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ALT 1 – Introduction to Commodities and Commodity Derivatives

Worked examples are fully visible. Check-yourself items are study aids you can reveal one at a time.

A commodity, in the economic sense used throughout this reading, is a physical good that comes from a natural resource, that can be traded, and that reaches the general public without meaningful differentiation between one producer and another. A barrel of West Texas Intermediate crude oil is the same barrel whoever pumped it. That single property, the absence of differentiation, is what makes standardised contracts possible and therefore what makes commodities investable at scale.

Commodities trade in two connected places. The physical or spot market involves the actual transfer of goods between a buyer and a seller, so spot prices reflect current or very near term supply and demand at a specific location. The futures and forward markets involve financial contracts. A commodity futures exchange establishes a price today for a defined quantity and quality of a commodity to be delivered at a future date, and completion may be permitted in cash or may require physical delivery.

Exchanges do two jobs at once. They transfer risk from those who do not want it to those who will accept it for a price, and they discover prices, because the traded price aggregates what every participant currently believes about future supply and demand. Because the contract is settled financially rather than physically in most cases, the exchange also admits participants who never touch the commodity: speculators, arbitrageurs, private equity, endowments and other institutional investors. Standardisation plus an organised venue produces trading volume, and volume is what lets a participant close, reduce, expand or open a hedge as circumstances change from one day to the next.

Forward markets sit alongside futures markets in certain commodities for entities that need terms a standard contract cannot provide, and swap markets are used for both hedging and speculation. A producer may want a swap that references the specific origin of its cattle or the chemical specification of its crude oil. This reading concentrates on futures and treats forwards only briefly.

The investment case rests on two historical observations. Average return correlation with stocks and bonds has been low, which is the diversification argument, and academic work including Gorton and Rouwenhorst (2006) and Erb and Harvey (2006) has found inflation hedging qualities in some commodities.

Why commodities are not securities

Equities and bonds are claims on productive capital or on financial assets, and they are expected to generate cash flows for their owners. Their intrinsic value is the present discounted value of those expected cash flows. A commodity has no such claim attached to it. Its value comes from being consumed or from being an input to the production of some other good or service. Many commodities must be processed, and many have a limited life before they spoil or decay, so an analyst has to think about growth and extraction patterns and about the logistics of moving physical goods. Familiar as they are from daily life, commodities present a distinct set of risk exposures.

The limits of a purely quantitative approach

Fundamental analysis of a commodity means analysing supply and demand for that product and then estimating how the market will react to the shocks that inevitably hit its equilibrium. A growing world population moves more goods and people and therefore demands more crude oil, but shale drilling or electric vehicles can disrupt that trend, and armed conflict or adverse weather can change it within days.

Three features make the statistics awkward. Returns show high degrees of non-normality and correlations that shift. Coefficients on the underlying variables are frequently non-stationary, so that a drought impact estimated from history overstates the damage to corn that has since been genetically modified to resist heat. And a large part of the raw data sits off market inside private oil and agricultural companies. The practical response is a framework applied at a high level, with discretionary or quantitative techniques layered on wherever the data allow.

Four tools of fundamental analysis

The same four tools apply to supply and to demand, so that distinction can be set aside until individual sectors are examined.

The fundamental analysis toolkit

Tool	What it does	Typical inputs
Direct announcements	Reads published production and inventory data to infer demand, which is often unobservable	USDA, OPEC, the National Bureau of Statistics of China, the IEA
Component analysis	Breaks high level supply and demand into a stock and a flow. The stock bounds what could be produced or wanted; the flow measures how much of that stock is actually used	Arable land in Europe, capacity of the Ghawar field, tanker traffic to China, historical US cotton yields, piglets per mother hog in Canada
Timing considerations	Adjusts stocks and flows for seasonality, logistics and sudden shocks, and therefore for the price reaction	Crop growing periods, winter heating demand for natural gas, pipeline outages
Money flow	Captures sentiment and macro monetary conditions that move prices independently of physical balances	Investor risk tolerance, inflation, interest rates and mine financing, subsidies for substitute technologies

Two of these deserve emphasis because they are easy to confuse. A shock is by definition a sudden switch in timing. An earthquake that destroys a pipeline does not change the stock of oil in the ground at all, but it stops the flow. Seasonality works the same way, and because it is predictable it feeds directly into the shape of the futures curve discussed later in this lesson. Money flow is different again: capital made available by low interest rates can trigger the building of new mines and therefore change supply years later, and government funding for electric cars affects the price of gasoline without any physical event occurring.

Qualitative judgement remains necessary. A stricter emissions standard can hit supply, because higher standards often strand lower quality material, and demand at the same time, because not every consumer is equipped to use the new standard. Political unrest may leave an isolated farm untouched and still disrupt consumption.

Example 1 · Worked

An analyst covering natural gas is handed four pieces of news on the same morning.

A newly permitted field will begin producing in four years.
An earthquake has severed a major transmission pipeline.
The national statistics agency reports storage injections above expectations.
A sharp fall in policy rates has cut the financing cost of new drilling programmes.

1. Classify each item as acting mainly on the stock, mainly on the flow, or mainly through money flow.

Solution. The new field changes the stock, because it alters the boundary of what could ultimately be produced, and it does so with a four year lag. The severed pipeline changes the flow only: the gas still exists but cannot reach the market, so the near term price reaction is large and the long dated reaction is small. The storage report is a direct announcement that lets the analyst infer demand, which is not directly observable, and it revises the flow estimate. The fall in policy rates works through money flow, because cheaper capital encourages new drilling and therefore future supply even though nothing physical has yet changed.

2. Which of the four is most likely to move the far end of the futures curve rather than the near end?

Solution. The new field. A stock effect arriving in four years has almost no bearing on the price of gas needed next month, but it changes what the market expects to be available in four years. The pipeline is the mirror image: a flow interruption that will be repaired hits the front of the curve hardest and fades with maturity.

The asset class can be segmented in several ways. The scheme adopted here is the one sitting beneath the Bloomberg Commodity Index, and it names six groups: energy; grains; industrial or base metals; livestock; precious metals; and softs, meaning cash crops. It is more granular than some index families, and it matches how most market participants actually specialise.

What separates one sector from another is a small set of physical facts: how easily and cheaply the commodity can be produced, how easily it can be stored, how often and when it is consumed, whether it spoils, what it costs to insure, and how hard it is to move to the consumer. Note also that many commodities, uranium and water among them, trade only in thin private markets. Those are individual transactions rather than markets in the sense used here, so the coverage below is restricted to primary commodities.

Commodity sectors, their main commodities and their primary influences

Sector	Role and primary commodities	Stock influences	Flow influences
Energy	Powers transport, factories and electricity generation. Its members are crude oil, natural gas, coal and refined output such as gasoline and heating oil	Field discovery set against field depletion; the cost of access and how politically certain that access is; refinery technology and its maintenance schedule; the type of power plant built and the pace of construction; the sheer size of the economy (GDP)	How reliably pipelines and tankers run; the swing between summer and winter demand; hostile weather, from deep cold to hurricanes; sales of cars and trucks; instability in producing regions; environmental rules; the growth rate of the economy (GDP)
Grains	Feeds people and animals, and is also distilled into fuels such as ethanol. Its members are corn, soy, wheat and rice	Farmland under the plough; silo and port capacity; how many people and how many animals have to be fed	Rainfall and temperature; crop disease; what consumers want to eat; seed genetics; how much is diverted into biofuel; the rate of population growth
Industrial (base) metals	Supplies durable consumer goods, industry and building work. Its members are copper, aluminium, nickel, zinc, lead, tin and iron	Acreage under mine; available smelter capacity; how far industrial and consumer development has progressed (GDP)	Industrial and environmental policy from governments; the growth rate of the economy (GDP); sales of cars and trucks; spending on infrastructure
Livestock	Animals reared to be eaten. Its members are hogs, cattle, sheep and poultry	The size of the herd; capacity at processing plants; consumer taste; whether feed is available and what it costs	How fast animals reach slaughter weight; growth in the economy (GDP) and in consumer income; disease; hostile weather
Precious metals	Metals that store monetary value and also serve industry. Its members are gold, silver and platinum	Acreage under mine; smelter capacity; the stock of fiat money and the development of the banking system	The monetary policy of central banks; geopolitical events; growth in the economy (GDP)
Softs (cash crops)	Crops grown to be sold rather than eaten by the grower, and once treated as luxuries. Its members are cotton, cocoa, sugar and coffee	Farmland under cultivation; silo and port capacity; the size of the economy (GDP)	Rainfall and temperature; crop disease; consumer taste; diversion into biofuel; growth in the economy (GDP) and in consumer income

The stock column bounds what could be supplied or wanted. The flow column governs how fast that stock is actually converted into supply or demand.

Reading down the table, a pattern appears. Every sector has economic and monetary data in common, because GDP appears somewhere in almost every row, but each sector then has a dominant idiosyncratic driver. Weather dominates grains and softs on the flow side. Industrial production dominates base metals. Monetary policy dominates precious metals, which is why weather barely registers there: metals store easily and indefinitely, so a bad winter does not change availability. Energy is unusual in that weather affects demand strongly, through winter heating and summer transportation, while affecting supply only through events such as hurricanes.

Example 2 · Worked

1. Demand for which of these is most likely to move with the level of industrial activity: copper, natural gas, or softs such as cotton, coffee, sugar and cocoa?

Solution. Copper. Copper goes into construction, infrastructure development and the manufacture of durable goods, and all three are economically sensitive. Natural gas is not the answer, because its demand is driven first by weather, through heating and cooling, and only secondarily by industrial activity. Softs are not the answer, because their demand is driven primarily by global income.

2. Which of energy, livestock and precious metals is least affected in the short term by weather-related risk?

Solution. Precious metals. Because they store so easily, weather has very little effect on their availability; inflation expectations, fund flows and industrial production matter far more. Energy is not the answer, because energy demand is strongly influenced by weather, for example heating demand in winter and transportation demand in summer. Livestock is not the answer, because the health of animals is vulnerable to extreme cold, wet and heat, which raise the risk of death and disease.

3. A single government announcement tightens emissions standards. Explain why this can reduce both supply and demand at once.

Solution. On the supply side a higher standard strands lower quality material, because the cheaper, dirtier grades no longer qualify for sale, so effective supply falls even though the physical stock is unchanged. On the demand side not every consumer owns equipment capable of using the new specification, so some demand disappears until equipment is replaced. This is why a purely quantitative model built on historical coefficients can misread a policy shock: the same event moves both curves.

The life cycle of a commodity is the path it takes from production through storage, processing and logistics to trading or consumption. It varies considerably with the economic, technical and structural profile of the commodity and of its sector. The reason it matters to an investor is simple: a short life cycle allows rapid adjustment to outside events, while a long life cycle limits how quickly supply or demand can react to new conditions. Those adjustment speeds feed straight into the price elasticities of supply and demand, and therefore into the shape of the futures curve.

Figure 1: The generic commodity life cycle

Every sector passes through the same five stages, but the time spent in each stage differs enormously. Natural gas can skip processing altogether; cattle spend years in the first stage.

Within the food group, both cropping and animal rearing run to sharply defined seasons and growth cycles that differ from one geography to the next. By March of any year corn planting may already be finished in the southern United States while it has not started in Canada, and at the same moment the corn harvest may be under way in Brazil and Argentina because their seasonal cycle in the Southern Hemisphere runs in reverse. Each location is also a local market with its own domestic and export demand, which changes both the level and the reliability of that demand and the power of buyers to stretch or compress the cycle.

