Commodity futures carry is the annualized return that would arise if all prices remained unchanged. It reflects storage and funding costs, supply and demand imbalances, convenience yield, and hedging pressure. Convenience and hedging can give rise to an implicit subsidy, i.e., a non-standard risk premium, and make commodity carry a valid basis for a trading signal. An empirical analysis of carry for the front futures in 23 markets shows vast differences in size and volatility, with storage costs being a key differentiator. Also, carry is, on average, not strongly correlated across commodities, making it a more diversified signal contributor. To align carry measures more closely with expected premia, one can adjust for inflation, seasonal fluctuations, return volatility, and carry volatility. Most adjusted carry metrics display highly significant predictive power for returns.
The below post is based on proprietary research of Macrosynergy.
The economic value of a carry trading signal and a downloadable Jupyter notebook will be published in a subsequent post.
This post ties in with this site’s summary of implicit subsidies, particularly the section on commodity futures.
What is commodity carry?
In general, one can define carry as the return of a funded financial market position over a certain period, provided that all prices and the equilibrium state of the economy remain unchanged (view post here). Carry may arise for different reasons, including expected price changes, standard risk premia, and implicit subsidies. For the commodities space, one can estimate carry based on prices in the futures market. A commodity futures contract is an agreement between two parties to buy or sell a specific quantity of a commodity at a predetermined price on a future date. The delivery dates are standardized and follow a regular (often monthly) pattern.
Commodity future carry is specific to the section of the curve considered. Since futures positions principally incur no funding costs, the carry can simply be calculated as the annualized relative difference between a front future and a back future price, divided by the back future.
Here CRY is the annualized carry in percent, Ft1 the (front) future price with settlement date t1, and Ft2 the back futures price with settlement date t2. The difference between these dates is the number of trading days. The carry definition implies that if a curve is in backwardation, the futures carry is positive, and if a curve is in contango, the futures carry is negative.
A representative carry is typically calculated from a commodity futures curve’s first and second front contracts since those are the most liquid. This post uses such generic carry metrics and related futures return data for 23 commodities from the J.P. Morgan Macrosynergy Quantamental System (JPMaQS). For details, view the documentation here and here. The commodity groups considered are the following:
- fuels,
- base metals,
- precious metals, and
- agricultural commodities.
See the below annex for the individual commodities and their acronyms.
What shapes commodity carry?
Four forces prominently influence the slope of the futures curve that determines the commodity carry:
- storage and funding costs,
- expected supply and demand (future cash prices),
- the convenience yield of holding the physical commodity,
- and hedging pressure.
According to economic theory, the influence of these forces is determined in equilibrium, and thus, they are interdependent. For example, intertemporal demand-supply differences only give rise to carry if significant storage costs exist. Also, a convenience yield only gives rise to positive carry if it is offset by sizable net consumer hedging in the futures market. For the construction of trading signals, it is important to conceptually distinguish the various forces since, of the above four, only the convenience yield and hedging premia can plausibly give rise to implicit subsidies for financial market investors.
Storage and funding costs
“A futures contract is…an agreement to deliver a specified quantity of a commodity at a specified future date, at a price (the futures price) to be paid at delivery time. Futures contracts are usually traded on organized exchanges, such as the New York Mercantile Exchange.” [Pindyck]
“The future price [of a commodity] F(t,T) at time t for the delivery of a commodity at time T can be calculated from arbitrage arguments by a cost-of-carry valuation formula. In general, F(t,T) equals the spot price, S(t), plus the cost of carrying the underlying asset until the maturity of the contract. The cost of carry consists of the cost of capital, which can be calculated using the interest rate, r(t,T), and the cost of storage rate, expressed as c(t,T), which covers all expenditures for storing the commodity [such as] warehouse rent or insurance fees.” [Rathgeber, Stepanek, and Walter]
“The centerpiece of the modern theory of storage is the competitive intertemporal arbitrage equation [which] asserts that, in equilibrium, expected appreciation in the commodity price discounted at the [relevant] interest rate must equal the marginal cost of storage…Whenever expected appreciation exceeds the marginal cost of storage, the attendant profits motivate storers to increase their stockholdings until the equilibrium is restored. Conversely, whenever the cost of storage exceeds expected appreciation, the attendant loses motivate storers to decrease their stockholdings until the equilibrium is restored. Stockholding links supply and demand across time, inducing serial dependence in prices, even when production and consumption are serially independent.” [Miranda & Rui]
Supply and demand (expected future cash prices)
