In economics and finance, arbitrage (US: /ˈɑːrbɪtrɑːʒ/, UK: /ˈɑːbɪtrɪdʒ/, UK: /ˌɑːbɪˈtrɑːʒ/) is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices. When used by academics, an arbitrage is a (imagined, hypothetical, thought experiment) transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage is present when there is the opportunity to instantaneously buy something for a low price and sell it for a higher price. In principle and in academic use, an arbitrage is risk-free; in common use, as in statistical arbitrage, it may refer to expected profit, though losses may occur, and in practice, there are always risks in arbitrage, some minor (such as fluctuation of prices decreasing profit margins), some major (such as devaluation of a currency or derivative). In academic use, an arbitrage involves taking advantage of differences in price of a single asset or identical cash-flows; in common use, it is also used to refer to differences between similar assets (relative value or convergence trades), as in merger arbitrage. People who engage in arbitrage are called arbitrageurs /ˌɑːrbɪtrɑːˈʒɜːr/—such as a bank or brokerage firm. The term is mainly applied to trading in financial instruments, such as bonds, stocks, derivatives, commodities and currencies.
1 Etymology 2 Arbitrage-free 3 Arbitrage-free pricing approach for bonds 4 Conditions for arbitrage 5 Price convergence 6 Risks
6.1 Execution risk 6.2 Mismatch 6.3 Counterparty risk 6.4 Liquidity risk
7 Types of arbitrage
7.1 Spatial arbitrage
7.2 Merger arbitrage
7.3 Municipal bond arbitrage
8 The fall of Long-Term Capital Management 9 See also
9.1 Types of financial arbitrage 9.2 Related concepts
10 Notes 11 References 12 External links
"Arbitrage" is a French word and denotes a decision by an arbitrator
or arbitration tribunal. (In modern French, "arbitre" usually means
referee or umpire.) In the sense used here, it was first defined in
Mathieu de la Porte
Investor goes short the bond at price at time t1. Investor goes long the zero-coupon bonds making up the related yield curve and strip and sell any coupon payments at t1. As t>t1 the price spread between the prices will decrease. At maturity the prices will converge and be equal. Investor exits both the long and short position, realizing a profit.
If the outcome from the valuation were the reversed case, the opposite positions would be taken in the bonds. This arbitrage opportunity comes from the assumption that the prices of bonds with the same properties will converge upon maturity. This can be explained through market efficiency, which states that arbitrage opportunities will eventually be discovered and corrected accordingly. The prices of the bonds in t1 move closer together to finally become the same at tT. Conditions for arbitrage Arbitrage is possible when one of three conditions is met:
The same asset does not trade at the same price on all markets ("the law of one price"). Two assets with identical cash flows do not trade at the same price. An asset with a known price in the future does not today trade at its future price discounted at the risk-free interest rate (or, the asset has significant costs of storage; as such, for example, this condition holds for grain but not for securities).
Arbitrage is not simply the act of buying a product in one market and selling it in another for a higher price at some later time. The transactions must occur simultaneously to avoid exposure to market risk, or the risk that prices may change on one market before both transactions are complete. In practical terms, this is generally possible only with securities and financial products that can be traded electronically, and even then, when each leg of the trade is executed the prices in the market may have moved. Missing one of the legs of the trade (and subsequently having to trade it soon after at a worse price) is called 'execution risk' or more specifically 'leg risk'.[note 1] In the simplest example, any good sold in one market should sell for the same price in another. Traders may, for example, find that the price of wheat is lower in agricultural regions than in cities, purchase the good, and transport it to another region to sell at a higher price. This type of price arbitrage is the most common, but this simple example ignores the cost of transport, storage, risk, and other factors. "True" arbitrage requires that there be no market risk involved. Where securities are traded on more than one exchange, arbitrage occurs by simultaneously buying in one and selling on the other. See rational pricing, particularly § arbitrage mechanics, for further discussion. Mathematically it is defined as follows:
≥ 0 ) = 1
≠ 0 ) > 0
displaystyle P(V_ t geq 0)=1 text and P(V_ t neq 0)>0,
displaystyle V_ 0 =0
displaystyle V_ t
denotes the portfolio value at time t.
