11.1.1 Trading Differences between Forward Contracts and Futures Contracts

In introductory material the terms forward contract and futures contract are often used interchangeably due to their similarities: the hallmark of both contracts is the deferred delivery, and both contracts are priced with similar principles. One major distinction between the two is that forward contracts are typically over-the-counter (OTC) contracts, whereas futures contracts are exchange traded. Since futures contracts are traded on an organized exchange, they share the same advantages as other listed securities: a central marketplace and transparent pricing. Compared to most forward contracts, futures contracts also enjoy clearinghouse security, uniform contract size and terms, and daily liquidity.

Forward contracts are ad hoc contracts negotiated between two parties, with flexibility regarding the details to help meet the needs and preferences of each party. As exchange-traded contracts, futures contracts are standardized. Each futures contract trades with a relatively high degree of uniformity with regard to the quantity and quality of the underlying asset and the location and time of delivery.

The standardization of futures contracts permits active trading and liquidity. At any point in time, the long futures position holder can close a position by establishing an identical short position (so that the long position and short position net to zero). Similarly, the short futures position can close a position by entering an offsetting long position. The outstanding quantity of unclosed contracts is known as open interest.

If the buyer (i.e., long) of the futures contract does not wish to take delivery of the underlying asset, the buyer closes out the long futures position at the prevailing market price of the contract by taking on a short position. Similarly, if the holder of a short position does not wish to deliver the underlying asset, the holder can establish an offsetting long position prior to delivery. Only a very small percentage of futures contracts (usually less than 1%) result in delivery of the underlying asset. The point is that the primary purpose of futures (and forward) contracts is to exchange risks, rather than to serve as vehicles for arranging physical transfers of goods. The idea is that by using futures markets to manage risk, a party can take or make delivery of physical goods using the cash market with the lowest transportation or other costs.

Forward contracts are over-the-counter contracts between two parties that contain the terms and conditions agreed on by the two parties. These terms and conditions include how much, if any, collateral is required; the size of the contract; and the delivery details (including time, quality, and location). Since the contracts are not standardized, there are usually no market prices that can be observed to directly value the position. If the holder of a long or short position in a forward contract wishes to terminate or hedge the exposure, there is no ready secondary market of identical contracts available. The entity wishing to terminate the exposure to a forward may attempt to negotiate an exit with the counterparty to the forward or establish a new forward contract with another party, which will serve to offset the risk. Whereas long and short positions in the same futures contract will close a position, the same is not true for forward contracts. Because forward contracts are specific to a given counterparty, a transaction can only be closed with the same counterparty. Although a long and short forward position with two different counterparties will neutralize market exposure, counterparty risk remains. Nevertheless, the flexibility of forward contracts makes them very popular. The most prominent forward market is the currency forward market, which is substantially more liquid than the currency futures market.

A swap is a string of forward contracts grouped together that vary by time to settlement. Thus, a commodity swap is a portfolio of commodity forwards. Typically, the settlement times are equally spaced. For example, an oil refinery might regularly need to purchase crude oil. Rather than bear the risk of fluctuating oil prices, the refinery may decide to lock in the purchase price of the oil by entering various forward contracts to purchase the oil at prespecified prices (i.e., to swap cash for oil). Instead of entering a series of separate forward contracts, the refinery may enter into a single swap that calls for quarterly or monthly exchanges through time at prices set at the initiation of the swap.

Many of the distinctions between forward and futures contracts may disappear over time. Due to the Dodd-Frank Act in the United States and new regulations throughout the world, market structures are changing. If OTC markets are required to offer greater transparency and participate in a central clearing system, forwards will become more like exchange-traded futures contracts.

11.1.2 The Mechanics of Marking-to-Market

A critical distinction between most futures and forward contracts is that futures contracts are marked-to-market. The term marked-to-market means that the side of a futures contract that benefits from a price change receives cash from the other side of the contract (and vice versa) throughout the contract's life. The cash exchanges resulting from positions being marked-to-market are intended to cause each side of the derivative to have a zero market value at the end of each day. The reason that each contract has a zero value at the end of the day is that the price at which the commodity is promised to be delivered is adjusted to the current futures price as a result of the marking-to-market process.

The following example provides a closer examination of the process of marking-to-market. Consider a trader who establishes a long position in a gold futures contract at €1,000 per ounce on Monday morning. The trader has promised to buy gold for €1,000 per ounce unless the trader closes the position by establishing a short position that offsets the original long position prior to the required delivery date. Suppose that the gold futures contract rises in price to close on Monday afternoon at €1,005 per ounce. In effect, the futures exchange collects €5 per ounce from the trader who established the short position and delivers €5 per ounce into the account of the trader who established the long position. Now the futures contract calls for delivery of the gold at €1,005 per ounce. Suppose that on Tuesday the futures contract falls to €998 per ounce. The exchange then takes €7 per ounce out of the account of the trader with the long position and delivers €7 per ounce to the trader with the short position (assuming that they both continue to hold their respective positions). The contract would then be changed to call for delivery of the gold at €998 per ounce.

The process continues each day until delivery day. Suppose that at the delivery date the price of gold has risen to €1,500. The holder of the long position must now pay €1,500 per ounce for the gold. But recall that the trader entered a contract to buy gold at €1,000, not €1,500. The final economic result is accomplished because, throughout the life of the contract, there was a net transfer of €500 per ounce from the short side of the contract to the long side of the contract through the marking-to-market process as the closing futures price of gold rose from €1,000 per ounce to €1,500 per ounce. The long position effectively combines the €500 of marked-to-market profit with the original promise to pay €1,000 and delivers €1,500 in exchange for the gold. The short position effectively nets the €500 loss accrued from marking-to-market from the €1,500 received at delivery to receive the promised net value of €1,000 per ounce.

