A sure-win betting scheme. If there are h horses in a race, with the odds quoted for horse j being oj to 1 against that horse winning, then an arbitrage is possible if δ>0, where
If such a set of odds exists, then it is referred to as a Dutch book. In this case a win of N (ignoring betting costs) is guaranteed by backing each horse, with xj, the bet on horse j, being given by
As a simple example, suppose that there are two horses in a race, each with odds of two to one against. A punter placing 1 cent on each (total cost 2 cents) would receive back 2 cents, together with the winning stake—for an assured gain of 1 cent.
Buying a good or asset in one market and simultaneously selling in another market where the price is higher. This earns a profit (the difference between the two prices) but does not involve taking any risk. In a financial market arbitrage can involve short-selling one asset, or portfolio, and using the funds to purchase another. Provided the assets (or portfolios) have the same return and risk characteristics this is risk-free. Arbitrage tends to prevent the price of the same good or asset in different markets from moving further apart than a margin equal to transactions costs. Interest arbitrage is borrowing in a market with lower interest rates and simultaneously lending in a market with higher ones. See also no arbitrage.