BlackLittermanCombinationEngine.java

  1. package org.drip.portfolioconstruction.bayesian;

  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>BlackLittermanCombinationEngine</i> implements the Engine that generates the Combined/Posterior
  82.  * Distributions from the Prior and the Conditional Joint R<sup>1</sup> Multivariate Normal Distributions.
  83.  * The References are:
  84.  *  
  85.  *  <br><br>
  86.  *      <ul>
  87.  *          <li>
  88.  *              He. G., and R. Litterman (1999): <i>The Intuition behind the Black-Litterman Model
  89.  *                  Portfolios</i> <b>Goldman Sachs Asset Management</b>
  90.  *          </li>
  91.  *          <li>
  92.  *              Idzorek, T. (2005): <i>A Step-by-Step Guide to the Black-Litterman Model: Incorporating
  93.  *                  User-Specified Confidence Levels</i> <b>Ibbotson Associates</b> Chicago, IL
  94.  *          </li>
  95.  *      </ul>
  96.  *
  97.  *  <br><br>
  98.  *  <ul>
  99.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  100.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AssetAllocationAnalyticsLibrary.md">Asset Allocation Analytics</a></li>
  101.  *      <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>
  102.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/portfolioconstruction/bayesian/README.md">Black Litterman Bayesian Portfolio Construction</a></li>
  103.  *  </ul>
  104.  *
  105.  * @author Lakshmi Krishnamurthy
  106.  */

  108. public class BlackLittermanCombinationEngine
  109. {
  110.     private org.drip.portfolioconstruction.bayesian.ProjectionSpecification _projectionSpecification = null;
  111.     private org.drip.portfolioconstruction.bayesian.PriorControlSpecification _priorControlSpecification =
  112.         null;
  113.     private org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation
  114.         _forwardReverseOptimizationOutputUnadjusted = null;

  116.     private org.drip.measure.bayesian.ScopingProjectionVariateDistribution
  117.         scopingProjectionVariateDistribution()
  118.     {
  119.         double[][] assetExcessReturnsCovarianceMatrix =
  120.             _forwardReverseOptimizationOutputUnadjusted.assetExcessReturnsCovarianceMatrix();

  122.         double[] priorExpectedAssetReturnsArray =
  123.             _forwardReverseOptimizationOutputUnadjusted.expectedAssetExcessReturnsArray();

  125.         int assetCount = assetExcessReturnsCovarianceMatrix.length;
  126.         double[][] priorCovarianceMatrix = new double[assetCount][assetCount];

  128.         double riskFreeRate = _priorControlSpecification.riskFreeRate();

  130.         double tau = _priorControlSpecification.tau();

  132.         for (int assetIndexI = 0; assetIndexI < assetCount; ++assetIndexI)
  133.         {
  134.             priorExpectedAssetReturnsArray[assetIndexI] = priorExpectedAssetReturnsArray[assetIndexI] +
  135.                 riskFreeRate;

  137.             for (int assetIndexJ = 0; assetIndexJ < assetCount; ++assetIndexJ)
  138.             {
  139.                 priorCovarianceMatrix[assetIndexI][assetIndexJ] =
  140.                     assetExcessReturnsCovarianceMatrix[assetIndexI][assetIndexJ] * tau;
  141.             }
  142.         }

  144.         try
  145.         {
  146.             org.drip.measure.bayesian.ScopingProjectionVariateDistribution
  147.                 scopingProjectionVariateDistribution =
  148.                     new org.drip.measure.bayesian.ScopingProjectionVariateDistribution (
  149.                         org.drip.measure.gaussian.R1MultivariateNormal.Standard (
  150.                             _forwardReverseOptimizationOutputUnadjusted.optimalPortfolio().meta(),
  151.                             priorExpectedAssetReturnsArray,
  152.                             priorCovarianceMatrix
  153.                         )
  154.                     );

  156.             return scopingProjectionVariateDistribution.addProjectionDistributionLoading (
  157.                 "VIEW",
  158.                 new org.drip.measure.bayesian.ProjectionDistributionLoading (
  159.                     _projectionSpecification.excessReturnsDistribution(),
  160.                     _projectionSpecification.assetSpaceLoadingMatrix()
  161.                 )
  162.             ) ? scopingProjectionVariateDistribution : null;
  163.         }
  164.         catch (java.lang.Exception e)
  165.         {
  166.             e.printStackTrace();
  167.         }

  169.         return null;
  170.     }

  172.     private double[] allocationTiltArray (
  173.         final org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation
  174.             forwardReverseOptimizationOutputAdjusted)
  175.     {
  176.         double[] adjustedWeightArray =
  177.             forwardReverseOptimizationOutputAdjusted.optimalPortfolio().weightArray();

