Risk Parity: A Portfolio Management Strategy – Python

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In the previous article we tried to understand fund allocation as per Risk Parity strategy. This article would give you an idea that how to implement Risk Parity strategy in Python.

To understand Risk Parity Strategy click on the link.

Risk Parity Strategy.

Source of code is:

Risk Parity GitHub

You can use below code to implement the strategy:

# Import the Libraries

import pandas as pd

pd.core.common.is_list_like = pd.api.types.is_list_like
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

 

2 COMMENTS

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