OLMAR Online Portfolio Rebalancing with Moving Average Reversion

# olmar.py


```py
import logging
import sys

import numpy as np

from zipline.finance import commission, slippage

# zipline_logging = logging.getLogger("zipline_logging")
# zipline_logging.addHandler(logging.NullHandler())
# zipline_logging.addHandler(
#     logging.StreamHandler(sys.stdout).setLevel(logging.INFO),
# )
# zipline_logging.addHandler(logging.StreamHandler(sys.stderr).setLevel(logging.ERROR))


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):
    r"""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


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"), "end": pd.Timestamp("2008")}

```