An arbitrage is a certain type of transaction or portfolio. Actually, the term is used in two different ways, so it refers to either of two very different types of transactions or portfolios. This article explains both. People also speak of arbitrage as an activity—the activity of seeking out and implementing either of the two types of arbitrage opportunities. An arbitrageur is an individual or institution who engages in one or the other form of arbitrage.">
Arbitrage
Explained:
arbitrage
arbitrage free
arbitrageur
no arbitrage
condition
statistical arbitrage
An
arbitrage is a
type of transaction or portfolio. Actually, the term is used in two
different ways, so it refers to either of two very different types of
transactions or portfolios. People also speak of
arbitrage as an activity—the activity of seeking out and implementing either of
the two types of arbitrage transactions or portfolios. An
arbitrageur
is an individual or institution who engages in such
arbitrage.
In finance theory, an arbitrage is a
"free lunch"—a transaction or portfolio that makes a profit without
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 and sell it at the other to make
a risk-free profit of a USD 0.02.
Such arbitrage 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 very 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
arbitrage, it is a usage that is shunned by theoretical purists. However, 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 or portfolio.
During the 1980s,
junk bond financing funded an overheated mergers and
acquisitions market. Arbitragers of this period were speculators who took
leveraged equity positions either in anticipation of a possible takeover or to
put a firm in play. They also engaged in greenmail. Ivan
Boesky was a famous arbitrager from this period who was ultimately convicted
of insider trading.
Today, the label arbitrage is often applied to the speculative
trading strategies associated with hedge funds. These include
statistical
arbitrage,
merger arbitrage,
fixed income
arbitrage, and
convertible
arbitrage.
To distinguish between the two definitions of arbitrage, we
might call them "true" arbitrage and "speculative" arbitrage.
They are different, but in a sense they represent two ends of a spectrum. In
practice, true arbitrage is rare. There is always some
risk—perhaps due to liquidity, the timing
of offsetting transactions, or perhaps some credit
exposure. If these "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. A market is said to have no arbitrage—or be arbitrage free—if prices in that market offer no arbitrage opportunities. This is a theoretical
condition that is usually assumed by economic and financial models. Much of the theory of asset valuation is based
on the assumption that prices must be set in a consistent manner that affords no
true arbitrage between them. This is called
arbitrage-free pricing. A market in equilibrium must be arbitrage free.
In practice, people don't write about true arbitrage or
speculative arbitrage. They just write about arbitrage. It is up to the reader
to infer from context what type of arbitrage is being referred 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—ask.
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 was
referring to the speculative arbitrage he had read about in books on hedge
funds. Journalists are notorious for confusing the two. A former colleague, Kin
Tam, once commented to me that journalists "write about [true] arbitrage as if it were
something unconscionable."
statistical 
