Arbitrage

From New World Encyclopedia


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.


Definition

In economics and finance, 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. 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.

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

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.

Many might recognize these words spoken by Gordon Gekko in the movie Wall Street. In the movie, Gekko makes a fortune as a pioneer of arbitrage. Unfortunately, such risk-free trading is not available to everyone; however, there are several other forms of arbitrage that can be used to enhance the odds of executing a successful trade.

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.

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).

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.

NOTE: In practical terms, this is generally only possible with securities and financial products which can be traded electronically.

Types of Arbitrage

Riskless or “true” arbitrage

In economics and finance, 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. This is also known as a "riskless profit." The Economics Glossary defines arbitrage opportunity as "the opportunity to buy an asset at a low price then immediately selling it on a different market for a higher price." If I can buy an asset for $5, turn around and sell it for $20 and make $15 for my trouble, that is arbitrage. The $15 I gain represents an arbitrage profit.

Alternatively, 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.

Arbitrage of the "One good, Two markets" variety is quite common in the world of sports gambling. Arbitrage on the sports market exists because different betting agencies often post different odds on the outcome of a game. ‘’’EXAMPLE’’’: Suppose the White Sox are playing the Red Sox. Bookmaker Billy is giving even money on the game, so a $100 bet placed on either team will earn you $100 if the team you picked wins. Sportsman Steve has the White Sox at +200, which means if you place a $100 bet with Steve on the White Sox to win, you will get $200 if they win, and $100 if they lose. You can guarantee yourself a profit if you make the following bets:

      * Place a $300 bet on the Red Sox with Billy at even odds. 
      * Place a $200 bet on the White Sox with Steve at +200. 

In baseball there are no ties. So either the Red Sox will win, or the White Sox will win.

  • Profit if the Red Sox Win

If the Red Sox win, Billy pays you $300. However since the White Sox lost, you lost your bet with Steve and must pay him $200. Your profit is $100, as that's the difference between what Billy pays you and what you must pay Steve.

  • Profit if the White Sox Win

Since the bet you made with Steve on the White Sox was at +200, Steve pays you $400 for your $200 bet. Since the Red Sox lost, you must pay Billy $300. Again your profit is $100, represented by the difference of what Steve pays you and what you must pay Billy.

Market Makers vs. Retail Traders

Let’s say a domestic stock also trades on a foreign exchange in another country, where it hasn't adjusted for the constantly changing exchange rate. A trader purchases the stock where it is undervalued and short sells the stock where it is overvalued, thus profiting from the difference. Purchasing and selling the same security at the same time in different markets to take advantage of a price difference between the two separate markets. But this is the case of Market Makers vs. Retail Traders.

There is one basic set of conditions that set the Market Makers quite apart from the Retail Traders. Especially in the “True Arbitrage” environments have the Market Makers ( big Wall Street, Bay Street etc. “movers” ) several advantages over retail traders. They have:


  • Far more trading capital.
  • Generally more skill.
  • Up-to-the-second news.
  • Faster computers.
  • More complex software.
  • Access to the dealing desk and more.


Combined, these factors make it nearly impossible for a retail trader to take advantage of pure arbitrage opportunities. Market makers use complex software that is run on top-of-the-line computers to locate such opportunities constantly. Once found, the differential is typically negligible, and requires a vast amount of capital in order to profit—retail traders would likely get burned by commission costs. Needless to say, it is almost impossible for retail traders to compete in the risk-free genre of arbitrage. Main types of risk-less arbitrage for the Market Makers ( in Reverre, 2001 ) :


  • Inward Arbitrage


A form of arbitrage involving 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 US. The larger the spread, the more money that can be made.


  • Outward Arbitrage


A form of arbitrage involving 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


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 you have $1 million and you are provided with the following exchange rates:

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


With these exchange rates there is an arbitrage opportunity:


  • 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.


From these transactions, you would receive an arbitrage profit of $1,373 (assuming no transaction costs or taxes) which is the positive difference between the “almost” simultaneous transactions 1), 2) , and 3) leading to $1,001,373 from which we subtract the original outlay of $1,000,000 with a yield of net profit of $1,373.


Risk arbitrages

Risk arbitrage ( sometimes called “statistical arbitrage” ) is the second form of arbitrage that we will discuss. Unlike “true” or risk-less arbitrage, risk arbitrage entails risk. Although considered "speculation," risk arbitrage has become one of the most popular ( and Retail-Trader friendly ) forms of arbitrage. As we noted above, just as the disadvantages in pure arbitrage for retail traders ( as opposed to the big firms of Wall Street or Bay Street ), risk arbitrage is more accessible to most Retail Traders.

EXAMPLE: Let us say Company A is currently trading at $10/share. Company B, which wants to acquire Company A, decides to place a takeover bid on Company A for $15/share. This means that all of Company A's shares are now worth $15/share, but are trading at only $10/share.

Let's say the early trades ( typically not retail trades ) bid it up to $14/share. Now, there is still a $1/share difference—an opportunity for risk arbitrage. So, where's the risk? Well, the risk lies in probability that the acquisition could fall through, in which case the shares would be worth only the original $10/share.


It must be said that the usage of this term ( i.e. “arbitrage” ) is shunned by theoretical purists. However, it has been in wide use for several decades, so it is fairly standard. According to this usage, an arbitrage is a leveraged speculative transaction or portfolio.


