Pair Trading Models

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Pair Trading Lab offers pair trading algorithms based on various mathematical models. These are models currently supported in PTL:

Ratio Model

This is one of the standard pair trading models described in literature. It is based in ratio of instrument prices, moving average and standard deviation. In other words, it is based on Bollinger Bands indicator.

Model parameters:

  • entry threshold En for Z-score, typical value range is <1.5, 2.5>, 2.0 is used most often
  • exit threshold Ex for Z-score, typical value is <-0.5, 0.5>, 0 is used most often
  • max Z-score Emax (optional, to filter out extremes, typical value is >4 if used)
  • moving average period Pm (typical range <10, 100>), default = 15
  • moving average type T (algorithm), default = exponential
  • standard deviation period Ps (typical range <10, 100>), default = 15
  • entry mode (simple, uptick, downtick)

Model support:

  • in PTL backtester: yes
  • in PTL portfolio backtester: yes
  • in PTL Trader: yes


  • we trade pair of stocks A, B, having price series A(t), B(t)
  • we need to calculate ratio time series R(t) = A(t) / B(t)
  • let's apply moving average of type T with period Pm on R(t) to get time series M(t)
  • let's apply standard deviation with period Ps on R(t) to get time series S(t)
  • now we can create Z-score series Z(t) as Z(t) = (R(t) - M(t)) / S(t), this time series can give us z-score to signal trading decision directly
  • another common approach (to visualize) is to create bands and put it above the moving average M(t):
    • upper entry band Un(t) = M(t) + S(t) * En
    • lower entry band Ln(t) = M(t) - S(t) * En
    • upper exit band Ux(t) = M(t) + S(t) * Ex
    • lower exit band Lx(t) = M(t) - S(t) * Ex
    • these bands are actually the same bands as in Bollinger Bands indicator and we can use crossing of R(t) and bands as trade signals
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