4.1.1. Uncertainty, spreads and future markets

Spreads are volatile:

• – over time; for example, two months from now, the September–December spread for wheat will be different from what it is today;
• – from one year to the next; for example, the September–December spread for wheat will be different in 2019 from that of 2018;
• – from one commodity to another; for example, the September–December spread for wheat is different from that of corn.

Of course, if this were not so future markets would be quite useless. As we saw in Chapter 3, it is uncertainty that explains the value of future contracts.

With a future that is certain and without storage costs, the changes in price would only be determined by the schedule of production and by the term structure of interest rates. The price of all futures contracts could be completely determined by knowing current prices and interest rates (for example, according to Hotelling’s rule, the price of a non-renewable resource increases at its interest rate). Under these conditions, no future transaction would be necessary; consequently, a futures market would be redundant as all futures prices would be known through a knowledge of the spot prices and interest rates. Similarly, storage costs would not explain the need for futures markets. Without uncertainty, with the storage costs being known, the price of futures contracts could be entirely determined using interest rates and storage costs. In situations of uncertainty, if the spreads for different commodities are equal, then a single future market is enough to determine the price of all markets.

4.2.1. The diversity of hedgers on futures markets

Let us now consider a formalized and more general approach for the intuitions discussed above. The motivations for committing to a futures contract can be studied in a relatively standardized modeling. We will base ourselves here on the following two references: [AND 83, EKE 12].

The model below will enable us to study the behaviors of three main categories of participants in the futures market: speculators, storers and processors. Once the properties of these three categories of agents are represented, it will be possible to study the properties of the considered market as a whole. The broad outlines of the model are as follows:

• – the economy is made up of two indexed periods, 1 for the initial period and 2 for the final period;
• – we consider three risk-averse agents, characterized by their preferences expressed in a mean-variance framework: a speculator, a storer and a processor;
• – to simplify the process, we will work without updating.

Each agent is characterized by a profit function π, which they seek to maximize, and by a utility function U. Only the first order condition for each agent is discussed; however, the other conditions are verified.

4.2.1.4. Market equilibrium

If the market is at equilibrium, the positions of the players is such that their sum is zero; the seller’s position is given a negative sign and the buyer’s position is given a positive sign.

The sign of the bias depends on the sign of (x − y), called hedging pressure.

• – x = y: the seller positions of storers perfectly offset the buyer positions of the processors. There is no bias and speculators are superfluous.
• – x < y: the seller positions of storers are lower than the buyer positions of the processors; EP₂ < P_f. At an aggregate level, speculators take the short position to offset the buyer positions of the processors.
• – x > y: storers’ sales are greater than the purchases of processors: EP₂ > P_f. This is a situation of normal backwardation. At an aggregate level, speculators take the long position to offset the seller positions of the storers.

In both these cases, the speculators collect a premium against the risk that they agree to take on. The value of the prime will increase with price volatility and with the risk aversion parameterized by α.

4.2.2. The empirical scope of the normal backwardation theory

The normal backwardation theory has been the subject of many empirical tests.

Most of the literature concludes that there is tangibly no risk premium for future markets taken separately, which can also be explained by the fact that the bias oscillates between positive values and negative values. Gorton and Rouwenhorst [GOR 15] show that a portfolio of futures contracts generating a premium is no more risky than a portfolio of shares and is negatively correlated with shares.

Gorton and Rouwenhorst’s article had a major impact as it made commodities seem like one class of assets among others; it offered support for investing in a commodities portfolio, both for the returns it might yield and for the diversification that commodities allow.

4.3.1. Some fundamental concepts

Storing a commodity results in different costs:

• – fixed costs, which do not depend on (or are very slightly dependent on) the quantities being stored; these must be borne even if warehouses are empty. These costs are mainly insurance costs and allocations for depreciation of fixed assets;
• – deterioration and obsolescence; commodities may lose certain qualities in storage, especially agricultural commodities (germination, attacks by pests, drying or humidification, etc.);
• – handling costs;
• – maintenance costs: the building and equipment must be maintained;
• – financial costs, especially the interest that must be paid on loans if the investment is debt financed.

