Across assets, carry is defined as return for unchanged prices and is calculated based on the difference between spot and futures prices (view post here). Unlike other markets, commodity futures curves are segmented by obstacles to intertemporal arbitrage. The costlier the storage, the greater is the segmentation and the variability of carry. The segmented commodity curve is shaped prominently by four factors: [1] funding and storage costs, [2] expected supply-demand imbalances, [3] convenience yields and [4] hedging pressure. The latter two factors give rise to premia that can be received by financial investors. In order to focus on premia, one must strip out apparent supply-demand effects, such as seasonal fluctuations and storage costs. After adjustment both direction and size of commodity carry should be valid, if imprecise, indicators of risk premia. Data for 2000-2018 show clear a persistent positive correlation of the carry with future returns.

The post ties in with SRSV’s summary lecture on implicit subsidies, particularly the section on commodity futures.

The below are quotes from various papers, listed at the end of the post. Emphasis and cursive text have been added. The empirical analysis of the final section has been undertaken by Macrosynergy LLP.

Limits to arbitrage

“The well-known arbitrage condition that determines the relationship between spot and futures prices for financial assets rarely holds for commodities. The role of commodities as consumption and processing goods, and the pivotal importance of physical inventories, among other factors, lead to a more complex and dynamic relationship.” [Roache/Erbil]

“In commodity markets, there are at least six sources of imperfections which naturally influence the [forward and spot] prices’ behaviour…

  • Arbitrage can be slowed down by difficulties associated to the localization of the delivery points of the futures contract of the commodity. Indeed, an operator undertaking a cash and carry between the physical and futures markets must necessarily deliver the commodity at the expiration of the contract…Not all operators have storage capacities…
  • The storage costs and the necessity to have at one’s disposal storage capacities may also hinder arbitrage operations…
  • Not all operators possess transport capacities…A strike preventing from the exploitation of the unique railway used for the transportation of raw materials can hinder a delivery…
  • Arbitrage is impossible if the regarded commodity is not storable. This is the case for electricity…
  • A possible consequence of quality differentials is the ‘cheapest to deliver’ bias. At the time of delivery of a futures contract, the buyer can rationally expect that the seller will try to deliver the lowest quality of the commodity…
  • In most of the financial markets, in order to undertake arbitrage operations, it is possible to borrow the assets and to carry out short sales. This is not possible in the case of commodities. Who, in backwardation, would take the risk to leave his merchandise during a few weeks or months and sustain a production’s disruption?” [Lautier]

The role of storage costs

“Relying on stocks and arbitrage operations, the explanation of contango situations, where the futures price is higher than the spot price, is quite straightforward. The spread between futures and spot prices is related to the cost of holding the commodity over time…The storage costs stand for fixed and variable costs. The fixed costs are due to insurance and warehouse expenses. They remain constant as long as the storage capacities are not saturated. The variable costs are due to deterioration and obsolescence, to the necessity to finance inventories and to maintenance expenses.” [Lautier]

“The level of contango cannot stay higher than the storage costs. Whenever such a situation occurs, cash and carry arbitrages restore the equilibrium: it becomes profitable to buy physical stocks in the spot market, to carry them and simultaneously to sell futures contracts. These sales lead to a decrease in the futures price, whereas the spot price increases as a result of inventory purchases. Finally, arbitrage opportunities disappear” [Lautier]

“In commodity markets, negative [forward-spot] prices spreads appear when stocks are low. Thus, reverse cash and carry arbitrages are all the more unlikely if shortage is pronounced: the operators on the physical market do not have any interest in selling the merchandise as long as they expect an additional rise in the spot price. So the basis behaves not in the same way when it is positive and negative. In contango, there are surplus stocks and, as long as storage capacities are not saturated, the basis is stable and limited to the storage costs. In backwardation however, stocks are rare and the basis is solely determined by the spot price the operators are willing to pay in order to immediately obtain the merchandise. There is no subjective limit to the basis. Moreover, because inventories are not sufficiently abundant to absorb the fluctuations in the demand, the spot price is volatile, and so is the basis.” [Lautier]

Supply-demand imbalances

“The relationship between commodity spot and futures prices reflects, in part, the perception of short-term physical scarcity and the prevailing level of inventories. The slope of the futures curve…can thus provide information on whether market participants anticipate relative abundance (an upward sloping curve) or scarcity (a flat or downward sloping curve) in the physical market.”  [Roache/Erbil]
N.B.: To the extent that a commodities future curve represent expected ‘scarcity’ and price changes it is not indicative of risk premia.

[Excluding the effects of risk premia and implicit subsidies] the slope of the futures curve can change for one of three reasons: a change in interest rates; a change in physical storage costs; or a change in the market’s perception of short-term scarcity…Large changes in the futures curve slope are rarely caused by the first two explanations…In most cases, …the effects of changes in actual or expected scarcity over short horizons…will reflect actual or expected supply disruptions, as most demand shocks exhibit a higher degree of persistence. [Roach/Erbil]

Convenience yields

“Stocks of all goods possess a yield: the convenience yield… the remuneration associated with the holding of physical stocks.” [Lautier]

“A factory who suddenly identifies a need for oil, may have to pay high transportation costs to arrange delivery at short notice…These costs can be avoided (or at least, reduced) by holding a small inventory of assets which might be needed in a hurry. This could be worth doing even if there were a penalty for holding physical assets, for example, lower returns as expressed by the convenience yield, sometimes also called a liquidity premium.” [Smith]

