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import sys
import logbook
import numpy as np
from zipline.finance import commission, slippage
zipline_logging = logbook.NestedSetup([
logbook.NullHandler(),
logbook.StreamHandler(sys.stdout, level=logbook.INFO),
logbook.StreamHandler(sys.stderr, level=logbook.ERROR),
])
zipline_logging.push_application()
STOCKS = ['AMD', 'CERN', 'COST', 'DELL', 'GPS', 'INTC', 'MMM']
# On-Line Portfolio Moving Average Reversion
# More info can be found in the corresponding paper:
# http://icml.cc/2012/papers/168.pdf
def initialize(algo, eps=1, window_length=5):
algo.stocks = STOCKS
algo.sids = [algo.symbol(symbol) for symbol in algo.stocks]
algo.m = len(algo.stocks)
algo.price = {}
algo.b_t = np.ones(algo.m) / algo.m
algo.last_desired_port = np.ones(algo.m) / algo.m
algo.eps = eps
algo.init = True
algo.days = 0
algo.window_length = window_length
algo.set_commission(commission.PerShare(cost=0, min_trade_cost=1.0))
algo.set_slippage(slippage.VolumeShareSlippage())
def handle_data(algo, data):
algo.days += 1
if algo.days < algo.window_length:
return
if algo.init:
rebalance_portfolio(algo, data, algo.b_t)
algo.init = False
return
m = algo.m
x_tilde = np.zeros(m)
# find relative moving average price for each asset
mavgs = data.history(algo.sids, 'price', algo.window_length, '1d').mean()
for i, sid in enumerate(algo.sids):
price = data.current(sid, "price")
# Relative mean deviation
x_tilde[i] = mavgs[sid] / price
###########################
# Inside of OLMAR (algo 2)
x_bar = x_tilde.mean()
# market relative deviation
mark_rel_dev = x_tilde - x_bar
# Expected return with current portfolio
exp_return = np.dot(algo.b_t, x_tilde)
weight = algo.eps - exp_return
variability = (np.linalg.norm(mark_rel_dev)) ** 2
# test for divide-by-zero case
if variability == 0.0:
step_size = 0
else:
step_size = max(0, weight / variability)
b = algo.b_t + step_size * mark_rel_dev
b_norm = simplex_projection(b)
np.testing.assert_almost_equal(b_norm.sum(), 1)
rebalance_portfolio(algo, data, b_norm)
# update portfolio
algo.b_t = b_norm
def rebalance_portfolio(algo, data, desired_port):
# rebalance portfolio
desired_amount = np.zeros_like(desired_port)
current_amount = np.zeros_like(desired_port)
prices = np.zeros_like(desired_port)
if algo.init:
positions_value = algo.portfolio.starting_cash
else:
positions_value = algo.portfolio.positions_value + \
algo.portfolio.cash
for i, sid in enumerate(algo.sids):
current_amount[i] = algo.portfolio.positions[sid].amount
prices[i] = data.current(sid, "price")
desired_amount = np.round(desired_port * positions_value / prices)
algo.last_desired_port = desired_port
diff_amount = desired_amount - current_amount
for i, sid in enumerate(algo.sids):
algo.order(sid, diff_amount[i])
def simplex_projection(v, b=1):
"""Projection vectors to the simplex domain
Implemented according to the paper: Efficient projections onto the
l1-ball for learning in high dimensions, John Duchi, et al. ICML 2008.
Implementation Time: 2011 June 17 by Bin@libin AT pmail.ntu.edu.sg
Optimization Problem: min_{w}\| w - v \|_{2}^{2}
s.t. sum_{i=1}^{m}=z, w_{i}\geq 0
Input: A vector v \in R^{m}, and a scalar z > 0 (default=1)
Output: Projection vector w
:Example:
>>> proj = simplex_projection([.4 ,.3, -.4, .5])
>>> proj # doctest: +NORMALIZE_WHITESPACE
array([ 0.33333333, 0.23333333, 0. , 0.43333333])
>>> print(proj.sum())
1.0
Original matlab implementation: John Duchi (jduchi@cs.berkeley.edu)
Python-port: Copyright 2013 by Thomas Wiecki (thomas.wiecki@gmail.com).
"""
v = np.asarray(v)
p = len(v)
# Sort v into u in descending order
v = (v > 0) * v
u = np.sort(v)[::-1]
sv = np.cumsum(u)
rho = np.where(u > (sv - b) / np.arange(1, p + 1))[0][-1]
theta = np.max([0, (sv[rho] - b) / (rho + 1)])
w = (v - theta)
w[w < 0] = 0
return w
# Note: this function can be removed if running
# this algorithm on quantopian.com
def analyze(context=None, results=None):
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
results.portfolio_value.plot(ax=ax)
ax.set_ylabel('Portfolio value (USD)')
plt.show()
def _test_args():
"""Extra arguments to use when zipline's automated tests run this example.
"""
import pandas as pd
return {
'start': pd.Timestamp('2004', tz='utc'),
'end': pd.Timestamp('2008', tz='utc'),
}