"In this study, we show that pairs trading, assuming the mean-reverting spread process, satises the denition of statistical arbitrage. However, we also show that a time independent error in trader's guess or forecast of the long-term mean level causes the failure of the statistical arbitrage denition. In other words, a perfect statistical arbitrage with the probability of loss decaying to zero is not available whenever there is uncertainty in the model parameters. The good news is that the probability of loss can be bounded as a function of the estimation error and given suciently good estimates, the trader can still implement pairs trading knowing the potential probability of loss involved.

Second, we derive optimal thresholds for starting the pairs trading, which can be used by the trader to select the best pairs of stocks for trade. In our framework, out of hundreds of possible pairs of assets, the trader can identify the pairs with highest probability of successful execution for a given investment horizon."

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