Speculation, Hedging, and Arbitrage

BIBLIOGRAPHY

Arbitrage is the simultaneous purchase and sale of equivalent assets at prices which guarantee a fixed profit at the time of the transactions, although the life of the assets and, hence, the consummation of the profit may be delayed until some future date. The key element in the definition is that the amount of profit be determined with certainty. It specifically excludes transactions which guarantee a minimum rate of return but which also offer an option for increased profits.

Hedging is the simultaneous purchase and sale of two assets in the expectation of a gain from different subsequent movements in the price of those assets. Usually the two assets are equivalent in all respects except maturity.

Speculation is the purchase or sale of an asset in the expectation of a gain from changes in the price of that asset.

Arbitrage . Arbitrage can occur in a number of ways. For example, a wholesale egg merchant in Chicago may find that eggs are being quoted in New York at a price that exceeds the Chicago price by more than the costs of transportation between New York and Chicago. He can then buy eggs in Chicago, simultaneously sell them for delivery in New York next week, and ship the eggs for an assured profit. The key consideration is that the instant the transactions are completed, the profit is assured, even though delivery may not take place until later. Similarly, a foreign exchange arbitrageur may be able to buy British pounds sterling in New York for $2.80 and sell them on the Swiss market for $2.8010. Since, in this case, there are no “shipping” costs, the entire difference, except for minor transaction costs, is profit.

In the pursuit of these profits, arbitrageurs tend to force prices in all markets toward equality. The arbitrageur’s transactions tend to raise prices in the cheap market and depress prices in the expensive one. Because of transaction costs and transportation costs, literal equality will not be achieved. But neglecting the former costs, completely effective arbitrage would eliminate the incentive to shop among markets. To the extent that arbitrageurs, through specialization, can seek out market imperfections more efficiently than other market participants can, they will increase social welfare.

Because arbitrage profits are riskless, they are hard to get. Since most obvious opportunities are quickly eliminated by the activity itself, most actual arbitrage activity involves more complicated operations than are suggested by the above examples. The foreign exchange arbitrageur is more likely to use his dollars to buy German marks, use those marks to buy pounds, and sell those pounds for dollars (Grubel 1963). Such profits as do exist are a recompense for the detailed attention and time invested in seeking out those opportunities.

Many operations customarily designated as arbitrage are not arbitrage at all. For example, if the egg merchant in the previous example had purchased eggs in Chicago at a price lower than in New York, but lower by less than costs of transport, in the hope that Chicago prices would go to a par with New York, he would not be engaging in bona fide arbitrage because the profit is not assured.

Hedging . An understanding of hedging requires an understanding of the elements of the theory of asset holding. Individuals will hold inventories of assets only in the expectation of increases in the value of those assets by at least enough to cover the costs of carrying the assets. In the case of financial assets, these carrying costs are largely the costs of the money tied up. In the case of physical inventories, there will also be costs of storage and spoilage or deterioration. Set against these costs will be certain benefits from the inventory: for merchants, for example, the inventory may be the means to increased sales or commissions.

The net costs of carrying inventory may be positive or negative, but in economic equilibrium the marginal cost of a unit of inventory must be equal to the expected price appreciation of that unit of inventory (Working 1933; Brennan 1958). This introduces an asymmetry into the behavior of expected changes in prices of storable assets. At no time can the expected price one period from now be greater than the current price by more than the marginal cost of storage for that period. Once the difference becomes equal to the costs of storage, an increase in expected future price will increase today’s price as well. On the other hand, there is no similar lower limit on the extent of expected price decreases: if prices are expected to fall, current prices will be depressed by a reduction in the amount of inventories held until the marginal value of those inventories is equal to the expected price decline. But while inventories can be accumulated indefinitely, they can be reduced only to zero.

When inventories are increased, the holder exposes himself to increased capital risk from fluctuations in the price of the goods being held. If the merchant is a risk averter, increasing his inventory increases his subjective costs of storage. To reduce that risk, he may hedge by selling for future delivery at some fixed price some or all of the inventory he owns. By doing so, he passes the risk to the speculator who buys the futures contracts.

