text: #!/usr/bin/python
  #
  # Copyright 2012 Quantopian, Inc.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  
  import matplotlib.pyplot as plt
  import numpy as np
  import statsmodels.api as sm
  
  from zipline.algorithm import TradingAlgorithm
  from zipline.transforms import batch_transform
  from zipline.utils.factory import load_from_yahoo
  
  
  @batch_transform
  def ols_transform(data, sid1, sid2):
      """Computes regression coefficient (slope and intercept)
      via Ordinary Least Squares between two SIDs.
      """
      p0 = data.price[sid1]
      p1 = sm.add_constant(data.price[sid2])
      slope, intercept = sm.OLS(p0, p1).fit().params
  
      return slope, intercept
  
  
  class Pairtrade(TradingAlgorithm):
      """Pairtrading relies on cointegration of two stocks.
  
      The expectation is that once the two stocks drifted apart
      (i.e. there is spread), they will eventually revert again. Thus,
      if we short the upward drifting stock and long the downward
      drifting stock (in short, we buy the spread) once the spread
      widened we can sell the spread with profit once they converged
      again. A nice property of this algorithm is that we enter the
      market in a neutral position.
  
      This specific algorithm tries to exploit the cointegration of
      Pepsi and Coca Cola by estimating the correlation between the
      two. Divergence of the spread is evaluated by z-scoring.
      """
  
      def initialize(self, window_length=100):
          self.spreads = []
          self.zscores = []
          self.invested = 0
          self.window_length = window_length
          self.ols_transform = ols_transform(refresh_period=self.window_length,
                                             window_length=self.window_length)
  
      def handle_data(self, data):
          ######################################################
          # 1. Compute regression coefficients between PEP and KO
          params = self.ols_transform.handle_data(data, 'PEP', 'KO')
          if params is None:
              return
          slope, intercept = params
  
          ######################################################
          # 2. Compute spread and zscore
          zscore = self.compute_zscore(data, slope, intercept)
          self.zscores.append(zscore)
  
          ######################################################
          # 3. Place orders
          self.place_orders(data, zscore)
  
      def compute_zscore(self, data, slope, intercept):
          """1. Compute the spread given slope and intercept.
             2. zscore the spread.
          """
          spread = (data['PEP'].price - (slope * data['KO'].price + intercept))
          self.spreads.append(spread)
          spread_wind = self.spreads[-self.window_length:]
          zscore = (spread - np.mean(spread_wind)) / np.std(spread_wind)
          return zscore
  
      def place_orders(self, data, zscore):
          """Buy spread if zscore is > 2, sell if zscore < .5.
          """
          if zscore >= 2.0 and not self.invested:
              self.order('PEP', int(100 / data['PEP'].price))
              self.order('KO', -int(100 / data['KO'].price))
              self.invested = True
          elif zscore <= -2.0 and not self.invested:
              self.order('KO', -int(100 / data['KO'].price))
              self.order('PEP', int(100 / data['PEP'].price))
              self.invested = True
          elif abs(zscore) < .5 and self.invested:
              self.sell_spread()
              self.invested = False
  
      def sell_spread(self):
          """
          decrease exposure, regardless of position long/short.
          buy for a short position, sell for a long.
          """
          ko_amount = self.portfolio.positions['KO'].amount
          self.order('KO', -1 * ko_amount)
          pep_amount = self.portfolio.positions['PEP'].amount
          self.order('PEP', -1 * pep_amount)
  
  if __name__ == '__main__':
      data = load_from_yahoo(stocks=['PEP', 'KO'], indexes={})
  
      pairtrade = Pairtrade()
      results = pairtrade.run(data)
      data['spreads'] = np.nan
      data.spreads[pairtrade.window_length:] = pairtrade.spreads
  
      ax1 = plt.subplot(211)
      data[['PEP', 'KO']].plot(ax=ax1)
      plt.ylabel('price')
      plt.setp(ax1.get_xticklabels(), visible=False)
  
      ax2 = plt.subplot(212, sharex=ax1)
      data.spreads.plot(ax=ax2, color='r')
      plt.ylabel('spread')
  
      plt.show()
  