There are different categories of stocks, which are not necessarily exclusive of one another. They do not have the same effects on the markets as they do not react to the same market signals:

• – speculative stocks and industrial stocks;
• – certified stocks (certified by an institutional authority);
• – strategic stocks;
• – underground stocks (mineral reserves);
• – stocks being transformed;
• – stocks being transported.

4.3.2. The theory of storage with occasional stockouts

The no-arbitrage condition implies that a positive spread cannot exceed storage costs. In an efficient market, the futures price must be equal to the sum of the cash price and the cost of storage. If the futures price is greater, arbitrageurs will find it advantageous to buy, store and then re-sell on the date of maturity; this type of arbitrage is called cash and carry. If the futures price is lower, an arbitrageur who has stock in hand can carry out a cash sale and buy it again in the future; in the interval between both they can save on storage costs and will also have liquidities available from the cash sale.

If we take into account the possibility of disruptions (that is, periods with null stock), storage obeys the following equations:

In the absence of a futures market, such storage is a speculative activity: the storer buys at a low price in the hope of reselling later at a higher price. If there are speculators who are neutral to risk and who have access to the same collection of information as other agents, their profit is given by: E_t (F_t,t+1 − P_t+1) ν_t, where ν_t is their position on the market. If ν_t > 0, the speculator takes the long position, and if ν_t < 0, they take the short position. The first-order condition gives: F_t,t+1 = E_tP_t+1.

Thus, with risk-neutral, perfectly informed speculators, the price of the futures contract is an unbiased predictor of the anticipated spot price.

The use of futures markets may then become simple arbitrage. An important reminder: arbitrage is a risk-free activity through which an arbitrageur takes advantage of a difference in price in space or time. In this case, the equations become:

The spread is thus written as:

If the spread exceeds , the storer may carry out the arbitrage by storing the merchandise and by selling futures contracts.

4.3.3. Spread and storage

The theory of storage has consequences on the behavior of spreads. We must here distinguish between two possible cases: contango and backwardation.

Contango: F_t,t+1 ≥ P_t.

When the stock levels are positive, the market will be in contango and the spread must be equal to the storage costs, or otherwise arbitrage opportunities will arise. Nevertheless, the market prices may be in contango but the spread may be insufficient to cover storage costs. In this case, the theory provides for an absence of speculative stock.

Backwardation: F_t,t+1 ≤ P_t.

• – When a market is in backwardation, a storer cannot arrive at a profitability threshold; thus, there is no storage. This results in a temporary situation of shortage when it is preferable to sell now, while the next harvest (or production) should suffice to reestablish market.
• – In backwardation, there is no limit to the spread between a spot price and futures price as the storage costs are irrelevant in this case. The spread is determined by the spot price that transformers are willing to pay. The storage model thus offers an explanation for the asymmetric behavior of the spreads seen in Table 4.1. The positive spreads are limited by storage costs, while negative spreads are not.

The spread thus has asymmetric behavior: the prices may reach more extreme values in a backwardation situation than a contango situation.

4.3.3.1. Long-term spread

Let us now consider a series of spreads: F_t+1,t+2 − F_t,t+1, F_t+2,t+3 − F_t+1,t+2, etc. If we start from an initial contango situation, we cannot expect that all successive spreads will be full carry as, in this case, the price of futures contracts would diverge. A full carry spread between two deadlines signifies that the difference between the price of the contracts with two successive dates of maturity is exactly equal to the storage costs. Consequently, we would expect that the spreads to come would be below full carry:

This dynamic can be explained as follows:

Even though we know that storage occurs in full carry situations in the initial period, in the later period there is a non-zero probability of stock disruptions, which implies that the anticipated spreads are below full carry. The farther away the horizon, the greater the probability of a stockout. Conversely, if there is temporary shortage and the spread is in backwardation, a shrinking of the spread is anticipated. To sum up, it appears that the price of futures contracts follow a mean-reverting process. Over the course of time, the spreads tend toward zero.

In a paradoxical manner, even if the uncertainty is much greater when looking to the long term than if we were to take a short-term position, contract prices are stable over the long term as they constitute an average among a large number of possible situations. Beyond a sufficient time (months or years), the futures contract prices are constant.