Energy and metals are extracted all year round, so their life cycle changes at the margin of a continuous process rather than at a discrete season. Their downstream products still carry seasonal demand, gasoline in summer and heating oil in winter, and that seasonality works back through the chain to the underlying commodity.

Energy

Energy shows how different two commodities inside one sector can be. Natural gas can be consumed almost immediately after it comes out of the ground. Crude oil cannot: it is useless in its innate form and has to be transformed into something else, and the refined products then pass through a number of further processing steps that depend on the quality of the crude input and on the relative demand for each product.

Steps for the energy complex

Step	Title	What happens
1	Extraction	A drilling location is chosen after survey work and the well is dug. Underground pressure may be sufficient for the hydrocarbons to flow naturally, or water and other tools may be needed to create that pressure. Water is also used in the fracturing process known as fracking, which breaks up shale formations so that oil or gas can be extracted.
2	Storage	Average commercial holding periods run to a few months, with the main pools sitting in the United States, in Singapore and in northern Europe, and many governments hold strategic stocks on top of that. Tanker ships serve as temporary storage. Gas may bypass this stage entirely and reach the end consumer directly, while volumes lifted over the summer are frequently pushed into storage to meet winter demand.
3	Consumption stage	Gas alone reaches the consumer here, since no refining is needed. Oil cannot, and has to be processed first.
4	Refining	Crude oil is distilled into its component parts by a process called cracking. Heat drives off each component in turn, and those are cooled and collected, gasoline and kerosene among them, leaving only remnants such as asphalt behind.
5	Consumption stage	The distilled products are separated and shipped by ship, pipe, train or truck to their various locations for use by the end consumer.

The capital intensity of this chain is easy to underestimate. Refineries typically cost several billion US dollars, and the figure depends on the specifications of the crude they are designed to accept: a low-grade, high sulphur input requires more investment than an assured lighter and sweeter source. Pipelines are also very costly. The Keystone XL expansion between Canada and the United States was originally estimated at $5 billion in 2010, and the estimate had doubled to $10 billion by 2014. Even in countries dealing with violent insurrections, such as Libya, Iraq and Nigeria, damage to refineries has generally been modest because every party values them, whereas pipelines are frequently destroyed or cut off. All of these numbers are still small beside the cost and the risk of exploration itself, particularly in deep offshore locations or in geographically remote and geopolitically risky regions.

The crude oil market carries many futures contracts and indexes tracking local grades and origins, but the two most commonly traded sets follow US-based West Texas Intermediate crude oil and UK-located Brent crude oil from the North Sea. There are also futures for natural gas, gasoil, gasoline and heating oil. Delivery locations and standards differ across all of them. Both WTI and Brent describe a good grade of refinery feedstock, and that is what makes them usable as hedging instruments by exploration and production companies.

Industrial and precious metals

Metals have the most flexible life cycle of all, because both the ore and the finished product resist spoilage and can be stored for months or years given proper conditions. Otherwise the chain parallels energy.

Copper purification process

Step	Name	What happens
1	Extracting and preparing	A mine or an open pit yields ore, raw earth carrying roughly 2% metal. Milling reduces the ore to a powder, and concentration lifts it to roughly 25% purity.
2	Smelting	Heating the concentrate drives further impurities off as slag and lifts metal content to 60%. Later stages carry it to 99.99%.
3	Storage and logistics	Refined metal generally waits in a bonded warehouse until an end user calls for shipment.

Economies of scale drive the economics of smelting just as they drive refining. These are huge facilities whose marginal cost, the cost of converting the last kilogram of processed ore into useful metal, falls substantially with both the size of the plant and its utilisation. The consequence is important for anyone forecasting supply. When supply exceeds demand for an industrial metal, producers find it very difficult to cut back or halt production, and excess output tends to persist until the weakest balance sheets in the industry give way and those plants close. Because demand for industrial metals moves with overall economic growth, producers have a strong incentive to invest in new capacity when utilisation and profit are high, and they face heavy economic and financial penalties for running those facilities when demand falls away in a downturn. Given the typical economic cycle and the lag between deciding to expand and completing the expansion, new supply often arrives exactly as demand is declining, which makes the price and profit decline worse.

With no annual seasonality in metals production and easy storage without spoilage, most of the variability over time comes from the demand side, principally construction and economic growth.

Livestock

Animals put on weight throughout the year, yet kind weather and better pasture and feed speed that process up, so the supply of animals at slaughter weight rises and falls. Time to maturity rises with size: poultry are ready within weeks, hogs within months and cattle only after some years. A hog cycle begins with a sow giving birth, and it normally takes about six months to raise a piglet to slaughter weight, during which it can be fed almost anything to reach bulk, with soymeal and cornmeal most common in mass-scale production. Cattle take much longer. Under mass-scale breeding an animal spends its first year or two as feeder cattle grazing on pasture, and the following 6 to 12 months are spent in a feed lot, where a corn-based ration brings them up to slaughter weight. The feeds themselves are traded commodities, which links the livestock and grains sectors directly.

The US livestock sector has historically been among the least export-oriented of all commodity sectors, because the risk of spoilage once an animal is slaughtered is high. Advances in cryogenic freezing for chicken, beef and pork have changed that, and these products increasingly move between regions in response to differences in production costs and demand. As emerging and frontier markets develop a middle class able to buy meat protein regularly, investment in livestock and meatpacking has risen in countries such as the United States and Brazil, which combine low-cost feed, large grazing acreage and strong domestic demand. Ranchers and slaughterhouses trade hog and cattle futures against their commitments, and ranchers can hedge both young animals still in pasture, through feeder cattle contracts, and animals being fattened for butchering, through live cattle contracts.

Grains

Grains in the Northern Hemisphere follow one growth cycle and those in the Southern Hemisphere follow an analogous but opposite one. Plants mature in four steps: planting, which is placing the seeds in the ground after preparation and fertilisation; growth, as the seedling emerges and reaches full height; pod, ear or head formation, when the plant creates the food grain; and harvest, when the farmer collects it.

Timing for grain production in North America

Stage	Corn	Soybeans	Wheat
Planting	April to May	May to June	Sep. to Oct.
Growth	June to Aug.	July to Aug.	Nov. to March
Pod, ear or head formation	Aug. to Sep.	Sep.	April to May
Harvest	Sep. to Nov.	Sep. to Oct.	June to July

The wheat column uses the hard winter wheat variety, which has a higher protein content. Note that its cycle straddles the calendar year end, so its harvest arrives when the corn crop is only halfway through growth.

Because demand for grains runs all year while supply arrives in a few weeks, grains are stored continuously in silos and warehouses worldwide. Some countries operate a central purchasing bureau, and others rely on local or international trading companies to hold stockpiles. Poor hygiene and poor logistics can destroy a substantial part of that value through mould or infestation by insects and animals. Monitoring the purchasing patterns of government tenders is one of the few reliable ways for a research analyst to read grain demand. Farmers and consumers hedge with futures whose delivery months line up with the growing cycle, and ranchers turn to grain futures to cover what it costs to feed an animal.

Softs

Cocoa, cotton, sugar and coffee have little in common beyond the label they share, so coffee serves as the illustration here. Coffee is harvested somewhere all year round in the countries that circle the Equator. Once the cherries are picked, still often by hand so that only ripe fruit is taken, the husk and fruit are removed and the remaining bean is dried. Over half of world output goes through the dry method, under which the picked cherries spend two to three weeks drying in open sun. The wet method soaks the cherries in fresh water, removes the soft pulp, ferments the bean for 12 to 48 hours and then dries it. The green beans are hulled, sorted and bagged for their final markets, shipped, and often stored in a bonded warehouse before a local buyer roasts them and sends them to a coffee house or supermarket.

Two main varieties matter for trading. Robusta is generally lower quality with less flavour than arabica, and the two have separate futures contracts: robusta trades in London and arabica trades in New York. Both contracts are for unroasted green beans. Physical delivery allows a seller to deliver beans to an authorised bonded warehouse to fulfil the contract at expiration, so farmers and distributors can sell futures to hedge their sales price while roasters can buy futures to hedge their purchase cost, each choosing maturities that match their own delivery schedules.

Example 3 · Worked

1. Where does the production life cycle of crude oil differ most sharply from that of natural gas?

Solution. Natural gas requires very little additional processing after extraction, whereas crude oil does. Gas can be used on delivery straight after it comes out of the ground, while crude must first be processed before it is of any use. It is not true that only crude oil needs to be stored, since both are stored before use, and it is not true that European companies are the only ones storing crude, since many countries store it both commercially and strategically.

2. Because of the large economies of scale in processing industrial metals, what do producers do when supply exceeds demand?

Solution. They struggle to trim either output or capacity, even once supply has run ahead of demand or demand has begun to slow. The facilities are large and capital intensive, so reducing capacity is hard once demand weakens. They do not shut new capacity down immediately, because of the time lag involved in responding to reduced demand, and they do not maintain maximum production levels either, because doing so while demand is falling produces financial losses.

3. Why has the US livestock sector historically been among the least export-oriented commodity sectors?

Solution. Because of the high risk of spoilage once animals are slaughtered unless the meat is frozen. Low technological innovation is not the reason, since advances in cryogenics have in fact improved the ability to export from the United States. Absence of foreign demand is not the reason either, since demand for US livestock has expanded internationally, particularly in emerging markets experiencing economic growth.

4. Using the grain timing table, explain why a wheat farmer and a corn farmer in North America would hedge in different months.

Solution. Hard winter wheat is planted in September and October and harvested in June and July, so the price risk the wheat farmer needs to cover runs from autumn planting through to an early summer harvest. Corn is planted in April and May and harvested from September to November, so the corn farmer needs cover from late spring through to late autumn. The two exposure windows barely overlap, so the delivery months each farmer selects differ, which is exactly why exchanges list contracts across the whole calendar rather than at a single date.

The contrast can be stated in one line. Stocks and bonds are financial assets, and each is a claim on output produced by a company, a state or a person. A commodity is almost always a physical asset instead. The qualification matters, because some newer classes such as electricity and weather are not physical in the sense that they can be touched or stored.

A commodity is a tangible item carrying an intrinsic economic value that varies: a nugget of gold, a heap of coal, a bushel of corn. It does not generate future cash flows beyond whatever can be realised by buying it and selling it again. On top of that, the standard financial instruments built on commodities are not financial assets in the way a share or a bond is. They are derivative contracts with finite lifetimes, principally futures. Such contracts do have value, but that value is contingent on something else, chiefly the price of the underlying commodity.

The valuation consequence follows directly. Commodity valuation is not an estimate of future profitability and cash flows. It is a discounted forecast of future possible prices, driven by factors such as the supply and demand for the physical item and the expected volatility of future prices. That forecast may be highly formal, as when an oil company models the labour and capital cost of extracting oil, refining it and moving it to the pump. It may equally be made instinctively by a floor trader with little fundamental analysis, relying on professional judgement built over years and perhaps on technical analysis. Both are legitimate; neither is a discounted cash flow model.

Carrying cost replaces income

A share pays a dividend and a bond pays a coupon. Owning a commodity does the opposite: it incurs transportation and storage costs. These ongoing outlays shape the forward price curve across expiration dates. Where storage and transportation costs are substantial, futures prices tend to be incrementally higher the further out one looks. Sometimes, though, current demand pushes the spot price above the futures price, because the alternative to going long a futures contract is to buy the commodity today and store it until the future date. In that case the outlay is today’s spot price plus, or net of, the costs of storing and holding it. This time element of storage and of supply and demand is what generates the roll return studied later in this lesson.

