KEY POINTS

• Riskless arbitrage is when there is a guaranteed positive payoff without the commitment of any capital. Statistical arbitrage is when the positive payoff is not guaranteed, but can be expressed as a probability. Statistical arbitrage also refers to the use of statistics to identify possible arbitrage opportunities.
• The biggest risk associated with statistical arbitrage is “model risk,” where the model of the world is not consistent with reality.
• Pairs trading is a fundamental type of statistical arbitrage. The question is, “What security is mispriced relative to the other security?” Once the mispricing is identified, then it is a matter of implementing the trade: buy the relatively underpriced security and short the relatively over-priced security. By doing this, one can create a “market neutral” portfolio where the profit is determined by the relative mispricing, not by the general level of the security prices.
• Cointegration analysis illuminates the long-run relationship between security prices. An error correction model shows how the deviations from the long-run relationship correct over time. This is perhaps one of the more interesting areas of statistical arbitrage research since it can be used to estimate the length of time a long or short position needs to be maintained to yield a profit.
• It is possible to create a completely general model of statistical arbitrage through stochastic, dynamic optimization. This involves creating a model of the price processes, subject to the constraint that the initial cost of the portfolio is zero and that the portfolio is self-financing.