chore: import upstream snapshot with attribution

2026-07-13 13:02:50 +08:00
commit 0fc60fdcb1
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+# QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals.
+# Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from AlgorithmImports import *
+from scipy.optimize import minimize
+
+### <summary>
+### Provides an implementation of a portfolio optimizer that calculate the optimal weights
+### with the weight range from -1 to 1 and minimize the portfolio variance with a target return of 2%
+### </summary>
+### <remarks>The budged constrain is scaled down/up to ensure that the sum of the absolute value of the weights is 1.</remarks>
+class MinimumVariancePortfolioOptimizer:
+    '''Provides an implementation of a portfolio optimizer that calculate the optimal weights
+    with the weight range from -1 to 1 and minimize the portfolio variance with a target return of 2%'''
+    def __init__(self,
+                 minimum_weight = -1,
+                 maximum_weight = 1,
+                 target_return = 0.02):
+        '''Initialize the MinimumVariancePortfolioOptimizer
+        Args:
+            minimum_weight(float): The lower bounds on portfolio weights
+            maximum_weight(float): The upper bounds on portfolio weights
+            target_return(float): The target portfolio return'''
+        self.minimum_weight = minimum_weight
+        self.maximum_weight = maximum_weight
+        self.target_return = target_return
+
+    def optimize(self, historical_returns, expected_returns = None, covariance = None):
+        '''
+        Perform portfolio optimization for a provided matrix of historical returns and an array of expected returns
+        args:
+            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).
+            expected_returns: Array of double with the portfolio annualized expected returns (size: K x 1).
+            covariance: Multi-dimensional array of double with the portfolio covariance of annualized returns (size: K x K).
+        Returns:
+            Array of double with the portfolio weights (size: K x 1)
+        '''
+        if covariance is None:
+            covariance = historical_returns.cov()
+        if expected_returns is None:
+            expected_returns = historical_returns.mean()
+
+        size = historical_returns.columns.size   # K x 1
+        x0 = np.array(size * [1. / size])
+
+        constraints = [
+            {'type': 'eq', 'fun': lambda weights: self.get_budget_constraint(weights)},
+            {'type': 'eq', 'fun': lambda weights: self.get_target_constraint(weights, expected_returns)}]
+
+        # https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html
+        opt = minimize(lambda weights: self.portfolio_variance(weights, covariance),     # Objective function
+                       x0,                                                        # Initial guess
+                       bounds = self.get_boundary_conditions(size),               # Bounds for variables
+                       constraints = constraints,                                 # Constraints definition
+                       method='SLSQP')     # Optimization method:  Sequential Least Squares Programming (SLSQP)
+
+        if not opt['success']: return x0
+
+        # Scale the solution to ensure that the sum of the absolute weights is 1
+        sum_of_absolute_weights = np.sum(np.abs(opt['x']))
+        return opt['x'] / sum_of_absolute_weights
+
+    def portfolio_variance(self, weights, covariance):
+        '''Computes the portfolio variance
+        Args:
+            weighs: Portfolio weights
+            covariance: Covariance matrix of historical returns'''
+        variance = np.dot(weights.T, np.dot(covariance, weights))
+        if variance == 0 and np.any(weights):
+            # variance can't be zero, with non zero weights
+            raise ValueError(f'MinimumVariancePortfolioOptimizer.portfolio_variance: Volatility cannot be zero. Weights: {weights}')
+        return variance
+
+    def get_boundary_conditions(self, size):
+        '''Creates the boundary condition for the portfolio weights'''
+        return tuple((self.minimum_weight, self.maximum_weight) for x in range(size))
+
+    def get_budget_constraint(self, weights):
+        '''Defines a budget constraint: the sum of the weights equals unity'''
+        return np.sum(weights) - 1
+
+    def get_target_constraint(self, weights, expected_returns):
+        '''Ensure that the portfolio return target a given return'''
+        return np.dot(np.matrix(expected_returns), np.matrix(weights).T).item() - self.target_return