Futures Markets, Hedging and Speculation

Abstract

Futures markets provide partial income risk insurance to producers whose output is risky, but very effective insurance to commodity stockholders at remarkably low cost. Speculators absorb some of the risk but hedging appears to drive most commodity markets. The equilibrium futures price can be either below or above the (rationally) expected future price (backwardation or contango). The various effects futures markets can have on market and income stability are discussed. Rollover hedges can extend insurance from short-horizon contracts over longer periods.

Futures markets for grain emerged in Chicago in the middle of the 19th century and spread rapidly to other commodities and centres. Forward contracts, in which two agents agree on the details of a transaction for delivery at a specified future date, must date back to the beginnings of commerce itself, but the distinctive feature of a futures market is that the contracts are standardized, transactions costs are minimized, and liquidity is high, so that contracts can be, and typically are, bought and sold many times during their lifetime, in contrast to most forward contracts. The standard explanation for the role of futures markets is that they help to spread and hence reduce risks, and to motivate the collection and dissemination of relevant information. Forward markets provide the same risk-sharing opportunities, but the greater transparency and liquidity of futures markets makes the latter far more potent institutions for ‘price discovery’.

The question of how well futures markets (and securities markets more generally) perform this role of collecting, aggregating and disseminating information is a large and important topic, best handled under the wider heading of ‘information’. If we assume agents have rational expectations and share common information, then the price-discovery role of futures markets can be ignored and remaining issues of risk-sharing studied in isolation. In this case there is little conceptual difference between futures and forward markets, and we can concentrate attention on the two characteristic modes of behaviour exhibited by these markets – speculation and hedging.

Speculation and Hedging in Commodity Markets

Speculation is the purchase (or temporary sale) of goods for later resale (repurchase), rather than use, in the hope of profiting from the intervening price changes. In principle, any durable good could be the subject of speculative purchase, but, if carrying costs are high, or the good is illiquid, then the margin between the buying and selling price will be large, and speculation in that good will be normally be unattractive. Liquidity in this context means that there exists a perfect, or nearperfect, market in which the good can be sold immediately for a well-defined price, and this requirement severely limits the range of assets available for large-scale speculation. There are two types of assets –commodities traded on organized futures markets, and financial assets (bonds, shares) whose properties lend themselves particularly to speculation. Hedging, on the other hand, typically refers to a transaction on a futures markets undertaken to reduce the risks arising from some other risky activity, whether producing the commodity, storing it, or processing it for final sale.

Thus a risk-averse wheat farmer may hedge his future harvest by selling October wheat futures in January, in which case he is ‘long’ in actuals and ‘short’ in futures. A risk-averse miller who anticipates being short of wheat may hedge by buying futures now, in which case he will be a ‘long’ hedger. Speculators may be on the long or short end of any transaction, but in aggregate their position must offset any net imbalance in the long and short hedgers’ positions.

It might appear from this that hedging consists in shifting the price risk onto the speculators in return for a risk premium. This view of speculation, advanced by Keynes (1923) and Hicks (1946), has been challenged by Working (1953, 1962), who denies any fundamental difference between the motivations of hedgers and those of speculators. One danger with looking exclusively at the price risk is that it ignores the more fundamental quantity risks that give rise to the price risks. Once this is appreciated, it is possible to formulate a simple theoretical model in which all agents are alike in attempting to maximize their expected utility but differ in the risks to which they are exposed, and these differences motivate trade on futures markets. While the activities of speculators are quite well defined, those of ‘hedgers’ are in general a mixture of insurance and speculation, as we shall see.