The net result is the same: Both sides of the trade perform as originally promised unless one or both close their positions prior to delivery.

An exchange-traded futures contract can be viewed as a forward contract that is settled in cash at the end of each day (i.e., marked-to-market) and then restruck at the prevailing price for new futures contracts. Thus, the long position in the first example began with a contract to buy gold at €1,000 per ounce and ended with a contract to buy gold at €1,500 per ounce. During the price move from €1,000 to €1,500, the holder of the long position in the contract received €500 from the holder of the short position. If the holder of the long position takes delivery of the gold at €1,500, the net cost will be the originally agreed-upon price of €1,000 (when the €500 of receipts from marking-to-market profits are included). Correspondingly, the short position holder delivers gold at €1,500 but nets only €1,000 after considering the mark-to-market losses of €500. In advanced pricing models, the impact of interest rates on the marking-to-market process is included in the original pricing of the futures contract. In this discussion, these minor interest effects were ignored.

11.1.3 Marking-to-Market and Counterparty Risk

Each side of a derivative contract refers to the other side of the contract as its counterparty to the contract. Forward contracts and, to a lesser extent, futures contracts expose each party to the risk that the counterparty holding the other side of the contract will default on its obligations. This risk of failure of the counterparty to perform contractual duties is known as counterparty risk and is discussed in greater detail in subsequent chapters.

The importance of the marking-to-market process is to avoid the counterparty risk known as the crisis at maturity. A crisis at maturity is when the party owing a payment is forced at the last moment to reveal that it cannot afford to make the payment or when the party obligated to deliver the asset at the original price is forced to reveal that it cannot deliver the asset. The key point is that the potential for a crisis at maturity creates uncertainty throughout the life of the contract when information is asymmetric. Rather, through the marking-to-market process, the party accruing an increasingly expensive obligation to the other party is forced each day to deliver the necessary funds or to reveal any financial problem.

Consider the previous example of a contract to deliver gold at €1,000. When the market price of gold soared from €1,000 to €1,500, the holder of an unhedged short position would be required to deliver the gold at a loss of €500. In the absence of a marking-to-market process, the holder of the long position would be incurring larger and larger counterparty risk as the price of gold soared. With marking-to-market, the short position would settle a portion of the loss each day that the price of gold rose, thus avoiding the crisis at maturity.

If a party does not have the financial resources to meet the requirements of daily marking-to-market, the party's position is closed into the market, and a new counterparty to the position takes over. Hence, daily marking of a position to market typically limits counterparty risk to one day's price movement.

During the marking-to-market process, financial settlement of the contract effectively takes place daily throughout the contract's life rather than simply at the delivery date. In essence, a long-term futures contract is a string of daily contracts that is restruck every day. Marking-to-market of exchange-traded futures contracts minimizes counterparty risk. In addition to the protection provided by the marking-to-market process, the exchange's clearing mechanism combines capital from all exchange members to guarantee the trades of any individual members who may default on their obligations. However, the failure of a large futures commission merchant (FCM), such as Lehman Brothers Europe, could create counterparty risk, depending on the jurisdiction and the legal segregation of the assets.

As an OTC-traded product, forward contracts are not usually marked-to-market and are therefore subject to greater counterparty risk. Some market participants prefer the forward market because of the lack of a marking-to-market process. Although forwards have greater counterparty risk than futures do, corporate users may prefer to participate in the forward market to avoid the volatility that futures positions can create in a firm's cash flow and financial statements.

11.1.4 Marking-to-Market and the Time Value of Money Effect on Risk

A critical difference between futures and forward contracts is that the marking-to-market feature of futures contracts accelerates the receipt of profits and losses relative to forward contracts. This acceleration has two distinct effects: one on risk and the other on pricing.

Let's first examine the effect of marking-to-market on risk. Acceleration of cash flows due to marking-to-market is tantamount to higher price volatility and higher risk.

For example, consider the difference between being long a futures contract and being long a forward contract on oil. For simplicity, let's assume that although the contract is a one-year contract, due to an important announcement in the first week of the contract the price of oil will either rise by $10 or fall by $10 per barrel. A $10 rise in the oil price in the first week generates a $10 profit for the long side of either the futures contract or the forward contract. But the long side of the futures contract receives that $10 profit in the form of cash during the first week through the marking-to-market process, whereas the long side of the forward contract receives the profits as cash at settlement in one year. If the price were to fall, the long side of the futures contract would pay $10 in one week, whereas a forward contract payment for the loss would be deferred until delivery in one year.

The marking-to-market process effectively requires participants to pay as they go. Paying now rather than later increases the present value, and therefore futures contracts have higher price risk than otherwise identical forward contracts.

11.1.5 Marking-to-Market and the Time Value of Money Effect on Prices

The second effect of the marking-to-market process can be to alter the market price of a futures contract relative to an otherwise identical forward contract. At inception, there should be no difference between the price of a futures contract and an otherwise identical forward contract if interest rate changes are uncorrelated with the spot price underlying the contracts.

To understand this complex issue, consider otherwise identical futures and forward contracts with underlying assets that contain no systematic risk and therefore offer no expected profit to the long position and no expected loss to the short position. Because of the marking-to-market process, the futures contract will generate daily cash flows between the long side and the short side as the futures price changes through time. The expected value of these cash flows is zero, since the underlying asset contains no systematic risk.

