An arbitrage is a type of transaction. Actually, the term is applied to two very different types of transactions, which are explained below. In either case, the act of trading into and out of such transactions is called arbitrage, so the term is both a noun and a verb. Someone who engages in such trading is an arbitrager.
In finance theory, an arbitrage is a “free lunch”—a trading strategy that can profit without cost or risk. Suppose a futures contract trades on two different exchanges. If, at one point in time, the contract is bid at USD 45.02 on one exchange and offered at USD 45.00 on the other, a trader could purchase the contract at one price, sell it at the other, and make a risk-free profit of a USD 0.02.
Such opportunities reflect minor pricing discrepancies between markets or related instruments. Per-transaction profits tend to be small, and they can be consumed entirely by transaction costs. Accordingly, most arbitrage is performed by institutions that have low transaction costs and can make up for small profit margins by doing a large volume of transactions.
Formally, theoreticians define an arbitrage as a trading strategy that requires the investment of no capital, cannot lose money, and has a positive probability of making money.
Turning now to the second use of the term, this is unrelated to finance theory. But it has been in wide use for several decades, so it is fairly standard. According to this usage, an arbitrage is a leveraged speculative transaction.
During the 1980s, junk bond financing funded an overheated mergers and acquisitions market. Speculators took leveraged equity positions either in anticipation of takeovers or to put firms in play. They also engaged in greenmail. Such activities were called arbitrage. Ivan Boesky was a famous arbitrager from this period who was ultimately convicted of insider trading.
To distinguish between the two definitions of arbitrage, we might call them “true” and “speculative”. In a sense they represent two ends of a spectrum. In practice, true arbitrage is rare. Almost every transaction entails some risk—perhaps due to liquidity, the timing of offsetting transactions, or perhaps some credit exposure. If ”true” arbitrages become increasingly complicated or sophisticated, the subtle risks multiply. From there, it is a slippery slope to “speculative” arbitrage.
The notion of true arbitrage is profoundly important in financial engineering and theoretical finance. Much of the theory of asset valuation is based on the assumption that equilibrium prices must be set in a consistent manner that affords no true arbitrage between them. See the article on arbitrage-free pricing.
In practice, people don’t write about true or speculative arbitrage. They just write about arbitrage. It is up to the reader to infer from context which type the author is referring to. In a theoretical or financial engineering context, this is usually true arbitrage. In a trading or portfolio management context, it is usually speculative arbitrage. In a risk management context, it could be either.
People from fields other than finance or economics sometimes confuse the two forms of arbitrage. I once helped a professor from an unrelated field who was writing a paper that mentioned arbitrage. He had read about the profound importance of arbitrage in finance theory but thought this referred to the speculative arbitrage he had read about in books on hedge funds. Journalists often confuse the two. A former colleague once commented about journalists who “write about [true] arbitrage as if it were something unconscionable.”