Interaction between futures and physical markets price formation

The interaction in price formation between futures and physical²⁹ markets materialises in two phases:

during the duration of the futures contract, and at maturity. During the duration of the futures contract, information about inventory levels and exogenous factors fuel increasing or decreasing divergence of futures prices with spot prices (Figure 19).

28 It is the annualised standard deviation of the natural logarithm of prices ratio.

29 The words ‘physical’ and ‘spot’ are used interchangeably in this report. ‘Spot price’ can be pure physical of rolling front month price.

Figure 19. Futures and spot prices interaction

Source: Author’s own.

When the futures price is above the spot price, i.e. the basis (difference between spot and futures price) is negative, the market is in ‘contango’. When the futures contract price is below the spot price (i.e. the basis is positive), the market is in ‘backwardation’. At maturity, the price of the futures should converge to the spot price due to the ‘commitment to deliver’ mentioned above, which does not allow arbitrage to become systematic. . Recent contributions, such as Hernandez and Torero (2010), claim that futures markets have been even leading price changes in spot markets.

The theory of storage

During the duration of the contract, futures prices (for different maturities) fluctuate and may diverge from spot prices. The difference between spot price, (at date t), and futures price, (at date t and maturity T) is typically called “basis”. The futures price can be written as follows:

(4) Where r is the interest rate for risk-free alternative investments, k is the cost of warehousing and ρ is risk-adjusted discount rate for the commodity, i.e. the benefit from holding the physical commodity.

Then, following the MCY formula (1) above:

(5)

As a result, the basis is the marginal convenience yield (full cost of carry of a commodity), minus the sum of the interest forgone on alternative risk-free investments and the costs of warehousing the commodity. This means that the basis is positive (backwardation), so the spot price is higher than the futures price, when the futures price is insufficient to cover interest foregone and the cost of warehousing (exogenous factors). There is therefore an incentive to sell the commodity immediately, which may result in a reduction of inventory levels. Besides the importance of warehousing systems and interest rates set through monetary policies, this suggests that several other factors put direct pressure on futures prices, but essentially through the increase or reduction of inventory levels that is a response function of demand and supply factors (Kaldor, 1939; Working, 1949; Telser, 1958; Brennan, 1958). Among these factors are monetary policies affecting interest rates (r), the costs and policies of the warehousing system (k), and the benefit from holding the commodity (ρ), which can be measured as follows:

(6)

This is the endogenous idiosyncratic factor that pushes anyone, whether a user or a producer, to hold a commodity. The first part of the equation is the reserve value that the holder gives to holding a commodity at date T, so the difference between expected spot price E(P) and current spot price. The second part is the net convenience yield, i.e. the dividend of the commodity, or the compounded value of current spot price at date T (using the risk-free interest rate) minus the current futures price, over the current spot price. As a consequence, both exogenous and endogenous factors (expectations) can affect inventories and, through them, the futures and spot price relationship (Figure 20).

Figure 20. Futures-spot price interaction through inventories

Source: Author’s own.

As inventories fall, the spot price gradually catches up with the futures price and the curve inverts into backwardation until, for one of the three reasons mentioned above, the inventory levels recover and futures prices begin to regain ground to converge at maturity. Following Section 1.2.1.1, Figure 21 illustrates the relationship between inventories and the marginal convenience yield, which ultimately affects the basis and so futures prices, creating a direct link between physical and futures markets.

Fama and French (1988) found evidence that inventory levels are positively related to the marginal convenience yield. This evidence has been also confirmed by the empirical analysis in the following chapters. The higher the level of inventory, the lower the MCY, so inventory levels are directly related to the three factors that ultimately affect future prices (r, k and ρ).

Figure 21. MCY-inventories relationship

Source: Fama and French (1988).

For metals, Fama and French (1988) found that when inventories are low, spot prices are more volatile than futures prices. The negative relationship between MCY and inventories has been also recognised by Routledge et al., (2000) and more recently by Gorton et al. (2008). This explains how futures prices are complementary tools to inventories in supporting the hedging strategies of commodities users and producers. For non-storable commodities, they are the only proper hedging tools available.

For storable commodities, as a consequence of the storage theory (i.e. the storage process, being a response function of supply and demand, drives futures and spot prices), when the futures curve is in contango a ‘cash and carry’ trade opportunity arises. More specifically, the commodity investor will have incentives to sell the forward contract and buy the commodity directly or through a loan, if the risk-free interest rate is sufficiently low. When the futures curve is in backwardation, though, the futures price is insufficient to cover cost of storage and interest foregone for alternative investments, so the commodities investor may enter in a ‘reverse cash and carry’ trade. He/she buys a future contract and sells the commodity immediately.

