Arbitrage

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In economics and finance, arbitrage is the practice of taking advantage of a price differential between two or more markets: a combination of matching deals are struck that capitalize upon the imbalance, the profit being the difference between the market prices. When used by academics, an arbitrage is a 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, a risk-free profit. A person who engages in arbitrage is called an arbitrageur. The term is mainly applied to trading in financial instruments, such as bonds, stocks, derivatives, commodities and currencies.

If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium or arbitrage-free market. An arbitrage equilibrium is a precondition for a general economic equilibrium. The assumption that there is no arbitrage is used in quantitative finance to calculate a unique risk neutral price for derivatives.

Statistical arbitrage is an imbalance in expected nominal values. A casino has a statistical arbitrage in almost every game of chance that it offers - referred to as the house edge or house advantage or even the Vigorish.

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[edit] Conditions for arbitrage

Arbitrage is possible when one of three conditions is met:

  1. The same asset does not trade at the same price on all markets ("the law of one price").
  2. Two assets with identical cash flows do not trade at the same price.
  3. 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 does not have negligible 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 only possible with securities and financial products which can be traded electronically.

In the most simple 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:

P(V_T \geq 0) = 1 and P(V_T \neq 0) > 0

where Vt means a portfolio at time t.

[edit] Examples

  • Suppose that the exchange rates (after taking out the fees for making the exchange) in London are £5 = $10 = ¥1000 and the exchange rates in Tokyo are ¥1000 = £6 = $12. Converting ¥1000 to $12 in Tokyo and converting that $12 into ¥1200 in London, for a profit of ¥200, would be arbitrage. In reality, this "triangle arbitrage" is so simple that it almost never occurs. But more complicated foreign exchange arbitrages, such as the spot-forward arbitrage (see interest rate parity) are much more common.
  • A common arbitrage involves borrowing at lower short term rates and investing at higher long term interest rates while pocketing the spread. The risk is that short term loan rates rise higher.
  • One example of arbitrage involves the New York Stock Exchange and the Chicago Mercantile Exchange. When the price of a stock on the NYSE and its corresponding futures contract on the CME are out of sync, one can buy the less expensive one and sell it to the more expensive market. Because the differences between the prices are likely to be small (and not to last very long), this can only be done profitably with computers examining a large number of prices and automatically exercising a trade when the prices are far enough out of balance. The activity of other arbitrageurs can make this risky. Those with the fastest computers and the smartest mathematicians take advantage of series of small differentials that would not be profitable if taken individually.
  • Economists use the term "global labor arbitrage" to refer to the tendency of manufacturing jobs to flow towards whichever country has the lowest wages per unit output at present and has reached the minimum requisite level of political and economic development to support industrialization. At present, many such jobs appear to be flowing towards China, though some which require command of English are going to India and the Philippines. In popular terms, this is referred to as offshoring. (Note that "offshoring" is not synonymous with "outsourcing", which means "to subcontract from an outside supplier or source", such as when a business outsources its bookkeeping to an accounting firm. Unlike offshoring, outsourcing always involves subcontracting jobs to a different company, and that company can be in the same country as the outsourcing company.)
  • Sports arbitrage - numerous internet bookmakers offer odds on the outcome of the same event. Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books. However, in order to remain competitive their margins are usually quite low. Different bookmakers may offer different odds on the same outcome of a given event; by taking the best odds offered by each bookmaker, a customer can under some circumstances cover all possible outcomes of the event and lock a small risk-free profit, known as a Dutch book. This profit would typically be between 1% and 5% but can be much higher. One problem with sports arbitrage is that bookmakers sometimes make mistakes and this can lead to an invocation of the 'palpable error' rule, which most bookmakers invoke when they have made a mistake by offering or posting incorrect odds. As bookmakers become more proficient, the odds of making an 'arb' usually last for less than an hour and typically only a few minutes. Furthermore, huge bets on one side of the market also alert the bookies to correct the market.
  • Exchange-traded fund arbitrage - Exchange Traded Funds allow authorized participants to exchange back and forth between shares in underlying securities held by the fund and shares in the fund itself, rather than allowing the buying and selling of shares in the ETF directly with the fund sponsor. ETFs trade in the open market, with prices set by market demand. An ETF may trade at a premium or discount to the value of the underlying assets. When a significant enough premium appears, an arbitrageur will buy the underlying securities, convert them to shares in the ETF, and sell them in the open market. When a discount appears, an arbitrageur will do the reverse. In this way, the arbitrageur makes a low-risk profit, while fulfilling a useful function in the ETF marketplace by keeping ETF prices in line with their underlying value.
  • Some types of hedge funds make use of a modified form of arbitrage to profit. Rather than exploiting price differences between identical assets, they will purchase and sell securities, assets and derivatives with similar characteristics, and hedge any significant differences between the two assets. Any difference between the hedged positions represents any remaining risk (such as basis risk) plus profit; the belief is that there remains some difference which, even after hedging most risk, represents pure profit. For example, a fund may see that there is a substantial difference between U.S. dollar debt and local currency debt of a foreign country, and enter into a series of matching trades (including currency swaps) to arbitrage the difference, while simultaneously entering into credit default swaps to protect against country risk and other types of specific risk.

[edit] Price convergence

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 to the same prices, in all markets, in each category. The speed at which prices converge is a measure of market efficiency. 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 markets.