“If we introduce the convenience yield…the [forward-spot] prices’ spread, also called the basis,  [should be equal to the difference between storage costs and convenience yield]…Such a characterization of the relationship between spot and futures prices is consistent with the no-arbitrage valuation of futures contracts on financial assets, where the futures price usually corresponds to the spot price, plus the financing costs related to the investment in the underlying asset, minus the remuneration of the underlying asset… When the convenience yield becomes higher than storage costs, there is backwardation.” [Lautier]

Risk or hedging premia

“The hedging pressure theory…analyzes the risk premium or the expected basis…In equilibrium, there might be a contango or a backwardation, the risk premium might be positive or negative.” [Ekeland/Lautier/Villeneuve]

“Commodity risk premiums can be defined as returns that speculators expect to receive as compensation for taking another party’s natural exposure to fluctuations in commodity prices…Explanations for the existence of a risk premium typically view futures markets as a risk-transfer mechanism between market participants and therefore focus on the role of hedging…the net hedging pressure theory implies that the futures price will be set below the expected future spot price to induce speculators – who do not have a commercial exposure they need to hedge – to balance the market by taking the opposing long position.” [Hambur/Stenner]

“[Typically] commodity producers take short futures positions in order to hedge against price drops and therefore pay a premium to an investor that offers this insurance and takes a long position in the futures contract; this positive premium comes in the form of the carry premium…[Similarly] commodity consumers take long futures positions in order to hedge against unexpected future price surges; in this scenario, they should pay a premium to the investor that offers the insurance and takes a short position, in which case contango arises…” [Baltas]

“Hedging pressure…tries to explain the price behavior of futures in relation to hedgers’ position data. It is hypothesized that if the (net) demand for short hedging exceeds the demand for (net) long speculation, then long speculators will need to be compensated by an additional return risk premium to encourage them to balance the excess demand for short hedging, and this may result in price impacts.” [Lehecka]

Key empirical facts since 2000

We looked at month-end carry estimates January 2000 – November 2018, based on the steepness of the futures curve between the front and second future. The analysis has been undertaken for 24 commodities or six different groups (energy, base metals, precious metals, U.S. corn belt crops, other agricultural commodities and livestock). See contract acronyms at the end of the post.

The following empirical features are noteworthy:

  • First, most commodities recorded a strong negative bias in carry values, i.e. their curves have mostly been in contango. In 75% of all monthly observations across all commodities posted negative values. The only commodities with a positive long-term carry have been nickel, corn, soy, wheat, and cocoa. Coffee never ever recorded a positive carry since 2000, which raises doubts as to whether carry on its own can generally be a valid measure of risk premia.
  • Second, standard deviations of carry have been vastly different across commodities. The commodity with the most volatile carry (natural gas) is 15 times as variable as the one with the least volatile carry (silver). Generally, commodities that are easily storable, such as metals, have displayed little variation because intertemporal arbitrage is cheap. Conversely, commodities that are hard to store, such as energy and livestock, have witnessed large variations in carry, underscoring that the market is intertemporally segmented.
  • Third, carry has been prone to outliers. Put differently, the distribution of carry has displayed fat tails. This has been true for all commodities pointing to the regular occurrence of extreme risk premia or convenience yields in conjunction with limitations to intertemporal substitution.
  • Fourth, carry has been autocorrelated on a monthly basis. This means if one month’s carry was high the subsequent month’s carry was usually on the high side as well. The average monthly autocorrelation coefficient has been 82%. It was highest in precious metals and agricultural commodities and lowest in some commodities that are hard to store, such as natural gas and lean hogs.
  • Fifth, carry has not been highly correlated across commodities. The average correlation across all 24 commodities has been just 6%. The highest correlation has been 91% between silver and gold carry, presumably because both are easily storable and depend heavily on the short-term interest rate.

The seasonal adjustment takes out pronounced seasonality in some energy commodities, agricultural commodities and livestock. Adjusting for seasonal fluctuations reveals pronounced medium-term cycles that can last for years.

Adjusted commodity carry has been positively correlated with subsequent returns. Statistically the probability of positive correlation for the whole panel has been near 100%. Balanced accuracy (average of positive and negative return hit ratios) has been 51.8% on a monthly basis. Cross-sectional correlation between carry and subsequent returns has been positive in 17 of the past 19 years.

Contracts used in the empirical overview

BRT: Brent Crude
GAS: Gasoline (U.S.)
HOL: Heating Oil (U.S.)
NGS: Natural Gas (U.S.)
WTI: WTI Crude

Base metals
ALM: Aluminium
CPR: Copper
LED: Lead
NIC: Nickel
ZNC: Zinc

Precious metals
GLD: Gold
PAL: Palladium
PLT: Platinum
SIV: Silver

Corn-belt crops (U.S.)
COR: Corn
CTN: Cotton
SOY: Soy
WHT: Wheat
WWH: Winter Wheat

Other agricultural commodities
CAO: Cocoa
CFE: Coffee
SGR: Sugar

CAT: Live Cattle
HOG: Lean Hogs


Baltas, Nick (2017), “Optimising Cross-Asset Carry”, “Factor Investing”, edited by Emmanuel Jurczenko, Elsevier & ISTE Press, 2017.

Ekeland, Ivar, Delphine Lautier and Bertrand Villeneuve (2018), “Hedging pressure and speculation in commodity markets”.

Hambur, Jonathan and Nick Stenner (2016), “The Term Structure of Commodity Risk Premiums and the Role of Hedging”.

Lehecka, Geoorg (2013), “Hedging and Speculative Pressures: An Investigation of the Relationships among Trading Positions and Prices in Commodity Futures Markets”.

Roache, Shaun and Neşe Erbil (2010), “How Commodity Price Curves and Inventories React to a Short-Run Scarcity Shock”

Smith, Andrew (2000), “Introduction to Convenience Yields””.


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