Why arbitrage is a boundary, not an equality

Some commodity contracts require actual delivery of the physical commodity at expiration, while others pay cash against the gap between the contracted futures price and whatever spot price rules at expiration. The force of arbitrage, which is the law of one price in action, is not fully enforced in commodities, because a large share of participants simply cannot make or take delivery of the physical good. Where that is true, the relationship linking spot and futures prices is not an equality. It is a range that indicates the limit or boundary within which value differences can persist. This is a genuine departure from the treatment of financial assets, where the arbitrage relation usually pins the forward price to a single number.

Hedging and price discovery in practice

Some of the largest users of commodity futures are businesses hedging a price that is a critical source of revenue or of cost. The airline industry depends heavily on the cost of jet fuel, and intense competition puts constant pressure on airfares while forcing carriers to fill as many seats as possible. Futures and swap markets in jet fuel let airlines reduce the risk of higher fuel costs, particularly against surprise shocks in oil prices, by hedging the price of future purchases.

Price discovery is the second benefit. The futures market tells an airline something about future fuel prices, which helps it decide what to charge for flights months ahead while still making a profit. Seen correctly, an airline ticket is itself a contract sold at a price set today for future delivery of a service. The airline typically manages the matching uncertainty about fuel by going long energy futures.

Example 4 · Worked

1. In contrast to financial assets such as stocks and bonds, which statement about commodities is correct: that commodities are always physical goods, that they generate periodic cash flows, or that commodity investment is primarily via derivatives?

Solution. Commodity investment is primarily via derivatives. The claim that commodities are always physical is wrong, because certain newer classes such as electricity and weather are not tangible. The claim that they generate periodic cash flows is wrong in sign as well as in substance: physical ownership of a commodity tends to incur periodic cash flow through transportation and storage costs rather than generate it.

2. What is the key distinction between valuing commodities and valuing stocks and bonds?

Solution. Commodity valuation focuses on supply and demand, while stock and bond valuation focuses on discounted cash flows. Commodity value rests on a forecast of future prices built from supply and demand factors together with expected price volatility, whereas stock and bond value rests on estimating future profitability or cash flow. It is not correct to say technical analysis cannot be used on commodities, since it is sometimes applied. Reversing the two descriptions is also wrong for the same reason the correct answer is right.

3. A pension fund manager asks which valuation factor applies to equities and bonds but has no counterpart in commodity valuation. What is the answer, and why do storage and transportation costs not qualify?

Solution. The answer is expected future cash flows. Financial assets are valued on the cash flows they are expected to produce, and a commodity produces none. Storage and transportation costs do not qualify, because they are precisely the inputs that a commodity valuation does incorporate: they enter the discounted forecast of the future commodity price, so they are common ground rather than a point of difference.

Markets in commodities that are open to the public take the form of futures markets, meaning a central exchange on which participants trade standardised contracts committing them to deliver, or to receive, at a stated place and on a stated future date. A futures contract qualifies as a derivative because its value comes from something else. Futures and forwards alike bind both parties to a price agreed now for a commodity handed over later, or for a cash payment at expiry.

Futures against forwards

The differences are structural rather than economic. Futures are standardised agreements traded on public exchanges such as the Chicago Mercantile Exchange, the Intercontinental Exchange and the Shanghai Futures Exchange, and gains and losses are marked to market every day. Standardisation lets a participant enter a contract without ever knowing the counterparty, and the exchange oversees trading and margin requirements while providing a layer of self-imposed regulatory oversight. Forwards are bilateral agreements between one party that wants to go long and another that wants to go short. That bilateral nature makes them over-the-counter contracts with less regulatory oversight and far more customisation for the hedging or speculating party, and the counterparty is often a financial institution supplying liquidity or customisation for a fee. Futures require daily cash movements from losing positions to winning positions; forwards are usually settled only at expiration or at some custom frequency written into the contract.

The daily settlement of futures exists for a reason worth remembering. Early commodity exchanges operated as forward markets, and participants too often went bankrupt when unrealised losses became realised at the end of a contract. The futures process was introduced to minimise that risk, with the exchange acting as payment guarantor. The first modern organised futures exchange was the Dojima Rice Exchange in Osaka, Japan, founded in 1710, though contracts of a futures type had already been traded in England during the 16th century.

Why longs and shorts are symmetric

For every producer of a commodity there is a consumer. Participants who are long the physical good and want to sell it are matched by participants who are short the physical good and want to buy it, so fairness requires that longs and shorts operate on an equal basis. One consequence is that commodity markets are net zero in aggregate futures positions: futures contract longs equal futures contract shorts. Stock and bond markets are different, because the market values of issued securities equal the net aggregate positions at the end of each day, which leaves a net long position.

The asymmetry shows up most clearly in the mechanics of shorting. Shorting an equity is constrained by the need to locate shares to borrow, by the obligation to reimburse dividends on those borrowed shares, and by margin requirements that generally exceed those for a long equity position, as under Regulation T in the United States. Shorting a commodity future involves none of that: short investors sell directly to long investors and post the same margin the longs post.

The five groups

Hedgers, who trade to hedge exposures related to the commodity itself.
Traders and investors, long term and short term, including index investors, who speculate on direction or volatility and who supply liquidity and price discovery in exchange for the expectation of a profit.
Exchanges and clearing houses, which set trading rules and provide the infrastructure that transmits prices and payments.
Analysts, who use exchange information for non-trading purposes such as evaluating commodity businesses, building products based on commodity futures including exchange-traded funds, swaps and notes, and making public policy decisions. This group also covers brokers and other intermediaries who participate without taking a position.
Regulators of both the exchange and the traders, who police market conduct, pursue malfeasance and give complainants somewhere to go.

Hedgers are knowledgeable but not clairvoyant

A driller can reasonably be assumed to understand the balance of oil supply and demand, and that of neighbouring fuels, over any long horizon. Knowing the market is not the same as forecasting it. Consider a baker who buys wheat for future delivery. A surprise drought benefits the baker, who has locked in a low price in a supply-constrained market, while beneficial weather hurts the baker, who has effectively overpaid during a bumper crop. Because a hedger can make delivery when short the futures contract or take delivery when long it, the motivation is risk mitigation with regard to cash flow, so the risk being run is an opportunity cost rather than an actual one.

It is a common error to equate hedging with being short and speculating with being long. Both long and short positions can serve either purpose.

Examples of hedging and speculating positions

Motive	Long position	Short position
Hedging	Snack chip maker fixing the price of the corn it will need	Gold miner protecting the price it will receive on future output against a fall
Speculating	Integrated oil group betting on price direction using what it knows about physical oil markets	Commodity trading adviser running a macro-commodity fund for client profit

Hedgers themselves speculate, in the sense that their view of market conditions determines how much of their exposure they choose to hedge. Because separating the two motives cleanly is so difficult, regulation in the United States separates commodity producers and consumers from other trading participants regardless of whether those commercial participants are in fact speculating.

Three kinds of trader

The commodity trading community, like any other, divides into informed investors, liquidity providers and arbitrageurs. Informed investors are largely the hedgers and speculators already described, including index and institutional investors. Speculators who believe they hold an information advantage try to outperform the hedger by buying or selling futures either alongside the hedger or against the hedger, on horizons ranging from a microsecond to several months. A speculator with a superior weather prediction process has exactly such an advantage.

A speculator may instead act as a liquidity provider, knowing that producers and consumers do not arrive in the market at the same moment. Taking the other side when the producer is a seller, then again when the consumer is a buyer, pays for standing in the middle. Framed that way, the liquidity provider is selling insurance to hedgers in return for an expected, though not guaranteed, profit. Arbitrageurs are the third group: those who can inventory physical commodities and who try to capitalise on mispricing between the commodity, including its storage and financing cost, and the futures price. They often own the storage itself, whether bonded warehouses, grain silos or feedlots, and they manage that inventory against futures prices to earn arbitrage-style profits.

Exchanges, analysts and regulators

Commodity futures markets are found worldwide. The CME and ICE are the primary US markets, having consolidated most of the older specialist exchanges. Elsewhere in the Americas the main venue is B3 in Brazil, covering softs, grains and livestock. Europe offers the London Metal Exchange, under the ownership of Hong Kong Exchanges and Clearing Limited, which is the leading industrial metals location worldwide, and energy and shipping also trade out of London. Asia contributes the Dalian Commodity Exchange and the Shanghai Futures Exchange in China, together with the Tokyo Commodity Exchange in Japan. Indonesia in palm oil, Singapore in rubber and Australia in energy, grains and wool run supplementary markets.

Non-market participants use exchange information for research and policy, which affects market behaviour indirectly. A manufacturer may forecast the energy cost of a new process, commodity prices are a key component in understanding sources of inflation and feed into indexes of household quality of life, and governments that control natural resource extraction or tax it want to understand futures markets in order to promote or discourage investment and to raise revenue.

On regulation, the United States is the outlier. Commodity and futures regulation falls under the Commodity Futures Trading Commission, a body separate from the better-known Securities and Exchange Commission, and the CFTC delegates much direct monitoring to the National Futures Association, a self-regulatory body whose members are the authorised direct participants with customer responsibilities, such as clearing firms, brokers and advisers. Most other countries have a unified structure. The China Securities Regulatory Commission regulates both futures and securities. In Europe most legislation begins at European Union level, primarily through the European Securities and Markets Authority. The Markets in Financial Instruments Directive, which first came into force in 2007, was a key element of financial market integration focused largely on deregulation, and MiFID II took effect in January 2018. Since 2009 the instruments covering commodity derivative markets in particular have been revised and extended with the aim of strengthening oversight, subject to G–20 commitments. Harmonising these bodies is the International Organization of Securities Commissions, the international association of the world’s securities and futures markets. In every region the interests of the financial sector strongly influence the debates and the legislation.

Example 5 · Worked

1. Commodity traders that often provide insurance to hedgers are best described as arbitrageurs, liquidity providers or informed investors?

Solution. Liquidity providers. They stand between producers and consumers who do not arrive at the same time, and in doing so they sell what amounts to insurance to hedgers looking to shed price risk through a futures contract. Arbitrageurs are not the answer, because they seek to profit from mispricing caused by a lack of information. Informed investors are not the answer either, because their role is to keep the market efficient by trading away that same information-driven mispricing.

2. A commodity fund holds storage facilities and takes delivery when it judges the futures price to be out of line with the spot price plus carrying costs. How should it be classified?

Solution. As an arbitrageur. The defining feature is the ability to inventory the physical commodity, which is what converts an observed gap between the futures price and the spot price plus storage and financing costs into a realisable profit. A hedger has an underlying commercial exposure to offset, and a speculator takes a directional view; neither description fits a fund whose edge is the storage capacity itself.

3. Explain why aggregate open interest in a commodity futures market is net zero while the aggregate position in a stock market is net long.

Solution. A futures contract is created when a buyer and a seller agree, so every long is matched by a short and the aggregate nets to zero by construction. A share is an issued claim that exists whether or not anyone trades it, so the aggregate market value of issued shares equals the net aggregate position held at the end of each day, which must be long. This is also why shorting differs so much between the two: an equity short seller must borrow an existing share, reimburse its dividends and post margin above the long requirement, whereas a futures short simply sells to a long and posts the same margin.