However, the expected discounted value of these cash flows will be positive to the long side of the contract if the interest rate is positively correlated with the spot price underlying the futures contract. If the interest rate and spot price are positively correlated, then the long position in the futures contract will receive cash flows from the marking-to-market process, which will be invested at a high interest rate (because high spot prices and high interest rates will tend to occur together). Conversely, the long side will deliver payments due to the marking-to-market process when the spot price falls, at which time the interest rate will tend to be low (due to the assumed positive correlation between spot prices and interest rates).

The net result is that with positive correlation between spot prices and interest rates, the long side of a futures contract tends to receive marking-to-market cash flows when interest rates move higher and tends to deliver marking-to-market cash flows when interest rates move lower. This asymmetric relationship, which tends to benefit the long side, forces the price of the futures contract above the price of an otherwise equivalent forward contract.

Conversely, with a negative correlation between spot prices and interest rates, the long side of a futures contract tends to deliver marking-to-market cash flows when interest rates move higher and tends to receive marking-to-market cash flows when interest rates move lower. This asymmetric relationship, combined with the opportunity cost of money, forces the price of the futures contract below the price of an otherwise equivalent forward contract when the spot price is negatively correlated with interest rates.

In summary, the price of a contract that is marked-to-market will be greater than, equal to, or less than the price of an otherwise identical contract that is not marked-to-market depending on whether interest rates are positively correlated, uncorrelated, or negatively correlated with the spot price of the contract's underlier.

11.1.6 Futures Trading and Initial Margin

Market participants in futures contracts are required to make a collateral deposit of a size determined by the futures exchange. The collateral deposit made at the initiation of a long or short futures position is called the initial margin. This margin requirement is a small percentage of the full purchase price of the underlying commodity, usually less than 10%. Margin requirements are set by the exchanges, are subject to change, and are expressed as currency per contract. For example, at a particular point in time, the initial margin requirement for each futures contract on silver might be $11,000. This means that the entity initiating a long or short position in silver futures must have $11,000 of available collateral per silver futures contract being traded to enter the order and establish the position. Thus, a jewelry-manufacturing firm wishing to take a long position in 10 silver contracts would have to have $110,000 of available collateral to place the trade order.

The initial margin reduces counterparty risk by ensuring the payment of daily losses on futures market positions (except in the case of very extreme price movements). Any collateral deposits for forward contracts are determined through negotiations between the parties.

11.1.7 Marking-to-Market and Maintenance Margin

When commodity prices change substantially, the promise of the long position to pay for delivery or the promise of the short position to make delivery could be placed in peril. To protect the integrity of the contracts, futures exchanges require that positions be marked-to-market, as discussed previously. After initiation of the position (which is done subject to initial margin requirements), market participants with open futures positions are subject to maintenance margin requirements. A maintenance margin requirement is a minimum collateral requirement imposed on an ongoing basis until a position is closed. Like the initial margin, the maintenance margin is expressed as units of currency per contract and is usually set at 75% to 80% of the initial margin. If the collateral of a market participant falls below the maintenance margin requirement, typically due to the marking-to-market of losses, a margin call is issued. A margin call is a demand for the posting of additional collateral to meet the initial margin requirement. If the investor cannot meet the margin call, the futures commission merchant has the right to liquidate the investor's positions in the account. (The positions may be closed at market prices without the investor's direction.) This daily process ensures that promises to make and take delivery have reduced counterparty risk.

Returning to the example of the jewelry manufacturer with a long position in 20 silver contracts, assume that the position was established at a futures price of $25 per ounce and that each contract called for delivery of 5,000 ounces. Thus, the manufacturer has promised to buy 100,000 ounces (20 contracts) at $25 per ounce, for a total purchase price of $2,500,000. Now suppose that the market price of the futures contract drops from $25 to $24. As holder of a long position, the jewelry manufacturer has lost $1 per ounce, and its position has dropped in value by $100,000 (based on all 100,000 ounces underlying the 20 contracts). The futures exchange marks the position to market by transferring $100,000 out of the account of the jewelry manufacturer and placing it into the accounts of entities with short positions in silver futures contracts. The silver manufacturer now has $100,000 less cash in its account, but now its promise is to buy the silver at $24 an ounce rather than $25 per ounce.

Suppose that the jewelry manufacturer originally had only enough collateral to meet the initial margin requirement of $220,000. After the $100,000 loss due to the marking-to-market process, the account contains only $120,000. If the required maintenance margin is not met, the jewelry manufacturer will receive a margin call and will be required to post an additional $100,000 in collateral to return the account to meeting the initial margin requirement and to prevent a forced closure of its positions. The process continues on a daily basis to provide assurances that each trader's obligations will be met. The exchange or the broker can alter margin requirements during a contract's lifetime, often in response to changes in past or anticipated volatility.

Futures contracts have other characteristics that differ from forward contracts, including transparent pricing and, usually, higher liquidity. Although these differences are often important, to focus on the basic principles of commodities futures, the remainder of this chapter generally ignores the distinction between forward and futures contracts, usually using the terms interchangeably.

11.2.1 Futures Contracts with Different Settlement Dates

Futures contracts have regular settlement dates, as determined by the exchanges that created the contracts. A typical interval for settlement dates is quarterly, but especially among the shorter-term contracts, the interval can be monthly or even weekly. On an exchange, the futures contract with the shortest time to settlement is often referred to as the front month contract. The front month contract is sometimes referred to as the front contract, the nearby contract, or the spot contract. Contracts with longer times to settlement are often called distant contracts, deferred contracts, or back contracts. Deferred contracts are sometimes ranked as first deferred, second deferred, and so forth, denoting their order, with first deferred representing the deferred contract with the shortest time to settlement (after the front month) and so on.

