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import sys |
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import logbook |
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import numpy as np |
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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.utils.factory import load_from_yahoo |
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from zipline.finance import commission |
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zipline_logging = logbook.NestedSetup([ |
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logbook.NullHandler(level=logbook.DEBUG, bubble=True), |
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logbook.StreamHandler(sys.stdout, level=logbook.INFO), |
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logbook.StreamHandler(sys.stderr, level=logbook.ERROR), |
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]) |
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zipline_logging.push_application() |
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STOCKS = ['AMD', 'CERN', 'COST', 'DELL', 'GPS', 'INTC', 'MMM'] |
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# On-Line Portfolio Moving Average Reversion |
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# More info can be found in the corresponding paper: |
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# http://icml.cc/2012/papers/168.pdf |
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def initialize(algo, eps=1, window_length=5): |
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algo.stocks = STOCKS |
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algo.sids = [algo.symbol(symbol) for symbol in algo.stocks] |
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algo.m = len(algo.stocks) |
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algo.price = {} |
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algo.b_t = np.ones(algo.m) / algo.m |
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algo.last_desired_port = np.ones(algo.m) / algo.m |
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algo.eps = eps |
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algo.init = True |
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algo.days = 0 |
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algo.window_length = window_length |
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algo.add_transform('mavg', 5) |
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algo.set_commission(commission.PerShare(cost=0)) |
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def handle_data(algo, data): |
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algo.days += 1 |
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if algo.days < algo.window_length: |
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return |
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if algo.init: |
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rebalance_portfolio(algo, data, algo.b_t) |
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algo.init = False |
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return |
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m = algo.m |
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x_tilde = np.zeros(m) |
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b = np.zeros(m) |
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# find relative moving average price for each asset |
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for i, sid in enumerate(algo.sids): |
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price = data[sid].price |
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# Relative mean deviation |
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x_tilde[i] = data[sid].mavg(algo.window_length) / price |
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########################### |
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# Inside of OLMAR (algo 2) |
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x_bar = x_tilde.mean() |
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# market relative deviation |
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mark_rel_dev = x_tilde - x_bar |
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# Expected return with current portfolio |
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exp_return = np.dot(algo.b_t, x_tilde) |
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weight = algo.eps - exp_return |
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variability = (np.linalg.norm(mark_rel_dev)) ** 2 |
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# test for divide-by-zero case |
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if variability == 0.0: |
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step_size = 0 |
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else: |
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step_size = max(0, weight / variability) |
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b = algo.b_t + step_size * mark_rel_dev |
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b_norm = simplex_projection(b) |
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np.testing.assert_almost_equal(b_norm.sum(), 1) |
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rebalance_portfolio(algo, data, b_norm) |
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# update portfolio |
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algo.b_t = b_norm |
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def rebalance_portfolio(algo, data, desired_port): |
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# rebalance portfolio |
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desired_amount = np.zeros_like(desired_port) |
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current_amount = np.zeros_like(desired_port) |
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prices = np.zeros_like(desired_port) |
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if algo.init: |
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positions_value = algo.portfolio.starting_cash |
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else: |
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positions_value = algo.portfolio.positions_value + \ |
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algo.portfolio.cash |
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for i, sid in enumerate(algo.sids): |
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current_amount[i] = algo.portfolio.positions[sid].amount |
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prices[i] = data[sid].price |
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desired_amount = np.round(desired_port * positions_value / prices) |
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algo.last_desired_port = desired_port |
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diff_amount = desired_amount - current_amount |
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for i, sid in enumerate(algo.sids): |
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algo.order(sid, diff_amount[i]) |
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def simplex_projection(v, b=1): |
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"""Projection vectors to the simplex domain |
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Implemented according to the paper: Efficient projections onto the |
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l1-ball for learning in high dimensions, John Duchi, et al. ICML 2008. |
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Implementation Time: 2011 June 17 by Bin@libin AT pmail.ntu.edu.sg |
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Optimization Problem: min_{w}\| w - v \|_{2}^{2} |
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s.t. sum_{i=1}^{m}=z, w_{i}\geq 0 |
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Input: A vector v \in R^{m}, and a scalar z > 0 (default=1) |
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Output: Projection vector w |
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:Example: |
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>>> proj = simplex_projection([.4 ,.3, -.4, .5]) |
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>>> print(proj) |
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array([ 0.33333333, 0.23333333, 0. , 0.43333333]) |
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>>> print(proj.sum()) |
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1.0 |
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Original matlab implementation: John Duchi ([email protected]) |
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Python-port: Copyright 2013 by Thomas Wiecki ([email protected]). |
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""" |
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v = np.asarray(v) |
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p = len(v) |
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# Sort v into u in descending order |
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v = (v > 0) * v |
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u = np.sort(v)[::-1] |
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sv = np.cumsum(u) |
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rho = np.where(u > (sv - b) / np.arange(1, p + 1))[0][-1] |
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theta = np.max([0, (sv[rho] - b) / (rho + 1)]) |
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w = (v - theta) |
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w[w < 0] = 0 |
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return w |
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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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import matplotlib.pyplot as plt |
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fig = plt.figure() |
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ax = fig.add_subplot(111) |
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results.portfolio_value.plot(ax=ax) |
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ax.set_ylabel('Portfolio value (USD)') |
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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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# Set the simulation start and end dates. |
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start = datetime(2004, 1, 1, 0, 0, 0, 0, pytz.utc) |
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end = datetime(2008, 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=STOCKS, indexes={}, start=start, end=end) |
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data = data.dropna() |
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# Create and run the algorithm. |
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olmar = TradingAlgorithm(handle_data=handle_data, |
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initialize=initialize, |
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identifiers=STOCKS) |
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results = olmar.run(data) |
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# Plot the portfolio data. |
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analyze(results=results) |
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quantopian /
zipline