  179.         double[] unAdjustedWeightArray =
  180.             _forwardReverseOptimizationOutputUnadjusted.optimalPortfolio().weightArray();

  182.         int assetCount = unAdjustedWeightArray.length;
  183.         double[] allocationTiltArray = new double[assetCount];

  185.         for (int assetIndex = 0; assetIndex < assetCount; ++assetIndex)
  186.         {
  187.             allocationTiltArray[assetIndex] = adjustedWeightArray[assetIndex] -
  188.                 unAdjustedWeightArray[assetIndex];
  189.         }

  191.         return allocationTiltArray;
  192.     }

  194.     /**
  195.      * BlackLittermanCombinationEngine Construction
  196.      * 
  197.      * @param forwardReverseOptimizationOutputUnadjusted The Unadjusted Instance of
  198.      *  ForwardReverseOptimizationOutput
  199.      * @param priorControlSpecification The Prior Control Specification Instance
  200.      * @param projectionSpecification The View Projection Specification Settings
  201.      * 
  202.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  203.      */

  205.     public BlackLittermanCombinationEngine (
  206.         final org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation
  207.             forwardReverseOptimizationOutputUnadjusted,
  208.         final org.drip.portfolioconstruction.bayesian.PriorControlSpecification priorControlSpecification,
  209.         final org.drip.portfolioconstruction.bayesian.ProjectionSpecification projectionSpecification)
  210.         throws java.lang.Exception
  211.     {
  212.         if (null == (_forwardReverseOptimizationOutputUnadjusted =
  213.                 forwardReverseOptimizationOutputUnadjusted) ||
  214.             null == (_priorControlSpecification = priorControlSpecification) ||
  215.             null == (_projectionSpecification = projectionSpecification))
  216.         {
  217.             throw new java.lang.Exception ("BlackLittermanCombinationEngine Constructor => Invalid Inputs");
  218.         }
  219.     }

  221.     /**
  222.      * Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator for 0% Confidence in the
  223.      *  Projection
  224.      * 
  225.      * @return Output of the Black Litterman Run
  226.      */

  228.     public org.drip.portfolioconstruction.bayesian.BlackLittermanOutput noConfidenceRun()
  229.     {
  230.         double tau = _priorControlSpecification.tau();

  232.         double[][] assetExcessReturnsCovarianceMatrix =
  233.             _forwardReverseOptimizationOutputUnadjusted.assetExcessReturnsCovarianceMatrix();

  235.         int assetCount = assetExcessReturnsCovarianceMatrix.length;
  236.         double[][] assetBayesianExcessReturnsCovarianceMatrix = new double[assetCount][assetCount];

  238.         for (int i = 0; i < assetCount; ++i)
  239.         {
  240.             for (int j = 0; j < assetCount; ++j)
  241.             {
  242.                 assetBayesianExcessReturnsCovarianceMatrix[i][j] = assetExcessReturnsCovarianceMatrix[i][j] *
  243.                     tau;
  244.             }
  245.         }

  247.         org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation
  248.             forwardReverseOptimizationOutputAdjusted =
  249.                 org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation.Forward (
  250.                     _forwardReverseOptimizationOutputUnadjusted.optimalPortfolio().meta().names(),
  251.                     _forwardReverseOptimizationOutputUnadjusted.expectedAssetExcessReturnsArray(),
  252.                     assetBayesianExcessReturnsCovarianceMatrix,
  253.                     _forwardReverseOptimizationOutputUnadjusted.riskAversion()
  254.                 );

  256.         try
  257.         {
  258.             return null == forwardReverseOptimizationOutputAdjusted ? null :
  259.                 new org.drip.portfolioconstruction.bayesian.BlackLittermanOutput (
  260.                     forwardReverseOptimizationOutputAdjusted,
  261.                     allocationTiltArray (
  262.                         forwardReverseOptimizationOutputAdjusted
  263.                     )
  264.                 );
  265.         }
  266.         catch (java.lang.Exception e)
  267.         {
  268.             e.printStackTrace();
  269.         }

  271.         return null;
  272.     }

  274.     /**
  275.      * Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator Using the specified Confidence
  276.      *  Level
  277.      * 
  278.      * @return Output of the Black Litterman Run
  279.      */

  281.     public org.drip.portfolioconstruction.bayesian.BlackLittermanCustomConfidenceOutput customConfidenceRun()
  282.     {
  283.         double[][] assetExcessReturnsCovarianceMatrix =
  284.             _forwardReverseOptimizationOutputUnadjusted.assetExcessReturnsCovarianceMatrix();

  286.         org.drip.measure.continuous.MultivariateMeta portfolioMeta =
  287.             _forwardReverseOptimizationOutputUnadjusted.optimalPortfolio().meta();

