Arbitrage

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In economics and finance, arbitrage refers to the simultaneous sale and purchase of identical securities or other financial instruments on different markets to take advantage of price differentials for profit. This is also known as a "riskless profit."

Alternatively, arbitrage is attempting to profit by exploiting price differences of identical or similar financial instruments, on different markets or in different forms. The ideal version is riskless arbitrage. Risk arbitrage, also known as "speculation," while technically not true arbitrage also exists in a variety of forms. Arbitrage is not illegal, although the temptation to make easy profit has led some to use confidential information about forthcoming situations for personal gain, an illegal activity known as insider trading.

Arbitrage opportunities are not necessarily available to all, and they are generally short-lived as the transactions affect prices so that the arbitrage opportunity is quickly eliminated. Nevertheless, the idea of profit that is essentially risk-free and requires no apparent work appears attractive to many who continue to seek and exploit arbitrage opportunities. Interestingly, it appears that they also contribute to market efficiency, a benefit to society as a whole.

Contents

Definition

Arbitrage is the simultaneous purchase and sale of an asset in order to profit from a difference in the price. This usually takes place on different exchanges or marketplaces.

For example, a domestic stock may also trade on a foreign exchange in another country, where it has not adjusted for the constantly changing exchange rate. A trader may purchase the stock where it is undervalued and short sell the stock where it is overvalued, thus profiting from the difference.

When the purchase and sale transactions are simultaneous, it may be called riskless profit.

An individual who seeks out and takes advantage of arbitrage opportunities to make profit is known as an arbitrageur.

Since the actions of arbitrageurs influence the market, particularly in takeover situations there is a temptation for parties involved to communicate information about such activities to arbitrageurs in advance of any public announcement. This is known as insider trading and is generally illegal.

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 in economics it was 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 ([U]ne combinaison que l’on fait de plusieurs Changes, pour connoître quelle Place est plus avantageuse pour tirer et remettre).

Conditions of arbitrage

I don't throw darts at a board. I bet on sure things. Read Sun-tzu, The Art of War. Every battle is won before it is ever fought.

These words come from the 1987 movie Wall Street, spoken by Gordon Gekko who makes a fortune as a pioneer of arbitrage.

Arbitrage opportunities exist when the "law of one price" is (temporarily) violated. This "law" states that: "In an efficient market all identical goods must have only one price." This is because all sellers flock to the highest prevailing price, and all buyers to the lowest current market price. In an efficient market the convergence on one price is instant. Under certain conditions, the convergence takes time, during which there exists an arbitrage opportunity.

In the derivatives market the law applies to financial instruments which appear different, but which resolve to the same set of cash flows. Any particular security must have a single price, although it may be created in a number of different ways. For example, if an option can be created using two different sets of underlying securities, then the total price for each would be the same. When they are not the same, an arbitrage opportunity exists.

Arbitrage is possible when one of three conditions is met (Kuepper 2008):

  1. The same asset does not trade at the same price on all markets
  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)

Thus, to summarize: 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, though, this is generally only possible with securities and financial products which can be traded electronically. Such risk-free trading is not available to everyone.

Types of arbitrage

In the world financial community, arbitrage refers to two basic types of activities. One requires little or no risk on the part of the investor, and the other can be highly speculative. As said above, in its purest form, arbitrage contains no element of risk. True arbitrage is a trading strategy that requires no investment of capital, cannot lose money, and the odds favor it making money. Any transaction or portfolio that is risk-free and makes a profit is also considered arbitrage.

The "market makers" (large firms operating on Wall Street, for example) have several advantages over retail traders (Kuepper 2008), including:

  • Great trading capital
  • More skill and experience
  • Instant news
  • More complex computer software
  • Access to the dealing deske

Market makers use complex software to locate arbitrage opportunities constantly. Once found, the differential is typically negligible, and requires a vast amount of capital in order to make a worthwhile profit; retail traders would lose their profit in commission costs. Thus, it is almost impossible for retail traders to compete in most types of arbitrage. Nevertheless, there are other arbitrage opportunities available.

