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Statistical arbitrage, as opposed to (deterministic) arbitrage, is the mispricing of one or more assets based on the expected value of these assets. For example, 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 $1x50% - $0.50x50% = $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. This is precisely the way in which casinos make their money.
Trading Strategy
As a trading strategy, Statistical Arbitrage, or StatArb, is a heavily quantitative and computational approach to equity trading. It describes a variety of automated trading systems which commonly make use of data mining, statistical methods and artificial intelligence techniques. A popular strategy is pairs trading, in which stocks are put into pairs by fundamental or market-based similarities. One stock in the pair is bought long, the other is sold short. This hedges risk from whole-market movements. Stephen N. P. Smith is one of the founders of this approach.
Reference:
Statistical Arbitrage, by Stephen N. P. Smith, Wiley publications
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