Arbitrage has the effect of causing prices in different markets to
converge. As a result of arbitrage, the currency exchange rates, the
price of commodities, and the price of securities in different markets
tend to converge. The speed at which they do so is a measure of
Arbitrage tends to reduce price discrimination by
encouraging people to buy an item where the price is low and resell it
where the price is high (as long as the buyers are not prohibited from
reselling and the transaction costs of buying, holding and reselling
are small relative to the difference in prices in the different
Arbitrage moves different currencies toward purchasing power parity.
As an example, assume that a car purchased in the United States is
cheaper than the same car in Canada. Canadians would buy their cars
across the border to exploit the arbitrage condition. At the same
time, Americans would buy US cars, transport them across the border,
then sell them in Canada. Canadians would have to buy American dollars
to buy the cars and Americans would have to sell the Canadian dollars
they received in exchange. Both actions would increase demand for US
dollars and supply of Canadian dollars. As a result, there would be an
appreciation of the US currency. This would make US cars more
expensive and Canadian cars less so until their prices were similar.
On a larger scale, international arbitrage opportunities in
commodities, goods, securities and currencies tend to change exchange
rates until the purchasing power is equal.
In reality, most assets exhibit some difference between countries.
These, transaction costs, taxes, and other costs provide an impediment
to this kind of arbitrage. Similarly, arbitrage affects the difference
in interest rates paid on government bonds issued by the various
countries, given the expected depreciation in the currencies relative
to each other (see interest rate parity).
Arbitrage transactions in modern securities markets involve fairly low
day-to-day risks, but can face extremely high risk in rare
situations, particularly financial crises, and can lead to
bankruptcy. Formally, arbitrage transactions have negative skew –
prices can get a small amount closer (but often no closer than 0),
while they can get very far apart. The day-to-day risks are generally
small because the transactions involve small differences in price, so
an execution failure will generally cause a small loss (unless the
trade is very big or the price moves rapidly). The rare case risks are
extremely high because these small price differences are converted to
large profits via leverage (borrowed money), and in the rare event of
a large price move, this may yield a large loss.
The main day-to-day risk is that part of the transaction fails –
execution risk. The main rare risks are counterparty risk and
liquidity risk – that a counterparty to a large transaction or many
transactions fails to pay, or that one is required to post margin and
does not have the money to do so.
In the academic literature, the idea that seemingly very low risk
arbitrage trades might not be fully exploited because of these risk
factors and other considerations is often referred to as limits to
Generally it is impossible to close two or three transactions at the
same instant; therefore, there is the possibility that when one part
of the deal is closed, a quick shift in prices makes it impossible to
close the other at a profitable price. However, this is not
necessarily the case. Many exchanges and inter-dealer brokers allow
multi legged trades (e.g. basis block trades on LIFFE).
Competition in the marketplace can also create risks during arbitrage
transactions. As an example, if one was trying to profit from a price
discrepancy between IBM on the NYSE and IBM on the London Stock
Exchange, they may purchase a large number of shares on the NYSE and
find that they cannot simultaneously sell on the LSE. This leaves the
arbitrageur in an unhedged risk position.
