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 advantage, house edge, vigorish or house vigorish.
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.
Mathematically it is defined as follows:
where means a portfolio at time t.
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).
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.
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.
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(Security Industry and Financial Markets Association) (merged with and preceded by BMA (short for Bond Market Association]) ). 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.
The price of a convertible bond is sensitive to three major factors:
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 good illustration of the risk of DLC arbitrage is the position in Royal Dutch Shell - which had a DLC structure until 2005 - by the hedge fund Long-Term Capital Management (LTCM, see also the discussion below). Lowenstein (2000) describes 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 long in Shell and the other half 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 equity pairs trading and more than half of this loss is accounted for by the Royal Dutch Shell trade.
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.
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.
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 price on US treasuries began to increase and the return 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 prices 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.