QuadraticMeanVarianceOptimizer.java

  1. package org.drip.portfolioconstruction.allocator;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * 
  14.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  15.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  16.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  17.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  18.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  19.  *      and computational support.
  20.  *  
  21.  *      https://lakshmidrip.github.io/DROP/
  22.  *  
  23.  *  DROP is composed of three modules:
  24.  *  
  25.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  26.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  27.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  28.  * 
  29.  *  DROP Product Core implements libraries for the following:
  30.  *  - Fixed Income Analytics
  31.  *  - Loan Analytics
  32.  *  - Transaction Cost Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Asset Liability Management Analytics
  37.  *  - Capital Estimation Analytics
  38.  *  - Exposure Analytics
  39.  *  - Margin Analytics
  40.  *  - XVA Analytics
  41.  * 
  42.  *  DROP Computational Core implements libraries for the following:
  43.  *  - Algorithm Support
  44.  *  - Computation Support
  45.  *  - Function Analysis
  46.  *  - Model Validation
  47.  *  - Numerical Analysis
  48.  *  - Numerical Optimizer
  49.  *  - Spline Builder
  50.  *  - Statistical Learning
  51.  * 
  52.  *  Documentation for DROP is Spread Over:
  53.  * 
  54.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  55.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  56.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  57.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  58.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  59.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  60.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  61.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  62.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  63.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  64.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  65.  * 
  66.  *  Licensed under the Apache License, Version 2.0 (the "License");
  67.  *      you may not use this file except in compliance with the License.
  68.  *   
  69.  *  You may obtain a copy of the License at
  70.  *      http://www.apache.org/licenses/LICENSE-2.0
  71.  *  
  72.  *  Unless required by applicable law or agreed to in writing, software
  73.  *      distributed under the License is distributed on an "AS IS" BASIS,
  74.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  75.  *  
  76.  *  See the License for the specific language governing permissions and
  77.  *      limitations under the License.
  78.  */

  80. /**
  81.  * <i>QuadraticMeanVarianceOptimizer</i> builds an Optimal Portfolio Based on MPT Using the Asset Pool
  82.  * Statistical Properties using a Quadratic Optimization Function and Equality Constraints (if any).
  83.  *
  84.  *  <br><br>
  85.  *  <ul>
  86.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  87.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AssetAllocationAnalyticsLibrary.md">Asset Allocation Analytics</a></li>
  88.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/portfolioconstruction/README.md">Portfolio Construction under Allocation Constraints</a></li>
  89.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/portfolioconstruction/allocator/README.md">MVO Based Portfolio Allocation Construction</a></li>
  90.  *  </ul>
  91.  *
  92.  * @author Lakshmi Krishnamurthy
  93.  */

  95. public class QuadraticMeanVarianceOptimizer extends
  96.     org.drip.portfolioconstruction.allocator.MeanVarianceOptimizer
  97. {

  99.     protected org.drip.portfolioconstruction.allocator.HoldingsAllocationControl constrainedPCP (
  100.         final org.drip.portfolioconstruction.allocator.HoldingsAllocationControl
  101.             designPortfolioConstructionParameters,
  102.         final double returnsConstraint)
  103.     {
  104.         try {
  105.             return new org.drip.portfolioconstruction.allocator.HoldingsAllocationControl (
  106.                 designPortfolioConstructionParameters.assetIDArray(),
  107.                 designPortfolioConstructionParameters.customRiskUtilitySettings(),
  108.                 new org.drip.portfolioconstruction.allocator.EqualityConstraintSettings (
  109.                     designPortfolioConstructionParameters.equalityConstraintSettings().constraintType() |
  110.                         org.drip.portfolioconstruction.allocator.EqualityConstraintSettings.RETURNS_CONSTRAINT,
  111.                     returnsConstraint
  112.                 )
  113.             );
  114.         }
  115.         catch (java.lang.Exception e)
  116.         {
  117.             e.printStackTrace();
  118.         }

  120.         return null;
  121.     }

  123.     /**
  124.      * Empty QuadraticMeanVarianceOptimizer Constructor
  125.      */

  127.     public QuadraticMeanVarianceOptimizer()
  128.     {
  129.     }

  131.     @Override public org.drip.portfolioconstruction.allocator.HoldingsAllocation
  132.         longOnlyMaximumReturnsAllocate (
  133.             final org.drip.portfolioconstruction.allocator.HoldingsAllocationControl
  134.                 portfolioConstructionParameters,
  135.             final org.drip.portfolioconstruction.params.AssetUniverseStatisticalProperties
  136.                 assetUniverseStatisticalProperties)
  137.     {
  138.         if (null == portfolioConstructionParameters || null == assetUniverseStatisticalProperties)
  139.         {
  140.             return null;
  141.         }

  143.         java.lang.String[] assetIDArray = portfolioConstructionParameters.assetIDArray();

