Arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more
marketsstriking a combination of matching deals to capitalize on the difference, the profit being the difference between the
market price
A price is the (usually not negative) quantity of payment or compensation expected, required, or given by one party to another in return for goods or services. In some situations, especially when the product is a service rather than a phy ...
s at which the unit is
trade
Trade involves the transfer of goods and services from one person or entity to another, often in exchange for money. Economists refer to a system or network that allows trade as a market.
Traders generally negotiate through a medium of cr ...
d. Arbitrage has the effect of causing prices of the same or very similar assets in different markets to converge.
When used by academics in
economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
, an arbitrage is a transaction that involves no negative
cash flow
Cash flow, in general, refers to payments made into or out of a business, project, or financial product. It can also refer more specifically to a real or virtual movement of money.
*Cash flow, in its narrow sense, is a payment (in a currency), es ...
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 opportunity is present when there is the possibility 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
In finance, statistical arbitrage (often abbreviated as Stat Arb or StatArb) is a class of short-term financial trading strategies that employ Mean reversion (finance), mean reversion models involving broadly diversified portfolios of securities (h ...
, it may refer to ''expected'' profit, though losses may occur, and in practice, there are always
risks
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environ ...
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 trade
Convergence trade is a trading strategy consisting of two positions: buying one asset forward—i.e., for delivery in future (going ''long'' the asset)—and selling a similar asset forward (going '' short'' the asset) for a higher price, in the e ...
s), as in
merger arbitrage
Risk arbitrage, also known as merger arbitrage, is an investment strategy that speculates on the successful completion of mergers and acquisitions. An investor that employs this strategy is known as an arbitrageur. Risk arbitrage is a type of eve ...
.
The term is mainly applied in the
financial field. People who engage in arbitrage are called arbitrageurs ().
Etymology
"Arbitrage" is a French word and denotes a decision by an arbitrator or arbitration tribunal (in modern French, "" usually means
referee
A referee is an official, in a variety of sports and competition, responsible for enforcing the rules of the sport, including sportsmanship decisions such as ejection. The official tasked with this job may be known by a variety of other title ...
or
umpire
An umpire is an official in a variety of sports and competition, responsible for enforcing the rules of the sport, including sportsmanship decisions such as ejection.
The term derives from the Old French , , and , : (as evidenced in cricke ...
). It was first defined as a financial term in 1704 by French mathematician
Mathieu de la Porte
Mathieu de la Porte (Nijmegen, 17th century - 1722) was a French mathematician.
Life
De la Porte was the son of a French merchant who had moved to the Netherlands. He moved back to France when he was 18 and recanted the Protestant faith. He ...
in his treatise "" as a consideration of different exchange rates to recognise the most profitable places of issuance and settlement for a bill of exchange ("
in modern spelling".)
Arbitrage equilibrium
If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium, or an arbitrage-free market. An arbitrage equilibrium is a precondition for a
general economic equilibrium. The '
no-arbitrage assumption
In financial mathematics, no-arbitrage bounds are mathematical relationships specifying limits on financial portfolio prices. These price bounds are a specific example of good–deal bounds, and are in fact the greatest extremes for good–deal ...
' is used in
quantitative finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field.
In general, there exist two separate branches of finance that requ ...
to calculate a unique
risk neutral
In economics and finance, risk neutral preferences are preference (economics), preferences that are neither risk aversion, risk averse nor risk seeking. A risk neutral party's decisions are not affected by the degree of uncertainty in a set of out ...
price for
derivatives.
Arbitrage-free pricing approach for bonds
Arbitrage-free pricing for bonds is the method of valuing a coupon-bearing financial instrument by
discounting its future cash flows by multiple discount rates. By doing so, a more accurate price can be obtained than if the price is calculated with a present-value pricing approach. Arbitrage-free pricing is used for bond valuation and to detect arbitrage opportunities for investors.
For the purpose of valuing the price of a bond, its cash flows can each be thought of as packets of incremental cash flows with a large packet upon maturity, being the principal. Since the cash flows are dispersed throughout future periods, they must be discounted back to the present. In the present-value approach, the cash flows are discounted with one discount rate to find the price of the bond. In arbitrage-free pricing, multiple discount rates are used.
The present-value approach assumes that the bond yield will stay the same until maturity. This is a simplified model because interest rates may fluctuate in the future, which in turn affects the yield on the bond. For this reason, the discount rate may differ for each cash flow. Each cash flow can be considered a zero-coupon instrument that pays one payment upon maturity. The discount rates used should be the rates of multiple zero-coupon bonds with maturity dates the same as each cash flow and similar risk as the instrument being valued. By using multiple discount rates, the arbitrage-free price is the sum of the discounted cash flows. Arbitrage-free price refers to the price at which no price arbitrage is possible.
The idea of using multiple discount rates obtained from zero-coupon bonds and discounting a similar bond's cash flow to find its price is derived from the yield curve, which is a curve of the yields of the same bond with different maturities. This curve can be used to view trends in market expectations of how interest rates will move in the future. In arbitrage-free pricing of a bond, a yield curve of similar zero-coupon bonds with different maturities is created. If the curve were to be created with Treasury securities of different maturities, they would be stripped of their coupon payments through bootstrapping. This is to transform the bonds into zero-coupon bonds. The yield of these zero-coupon bonds would then be plotted on a diagram with time on the ''x''-axis and yield on the ''y''-axis.
Since the yield curve displays market expectations on how yields and interest rates may move, the arbitrage-free pricing approach is more realistic than using only one discount rate. Investors can use this approach to value bonds and find price mismatches, resulting in an arbitrage opportunity. If a bond valued with the arbitrage-free pricing approach turns out to be priced higher in the market, an investor could have such an opportunity:
#Investor
shorts
Shorts are a garment worn over the pelvic area, circling the waist and splitting to cover the upper part of the legs, sometimes extending down to the knees but not covering the entire length of the leg. They are called "shorts" because they ar ...
the bond at price at time t
1.
#Investor
longs the zero-coupon bonds making up the related yield curve and strips and sells any coupon payments at t
1.
#As t>t
1, the price spread between the prices will decrease.
#At maturity, the prices will converge and be equal. Investor exits both the long and short positions, realising a profit.
If the outcome from the valuation were the reverse 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. The prices of the bonds in t
1 move closer together to finally become the same at t
T.
Conditions for arbitrage
Arbitrage may take place when:
* 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
In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee.See "Time Value", "Discount", "Discount Yield", "Compound Interest", "Effi ...
at the
risk-free interest rate
The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations.
Since the risk-free r ...
(or the asset has significant costs of storage; so this condition holds true for something like grain but not for
securities
A security is a tradable financial asset. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any for ...
).
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 in 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 an 'execution risk' referred to as 'leg risk'.
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 is 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
Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assu ...
, particularly
§ arbitrage mechanics, for further discussion.
Mathematically it is defined as follows:
: