chore: import upstream snapshot with attribution
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wehub-resource-sync
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/*
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* 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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*/
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using QuantConnect.Data;
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using MathNet.Numerics.LinearAlgebra;
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using MathNet.Numerics.Statistics;
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using System.Collections.Generic;
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using System.Linq;
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using System;
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using QuantConnect.Indicators;
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using static QuantConnect.StringExtensions;
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namespace QuantConnect.Algorithm.CSharp
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{
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/// <summary>
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/// This algorithm uses Math.NET Numerics library, specifically Linear Algebra object (Vector and Matrix) and operations, in order to solve a portfolio optimization problem.
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/// </summary>
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/// <meta name="tag" content="strategy example" />
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/// <meta name="tag" content="portfolio optimization" />
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public class PortfolioOptimizationNumericsAlgorithm : QCAlgorithm
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{
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private const double _targetReturn = 0.1;
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private const double _riskFreeRate = 0.01;
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private double _lagrangeMultiplier;
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private double _portfolioRisk;
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private Matrix<double> Sigma;
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private List<SymbolData> SymbolDataList;
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public Vector<double> DiscountMeanVector
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{
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get
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{
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if (SymbolDataList == null)
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{
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return null;
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}
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return
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Vector<double>.Build.DenseOfArray(SymbolDataList.Select(x => (double)x.Return).ToArray()) -
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Vector<double>.Build.Dense(SymbolDataList.Count, _riskFreeRate);
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}
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}
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/// <summary>
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/// Initialise the data and resolution required, as well as the cash and start-end dates for your algorithm. All algorithms must initialized.
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/// </summary>
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public override void Initialize()
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{
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SetStartDate(2013, 10, 07); //Set Start Date
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SetEndDate(2013, 10, 11); //Set End Date
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SetCash(100000); //Set Strategy Cash
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// Find more symbols here: http://quantconnect.com/data
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AddEquity("SPY", Resolution.Daily);
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AddEquity("AIG", Resolution.Daily);
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AddEquity("BAC", Resolution.Daily);
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AddEquity("IBM", Resolution.Daily);
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var allHistoryBars = new List<double[]>();
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SymbolDataList = new List<SymbolData>();
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foreach (var security in Securities)
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{
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var history = History(security.Key, TimeSpan.FromDays(365));
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allHistoryBars.Add(history.Select(x => (double)x.Value).ToArray());
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SymbolDataList.Add(new SymbolData(security.Key, history));
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}
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// Diagonal Matrix with each security risk (standard deviation)
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var S = Matrix<double>.Build.DenseOfDiagonalArray(SymbolDataList.Select(x => (double)x.Risk).ToArray());
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// Computes Correlation Matrix (using Math.NET Numerics Statistics)
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var R = MathNet.Numerics.Statistics.Correlation.PearsonMatrix(allHistoryBars);
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// Computes Covariance Matrix (using Math.NET Numerics Linear Algebra)
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Sigma = S * R * S;
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ComputeLagrangeMultiplier();
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ComputeWeights();
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ComputePortfolioRisk();
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Log($"Lagrange Multiplier: {_lagrangeMultiplier.ToStringInvariant("7:F4")}");
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Log($"Portfolio Risk: {_portfolioRisk.ToStringInvariant("7:P2")} ");
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}
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/// <summary>
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/// OnData event is the primary entry point for your algorithm. Each new data point will be pumped in here.
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/// </summary>
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/// <param name="data">Slice object keyed by symbol containing the stock data</param>
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public override void OnData(Slice slice)
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{
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if (!Portfolio.Invested)
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{
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foreach (var symbolData in SymbolDataList.OrderBy(x => x.Weight))
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{
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SetHoldings(symbolData.Symbol, symbolData.Weight);
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Debug("Purchased Stock: " + symbolData);
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}
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}
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}
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/// <summary>
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/// Computes Lagrange Multiplier
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/// </summary>
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private void ComputeLagrangeMultiplier()
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{
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var denominatorMatrix = DiscountMeanVector * Sigma.Inverse() * DiscountMeanVector.ToColumnMatrix();
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_lagrangeMultiplier = (_targetReturn - _riskFreeRate) / denominatorMatrix.ToArray().First();
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}
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/// <summary>
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/// Computes weight for each risky asset
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/// </summary>
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private void ComputeWeights()
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{
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var weights = _lagrangeMultiplier * Sigma.Inverse() * DiscountMeanVector.ToColumnMatrix();
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for (var i = 0; i < weights.RowCount; i++)
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{
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SymbolDataList[i].SetWeight(weights.ToArray()[i, 0]);
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}
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}
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/// <summary>
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/// Computes Portfolio Risk
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/// </summary>
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private void ComputePortfolioRisk()
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{
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var weights = Vector<double>.Build.DenseOfArray(SymbolDataList.Select(x => (double)x.Return).ToArray());
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var portfolioVarianceMatrix = weights * Sigma * weights.ToColumnMatrix();
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_portfolioRisk = Math.Sqrt(portfolioVarianceMatrix.ToArray().First());
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}
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/// <summary>
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/// Symbol Data class to store security data (Return, Risk, Weight)
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/// </summary>
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class SymbolData
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{
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private RateOfChange ROC = new RateOfChange(2);
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private SimpleMovingAverage SMA;
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private StandardDeviation STD;
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public Symbol Symbol { get; private set; }
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public decimal Return { get { return SMA.Current; } }
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public decimal Risk { get { return STD.Current; } }
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public decimal Weight { get; private set; }
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public SymbolData(Symbol symbol, IEnumerable<BaseData> history)
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{
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Symbol = symbol;
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SMA = new SimpleMovingAverage(365).Of(ROC);
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STD = new StandardDeviation(365).Of(ROC);
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foreach (var data in history)
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{
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Update(data);
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}
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}
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public void Update(BaseData data)
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{
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ROC.Update(data.Time, data.Value);
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}
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public void SetWeight(double value)
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{
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Weight = (decimal)value;
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}
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public override string ToString()
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{
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return Invariant($"{Symbol.Value}: {Weight,10:P2}\t{Return,10:P2}\t{Risk,10:P2}");
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}
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}
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}
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}
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