The theory of ‘normal backwardation’

In addition to the storage theory, there is an additional theory, generally attributed to Keynes (1923), which assigns to futures markets the role of a risk transfer mechanism where investors earn a risk premium for bearing the future spot price risk for classic hedgers. If hedging demand (net shorts) exceeds the supply of long investors (net long positions), the risk premium would be positive. As a result, futures markets should usually be backwarded (spot prices higher than futures prices), as the hedgers have to pay a risk premium to speculators. Futures prices are thus biased estimates of expected cash prices (Carter, 2000). The risk premium (π) can be defined as,

(7)

where E(PT) is the expected spot price at date T and is the value of the future price with maturity T. This theory, however, has found very weak evidence over the years (see, among others, Gray, 1961;

Rockwell 1967; Gray and Routledge, 1971). As Table 15 shows, when looking at trading patterns for seven key commodities, for only a few of the past 23 years was the curve in backwardation for the majority of the trading days (using a differential between 3-months or second month and cash forward contracts or front-month).

Table 15. Contango and backwardation by commodity (years) 1990-2012*

Source: Author’s calculation from CME Group, LME, LIFFE.

Cocoa and aluminium have not had prolonged periods in backwardation at all in the last 23 years. Only sugar still has a future-spot prices curve in backwardation today.

There are two problems with this theoretical framework. First, the hypothesis is that hedgers are all net shorts. As explained above, not all hedging positions are short (hedging may have very complex and diversified strategies). Second, as Gray and Routledge (1971) pointed out, Keynes may have been misinterpreted in his original idea. At his time, backwardation had several meanings and was also used to denote the risk premium paid by a seller to a buyer that allows postponing the delivery of a stock certificate. Following the two authors, Keynes may have just said that whether markets can reflect contango or backwardation, a risk premium is a “normal” component of the difference between spot and futures prices. In effect, if we disentangle the costs of storage and interest foregone from the basis, in the vast majority of cases the curve should offer a risk premium and so become backwardated. If this does not happen, there should be greater incentives to stock the commodity and benefit from contango later on. Keynes claimed that this was an exceptional situation vis-à-vis a ‘normal’ market activity.

Price convergence

A second important factor in the interaction among futures and spot markets is the convergence of futures contracts to the spot price. As mentioned above, this is mainly due to the ‘commitment to deliver’ embedded in the futures contract. When close to delivery, markets start to discount the fact that if the price of the future diverges at delivery, there is an opportunity of arbitrage among markets and so the market will adjust its value to the spot market. For instance, if at delivery day the futures price is lower than the spot price, the market will buy the futures contract until the two prices become equal (taking into account costs of delivery and differences due to different grades, etc.). Anticipating this behaviour, futures prices (front-month and other contracts with same maturity) will then adjust automatically to the spot price close to maturity (plus a differential). For corn futures contract traded on CBOT and spot price (US No.2, Yellow, U.S. Gulf, Friday, published by USDA), the differential around the last trade date (premium over futures price) was on average around 10% of the spot price in 2011.

As illustrated in Figure 22, the front-month begins to converge to the December month contract in August, at the end of the harvest, as both front and December month discount same information about supply and demand so the differential with spot prices (dashed line) is converging to the front-month one by arbitrages opportunities.

Figure 22. Futures price convergence in corn futures contracts

Note: $cents/bushel; spot price is US No.2, Yellow, U.S. Gulf (Friday).

Source: Author’s elaboration from CBOT, FAO, USDA.

The ‘commitment to deliver’ also ensures that futures market dynamics do not affect the spot market price directly. If prices do not catch up, arbitrage will produce convergence anyway. However, as suggested by Figure 22, futures and spot prices will in any case have some difference at maturity, as the futures prices embed delivery and interest foregone before you can actually hold the commodity.

Futures/spot price divergence can be determined by two sets of factors:

a. The underlying commodity and delivery.

b. Problems with physical settlement.

First, there is divergence if the physical underlying asset to be hedged is different from the commodity underlying the futures contract (e.g. using a crude oil futures contract to hedge jet fuel costs), as well as delivery features of the contract that are embedded in the final price (f.o.b., in-store, etc). Second, divergence can be caused by any impediment that does not allow delivery of the physical commodity. These impediments can arise because of problems with the grade of the commodity (and its chemical attributes), or the location of the delivery. As discussed in the Chapter 2, a prolonged delay in delivering the commodity may cause a spike in order cancellations and a sudden increase in price of physical and futures because the supply of the commodity is constrained.