Two price forms sit side by side. One is the spot price struck in physical markets, the other the futures price for delivery at a later date. Spot means what it costs right now either to bring the physical good to a named place or to lift it away from one. Quotes of that kind attach to the gate of a silo, to a gas pipeline, to an oil tank or to a sugar refinery, which makes them intensely local.

A futures price is a price agreed today to deliver or receive a defined quantity, and often a defined quality, of a commodity at a future date. A producer and a consumer could write a bilateral forward instead, but many standardised contracts already trade on exchanges. The advantage of the exchange is publicity: contract numbers and prices are publicly available, so the price discovery process that brings buyers and sellers together is shared broadly and in real time. The longest-maturity futures contract outstanding stretches from about a year in livestock to several years in crude oil.

Basis, backwardation and contango

That gap between the spot price and the futures price goes by the name of basis. Which of the two stands higher depends on the commodity and on the circumstances it faces at the time. When the spot price exceeds the futures price the market is in backwardation; the opposite case is contango.

The words themselves are old. The origin of contango is murky, but one theory traces it to the word continuation, used on the London Stock Exchange in the mid-1800s, when the word described a charge handed by the buyer to the seller in order to postpone settlement, leaving the nearer price as the cheaper of the two. Backwardation described the same arrangement reversed, with the payment to defer settlement made by the seller to the buyer.

Both terms are also applied to the relationship between two futures contracts on the same commodity. When the near-term contract price is higher than the longer-term contract price, the market is in backwardation. When the near-term price is lower than the longer-term price, the market is in contango. The price difference either way is the calendar spread.

A positive calendar spread goes with backwardation; a negative calendar spread goes with contango.

Figure 2: The two shapes a futures curve can take

Both curves begin at the same spot price. In contango the deferred contract costs more than the near one, so a long roll buys fewer contracts. In backwardation the deferred contract is cheaper, so a long roll buys more.

Two stylised examples make the arithmetic concrete. Crude oil on the New York Mercantile Exchange might show July delivery at US$65.50 per barrel against December delivery at US$64.00 per barrel, which is backwardation. Lean hogs on the CME might show July delivery at 95 US cents per pound against August delivery at 96 US cents per pound, which is contango.

Two stylised calendar spreads

Market	Near contract	Deferred contract	Calendar spread	State
WTI crude oil	July, US$65.50 per barrel	December, US$64.00 per barrel	+$1.50 per barrel	Backwardation
Lean hogs	July, 95 US cents per pound	August, 96 US cents per pound	−1.0 cent per pound	Contango

The crude oil spread is 65.50 − 64.00 = 1.50. The lean hogs spread is 95 − 96 = −1.0.

Calendar spreads trade in their own right, with their own bid and ask prices, their own trading range and their own order book, exactly like a single-month contract. A single spread trade produces two contracts on the exchange account, one for each leg, and each leg is valued at its own closing price, so all trades and positions end the day marked at close-of-day prices.

Why the shape exists at all

Assuming stable spot prices, a producer is willing to accept a future price below the current spot price, because certainty is worth paying for and it stabilises the producer’s business. Whoever sells that insurance profits as the lower futures price converges upward to the higher spot price over time. The reverse arises when future prices are expected to be higher for reasons connected to economic growth, weather, geopolitical risk or supply disruption. For a long holder of a contract in contango, value erodes over time as the contract price moves toward the spot price, all else unchanged, and that erosion can be very costly for anyone who rolls positions repeatedly. Backwardation is normal for some contracts while other commodities frequently trade in contango.

Settlement and convergence

Commodity futures settle either in cash or by physical delivery. A cash-settled contract, feeder cattle on the CME being one, is worth nothing once the maturity date passes. Cash settlement was an important innovation, because it drew speculators and arbitrageurs into the market and gave hedgers on either side a way to transfer future price risk without the complications of physical delivery. A physically settled contract requires title to the commodity itself to move from seller to buyer at a named place, by a named date, and against a named quality specification. Oil satisfying the minimum specification of the WTI contract has to arrive at one named group of tanks in Cushing, Oklahoma, whereas the equivalent Brent contract nominates points in the North Sea, offshore of the United Kingdom and of Norway. Because those two places lie so far apart, local imbalances can drive a wedge between the prices even where specifications are close.

Physical delivery also forces the futures and spot markets to converge, which does not necessarily happen in a cash-settled market. That is not an accusation of manipulation: trading costs and other frictions can limit complete convergence on their own. The emergence of central exchanges assisted convergence through standardised contracts and centrally established, publicly available pricing, which quickly displaced private pricing that depended on the individual contract terms and on where the transaction happened to take place.

Delivery becomes complicated where quality or variety differ. Robusta traded in London cannot be tendered against the arabica contract traded in New York, since the variety differs and so does the delivery venue, and raw unprocessed sugar traded in the United States cannot be delivered against white processed sugar traded in the United Kingdom. Contracts handle some of this by attaching a premium or a discount to the specification, and arabica coffee prices are automatically adjusted for the country of origin and for the location of the warehouse at which delivery is made.

In summary, spot prices are highly localised and tied to physical delivery, which limits how far participants can hedge or speculate on their direction. Futures prices are global, or at least regional or national, standardised to promote liquidity, used as the reference price for customised forward contracts, and a source of widely available and minimally biased data for participants and governments judging supply and demand. Trading may look chaotic at the level of a single tick, and still deliver a social benefit by signalling to producers and consumers how to hedge and how large an inventory to hold, and to governments what a policy decision may cost.

Example 6 · Worked

The nearest-to-expiration futures contract for West Texas Intermediate crude oil is priced at $65.00 per barrel, while the six-month WTI futures contract is priced at $60.75 per barrel.

1. What state is the WTI futures market in?

Solution. Backwardation. Backwardation is the state in which spot sits above the near-term contract price and the near-term price in turn sits above the longer-term price. Here $65.00 exceeds $60.75, so the curve slopes downward. It would be contango only if the deferred price exceeded the nearby price.

2. A colleague argues that the $4.25 gap must equal the shipping and delivery cost of physically delivering the six-month contract. Is that right?

Solution. No. The gap is 65.00 − 60.75 = $4.25 per barrel, but shipping and delivery costs are only one component of a futures price. Geopolitical conditions, seasonality and other factors also drive the difference between delivery months, so the calendar spread cannot be read as a pure logistics charge.

3. An arbitrageur runs two positions. The lean hogs calendar spread is quoted at −50 cents per pound and the natural gas calendar spread at +$1.10 per million BTU. What does each imply?

Solution. The lean hogs market is in contango and the natural gas market is in backwardation. The spread is the near price minus the deferred price. When futures prices exceed the nearer price, the market is in contango and the spread carries a negative sign, which is the lean hogs case. When the nearer price is the higher one, the market is in backwardation and the spread is positive, which is the natural gas case. Note also that both the individual contract prices and the combined spread can be traded, so it is not true that only spreads are tradable.

4. Is a curve in backwardation likely to stay in backwardation?

Solution. No. A futures price curve can fluctuate between contango and backwardation in the long term. During periods of market stress or fundamental structural change, some commodity curves shift rapidly from one state to the other. The shape reflects both long-term structural industry factors and market expectations of future supply and demand, so it is not a fixed characteristic of the commodity.

5. An analyst claims spot prices are universal across regions while futures prices vary by location. Correct the statement.

Solution. It is the other way round. Spot prices vary across regions, reflecting logistical constraints and local supply and demand imbalances that hinder the movement of material, while futures contracts are deliberately standardised to make trading possible. It is also wrong to say futures ignore quality: contracts are written on standardised specifications, and composition and quality can attract premiums or discounts for delivery.

Volatility is what commodity futures markets are known for, and yet, like any other asset class, they rest on theoretical foundations that govern their long-run behaviour. The original purpose of these markets was to let producers and consumers hedge physical raw materials, and three theories try to explain the resulting shape of the futures price curve: insurance theory, the hedging pressure hypothesis and the theory of storage. Because the shape of the curve drives roll return, and roll return is one of the three components of total return, these theories are not decoration. They are the reason a curve slopes the way it does.

Insurance theory

Keynes (1930), an economist and an active market speculator, proposed one of the earliest theories of curve shape in his 1930 work A Treatise on Money. It is also known as the theory of normal backwardation. The argument is that producers use futures markets as insurance, locking in prices to make revenue predictable. A producer is long the physical good and is therefore motivated to sell it for future delivery to hedge the sales price. Imagine a farmer who expects to grow a certain quantity of soybeans on her land next year. She can sell part of that future crop today, then spend on fertiliser and seed with more confidence in her budget. She is not necessarily locking in a profit, but she understands her financial position better.

Two consequences follow. Persistent forward selling by producers pushes down the prices of deferred contracts, so the curve is in backwardation as its normal state. Equivalently, the futures price has to sit below the current spot price as remuneration to the speculator who takes on the price risk and supplies the price insurance.

Normal backwardation: a stylised cotton curve

Delivery month	Price (US cents per pound)	Position in the crop year
March	76.75	Pre-harvest
May	76.50	Pre-harvest
July	76.00	Pre-harvest
October	74.50	Post-harvest
December	73.75	Post-harvest

Example 7 · Worked

Use the cotton curve above. A cotton futures contract covers 50,000 pounds. Assume the front price stays at 76.75 cents per pound throughout.

1. An investor buys the October contract at 74.50 cents and holds it until October becomes the current contract. What is the gain per pound and per contract?

Solution. As October approaches, and with the front price unchanged, the October contract converges upward to the front price of 76.75 cents.

Gain per pound = 76.75 − 74.50 = 2.25 cents.

Gain per contract = 2.25 cents × 50,000 pounds = 112,500 cents = $1,125 per contract.

Even where convergence is incomplete, the theory holds that this process should deliver positive excess returns, sometimes called the risk premium, in order to induce anyone to buy. That return is the mirror image of the insurance the farmer receives.

2. Which statement best describes insurance theory: that speculators refuse to supply insurance unless futures trade above spot; that producers will accept a lower future price in exchange for certainty; or that markets end up in contango because speculators insist on a risk premium?

Solution. Producers will accept a lower future price in exchange for the certainty of locking it in. Keynes argued that a producer would prefer a discount to the potential future spot price in return for knowing the selling price in advance. The first alternative has the sign backwards, because under insurance theory the futures price must sit below the spot price, which is what normal backwardation means. The third alternative names the wrong state: insurance theory implies backwardation, not contango.

The evidence has not been kind. Kolb (1992) examined 29 futures contracts and concluded, with some humour, that normal backwardation is not normal. In other words, the presence of backwardation does not reliably generate statistically significant positive returns for the investor, and contango does not reliably generate negative ones. That result confirmed earlier work including Fama and French (1987). A more sophisticated account was therefore needed for the many commodity futures markets that show persistently higher prices further out, which is what the hedging pressure hypothesis attempts.

The hedging pressure hypothesis

This view came out of several strands of work, most notably De Roon, Nijman and Veld (2000), who drew on Cootner (1960). Working across 20 futures markets over the years 1986 to 1994, they found that hedging pressure carries real explanatory power for futures returns. Hedging pressure arises when producers and consumers both seek protection from price volatility so as to stabilise projected profits and cash flow. Producers want to sell forward and therefore sell futures. Consumers want to lock in purchase prices and therefore buy futures. The farmer selling part of next year’s crop is one side; a central bank scheduled to buy gold in every one of the coming 12 months for its monetary operations, or a refinery fixing the price of the crude it buys and of the gasoline and heating oil it makes, is the other.