Traditionally, this reduction in risk is supposed to be the primary advantage of hedging. To illustrate this argument, assume that a Chicago wheat merchant purchases 1,000,000 bushels of No. 2 soft red winter wheat in July at $1.45 a bushel for his inventory. He is now exposed to the risk of changes in the value of his inventory due to fluctuations in the price of his wheat: he is speculating on the price of wheat. If he prefers, however, he may sell futures contracts on the Chicago Board of Trade, promising delivery of 1,000,000 bushels of No. 2 soft red winter wheat any time in December at the price currently quoted for December futures, say, $1.52. If he does so, he is clearly “hedging,” as we have defined it, since his wealth is now affected only by relative movements in the prices of the wheat and of the futures contracts. Conventional usage stresses the fact that by waiting until December and delivering his wheat on the futures contracts, the merchant is assured of a seven-cent gain on each and every bushel of wheat he owns. (Note that since he must pay storage costs on the wheat from July to December, this is not necessarily a profitable transaction.) This traditional view likens hedging to an arbitrage in which the merchant has eliminated his risk by passing it on to the speculator who purchases the futures contract.

This transaction, however, is not genuine arbitrage, nor is it typical of hedging at all. To be sure, the price of actual wheat will gain by seven cents relative to Chicago December futures if the wheat is held until December. It is possible, however, that some temporary shortage in supplies (due either to a spurt in demand or to a natural catastrophe) might occur, so that in October the price of wheat might rise to $1.52 or higher without a concomitant rise in the December futures. In such an event, the merchant would make a profit by selling the wheat and buying back the futures contract in October, since he would experience the same or a greater relative movement in prices while paying storage charges for a shorter period of time. In addition, by selling the wheat he would earn a commission which he would not get if he delivered the wheat on the futures contract. In other words, his hedge is really an option to benefit from a certain minimum relative price movement, but with freedom to take a larger gain if the opportunity arises.

In view of this, the premium of the December futures contract price over the actual wheat price in July is rarely enough to cover the actual costs of storing wheat from July to December. If the premium were usually that large, any amateur could earn a riskless profit, since hedging would result in zero profits at worst and positive profits whenever random events made it possible. As a result, hedging rarely takes the form of the textbook example.

In the usual case, hedging is undertaken in the hope or expectation that the gain on the hedge transaction will be greater than the current difference between the price of the futures contract and the price of the corresponding physical commodity. This may arise as in the illustration above or in a number of other ways. For example, the hedger may feel that wheat in Indianapolis is cheap relative to Chicago wheat and will rise by more, relative to the Chicago futures contract, than will Chicago wheat. Note that the Indianapolis wheat is not deliverable on the Chicago futures contract without incurring the cost of shipment to Chicago, and so the prospect of actual delivery is even more remote than in the earlier case. Similarly, the wheat hedged might be No. 1 white wheat at Toledo—different both in grade and in location from the Chicago futures contract.

Notice that, in financial terminology, the merchant has bought a “callable” asset and has sold an asset (bought a liability) with a maturity of five months. This is just the reverse of the bank that accepts (”buys”) a demand deposit (a call liability) and invests the funds in (buys) a five-month loan or Treasury security. The merchant buys “shortlived assets” and “long-lived liabilities”; the bank buys “long-lived assets” and “short-lived liabilities.” In both cases hedger and bank alike can (and do) benefit from appropriate changes in the relative prices of the assets they hold. Their position is much safer than outright holding of either the asset or the liability alone, but it retains some risk and some hope of gain in each case (Cootner 1963). This is true even though in practice bank demand deposits are rather long-lived assets (Samuelson 1945).

These examples are known as “short” hedges, because the futures contracts are sold short first and bought back, or delivered against, later. Another form of hedge, the “long” hedge, arises when, for example, a merchant is asked in March, at a time when he has no wheat on hand, to deliver wheat to a flour mill at a fixed price of $2.00 in May. The merchant has the option of buying the wheat in March and holding it until May, or, if he feels that the current price difference between March and May wheat is too small, of buying May wheat futures. In the latter case, he would wait until May, take delivery of wheat on the futures contract, and in turn deliver the wheat to the flour mill (an unlikely procedure). Or he could hold the futures contract as protection until a lot of wheat of suitable price and quality becomes available, say in April, and then liquidate the contract. The transactions involving the initial purchase of futures and later selling the futures or taking delivery are called long hedges—protection against price rises.