“How then is the futures price determined? Think of the alternative to obtaining the commodity in the future: simply wait and purchase the commodity in the future spot market. Because the future spot price is unknown today, a futures contract is a way to lock in the terms of trade for future transactions. In determining the fair futures price, market participants will compare the current futures price to the spot price that can be expected to prevail at the maturity of the futures contract. In other words, futures markets are forward looking and the futures price will embed expectations about the future spot price. If spot prices are expected to be much higher at the maturity of the futures contract than they are today, the current futures price will be set at a high level relative to the current spot price. Lower expected spot prices in the future will be reflected in a low current futures price.” [Gorton & Rouwenhorst]
“Total demand in the cash market is a function of the spot price and may also be a function of other variables such as the weather, aggregate income, certain capital stocks (e.g., stocks of automobiles in the case of gasoline and industrial boilers in the case of residual fuel oil or natural gas), and random shocks reflecting unpredictable changes in tastes and technologies. The supply of the commodity in the cash market is likewise a function of the spot price, and also of a set of (partly unpredictable) variables affecting the cost of production, such as energy and other raw material prices, wage rates, and various capital stocks (such as oil rigs, pipelines, and refineries), as well as random shocks reflecting unpredictable changes in operating efficiency, strikes and so forth.” [Pindyck]
“Inventory decisions link current and future scarcity of the commodity and consequently provide a connection between the spot price and the expected future spot price. But commodities, and hence commodity futures, display many differences. Some commodities are storable and some are not.” [Gorton & Rouwenhorst]
“In markets for storable commodities…inventories play a crucial role in price formation. As in manufacturing industries, inventories are used to reduce costs of changing production in response to fluctuations in demand. In a competitive commodity market subject to stochastic fluctuations in production and/or consumption, producers, consumers, and possibly third parties will hold inventories…Producers can reduce their costs over time by selling out of inventory during high-demand periods, and replenishing inventories during low-demand periods…
To the extent that inventories can be used…in the face of fluctuating demand conditions, they will have the effect of reducing the magnitude of short-run market price fluctuations…When inventory holdings can change, production in any period need not equal consumption. As a result, the market-clearing price is determined not only by current production and consumption, but also by changes in inventory holdings…
Producers must determine their production levels jointly with their expected inventory drawdowns or build-up’s. These decisions are made in light of two prices – a spot price for sale of the commodity itself, and a price for storage. This price of storage is equal to the marginal value of storage, i.e., the flow of benefits to inventory holders from a marginal unit of inventory.” [Pindyck]
“The current futures contract price equals the expected spot price at contract maturity assuming no risk premium and no basis risk…The variance of futures prices for an individual contract is influenced mainly by the flow of information and its uncertainty. Variability is expected to increase as contract maturity approaches and is affected by the seasonality in the information flow in the underlying market.” [Nielsen & Schwartz]
Convenience yield
“The simple cost of carry model includes the price of the underlying asset, interest rates, and physical storage cost. For commodities it is necessary to extend the simple model to include the impact of convenience yields to reflect benefits unique to holding the physical commodity.” [Heaney]
“Consumers of relatively durable but consumable commodities obtain a benefit from physically holding certain commodities for a given period. This benefit is not available to holders of forward or futures contracts held over the same commodities. Such benefits to the holder include the ability to profit from temporary shortages of the commodity as well as the ‘convenience’ benefits gained from ready access to supply for use in production processes or to meet certain other obligations. Scholars define these benefits collectively as a ‘convenience yield’, which aims to capture all the implicit benefits accrued to the owner due to having ready access to the commodity.” [Omura and West]
“The widely accepted theory of storage tries to interpret the convenience yield and the related benefits…The case of industrial metals particularly illustrates the economic meaning of this flow of services. The owner of the commodity, who is free to consume it until maturity, is prepared for unexpected shortages in supply or increases in demand. For example, a producer of industrial goods can avoid a disruption in the manufacturing process by having the commodity in a warehouse…Convenience yields are driven by the benefit of physically holding the commodity and thus by the liquidity premium or a flow of services.” [Rathgeber, Stepanek & Walter]
“Convenience yields arise endogenously as a result of the interaction among supply, demand, and storage decisions…When storage in the economy is driven to its lower bound, for example in periods of relative scarcity of the commodity available for trading, convenience yields should be high.” [Casassus & Dufresne]
“[Convenience yield] is analogous to the dividend yield in the price of a stock future and quantifies the income for the owner of the underlying commodity. As commodities usually do not generate direct cash flows (except in the case of gold, where leasing contracts can provide an income for the owner), the income has to be interpreted as a benefit of physically holding the commodity. It can be seen as a ‘flow of services’ which the owner of a resource receives until maturity. Hence, a positive convenience yield reduces the future price, which explains backwardated forward curves.” [Rathgeber, Stepanek & Walter]