The shape of the curve then depends on which side pushes harder.

Hedging pressure and the resulting curve, stylised cotton prices in US cents per pound

Delivery month	Balanced hedging	Producers exceed consumers	Consumers exceed producers
March	75	76.75	75.00
May	75	76.50	75.25
July	75	76.00	75.75
October	75	74.50	77.00
December	75	73.75	78.00
Resulting shape	Flat	Backwardation	Contango

March, May and July are pre-harvest months; October and December are post-harvest. The middle column reproduces the insurance theory curve, which is what the hedging pressure hypothesis predicts when producers dominate.

If the two forces are equal in weight the curve is flat, as the first column shows. The natural need for price insurance among buyers and sellers offsets, so no discount is required to induce speculators to accept price risk, because the hedging needs of the two sides complement each other. A vivid non-commodity illustration is snowfall in New England. Small municipalities in Vermont, New Hampshire or Maine face a budget risk from heavy annual snowfall, because snow removal costs rise. Ski resorts in the same region face the opposite risk, because low snowfall means revenue shortfalls and the added cost of making snow, while heavy snowfall raises revenue and lowers operating cost. Two parties with mirror-image exposures can transact with each other and both come out ahead.

If producers as a group want to sell forward more than consumers want to buy forward, the imbalance in demand for price protection has to be absorbed by speculators, and speculators only step in when futures prices trade at a sufficient discount to compensate them for the risk. That produces backwardation and reproduces Keynes. If instead the buyers of a crop are especially worried about availability at the next harvest while the growers are relaxed about prices, the imbalance runs the other way. Buyers bid the futures price up to induce speculators to take on the uncertainty, and the curve is in contango.

Why the hedging pressure hypothesis is still incomplete

Exposure to commodity price risk is generally larger on the producing side than on the consuming side, a point Hicks (1939) made. There are companies, and indeed countries, almost entirely dependent on commodity production and therefore concentrated in a single sector: energy names such as British Petroleum and ExxonMobil, grain names such as Cargill and Louis Dreyfus, and metals names such as BHP Billiton, Vale, Rio Tinto and Shenhua. Consumers are far more diffuse, and few individuals hedge their meat consumption or their gasoline spending at all.

Companies that buy commodities as inputs have a mixed record that depends on how important the input is. Clothing companies such as Gap generally do not hedge cotton, because the spend is only a few percentage points of the expense base, and marketing and store experience, visible in rent, occupancy and depreciation expenses, matter far more. Fast food companies such as McDonald’s, Burger King and Wendy’s hedge a wide range of inputs across livestock, grains and energy, because competition for prepared food at a low price point is intense.

Both sides also speculate, whether they intend to or not. Corporate treasury departments run as profit centres adjust hedges according to their view of the market, so a function whose primary purpose is hedging can drift into speculation under a profit incentive. Individual farmers may not follow the futures market closely and hedge inconsistently. Trading companies actively trade both futures and physical markets in energy, metals and grains, and their entire business model is to know what is happening along the value chain and to profit from that informational advantage while bringing buyers and sellers together; their profit comes from trading around production rather than from production itself. In each of these cases an attempted hedge can become an unintended speculative position in which the company takes on more risk rather than transferring it away. The 1993 collapse of Metallgesellschaft AG, then one of Germany’s largest industrial conglomerates, from a poorly constructed gasoline, fuel oil and heating oil hedge remains the defining example. The deeper practical problem is that measuring the asymmetry in hedging pressure between the buyers and the sellers of a commodity is very difficult.

The theory of storage

Kaldor (1939) approached the problem from inventories instead. The question the theory addresses is whether supply or demand dominates the price economics of a given commodity. Commodities are physical assets, not virtual ones, so they have to be stored, and storage costs money: rent, insurance, inspections, spoilage. A commodity that is regularly stored should therefore have a higher price in the future, which is contango, to account for those costs. In that case supply dominates demand. A commodity consumed along a value chain that permits just-in-time delivery and use, and therefore minimal inventory, avoids those costs. There demand dominates supply, and current prices exceed futures prices, which is backwardation.

Working against storage cost is a benefit called the convenience yield. Having physical supply available is convenient for consumers of the commodity, whether individuals, bread companies, meat processors or refiners, because inventory buffers a supply disruption that would otherwise shut their operations down. That concern is inversely related to inventory size and to general availability, so the convenience yield is low when stock is abundant and rises as inventories run down and worries about future availability grow.

The theory of storage. Storage costs push the curve into contango; convenience yield pulls it toward backwardation.

Figure 3: Convenience yield against the level of inventory

The benefit of holding physical inventory is worth most when there is least of it. As stocks build, the marginal buffer value falls away and storage cost dominates, which pushes the curve toward contango.

The equation says that price returns and curve shape move together with available inventory and with actual and expected supply and demand. The Libyan civil war of 2011 is the standard illustration. Output of that country’s high-grade crude came under threat, supply tightened, and the spot price of high-grade barrels rose. At the same time the convenience yield rose in the contracts closest to expiration, because European refiners scrambled for alternative supply. The high quality of Libyan crude restricted which substitute grades could replace it and how soon those replacements could arrive, and the geography and logistics of the oil industry imposed a multi-month delay. Further-out contracts reacted far less, because traders assumed replacement supply would be available by then, so the convenience yield stayed lower in the deferred months. That configuration, high near-dated convenience yield and low deferred convenience yield, is precisely what pressures crude oil into backwardation, which is what happened during 2011.

All three theories are reasonable and all three contain components that are unobservable or highly volatile and therefore not reliably calculable. Producers and consumers treat storage costs as proprietary information. Weather, war and technology can move the convenience yield sharply and by an unknown amount within days. Even defining inventory is awkward, because corn suitable for animal feed may not be suitable for human consumption. What remains are frameworks that require judgement and analysis from a trader or a valuation system rather than formulas that can be applied mechanically.

Are the three theories rivals or complements

They answer slightly different questions, which is why an examiner can ask you to attribute one observed curve to one theory. Insurance theory asks who needs protection and concludes that producers do, so it predicts backwardation always. The hedging pressure hypothesis relaxes that to ask which side needs protection more, so it can predict backwardation, contango or a flat curve. The theory of storage ignores hedging motives entirely and asks whether the commodity is being stored, so it predicts contango for storable commodities and backwardation where consumption is just-in-time. A question that emphasises the balance of producer and consumer activity is pointing at hedging pressure. A question that emphasises inventories, storage cost or scarcity is pointing at the theory of storage. A question that describes producers accepting a discount for certainty is pointing at insurance theory.

Example 8 · Worked

1. Under the hedging pressure hypothesis, what happens when the hedging activity of commodity futures buyers exceeds that of commodity futures sellers?

Solution. The market is most likely in contango. Excess demand for price insurance among buyers drives the futures price up to induce speculators to take on price uncertainty risk. A flat market would require futures demand activity roughly equal to supply, and backwardation would require the opposite imbalance, with producers seeking protection more than consumers.

2. Under the theory of storage, how does the convenience yield behave when supply of a commodity is scarce?

Solution. It is typically high. The convenience yield rises as inventories diminish and worries about future availability increase, because the buffer value of holding physical stock is greatest exactly when stock is hardest to obtain. Saying the yield is unaffected by supply is wrong, since supply levels have a discernible effect, and saying it is low when supply is scarce reverses the relationship.

3. Write the theory of storage relationship and explain the sign on each term.

Solution. Futures price = Spot price of the physical commodity + Direct storage costs − Convenience yield.

Direct storage costs, such as inventory and insurance costs, are added because they are real expenses incurred in holding the commodity until delivery, and anyone who buys forward avoids them. The convenience yield is subtracted because it is a benefit of ownership: holding the physical good insures the holder against supply disruption, and whoever buys forward gives that insurance up. Adding the convenience yield, or subtracting storage cost, reverses the economics in both cases.

4. A coffee market has just had a larger than expected global harvest, and futures trading activity is balanced between producers and consumers, with no change expected over the next year. The curve slopes upward. Which theory best explains it?

Solution. The theory of storage. The balanced trading activity explicitly rules out the hedging pressure explanation, because neither side is exerting more pressure than the other, and it rules out insurance theory, which would require producers to be selling forward heavily and would predict backwardation rather than an upward slope. What is left is inventory: a large harvest must be stored, storage costs money, and a commodity that is regularly stored should carry a higher price further out.

The total return on a commodity investment made through futures is not the same as the total return on the physical asset. The reason investors overwhelmingly choose futures is that physical commodities have to be stored, fed or treated against spoilage, and the requirements differ enormously from one commodity to another. Sustaining a hog in Mexico has almost nothing in common with storing crude oil in Nigeria. Futures strip that operational problem away and leave a financial exposure, but they introduce a return component of their own.

Total return on commodity futures is traditionally broken into three parts: the price return, also called the spot yield; the roll return, also called the roll yield; and the collateral return, also called the collateral yield.

For a fully collateralised position, meaning no leverage. With an index, a rebalance return is added as well.

Price return

The price return is the change in commodity futures prices, generally on the front month contract. It is not the same as the change in the price of the physical commodity, because the lack of standardisation in physical markets makes that quantity difficult to measure at all.

Roll return

A futures contract expires. An investor who wants continuing exposure must roll, selling the current contract as it approaches expiration and buying the next one, assuming a long position. Because the two contracts trade at different prices, the number of contracts needed to maintain a constant exposure changes at each roll.

It is important to be precise about what roll return is not. It is not a return that can be captured independently: no portfolio can be constructed that holds only roll return. It is an accounting calculation used to replicate part of the total return of a fully collateralised commodity index. Defined as a percentage, it is the accounting difference between the near-term and the farther-term contract prices, scaled by how much of the position is being rolled. Some presentations define it in monetary terms instead.

Both prices are closing prices. The sign follows the calendar spread, so contango produces a negative roll return.

Example 9 · Worked

Take a WTI crude oil roll out of March and into April dated 7 February 2019, priced under the S&P GSCI rulebook. That rulebook spreads a roll across five trading days, moving one fifth, or 20%, of the position on each of them.

WTI closing prices, 7 February 2019

Contract	Closing price
March	$52.64 per barrel
April	$53.00 per barrel

Calculate the gross and net roll return for that day.

Solution. Apply the roll return formula to the two closing prices.

Gross roll return = ($52.64 − $53.00) ÷ $52.64 = −0.68%.

Net roll return = −0.68% × 20% = −0.13%.

The negative sign is the signature of contango: the April contract is dearer than the March contract, so the roll sells cheap and buys dear. Note that different indexes use different periods and weights in their rolling methodology, so the same market can produce a different reported roll return under a different index rulebook.

In Expected Returns, Ilmanen (2011) argued, and others have challenged, that roll return is approximately equal to a risk premium. The idea traces straight back to Keynes and normal backwardation: speculators take the other side from producers who sell forward to lock in cash flows, and they expect an excess return for supplying that price insurance. Ilmanen attempted to show that positive long-run average returns go with positive roll return, meaning commodities whose futures prices are in backwardation, and negative long-run average returns go with negative roll return. The evidence in his own data does not support a clean conclusion, because 40% of the commodities he examined had negative roll returns and positive total returns at the same time. One therefore cannot conclude that backwardation earns a positive total return.

Collateral return

The collateral return is the yield on the bonds or cash used to maintain the futures position. The minimum amount of funds required is the initial margin. If an investor holds less cash than the exchange requires to maintain the position, the broker acting as custodian will demand more funds, which is a margin call, or will close the position, buying to cover a short or selling to eliminate a long. Collateral works as the assurance to the exchange that an investor is able to meet losses.