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, and 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 for the exported cars. Both actions would increase demand for US Dollars, and supply of Canadian Dollars, and as a result, there would be an appreciation of the US Dollar. Eventually, if unchecked, this would make US cars more expensive for all buyers, and Canadian cars cheaper, until there is no longer an incentive to buy cars in the US and sell them in Canada. More generally, international arbitrage opportunities in commodities, goods, securities and currencies, on a grand scale, tend to change exchange rates until the purchasing power is equal.

In reality, of course, one must consider taxes and the costs of travelling back and forth between the US and Canada. Also, the features built into the cars sold in the US are not exactly the same as the features built into the cars for sale in Canada, due, among other things, to the different emissions and other auto regulations in the two countries. In addition, our example assumes that no duties have to be paid on importing or exporting cars from the USA to Canada. Similarly, most assets exhibit (small) differences between countries, 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 depreciations in the currencies, relative to each other (see interest rate parity).

[edit] Risks

Arbitrage transactions in modern securities markets involve fairly low risks. 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. There is also counter-party risk, that the other party to one of the deals fails to deliver as agreed; though unlikely, this hazard is serious because of the large quantities one must trade in order to make a profit on small price differences. These risks become magnified when leverage or borrowed money is used.

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. In the extreme case this is risk arbitrage, described below. In comparison to the classical quick arbitrage transaction, such an operation can produce disastrous losses.

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 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 the 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 Michael Milken and Ivan Boesky.

[edit] Types of arbitrage

[edit] Merger arbitrage

Also called risk arbitrage, merger arbitrage generally consists of buying 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.

[edit] 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.

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 [1] or SIFMA(Security Industry and Financial Markets Association)[2] (merged with and preceded by BMA (short for Bond Market Association]) [3]). 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 U.S. dollars. 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.

[edit] Convertible bond arbitrage

A convertible bond is a bond that 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 a corporate bond with a stock call option attached to it.

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

  • 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.

[edit] Depository receipts

A depository 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 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 Depositary Receipt) depending on where they are issued, are typically considered "foreign" and therefore trade at a lower value when first released. However, they are exchangeable into the original security (known as fungibility) and actually have the same value. In this case there is a spread between the perceived value and real value, which can be extracted. 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 you can hedge that risk.

[edit] Regulatory arbitrage

Regulatory arbitrage is where a regulated institution takes advantage of the difference between its real (or economic) risk and the regulatory position. For example, if a bank, operating under the Basel I accord, has to hold 8% capital against default risk, but the real risk of default is lower, it is profitable to securitise the 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.

This process can increase the overall riskiness of institutions under a risk insensitive regulatory regime, as described by Alan Greenspan in his October 1998 speech on The Role of Capital in Optimal Banking Supervision and Regulation.

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, an insurance company may choose to locate in Bermuda due 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.

[edit] Telecom arbitrage

Main article: International telecommunications routes

Telecom arbitrage companies allow mobile phone users to make international calls for free through certain access numbers. The telecommunication arbitrage companies get paid an interconnect charge by the UK mobile networks and then buy international routes at a lower cost. The calls are seen as free by the UK contract mobile phone customers since they are using up their allocated monthly minutes rather than paying for additional calls. The end effect is telecom arbitrage. This is usually marketed as "free international calls". The profit margins are usually very small. However, with enough volume, enough money is made from the cost difference to turn a profit.

[edit] The debacle of Long-Term Capital Management

Main article: Long-Term Capital Management

Long-Term Capital Management (LTCM) lost 4.6 billion U.S. dollars in fixed income arbitrage in September 1998. LTCM had attempted to make money on the price difference between different bonds. For example, it would sell U.S. Treasury securities and buy Italian bond futures. The concept was that because Italian bond futures had a less liquid market, in the short term Italian bond futures would have a higher return than U.S. bonds, but in the long term, the prices would converge. Because the difference was small, a large amount of money had to be borrowed to make the buying and selling profitable.

The downfall in this system began on August 17, 1998, when Russia defaulted on its ruble debt and domestic dollar debt. Because the markets were already nervous due to the Asian financial crisis, investors began selling non-U.S. treasury debt and buying U.S. treasuries, which were considered a safe investment. As a result the return on U.S. treasuries began decreasing because there were many buyers, and the return on other bonds began to increase because there were many sellers. This caused the difference between the returns of U.S. treasuries and other bonds to increase, rather than to decrease as LTCM was expecting. Eventually this caused LTCM to fold, and their creditors had to arrange a bail-out. More controversially, officials of the Federal Reserve assisted in the negotiations that led to this bail-out, on the grounds that so many companies and deals were intertwined with LTCM that if LTCM actually failed, they would as well, causing a collapse in confidence in the economic system. Thus LTCM failed as a fixed income arbitrage fund, although it is unclear what sort of profit was realized by the banks that bailed LTCM out.

[edit] Etymology

"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 is first defined in 1704 by Mathieu de la Porte in his treatise "La science des négocians et teneurs de livres" as a consideration of different exchange rates to recognize the most profitable places of issuance and settlement for a bill of exchange ("L'arbitrage est une combinaison que l’on fait de plusieurs changes, pour connoitre [connaître, in modern spelling] quelle place est plus avantageuse pour tirer et remettre"). See "Arbitrage" in Trésor de la Langue Française.

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