The simplest model of speculation and hedging has just two time periods. In the first period farmers plant their wheat, and the futures market opens. In the second period the wheat is harvested, sold, and the futures contracts expire. There are only three types of agents – farmers, who produce wheat but do not consume it; speculators, who neither produce nor consume wheat; and consumers, who neither produce wheat nor trade on futures markets. All agents are assumed to have beliefs about the relevant variables, which can be described by (subjective) probability distributions, and their behaviour is described by the theory of expected utility maximization. There are n farmers, and for the moment suppose that they have no choice over the amount of wheat to plant, but only over the size of their sales on the futures market. In the first period farmer i believes that his second period output will be ${\tilde{q}}_i$ (a random variable), and that the market clearing price will be ${\tilde{p}}^i,$ also a random variable. In particular, he believes that ${\tilde{q}}_i$and ${\tilde{p}}^i$ are jointly normally distributed. The price of futures is f observable now, and he sells z_i futures, so that he believes his second period income will be

$$ {\tilde{y}}_i={\tilde{p}}^i{\tilde{q}}_i+{z}_i\left(f-{\tilde{p}}^i\right), $$

(1)

a random variable. The farmer’s utility function exhibits constant absolute risk aversion, A_i, and takes the form ${U}^i(y)=\hbox{--} {k}_i\exp \left(-{A}_i\tilde{y}\right),$where $\tilde{y}$ is the random component of his income. (Any non-random components can be absorbed into the constant, k_i.) This particular form has the property that maximizing expected utility is equivalent to maximizing.

$$ W= Ey-\frac{1}{2}A\;\mathrm{Var}\;y, $$

(2)

where Ey is the expected value of income, Var y is its variance, provided, as in the case here, that y is normally distributed. (These are the standard assumptions of the capital asset pricing model for portfolio choice, and can be viewed as second-order approximations to more general utility functions; see Newbery and Stiglitz 1981.) If Eq. 1 is substituted in (2), and if z_i can be positive (futures sales) or negative (purchases), then the value of z_i that maximizes W is

$$ {z}_i=\frac{\mathrm{Cov}\left({\tilde{p}}^i,{\tilde{p}}^i{\tilde{q}}_i\right)}{\mathrm{Var}\;{\tilde{p}}^i}-\, \frac{E{\tilde{p}}^i-f}{A_i\;\mathrm{Var}\;{\tilde{p}}^i}. $$

(3)

Speculator j has no risky production, so for him ${\tilde{q}}_j$is zero, and the first terms in (1) and (3) vanish. Thus the second term in (3) can be identified as the speculative term, and is readily interpreted. The perceived riskiness of the futures contract is measured by $\mathrm{Var}\;{\tilde{p}}^i$ and the cost of this risk as $1/2\;{A}_i\;\mathrm{Var}\;{\tilde{p}}^i$, The expected return to selling a futures contract is f – Epⁱ. In order to persuade a risk-averse speculator to buy futures and accept the risk, the return to selling must be negative, hence f must be below the expected spot price, − a situation of normal backwardation. The first term in (3) is the pure hedging term, for if the futures market appears unbiased (that is, $f=E{\tilde{p}}^i$) then there is no expected speculative profit, and the only motive for trade is the income insurance offered by the price insurance. The quality of income insurance depends on how well income pq and price risks are correlated; that is, on the ratio of the covariance to the variance. If output is perfectly certain, then income and price are perfectly correlated, the first term will be equal to q_i, and the farmer would sell his entire crop on the futures market if he believed it to be unbiased. In general, though, he will not believe it to be unbiased, and he will wish to speculate in addition to hedging. His net futures trade will reflect the balance of the desire to insure and the returns to speculating.

The futures market clears, so that the sum of z_i across all participants must be zero, and this condition will yield a value for the futures price. What this implies for the value of f and its relation for the subsequent spot price, p, depends on beliefs, as well as preferences. If agents hold rational expectations, and have full information about the nature of all production and demand risks, then they will agree on the common values of the expected spot price, Ep, and its variance, Var p. In such a case the only motive for trading on the futures market is to share risk, and speculators will be willing to absorb some of the risk in return, on average, for some profit. If all farmers face perfectly correlated production risk, and if the coefficient of variation of output is σ_q, of price is σ_p, and the correlation coefficient between price and output is r, then market clearing on the futures market gives the bias as

$$ \frac{Ep-f}{Ep}=\frac{\overline{Q}. Ep{\sigma}_p^2\left(1+r{\sigma}_q/{\sigma}_p\right)}{\sum 1/{A}_i} $$