In index return calculations the cash balance is set equal to the notional value of the futures, and that equality is what makes a position fully collateralised and unleveraged. For expected returns the convention is to use a risk-free government bond matching the horizon being projected. Most commodity indexes use short-term US Treasury bills, but an analyst forecasting 10-year returns should use a 10-year constant maturity government bond, because the term of the collateral instrument should match the term of the forecast.

Putting the three together

The S&P GSCI has one of the longest backtested and live histories among investable commodity indexes, which makes it a convenient object for decomposition.

Average annual return components of the S&P GSCI, January 1970 to March 2019

Component	Index total	Spot	Roll	Collateral
Average annual return	6.8%	3.0%	−1.3%	5.0%
Annualised standard deviation	19.8%	19.8%	4.2%	1.1%
Correlation with index total return		0.97	−0.11	−0.14

Here the roll figure is the index excess return less its spot return, and the collateral figure is the index total return less that excess return. Excess return itself captures what an uncollateralised holding of nearby commodity futures would have accrued. Monthly data underlie every entry.

Read the table carefully, because it overturns a common intuition. Over more than 40 years the index generated 6.8% in geometrically compounded annualised returns, and about three-quarters of that came from interest rates through the collateral return, which was 5.0%. The commodity price spot return, which has varied a great deal over time, contributed roughly 45% of the total, being 3.0% out of 6.8%. Roll return subtracted 1.3%, or 130 basis points, per year. Note that the three components sum to 6.7% rather than the 6.8% shown for total return, because the total is a geometrically compounded figure while the components are reported separately; the small gap is a compounding artefact, not an error to be reconciled away. The inflation exposure investors seek from commodities arrives through the price return.

The risk row tells the same story from the other side. The spot return has effectively the same annualised standard deviation as the index itself, 19.8% against 19.8%, and a correlation of 0.97 with the index total return. Roll return and collateral return do not, in general, drive monthly returns: their standard deviations of 4.2% and 1.1% are small beside 19.8%, and their correlations with the index are slightly negative at −0.11 and −0.14. This link between commodity futures prices and commodity total return indexes is part of what defines commodities as a separate and investable asset class.

Figure 4: Building the total return of a fully collateralised position

The roll bar is drawn hanging down from the top of the price bar because a market in contango takes value away. In backwardation that bar would sit above the price bar instead and the total would be taller.

Example 10 · Worked

An investor realised a 5% price return on a commodity futures position and a 2.5% roll return after all contracts were rolled forward. It was held for a full year, collateralised at 100% of the position, earning a risk-free 2% per year.

1. What was the total return, annualised and excluding leverage?

Solution. Total return = Price return + Roll return + Collateral return.

The position was held for one year, so the 5% price return is already annualised, and the roll return is likewise an annual 2.5%. The collateral return is 2% per year × 100% initial collateral investment = 2%.

Total return = 5% + 2.5% + 2% = 9.5%.

2. A second investor holds a $10,000 position in long futures contracts that he wants to roll forward. The current contracts, close to expiration, are valued at $4.00 per contract, and the longer-term contract he wants to move into is valued at $2.50 per contract. What transactions maintain his exposure?

Solution. Exposure is held constant by dividing the dollar exposure by the price of each contract.

Sell: $10,000 ÷ $4.00 per contract = 2,500 existing contracts.
Buy: $10,000 ÷ $2.50 per contract = 4,000 longer-term contracts.

So he closes out 2,500 near-term contracts and initiates 4,000 longer-term contracts. Note the direction of the trades: closing a long means selling and initiating a long means buying, so reversing those verbs is wrong. Letting the near contracts simply expire and buying an extra 2,500 would leave him with 2,500 contracts at $2.50, or $6,250 of exposure, which is not the position he started with.

3. Why is the deferred contract in question 2 cheaper, and what does that imply for the sign of the roll return?

Solution. The deferred price of $2.50 is below the near price of $4.00, so the curve slopes downward and the market is in backwardation. Applying the roll return formula, ($4.00 − $2.50) ÷ $4.00 = +37.5% on the portion rolled, a positive roll return. That is the general rule: backwardation gives a positive roll return and requires buying more contracts, while contango gives a negative roll return and requires buying fewer.

Contango and backwardation, and the roll return that follows from them, reflect underlying supply and demand expectations, and they are accounting mechanisms for the commodity term structure rather than independent sources of profit. This section contrasts what actually happens to a portfolio in each state, then looks at what the historical record says.

The mechanics of a roll

An investor holding a fixed amount of exposure must buy a different number of contracts after a roll whenever the two contract prices differ. In backwardation the deferred contract is cheaper, so more of them are needed. In contango the deferred contract is dearer, so fewer are needed.

Example 11 · Worked

1. An investor has £110 of exposure in wheat futures. The near contract is worth £10 of exposure and the far contract is worth only £9. How does the investor roll and keep exposure constant?

Solution. Count the contracts on each side.

Before the roll: £110 ÷ £10 per contract = 11 contracts.
After the roll: £110 ÷ £9 per contract = 12.2, or 12 contracts rounded.

The investor rolls the 11 contracts forward and buys 1 additional contract so that post-roll exposure stays close to pre-roll exposure. This is the backwardation case, and it is why backwardation is described as requiring the purchase of more contracts.

2. A second investor has £108 of exposure in regular unleaded gasoline futures. The near contract is worth £9 of exposure and the far contract is worth £10. What does she do?

Solution. Again count both sides.

Before the roll: £108 ÷ £9 per contract = 12 contracts.
After the roll: £108 ÷ £10 per contract = 10.8, or 11 contracts rounded.

She rolls only 11 contracts forward and sells the extra near contract, so that post-roll exposure stays close to pre-roll exposure. This is the contango case, and fewer contracts are required than were held in the near position.

3. A commodity futures market is priced in backwardation. What happens to the roll return and to the number of contracts needed at the roll?

Solution. Rolling forward requires buying more contracts to maintain the same dollar position. In backwardation longer-dated futures are priced below near-dated contracts and the nearest contract is priced below the current spot price, so the cheaper deferred contract buys less exposure per contract. The roll return in backwardation is usually positive, not negative, and the claim that fewer contracts are needed describes contango instead.

What history shows

Over the window running from January 1970 through March 2019, roll return took 1.3% a year out of the average annual total return of the S&P GSCI. The reading quotes a standard deviation of 4.7% for that roll return series in its discussion of term structure, while the return decomposition table in the previous section reports 4.2% for the same measure; either figure is small relative to the 19.8% standard deviation of the index itself, which is the point being made. Plotting one-year price return against one-year roll return on monthly data from January 1970 to December 2019 produces two series that wander independently. Periods of backwardation and periods of contango do not persist indefinitely, and with a correlation of only 3% between the two series, roll return turns out not to be very indicative of price return at all. Positive price returns are associated with negative roll returns just as often as with positive ones.

Sector, on the other hand, matters a great deal.

Average annual sector roll return and standard deviation

Measure	S&P GSCI total	Energy	Industrial metals	Agriculture	Livestock	Precious metals	Softs
Mean roll return (annual)	−1.3%	−1.5%	−1.3%	−4.5%	−1.1%	−5.1%	−5.5%
Standard deviation of the mean (annual)	0.4%	0.8%	0.5%	0.4%	0.5%	0.2%	0.6%
Maximum roll return (annual)	18.9%	31.5%	45.9%	29.2%	35.5%	−0.4%	25.6%
Minimum roll return (annual)	−29.6%	−39.5%	−16.6%	−18.6%	−31.2%	−15.4%	−24.9%

Figures are calculated using rolling 12-month periods of monthly data. Sample periods differ by sector: S&P GSCI total, agriculture and livestock run from December 1969 to March 2019; industrial metals from December 1976; precious metals from December 1972; energy from December 1982; and softs from December 1994.

Three readings of this table are worth making. First, industrial metals, agriculture, livestock, precious metals and softs all show statistically strong negative mean roll returns, since each mean is several times its own standard deviation. Energy alone leaves open the statistical possibility of a positive mean, and even that possibility has narrowed since 2010. Second, every one of the sectors with a strongly negative mean is a sector whose commodities are stored for extended periods in warehouses, silos and feedlots, which is exactly what the theory of storage predicts. Precious metals are the extreme case: the maximum rolling 12-month roll return in the sample is −0.4%, so the series never turned positive at all, which follows from gold being stored perpetually as an alternative currency.

Third, energy is the exception that proves the mechanism. Energy is historically consumed on a real-time basis apart from various strategic reserves, and that minimal storage buffer creates a lower or negative convenience yield relative to storage cost, which is what allows a positive roll return. Three things changed after 2010. Shale oil production in the United States increased oil’s convenience yield to the point where historical scarcity risk is much lower than before. Oil supply risk shifted toward China, as that country took over the position of lead oil importer from the United States. And OPEC, with Russia and a few other non-OPEC members included, regained some pricing power as the group achieved a degree of success in restricting supply.

Bringing this together, any index or long-only strategy tilted toward agriculture, livestock, precious metals or softs ought to plan for negative roll returns. Energy commodities, natural gas aside, offer an opportunity for positive roll return provided producers succeed in withholding supply from the market. Roll return can matter a great deal in any single period, but over long horizons it has been relatively modest compared with price return, and because it is so sector dependent, the decision to diversify across sectors or to concentrate in one has a profound effect on the roll return of a commodity portfolio.

Why avoiding negative roll return is not by itself a strategy

A committee member who sees a persistently negative roll return on a position and asks why it is not simply avoided is making an accounting statement, not an investment one. Roll return is one of three components, and a position can carry a negative roll return and still outperform a position with a positive roll return, because the price return dominates the variance of the total. The empirical support is direct: the correlation between roll return and price return is about 3%, and 40% of the commodities in Ilmanen’s sample combined negative roll returns with positive total returns. Screening on roll return alone therefore throws away most of the information about expected total return while adding a sector bet, since the sectors with the least negative roll returns are concentrated in energy.

Example 12 · Worked

1. How should the roll return be characterised as a contributor to the total return of a futures position?

Solution. It can matter a good deal inside any one period while staying modest once several periods are strung together. Historically the roll return has been small beside the price return over long horizons while still being meaningful in an individual period. It is not true that the contribution is significant over both single and multiple periods, and it is not close to zero either, since a futures contract throws off a roll return of either sign according to the commodity and to conditions at the time.

2. Using the sector table, rank agriculture, energy and precious metals by how attractive their roll return history has been, and say what the ranking reflects.

Solution. Energy is the most attractive at −1.5%, agriculture next at −4.5%, and precious metals the least attractive at −5.1%. The ranking reflects storage. Energy is largely consumed as it is produced, so its convenience yield can exceed storage cost and pull the curve into backwardation. Agriculture is stored in silos between harvests. Precious metals are stored permanently, which is why their maximum rolling 12-month roll return in the sample is −0.4%, never once positive.

3. A long-only fund is benchmarked to a broad commodity index and wants to improve roll return without leaving the asset class. What does the table suggest, and what is the cost?

Solution. The table suggests overweighting energy, which is the only sector with any statistical possibility of a positive mean roll return, and underweighting softs at −5.5%, precious metals at −5.1% and agriculture at −4.5%. The cost is concentration. Energy also carries the widest range of outcomes in the sample, from a maximum of 31.5% to a minimum of −39.5%, and the largest standard deviation of the mean at 0.8%, so the improvement in expected roll return is bought with a large increase in sector-specific risk and with a bet that producers continue to withhold supply.

