Convenience Yield
Convenience yield is the value of holding a physical commodity right now rather than a promise of it later — it never shows up as an explicit cash flow, only as a discount that pulls the futures price below where pure cost-of-carry says it should sit.
Prerequisites: The Spot-Futures Basis in Commodities, Cost Of Carry Model
A refiner who runs out of crude oil doesn't get to wait three months for a futures contract to deliver — the plant stops. That refiner will pay a premium to hold actual barrels in a tank today, over and above whatever storing them costs, purely for the insurance of never running dry. That premium, imputed rather than paid in cash, is the convenience yield: the benefit of holding the physical good itself, which financial models treat like a dividend the commodity pays to whoever is holding it right now, even though no check is ever written.
Convenience yield is not observed directly — it's backed out as whatever number makes the cost-of-carry formula match the actual futures price. It rises when inventories are tight (physical supply is precious, so holding it now is valuable) and falls toward zero when inventories are abundant (there's no benefit to holding stock you could easily buy later).
Backing it out of the market
Rearranging the cost-of-carry relationship isolates convenience yield as the residual:
In words: take the financing cost and storage cost of holding the commodity, subtract the annualized premium the futures price actually charges over spot, and whatever's left is the convenience yield the market is implicitly pricing. When futures trade unusually cheap relative to spot given normal financing and storage costs, the gap has to be explained by something — and that something is the value the market places on physical, immediate ownership.
Worked example
Spot copper is $4.00/lb. Financing costs 5% annualized and storage runs 2% annualized, so with zero convenience yield the 1-year future should sit near 4.00 \times 1.07 = \4.28. The actual 1-year future trades at \4.10. Solving gives — the market is implicitly saying holding physical copper right now is worth about 4.5% a year, likely because warehouse stocks are low and industrial buyers don't want to risk being short of metal while waiting on a futures delivery.
What this means in practice
Convenience yield is the main reason cost-of-carry, which works almost perfectly for financial futures like stock indices, needs an extra fudge factor for physical commodities: unlike a share of stock, a barrel of oil or a bushel of wheat is genuinely more useful to hold in hand than to hold a paper claim on, and that usefulness varies with how scarce the physical good currently is. Traders infer convenience yield from the futures curve to read inventory tightness without needing to see the actual warehouse data.
High convenience yield and backwardation are two names for the same underlying condition — tight physical supply — viewed from different angles: one is the imputed benefit, the other is the resulting curve shape.
Practice in interviews
Further reading
- Kaldor, 'Speculation and Economic Stability', Review of Economic Studies (1939)
- Geman, Commodities and Commodity Derivatives (ch. 3)