) is the practice of taking advantage of a price difference between two or moremarkets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between themarket pricesat which the unit istraded. When used by academics, an arbitrage is a transaction that involves no negativecash flowat 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 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 instatistical arbitrage, it may refer toexpectedprofit, though losses may occur, and in practice, there are alwaysrisksin 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 asingleasset oridenticalcash-flows; in common use, it is also used to refer to differences betweensimilarassets (relative valueorconvergence trades), as inmerger arbitrage.

People who engage in arbitrage are calledarbitrageurs/ːrbɪtrːʒɜːr/such as a bank or brokerage firm. The term is mainly applied to trading infinancial instruments, such asbondsstocksderivativescommoditiesandcurrencies.

Arbitrage has the effect of causing prices of the same or very similar assets in different markets to converge.

Arbitrage is a French word and denotes a decision by an arbitrator or arbitration tribunal. (In modern French,arbitreusually meansrefereeorumpire.) In the sense used here, it was first defined in 1704 byMathieu de la Portein his treatiseLa science des ngociants et teneurs de livresas a consideration of different exchange rates to recognise the most profitable places of issuance and settlement for a bill of exchange (Larbitrage est une combinaison que lon fait de plusieurs changes, pour connoitre[connaître, in modern spelling]quelle place est plus avantageuse pour tirer et remettre.)1

If the market prices do not allow for profitable arbitrage, the prices are said to constitute anarbitrage equilibrium, or anarbitrage-freemarket. An arbitrage equilibrium is a precondition for ageneral economic equilibrium. The no arbitrage assumption is used inquantitative financeto calculate a uniquerisk neutralprice forderivatives.2

This refers to 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 yield of the bond 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. The discount rate may be different for each of the cash flows for this reason. 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 thediscounted cash flows. Arbitrage-free price refers to the price at which no price arbitrage is possible.

The ideas of using multiple discount rates obtained from zero-coupon bonds and discount a similar bonds cash flow to find its price is derived from the yield curve. The yield curve 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 thex-axis and yield on they-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 mismatches in prices, 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 goes short the bond at price at time t

Investor goes long the zero-coupon bonds making up the related yield curve and strip and sell any coupon payments at t

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 t1move closer together to finally become the same at tT.

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 pricediscountedat therisk-free interest rate(or, the asset has significant costs of storage; as such, for example, this condition holds for grain but not forsecurities).

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 occursimultaneouslyto 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.Tradersmay, 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.

Seerational pricing, particularly arbitrage mechanics, for further discussion.

Arbitrage has the effect of causing prices in different markets to converge. As a result of arbitrage, the currencyexchange rates, the price ofcommodities, and the price of securities in different markets tend to converge. The speed3at which they do so is a measure of market efficiency. Arbitrage tends to reduceprice discriminationby 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 markets).

Arbitrage moves different currencies towardpurchasing 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 incommodities, goods,securitiesandcurrenciestend to changeexchange ratesuntil thepurchasing poweris equal.

In reality, mostassetsexhibit 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 (seeinterest rate parity).

Arbitrage transactions in modern securities markets involve fairly low day-to-day risks, but can face extremely high risk in rare situations,3particularlyfinancial crises, and can lead tobankruptcy. Formally, arbitrage transactions havenegative 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 vialeverage(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 postmarginand 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 aslimits to arbitrage.456

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 arbitragewas common. In this form ofspeculation, 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 priceif 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 theillegal use of inside information, and in fact risk arbitrage with regard toleveraged buyoutswas associated with some of the famous financial scandals of the 1980s such as those involvingMichael MilkenandIvan Boesky.

Another risk occurs if the items being bought and sold are not identical and the arbitrage is conducted under the assumption that the prices of the items are correlated or predictable; this is more narrowly referred to as aconvergence trade. In the extreme case this is merger arbitrage, described below. In comparison to the classical quick arbitrage transaction, such an operation can produce disastrous losses.

As arbitrages generally involvefuturemovements of cash, they are subject tocounterparty risk: if a counterparty fails to fulfill their side of a transaction. This is a serious problem if one has either a single trade or many related trades with a single counterparty, whose failure thus poses a threat, or in the event of a financial crisis when many counterparties fail. This hazard is serious because of the large quantities one must trade in order to make a profit on small price differences.

