| Overall Statistics |
|
Total Orders 36 Average Win 2.20% Average Loss -3.80% Compounding Annual Return -9.072% Drawdown 14.500% Expectancy -0.122 Start Equity 1000000 End Equity 909386.19 Net Profit -9.061% Sharpe Ratio -1.152 Sortino Ratio -0.942 Probabilistic Sharpe Ratio 2.615% Loss Rate 44% Win Rate 56% Profit-Loss Ratio 0.58 Alpha -0.106 Beta -0.05 Annual Standard Deviation 0.099 Annual Variance 0.01 Information Ratio -1.953 Tracking Error 0.145 Treynor Ratio 2.291 Total Fees $505.31 Estimated Strategy Capacity $690000000.00 Lowest Capacity Asset MSFT R735QTJ8XC9X Portfolio Turnover 5.11% |
import numpy as np import pandas as pd import statsmodels.api as sm from AlgorithmImports import * class PairsTradingStrategy(QCAlgorithm): def Initialize(self): self.SetStartDate(2023, 12, 1) self.SetEndDate(2024, 12, 1) self.SetCash(1_000_000) # $1M initial capital self.lookback = 20 # Lookback period for z-score calculation self.entry_threshold = 2 self.exit_threshold = 0 self.pair = ["NVDA", "MSFT"] # Replace with the selected pair with lowest ADF # Add securities self.symbols = [self.AddEquity(ticker, Resolution.Daily).Symbol for ticker in self.pair] # Store historical data self.history = {sym: [] for sym in self.symbols} self.portfolio_state = 0 # 1: long, -1: short, 0: no position # Track current hedge ratio self.hedge_ratio = None def OnData(self, data): if not all(symbol in data for symbol in self.symbols): return # Store latest closing prices for symbol in self.symbols: self.history[symbol].append(data[symbol].Close) if len(self.history[symbol]) > self.lookback: self.history[symbol].pop(0) # Maintain rolling window if len(self.history[self.symbols[0]]) < self.lookback: return # Wait until we have enough data # Perform linear regression on log prices log_prices_P = np.log(self.history[self.symbols[0]]) log_prices_Q = np.log(self.history[self.symbols[1]]) model = sm.OLS(log_prices_P, sm.add_constant(log_prices_Q)).fit() self.hedge_ratio = model.params[1] # Beta coefficient # Compute spread and z-score spread = log_prices_P - self.hedge_ratio * log_prices_Q mean_spread = np.mean(spread) std_spread = np.std(spread) zscore = (spread[-1] - mean_spread) / std_spread if std_spread != 0 else 0 self.wt1 = 1/(1+self.hedge_ratio) self.wt2 = self.hedge_ratio/(1+self.hedge_ratio) # Entry conditions if self.portfolio_state == 0: if zscore < -self.entry_threshold: # Long P, short Q self.SetHoldings(self.symbols[0], self.wt1) self.SetHoldings(self.symbols[1], -self.wt2) self.portfolio_state = 1 elif zscore > self.entry_threshold: # Short P, long Q self.SetHoldings(self.symbols[0], -self.wt1) self.SetHoldings(self.symbols[1], self.wt2) self.portfolio_state = -1 # Exit conditions elif self.portfolio_state == 1 and zscore > self.exit_threshold: self.Liquidate() # Close all positions self.portfolio_state = 0 elif self.portfolio_state == -1 and zscore < self.exit_threshold: self.Liquidate() # Close all positions self.portfolio_state = 0