Exhibit 11.1 illustrates the concept of regularly extending the settlement dates of the positions by closing nearby positions and opening deferred positions simultaneously to maintain a continuous exposure to the underlying commodity. Exhibit 11.1 simplifies the diagram by assuming that all of the opening trades occur at one price and that all of the closing trades occur at another price. In practice, the opening and closing prices would vary.

To be consistent with concepts of finance other than commodities, the terminology for the process in Exhibit 11.1 would be that an investor holds, or rides, a given position as its time to settlement nears. At the point that the old position is closed and is replaced by a new position in the same commodity with a longer time to settlement, the investor is said to have rolled the position over. Thus, a long-term exposure can be constructed and maintained with a series of rides and rolls. However, in commodities, the expression roll can also be used to describe the holding of a forward position through time.

11.2.2 Rollover Decisions Alter Long-Run Returns

The timing of each rollover transaction is at the discretion of the investor. Some investors may wait until the contract settles or is about to settle before closing the old position and initiating a new position with a longer settlement date. Others may extend their settlement dates while their positions still have considerable time to settlement. Further, some investors may move into contracts with only a slightly longer time to settlement, whereas others may move into contracts with a much longer time to settlement.

The critical point is that, unlike financial assets such as equities, the long-term returns on futures contracts vary based on the particular decisions made by the holder of the position regarding the procedures used to extend the position into a longer position. The result is that the long-term returns of futures and forward contracts can be calculated only by making important assumptions about how and when the contracts are rolled over. Traders with different preferences for rolling contracts experience different long-term returns.

11.3.1 Costs of Carry for Commodity Contracts

In the context of futures and forward contracts, a cost of carry (or carrying cost) is any financial difference between maintaining a position in the cash market and maintaining a position in the forward market. Cost-of-carry models identify two strategies that have identical payoffs and attribute differences in current prices to differences in the costs of carrying each strategy. A cost-of-carry model assumes that in an informationally efficient market, when two positions converge to an equivalent value at some point in the future, any differences in their current prices will be determined exactly by the differences in their carrying costs.

In the case of commodity forward contracts (which have no carrying costs), the model computes the cost of acquiring and carrying a long position in the underlying physical commodity and sets it equal to the price of a forward contract:

(11.1)

In the case of zero carrying costs for a cash position in the commodity, Equation 11.1 forces the forward price relationship to be a flat line in which forward prices of all delivery dates equal the spot price of the underlying commodity. Therefore, it must be that carrying costs explain any slope and shape of the term structure. For forwards on financial contracts, the carrying costs are simply interest rates and distribution rates. Exhibit 11.3 compares the benefits and costs of holding real assets, such as commodities, and financial assets. In the case of financial assets, these benefits and costs are observable, with each market participant generally having access to the same interest rates and distribution rates.

Note that in equations and discussions, the benefits of carry are often listed as a cost of carry. When a benefit of carry is included as a cost of carry, it is assigned a negative value. Exhibit 11.3 introduces new carrying costs (storage costs) and a new benefit of convenience yield (a negative cost). Note that interest rates, dividend yields, storage costs, and convenience yields are often expressed as annual rates. Rates can also be expressed in other units of time (e.g., daily) or even as currency, as long as all variables, including T (i.e., time), are expressed in the same units. In this chapter, we use annual rates with continuous compounding, which is commonly used in derivative pricing and which tends to provide more clarity than does discrete or non-annual compounding.

Storage costs of physical commodities involve such expenditures as warehouse fees, insurance, transportation, and spoilage. Storage costs are of the sign opposite to that of dividends, since they are costs of holding the underlying asset rather than benefits. Accordingly, the storage costs expressed as a continuous rate, c, can be included in the pricing relationship using the same sign as r, the opportunity cost of capital, since both reflect costs of ownership of the physical commodity. In fact, the financing cost, r, of holding the physical commodity can be included as part of c.

Convenience yield, y, is the economic benefit that the holder of an inventory in the commodity receives from directly holding the inventory rather than having a long position in a forward contract on the commodity. Gold provides a vivid example of convenience yield. For a firm that uses gold in its production process, such as a jewelry manufacturer, an inventory of gold helps protect it from supply disruptions. A futures contract on gold might offer economic exposure, but ultimately the jewelry manufacturer needs physical inventory for production. To the owner, the economic value of having that inventory is the owner's convenience yield.

For another holder of gold, the convenience yield of the gold inventory may be the value to the holder of having an emergency asset that might offer exchange value during even the most terrible times for the economy. In both cases, physical ownership of the asset may be viewed as more valuable than synthetic ownership (i.e., ownership through a forward contract to take delivery), since the physical ownership provides more immediate and certain ability to use the asset for an intended purpose. Convenience yield serves the holder of a nonfinancial commodity in the same direction that dividend yield serves the owner of a financial asset, so they both enter pricing models with the same sign (a negative sign to denote that a benefit is the same as a negative cost).

11.3.2 Arbitrage-Free Forward Pricing for Physical Assets

Physical assets, such as commodities, typically involve storage costs and convenience yields. The introduction of storage costs (c) and convenience yield (y) shown in Exhibit 11.3 brings more complexity to the pricing relationships and potentially brings profitable opportunities to market participants with superior skill. The prices of forward contracts on physical commodities, such as energy products, food products, and metals, involve these additional factors and tend to generate more complex pricing relationships.

Expressing the storage costs and convenience yield as marketwide continuously compounded rates, the price of a forward contract on a physical asset is:

(11.2)

Note that Equation 11.2 regarding forwards on physical assets differs from the pricing relationship of a forward on a financial asset (see Equation 6.10) only through the inclusion of c – y and the deletion of d.