It is a bit like “leveling the field advantages.” Although this type of arbitrage requires taking on some risk, it is generally considered "playing the odds." Here we will examine some of the most common forms of arbitrage available to retail traders. These include:


  • Statistical arbitrage.


It 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. Unlike pure arbitrage, statistical arbitrage is not riskless. Statistical arbitrage—or stat arb—is an equity trading strategy that employs time series methods to identify relative mispricings between stocks ( see Ross 1976, Burmeister 1986).


  • One technique is pairs trading:

Pairs trading (also known as relative-value arbitrage; see Reverre 2001) is far less common than the two forms discussed above. 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.

Here's how it works. First, you must find "pairs." Typically, high-probability pairs are big stocks in the same industry with similar long-term trading histories. Look for a high percent correlation. Then, you wait for a divergence in the pairs between 5-7% divergence that lasts for an extended period of time (2-3 days). Finally, you can go long and/or short on the two securities based on the comparison of their pricing. Then, just wait until the prices come back together.

EXAMPLE: One example of securities that would be used in a pairs trade is GM and Ford. These two companies have a 94% correlation which means that both securities mapped on the time plot move almost exactly in parallel. You can simply plot these two securities and wait for a significant divergence; then chances are these two prices will eventually return to a higher correlation ( i.e. the parallel behaviour), offering opportunity in which profit can be attained.


  • Merger arbitrage.


The example of risk arbitrage we saw in the above EXAMPLE that demonstrates takeover and merger arbitrage. It is probably the most common type of arbitrage. It typically involves locating an undervalued company that has been targeted by another company for a takeover bid. This bid would bring the company to its true, or intrinsic, value. If the merger goes through successfully, all those who took advantage of the opportunity will profit handsomely; however, if the merger falls through, the price may drop. That’s why the element of risk 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. The second something is announced, they try to get in on the action before anyone else.

Let's say you are a retail trader and, hence, you aren't among the first in, however. How do you know if it is still a good deal? Well, one way is to use Benjamin Graham's risk-arbitrage formula to determine optimal risk/reward. His equations state the following:


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


  • C is the expected chance of success (%).
  • 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).


Granted, this is highly empirical, but it will give you an idea of what to expect before you get into a merger arbitrage situation (Graham& Buffet, 1985)


  • Fixed income trading.


Fixed income arbitragers try to identify when historical patterns for spreads or term structure relationships have been violated and put on a long-short position in anticipation of the historical relationship being re-established. They also look for situations where credit risk or liquidity risk is being over compensated and will then put on a long-short position that earns positive carry. Central bank intervention in the markets often creates abnormalities that can be exploited. A typical example is the 2008 crash of sub-prime mortgage market. Apart from the multi-billion losses, there must have been quite a lot a profit made on expectation that the Feds eventually steps in and invigorates the market, albeit for a short-term. There were certainly a lot of money made on expectation that the “invigoration” will last only a few days; as opposed to general euphoria of a forever-lasting cure.

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). 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 (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 (Ross, 1976 and Burmeister, 1986).


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 ( Bjork, 2004 and 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 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.

Conclusion

Arbitrage is a very broad form of trading that encompasses many strategies; however, they all seek to take advantage of increased chances of success. Although the risk-free forms of pure arbitrage are typically unavailable to retail traders, there are several high-probability forms of risk arbitrage that offer retail traders many opportunities to profit.

When applied to the public sector, arbitrage involves state and local government use of proceeds from tax-exempt bonds on investments that yield a higher rate of return than the interest on the bonds themselves. The difference between the two rates is considered profit or arbitrage, and since 1986 must, with few exceptions, be rebated to the IRS.

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. The price differential or profit is also known as the spread. Transaction costs must, of course, be deducted from the spread 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; it does suggest, however, that arbitrageurs have had to modify their approach as they look for new opportunities in increasingly efficient markets. There are essentially five types of arbitrage in the private sector: simultaneous, risk, index, pair trading, and technical trading. In the public sector, there is only public debt arbitrage, which is essentially a form of simultaneous arbitrage—although it does not exactly occur simultaneously. 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).


References
ISBN links support NWE through referral fees

  • Bjork, T. 2004. Arbitrage Theory in Continuous Time. Oxford University Press.
  • Burmeister, E. and Wall, K.D., “The arbitrage pricing theory and macroeconomic factor measures”, The Financial Review, 21:1-20, 1986
  • Chen, N.F, and Ingersoll, E., “Exact pricing in linear factor models with finitely many assets: A note”, Journal of Finance June 1983
  • Greider, William. 1997. One World, Ready or Not. Penguin Press. ISBN 0713992115.
  • Prentis, E. 2004. The Astute Investor. Amazon Books.
  • Reverre, S. 2001. The Complete Arbitrage Deskbook. McGraw-Hill.
  • Roll, Richard, “An empirical investigation of the arbitrage pricing theory”, Journal of Finance, Dec 1980
  • Ross, Stephen, “The arbitrage theory of capital asset pricing”, Journal of Economic Theory, v.13, issue 3, 1976
  • Tuckman, B. 2002. Fixed Income Securities: Tools for Today`s Markets. John Wiley & Sons, Inc.

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