- Arbitrage is the possibility of making a risk-free profit without investing capital or, alternatively, as risk-less instantaneous profit.
Arbitrage is the possibility of making risk-less instantaneous profit. For example, if one investor could purchase 10 dollars for 9 euros at one bank and then go to a different bank and sell the 10 dollars for 10 euros, he or she would have made a risk-less profit of 1 euro and arbitrage would have been achieved. One can see the benefits of arbitrage; it is essentially the process of making free money! However, this reminds one of the adage, “There is no free lunch.”  Alas, arbitrage is no exception because, in reality, it does not exist.
On a basic level, nothing of the same value should ever be sold for two different prices, and thus there should be no arbitrage. However, this is not a perfect financial world in which we live. There are discrepancies that allow arbitrage to persist. For instance, arbitrage can be achieved through differing exchange rates in multiple countries or through differences in stock prices in different markets. These are two examples of one of the two types of arbitrage, pure arbitrage. Pure arbitrage is rare but highly valued in today’s financial world. On the other hand, relative value arbitrage is much more common and is the basis for many hedge funds and other trading businesses.
A More Mathematical Explanation
- Note: understanding of this explanation requires: *Selling Short
Pure arbitrage is defined as, “Generating riskless profit today by statically or dynamically matchi [...]
Pure arbitrage is defined as, “Generating riskless profit today by statically or dynamically matching current and future obligations to exactly offset each other, inclusive of incurring known financial costs.”  The example of differing exchange rates in different countries is a good example of pure arbitrage. If the exchange rate in the US is 10 dollars for 10 euros and the exchange rate in France is 10 euros for 700 rupees and the exchange rate in India is 700 rupees for 9 dollars, one can make a profit by converting dollars to rupees to euros back to dollars. An example of pure arbitrage can be found in the stock markets. Any discrepancy between a stock price in two different markets is an opportunity for arbitrage. If a stock is selling higher on the New York Exchange than the London Exchange, one could purchase the stock in the London market for a lower price and sell it in the New York Exchange for a profit. Other examples of pure arbitrage are very rare in the current market. This can be attributed to the high speed nature of financial transactions and interactions with the Law of One Price, which states that the same item cannot sell for two different prices at the same time.  When such a discrepancy occurs, it is instantly taken advantage of to turn a profit. These actions immediately start to enforce the Law of One Price. Therefore, as transactions take advantage of the discrepancy it begins to stabilize, effectively eliminating the opportunity for pure arbitrage. In the example of differing exchange rates, the Law of One Price would cause the values to begin stabilize as more between currencies. Relative value arbitrage is defined as, “Generating profit today by statically or dynamically matching current and future obligations to nearly offset each other, net of incurring closely estimable financing costs.”  Note that while pure arbitrage is riskless profit, relative value arbitrage regulates risk to estimable levels. The idea of relative value arbitrage rests on the substitution of risk. In practice, one must start with a broadly defined hedge with certain known risks. To control these risks, one must find and substitute a comparable risk that is, preferably, exactly opposite for both risks. Take US bonds, for example. Suppose one purchases $50 million in 30 year US bonds while at the same time selling short $51 million of a 26 year bond. The risks in this instance are the interest rates. The investor does not know how much profit he or she will be making off either of the bonds. However, the investor does know that the pair of investments has related interest rates. As the rate of one goes down, the other goes up and vice versa. Therefore, as one investment loses money, the other will gain it and none of the investment will be lost. Risk is still present, as the interest rates are not concretely linked and could differ slightly. However, the differences will be small and still allow for a profit. Since the investor will have some operating costs, the profits made through the investments must be greater that the operating costs. Through this elimination of primary risk, relative value arbitrage is achieved. The basis of hedge funds and also the primary tool of many large financial firms is relative value arbitrage. They follow the same basic pattern, balancing risks in stocks and bonds to maximize profit. In order to generate substantial profit, these firms rely on a large number of different investments that must be constantly reevaluated to maximize the profits yielded. Relative value arbitrage is vital in today’s financial markets.
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