If c and y are observable marketwide values, forward contracts would be strictly priced according to Equation 11.2 in perfect and competitive markets. However, storage costs and convenience yields of physical assets have a very important difference relative to the dividend yield on financial assets: Storage costs and convenience yield can be expected to vary with location and market participants, as well as with supply and demand.

For example, storage costs for natural gas are seasonal on account of increased winter demand. Storage costs for agricultural and other products can be seasonal as well, relating to harvest times. Since anticipated supply and demand factors can cause storage costs to vary through time, the pricing relationships between forward contracts of different delivery dates (i.e., the term structure of forward prices) can reflect anticipated supply and demand. Further, storage costs vary between participants.

From the perspective of an individual entity, Equation 11.2 can be viewed as associating the entity's storage costs and convenience yields with the relative values of the spot and forward prices of the commodity. From the marketwide perspective, Equation 11.2 can be viewed as relating the relationship between the forward and spot prices of a commodity to the spread between the storage costs and convenience yield of the marginal market participant (c – y). The marginal market participant to a derivative contract is any entity with individual costs and benefits that make the entity indifferent between physical positions and synthetic positions.

As in the case of storage costs, convenience yield can be expected to vary through time and across market participants and locations. One entity might perceive tremendous advantage from having a commodity in inventory (i.e., being able to meet unexpected demand), and another entity might perceive little advantage.

The convenience yield of a particular commodity to a consumer or a producer would typically be much higher when there is a general shortage of the commodity (i.e., low inventories). Thus, a manufacturer of silver-plated products would derive more convenience yield from holding an inventory of silver at a time when silver is scarce and the danger of being unable to obtain adequate silver supplies is higher.

The potential for storage costs and convenience yield to vary through time and have predictable changes through time adds to the reasons that the term structure of forward prices will not be monotonically upward sloping or downward sloping. In the case of a commodity such as natural gas, Exhibit 11.2 demonstrates a pronounced wave pattern of the term structure of forward prices to reflect the anticipated effects of seasonal demand on storage costs and convenience yield.

Further, the idea that the slope and shape of the term structure of forward prices depends not only on observed values (e.g., the riskless rates and dividend yields) but also on predictions of supply and demand means that superior supply and demand forecasting may permit market participants to generate alpha. In other words, market participants can speculate on the shapes and slopes of the term structure of forward prices and may consistently generate superior returns if their abilities to forecast supply and demand (and, to a lesser extent, storage costs and convenience yields) are superior.

Thus, an important distinction between financial forward contracts and commodity forward contracts is that the term structure of commodity forward prices is often determined by forecasts of supply and demand, and, therefore, market participants in commodity forward contracts face greater complexities, challenges, and opportunities.

11.3.3 Two Limitations to Arbitrage-Free Forward Pricing for Physical Assets

Two major challenges with Equation 11.2 as a description of future contract prices in the case of an underlying physical asset are that (1) a short position in the underlying physical asset may be very difficult or expensive to obtain, and (2) the convenience yields and storage costs of market participants may differ and are unobservable. With regard to the potential inability to take a cost-effective short position in a physical asset, the equation may be better viewed as an inequality: The forward price on the left-hand side is less than or equal to the right-hand side, as depicted in Equation 11.3:

(11.3)

The reason for the inequality is that long positions in the spot price can be used to perform arbitrage when the forward price is too high, but short positions in the spot price may not be available to perform arbitrage when the forward price is too low. In some cases, short positions in physical assets may be available but cost-prohibitive.

Market conditions that impede short selling can add to the complexity of determining the relationship between forward prices and current spot prices. In fact, merely the possibility of uncertainty regarding the ability to borrow a commodity can drive speculation, which helps shape the term structure of forward prices.

The other limitation to arbitrage (and hence the inequality in Equation 11.3) involves the inability to observe storage costs and convenience yields of all market participants and the fact that these costs and benefits can vary tremendously between market participants.

11.3.4 Harvests, Supply Elasticity, and Shifts in Supply and Demand

A key issue in understanding the term structure of forward prices is the rate at which and the extent to which the supply and demand of a commodity can change. With regard to supply, on one end of the spectrum is a perfectly elastic supply, in which any quantity demanded of a commodity can be instantaneously and limitlessly supplied without changes in the market price. Currencies provide an example of an item with a supply that can be changed rapidly (in this case, by a central bank). On the other end of the spectrum are commodities with inelastic supply. Inelastic supply is when supplies change slowly in response to market prices or when large changes in market prices are necessary to effect supply changes. An example of sluggishly responding supply is an agricultural commodity that is harvested annually. At any particular point in time, not only is additional supply not available until the next harvest, but the size of the next harvest may have already been determined by such decisions as the acreage planted. When the supply of a commodity cannot respond quickly to meet changing demand, it is likely that its convenience yield will be higher, since users of the commodity may have greater fear of shortages.

Demand for commodities can shift, based on factors such as levels of economic activity and consumer preferences. Demand for some goods, such as grain, may shift slowly or moderately as needs for livestock feed shift. The demand for other goods, such as natural gas, may change more rapidly due to factors such as weather. When demand can change quickly, the convenience yield is likely to be higher, since, again, users of the commodity may have greater fear of shortages.

Thus, supply and demand shifts can affect not only the price level of a commodity but also the slope and shape of the term structure of forward prices. These potential complexities add to both the threats and the opportunities for commodities traders and managers of managed futures programs. The challenges can be addressed with both fundamental and technical analysis, with those performing and implementing superior analysis earning better returns than those performing and implementing poor analysis.

