Convenience yield represents the implied interest paid for borrowing physical commodity. Holding physical inventories carries benefits of flexibility for industrial consumers. The value of such inventories increases when scarcities arise. As a consequence, convenience yields help predicting future demand and price changes. A new Bank of Canada paper illustrates this for the crude oil market.

Alquist, Ron, Gregory Bauer and Antonio Diez de los Rios (2014), “What Does the Convenience Yield Curve Tell Us about the Crude Oil Market?”, Bank of Canada, Working Paper 2014-42
http://www.bankofcanada.ca/wp-content/uploads/2014/09/wp2014-42.pdf

The below are excerpts from the paper. Emphasis and cursive text have been added. 

The convenience of storage and its yield

“One of the fundamental drivers of the price of crude oil is inventories. Since crude oil is a storable commodity, stocks…link…current demand and supply to expectations of future demand and supply… inventories play a fundamental role in the formation of a commodity price because holding stocks is intrinsically valuable given the operational flexibility they provide. For example, owing to technological constraints, an oil refinery has the incentive to hold stocks to optimize its output of petroleum products…reducing the costs of changing production and helping them to avoid stock-outs. Consequently, the optimal levels of production and inventories are jointly determined given the spot price of oil and the price of storage.”

“The convenience yield can be thought of as the interest rate paid in barrels of oil for borrowing one barrel of oilWe observe that by borrowing a barrel of crude oil, the borrower is supplying storage in the form of crude oil inventories to the lender. Consequently, the lender must be compensated for forgoing the benefit associated with holding the barrel of oil. In equilibrium, this requirement links the convenience yield to the price of storage that is, the marginal value of the…services that accrue from holding an additional unit of inventory net of the cost of physically storing crude oil.”

The relationship between convenience yield and inventories

“The theory of storage…suggests that (i) the marginal benefit for holding inventories increases at a decreasing rate with the scarcity of a commodity, and (ii) the marginal cost of physically storing oil can be treated as constant…That is, the one-period convenience yield is assumed to be a [decreasing] function of the level of inventories We therefore expect to observe a negative and monotonic relationship between the convenience yield and the current level of crude oil stocks…We verify…that this relationship exists in the market for U.S. crude oil inventories.”

For a more comprehensive explanation of how inventory levels affect commodity futures curves and returns view post here.

How to measure convenience yield and its curve

“While convenience yields are not directly observable, they can be synthetically replicated by taking simultaneous positions in money, crude oil spot and futures markets…[based] on the premise that the spot and futures markets are linked together in a way consistent with the absence of arbitrage opportunities [which implies that high convenience yield is indicated by a high spot relative to futures price]… By analyzing futures contracts with different expiration dates, we assess the information contained in the term structure of convenience yield about the implicit benefit of physical storage over different horizons. For example, an upward- sloping convenience yield curve indicates a situation in which refineries assign a higher value to future inventories than they do to todays inventories. Such periods indicate that oil inventory is expected to be scarcer in the future.”

“There has been a substantial increase in the liquidity of the market for oil futures contracts. On the sell side, financial institutions have become more actively involved in commodity derivatives markets, including futures contracts of longer maturity. On the buy side, increased investor interest has resulted in large quantities of financial capital owing into these markets during the past decade… Over a sample period between April 1989 and June 2013, we exploit the increase in the liquidity of longer-maturity oil [WTI] futures contracts to construct the term structure of convenience yields out to the one-year horizon.”

On the financialization of commodity markets view post here.

Basic traits of the crude oil convenience yield curve

“The cross-section of crude oil convenience yields across maturities can be explained by a small number of principal components. Similar to the term structure of interest rates, the first component resembles a level factor that is common across maturities. The second component is related to the slope of the curve. [All of this is a technical way of saying that oil futures curves are typically smooth rather than segmented and kinked as in the case of some agricultural commodities or livestock.].”

“The convenience yield curve exhibits a funnel shape, indicating that the sensitivity of long-term convenience yields to movements in the short-term convenience yield decays with the maturity of the oil bond…Interestingly, the funnel shape implies that the volatility of convenience yields is a decreasing function of the maturity of the contract.”

Convenience yield as predictor of changes in stocks

“[We] test whether the term structure of convenience yields contains information about the future path of inventories in PADD 2…, the administrative region in the United States oil distribution network where Cushing, Oklahoma (the delivery point for the WTI futures contract) is located…Both the level and slope components have predictive power for future changes of crude oil stocks up to the one-year horizon… Consistent with the theory of storage, longer-maturity convenience yields are forward-looking variables related to the scarcity of crude oil.”

Convenience yield as a predictor of production and price

“Because convenience yields are determined by the interaction of storage decisions with the supply and demand of crude oil, we also expect convenience yields to contain information about future conditions in the physical market for crude oil and future oil prices….[Indeed, empirical evidence suggests that] the term structure of convenience yields contains information about future crude oil production, global real economic activity and the real price of crude oil.”

“If agents expect a shortfall of future oil supply relative to future oil demand, they will increase their demand for crude oil stocks today in anticipation of the shortfall in the net oil supply. On the supply side, the optimal response to this situation is to increase the production of crude oil, although the increase in production is likely to take time given the inelasticity of the oil supply curve. This set of forces creates a situation in which an increase in inventories today is followed by an increase in crude oil production to meet the additional demand for crude oil stocks…Empirical evidence is consistent with the view that production is inelastic in the short term.”

“[Empirical evidence also suggests that ] the first principal component of convenience yields [i.e. their level] is negatively related to future crude oil prices in real and nominal terms. When convenience yields are high (i.e., crude oil is scarce), crude oil prices are predicted to subsequently fall [which really just means that the futures curve, which would be ‘backwardated”, gives the right prediction about the direction of future spot prices]… We attribute this effect to the sluggishness of the supply response and the mean reversion of convenience yields and crude oil scarcity. As discussed above, an unexpected increase in demand causes the spot price of oil to overshoot in the short run, given that supply takes time to respond fully to such a change.”