“The convenience yield can be thought of as the interest rate paid in [units of physical commodity] for borrowing one [physical unit of the commodity]…The borrower…is, in essence, supplying storage in the form of…inventories to the lender. As a result, the lender must be compensated for forgoing the benefits associated with holding the [physical commodity]. In equilibrium, this condition links the convenience yield to the price of storage, and periods of relative scarcity of the commodity are related to high convenience yields. [This means that in equilibrium inventories are filled up or depleted to the point where storage costs equal the convenience yield.]” [Alquist, Bauer and Diez de los Rios]
Hedging pressure
“[Historically] the first hypothesis for the source of a commodity futures risk premium was the risk transfer or hedging pressure hypothesis of Keynes (1930) and Hicks (1939), where a risk premium accrued to speculators as a reward for accepting the price risk which hedgers sought to transfer. This theory was extended by several authors, culminating in the equilibrium-based generalized hedging pressure hypothesis.” [Basu & Miffre]
“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]
“Price volatility drives the demand for hedging, whether it is done via financial instruments such as futures contracts or options, or via physical instruments such as inventories. Volatility is a key determinant of the values of commodity-based contingent claims, such as futures contracts, options on futures, and commodity production facilities.” [Pindyck]
Empirical features of commodity carry and the benefits of adjustments
Standard nominal and real carry
One of the most striking features of futures carry is the extreme differences in variation across commodities. At the volatile end are commodities with limited and expensive storage space, such as natural gas, gasoline, and soy, since those can incur large short-term intertemporal price swings. At the other extreme are easily storable precious metals, particularly palladium, gold, and silver. Since 2000, the standard deviation of carry from its mean in natural gas has been 156% (annualized) versus just 2% for silver. Carry itself has, on average, been slightly negative across the panel of 25 commodities. U.S. gasoline posted, on average, the highest carry over the sample period (12% annualized), and coffee and wheat the lowest (-11%).
Please see the explanations of the commodity acronyms in the annex below.
To use carry as a trading signal, one would ideally separate the premium part from the price expectation part since the former indicates positive expected returns while the latter does not. Moreover, one would like to distinguish between standard risk premia that merely compensate for volatility and correlation risk and excess risk premia that indicate implicit subsidies (add link). A range of models seeks to back out convenience yield from commodity futures prices, volatility, and other data, such as inventories. Yet even without a full equilibrium model, one can make carry more meaningful as proxy risk premia and implicit subsidies by applying common sense adjustment.
The simplest one is inflation adjustment. Inflation plausibly influences the expected price drift of a commodity in its traded currency since the physical commodity is a real asset. In high inflation times, prices should be expected to rise faster than in low inflation periods. Hence, inflation-adjusted real carry should be a better proxy for actual implied premia over time than nominal carry. Since all commodity futures contracts considered in this post are denominated in U.S. dollars, we need only consider U.S. inflation expectations. This is approximated by the 1-year ahead estimated inflation expectation according to Macrosynergy methodology (view documentation here).
The line plot below shows the development of nominal and real carry across all 25 commodities. The differences between real and nominal measures are mostly minor but notable for commodities with low carry variance. Also, inflation adjustment pushes the average panel carry since 2000 from negative to positive territory.
Real and nominal futures carry series have two important empirical features in common.
- There have been occasional extreme outliers across all commodities. These may distort empirical analyses, particularly if the data points reflect quotes at times of low liquidity that one could not have actually traded on in size. Therefore, empirical analysis of the predictive power of carry should de-emphasize outliers, for example, by winsorization (replacement of extreme values with an acceptable threshold).
- A range of commodities shows regular cyclical and seasonal patterns. These are plausible structural features in the presence of weather effects and harvest conditions and call for some form of seasonal adjustment to isolate the carry premium from normal seasonal price dynamics.
From the angle of operating trading strategies, an important feature of commodity carry is its low average cross-sectional correlation. Unlike equity carry, for example, commodity carry is not highly correlated across markets, and hence, carry-based positions should tend to be more diversified.
Volatility adjustment
Futures return volatility reduces the risk-adjusted value of any estimated premium implied in the carry. Volatility changes over time and differs materially across commodities. For example, the average daily return standard deviations of natural gas futures are roughly three times as large as those of gold.
To mitigate this heteroscedasticity, one can calculate “volatility-targeted carry.” JPMaQS calculates such carry based on positions that are scaled to a 10% vol target based on a historical standard deviation of the commodity future returns for an exponential moving average with a half-life of 11 days. Positions are rebalanced at the end of each month.
Notably, calculating carry based on vol-targeted positions reduces cross-sectional differences in carry variance but does not remove them. After all, we do not adjust for the volatility of carry but for the volatility of returns. To the extent that carry is explained by predictable price changes and intertemporal market segmentation, carry volatility does not transmit to returns volatility.