11.4.1 Terminology Regarding the Forward Curve Slope

When the term structure of forward prices is upward sloping (i.e., when more distant forward contracts have higher prices than contracts that are nearby), the market is said to be in contango. Contango also refers to a forward price exceeding the current spot price (viewing a spot price as a forward price with zero time to delivery may provide clarity).

When the slope of the term structure of forward prices is negative, the market is in backwardation, or is backwardated. The concept of backwardation is the complement to contango.

Recall from Chapter 6 that the term structure of forward prices on financial securities is upward sloping (i.e., in contango) when the riskless rate exceeds the underlying asset's dividend yield. In rare cases, the slope may be downward (i.e., in backwardation) if the dividend yield on the deliverable (underlier) exceeds the risk-free rate.

11.4.2 Backwardation and Contango Reflect Cost of Carry in an Efficient Market

Chapter 6 demonstrated that in the case of forward contracts on financial assets, the slope of the term structure of forward prices was driven entirely by the two costs of carry: interest rates and dividends (the benefits of dividends are included as a negative cost).

In an informationally efficient market for financial assets, contango and backwardation occur to prevent arbitrage opportunities that would otherwise exist if the term structure of forward contracts on financial assets were flat when the riskless rate differed from the dividend yield. A close look at the determination of financial forward prices illustrates two important points: (1) backwardation, contango, and, in fact, the entire slope and shape of the term structure are entirely driven by differences in cost of carry, and (2) in an efficient market, all forward contracts offer equal risk-adjusted expected returns, regardless of the slope and shape of the term structure of forward prices.

Equation 11.3 depicted forward prices on real assets, such as commodities, as being determined by costs of carry that include three components: convenience yield, storage costs, and interest rates. The differences between the components for financial futures and commodity futures do not change the basic concept that the slope of the forward curve is driven predominantly by costs of carry. However, convenience yields and storage costs vary between participants and are usually unobservable. These factors and others, such as the difficulty of short selling commodities in the cash market, support the argument that the forward markets on physical assets are less informationally efficient than the forward markets on financial assets.

11.4.3 Normal Backwardation and Normal Contango

This section discusses the relationship between expected spot prices and forward prices. When the discussion involves expected spot prices rather than current spot prices, the terms normal backwardation and normal contango are used.

A somewhat subtle distinction exists between backwardation and normal backwardation. In normal backwardation, the forward price is believed to be below the expected spot price. We say “believed to be” because we cannot observe the expected spot price; we can only estimate it, and those estimations may differ between market participants. Since in normal backwardation the expected spot price exceeds the forward price, there is a positive expected return from holding the futures contract. Thus, a long position in a forward contract involves an expected profit in the case of normal backwardation (with no investment other than the posting of collateral that can earn interest).

Normal backwardation does not mean that markets are inefficient, even though a forward contract would offer an expected profit with no investment; this is because any expected profit could be due to compensation for bearing risk. The concept of normal backwardation is silent on whether the expected profit of a long position is ex ante alpha or is a risk premium for bearing systematic risk. The entity on the long side of the forward contract should expect to earn a profit (a risk premium) for bearing the risk of being long the commodity whenever the underlying systematic risk (i.e., beta) is positive.

Normal contango is an infrequently used term that, like normal backwardation, refers to the relationship between forward prices and expected spot prices. In normal contango, the forward price is believed to be above the expected spot price. In normal contango, the entity on the short side of the forward contract should expect to earn a profit from bearing the risk of being short the commodity. Conversely, the entity on the long side of the forward contract should expect to bear a loss. In an informationally efficient market, normal contango would only exist for commodity forwards with negative betas (i.e., systematic risk). Since it would be relatively rare to expect a commodity to have negative beta, normal contango should be viewed as a rare occurrence. In an inefficient market, normal contango could exist because a particular forward contract is overpriced and offers negative ex ante alpha to the long side and positive ex ante alpha to the short side.

Unlike backwardation and contango, normal backwardation and normal contango cannot be directly observed, because expected spot prices cannot be observed. It should be noted that the literature on commodities differs with regard to the distinction between backwardation and normal backwardation. The literature also differs about the distinction between contango and normal contango, and many sources do not even use the term normal contango. The definitions used in this chapter may not match the definitions that are found elsewhere, but they reflect the most consistent and useful definitions of the terms. The concepts involved are central to an organized understanding of the risks and returns of commodities and forward contracts on commodities, so it is necessary to use these terms with precision, even at the risk of having definitions that conflict with other sources.

11.4.4 Normal Backwardation and Normal Contango in an Informationally Efficient Market

Novices to forward markets sometimes assume that forward prices are equal to expected spot prices. But in an efficient market, forward prices must differ from expected spot prices whenever the position involves systematic risk. The excess of the expected spot price over the forward price is the expected reward for bearing the risk of being long the forward contract when the underlying asset has positive systematic risk. The expected loss to the short side of the contract is the cost of using the forward contract to hedge systematic risk.

The only time that forward prices should equal expected spot prices in an informationally efficient market is when the underlying asset contains no systematic risk.

11.4.5 Normal Backwardation and Normal Contango in an Informationally Inefficient Market

Forward and futures contracts on real assets are not as easily arbitraged against spot market exposures as are contracts on financial assets. Thus, the term structure of forward prices for commodities may be driven by factors other than those that would exist in a scenario of perfect competition. The resulting term structure of forward prices may not adhere to the predictions of economic equilibrium models based on perfect diversification. Accordingly, opportunities to earn superior returns without bearing additional systematic risk may emerge in commodities and other real assets. In those cases, the analysis of the slopes and shapes of forward curves can be a source of ex ante alpha through investment in alternatives, especially commodities.