Riskless or “true” arbitrage

Risk-less arbitrage is arbitrage when attempting to profit by exploiting price differences of identical or similar financial instruments, on different markets or in different forms:

A combination of transactions designed to profit from an existing discrepancy among prices, exchange rates, and/or interest rates on different markets without risk of these changing. Simplest is simultaneous purchase and sale of the same thing in different markets (Deardoff 2006).

If an item can be bought for $5, and sold immediately for $20 on a different market, that is arbitrage. The $15 difference represents an arbitrage profit.

Arbitrage of this "One good, Two markets" variety is quite common in the world of sports gambling, since different betting agencies often post different odds on the outcome of a game. There are numerous bookmakers especially on the internet, and they offer a variety of odds on the same event. Any given bookmaker weights their odds so that no single customer can cover all outcomes at a profit. However, different bookmakers may offer different odds on the various outcomes. By taking the best odds offered by each bookmaker a customer may be able to cover all possible outcomes of the event and lock in a (small) risk-free profit.

Several other types of risk-less arbitrage exist (Reverre, 2001):

Inward arbitrage

This form of arbitrage involves rearranging a bank's cash by borrowing from the inter-bank market, and re-depositing the borrowed money locally at a higher interest rate. The bank will make money on the spread between the interest rate on the local currency, and the interest rate on the borrowed currency.

Inward arbitrage works because it allows the bank to borrow at a cheaper rate than it could in the local currency market. For example, assume an American bank goes to the Interbank market to borrow at the lower eurodollar rate, and then deposits those eurodollars at a bank within the U.S. The larger the spread, the more money that can be made.

Outward arbitrage

This form of arbitrage involves the rearrangement of a bank's cash by taking its local currency and depositing it into eurobanks. The interest rate will be higher in the inter-bank market, which will enable the bank to earn more on the interest it receives for the use of its cash.

Outward arbitrage works because it allows the bank to lend for more abroad then it could in the local market. For example, assume an American bank goes to the inter-bank market to lend at the higher eurodollar rate. Money will be shifted from an American bank's branch within the U.S. to a branch located outside of the U.S. The bank will earn revenues on the spread between the two interest rates. The larger the spread, the more will be made.

Triangular arbitrage

This is the process of converting one currency to another, converting it again to a third currency, and finally converting it back to the original currency within a short time span. This opportunity for riskless profit arises when the currency's exchange rates do not exactly match up. Triangular arbitrage opportunities do not happen very often and when they do, they only last for a matter of seconds. Traders that take advantage of this type of arbitrage opportunity usually have advanced computer equipment and/or programs to automate the process.

EXAMPLE: Suppose the following exchange rates exist:

EUR/USD = 0. 8631, EUR/GBP = 1. 4600 and USD/GBP = 1. 6939.

With these exchange rates there is an arbitrage opportunity. For example, starting with $1 million, the following transactions can be made:

  1. Sell dollars for euros: $1 million x 0.8631 = 863,100 euros
  2. Sell euros for pounds: 863,100/1.4600 = 591,164.40 pounds
  3. Sell pounds for dollars: 591,164.40 x 1.6939 =$1,001,373 dollars

These transactions yield an arbitrage profit of $1,373 (assuming no transaction costs or taxes) which is the positive difference between the three “almost” simultaneous transactions leading to $1,001,373, from which one subtracts the original outlay of $1,000,000 to yield of net profit of $1,373.

Risk arbitrage

Risk arbitrage, unlike “true” or risk-less arbitrage, does entail risk. Although considered "speculation," risk arbitrage has become one of the most popular (and retail trader friendly) forms of arbitrage.

EXAMPLE: Corporation A trades trading at $12 per share. Corporation B determines to acquire Corporation A, placing a takeover bid on Corporation A for $16 per share. This means that all shares in Corporation A increase their value to $16 per share, although they are trading at only $12 per share.

Early trades bid the price up to $15 per share. A $1 per share difference still exists—an opportunity for risk arbitrage. The risk lies in the probability that the acquisition might fail to take place, in which case the shares would be worth only the original $12 per share.

Some of the most common forms of risk arbitrage available to retail traders include:

Statistical arbitrage

This is an attempt to profit from pricing inefficiencies that are identified through the use of mathematical models. Statistical arbitrage attempts to profit from the likelihood that prices will trend toward a historical norm. It is an equity trading strategy that employs time series methods to identify relative mispricings between stocks (Ross 1976, Burmeister 1986).

