2. 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.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.