Consider the demand for hedging products from huge operating firms. For example, suppose that an unusually high number of natural gas suppliers decide to hedge their natural long positions in the underlying commodity through short positions in natural gas futures. The result would typically be high demand for short positions in natural gas futures. Some natural gas users would take the other side of these futures contracts by taking long positions in natural gas futures, thereby hedging their risk of having a short position in the underlying asset. The remaining long positions in futures contracts would have to be undertaken by speculators, who would demand a return for providing this service to natural gas suppliers. In this case, the price of natural gas futures would have been driven down in order to induce speculators to take long positions. The lower futures prices might then drive the natural gas futures market to be in normal backwardation. Normal backwardation would mean that expected spot prices exceed futures prices, and therefore speculators would perceive an expected profit from establishing the long positions in natural gas futures (which enable the natural gas suppliers to establish the short positions they desire).

The idea is that firms in the business of processing or distributing a commodity may be willing to “purchase” protection against price declines in that commodity, even if it requires “paying a premium” to entities providing that protection. By the same token, if there were an unusually high demand for long positions by natural gas users, then speculators would step in and take the opposite position, meaning that speculators would expect to earn a return for taking short positions in futures contracts. In this case, the market might be driven to be in normal contango.

With limited competition among speculators, the term structure of forward prices might be distorted into a shape that reflects risk premiums for speculators to bear risks. In summary, the demand for and supply of futures contracts by major firms for the purpose of hedging against operational risks could have an effect on the slope of the term structure of forward prices. These concepts are discussed further in Chapter 17.

11.5.1 Forward Returns, Alpha, and Beta

Futures and forward contracts may be used as beta drivers or alpha drivers. A market participant who uses forward contracts as a beta driver is simply trying to obtain the risk and returns of the underlying commodity in the most cost-effective manner possible. For example, a portfolio manager wishing to diversify into Japanese equities may establish a position in a forward contract on the Nikkei 225. To the seeker of beta, the delivery month selected would typically be a matter of convenience, relating to the horizon over which the position is planned to be held and perhaps an appraisal of the relative trading costs of establishing positions in contracts of different settlement dates. If the portfolio manager wished to hold the position for one year, the manager might select a forward contract with one year to delivery. A manager with an indefinite time horizon might analyze the trading costs of different lengths of contracts and perhaps decide to use a three-month contract, with the expectation that the position could be rolled over into a new position when it neared settlement after three months.

A market participant with a long-term investment horizon could establish commodity exposures with vehicles other than direct positions in commodity futures, such as by investing in an appropriate ETF (exchange-traded fund). The ultimate question is: Which path provides the desired risk exposure (beta) with the lowest total expenses? An ETF might offer lower total expenses than futures contracts if the expenses to a particular investor of rolling over the futures contracts exceed the expenses of the ETF. Alternatively, an ETF might obtain its beta exposure from a futures strategy that includes similar costs of rolling contracts over, such that the use of the ETF simply adds a layer of management fees and other expenses. Methods of obtaining commodity exposure other than through futures contracts are discussed in detail in Chapter 12.

A market participant who uses futures contracts or forward contracts as an alpha driver might be viewing the forward contracts on a commodity as mispriced relative to the underlying spot price or to other vehicles for obtaining commodity exposure, such as ETFs. However, to the extent that markets are liquid, relative prices of products with highly similar risk exposures should be driven toward the same price, a concept known as the law of one price. The law of one price states that in the absence of trading restrictions, two identical assets will not persist in trading at different prices in different markets because arbitrageurs will buy the relatively underpriced asset and sell the relatively overpriced asset until the discrepancy disappears.

The primary point is this: Forward and futures contracts on commodity prices tend to offer exposure to commodities that is cost-effective and convenient. However, there are typically few consistent opportunities to generate alpha from simple strategies, such as identifying the mispricing of commodity forward contracts relative to other similar methods of obtaining commodity exposure, such as ETFs. Such market inefficiencies, even if possible, are likely to be short lived. Rather, seekers of alpha using commodity futures tend to search for relative mispricing within futures and forward markets, as discussed in the next section.

11.5.2 Alpha and the Shape of the Term Structure

An example of an alpha-driven strategy using futures or forward contracts is the case of a market participant that speculates on the shape of the term structure. A famous example of speculation based on the shape of the term structure of forward prices is the case of hedge fund Amaranth Advisors, LLC. Amaranth speculated on the spread (or difference) between the price of natural gas contracts in winter and summer delivery months. The combination of a long position and a short position in forward contracts that have the same underlying commodity but differ by time to delivery is known as a calendar spread. Thus, Amaranth's primary strategy in the natural gas forward market was a calendar spread, with long positions in November, January, and March offset by short positions in October, December, and April. If the demand for natural gas rose beyond expectations during the winter of 2006–07, this calendar spread should have created a substantial profit for Amaranth. Calendar spreads are direct plays, or bets, on the shape of the term structure of forward prices. Amaranth's famous trading experience is discussed in detail in Chapter 29 as a fund collapse, which should provide a good clue as to how well the trading strategy ultimately performed!

A key issue is the relationship between ex ante alpha and the shape of the term structure. Simply put, ex ante alpha exists when the term structure of forward prices takes on a shape that is informationally inefficient. An informationally inefficient term structure has pricing relationships that do not properly reflect available information. If the term structure is informationally inefficient, analysts and arbitrageurs may use currently available information to take long positions in relatively underpriced contracts and short positions in relatively overpriced contracts. In doing so, ex ante alpha can be generated. But market participants who misinterpret the relationships may receive consistently inferior returns.

