# Statistical Arbitrage

In statistical arbitrage strategy, there is a statistical mispricing of one or more assets based on the expected value of these assets. Statistical arbitrage is not without risk; it depends heavily on the ability of market prices to return to a historical or predicted normal.

As a trading strategy, statistical arbitrage is a heavily quantitative and computational approach to equity trading. It involves data mining and statistical methods, as well as automated trading systems.

A popular strategy is pairs trade, in which stocks are put into pairs by fundamental or market-based similarities. When one stock in a pair outperforms the other, the poorer performing stock is bought long with the expectation that it will climb towards its outperforming partner, the other is sold short. This hedges risk from whole-market movements.

Examples:

• Consider a game in which one flips a coin and collects \$1 on heads or pays \$0.50 on tails. In any single flip it is uncertain if one will win or lose money. However, in the statistical sense, there is an expected value of \$1×50% − \$0.50×50% = \$0.25 for each flip. According to the law of large numbers, the mean return on actual flips will approach this expected value as the number of flips increases.