(4)

and a farmer’s futures sales will be

$$ \frac{z_i}{Eq_i}={\beta}_i\left(1+r{\sigma}_q/{\sigma}_p\right),{\beta}_i\equiv 1-\frac{\overline{Q}}{Eq_i{A}_i{\sum}_j1/{A}_j}, $$

(5)

where $\overline{Q}=\sum {Eq}_i$is average total output (see Newbery and Stiglitz 1981, p. 186). Thus β_i is a measure of the extent to which the farmer is more risk-averse than the average (the term in A_i) and more exposed to risk $\left({\overline{q}}_i/\overline{Q}\right)$. If there are n identical farmers and m identical speculators, all with the same coefficient of absolute risk aversion, A, then β = m|(n + m). If there is no output risk, so σ_q = 0, then, while a farmer would sell his entire crop forward on an unbiased futures market, here he would only sell a fraction β representing the fraction of the total risk which the speculators are willing to bear. If the only source of risk is supply variability, then r = − 1 , σ_q/σ_p = ε, the elasticity of demand, and the farmer will sell a fraction of his crop β(1 – ε) on the futures market, possibly negative.

What lesson can be drawn from this very simplified model? First, futures markets allow speculators to bear some of the farmer’s risks. The more highly correlated income and price risks, the better the market is at insuring farmers, but in general it will provide only partial insurance. It is, however, much better suited to providing insurance to stockholders who store the commodity after the harvest until needed for consumption or processing, and it is not surprising that most hedging is done by stockholders rather than farmers. Second, the greater the agreement over the expected spot price, and the less risk-averse are the speculators, the smaller will be the average perceived bias, and the larger will be the fraction of hedging to speculative sales by producers (or stockholders). Third, the greater the degree of agreement on the expected spot price, the more will speculation be a response to the demand for hedging services. The greater the disagreement on the expected spot price, the more likely it is that speculation, in the form of gambling over the expected spot price, will dominate the market. In a masterly series of studies, Holbrook Working showed that most commodity futures markets depend primarily on hedging for their existence, that the size of the open interest follows closely the demand for hedging of seasonal storage, with speculators standing ready to assume the risks offered by the hedgers (Working 1962). The cost of these hedging services (that is, the return to the speculators) was quite remarkably small. Thus for cotton traders, the gross profit per dollar of sales over a sample of some 3,000 trades was 0.023 of one per cent with the traders making losses on 15 out of 43 trading days. (Net profits after paying commissions and expenses were substantially less; Working 1953).

The issue of bias turns out to be more complex than the simple Keynes–Hicks risk-premium view, for even in a bilateral market of farmers and speculators the bias can go either way. Once stockholders and processors are brought into the picture, the relative demands for long and short hedges will change yet again, and in turn influence the direction of speculation (long or short) and hence of the risk premium, or bias. Hirshleifer (1988) examines the determinants of bias in a market with primary producers subject to output risk (growers) and intermediate producers (processors). He finds that processors tend to hedge long, but, if transaction costs are low, there is a downward bias in futures prices (backwardation). If transaction costs are high, growers are differentially driven from the futures market, and could reverse the bias to contango.

Effect of Speculators on Stability

Several important questions can be asked about the role of speculators. Do they tend to destabilize the spot market and/or the futures market? Do they improve efficiency? Do they have adverse macroeconomic effects? To the layman the association of speculative activity with volatile markets is often taken as proof that speculators are the cause of the instability, though the body of informed opinion is that the volatility creates a demand for hedging or insurance, which is met by the willingness of speculators to bear the risk. It is hard to test the proposition that speculation is stabilizing, for speculative activity (notably, stockholding) can take place without futures markets. In practice, the usual question is: do futures markets, which, by lowering transaction costs, greatly facilitate speculative behaviour, improve the stability of the spot market? Even this question is not straightforward. Futures markets provide an incentive to collect information about the future market-clearing spot price, though, as often with information gathering, there are public-good problems associated with its use. Much theoretical effort has been devoted to the question of whether futures prices perfectly reveal the relevant information available to participants, and, if so, what incentives would remain for its collection. It now appears that, except in special cases, the information is only partially revealed in the market, leaving incentives for its collection, but nevertheless improving the forecasts of otherwise uninformed traders. If so, and if the spot market is intrinsically volatile (because of variations in supply caused by weather, or demand caused by the trade cycle), then better forecasts of future spot prices will tend to elicit compensating supply responses – if prices are expected to be high tomorrow, then it will pay to produce more, and to carry more stocks forward, tending to reduce, or stabilize, price fluctuations. To the extent that futures markets reduce storage risks, storage becomes cheaper, and this will tend to stabilize supplies and prices directly. On the other hand, anticipated disturbances will have a more immediate effect on current prices, and will tend to make them more responsive to news. A frost in Brazil expected to affect next year’s coffee production is likely to have a more rapid effect on current coffee prices in the presence of a futures market than in its absence. Nevertheless, it improves the efficiency of the current market if it does respond to this relevant information.

