Generally speaking, arbitrage occurs where a state of imbalance exists between two (or possibly more) markets and a combination of matching deals are struck which exploit the imbalance, the profit being the difference between the market prices.
One example of arbitrage involves the stock market in New York and the futures market in Chicago. By examining the price of a stock in New York and its corresponding future in Chicago one can buy the less expensive one and sell the more expensive one when the prices are not in balance. Because the differences between the prices are likely to be small, this can only be done profitably with computers examining a large number of prices and automatically exercising a trade when the prices are out of balance.
Although theoretically riskless, arbitrage can be problematic if prices shift adversely during the execution of trades. Another risk occurs if the items being bought and sold are not identical and the arbitrage is conducted under the assumption that the prices of the items are correlated or predictable. The risk is especially great when money is borrowed in order to leverage or magnify small differences in prices.
LTCM lost $100 billion mis-managing this concept in September 1998. LTCM had attempted to make money on the difference between different bond instruments. For example, it would buy U.S treasury bonds and sell Italian bond futures. The concept was that because Italian bond futures had a less liquid market, in the short term Italian bond futures would have a higher return than U.S. bonds, but in the long term, the prices would converge. Because the difference was small, large amount of money had to be borrowed to make the buying and selling profitable.
The downfall in this system began on August 17, 1998, when Russia defaulted on its rouble debt and domestic dollar debt. Since the markets were already nervous due to the Asian crisis, investors began selling non-U.S. treasury debt and buying U.S. treasuries, which were considered a safe investment. As a result the return on U.S. treasuries began decreasing because there were many buyers, and the return on other bonds began to increase because there were many sellers. This caused the difference between the returns of U.S. treasuries and other bonds to increase, rather than to decrease as LTCM was expecting. Eventually this caused LTCM to fold, and a bailout had to be arranged to prevent a collapse in confidence in the economic system.
An ironic footnote is that they were right long-term (the LT in LTCM), and a few months after they folded their portfolio became very profitable. However the long-term does not matter if you cannot survive the short-term, and that they failed to do.