For example, if one purchases many risky bonds, then hedges them withCDSes, profiting from the difference between the bond spread and the CDS premium, in a financial crisis the bonds may defaultandthe CDS writer/seller may itself fail, due to the stress of the crisis, causing the arbitrageur to face steep losses.

Arbitrage trades are necessarily synthetic,leveragedtrades, 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 postmargin(faces amargin 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 aput optionon their ability to finance themselves.7

Prices may diverge during a financial crisis, often termed aflight 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 it most.7

Also known asgeographical 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 dealer.

Also calledrisk arbitrage, merger arbitrage generally consists of buying/holding the stock of a company that is the target of atakeoverwhileshortingthe 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.

Also calledmunicipal bond relative value arbitrage,municipal arbitrage, or justmuni 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 issuers 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 incomebuy and holdinvestors 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 byshortingthe appropriate ratio of taxable corporate bonds. These corporate equivalents are typicallyinterest rate swapsreferencingLiboror. 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 municipalyield curveallows 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 instrumentsmunicipal bonds and interest rate swapswill 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.

Aconvertible bondis abondthat an investor can return to the issuing company in exchange for a predetermined number of shares in the company.

A convertible bond can be thought of as acorporate bondwith a stockcall optionattached to it.

The price of a convertible bond is sensitive to three major factors:

. 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).

. When the price of the stock the bond is convertible into moves higher, the price of the bond tends to rise.

. If the creditworthiness of the issuer deteriorates (e.g.ratingdowngrade) 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 arbitrageconsists 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 sellorinterest rate futures(to hedge the interest rate exposure) and buy somecredit protection(to hedge the risk of credit deterioration). Eventually what hed 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 ordelta hedginghis exposure to the underlying shares.

Adepositary receiptis a security that is offered as a tracking stock on another foreign market. For instance, aChinesecompany wishing to raise more money may issue a depository receipt on theNew York Stock Exchange, as the amount of capital on the local exchanges is limited. These securities, known as ADRs (American depositary receipt) or GDRs (global depository receipt) depending on where they are issued, are typically considered foreign and therefore trade at a lower value when first released. Many ADRs are exchangeable into the original security (known asfungibility) and actually have the same value. In this case there is a spread between the perceived value and real value, which can be extracted. Other ADRs that are not exchangeable often have much larger spreads. Since the ADR is trading at a value lower than what it is worth, one can purchase the ADR and expect to make money as its value converges on the original. However, there is a chance that the original stock will fall in value too, so by shorting it one can hedge that risk.

Cross-border arbitrage exploits different prices of the same stock in different countries:

Example:Appleis trading onNASDAQat US$108.84. The stock is also traded on the German electronic exchange,XETRA. If 1 euro costs US$1.11, a cross-border trader could enter a buy order on the XETRA at €98.03 per Apple share and a sell order at €98.07 per share.

Some brokers in Germany do not offer access to the U.S. exchanges. Hence if a German retail investor wants to buy Apple stock, he needs to buy it on the XETRA. The cross-border trader would sell the Apple shares on XETRA to the investor and buy the shares in the same second on NASDAQ. Afterwards, the cross-border trader would need to transfer the shares bought on NASDAQ to the German XETRA exchange, where he is obliged to deliver the stock.

In most cases, the quotation on the local exchanges is done electronically byhigh-frequency traders, taking into consideration the home price of the stock and theexchange rate. This kind of high-frequency trading benefits the public as it reduces the cost to the German investor and enables him to buy U.S. shares.

Adual-listed company(DLC) structure involves two companies incorporated in different countries contractually agreeing to operate their businesses as if they were a single enterprise, while retaining their separate legal identity and existing stock exchange listings. In integrated and efficient financial markets, stock prices of the twin pair should move in lockstep. In practice, DLC share prices exhibit large deviations from theoretical parity. Arbitrage positions in DLCs can be set up by obtaining a long position in the relatively underpriced part of the DLC and a short position in the relatively overpriced part. Such arbitrage strategies start paying off as soon as the relative prices of the two DLC stocks converge toward theoretical parity. However, since there is no identifiable date at which DLC prices will converge, arbitrage positions sometimes have to be kept open for considerable periods of time. In the meantime, the price gap might widen. In these situations, arbitrageurs may receivemargin calls, after which they would most likely be forced to liquidate part of the position at a highly unfavorable moment and suffer a loss. Arbitrage in DLCs may be profitable, but is also very risky.89