The clearest example of the stabilizing effect of futures market is provided by cobweb models, in which producers base current production decisions on last year’s realized price, with consequent self-sustaining fluctuations in output without any exogenous shocks. If a futures market is set up, then producers initially planning to expand production in response to last year’s high price, and selling futures, would cause the futures price to fall to the predicted spot price, and would lead them to revise their incorrect production plans, hence eliminating the cobweb and stabilizing the market.

Two other factors bear on the question of market stability. It is clear that much hinges on the nature of expectations. Speculation without hedging is a zero-sum game, and, if two speculators, each holding different views of the future price, $E\tilde{p}$ trade with each other, one will gain while the other will lose. If they are rational, and risk-averse, they should not be willing to engage in such swaps. On this view, speculators who are more successful at forecasting the future price will make money, and those who are less successful will lose, and be forced to leave the market, until only the good forecasters are left, and they make money only in the course of moving futures prices towards the forecast spot price. However, it is possible that a steady supply of less good speculators, who add noise to the system, lose money and exit, to be replaced by others. Their presence may worsen the predictive power of the futures price or, by increasing the returns to information gathering by the informed speculators, may actually improve the predictive power of the futures prices (Anderson 1984a; Kyle 1984). Depending on the direction of the net effect of uninformed speculators, the presence of a futures market (which provides them with the opportunity to gamble) may improve or worsen the efficiency of the spot market.

The other possibility is that futures markets will provide opportunities for market manipulation, by the better informed at the expense either of the less well informed (corners, squeezes) or of the larger at the expense of the smaller. It is easy to show that the futures price has an effect on production decisions by extending the model of Eq. 1 to allow producers to choose inputs. In the case of pure demand risk (no output uncertainty) it can be shown that the producer will base his production decisions solely on the future price. Large producers (Brazil for coffee, OPEC for oil, and so on) may then find it profitable to intervene in the futures market to influence the production decisions of their competitors in the spot market, and in extreme cases may find it profitable to increase price instability, though the extent to which this is feasible will be limited by the supply of and risk tolerance of other speculators in the futures market (Newbery 1984). This is true even if all agents hold rational expectations, and share full information (except about the actions of the large producers). If some agents use naive forecasting rules to guide their futures trading, and if these rules are known to other agents who possess market power, then it may pay the large rational agents to destabilize the price and exploit the irrationalities in the forecasting behaviour of the naive agents (Hart 1977).

Although speculation may stabilize prices, it is quite possible for it to make prices more unstable, even if all agents have equal information and hold rational expectations. Compare two possible arrangements. In the first, futures markets are prohibited, the commodity is perishable, so there is no scope for speculative storage or speculation on the futures market. The commodity can be produced by two methods, one perfectly safe, the other risky, but on average more profitable (for example, two varieties of irrigated rice, one higher-yielding but susceptible to rust in certain weather conditions). Farmers allocate their land between the two production techniques but, in the absence of the futures market, find the risky technique relatively unattractive and so produce little. In the second arrangement, futures markets are permitted and speculators are willing to trade for a very low risk premium. Farmers are now able to sell the crop forward, and are therefore more willing to produce the risky crop, whose supply is very variable. Total supply variability increases, and hence the spot price becomes more variable.