Although transactions involving futures constitute most of what we call hedges, futures markets are not a prerequisite to hedging. One might buy shares of one textile company while selling those of another if one had feelings about the relative prosperity of the former but little assurance about the over-all prospects of the industry.

Regardless of whether merchants hedge to eliminate risk or to anticipate movements of relative prices, the hedge generally has less risk associated with it than does holding of either of the two assets constituting the hedge: the variance in value of the hedge is less than that of the assets themselves. When a merchant hedges, however, he need not reduce his risk exposure, since the lower risk per unit of inventory can be offset by holding a larger total volume of inventory. Since a larger level of inventories permits an individual merchant to increase his profitable sales opportunities, he has an incentive to hedge in order to increase inventories. Thus, even if the expected gain from holding a bushel of wheat outright is greater than the expected gain from holding a bushel of wheat hedged, the merchant may prefer to hedge in order to be able to finance a larger inventory holding. A common figure used in trade circles is that banks will permit a merchant to finance three to five times as much hedged inventory as unhedged.

Thus, the merchant may assume the same total risk in hedged contracts as he would have if he had held a smaller volume unhedged. In doing so, he exercises his opinion that he is better able to predict relative price movements than changes in the absolute level of prices and has increased the rate of return associated with the risk by specializing in the area in which he has a comparative advantage.

Hedging provides the economic rationale for the speculator. When the merchant hedges to reduce his personal risk, he does not change the total risk faced in the market. The risk of price fluctuation is merely transferred from the merchant to the futures speculator. The speculator accepts that risk voluntarily, in expectation of making money from the futures price changes.

For speculators as a group actually to earn a profit requires that merchants be willing to sell for future delivery at prices lower than those they expect in the future. One reason why they might do so is that by hedging, they eliminate risk; and the difference between the price at which they sell and the price they expect in the future is the risk premium—somewhat analogous to the premium one pays for insurance (over and above the actuarial value of the risk). Speculators, like insurance companies, would not furnish their services without being paid the premium. In this view, the speculator receives what the merchant is willing to pay for his services. Whether the speculator actually makes money or whether he is willing to accept the risk for the love of the gamble has been a matter of some controversy. The weight of the evidence now is that speculators do make money (Cootner I960; Houthakker 1957), although some writers disagree (see Telser in Cootner 1960).

If speculators do make money, futures prices must rise over the period that they own futures, and fall during the period that they are “short” futures. Since hedgers are usually short and speculators usually long, Keynes (1930) argued that futures prices will normally rise over the lifetime of each contract. More recently, Cootner (1960) has shown that in agricultural commodities, hedgers are frequently long (and speculators are short) in the period prior to harvest when inventories are low. In cases where that pattern usually obtains, if speculators are to profit, futures prices must fall prior to harvest and rise thereafter. In short, payment of risk premiums would imply a seasonal pattern for futures prices.

In the view of hedging presented here, however, the individual merchant, by hedging and paying the risk premium, gets the opportunity to increase his merchandising profits by an equal or greater amount. While this is true for every merchant individually, it can be true for the market as a whole only if speculation (1) increases the average price to the consumer or (2) reduces the costs of merchandising. The evidence on this point is that (1) is not true but that (2) is likely to be true, although it has not been proved (Working 1953).

The social value of speculation . In a world characterized by uncertainty, speculation is essential to the allocation of economic resources over time. There is no question of whether or not speculation should be permitted; the only economic issue is who will perform the service most effectively. The sometimes-heard charge of “overspeculation” is incorrectly framed: The issue is not one of amount but, rather, whether it is done well or poorly.

The role of speculation is to allocate resources among periods. If one expects, as did Joseph and the Pharaoh in the Old Testament, seven lean years to follow the seven fat, economic theory tells us that social welfare can be increased by refraining from some present consumption and storing the unconsumed goods until the lean years are upon us, so long as the price expected in the lean years is greater than today’s price by at least the costs of storage (including capital costs). If the future is certain (Samuelson 1957), there is no need for speculation, but with uncertainty, whoever carries the inventories is exposed to the risk that the expected lean years will not materialize. Unless that risk is taken, resources will be used wastefully today and unnecessary hardship will be induced tomorrow, relative to intertemporal distribution under certainty.