Futures are not the only route into the asset class. A commodity swap is a legally binding arrangement under which payments change hands on several dates, sized by nominated reference prices or by indexes tied to commodities. In commodities the reference prices are very often a series of futures contracts, so a swap is frequently a repackaging of the futures market rather than an alternative to it.

The motivation is easiest to see through a user. An independent oil refiner wants to hedge its crude purchases over an extended period. Running a large book of futures contracts is administratively heavy and locks the refiner into standardised delivery terms. A swap, particularly one that is cash settled rather than physically settled, protects the refiner against a price spike while leaving it free to buy its actual barrels wherever it likes. Commercial participants therefore use swaps for two reasons at once: risk management and risk transfer without the need to set up and manage many futures contracts, and a degree of customisation that a standardised contract cannot offer. The refiner might negotiate a specific grade as the reference price, Heavy Louisiana Sweet rather than West Texas Intermediate, or a blend of crudes that shifts through the year with the season. It might also vary the hedged quantity over time, lowering exposure during a planned shutdown and maintenance period at the refinery.

Facing the refiner sits a swap dealer, normally a financial intermediary of some kind, a bank or a trading house. The dealer can hedge the price risk it has assumed in the futures market, or negotiate an offsetting swap with a second dealer, or arrange a physical purchase contract with a crude oil producer. It may also simply keep the exposure, seeking to profit from its own market information.

Excess return swaps

Under an excess return swap what each party pays or receives is driven mainly by the price movement on every futures contract inside the index. The net change in those underlying futures prices is defined as the excess return, and that excess return is multiplied by the notional amount of the contract to determine the payments between buyer and seller. The refiner arrangement below is an excess return swap.

Example 13 · Worked

At the end of December an oil refiner takes the long side of a swap that pays out whatever the reference price runs above $70 per barrel, settled at each month-end through September. Because the structure is effectively a long series of call options, the refiner pays the counterparty a premium of $25 up front.

Flow of funds on the refiner swap

Month	Reference price	Cash flow to the refiner against $70
December	$64	−$25 (premium)
January	$70	$0
February	$75	+$5
March	$71	$1
April	$66	$0
May	$65	$0
June	$63	$0
July	$66	$0
August	$72	$2
September	$78	$8
Total gain or loss on this swap		−$9

1. Confirm the total gain or loss and explain how each monthly figure arises.

Solution. Each monthly cash flow is the reference price less $70 when that difference is positive and zero otherwise, because the refiner is only paid the excess.

February: 75 − 70 = $5. March: 71 − 70 = $1. August: 72 − 70 = $2. September: 78 − 70 = $8. Every other month has a reference price at or below $70, so the payment is $0.

The nine monthly payments therefore total 0 + 5 + 1 + 0 + 0 + 0 + 0 + 2 + 8 = $16, against a premium of $25 paid in December.

Total = $16 − $25 = −$9, found by summing the cash flows and ignoring present value calculations and other considerations.

2. The swap lost money. Was entering it a mistake?

Solution. Not necessarily. The net loss of $9 over the nine months from January to September raised the effective cost of a barrel by $1 per month across that period, which is the price of the protection. What the refiner bought was insurance against a cash squeeze in any month when an oil price spike could have impaired its liquidity, and a cost defined up front, which gives cash flow predictability. Many of the events that move oil prices lie outside any single company’s control, so a firm guarding against financing risk can find the instrument worth holding even across a period in which the payoff came out negative. Accounting standards and practices for swaps also feed into whether the instrument is attractive.

Total return swaps

In a total return swap the index level moves with the price change on every constituent futures contract and, on top of that, with interest earned on whatever cash collateral backs the purchase of those contracts. If the index level rises, the buyer is paid, net of the fee it owes the seller. Should the level drop between one valuation date and the next, the seller collects instead, along with the fee it charges the buyer.

This structure is generally used by large institutional investors such as pension plans rather than by commodity producers or buyers. The investor is seeking exposure to commodity returns, usually on the grounds that commodity returns correlate weakly with those of other asset classes, or on the view that commodities hedge inflation usefully when assets are matched against liabilities. Accounting treatment with respect to futures often drives the choice between a swap and a direct futures programme.

Example 14 · Worked

A manager of a defined benefit retirement plan with £2 billion of plan assets wants approximately 5% of those assets in commodities. The exposure is to be to the hypothetical China Futures Commodity Index and is to run for five years. After issuing a request for proposals and evaluating the bidders, the manager contracts with a Swiss bank for a total return swap providing that exposure.

1. What notional exposure does the swap carry?

Solution. 5% of £2 billion = £100 million.

2. On the first day of the agreement the index rises 1%. On the second day it falls 5%. What payments occur?

Solution. Day one: £100 million × 1% = £1 million owed by the swap dealer to the manager, because the manager is long the index.
Day two: £100 million × 5% = £5 million owed by the manager to the dealer.

The dealer will commonly hedge its short index exposure with futures or with physical commodity investments. The manager will not hedge, because the risk and return exposure offered by commodities is precisely what the manager is paying to obtain.

3. A different manager enters a $100 million notional total return commodity swap to obtain long commodity exposure, reset monthly against a broad-based commodity index. The index rises 3% in month one and falls 2% in month two. What are the two payments?

Solution. Because the manager is long the total return swap, payments are received when the index rises and made when it declines.

Month 1: $100 million × 3% = $3 million paid by the swap dealer to the manager.
Month 2: $100 million × −2% = $2 million paid by the manager to the swap dealer.

Payments are exchanged periodically, in this case monthly, and are not withheld until the contract expires, so an answer of no payments until expiry is wrong. Reversing the direction of the two payments is also wrong, since it would describe a short position.

Basis swaps

A basis swap exchanges payments at intervals, keyed to two commodity reference prices that are related without being perfectly correlated. Its purpose is to bridge the gap, known as the basis, that opens between a deeply liquid futures contract and some thinner but related material. One such contract might settle on the difference between average daily Brent prices, at the liquid end, and heavy crude deliverable into the Gulf of Mexico, at the illiquid end. That is valuable for refineries on the US Gulf Coast that have invested heavily in processing cheaper heavy crudes from countries such as Mexico or Venezuela, because the prices of those crudes do not always move in tandem with more common grades such as Brent, so a price basis develops between the two. Note that the word basis carries other meanings depending on the commodity: in grains the word can mean the gap between the soybean contract and physical beans deliverable on the Mississippi River.

Variance and volatility swaps

Commodity variance swaps work like equity variance swaps. One side buys variance and the other sells it. The pair then swap payments at intervals, sized by the proportional gap between realised variance in the commodity price across successive periods and a fixed variance level agreed when the contract was written. If that difference is positive the buyer receives a payment, and if it is negative the seller receives payment. The variance differences, observed against fixed, are often capped in order to limit both upside and losses.

Volatility swaps are very similar, with the direction and amount of payments determined relative to observed against expected volatility for a reference price commodity. Neither side is speculating on the level or the direction of prices. Both are taking a view on how volatile prices will be against expectations. A volatility seller profits if realised volatility comes in below expectations, while the volatility buyer is anticipating higher than expected volatility.

Example 15 · Worked

1. For a commodity volatility swap, which observed quantity is compared against its reference level in order to size and direct the payments: price direction, price variance, or price volatility?

Solution. Volatility for the price of the commodity. The two sides are speculating on expected volatility: the seller profits if realised volatility is lower than expectations and the buyer benefits if it is higher. Direction is not the answer, because a volatility swap is deliberately indifferent to which way the price moves. Variance is not the answer either, because variance is volatility squared and belongs to the separate variance swap contract.

2. A manager believes Brent crude will rise more than heavy crude, that realised Brent volatility will stay below expected volatility, and that a crude oil index level will rise. Match each view to a swap.

Solution. The relative price view is expressed through a basis swap that is long Brent and short heavy crude, because a basis swap pays on the difference between two related reference prices. The volatility view calls for a short position in a volatility swap, since the seller of volatility profits when realised volatility is below expectations; a long volatility position would express the opposite view. The index level view calls for a long position in an excess return swap referencing that index, because the long receives when the index level rises; a short position would express the opposite view.

Indexes exist in commodities as they do everywhere else, to portray the aggregate movement of prices, investment vehicles and investing approaches. It is fair to say that an asset class does not exist until at least one representative index does.

Commodity indexes play three roles. An index is a benchmark against which broader moves in commodity pricing are evaluated. As a broad indicator it serves macroeconomic and forecasting purposes, by exposing statistically significant relationships between index movements and other macroeconomic variables. And it acts as the basis for an investment vehicle or contract, supplying the information needed to record, monitor and evaluate the price changes that determine contract value.

Five construction choices, and why each one matters

Breadth of coverage. How many commodities and sectors are included, noting that some commodities have multiple reference contracts, as crude oil does with West Texas Intermediate in the United States and Brent in Europe.
Weighting. The relative weightings assigned to each component and the methodology by which those weights are determined.
Rolling methodology. How contracts about to expire are rolled into future months. This choice has a direct effect on the roll return of the overall index, and roll return is one of the three components of total return.
Rebalancing. The methodology and frequency for restoring the weights of individual commodities, sectors and contracts. As with stocks and bonds, the opportunity to earn positive rebalance returns depends on the correlation of the underlying components and on the tendency of underperforming components to revert to the mean. A drought may push cotton prices up, and a strong crop the following year may cause them to collapse; a rebalance sale of the now overvalued cotton exposure into an undervalued exposure locks in part of that gain.
Governance. The process by which all the other rules are implemented. Some indexes are rules-based, following a quantitative methodology, and others are selection-based, with an index committee picking the commodities qualitatively. Governance also oversees the independence of providers, so that, following the best practices of the Index Industry Association, the asset price is independent of the index provider, which in turn is independent of the product provider such as an exchange-traded fund or swap provider.

Figure 5: The construction choices that feed an index return

None of the five choices is cosmetic. Coverage and weighting set the sector exposure, rolling sets the sign and size of roll return, rebalancing sets the rebalance return, and governance decides who is allowed to change any of it.

Investability

For an index to be a viable construct it must be investable, meaning that investors or their agents can replicate the stated methodology and turn the index concept into a representation of the asset class. Providers and investors therefore have to be mindful of the venues, physical or electronic, on which each component trades, of the liquidity and turnover of the relevant contracts, and of the term structure of the index, meaning how far into the future it extends and which months it covers.

Each of those has a cost attached. An index requiring investments on exchanges all over the world is harder and more expensive to replicate. An emphasis on illiquid contracts raises transaction costs. Contracts without a full yield curve are difficult to analyse and to trade. Small execution concerns are magnified when the object being constructed is a benchmark for an entire asset class. And an index whose constituents happen, whether by design or by accident, to spend most of their time in backwardation will flatter forward-looking performance through a positive roll return, while one tilted toward contracts that usually sit in contango drags on performance by the identical mechanism.