It is quite possible that destabilizing speculation of this type yields higher potential social welfare, for yields are higher, if riskier, and the risks are borne at relatively low cost. It is also perfectly possible for speculation on a futures market to be stabilizing (by reducing the costs of storage and therefore improving arbitrage between crop years) and yet make everyone worse off (see, for example, Newbery and Stiglitz 1981). We now know that, if the market structure is incomplete, creating additional markets can make matters worse. Speculation, which creates a market in price risks, does not thereby complete the market structure because quantity risks may remain imperfectly insured. The reason is that the market in price risks causes changes in the market equilibrium which affects the degree to which the other risks (income and quantity risks) are effectively insured. In particular, if prices are stabilized but quantities remain unstable, incomes may be less stable than if prices were free to move in response to the quantity changes.

Finally, there remains the old Keynesian question of whether speculation which succeeds in stabilizing prices will exacerbate income fluctuations. The argument, due to Kaldor (1939), is straightforward. Speculators undertake or assume the risks for storage, which then responds to mismatches in supply and demand. These stocks, or inventories of goods, will fluctuate markedly and will have the same macroeconomic effect as fluctuations in investment, tending, through the multiplier, to have a magnified effect on national income. Whether these speculative stock movements are stabilizing or destabilizing then turns on whether they offset or amplify the fluctuations in income associated with the mismatch in demand and supply that caused the stock change. Kaldor’s view was that stock changes caused by supply shocks would tend to stabilize total income, while those caused by demand stocks would be destabilizing, but much will depend on the commodity price elasticities of demand and the nature of the various transmission mechanisms, particularly the lag structure. Nevertheless, the OPEC oil shocks have demonstrated that commodity supply shocks can cause significant macroeconomic disturbances, while the increasing ease of currency speculation as restrictions are removed and transaction costs lowered has reawakened the fear that speculation may, in some cases, destabilize income and impose needless costs.

Commodity Stabilization Schemes and Longer-Term Insurance

At various times governments and international agencies have argued that primary commodity price variability is costly to vulnerable, often poor, primary exporters, and that therefore some form of commodity stabilization scheme should be implemented. Such schemes are often poorly designed to minimize the cost of reducing risk and have a doubtful record (Newbery and Stiglitz 1981). One might also expect that, in the presence of the kind of market failure suggested by this costly risk, alternative institutions might emerge to reduce risk, and that is indeed the case, with futures markets being the most obvious solution to commodity price risk. If primary exporting countries can hedge the export commodity price variability, then their risk will be reduced, and would seem to be eliminated if all the risk arose from price variability, with no variability in output. This would be true if there were no serial correlation in prices from year to year, but, as Deaton and Laroque (1992) found, there is considerable serial correlation for the 24 commodities they studied over the period 1900-87. Their results suggest that about one-quarter of price shocks are permanent, that three-quarters or more of the price shock will persist for at least a year, and even after two years typically 60 per cent of the price shock will persist. If countries (or producers) hedge only for the coming year, their income will still vary considerably from year to year. If they could hedge for many years ahead this problem would be reduced.

Most futures markets extend only a relatively short period ahead and, even when they extend out several years, active trading and hence liquidity is mostly confined to the near-term future, measured in months rather than years. Apart from primary exporters having to deal with serial correlation (or persistence in price shocks), producers making large, irreversible sunk investment decisions (for example, in an oil refinery, offshore oil exploitation, LNG liquefaction and regasification facilities, aluminium smelters, nuclear power stations) would make better investment decisions knowing future prices (of inputs and outputs). They would be able to borrow more cheaply if risk were reduced by contracts or hedging, reducing the cost of capital-intensive products.

Liquid futures extending out ten years would clearly help, but are lacking. In their absence, companies may prefer to vertically integrate down the supply chain to provide an implicit (if partial) hedge. Electricity and gas liberalization has been premised on separating out natural monopoly pipes and wires from potentially competitive services supplied over the networks, regulating the former and creating wholesale and retail markets for the latter. Vertical unbundling (particularly of generation and transmission) appears critical to delivering the efficiency benefits of competition (Newbery 2005), but increases risk as wholesale electricity and fuel markets are so volatile. Forward and futures markets for electricity (and fuels such as gas) exist but basis risk (the difference between the price of the product traded and that of interest to the contractor) is high and markets are very illiquid. Vertical integration between generation and supply (or retailing) reduces spot price risk but makes the market less contestable.

