Overall Statistics Total Trades 270 Average Win 1.79% Average Loss -1.69% Compounding Annual Return 3.767% Drawdown 12.900% Expectancy 0.153 Net Profit 34.436% Sharpe Ratio 0.555 Loss Rate 44% Win Rate 56% Profit-Loss Ratio 1.06 Alpha 0.067 Beta -2.163 Annual Standard Deviation 0.058 Annual Variance 0.003 Information Ratio 0.27 Tracking Error 0.058 Treynor Ratio -0.015 Total Fees \$270.00
```from sklearn import linear_model
import numpy as np
import pandas as pd
from scipy import stats
from math import floor
from datetime import timedelta

def Initialize(self):

self.SetStartDate(2009,1,1)
self.SetEndDate(2017,1,1)
self.SetCash(10000)
self.numdays = 250  # set the length of training period
tickers = ["XOM", "CVX"]
self.symbols = []

self.threshold = 1.
for i in tickers:
for i in self.symbols:

def OnData(self, data):

if not (data.ContainsKey("CVX") and data.ContainsKey("XOM")): return

for symbol in self.symbols:

price_x = pd.Series([float(i.Close) for i in self.symbols[0].hist_window],
index = [i.Time for i in self.symbols[0].hist_window])

price_y = pd.Series([float(i.Close) for i in self.symbols[1].hist_window],
index = [i.Time for i in self.symbols[1].hist_window])
if len(price_x) < 250: return
spread = self.regr(np.log(price_x), np.log(price_y))
ratio = floor(self.Portfolio[self.symbols[1]].Price / self.Portfolio[self.symbols[0]].Price)
# quantity = float(self.CalculateOrderQuantity(self.symbols[0],0.4))

if spread[-1] > mean + self.threshold * std:
if not self.Portfolio[self.symbols[0]].Quantity > 0 and not self.Portfolio[self.symbols[0]].Quantity < 0:
self.Sell(self.symbols[1], 100)
self.Buy(self.symbols[0],  ratio * 100)

elif spread[-1] < mean - self.threshold * std:
if not self.Portfolio[self.symbols[0]].Quantity < 0 and not self.Portfolio[self.symbols[0]].Quantity > 0:
self.Sell(self.symbols[0], 100)
self.Buy(self.symbols[1], ratio * 100)

else:
self.Liquidate()

def regr(self,x,y):
regr = linear_model.LinearRegression()
x_constant = np.column_stack([np.ones(len(x)), x])
regr.fit(x_constant, y)
beta = regr.coef_[0]
alpha = regr.intercept_
spread = y - x*beta - alpha