What Is Arbitrage?

Arbitrage Examined

[Q:] What is arbitrage? What markets do arbitrageurs usually trade on?

[A:] Terrific question! Let's start from the definition. 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.

Arbitrage profits can occur in a number of different ways. We'll look at a few examples:

One Type of Arbitrage - One Good, Two Markets

Suppose Walmart is selling the DVD of Shaft in Africa for $10. However, I know that on eBay the last 20 copies of Shaft in Africa on DVD have sold for between $25 and $30. Then I could go to Walmart, buy copies of the movie and turn around and sell them on eBay for a profit of $15 to $20 a DVD. It is unlikely that I will be able to make a profit in this manner for too long, as one of three things should happen:
  1. Walmart runs out of copies of Shaft in Africa on DVD
  2. Walmart raises the price on remaining copies as they've seen an increased demand for the movie
  3. The supply of Shaft in Africa DVDs skyrockets on eBay, which causes the price to fall.
This kind of arbitrage is actually quite common on eBay. Many eBay sellers will go to flea markets and yard sales looking for collectibles that the seller does not know the true value of and has priced much too low.
They will buy the rare collection of Colecovision games from the yard sale for $10 then turn around and sell them on eBay for $100. There are costs to this however. First of all, you don't find rare Colecovision games just lying around, you have to spend time and energy looking for them. Secondly, you have to spend time learning what is valuable and what is not valuable so you don't find out later what you thought was worth $100 is only worth $5.
Lastly, just because something has sold for $100 in the past does not mean it will sell for $100 again in the future. So given both the financial costs and the opportunity costs involved, we would expect arbitrageurs on this market to make as much money as they would doing other productive activities that require the same set of skills.

One Good, Two Markets Arbitrage in Sports Gambling

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. 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:
  1. Place a $300 bet on the Red Sox with Billy at even odds.
  2. 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.

There are a number of gamblers who try to exploit differences in odds from bookmaker to bookmaker. It's not quite as profitable as it seems, as the odds do not generally differ as much as they do in this example, plus you have to pay the bookmaker in order to place the bet as that's how they make their money.

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Second Type of Arbitrage - Two or More Goods, Same Market

This kind of arbitrage is explained in great detail in Part 2 of A Beginner's Guide to Exchange Rates and the Foreign Exchange Market: "Suppose the Algerian dinars-to-Bulgarian leva exchange rate is 2. We would expect then that the Bulgarian-to-Algerian exchange rate would be 1/2 or 0.5. But suppose for a second that it wasn't. Instead assume that the current market Bulgarian-to-Algerian exchange rate is 0.6. Then an investor could take five Algerian dinars and exchange them for 10 Bulgarian leva. She could then take her 10 Bulgarian leva and exchange them back for Algerian dinars. At the Bulgarian-to-Algerian exchange rate, she'd give up 10 leva and get back 6 dinars. Now she has one more Algerian dinar than she did before. This type of exchange is known as arbitrage. Since our investor gained a dinar, and since we're not creating or destroying any currency, the rest of the market must have lost a dinar. This of course is bad for the rest of the market. We would expect that the other agents in the currency exchange market will change the exchange rates that they offer so these opportunities to get exploited are taken away. Still there is a class of investors known as arbitrageurs who try to exploit these differences.

Real World Currency Arbitrage

Arbitrage generally takes on more complex forms than this, involving several currencies. Suppose that the Algerian dinars-to-Bulgarian leva exchange rate is 2 and the Bulgarian leva-to-Chilean peso is 3. To figure out what the Algerian-to-Chilean exchange rate needs to be, we just multiply the two exchange rates together:

A-to-C = (A-to-B)*(B-to-C)

This property of exchange rates is known as transitivity. To avoid arbitrage we would need the Algerian-to-Chilean exchange rate to be 6 and the Chilean-to-Algerian exchange rate needs to be 1/6. Suppose it was only 1/5. Then our investor could again take five Algerian dinars and exchange them for 10 Bulgarian leva. She could then take her 10 leva and get 30 Chilean pesos at the Bulgarian-to-Chilean exchange rate of 3. If she then exchanged her 30 Chilean pesos at the Chilean-to-Algerian rate of 1/5, she'd get 6 Algerian dinars in return. Once again our investor has gained a dinar and the rest of the market has lost one. For any three currencies A, B, and C, trading A for B, B for C and C for A is known as a currency cycle. The A-to-C exchange rate not only places restrictions on the C-to-A exchange rate, but it also places restriction on the A-to-B and B-to-C pair of exchange rates. Most of the time all the exchange rates on the market will be synchronized like this, but occasionally they'll become out of sync and arbitrageurs can make a profit from currency cycles."

Arbitrageurs can often be found in currency markets. Financial markets have the advantage of being quite liquid, so you don't take the risk of acquiring an asset that may take some time to sell, such as the Colecovision example.

That kind of arbitrage and the sports gambling arbitrage have the problem of significant transaction costs in buying and selling. That is generally not a problem in currency markets, as the transaction costs are minimal for large currency transactions. Since foreign currency markets are an ideal environment for arbitrageurs, arbitrage opportunities tend to be very limited, as any discrepancies in exchange rates tend to be corrected quite quickly by investors trying to exploit those differences.

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A Third Type of Arbitrage - Arbitrage on Financial Markets

There are all kinds of arbitrage opporunities in financial markets. Most of these opportunities come from the fact that there are many ways to trade esstentially the same asset, and many different assets are influenced by the same factors. A few examples:
  • Options. A call option is the right (but not the obligation) to buy a stock at a price given in the option. Suppose Microsoft is selling for $200 a share, and an option which allows me to buy 1 share of Microsoft stock at a price of $120 is selling for $50. I buy the option for $50, then exercise the option and pay $120 for one share of Microsoft stock. I now own one share of Microsoft stock, and have paid $170 for it. I can then turn around and sell the stock for $200, so I'm now up $30. Most arbitrage involving options are more complicated than this, but they all have the same underlying logic. This type of arbitrage is commonly known as "relative value arbitrage".
  • Convertible Bonds. Instead of using options, you can also perform a similar type of arbitrage by using convertible bonds. A convertible bond is a bond issued by a corporation which can be converted into the stock of the bond issuer. This type of arbitrage is known as convertible arbitrage.
  • Stocks and Stock Indicies. There is a class of assets known as Index Funds which are basically stocks which are designed to emulate the performance of a stock market index. An example of such an index is a Diamond (AMEX: DIA) which mimics the performance of the Dow Jones Industrial Average. Occasionally the price of the diamond will not be the same as the 30 stocks which make up the Dow Jones Industrial Average. If this is the case, then an arbitrageur can make a profit buy buying those 30 stocks in the right ratio and selling the diamonds (or vice-versa). This kind of arbitrage is quite complex, as it requires you to buy a lot of different assets. This type of opportunity generally does not last very long as there are millions of investors who are looking to beat the market any way they can.
    The possibilities for arbitrage are everywhere, from financial wizards selling complicated stock derivatives, to video game collectors selling cartridges on eBay they found at yard sales. Arbritrage opporunities are often hard to come by, due to transaction costs, the costs involved with finding an arbitrage opportunity, and the number of people who are also looking for that opportunity. Arbitrage profits are generally short-lived, as the buying and selling of assets will change the price of those assets in such a way as to eliminate that arbitrage opportunity. None of this has seemed to deter the thousands upon thousands of people who look for arbitrage opportunities every day.

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