Ex ante alpha generation requires knowledge of when the shape of a term structure is informationally inefficient and therefore out of equilibrium and able to be arbitraged. Finding inefficient prices and forecasting in which direction they are likely to move requires an understanding of relationships that are consistent with efficient pricing, equilibrium pricing, and arbitrage-free pricing. Thus, even if markets are continuously inefficient and in disequilibrium, the primary method of generating alpha is understanding equilibrium pricing and anticipating the forces that ultimately guide prices toward their informationally efficient levels. This point is essential: Understanding the theory of equilibrium pricing can be valuable even if prices are never perfectly efficient, because the theory provides insight into the direction in which prices in disequilibrium are more likely to move.

11.5.3 The Basis of a Forward Contract

Strategies for generation of alpha using futures contracts often focus on hedging futures contracts against spot prices or hedging futures contracts against each other. These strategies are usually described with the terms basis and spread. The basis in a forward contract is the difference between the spot (or cash) price of the referenced asset, S, and the price (F) of a forward contract with delivery T, as depicted in Equation 11.4:

(11.4)

In some literature, the basis is defined as the forward price minus the spot price. Taken together, Equations 11.1, 11.2, and 11.4 show that the basis is equal to the present value of the carrying costs (multiplied by –1). A trader hedging spot positions against forward positions analyzes the basis, compares it to carrying costs, and attempts to identify mispricing.

To the extent that markets are informationally efficient, a position that is short the forward contract and long the spot price is hedged and should offer an expected return equal to the cost of carry (before transaction costs). For example, consider a classic carry trade in the case of a non-dividend-paying financial asset (where d, y, and c are zero) in which a trader is long a cash position in the underlying asset and short the forward contract, or vice versa. Note that the carrying cost of a short forward position relative to a cash position is r because the cash position requires a cash investment and the forward position does not. In the absence of transaction costs and other frictions, a trader that is long the spot position and short the forward position earns the cost of carry, r. Thus, the hedged position has zero risk and earns the riskless return on the arbitrageur's riskless investment. The opposite position (long the futures and short the spot) is, in effect, borrowing money by selling or short selling an asset. That trade is also riskless and generates a borrowing cost equal to the riskless rate, r. The interest earned on the proceeds of the sale (r) nets with the cost of carry (–r) to generate a zero return.

11.5.4 Calendar Spreads on Forward Contracts

Traders hedging forward contracts against each other focus on the calendar spread between the prices of the contracts, as depicted in Equation 11.5:

(11.5)

where t is the length of time separating the settlement dates of the contracts.

A calendar spread can be viewed as the difference between futures or forward prices on the same underlying asset but with different settlement dates. A calendar spread can also be viewed as a position: the simultaneous long and short positions in forward contracts with the same underlying commodity but with different times to delivery. Thus, the trader may calculate the calendar spread as a numerical concept, and may put on a calendar spread by taking hedged positions in the contracts. Other types of spreads may be formed based on distinctions between contracts other than settlement dates.

Calendar spread trading focuses on the search for relatively mispriced futures or forward contracts on the same commodity but with different settlement dates. Calendar spread trading is therefore a speculation on changes in the shape and slope of the term structure of forward prices.

11.5.5 The Return on a Calendar Spread

The return on a calendar spread (ignoring dividends) must depend on the same variables that determine forward prices, which in Equation 11.2 are the spot price (S), the riskless financing rate (r), the storage costs (c), and the convenience yield (y).

Note that in this example, the forward contracts had the same prices at the start of the example, and the trader had equally sized long and short positions. In this unique situation of a level-term structure of forward contracts, a trader can have the same notional value in each position by having the same number of contracts. If the term structure of forward prices has a slope, then the notional value of each contract differs, and a trader with offsetting positions with equal numbers of contracts will not be hedged in terms of notional values.

With equal notional values in the long and short positions, the return of the calendar spread did not depend on the level of the spot price. The spread position of being long the same number of contracts as being short was hedged against changes in the spot price because r + c – y was assumed to be zero. If r + c – y were not equal to zero, the ratio of long contracts to short contracts would have to be slightly adjusted to form a hedge against changes in the spot price based on equal notional values.

In summary, calendar spreads that contain long and short positions of equal notional value are hedged against changes in the spot price. Changes in the spot price (everything else being equal) may be viewed as causing a parallel or additive shift in the entire term structure of forward prices. Changes in the costs of carry cause a slope change in the term structure of forward prices. Returns on calendar spreads are primarily driven by two equivalent concepts: changes in the slope of the term structure of forward prices, and changes in carrying costs.

11.5.6 The Risks of a Calendar Spread

Individual positions in forward contracts are quite sensitive to the price of the underlying asset. But as illustrated in section 11.5.5, a calendar spread based on notional values may have little or no sensitivity to the price of the underlying asset.

Note from Equation 11.2 that the sensitivity of the price of a forward contract with respect to the carrying costs is proportional to the time to settlement of the contract (T). This leads to two properties regarding the risks of calendar spreads:

1. The value of a calendar spread is sensitive to carrying costs. The degree of sensitivity that a calendar spread has to carry costs is driven by the amount of time that separates the times to settlement of the contracts that form the spread. Thus, spreads with underlying contracts that differ more in longevity tend to be riskier.
2. Spreads that are long the longer-term contract benefit when costs of carry rise, and suffer when costs of carry decline. The intuition is that the benefit of a forward contract is avoiding the costs of carrying a cash position in an asset. When carrying costs rise, longer-term forward contracts enjoy a larger increase in total benefits than is enjoyed by shorter-term contracts.

The concept that longer-term forward contracts are positively related to carrying costs and more sensitive than shorter-term contracts can be confirmed by noting that the partial derivative of F(T) in Equation 11.2 with respect to carrying costs (r and c) is T F(T).