Pairs trading

Pairs trading, also known as relative-value arbitrage, is a far less common form (Reverre 2001). This form of arbitrage relies on a strong correlation between two related or unrelated securities. It is primarily used during sideways markets as a way to profit.

The basis of this arbitrage is finding "pairs." Typically, high-probability pairs are stocks in the same industry with similar long-term trading histories. One example of securities that would be used in a pairs trade is GM and Ford. These two companies have a 94 percent correlation which means that both securities mapped on the time plot move almost exactly in parallel. If a significant divergence occurs, the chances are high that these two prices will eventually return to a higher correlation (the parallel behavior), offering an opportunity in which profit can be attained (Kuepper 2008).

Takeover and merger arbitrage

The earlier example of risk arbitrage involving the acquisition of Corporation A by Corporation B demonstrates takeover and merger arbitrage. It is probably the most common type of arbitrage. This typically involves an undervalued business that has been targeted by another corporation for a takeover bid. The takeover bid raises the value because in order to purchase the target corporation they must offer to buy their stock at higher than market price. Once the takeover is announced, the market price price rises to (or at least close to) that offered price. By identifying a company targeted for takeover arbitrageurs can buy stock at the pre-takeover price and sell them after the takeover has been completed at the higher price. If the merger or takeover goes through successfully, all those who took advantage of the opportunity make a significant profit; if it falls through, however, the price usually falls. That is, the element of risk that is always there.

The key to success in this type of arbitrage is speed; traders who utilize this method usually have access to streaming market news. Within seconds of an announcement they can act, before regular retail traders. However, even though retail traders are not the first to take advantage of a merger arbitrage opportunity, there is still some chance of profit. Benjamin Graham developed a risk-arbitrage formula to determine optimal risk/reward (Graham and Buffet 1985). The equations state the following:

Annual Return = [C. (G-L). (100%-C)] /YP, where:

  • C is the expected chance of success (percent)
  • P is the current price of the security
  • L is the expected loss in the event of a failure (usually original price)
  • Y is the expected holding time in years (usually the time until the merger takes place)
  • G is the expected gain in the event of a success (usually takeover price)
Liquidation arbitrage

This type of arbitrage involves identifying companies that have a higher liquidation value than their market price. For example, a business has a book value of $15 per share but is trading at $12 per share. If the business is liquidated its share rise to the higher value. In the Wall Street movie, Gordon Gekko bought companies, breaking them apart and selling them at higher prices, and was able to realize significant profit through this type of arbitrage.

Fixed income trading

Fixed income arbitrageurs try to identify when historical patterns for spreads or term structure relationships have been violated and there is anticipation of the historical relationship being re-established. They also look for situations where credit risk or liquidity risk is being over compensated.

Central bank intervention in the markets often creates abnormalities that can be exploited. A typical example is the 2008 crash of the sub-prime mortgage market in the U. S. Apart from the multi-billion losses, there was an opportunity to make a profit on the expectation that the Federal Reserve would eventually step in and invigorate the market, albeit for a short-term.

Fixed income arbitrage strategies are generally implemented to be duration neutral, but they are exposed to various other market risks. By their nature, particular strategies may be exposed to tilts in the term structure, spread risk, and foreign exchange risk.

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 (Chen, 1983). 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 (Ross 1976, Burmeister 1986).

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

  1. Interest rate: When rates move higher, the corporate 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).
  2. Stock price: When the price of the stock the bond is convertible into moves higher, the price of the bond tends to rise.
  3. Credit spread: If the creditworthiness of the issuer deteriorates (for example, 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).

Convertible arbitrage consists of buying a convertible bond and hedging (making an investment specifically to reduce or cancel out the risk in another investment) two of the three factors in order to gain exposure to the third factor at a very attractive price (Bjork 2004, Chen 1983). 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 is left is something similar to a call option on the underlying stock, acquired at a very low price. Profit can then be made either selling some of the more expensive options that are openly traded in the market or delta hedging his exposure to the underlying shares.

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. 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.

