannot. That benefit is inversely related to inventory levels. When stocks are ample, the yield is negligible and the curve slopes upward; when stocks are drawn down and stockout risk rises, the yield spikes and the front of the curve is bid above deferred contracts.

The total return on a fully collateralised long futures position is conventionally split into three parts: the collateral return earned on posted cash, the price or spot return on the underlying, and the roll return generated by replacing an expiring contract with a deferred one. Roll return is positive when the deferred contract is cheaper than the contract being sold, which is precisely the geometry of a backwardated curve.

Mechanically, the futures price must converge to spot at expiry because basis risk collapses to zero. If spot is unchanged over the holding period, a contract bought at a discount accretes upward toward spot, delivering gain. The critical qualification is that roll return is not risk-free income: it is the compensation embedded in the curve, and a decline in the spot price can easily exceed it. Candidates should be able to sign the roll return from the slope alone and then state what else must hold for the position to profit.

Energy and agricultural markets backwardate during genuine physical tightness, when refiners, utilities or processors bid aggressively for prompt delivery. Precious metals almost never do: gold is cheap to store, effectively non-perishable and held in vast above-ground inventory, so convenience yield is close to zero and the curve sits in near-permanent contango.

The condition is not confined to commodities. VIX futures typically trade in contango in calm markets but flip into backwardation during equity selloffs, when spot volatility spikes above the level expected to persist. Equity index futures show an analogous structure: since the carry is the financing rate less the dividend yield, an index whose dividend yield exceeds short-term rates will price futures below spot. Currency forwards behave the same way through the interest rate differential.

These two terms are distinct and are routinely tested against each other. Backwardation is an observable relationship between the futures price and the current spot price. Normal backwardation, following Keynes, is a relationship between the futures price and the market's expected future spot price, and it is unobservable because expectations cannot be read directly from quoted prices. The hedging-pressure argument holds that when short hedgers dominate, speculators must be induced to go long by a futures price set below expected spot, so the contract drifts upward as expiry nears and the long earns a risk premium.

At Level I, be able to classify a curve from a strip of quotes, decompose carry into financing, storage and convenience yield, sign the roll return for a long or short position, and distinguish an expectations-based statement from a carry-based one.