In the 1980s, risk arbitrage was common. In this form of speculation,
one trades a security that is clearly undervalued or overvalued, when
it is seen that the wrong valuation is about to be corrected by
events. The standard example is the stock of a company, undervalued in
the stock market, which is about to be the object of a takeover bid;
the price of the takeover will more truly reflect the value of the
company, giving a large profit to those who bought at the current
price—if the merger goes through as predicted. Traditionally,
arbitrage transactions in the securities markets involve high speed,
high volume and low risk. At some moment a price difference exists,
and the problem is to execute two or three balancing transactions
while the difference persists (that is, before the other arbitrageurs
act). When the transaction involves a delay of weeks or months, as
above, it may entail considerable risk if borrowed money is used to
magnify the reward through leverage. One way of reducing this risk is
through the illegal use of inside information, and in fact risk
arbitrage with regard to leveraged buyouts was associated with some of
the famous financial scandals of the 1980s such as those involving
“ Markets can remain irrational far longer than you or I can remain solvent. ”
— John Maynard Keynes
Arbitrage trades are necessarily synthetic, leveraged trades, as they
involve a short position. If the assets used are not identical (so a
price divergence makes the trade temporarily lose money), or the
margin treatment is not identical, and the trader is accordingly
required to post margin (faces a margin call), the trader may run out
of capital (if they run out of cash and cannot borrow more) and be
forced to sell these assets at a loss even though the trades may be
expected to ultimately make money. In effect, arbitrage traders
synthesize a put option on their ability to finance themselves.
Prices may diverge during a financial crisis, often termed a "flight
to quality"; these are precisely the times when it is hardest for
leveraged investors to raise capital (due to overall capital
constraints), and thus they will lack capital precisely when they need
Types of arbitrage
Also known as geographical arbitrage, this is the simplest form of
arbitrage. In spatial arbitrage, an arbitrageur looks for price
differences between geographically separate markets. For example,
there may be a bond dealer in Virginia offering a bond at 100-12/23
and a dealer in Washington bidding 100-15/23 for the same bond. For
whatever reason, the two dealers have not spotted the difference in
the prices, but the arbitrageur does. The arbitrageur immediately buys
the bond from the Virginia dealer and sells it to the Washington
Also called risk arbitrage, merger arbitrage generally consists of
buying/holding the stock of a company that is the target of a takeover
while shorting the stock of the acquiring company.
Usually the market price of the target company is less than the price
offered by the acquiring company. The spread between these two prices
depends mainly on the probability and the timing of the takeover being
completed as well as the prevailing level of interest rates.
The bet in a merger arbitrage is that such a spread will eventually be
zero, if and when the takeover is completed. The risk is that the deal
"breaks" and the spread massively widens.
Municipal bond arbitrage
Also called municipal bond relative value arbitrage, municipal
arbitrage, or just muni arb, this hedge fund strategy involves one of
two approaches. The term "arbitrage" is also used in the context of
the Income Tax Regulations governing the investment of proceeds of
municipal bonds; these regulations, aimed at the issuers or
beneficiaries of tax-exempt municipal bonds, are different and,
instead, attempt to remove the issuer's ability to arbitrage between
the low tax-exempt rate and a taxable investment rate.
Generally, managers seek relative value opportunities by being both
long and short municipal bonds with a duration-neutral book. The
relative value trades may be between different issuers, different
bonds issued by the same entity, or capital structure trades
referencing the same asset (in the case of revenue bonds). Managers
aim to capture the inefficiencies arising from the heavy participation
of non-economic investors (i.e., high income "buy and hold" investors
seeking tax-exempt income) as well as the "crossover buying" arising
from corporations' or individuals' changing income tax situations
(i.e., insurers switching their munis for corporates after a large
loss as they can capture a higher after-tax yield by offsetting the
taxable corporate income with underwriting losses). There are
additional inefficiencies arising from the highly fragmented nature of
the municipal bond market which has two million outstanding issues and
50,000 issuers, in contrast to the Treasury market which has 400
issues and a single issuer.
