Pair Trading Models

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 E_n for Z-score, typical value range is <1.5, 2.5>, 2.0 is used most often
• exit threshold E_x for Z-score, typical value is <-0.5, 0.5>, 0 is used most often
• max Z-score E_max (optional, to filter out extremes, typical value is >4 if used)
• moving average period P_m (typical range <10, 100>), default = 15
• moving average type T (algorithm), default = exponential
• standard deviation period P_s (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

Description:

• 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 P_m on R(t) to get time series M(t)
• let's apply standard deviation with period P_s 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 U_n(t) = M(t) + S(t) * E_n
  • lower entry band L_n(t) = M(t) - S(t) * E_n
  • upper exit band U_x(t) = M(t) + S(t) * E_x
  • lower exit band L_x(t) = M(t) - S(t) * E_x
  • 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