A good illustration of the risk of DLC arbitrage is the position inRoyal Dutch Shellwhich had a DLC structure until 2005by the hedge fundLong-Term Capital Management(LTCM, see also the discussion below). Lowenstein (2000)10describes that LTCM established an arbitrage position in Royal Dutch Shell in the summer of 1997, when Royal Dutch traded at an 8 to 10 percent premium. In total, $2.3 billion was invested, half of which was long in Shell and the other half was short in Royal Dutch (Lowenstein, p.99). In the autumn of 1998, large defaults on Russian debt created significant losses for the hedge fund and LTCM had to unwind several positions. Lowenstein reports that the premium of Royal Dutch had increased to about 22 percent and LTCM had to close the position and incur a loss. According to Lowenstein (p.234), LTCM lost $286 million in equitypairs tradingand more than half of this loss is accounted for by theRoyal Dutch Shelltrade. (See further underLimits to arbitrage.)

The market prices for privately held companies are typically viewed from a return on investment perspective (such as 25%), whilst publicly held and or exchange listed companies trade on aPrice to earnings ratio(P/E) (such as a P/E of 10, which equates to a 10%ROI). Thus, if a publicly traded company specialises in the acquisition of privately held companies, from a per-share perspective there is a gain with every acquisition that falls within these guidelines. E.g.,Berkshire HathawayandHalydean Corporation. Private to public equities arbitrage is a term which can arguably be applied toinvestment bankingin general. Private markets to public markets differences may also help explain the overnight windfall gains enjoyed by principals of companies that just did aninitial public offering(IPO).

Regulatory arbitrage is an avoidance strategy of regulation that is exercised as a result of a regulatory inconsistency.11In other words, where a regulated institution takes advantage of the difference between its real (or economic)riskand the regulatory position. For example, if a bank, operating under theBasel Iaccord, has to hold 8% capital againstdefault risk, but the real risk of default is lower, it is profitable tosecuritisethe loan, removing the low risk loan from its portfolio. On the other hand, if the real risk is higher than the regulatory risk then it is profitable to make that loan and hold on to it, provided it is priced appropriately. Regulatory arbitrage can result in parts of entire businesses being unregulated as a result of the arbitrage.

This process can increase the overall riskiness of institutions under a risk insensitive regulatory regime, as described byAlan Greenspanin his October 1998 speech onThe Role of Capital in Optimal Banking Supervision and Regulation.

The term Regulatory Arbitrage was used for the first time in 2005 when it was applied by Scott V. Simpson, a partner at law firm Skadden, Arps, to refer to a new defence tactic in hostile mergers and acquisitions where differing takeover regimes in deals involving multi-jurisdictions are exploited to the advantage of a target company under threat.

In economics, regulatory arbitrage (sometimes, tax arbitrage) may be used to refer to situations when a company can choose a nominal place of business with a regulatory, legal or tax regime with lower costs. For example, aninsurancecompany may choose to locate inBermudadue to preferential tax rates and policies for insurance companies. This can occur particularly where the business transaction has no obvious physical location. In the case of many financial products, it may be unclear where the transaction occurs.

Regulatory arbitrage can include restructuring a bank by outsourcing services such as IT. The outsourcing company takes over the installations, buying out the banks assets and charges a periodic service fee back to the bank. This frees up cashflow usable for new lending by the bank. The bank will have higher IT costs, but counts on the multiplier effect ofmoney creationand the interest rate spread to make it a profitable exercise.

Example: Suppose the bank sells its IT installations for US$40 million. With a reserve ratio of 10%, the bank can create US$400 million in additional loans (there is a time lag, and the bank has to expect to recover the loaned money back into its books). The bank can often lend (and securitize the loan) to the IT services company to cover the acquisition cost of the IT installations. This can be at preferential rates, as the sole client using the IT installation is the bank. If the bank can generate 5% interest margin on the 400 million of new loans, the bank will increase interest revenues by 20 million. The IT services company is free to leverage t