Overview of major commodity indexes

Feature	S&P GSCI	BCOM	DBLCI	TR/CC CRB	RICI
Year adopted	1991	1998	2003	2005 (current version)	1998
Commodities covered	24	23	14	19	38
Weighting basis	Production weighted	Production and liquidity weighted	Fixed weight	Fixed weight	Fixed weight
Roll rule	Nearby most liquid contract, monthly	Front month into the next or the second month	Optimised on roll return	Front month into the next month	Front month into the next month
Rebalance frequency	Annually	Annually	Annually	Monthly	Monthly
Retail funds available	Yes	Yes	Yes	Yes in some jurisdictions, as well as an exchange-traded fund on a related index	Yes

Information is as of 30 April 2019. BCOM is the Bloomberg Commodity Index, formerly the Dow Jones–UBS Commodity Index. DBLCI is the Deutsche Bank Liquid Commodity Index. TR/CC CRB is the Thomson Reuters/CoreCommodity CRB Index. RICI is the Rogers International Commodities Index.

All five indexes have broad sector coverage across energy, grains, livestock, precious metals, industrial metals and softs. One exception stands out: the DBLCI holds nothing in livestock. The RICI sits at the opposite pole, admitting comparatively exotic and therefore thinly traded names such as lumber, oats and rubber, and at one time it carried palm oil together with adzuki beans, the small red beans common in Asian cooking.

The five indexes in turn

S&P GSCI. The second oldest of the five selected here, based on 24 commodities, with liquidity screens that admit only contracts clearing a minimum trading volume and carrying usable price history. Its weighting uses a world production value scheme, so that the commodity with the greatest physical trade value carries the biggest weight. Crude oil accordingly carries the highest single weight and energy the highest sector weight, historically as high as 80%. The approach is closest in spirit to the market-capitalisation weighting of nearly all major bond and stock indexes, and, like some capitalisation-weighted indexes in emerging or frontier markets, the resulting weights can be highly concentrated. The rolling methodology owns the front contracts, where liquidity is highest and where supply and demand shocks are most likely to bite.

Bloomberg Commodity Index. Based on 23 commodities, using liquidity as both a weighting factor and a screening factor, though the index is selection-based, meaning a committee uses judgement to pick the constituents. The construction rules cap sectors at a 33% maximum and floor individual commodities at a 2% minimum, and those two rules alone produce very different composition and weights from a production-weighted index. Energy currently dominates the S&P GSCI at a weight as high as 80%, while BCOM exposure is much lower at approximately 30%. Natural gas as a single component runs the other way, at approximately 9% in BCOM against approximately 3% in the S&P GSCI. Since natural gas has carried an annualised roll cost near 19%, frequently the steepest of any commodity, that heavier weighting means BCOM must find other sources of return, in price return and rebalance return, to overcome the drag created by natural gas inventory storage. Its rolling methodology also owns the front contracts.

Deutsche Bank Liquid Commodity Index. A fixed-weighting scheme across 14 commodities. Its distinguishing feature is the rolling methodology. Instead of focusing on near-term contracts, the roll is optimised on the time value of maximised backwardation and minimised contango across the contracts falling within the next 12 calendar months. That makes the DBLCI, arguably, the one index taking an active decision on roll return positioning.

Thomson Reuters/CoreCommodity CRB Index. Nineteen commodities, and the direct descendant of the earliest investable commodity index, which the Commodities Research Bureau brought out in 1978 after an initial version dating from 1957. It uses fixed weights decided by an index management committee on the basis of diversification, sector representation, liquidity and economic importance, and it clusters those fixed weights into tiers so that constituents move from tier to tier over time. The roll mechanically targets the front month or the second front month and requires no particular calculation.

Rogers International Commodities Index. A fixed-weighting scheme across 38 different commodities, designed by the investor Jim Rogers in the late 1990s. As with the TR/CC CRB, an index management committee sets weights on diversification, sector representation, liquidity and economic importance, and clusters them into tiers, with constituents moving between tiers as the committee reassesses their relative importance. Energy carries the largest weight, but the basket remains highly diversified. Some constituents are denominated in currencies other than the US dollar, rubber trading in Japan in yen and cocoa trading in London in sterling, which adds a foreign exchange element to index returns.

How often the index rebalances

The frequency of rebalancing feeds into index returns, and it does so most visibly for the two indexes that rebalance every month, the TR/CC CRB and the RICI. Portfolio theory says rebalancing matters more when a market mean reverts frequently, because there are more peaks to sell into and more valleys to buy. The same mechanism works against the investor in a trending market, because the outperforming assets are sold and continue upward while the underperforming assets are bought and continue to drift lower.

Relative performance of the monthly rebalanced indexes against the three annually rebalanced ones therefore depends on the length of price trends. More frequent mean reversion favours the TR/CC CRB and the RICI; a longer-lasting trend favours the annual rebalancers. Weighting scheme interacts with this. Where weights float, wholly or in part, with something such as production value, a higher futures price normally arrives alongside a higher physical price, so the post-rebalance weights drift broadly in line with current portfolio weights and the magnitude of each rebalance is smaller than under a fixed-weight scheme. The S&P GSCI and BCOM therefore tend to have lower rebalancing costs and, in a trending market, an opportunity to outperform their fixed-weight counterparts, especially those rebalancing frequently.

What the comparison finally shows

There is no dominant index and no dominant methodology. Relative performance depends on market circumstances and on the period examined, and deciding which of them is best suited to a long-term holding adds modest value at best. These indexes have all been highly correlated with one another, well above 70%, and have had low correlations, roughly 0%, with traditional asset classes such as US large-cap stocks, US bonds and international stocks. Just as with equity index providers, commodity indexes move in parallel even when their returns, and their Sharpe ratios, differ dramatically over individual periods.

Example 16 · Worked

1. All else equal, compared with an equally weighted commodity index, how sensitive is a production value-weighted index such as the S&P GSCI to energy sector returns?

Solution. More sensitive. Energy takes up a sizeable share of any index weighted by production value, historically as much as 80% of the S&P GSCI, which makes it a meaningful driver of that index and of its returns. An equally weighted index would give energy the same weight as every other constituent, so it would be less sensitive, not more, and the two cannot be equally sensitive.

2. Which of the following statements about commodity futures indexes is not correct: that commodity sectors in backwardation typically improve index returns; that an index investing across several futures exchanges provides a high degree of diversification; or that the total returns of the leading commodity indexes correlate weakly with conventional asset classes?

Solution. The incorrect statement is that an index investing across several futures exchanges provides a high degree of diversification. Commodity futures exchanges around the world are highly correlated with each other, so spreading across venues adds cost and complexity without adding much diversification. The other two statements are correct: markets in backwardation typically produce positive roll yields and so tend to improve index returns, though the price return may still be negative and therefore the total return may still be negative; and commodity index returns do historically have low correlation with equities and bonds.

3. A May 2014 copper futures contract is the current contract. The June 2014 contract sits at 1% backwardation against it, and the July 2014 contract sits at 3% backwardation. Which contract does the DBLCI roll into, and why?

Solution. The July 2014 contract. The comparison has to be put on a common time basis. June is one month away, so its 1% backwardation is 1% per month. July is two months away, so its 3% backwardation is 3% divided by two months, or 1.5% per month. Because 1.5% per month exceeds 1% per month, the July contract offers the greater backwardation per unit of time, and the DBLCI rolling rule optimises on exactly that, choosing the contract within the next 12 calendar months that maximises backwardation or minimises contango.

4. Two candidate indexes use similar weighting and rebalancing schemes. Index A holds contracts typically in contango and Index B holds contracts typically in backwardation. Which performs better in a market trending upward?

Solution. Index B, whose returns are most likely to be higher than those of Index A. An index that contains contracts commonly trading in backwardation generates a positive roll return, which improves forward-looking performance, while an index containing contracts commonly trading in contango generates a negative roll return, which hurts it for exactly the same reason. Since weighting and rebalancing are held similar between the two, the roll return is the component left to separate them.

Check yourself

1. A gold futures curve shows the same price for July, September and December delivery, while a gasoline curve shows July at 2.2701, September at 2.2076 and December at 2.0307. Which market is in backwardation, and what is the state of the gold market?

The gasoline market is in backwardation, because the near-term price of 2.2701 exceeds the longer-term price of 2.0307, so the curve slopes downward and the calendar spread is positive. The gold market is flat, since all three delivery months carry the same price, which under the hedging pressure hypothesis is what a balance between producer and consumer hedging looks like.

2. Why is roll return described as an accounting calculation rather than a source of return that can be captured on its own?

Because no portfolio can be built that holds only roll return. It is the percentage difference between the near-term and farther-term contract prices, weighted by the portion of the position being rolled, and it exists only as one line in the decomposition of the total return of a fully collateralised position. An investor buying the deferred contract necessarily takes the price risk of that contract as well, so the roll component cannot be isolated.

3. An investor holds $12,000 of exposure with the near contract worth $6.00 per contract and the deferred contract worth $8.00 per contract. How many contracts are held before and after the roll, and what is the gross roll return?

Before the roll, $12,000 divided by $6.00 is 2,000 contracts. After the roll, $12,000 divided by $8.00 is 1,500 contracts, so 500 contracts are sold and not replaced. The gross roll return is ($6.00 minus $8.00) divided by $6.00, or minus 33.3%. Both the contract count and the sign identify a market in contango.

4. The convenience yield on a commodity exceeds its direct storage costs. What does the theory of storage predict for the shape of the futures curve?

Backwardation. The relationship is futures price equals spot price plus direct storage costs minus convenience yield, so when the convenience yield term is larger than the storage cost term the futures price falls below the spot price. Economically, the commodity is scarce enough that holding physical inventory is worth more than the cost of holding it, which is the just-in-time, demand-dominated case.

5. A commodity index reports an annual total return of 6.8% made up of a 3.0% spot return, a roll return of minus 1.3% and a collateral return of 5.0%. Why do the three components not sum to the headline figure, and which component carries the volatility?

The components sum to 6.7%, while the headline 6.8% is a geometrically compounded annualised figure, so the small gap is a compounding artefact rather than an inconsistency to be reconciled. The volatility sits almost entirely in the spot return, whose annualised standard deviation of 19.8% matches the index and whose correlation with the index total return is 0.97, against 4.2% and 1.1% standard deviations for roll and collateral return.

6. A refiner wants protection against a rise in crude prices over the next year but expects to shut one unit for maintenance in the third quarter, and it wants to reference a specific heavy grade. Why is a swap a better fit than a strip of futures?

Because a swap can be customised in ways a standardised contract cannot. The notional quantity can be varied month by month to fall during the maintenance shutdown, the reference price can be the specific grade or a seasonal blend rather than the exchange benchmark, and a single contract replaces the administration of many futures positions. Cash settlement also leaves the refiner free to buy its physical barrels wherever it chooses.

7. Two indexes hold the same commodities with the same weights, but one rebalances monthly and the other annually. Under what market conditions does each win?

The monthly rebalancer wins when the market mean reverts frequently, because it sells more peaks and buys more valleys. The annual rebalancer wins in a sustained trend, because frequent rebalancing sells outperforming components that keep rising and buys underperforming components that keep falling. A floating weighting scheme such as production value dampens the whole effect, since the weights drift with prices and the required rebalance is smaller.

8. An analyst screens commodity sectors purely on historical mean roll return and concludes that a portfolio should hold energy alone. Give two reasons this is a weak conclusion.

First, roll return is a poor guide to total return: its correlation with price return has been about 3%, and 40% of the commodities in Ilmanen’s sample had negative roll returns together with positive total returns. Second, the screen is a concentrated sector bet. Energy shows the widest range of rolling 12-month roll returns in the sample, from 31.5% to minus 39.5%, and the largest standard deviation of the mean at 0.8%, and its recent roll behaviour depends on producers continuing to restrict supply.

End of lesson.

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