Statistical arbitrage is a situation where there is a disparity between an asset's "natural" price, based on its inherent value, and its actual market price. Some traders will attempt to take advantage of this disparity in the belief that they can profit when it is corrected. There is a school of thought that on paper, a trader would always end up making a profit from statistical arbitrage. In reality, however, limited resources or unexpected events may limit their ability to do so.
The phrase "statistical arbitrage" is normally specified to distinguish it from more general arbitrage. This simply refers to the technique of taking advantage of a disparity between two markets. One example would be where a stock is priced much more highly in one country's stock market than in another. A trader could theoretically make a guaranteed profit by buying stock on one market and immediately selling it on another. In practice, this guarantee is limited by the transaction costs and the risk that prices may change between buying and selling the asset.
With statistical arbitrage, the disparity is not between different markets, but rather between the current price of an asset and its underlying value. One very generalized example would be with a company stock. While the market price is determined by demand and supply among traders, the stock has an inherent value based upon the dividends it pays to the holders and how this compares to other investments. Some changes in market price may be down to external and temporary measures, such as good or bad news in the relevant industry.
A trader carrying out statistical arbitrage works on the basis that ultimately asset prices will return to their underlying value. Where there is a disparity, they can therefore expect a future change in the pricing and aim to profit accordingly. Normally, such traders will use hundreds of different stocks to minimize the risks that unexpected events prevent individual stocks from returning to their "natural" price quickly enough to avoid the trader losing out.
Statistical arbitrage can also simply mean some form of imbalance from the values that would normally be expected. The main example of this would be in casino games, such as roulette. For example, a player betting on red would win two times their stake if they guess correctly. Because the wheel has a non-paying 0, the odds of guessing the color correctly is slightly lower than one in two. This disparity, known as the house advantage, is a form of statistical arbitrage.