wehub-resource-sync
64 lines
3.2 KiB
Python
64 lines
3.2 KiB
Python
# QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals.
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# Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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from AlgorithmImports import *
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from scipy.optimize import *
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### <summary>
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### Provides an implementation of a risk parity portfolio optimizer that calculate the optimal weights
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### with the weight range from 0 to 1 and equalize the risk carried by each asset
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### </summary>
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class RiskParityPortfolioOptimizer:
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def __init__(self,
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minimum_weight = 1e-05,
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maximum_weight = sys.float_info.max):
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'''Initialize the RiskParityPortfolioOptimizer
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Args:
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minimum_weight(float): The lower bounds on portfolio weights
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maximum_weight(float): The upper bounds on portfolio weights'''
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self.minimum_weight = minimum_weight if minimum_weight >= 1e-05 else 1e-05
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self.maximum_weight = maximum_weight if maximum_weight >= minimum_weight else minimum_weight
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def optimize(self, historical_returns, budget = None, covariance = None):
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'''
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Perform portfolio optimization for a provided matrix of historical returns and an array of expected returns
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args:
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historical_returns: Matrix of annualized historical returns where each column represents a security and each row returns for the given date/time (size: K x N).
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budget: Risk budget vector (size: K x 1).
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covariance: Multi-dimensional array of double with the portfolio covariance of annualized returns (size: K x K).
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Returns:
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Array of double with the portfolio weights (size: K x 1)
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'''
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if covariance is None:
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covariance = np.cov(historical_returns.T)
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size = historical_returns.columns.size # K x 1
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# Optimization Problem
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# minimize_{x >= 0} f(x) = 1/2 * x^T.S.x - b^T.log(x)
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# b = 1 / num_of_assets (equal budget of risk)
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# df(x)/dx = S.x - b / x
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# H(x) = S + Diag(b / x^2)
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# lw <= x <= up
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x0 = np.array(size * [1. / size])
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budget = budget if budget is not None else x0
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objective = lambda weights: 0.5 * weights.T @ covariance @ weights - budget.T @ np.log(weights)
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gradient = lambda weights: covariance @ weights - budget / weights
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hessian = lambda weights: covariance + np.diag((budget / weights**2).flatten())
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solver = minimize(objective, jac=gradient, hess=hessian, x0=x0, method="Newton-CG")
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if not solver["success"]: return x0
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# Normalize weights: w = x / x^T.1
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return np.clip(solver["x"]/np.sum(solver["x"]), self.minimum_weight, self.maximum_weight)
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