Efficient financial markets should operate without allowing the existence of arbitrage opportunities, since potential borrowers and lenders have continuous access to the information that allows them to make changes eliminating the price differences. However, if such were the case an "arbitrage paradox" would exist (Grossman and Stiglitz 1980). If arbitrage was never observed market participants would not have any incentive to monitor the markets continuously, in which case persistent opportunities for arbitrage would arise. The resolution of this paradox is that short-term arbitrage opportunities do arise, are noted by traders who exploit them, thus eliminating the opportunities ((Akram et al. 2008).

Conclusion

Arbitrage has many forms and encompasses many strategies; however, they all seek to take advantage of increased chances of success. Many of the the risk-free forms of pure arbitrage are typically unavailable to retail traders, although several types of risk arbitrage do offer significant profit opportunities to all arbitrageurs.

In the private sector, true arbitrage is completely hedged. In other words, both sides of the transaction are guaranteed at the time the position is taken so there is no risk of loss. If Security X is selling in New York for $50 per share and in Chicago for $49.50, the arbitrageur would purchase shares in Chicago and sell them simultaneously in New York, making a profit of $0.50 per share. Transaction costs must, of course, be deducted from the spread (price differential or profit) and they may include commissions and interest, if money is borrowed to purchase the shares. Arbitrage differs from traditional investing in that profits are made by the trade itself, not from the appreciation of a security. In fact, holding securities long enough for them to change in value is generally considered a risk by the arbitrageur.

Efficient markets do not, by definition, afford many opportunities for profit making through this type of trade, and arbitrage has been credited with contributing to market efficiency and “the law of one price.” This does not mean that efficient markets afford no opportunities for arbitrage; in fact the "arbitrage paradox" implies that they should (Grossman and Stiglitz 1980). Indeed, short-lived arbitrage opportunities that provide significant profit do arise in the major foreign exchange and capital markets. These are the result of violations of the law of one price and covered interest rate parity (Akram et al. 2008).

However, arbitrageurs have had to modify their approach in order to find new opportunities in increasingly efficient markets. Several factors have been instrumental in changing the nature of arbitrage over time; these include new market opportunities; new technology, especially in telecommunications and data processing; and advances in mathematical and statistical theory (Reverre, 2001). Riskless, or near riskless, profit opportunities without the need for actual work are so attractive to arbitrageurs that they continue to search and exploit them using whatever means necessary. In so doing, it appears that they also contribute to the smooth functioning of the market.

References

  • Akram, Farooq, Dagfinn Rime, and Lucio Sarno. 2008. Arbitrage in the foreign exchange market: Turning on the microscope. VoxEU.org. Retrieved October 31, 2008.
  • Bjork, T. 2004. Arbitrage Theory in Continuous Time. Oxford University Press. ISBN 978-0199271269.
  • Burmeister, E., and K. D. Wall. 1986. The arbitrage pricing theory and macroeconomic factor measures. The Financial Review 21: 1-20.
  • Chen, N. F, and E. Ingersoll. 1983. Exact pricing in linear factor models with finitely many assets: A note. Journal of Finance 38 (3): 985-88.
  • Deardoff, Alan V. 2006. Terms of Trade: Glossary of International Economics. World Scientific Publishing Company. ISBN 978-9812566034.
  • Greider, William. 1997. One World, Ready or Not. Penguin Press. ISBN 0713992115.
  • Grossman, S. J., and J. E. Stiglitz. 1980. On the impossibility of informationally efficient markets. American Economic Review 70 (3): 393-408.
  • Kuepper, Justin. 2008. Trading the Odds with Arbitrage. Investopedia. Retrieved October 31, 2008.
  • Prentis, Eric L. 2006. The Astute Investor. Prentice Business. ISBN 978-0975966013.
  • Reverre, Stephane. 2001. The Complete Arbitrage Deskbook. McGraw-Hill. ISBN 0071359958.
  • Roll, Richard. 1980. An empirical investigation of the arbitrage pricing theory. Journal of Finance 35 (5): 1073-1103.
  • Ross, Stephen. 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13(3): 341-360.
  • Tuckman, Bruce. 2002. Fixed Income Securities: Tools for Today`s Markets. John Wiley & Sons, Inc. ISBN 0471063223.

External links

All links retrieved October 26, 2012.

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