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#!/usr/bin/env python |
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# Copyright 2013 Quantopian, Inc. |
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# |
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# Licensed under the Apache License, Version 2.0 (the "License"); |
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# you may not use this file except in compliance with the License. |
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# You may obtain a copy of the License at |
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# |
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# http://www.apache.org/licenses/LICENSE-2.0 |
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# |
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# Unless required by applicable law or agreed to in writing, software |
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# distributed under the License is distributed on an "AS IS" BASIS, |
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
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# See the License for the specific language governing permissions and |
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# limitations under the License. |
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import logbook |
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import matplotlib.pyplot as plt |
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import numpy as np |
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import statsmodels.api as sm |
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from datetime import datetime |
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import pytz |
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from zipline.algorithm import TradingAlgorithm |
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from zipline.transforms import batch_transform |
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from zipline.utils.factory import load_from_yahoo |
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from zipline.api import symbol |
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@batch_transform |
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def ols_transform(data, sid1, sid2): |
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"""Computes regression coefficient (slope and intercept) |
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via Ordinary Least Squares between two SIDs. |
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""" |
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p0 = data.price[sid1] |
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p1 = sm.add_constant(data.price[sid2], prepend=True) |
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slope, intercept = sm.OLS(p0, p1).fit().params |
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return slope, intercept |
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class Pairtrade(TradingAlgorithm): |
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"""Pairtrading relies on cointegration of two stocks. |
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The expectation is that once the two stocks drifted apart |
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(i.e. there is spread), they will eventually revert again. Thus, |
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if we short the upward drifting stock and long the downward |
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drifting stock (in short, we buy the spread) once the spread |
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widened we can sell the spread with profit once they converged |
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again. A nice property of this algorithm is that we enter the |
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market in a neutral position. |
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This specific algorithm tries to exploit the cointegration of |
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Pepsi and Coca Cola by estimating the correlation between the |
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two. Divergence of the spread is evaluated by z-scoring. |
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""" |
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def initialize(self, window_length=100): |
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self.spreads = [] |
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self.invested = 0 |
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self.window_length = window_length |
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self.ols_transform = ols_transform(refresh_period=self.window_length, |
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window_length=self.window_length) |
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self.PEP = self.symbol('PEP') |
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self.KO = self.symbol('KO') |
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def handle_data(self, data): |
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###################################################### |
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# 1. Compute regression coefficients between PEP and KO |
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params = self.ols_transform.handle_data(data, self.PEP, self.KO) |
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if params is None: |
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return |
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intercept, slope = params |
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###################################################### |
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# 2. Compute spread and zscore |
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zscore = self.compute_zscore(data, slope, intercept) |
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self.record(zscores=zscore, |
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PEP=data[symbol('PEP')].price, |
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KO=data[symbol('KO')].price) |
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###################################################### |
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# 3. Place orders |
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self.place_orders(data, zscore) |
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def compute_zscore(self, data, slope, intercept): |
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"""1. Compute the spread given slope and intercept. |
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2. zscore the spread. |
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""" |
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spread = (data[self.PEP].price - |
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(slope * data[self.KO].price + intercept)) |
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self.spreads.append(spread) |
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spread_wind = self.spreads[-self.window_length:] |
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zscore = (spread - np.mean(spread_wind)) / np.std(spread_wind) |
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return zscore |
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def place_orders(self, data, zscore): |
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"""Buy spread if zscore is > 2, sell if zscore < .5. |
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""" |
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if zscore >= 2.0 and not self.invested: |
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self.order(self.PEP, int(100 / data[self.PEP].price)) |
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self.order(self.KO, -int(100 / data[self.KO].price)) |
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self.invested = True |
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elif zscore <= -2.0 and not self.invested: |
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self.order(self.PEP, -int(100 / data[self.PEP].price)) |
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self.order(self.KO, int(100 / data[self.KO].price)) |
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self.invested = True |
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elif abs(zscore) < .5 and self.invested: |
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self.sell_spread() |
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self.invested = False |
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def sell_spread(self): |
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""" |
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decrease exposure, regardless of position long/short. |
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buy for a short position, sell for a long. |
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""" |
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ko_amount = self.portfolio.positions[self.KO].amount |
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self.order(self.KO, -1 * ko_amount) |
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pep_amount = self.portfolio.positions[self.PEP].amount |
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self.order(self.PEP, -1 * pep_amount) |
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# Note: this function can be removed if running |
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# this algorithm on quantopian.com |
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def analyze(context=None, results=None): |
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ax1 = plt.subplot(211) |
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plt.title('PepsiCo & Coca-Cola Co. share prices') |
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results[['PEP', 'KO']].plot(ax=ax1) |
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plt.ylabel('Price (USD)') |
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plt.setp(ax1.get_xticklabels(), visible=False) |
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ax2 = plt.subplot(212, sharex=ax1) |
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results.zscores.plot(ax=ax2, color='r') |
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plt.ylabel('Z-scored spread') |
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plt.gcf().set_size_inches(18, 8) |
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plt.show() |
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# Note: this if-block should be removed if running |
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# this algorithm on quantopian.com |
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if __name__ == '__main__': |
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logbook.StderrHandler().push_application() |
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# Set the simulation start and end dates. |
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start = datetime(2000, 1, 1, 0, 0, 0, 0, pytz.utc) |
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end = datetime(2002, 1, 1, 0, 0, 0, 0, pytz.utc) |
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# Load price data from yahoo. |
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data = load_from_yahoo(stocks=['PEP', 'KO'], indexes={}, |
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start=start, end=end) |
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# Create and run the algorithm. |
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pairtrade = Pairtrade() |
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results = pairtrade.run(data) |
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# Plot the portfolio data. |
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analyze(results=results) |
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quantopian /
zipline
