Under the distance method, the co-movement in a pair is measured by what is known as the distance, or the sum of squared differences between the two normalized price series. Trading is triggered when the distance reaches a certain threshold, as determined during a formation period. In Gatev et al (1999), the pairs are selected by choosing, for each stock, a matching partner that minimizes the distance. The trading trigger is two historical standard deviations as estimated during the formation period. Nath (2003) keeps a record of distances for each pair in the universe, in an empirical distribution format so that each time an observed distance crosses a trigger of 15 percentile, a trade is entered for that pair. Risk control is instigated by limiting a trading period at the end of which positions have to be closed out regardless of outcomes. Nath (2003) also adopts a stop-loss trigger to close the position whenever the distance widens further to hit the 5 percentile. In overall, the distance approach purely exploits the statistical relationship of a pair, at a price level. As the approach is economic model-free, it has the advantage of not being exposed to model mis-specification and mis-estimation. On the other hand, being non-parametric means that the strategy lacks forecasting ability regarding the convergence time or expected holding period. What is a more fundamental issue is its underlying assumption that the
price level distance is static through time, or returns of the two stocks are in parity. Although such assumption may be valid in short periods of time, it is so only for a certain group of pairs whose risk-return profiles are close to identical. In fact, it is a common practice in existing pairs trading strategies that mispricing is measured in terms of price
level.