Second, managers construct leveraged portfolios of AAA- or AA-rated
tax-exempt municipal bonds with the duration risk hedged by shorting
the appropriate ratio of taxable corporate bonds. These corporate
equivalents are typically interest rate swaps referencing Libor or
SIFMA  . The arbitrage manifests itself in the form of a
relatively cheap longer maturity municipal bond, which is a municipal
bond that yields significantly more than 65% of a corresponding
taxable corporate bond. The steeper slope of the municipal yield curve
allows participants to collect more after-tax income from the
municipal bond portfolio than is spent on the interest rate swap; the
carry is greater than the hedge expense. Positive, tax-free carry from
muni arb can reach into the double digits. The bet in this municipal
bond arbitrage is that, over a longer period of time, two similar
instruments—municipal bonds and interest rate swaps—will correlate
with each other; they are both very high quality credits, have the
same maturity and are denominated in the same currency. Credit risk
and duration risk are largely eliminated in this strategy. However,
basis risk arises from use of an imperfect hedge, which results in
significant, but range-bound principal volatility. The end goal is to
limit this principal volatility, eliminating its relevance over time
as the high, consistent, tax-free cash flow accumulates. Since the
inefficiency is related to government tax policy, and hence is
structural in nature, it has not been arbitraged away.
Note, however, that many municipal bonds are callable, and that this
imposes substantial additional risks to the strategy.
interest rate. When rates move higher, the bond part of a convertible bond tends to move lower, but the call option part of a convertible bond moves higher (and the aggregate tends to move lower). stock price. When the price of the stock the bond is convertible into moves higher, the price of the bond tends to rise. credit spread. If the creditworthiness of the issuer deteriorates (e.g. rating downgrade) and its credit spread widens, the bond price tends to move lower, but, in many cases, the call option part of the convertible bond moves higher (since credit spread correlates with volatility).
Given the complexity of the calculations involved and the convoluted
structure that a convertible bond can have, an arbitrageur often
relies on sophisticated quantitative models in order to identify bonds
that are trading cheap versus their theoretical value.
Convertible arbitrage consists of buying a convertible bond and
hedging two of the three factors in order to gain exposure to the
third factor at a very attractive price.
For instance an arbitrageur would first buy a convertible bond, then
sell fixed income securities or interest rate futures (to hedge the
interest rate exposure) and buy some credit protection (to hedge the
risk of credit deterioration). Eventually what he'd be left with is
something similar to a call option on the underlying stock, acquired
at a very low price. He could then make money either selling some of
the more expensive options that are openly traded in the market or
delta hedging his exposure to the underlying shares.
A depositary receipt is a security that is offered as a "tracking
stock" on another foreign market. For instance, a Chinese company
wishing to raise more money may issue a depository receipt on the New
Covered interest arbitrage
Airline booking ploys
Arbitrage pricing theory
Coherence (philosophical gambling strategy), analogous concept in
^ As an arbitrage consists of at least two trades, the metaphor is of putting on a pair of pants, one leg (trade) at a time. The risk that one trade (leg) fails to execute is thus 'leg risk'.
^ See "Arbitrage" in Trésor de la Langue Française.
Arbitrage – Knowledge Base". www.corespreads.com. Retrieved
^ a b c Mahdavi Damghani, Babak (2013). "The Non-Misleading Value of
Inferred Correlation: An Introduction to the Cointelation Model".
Wilmott. 2013 (1): 50–61. doi:10.1002/wilm.10252.
^ Shleifer, Andrei; Vishny, Robert (1997). "The limits of arbitrage".
Journal of Finance. 52: 35–55. CiteSeerX 10.1.1.184.9959 .
^ Xiong, Wei (2001). "Convergence trading with wealth effects".
Journal of Financial Economics. 62 (2): 247–292.
^ Kondor, Peter (2009). "
Greider, William (1997). One World, Ready or Not. Penguin Press.
Look up arbitrage in Wiktionary, the free dictionary.
What is Arbitrage? (About.com)
Arbitrage opportunities in pending merger deals
in the U.S. market
Information on arbitrage in dual-listed companies on the website of
Mathijs A. van Dijk.
What is Regulatory Arbitrage. Regulatory
Arbitrage after the Basel ii
framework and the 8th Company Law Directive of the European Union.
Institute for Arbitrage.