Arbitrage
Arbitrage is the practice of simultaneously buying and selling an asset, security, or commodity in different markets in order to profit from a difference in price. Because arbitrage transactions involve no net investment and, in their purest form, no risk, the presence of arbitrage opportunities indicates that markets are not fully in equilibrium. The elimination of arbitrage opportunities by profit-seeking traders is one of the mechanisms through which markets achieve price consistency.
Definition
Pure arbitrage involves the purchase of an asset at a lower price in one market and its simultaneous sale at a higher price in another, yielding a riskless profit equal to the price difference minus transaction costs. Because the transactions are executed simultaneously, the arbitrageur is not exposed to the risk of price movements.
A more general definition treats arbitrage as any transaction that seeks to profit from the divergence of prices of equivalent or related assets. This includes forms of arbitrage that are not strictly riskless, such as statistical arbitrage, in which traders exploit temporary pricing anomalies that are expected to revert to normal.
The law of one price
Arbitrage is grounded in the law of one price, which holds that identical assets should sell for the same price in different markets, once exchange rates and transaction costs are accounted for. If the law of one price were violated—if the same security traded at different prices in two markets—arbitrageurs would buy in the cheaper market and sell in the more expensive one, and the resulting pressure would rapidly eliminate the discrepancy.
The law of one price is the foundation of many propositions in finance and international economics, including purchasing power parity and interest rate parity. In practice, the law holds only approximately, because of transaction costs, differences in timing, barriers to trade, and other frictions.
Types of arbitrage
Spatial arbitrage arises when the same asset trades at different prices in different locations. It is limited by transportation costs and by the speed of information flows.
Temporal arbitrage exploits price differences over time, such as buying a commodity now and selling it under a futures contract for future delivery. The basis between spot and futures prices reflects the cost of carrying the asset, including storage, insurance, and financing.
Triangular arbitrage operates in the foreign exchange market, exploiting inconsistencies among the exchange rates of three currencies. If the cross rate implied by two exchange rates differs from the directly quoted rate, a trader can profit by buying and selling in sequence through three currencies.
Statistical arbitrage uses quantitative models to identify securities whose prices have diverged from their historical relationship and are expected to converge. Unlike pure arbitrage, statistical arbitrage carries risk, because the expected convergence may not occur.
Covered interest arbitrage involves borrowing in one currency, converting to another, investing, and hedging the exchange rate risk with a forward contract, in order to exploit differences between interest rates and forward exchange rates.
Arbitrage and market efficiency
The concept of arbitrage is central to the theory of market efficiency, which holds that asset prices reflect all available information. In an efficient market, arbitrage opportunities are eliminated almost instantly, because any discrepancy in prices is immediately exploited by traders. This reasoning underlies the no-arbitrage principle, which states that in equilibrium no riskless profit can be earned by trading.
The strength of these conclusions depends on the conditions under which arbitrage operates. Arbitrage is limited by transaction costs, by the availability of capital, by constraints on short selling, and by the risk that prices may diverge further before converging—a phenomenon known as limits to arbitrage. In periods of market stress, these limits can become binding, allowing significant and persistent mispricings to develop.
Arbitrage and the efficient markets hypothesis
The efficient markets hypothesis distinguishes among three forms of efficiency: weak, semi-strong, and strong. Weak-form efficiency holds that current prices reflect all past price information; semi-strong-form efficiency holds that prices reflect all publicly available information; strong-form efficiency holds that prices reflect all information, public and private. Arbitrage is the mechanism that enforces these forms of efficiency.
Empirical research has identified numerous anomalies that appear to violate the efficient markets hypothesis, including the small-firm effect, the value premium, and momentum. Whether these represent true inefficiencies or reflect unrecognised risk factors remains debated, but they illustrate that arbitrage is not always sufficient to enforce perfect price consistency.
The role of arbitrage in finance
Arbitrage serves several important economic functions. It promotes price consistency across markets and instruments, contributing to the efficient allocation of capital. It enhances liquidity by providing trading volume. It aids price discovery, the process by which market prices incorporate information. And it links markets together, so that prices in one market reflect conditions in related markets.
The concept of no-arbitrage is central to modern asset pricing theory. The capital asset pricing model, the Black–Scholes option pricing formula, and the Modigliani–Miller theorems all rest on the assumption that arbitrage opportunities do not persist.