Arbitrage: Historical Perspectives

The concept of arbitrage has acquired a precise, technical meaning in quantitative finance (see Arbitrage Pricing Theory; Arbitrage Strategy; Arbitrage Bounds). 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 nonnegative, 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 Fundamental Theorem of Asset Pricing; Equivalent Martingale Measures). 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 a 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 definition of arbitrage 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 definitions of arbitrage in modern usage.