State what storage costs, carry markets, the lease rate and convenience yield mean, and apply these concepts to commodities.
The idea
Storage costs are the warehousing, insurance and handling expenses of holding a physical commodity. They raise the forward price. In a carry market the forward price exceeds spot by interest plus storage costs, and the curve slopes upward. The convenience yield is the benefit of owning the physical commodity, such as keeping a plant running or avoiding a stockout, which a forward holder does not get. It is high when inventories are low and it lowers the forward price. The lease rate is what a lender of the commodity earns, paid in units of the commodity, as with gold. It works like a dividend yield. The usual mistake is to confuse the lease rate, a market payment, with the convenience yield, which is an implied benefit.
A practice question
Which of the following best defines the convenience yield of a commodity?
- The payment made in units of the commodity to someone who lends it.Why not: This is the lease rate, a market payment, not the implied benefit of physical ownership.
- The benefit from holding the physical commodity, such as keeping production going, that a holder of a forward contract does not receive. - correct
- The cost of warehousing, insuring and handling the commodity.Why not: This describes the storage cost, which raises the forward price; the convenience yield lowers it.
- The amount by which the forward price exceeds the spot price.Why not: This is the forward premium or basis; it is an outcome of carry costs and yield, not the yield itself.
Convenience yield is the implied benefit of owning the physical commodity (avoiding stockouts, keeping plants running). It lowers the forward price relative to full carry.
A harder one
Inventories of crude oil fall sharply after a supply disruption. Holding all else constant, which change would the cost-of-carry model most likely show?
- The convenience yield falls, so forward prices rise relative to spot.Why not: Reverses the effect: scarce inventory raises the benefit of physical holding.
- The storage cost rises, so forward prices rise relative to spot.Why not: Treats the disruption as a rise in storage costs; low inventories raise the benefit of holding oil, not the cost.
- The convenience yield rises, so forward prices fall relative to spot and the curve moves toward backwardation. - correct
- The lease rate falls to zero, so the forward equals spot.Why not: There is no market for leasing crude oil in the way gold is lent, and a zero lease rate does not follow from a supply cut.
Scarce inventory makes owning the physical commodity more valuable, raising c in F = S x exp((r + lambda - c) x T). A higher c lowers the forward relative to spot.
The hardest tier
A commodity trades at USD 50. The risk-free rate is 5%, storage costs are 1.5% and the convenience yield is 3%, all per year and continuously compounded. The no-arbitrage two-year forward price is closest to:
- USD 53.63 - correct
- USD 56.94Why not: Ignores the convenience yield and so gives the full cost of carry.
- USD 50.50Why not: Subtracts the storage cost; storage is a cost of carrying and is added.
- USD 60.46Why not: Adds the convenience yield; it is a benefit of holding and is subtracted.
Net carry = 0.050 + 0.015 - 0.030 = 0.035; F = 50 x exp(0.035 x 2) = 53.63.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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