Seasonal adjustment
Front and second futures contracts have distinct changing settlement dates. For various agricultural and energy contracts, expected spot supply and demand are subject to seasonal fluctuations across those dates. For example, energy demand is often elevated during the winter season in the northern hemisphere, and the supply of agricultural commodities is naturally higher in harvest months.
The below panel shows real-time estimated seasonal factors across all 23 commodities according to the JPMaQS data in percent annualized carry. Prominent regular influences can be seen in gasoline, natural gas, lumber, and – to a lesser degree – in cotton, heating oil, orange juice, sugar, and soy.
The purpose of seasonal adjustment is to remove regular seasonal price differences from carry calculations because those do not plausibly reflect premia, such as those arising from convenience yields and hedging pressure. JPMaQS applies additive point-in-time seasonal adjustment to nominal carry at each point in time based on the concurrently available vintage. The seasonal adjustment uses the U.S. Census Bureau’s X-13 seasonal adjustment tools.
To estimate seasonal factors, nominal carry is down-sampled from trading daily to monthly frequency. For all the months in the vintage except the last one, the average monthly value of the carry is used as the basis of seasonal adjustment. The seasonal component estimated for each point in time is then subtracted from the daily carry values based on future prices. Although this adjustment is applied daily, the seasonal factor naturally changes only monthly following changes in settlement dates. For commodities whose settlement dates do not change at monthly frequency but remain unchanged for a few months, we still estimate monthly carry adjustment factors as proximity of settlement data may also be a potential seasonal influence.
While the case for seasonal adjustment is compelling, its influence on commodity carry series is typically modest and naturally focused on the commodities with large seasonal price fluctuations. Also, seasonal adjustment does not remove all seasonal influences. It only removes the average bias of price changes for a given month, not the seasonal patterns in volatility that arise, for example, from the critical importance of weather for harvests and energy demand.
Normalization and winsorization
Since volatility carry depends on storage costs, there is plausibly a positive relation between commodity carry and expected price changes. This matters because predictable price changes compromise the relation between carry and trading-relevant premia. Put differently, a case can be for adjusting carry for its own volatility, as opposed to adjustment for price volatility. Moreover, the proclivity of commodity carry for occasional outliers that may not be actually tradable snapshots of market states argues for containing extreme values. The simplest way to do so is to take a “normalized and winsorized score,” i.e., to adjust carry values by their mean absolute values (on a rolling basis to avoid look-ahead bias) and to contain values at a set multiple, here 3.
The normalized and winsorized carry scores have similar standard deviations across commodities but maintain most of the intertemporal dynamics of the original series.
A preview of predictive power
In almost all plausible forms, commodity futures carry displays a significant positive relation with subsequent futures returns since 2000 at a weekly, monthly, or quarterly frequency. The relationship has been subtle, with a Pearson correlation coefficient of just around 5% for most types of carry at the monthly level but pervasive, with a positive relation prevailing for 70% of all markets and almost 90% of all years.
A detailed analysis of the predictive power of commodity across various concepts for directional and relative commodity futures positions, as well as stylized PnLs, will be discussed in next week’s post (Commodity carry as trading signal – part 2)
Annex: commodity contracts and acronyms
For this post, we looked at four commodity groups: energy, base metals, precious metals, and agricultural commodities.
The energy commodity group contains:
- BRT: ICE Brent crude
- WTI: NYMEX WTI light crude
- NGS: NYMEX natural gas, Henry Hub
- GSO: NYMEX RBOB Gasoline
- HOL: NYMEX Heating oil, New York Harbor ULSD
The base metals group contains:
- ALM: London Metal Exchange aluminium
- CPR: Comex copper
- LED: London Metal Exchange Lead
- NIC: London Metal Exchange Nickel
- TIN: London Metal Exchange Tin
- ZNC: London Metal Exchange Zinc
The precious metals group contains:
- GLD: COMEX gold 100 Ounce
- SIV: COMEX silver 5000 Ounce
- PAL: NYMEX palladium
- PLT: NYMEX platinum
The agricultural commodity group contains:
- COR: Chicago Board of Trade corn composite
- WHT: Chicago Board of Trade wheat composite
- SOY: Chicago Board of Trade soybeans composite
- CTN: NYBOT / ICE cotton #2
- CFE: NYBOT / ICE coffee ‘C’ Arabica
- SGR: NYBOT / ICE raw cane sugar #11
- NJO: NYBOT / NYCE FCOJ frozen orange juice concentrate
- CLB: Chicago Mercantile Exchange random-length lumber