Although the issue is stated in terms of grain, it is formally identical with the problem of financing fixed capital investment. The terminology of capital markets is less precise, but the suppliers of capital for investment projects play a similar role in determining whether resources should be “non-consumed” today so as to permit greater production of goods in the future.

In futures markets, the influence of the speculator is easier to see. If the speculator anticipates higher prices in the future, he buys futures contracts, tending to force up their price. As indicated in our hedging example, this gives a larger prospective profit to the hedger for carrying inventory and causes him to increase his holdings. Thus, if speculators as a group make correct judgments, their self-interest results in correct intertemporal decisions.

Several studies of commodity markets before and after futures trading have been undertaken. All suggest that prices are more stable with futures trading than without: that prices do not fall as low or rise as high after the introduction of futures trading (e.g., Working 1960). This implies that futures traders tend to buy at low prices and sell at high ones, i.e., that they profit. Despite this evidence, periods of very low prices or very high prices still are often blamed on speculators, and futures trading has been regulated or prohibited on many occasions. Interestingly enough, however, because it works very well, futures trading has sometimes been banned when, for political or social motives, interference with the economic mechanism is desired. Abolition of foreign exchange futures markets frequently accompanies foreign exchange controls, and some regulation of bond speculation was introduced in the United States in the 1960s because the speculation interfered with the operation of monetary policy intended to destabilize bond prices (Cootner 1964).

Even among those who recognize that futures markets may reduce the range of price variation, there are some who believe that speculative activity may cause prices to move more frequently between the narrower boundaries. According to this view, alternate waves of buying and selling may cause excessive fluctuations: price changes over successive periods would be positively correlated. On the other hand, in a perfect market, future price changes would be completely independent of past history. The price at the end of the previous day would discount all factors of importance known at that time—a price change would result only from new information. To a very close approximation, if we correct for the seasonality of risk premiums, speculative markets seem to be perfect (Cootner I960; 1964; Working 1934).

Paul H. Cootner

[See alsoDecision Making, article on Economic Aspects; Economic Expectations; International Monetary Economics, article on Exchange Rates.]

BIBLIOGRAPHY

Brennan, Michael J. 1958 The Supply of Storage. American Economic Review 48:50-72.

Cootner, Paul H. 1960 Returns to Speculators: Telser Versus Keynes. Journal of Political Economy 68:396-404. → A reply by Lester G. Telser appears on pages 404-415; a rejoinder by Cootner appears on pages 415-418.

Cootner, Paul H. 1963 Speculation in the Government Securities Market. Pages 267-310 in Commission on Money and Credit, Fiscal and Debt Management Policies. Englewood Cliffs, N.J.: Prentice-Hall.

Cootner, Paul H. (editor) 1964 The Random Character of Stock Market Prices. Cambridge, Mass.: M.I.T. Press.

Grubel, Herbert G. 1963 A Multicountry Model of Forward Exchange: Theory, Policy, and Empirical Evidence 1955-1961. Yale Economic Essays 3:105-169.

Houthakker, HzNDRiK S. 1957 Can Speculators Forecast Prices? Review of Economics and Statistics 39: 143-151.

Keynes, John Maynard (1930) 1960 A Treatise on Money. Volume 2: The Applied Theory of Money. London: Macmillan.

Larson, Arnold B. 1960 Measurement of a Random Process in Futures Prices. Stanford University, Food Research Institute, Food Research Institute Studies 1:313-324.

Samuelson, Paul A. 1945 The Effect of Interest Rate Increases on the Banking System. American Economic Review 34:16-27.

Samuelson, Paul A. 1957 Intertemporal Price Equilibrium: A Prologue to the Theory of Speculation. Weltwirtschaftliches Archiv 79:181-221.

Telser, Lester G. 1955 Safety First and Hedging. Review of Economic Studies 23, no. 1:1-16.

Working, Holbrook 1933 Price Relations Between July and September Wheat Futures at Chicago Since 1885. Stanford University, Food Research Institute, Wheat Studies of the Food Research Institute 9:187-238.

Working, Holbrook 1934 A Random-difference Series for Use in the Analysis of Time Series. Journal of the American Statistical Association 29:11-24.

Working, Holbrook 1953 Hedging Reconsidered. Journal of Farm Economics 35:544-561.

Working, Holbrook 1960 Price Effects of Futures Trading. Stanford University, Food Research Institute, Food Research Institute Studies 1:3-31.