Nevertheless, it is possible to use a sequence of short-term futures markets to hedge longer-term risks through a sequence of rollover hedges. Kletzer et al. (1992) show how to compute an n-year rollover hedge for a commodity with serially correlated price risk, no output risk but supply responsive to expected price. The way the rollover works is to sell more futures initially than needed for one-period hedging, and then use the surplus futures sales to finance the next year’s futures transactions. This is not perfect, for the amount of hedging required next year will depend on production, and that will depend on the futures price prevailing next year, not as yet known. Consequently, despite the absence of production risk, future output cannot be perfectly hedged, and there remains some residual risk (as there would be if there were output risk). Nevertheless, because the costs of risk increase with the square of the deviation, reducing the risk by a given fraction reduces the cost of risk by more than that fraction and can be worthwhile. The further forward the hedge extends, the lower is the extra risk benefit provided, until the extra costs outweigh the benefit, so there is an optimal length of such a hedge.

The idea of using rollover hedging and portfolios of futures of different maturities to reduce risk has proved powerful both in theory and in hedging practice. Ross (1997) considers a world in which commodity prices are determined by many factors, and that, given enough different futures contracts and sufficiently precise knowledge of the underlying model determining prices, it would be possible to devise a perfect hedge, although in practice any such hedge would be imperfect. Neuberger (1999) develops this approach to identify an optimal hedging strategy using futures of different maturities and thus hedge long-term exposures with a combination of short-term futures. Neuberger tests his model on crude oil futures traded on NYMEX from 1986 to 1994. He asks how well one can hedge a forward commitment to deliver oil in five years’ time using two futures contracts of not more than nine months to maturity. The annualized volatility of the five-year contract is 26 per cent and that of the hedged portfolio is less than one per cent, with a hedge of short 2.89 seven-month contracts (of 1,000 barrels) and long 3.93 nine-month contracts, for each contract to deliver in five years’ time. In a model in which a trader wishes to hedge for delivery in 36 months’ time, if the portfolio is balanced monthly, 488 contracts are traded per contract delivered, although this can be cut to fewer than 60 with bimonthly rebalancing (and at lower risk).

The fact that rollover hedges allow one to reduce risk over a longer time horizon than the duration of current futures offered in the market has a number of interesting implications. It can explain why near-term futures are more popular and liquid than longer-term contracts, for they may provide a substitute for the latter at lower cost. It also explains why the volume of liquid futures can so greatly exceed the underlying physical trade, often by factors of 10–20. Rollovers require both a greater ratio of futures to physicals and a higher rate of trading to rebalance the portfolio over time, contributing to volume, liquidity and hence cost reduction.

Rollovers are, however, not perfect, and they may tempt traders to take imprudently large risks. One such famous case was the near-bankruptcy of Metallgesellschaft (MG), whose losses were estimated at DM 4 billion and whose survival was ensured only by a major rescue operation (Wahrenburg 1996). At one time MG was reportedly holding short-term positions equivalent to 160 million barrels of oil or 80 times the daily output of Kuwait (Hilliard 1999).

The case became celebrated as a test of whether MG had adopted a sound or imperfect hedging strategy. Some writers such as Culp and Miller (1995) argued that MG was following ‘a textbook hedging strategy which was not properly understood by MG’s supervisory board and house banks’ (Wahrenburg 1996, S29). Others, such as Edwards and Canter (1995), Mello and Parsons (1995), and Verleger (1999) argue that MG was excessively exposed in the wrong products. Wahrenburg argues that the MG’s hedging strategy could indeed significantly reduce risk, but not completely, and that MG’s equity capital was insufficient to cover the remaining risk.

See Also

• Arbitrage

• Hedging

• Information Aggregation and Prices

• Options

• Options (New Perspectives)

• Present Value