Statistical Arbitrage EA in MetaTrader 4 (MT4) and MetaTrader 5 (MT5)

Implementing statistical arbitrage strategies in MetaTrader 4 (MT4) and MetaTrader 5 (MT5) requires a deep understanding of mathematical models and algorithms. Here’s a more in-depth exploration, focusing on the key formulas and concepts essential for these strategies.

Statistical Arbitrage: The Core Concepts

1. Pair Trading

  • Identification: Choose pairs of stocks, currencies, or commodities that have historically moved together.
  • Formula: Use correlation coefficients to measure how closely the prices of the two assets move together.
correlation coefficient for stats arbitrage
  • Strategy: Go long on the underperforming asset and short on the overperforming one, betting on their price convergence.

2. Mean Reversion

  • Concept: Prices will revert to their historical average over time.
  • Formula: Calculate the z-score to identify when to enter and exit trades.

​ where μ is the mean and σ is the standard deviation.

  • Application: A high positive z-score indicates a selling point, whereas a high negative z-score suggests a buying point.

3. Cointegration

  • Purpose: Identify pairs of assets whose price series move together in the long run.
  • Method: Use the Engle-Granger two-step method for testing cointegration.
    • Step 1: Regress one asset price on another and obtain the residual series.
    • Step 2: Test the residual for stationarity using an Augmented Dickey-Fuller (ADF) test.

Statistical Arbitrage Implementation in MT4 and MT5


  • MQL4 Limitations: Given MQL4’s simpler nature, implementing complex statistical models might be more challenging.
  • Execution: Suitable for less computation-intensive models, as MT4’s execution might be slower compared to MT5.


  • MQL5 Advantages: The advanced nature of MQL5 aids in implementing sophisticated models that require extensive computation.
  • Backtesting: MT5’s advanced backtesting capabilities allow for a more accurate simulation of statistical arbitrage models using historical data.

Calculating standard deviation for MT4 Statistical Arbitrage EA

double StdDev_Func(int position,const double &price[],const double &MAprice[],int period)
//--- variables
   double StdDev_dTmp=0.0;
//--- check for position
      //--- calcualte StdDev
      for(int i=0; i<period; i++)
//--- return calculated value
double SimpleMA(const int position,const int period,const double &price[])
   double result=0.0;
   //--- check position
   if(position >= period - 1 && period > 0)
      //--- calculate value
      for(int i = 0; i < period; i++) 

Risk Management and Optimization

1. Risk Management

  • Value at Risk (VaR): A statistical measure to assess the level of risk associated with a portfolio over a specific time frame.
  • Stop-Loss/Take-Profit: Set these thresholds based on historical volatility and mean-reversion tendencies.

2. Optimization

  • Parameter Tuning: Use MT4/MT5 optimization tools to fine-tune parameters like entry/exit thresholds, look-back periods, and position sizes.

3. Model Robustness

  • Walk-Forward Analysis: Test the strategy on out-of-sample data to ensure its robustness over different market conditions.


While both MT4 and MT5 can facilitate statistical arbitrage strategies, MT5’s advanced features are more conducive to implementing complex, computation-heavy models. Successful application requires not just programming skills but also a deep understanding of statistical concepts and market dynamics. Moreover, rigorous backtesting, risk management, and continuous optimization are crucial to navigating the challenges of statistical arbitrage in the ever-evolving financial markets.

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