Arbitrage: Historical Perspectives
Geoffrey Poitras
Faculty of Business Administration
Simon Fraser University
Vancouver, B.C.
CANADA V5A lS6
Abstract
This article discusses the history of arbitrage from ancient times until the beginning of the twentieth century. Opportunities for arbitrage trading in ancient times are related to the movement of goods over distance. The key role of the bill of exchange in arbitrage trading during the Middle Ages is identified and the connection to ‘arbitration of exchange’ discussed. A 17th century arbitrage involving the gold and bill of exchange markets is detailed. As reflected in merchant manuals of that period, the connection between riskless arbitrage trading and the method of conducting arbitration of exchange in the 18th and 19th centuries is detailed. An overview of 19th century arbitrage trading in securities and commodities is also provided. The article concludes with an examination of the etymology and historical usage of the word ‘arbitrage’ and the associated ‘arbitration of exchange’.
Introduction
The concept of arbitrage has acquired technical and precise definitions in quantitative finance (see eqf03/003; eqf04/001; eqf04/017; eqf05/010). In theoretical pricing of derivative securities, an arbitrage is a riskless trading strategy that generates a positive profit with no net investment of funds. This definition can be loosened to allow the positive profit to be non-negative, with no possible future state having a negative outcome and at least one state with a positive outcome. Pricing formulas for specific contingent claims are derived by assuming an absence of arbitrage opportunities. Generalizing this notion of arbitrage, the fundamental theorem of asset pricing provides that an absence of arbitrage opportunities implies the existence of an equivalent martingale measure (see eqf04/002; eqf04/007). Combining absence of arbitrage with a linear model of asset returns, the arbitrage pricing theory decomposes the expected return of a financial asset into a linear function of various economic risk factors, including market indices. Sensitivity of expected return to changes in each factor is represented by a factor-specific beta coefficient. Significantly, while riskless arbitrage imposes restrictions on prices observed at a given point in time, the arbitrage pricing theory seeks to explain expected returns, which involve prices observed at different points in time.
In contrast to the technical definitions of arbitrage used in quantitative finance, colloquial usage of arbitrage in modern financial markets refers to range of trading strategies, including: municipal bond arbitrage; merger arbitrage; and convertible bond arbitrage. Correctly executed, these strategies involve trades that are low risk relative to the expected return but do have possible outcomes where profits can be negative. Similarly, uncovered interest arbitrage seeks to exploit differences between foreign and domestic interest rates leaving the risk of currency fluctuations unhedged. These notions of risky arbitrage can be contrasted with covered interest arbitrage which corresponds to the arbitrage definition used in quantitative finance of a riskless trading strategy that generates a positive profit with no net investment of funds. Cash-and-carry arbitrages related to financial derivatives provide other examples of arbitrages relevant to the quantitative finance usage. Among the general public, confusion about the nature of arbitrage permitted Bernard Madoff to use the illusion of arbitrage profit opportunities to attract ‘hedge fund investments’ into the gigantic Ponzi scheme that collapsed in late 2008. Tracing the historical roots of arbitrage trading provides some insight into the various and different definitions of arbitrage in modern usage.
Arbitrage in Ancient Times
Records about business practices in antiquity are scarce and incomplete. Available evidence is primarily from the Middle East and suggests that mercantile trade in ancient markets was extensive and provided a number of avenues for risky arbitrage. Potential opportunities were tempered by: the lack of liquidity in markets; the difficulties of obtaining information and moving goods over distances; and, inherent political and economic risks. Trading institutions and available securities were relatively simple. Circa 1760 BC, the Code of Hammurabi dealt extensively with matters of trade and finance. Sumerian cuneiform tablets from that era indicate a rudimentary form of bill of exchange transaction was in use where a payment (disbursement) would be made in one location in the local unit of account, e.g., barley, in exchange for disbursement (payment) at a later date in another location of an agreed upon amount of that local currency, e.g., lead [20]. The date was typically determined by the accepted transport time between the locations. Two weeks to a month was a commonly observed time between the payment and repayment. The specific payment location was often a temple.
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