# Arbitrage

In economics, arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets: a combination of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices. A person who engages in arbitrage is called an arbitrageur.

Statistical arbitrage is an imbalance in expected values. A casino has a statistical arbitrage in every game of chance played, even though it could lose money on any single game.

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## Conditions for arbitrage

Arbitrage is possible when one of three conditions is not met:

1. The same asset must trade at the same price on all markets ("the law of one price").
2. Two assets with identical cash flows must trade at the same price.
3. An asset with a known price in the future, must today trade at its future price discounted at the risk free rate.
See Rational pricing, particularly Arbitrage mechanics, for further discussion.

The term "arbitrage", is usually applied only to trading in money and investment instruments (such as stocks, bonds, and other securities), not to goods. Examples

• Suppose that the exchange rates (after taking out the fees for making the exchange) in London are £5 = \$10 = ¥1000 and the exchange rates in Tokyo are ¥1000 = £6 = \$10. Converting \$10 to £6 in Tokyo and converting that £6 into \$12 in London, for a profit of \$2, would be arbitrage.
• One real-life example of arbitrage involves the stock market in New York and the futures market in Chicago. When the price of a stock in New York and its corresponding future in Chicago are out of sync, one can buy the less expensive one and sell the more expensive. Because the differences between the prices are likely to be small (and not to last very long), this can only be done profitably with computers examining a large number of prices and automatically exercising a trade when the prices are far enough out of balance. The activity of other arbitrageurs can make this risky. Those with the fastest computers and the smartest mathematicians take advantage of series of small differentials that would not be profitable if taken individually.
• If you can buy items at one price at a factory outlet and sell them for a higher price on an internet auction website such as eBay, you can exploit the imbalance between those two markets for those items.
• Economists use the term "global labor arbitrage" to refer to the tendency of manufacturing jobs to flow towards whichever country has the lowest wages at present and has reached the minimum requisite level of political and economic development to support industrialization. At present, all such jobs appear to be flowing towards China. In the future, they may flow towards even poorer countries in Africa or south Asia.
• 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 assure that they receive a small risk-free profit.

## Price convergence

Arbitrage has the effect of causing prices in different markets to converge. It's like a free lunch. As a result of arbitrage, the currency exchange rates, the price of commodities, and the price of securities in different markets tend to converge to the same prices, in all markets, in each category. The speed at which prices converge is a measure of market efficiency. Arbitrage tends to reduce price discrimination by encouraging people to buy an item where the price is low and resell it where the price is high, as long as the buyers are not prohibited from reselling and the transactions cost of buying, holding and reselling are small relative to the difference in prices in the different markets.

Arbitrage moves different currencies toward purchasing power parity. For example if a car purchased in America is cheaper than the same car in Canada, Canadians would buy their cars across the border to exploit the arbitrage condition. When people arbitrage commodities, goods, securities and currencies, on a large scale, the higher demand for US Dollars and the higher supply of Canadian Dollars (Canadians would have to exchange their Dollars into US Dollars) leads to an appreciation of the US Dollar and eventually, if unchecked, would make US cars more expensive for all buyers, especially for the Canadians.

(However, in reality, one must consider taxes and the costs of travelling to the U.S. and driving the new car back to Canada. Also, the features built into the cars sold in the U.S. are not exactly the same as the features built into the cars for sale in Canada. This is due to the different emissions and other auto regulations in the two countries.)

Similarly, arbitrage affects the difference in interest rates paid on government bonds, issued by the various countries, given the expected depreciations in the currencies, relative to each other.

## Risks

Arbitrage transactions in modern securities markets involve fairly low risks. Generally it is impossible to close two or three transactions at the same instant; therefore, there is the possibility that when one part of the deal is closed, a quick shift in prices makes it impossible to close the other at a profitable price. There is also counter-party risk, that the other party to one of the deals fails to deliver as agreed; though unlikely, this hazard is serious because of the large quantities one must trade in order to make a profit on small price differences. These risks become magnified when leverage or borrowed money is used.

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. In the extreme case this is risk arbitrage, described below. In comparison to the classical quick arbitrage transaction, such an operation can produce disastrous losses.

In the 1980s a practice with the oxymoronic name of risk arbitrage became common. In this form of speculation, one trades a security that is clearly undervalued or overvalued, when it is seen that the wrong valuation is about to be corrected by events. The standard example is the stock of a company, undervalued in the stock market, which is about to be the object of a takeover bid; the price of the takeover will more truly reflect the value of the company, giving a large profit to those who bought at the current price—if the merger goes through as predicted. Traditionally, arbitrage transactions in the securities markets involve high speed and low risk. At some moment a price difference exists, and the problem is to execute two or three balancing transactions while the difference persists (that is, before the other arbitrageurs act). When the transaction involves a delay of weeks or months, as above, it may entail considerable risk if borrowed money is used to magnify the reward through leverage. One way of reducing the risk is through the illegal use of inside information, and in fact risk arbitrage with regard to leveraged buyouts was associated with some of the famous financial scandals of the 1980s such as those involving Michael Milken and Ivan Boesky.

### Long-Term Capital Management

Long-Term Capital Management (LTCM) lost more than four billions 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, a 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 ruble 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 their creditors had to arrange a bail-out. More controversially, officials of the Federal Reserve assisted in the negotiations that led to this bail-out, on the ground that this was necessary 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.

and that cost them the price they had to pay for.

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