4.3.3.3. Storage with two types of shock

The earlier storage model included only one type of shock, with no serial correlation. For certain commodities, it would seem normal to consider shocks that are serially correlated. For example:

• – demand shocks for metals and oil are strongly associated with cycles of activity that present positive serial correlations;
• – supply shocks for perennial crops may have lasting effects as unfavorable weather that reduces harvests may also damage plants and thus reduce future harvests.

With a serially correlated shock and a non-serially correlated shock, the behavior of the model is modified. Two categories of price peaks may come about:

• – price peaks may be produced when stocks are positive and, thus, when futures markets are in contango. This situation arises when a price peak results from a serially correlated negative shock;
• – price peaks may arise out of a situation of backwardation if a negative shock that is not serially correlated is produced.

Two situations with a sharp drop, or even price collapse, may come about if:

• – the futures markets are in backwardation with a positive supply shock and serial correlation;
• – the futures markets are in contango with a positive supply shock and no serial correlation.

In practice, pricing models for commodities always carry at least two explanatory factors in order to integrate these various curve shapes.

4.3.4. The concept of convenience yield

The storage model discussed earlier presents a significant flaw: in reality, we never observe stock disruptions. At any point in time, there are always certain stocks and thus stocks are held below fully carry, even when the markets are in backwardation. In 1939, Kaldor [KAL 30] introduced the concept of convenience yield: holding stocks yielded an advantage, this mainly being the fact that one could be sure about their availability. In this situation, storage obeys the following equation:

where represents the convenience yield. In this case, the convenience yield represents an implicit return resulting from the holding of stock. This return is not directly observed; however, it can be deduced from the no arbitrage condition and other variables that can be observed.

When available stocks are low, futures prices may become lower than the spot price. This phenomenon may be represented using a Working curve.

The coexistence of positive stocks and negative spreads shows that there are reasons, other than speculation, for holding stock. These other reasons for holding stock are, for example, that stocks make it possible to reduce delivery costs and timeframes and, thus, to enhance customer satisfaction, to meet unexpected orders and to ensure the continuity of operations.

It may be noted that these justifications are similar to those that were used to explain the holding of cash by households or companies, despite the interest that they may earn from financial investments [WIL 86]: a reason for transaction, precaution and speculation.

The demand for stock for transaction is brought about by the fact that there are transaction costs related to the exchange of commodities. Large transactions, which could lead to stocks, make it possible to reduce buying or selling costs, or the transport cost per unit. This demand for stock for transaction exists even in the absence of uncertainty and, therefore, the absence of a motive for speculation.

The demand for security is born out of the uncertainty related to supply or demand that a company faces. For example, if a transformer faces uncertain supply but has a fixed and rigid production capacity, they may wish to hold stock in order to avoid interruption of their activity. They will not be ready to sell their stocks unless the price is high and will hold them despite the fact that the spread does not cover storage costs.

4.4.1. Hedging and volatility

Hedging makes it possible for an agent to transfer a risk to another agent through futures contracts. The impact on price volatility can go in one of two directions:

• – if holders of stock carrying out a risky activity are averse to risk, they must stock less if they are not able to hedge. The increase in stock levels that hedging brings about will help stabilize the market; in this case, futures markets play a stabilizing role;
• – if producers are averse to risk and can choose between different technologies that are more or less risky, the possibility of hedging may lead them to choose riskier technologies, which could destabilize prices; in this case, futures markets may play a destabilizing role.

Even if futures markets were destabilizing, this would not mean that they diminished well-being. Well-being and price volatility are two different things. It is, for instance, possible that riskier technology is more productive and allows for higher production levels, after the commencement of futures contracts.

4.4.2. Futures markets and information

How does the introduction of futures markets modify available and public information?

• – The mainstream theory considers that futures prices, by aggregating the positions of traders that benefit from private information, reflect all the available information, which allows better allocation of resources. The prices would thus have a stabilizing effect.
• – If the creation of futures markets implies the presence of traders who generate noise or carry bad information (because they are not specialists in commodities), then one may fear a deterioration in the informational content of the prices and a destabilization of the market.