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."

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 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.

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. Here we look at the concept of arbitrage, how market makers utilize "true arbitrage," and, finally, how retail investors can take advantage of arbitrage opportunities.

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 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. )

What is not "risk-less" arbitrage

In view of previous discussion, we present an example what is not an ”arbitrage” in the real sence of the world.

EXAMPLE: Say the keyword ‘dvd player’ costs $1 on Google’s auction market. On Nextag’s market it costs $2. Nextag does add value, by decreasing search costs for vertical merchants, say by $0.50 and Nextag also does have its own transaction costs, say $0.50.

Overall, Nextag pockets a profit of $0.50 for their '''value add'''—but if you assume the transaction was straight through processed and there were no credit or operational risks, this looks like a risk-free profit.

However, the most significant risk of all: Paid traffic coming in doesn’t necessarily convert to paid traffic going out.

So, Nextag can justify its higher cost-per-click fees, a comparison shopping site has to send its clients leads from people more likely to buy, which means the comparison shopping site---completely different from Google’s one--- has to qualify and filter the traffic it purchases.

If a site attracts a user for $1 and sends that user to a merchat for $2, it makes money. But what happens if a site attracts a user for $1 and that user never clicks-out to a paying merchant?

Besides, there’s more than a bit of risk involved here. A comparison-shopping sites aren’t “buying from one market where there is a low price and selling in another where the price is higher” - instead, a comparison-shopping site buys from one market at a low price, attempt to add value to its purchase, and then tries to resell what it’s bought for a higher price - a transaction that’s not always successful.

Because of this, what a comparison-shopping site does can’t be called risk-free arbitrage in any sense of the word; in fact it sits on the boundary to call it "arbitrage" at all. There’s no such thing as easy money.

Types of Arbitrage

Riskless or “True” Arbitrage

In finance theory, an arbitrage is a "free lunch"—a transaction or portfolio that makes a profit without risk. Suppose a futures contract trades on two different exchanges. If, at one point in time, the contract is bid at USD 45.02 on one exchange and offered at USD 45.00 on the other, a trader could purchase the contract at one price and sell it at the other to make a risk-free profit of a USD 0.02.

Such arbitrage opportunities reflect minor pricing discrepancies between markets or related instruments. Per-transaction profits tend to be small, and they can be consumed entirely by transaction costs. Accordingly, most arbitrage is performed by institutions that have very low transaction costs and can make up for small profit margins by doing a large volume of transactions.

Formally, theoreticians define an arbitrage as a trading strategy that requires the investment of no capital, cannot lose money, and has a positive probability of making money.

A market is said to have no arbitrage, or to be arbitrage-free, if prices in that market offer no arbitrage opportunities. This is a theoretical condition that is usually assumed for markets in economic and financial models. The assumption underlies the financial engineering theory of arbitrage-free pricing. This is what we have seen in the “conditions of arbitrage” in the above section.

Following are the basic types of riskless or “true” arbitrage”:

• Market Arbitrage

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. The example for this type of arbitrage is just at the beginning of this section ( two exchanges with different contract prices--- $ 45.00 and $ 45.02. )

An arbitrageur would short sell the higher priced stock and buy the lower priced one. The profit is the spread between the two assets.

There is one basic condition ( or set of conditions ) that set the Market Makers quite apart from the Retail Traders. Even 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.

• 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.

• 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.

EXAMPLE: During Wimbledon 2001, the ladies singles match between Lindsay Davenport and Kim Clijsters was priced differently by bookies Victor Chandler and Tote. Victor Chandler saw Davenport to win at odds of 2/5 while Tote saw Clijsters at 3/1.

At 2/5 the total amount to invest in Davenport to return $100 was $71.42. At 3/1 the total amount to invest in Clijsters to return $100 was $25.

This means that the total investment required to return $100 - whichever player wins - is just $96.42. A return of 3.58% within under 2 hours ( this is a very conservative example ).

Although 3.58% may seem like a small return, we should remember that it was totally certain, risk free, took only 2 hours to achieve and there was never a possibility of ever losing the money or not getting the profit. It was a mathematical certainty.

Risk arbitrages

Risk arbitrage ( sometimes called “statistical arbitrage” ) is.the second form of arbitrage that we will discuss. Unlike “true” or riskless 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 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.

• One technique is pairs trading:

Pairs trading (also known as relative-value arbitrage) 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. 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, 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.

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.

• 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 reestablished. 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.

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

• 1) 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).

• 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.

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.

Conclusion

We shall conclude with a few words about the online marketing and advertising "arbitrage," that raises probably more diverse opinions than any other single word ( as it involves everybody who uses internet and thus computer. )

The arbitrager is paid when searchers click out on yet another ad. The arbitrager pockets the difference between what they paid per click and what they get paid per click.

An arbitrager has to know what they are being paid per click, understand the click-through rate on any given phrase, and combine that information with what they are paying for the traffic. If any of those numbers suddenly change, it's possible to lose a lot of money very quickly.

Caught in the middle is an advertiser. Most advertisers find their ads on arbitrage sites by actually clicking on an ad and seeing one of these ad pages and then the realization that their ad dollars are funding these sites that quickly lead to emotional responses.

• In Defense Of Arbitrage:

One of the advantages of arbitrage sites is that advertisers can receive traffic from ad positions they don't control on a search page. Usually an advertiser only controls a single ad position, and if the advertiser didn't attract the first click, then it becomes increasingly difficult to receive traffic from that consumer. Since an arbitrage site is displaying a page full of ads, if an advertiser appears in one of those they have a second chance to receive the click. In essence, advertisers can receive traffic from ad positions they don't control and which might be a bonus.

• A Blight Upon The Web:

Some advertisers consider arbitrage an offense akin to spam—and not necessarily just search spam, but the vile kind that fills up your email inbox.

The first argument against arbitrage pleads for the user experience. If a searcher is taken from a search result to a set of ads without any meaningful content, then they really didn't find any answers. The searcher now has to click on yet another ad to get to an advertiser's page. If the page full of ads wasn't in the middle between the search result and the advertiser’s page, the searcher would have found the information one click sooner and had a better experience.

One way of being profitable with arbitrage is to buy inexpensive words and send them to a page of similar, yet more expensive words. Thus, the second argument against arbitrage resolves around ad relevancy.

EXAMPLE: If the search was "lawyer," one can assume it's a fairly ambiguous query. Because this is an ambiguous query, it's often not an overly expensive click compared to other legal terms. So, an arbitrager will buy the keyword "lawyer" and send it to a page about "personal injury lawyers," a click cost that is often four or more times more expensive than "lawyer."

Should an advertiser be charged for a "personal injury lawyer" click when the search was just for "lawyer?" Why should a company be able to buy an ad about one keyword and send traffic to ads about an entirely different keyword?

In short: Arbitrage is a word that is sure to evoke a response in any internet marketer ( and in every internet user ). However, the responses will vary as greatly as those found in a heated political debate.

There isn't necessarily a magic answer, but advertisers clearly want more control and a greater visibility into how their ad dollars are spent.

When marketers have full visibility and control of ad dollars, they will have the ability to not just debate arbitrage—they will have the power to act on their feelings.

References

ISBN links support NWE through referral fees

• Bjork, T. 2004. Arbitrage Theory in Continuous Time. Oxford University Press.
• 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.
• Tuckman, B. 2002. Fixed Income Securities: Tools for Today`s Markets. John Wiley & Sons, Inc.

External links

• What is Arbitrage? (About.com)
• ArbitrageView.com - Arbitrage opportunities in pending merger deals in the U.S. market
• Online Arbitrage
• Trésor de la Langue Française

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