  145.         int assetCount = assetIDArray.length;
  146.         org.drip.portfolioconstruction.asset.AssetComponent[] assetComponentArray = new
  147.             org.drip.portfolioconstruction.asset.AssetComponent[assetCount];

  149.         double[] expectedAssetReturnsArray = assetUniverseStatisticalProperties.expectedReturns (
  150.             assetIDArray
  151.         );

  153.         if (null == expectedAssetReturnsArray || assetCount != expectedAssetReturnsArray.length)
  154.         {
  155.             return null;
  156.         }

  158.         double maximumReturns = expectedAssetReturnsArray[0];
  159.         java.lang.String maximumReturnsAssetID = assetIDArray[0];

  161.         for (int i = 1; i < assetCount; ++i)
  162.         {
  163.             if (expectedAssetReturnsArray[i] > maximumReturns)
  164.             {
  165.                 maximumReturnsAssetID = assetIDArray[i];
  166.                 maximumReturns = expectedAssetReturnsArray[i];
  167.             }
  168.         }

  170.         try
  171.         {
  172.             for (int i = 0; i < assetCount; ++i)
  173.             {
  174.                 assetComponentArray[i] = new org.drip.portfolioconstruction.asset.AssetComponent (
  175.                     assetIDArray[i],
  176.                     assetIDArray[i].equalsIgnoreCase (maximumReturnsAssetID) ? 1. : 0.
  177.                 );
  178.             }
  179.         }
  180.         catch (java.lang.Exception e)
  181.         {
  182.             e.printStackTrace();

  184.             return null;
  185.         }

  187.         return org.drip.portfolioconstruction.allocator.HoldingsAllocation.Create (
  188.             assetComponentArray,
  189.             assetUniverseStatisticalProperties
  190.         );
  191.     }

  193.     @Override public org.drip.portfolioconstruction.allocator.HoldingsAllocation
  194.         globalMinimumVarianceAllocate (
  195.             final org.drip.portfolioconstruction.allocator.HoldingsAllocationControl
  196.                 portfolioConstructionParameters,
  197.             final org.drip.portfolioconstruction.params.AssetUniverseStatisticalProperties
  198.                 assetUniverseStatisticalProperties)
  199.     {
  200.         if (null == portfolioConstructionParameters || null == assetUniverseStatisticalProperties)
  201.         {
  202.             return null;
  203.         }

  205.         java.lang.String[] assetIDArray = portfolioConstructionParameters.assetIDArray();

  207.         int assetCount = assetIDArray.length;
  208.         org.drip.function.rdtor1.LagrangianMultivariate lagrangianMultivariate = null;
  209.         org.drip.portfolioconstruction.asset.AssetComponent[] assetComponentArray = new
  210.             org.drip.portfolioconstruction.asset.AssetComponent[assetCount];

  212.         try
  213.         {
  214.             lagrangianMultivariate = new org.drip.function.rdtor1.LagrangianMultivariate (
  215.                 portfolioConstructionParameters.customRiskUtilitySettings().riskObjectiveUtility (
  216.                     assetIDArray,
  217.                     assetUniverseStatisticalProperties
  218.                 ),
  219.                 new org.drip.function.definition.RdToR1[]
  220.                 {
  221.                     portfolioConstructionParameters.fullyInvestedConstraint()
  222.                 }
  223.             );
  224.         }
  225.         catch (java.lang.Exception e)
  226.         {
  227.             e.printStackTrace();
  228.         }

  230.         int lagrangianDimension = lagrangianMultivariate.dimension();

  232.         double[] rhsArray = new double[lagrangianDimension];
  233.         double[] variateArray = new double[lagrangianDimension];

  235.         double riskToleranceFactor =
  236.             portfolioConstructionParameters.customRiskUtilitySettings().riskTolerance();

  238.         double[] equalityConstraintRHSArray = portfolioConstructionParameters.equalityConstraintRHS();

  240.         for (int lagrangianIndex = 0; lagrangianIndex < lagrangianDimension; ++lagrangianIndex)
  241.         {
  242.             variateArray[lagrangianIndex] = 0.;

  244.             if (lagrangianIndex < assetCount)
  245.             {
  246.                 if (0. != riskToleranceFactor)
  247.                 {
  248.                     org.drip.portfolioconstruction.params.AssetStatisticalProperties
  249.                         assetStatisticalProperties =
  250.                             assetUniverseStatisticalProperties.assetStatisticalProperties (
  251.                                 assetIDArray[lagrangianIndex]
  252.                             );

  254.                     if (null == assetStatisticalProperties)
  255.                     {
  256.                         return null;
  257.                     }

