risk_parity_strategy.py

import pandas as pd
import pandas_datareader.data as web
import numpy as np
import datetime
from scipy.optimize import minimize
TOLERANCE = 1e-10


def _allocation_risk(weights, covariances):

    # We calculate the risk of the weights distribution
    portfolio_risk = np.sqrt((weights * covariances * weights.T))[0, 0]

    # It returns the risk of the weights distribution
    return portfolio_risk


def _assets_risk_contribution_to_allocation_risk(weights, covariances):

    # We calculate the risk of the weights distribution
    portfolio_risk = _allocation_risk(weights, covariances)

    # We calculate the contribution of each asset to the risk of the weights
    # distribution
    assets_risk_contribution = np.multiply(weights.T, covariances * weights.T) \
        / portfolio_risk

    # It returns the contribution of each asset to the risk of the weights
    # distribution
    return assets_risk_contribution


def _risk_budget_objective_error(weights, args):

    # The covariance matrix occupies the first position in the variable
    covariances = args[0]

    # The desired contribution of each asset to the portfolio risk occupies the
    # second position
    assets_risk_budget = args[1]

    # We convert the weights to a matrix
    weights = np.matrix(weights)

    # We calculate the risk of the weights distribution
    portfolio_risk = _allocation_risk(weights, covariances)

    # We calculate the contribution of each asset to the risk of the weights
    # distribution
    assets_risk_contribution = \
        _assets_risk_contribution_to_allocation_risk(weights, covariances)

    # We calculate the desired contribution of each asset to the risk of the
    # weights distribution
    assets_risk_target = \
        np.asmatrix(np.multiply(portfolio_risk, assets_risk_budget))

    # Error between the desired contribution and the calculated contribution of
    # each asset
    error = \
        sum(np.square(assets_risk_contribution - assets_risk_target.T))[0, 0]

    # It returns the calculated error
    return error


def _get_risk_parity_weights(covariances, assets_risk_budget, initial_weights):

    # Restrictions to consider in the optimisation: only long positions whose
    # sum equals 100%
    constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1.0},
                   {'type': 'ineq', 'fun': lambda x: x})

    # Optimisation process in scipy
    optimize_result = minimize(fun=_risk_budget_objective_error,
                               x0=initial_weights,
                               args=[covariances, assets_risk_budget],
                               method='SLSQP',
                               constraints=constraints,
                               tol=TOLERANCE,
                               options={'disp': False})

    # Recover the weights from the optimised object
    weights = optimize_result.x

    # It returns the optimised weights
    return weights


def get_weights(yahoo_tickers=['GOOGL', 'AAPL', 'AMZN'],
                start_date=datetime.datetime(2016, 10, 31),
                end_date=datetime.datetime(2017, 10, 31)):

    # We download the prices from Yahoo Finance
    prices = pd.DataFrame([web.DataReader(t,
                                          'yahoo',
                                          start_date,
                                          end_date).loc[:, 'Adj Close']
                           for t in yahoo_tickers],
                          index=yahoo_tickers).T.asfreq('B').ffill()

    # We calculate the covariance matrix
    covariances = 52.0 * \
        prices.asfreq('W-FRI').pct_change().iloc[1:, :].cov().values

    # The desired contribution of each asset to the portfolio risk: we want all
    # asset to contribute equally
    assets_risk_budget = [1 / prices.shape[1]] * prices.shape[1]

    # Initial weights: equally weighted
    init_weights = [1 / prices.shape[1]] * prices.shape[1]

    # Optimisation process of weights
    weights = \
        _get_risk_parity_weights(covariances, assets_risk_budget, init_weights)

    # Convert the weights to a pandas Series
    weights = pd.Series(weights, index=prices.columns, name='weight')

    # It returns the optimised weights
    return weights

Nice demo! Very clear code too! I get the most weight on AAPL unless I restrict the time period to only the past few months, in which case GOOGL dominates. Pretty much what you'd expect considering the recent events/talk!

Just a heads up for those trying to run this in the future that lines 108 and 111 should be initialized with 1.0 rather than 1. Otherwise we'll just get zeros for these values :)

I tried this and it keeps giving me back weights in the optimizer that are the same as the initial weights. Also, the optimizer only runs one iteration. Any idea why this is?

line 103, why you multiply covariance with 52.0? even though I know it may help get correct weights.

line 103, why you multiply covariance with 52.0? even though I know it may help get correct weights.

probably because he's using weekly data