Overall Statistics Total Trades 20 Average Win 10.45% Average Loss -4.22% Compounding Annual Return 6.416% Drawdown 15.000% Expectancy 1.086 Net Profit 45.244% Sharpe Ratio 0.651 Loss Rate 40% Win Rate 60% Profit-Loss Ratio 2.48 Alpha 0.109 Beta -2.074 Annual Standard Deviation 0.104 Annual Variance 0.011 Information Ratio 0.459 Tracking Error 0.104 Treynor Ratio -0.033 Total Fees \$63.32
```import numpy as np
from sklearn.linear_model import LinearRegression

class ScikitLearnLinearRegressionAlgorithm(QCAlgorithm):

def Initialize(self):
self.SetStartDate(2013, 1, 1)  # Set Start Date
self.SetEndDate(2019, 1, 1) # Set End Date

self.lookback = 30 # number of previous days for training

self.SetCash(100000)  # Set Strategy Cash
spy = self.AddEquity("SPY", Resolution.Minute)

self.symbols = [ spy.Symbol ] # In the future, we can include more symbols to the list in this way

self.Schedule.On(self.DateRules.EveryDay("SPY"), self.TimeRules.AfterMarketOpen("SPY", 28), self.Regression)
self.Schedule.On(self.DateRules.EveryDay("SPY"), self.TimeRules.AfterMarketOpen("SPY", 30), self.Trade)

def Regression(self):
# Daily historical data is used to train the machine learning model
history = self.History(self.symbols, self.lookback, Resolution.Daily)

# price dictionary:    key: symbol; value: historical price
self.prices = {}
# slope dictionary:    key: symbol; value: slope
self.slopes = {}

for symbol in self.symbols:
if not history.empty:
# get historical open price
self.prices[symbol] = list(history.loc[symbol.Value]['open'])

# A is the design matrix
A = range(self.lookback + 1)

for symbol in self.symbols:
if symbol in self.prices:
# response
Y = self.prices[symbol]
# features
X = np.column_stack([np.ones(len(A)), A])

# data preparation
length = min(len(X), len(Y))
X = X[-length:]
Y = Y[-length:]
A = A[-length:]

# fit the linear regression
reg = LinearRegression().fit(X, Y)

# run linear regression y = ax + b
b = reg.intercept_
a = reg.coef_

# store slopes for symbols
self.slopes[symbol] = a/b

# if there is no open price
if not self.prices:
return

thod_buy = 0.001 # threshold of slope to buy
thod_liquidate = -0.001 # threshold of slope to liquidate

for holding in self.Portfolio.Values:
slope = self.slopes[holding.Symbol]
# liquidate when slope smaller than thod_liquidate
if holding.Invested and slope < thod_liquidate:
self.Liquidate(holding.Symbol)

for symbol in self.symbols:
# buy when slope larger than thod_buy
if self.slopes[symbol] > thod_buy:
self.SetHoldings(symbol, 1 / len(self.symbols))                        ```