  259.                     rhsArray[lagrangianIndex] = assetStatisticalProperties.expectedReturn() *
  260.                         riskToleranceFactor;
  261.                 }
  262.                 else
  263.                 {
  264.                     rhsArray[lagrangianIndex] = 0.;
  265.                 }
  266.             }
  267.             else
  268.             {
  269.                 rhsArray[lagrangianIndex] = equalityConstraintRHSArray[lagrangianIndex - assetCount];
  270.             }
  271.         }

  273.         org.drip.numerical.linearalgebra.LinearizationOutput linearizationOutput =
  274.             org.drip.numerical.linearalgebra.LinearSystemSolver.SolveUsingMatrixInversion (
  275.                 lagrangianMultivariate.hessian (variateArray),
  276.                 rhsArray
  277.             );

  279.         if (null == linearizationOutput)
  280.         {
  281.             return null;
  282.         }

  284.         double[] assetHoldingsArray = linearizationOutput.getTransformedRHS();

  286.         if (null == assetHoldingsArray || assetHoldingsArray.length != lagrangianDimension)
  287.         {
  288.             return null;
  289.         }

  291.         try
  292.         {
  293.             for (int assetIndex = 0; assetIndex < assetCount; ++assetIndex)
  294.             {
  295.                 assetComponentArray[assetIndex] = new org.drip.portfolioconstruction.asset.AssetComponent (
  296.                     assetIDArray[assetIndex],
  297.                     assetHoldingsArray[assetIndex]
  298.                 );
  299.             }
  300.         }
  301.         catch (java.lang.Exception e)
  302.         {
  303.             e.printStackTrace();

  305.             return null;
  306.         }

  308.         return org.drip.portfolioconstruction.allocator.HoldingsAllocation.Create (
  309.             assetComponentArray,
  310.             assetUniverseStatisticalProperties
  311.         );
  312.     }

  314.     @Override public org.drip.portfolioconstruction.allocator.HoldingsAllocation allocate (
  315.         final org.drip.portfolioconstruction.allocator.HoldingsAllocationControl
  316.             portfolioConstructionParameters,
  317.         final org.drip.portfolioconstruction.params.AssetUniverseStatisticalProperties
  318.             assetUniverseStatisticalProperties)
  319.     {
  320.         if (null == portfolioConstructionParameters || null == assetUniverseStatisticalProperties)
  321.         {
  322.             return null;
  323.         }

  325.         java.lang.String[] assetIDArray = portfolioConstructionParameters.assetIDArray();

  327.         int assetCount = assetIDArray.length;
  328.         org.drip.function.rdtor1.LagrangianMultivariate lagrangianMultivariate = null;
  329.         org.drip.portfolioconstruction.asset.AssetComponent[] assetComponentArray = new
  330.             org.drip.portfolioconstruction.asset.AssetComponent[assetCount];

  332.         try
  333.         {
  334.             lagrangianMultivariate = new org.drip.function.rdtor1.LagrangianMultivariate (
  335.                 portfolioConstructionParameters.customRiskUtilitySettings().riskObjectiveUtility (
  336.                     assetIDArray,
  337.                     assetUniverseStatisticalProperties
  338.                 ),
  339.                 portfolioConstructionParameters.equalityConstraintArray (
  340.                     assetUniverseStatisticalProperties
  341.                 )
  342.             );
  343.         }
  344.         catch (java.lang.Exception e)
  345.         {
  346.             e.printStackTrace();
  347.         }

  349.         int lagrangianDimension = lagrangianMultivariate.dimension();

  351.         double[] variateArray = new double[lagrangianDimension];

  353.         org.drip.numerical.linearalgebra.LinearizationOutput linearizationOutput =
  354.             org.drip.numerical.linearalgebra.LinearSystemSolver.SolveUsingMatrixInversion (
  355.                 lagrangianMultivariate.hessian (variateArray),
  356.                 lagrangianMultivariate.jacobian (variateArray)
  357.             );

  359.         if (null == linearizationOutput)
  360.         {
  361.             return null;
  362.         }

  364.         double[] assetHoldingsArray = linearizationOutput.getTransformedRHS();

  366.         if (null == assetHoldingsArray || assetHoldingsArray.length != lagrangianDimension)
  367.         {
  368.             return null;
  369.         }

  371.         try
  372.         {
  373.             for (int assetIndex = 0; assetIndex < assetCount; ++assetIndex)
  374.             {
  375.                 assetComponentArray[assetIndex] = new org.drip.portfolioconstruction.asset.AssetComponent (
  376.                     assetIDArray[assetIndex],
  377.                     -1. * assetHoldingsArray[assetIndex]
  378.                 );
  379.             }
  380.         }
  381.         catch (java.lang.Exception e)
  382.         {
  383.             e.printStackTrace();

  385.             return null;
  386.         }

  388.         return org.drip.portfolioconstruction.allocator.HoldingsAllocation.Create (
  389.             assetComponentArray,
  390.             assetUniverseStatisticalProperties
  391.         );
  392.     }
  393. }
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