  289.         org.drip.measure.bayesian.ScopingProjectionVariateDistribution scopingProjectionVariateDistribution =
  290.             scopingProjectionVariateDistribution();

  292.         if (null == scopingProjectionVariateDistribution)
  293.         {
  294.             return null;
  295.         }

  297.         org.drip.measure.bayesian.R1MultivariateConvolutionMetrics jointPosteriorMetrics =
  298.             org.drip.measure.bayesian.TheilMixedEstimationModel.GenerateComposite (
  299.                 scopingProjectionVariateDistribution,
  300.                 "VIEW",
  301.                 org.drip.measure.gaussian.R1MultivariateNormal.Standard (
  302.                     portfolioMeta,
  303.                     scopingProjectionVariateDistribution.scopingDistribution().mean(),
  304.                     assetExcessReturnsCovarianceMatrix
  305.                 )
  306.             );

  308.         if (null == jointPosteriorMetrics)
  309.         {
  310.             return null;
  311.         }

  313.         org.drip.measure.continuous.R1Multivariate r1mPosterior = jointPosteriorMetrics.posterior();

  315.         org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation
  316.             forwardReverseOptimizationOutputAdjusted =
  317.                 org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation.Forward (
  318.                     portfolioMeta.names(),
  319.                     r1mPosterior.mean(),
  320.                     _priorControlSpecification.useAlternateReferenceModel() ?
  321.                         assetExcessReturnsCovarianceMatrix :
  322.                         ((org.drip.measure.gaussian.R1MultivariateNormal)
  323.                             r1mPosterior).covariance().covarianceMatrix(),
  324.                     _forwardReverseOptimizationOutputUnadjusted.riskAversion()
  325.                 );

  327.         if (null == forwardReverseOptimizationOutputAdjusted)
  328.         {
  329.             return null;
  330.         }

  332.         try {
  333.             return new org.drip.portfolioconstruction.bayesian.BlackLittermanCustomConfidenceOutput (
  334.                 forwardReverseOptimizationOutputAdjusted,
  335.                 allocationTiltArray (
  336.                     forwardReverseOptimizationOutputAdjusted
  337.                 ),
  338.                 jointPosteriorMetrics
  339.             );
  340.         }
  341.         catch (java.lang.Exception e)
  342.         {
  343.             e.printStackTrace();
  344.         }

  346.         return null;
  347.     }

  349.     /**
  350.      * Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator For 100% Confidence in the
  351.      *  Projection
  352.      * 
  353.      * @return Output of the Black Litterman Run
  354.      */

  356.     public org.drip.portfolioconstruction.bayesian.BlackLittermanOutput fullConfidenceRun()
  357.     {
  358.         org.drip.measure.continuous.MultivariateMeta portfolioMeta =
  359.             _forwardReverseOptimizationOutputUnadjusted.optimalPortfolio().meta();

  361.         double[][] assetExcessReturnsCovarianceMatrix =
  362.             _forwardReverseOptimizationOutputUnadjusted.assetExcessReturnsCovarianceMatrix();

  364.         double riskAversion = _forwardReverseOptimizationOutputUnadjusted.riskAversion();

  366.         java.lang.String[] assetIDArray = portfolioMeta.names();

  368.         org.drip.measure.bayesian.ScopingProjectionVariateDistribution scopingProjectionVariateDistribution =
  369.             scopingProjectionVariateDistribution();

  371.         if (null == scopingProjectionVariateDistribution)
  372.         {
  373.             return null;
  374.         }

  376.         org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation
  377.             forwardReverseOptimizationOutputAdjusted = null;

  379.         if (_priorControlSpecification.useAlternateReferenceModel())
  380.         {
  381.             forwardReverseOptimizationOutputAdjusted =
  382.                 org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation.Forward (
  383.                     assetIDArray,
  384.                     org.drip.measure.bayesian.TheilMixedEstimationModel.ProjectionInducedScopingMean (
  385.                         scopingProjectionVariateDistribution,
  386.                         "VIEW"
  387.                     ),
  388.                     assetExcessReturnsCovarianceMatrix,
  389.                     riskAversion
  390.                 );
  391.         }
  392.         else
  393.         {
  394.             org.drip.measure.gaussian.R1MultivariateNormal combinedDistribution =
  395.                 org.drip.measure.bayesian.TheilMixedEstimationModel.ProjectionInducedScopingDistribution (
  396.                     scopingProjectionVariateDistribution,
  397.                     "VIEW",
  398.                     org.drip.measure.gaussian.R1MultivariateNormal.Standard (
  399.                         portfolioMeta,
  400.                         scopingProjectionVariateDistribution.scopingDistribution().mean(),
  401.                         assetExcessReturnsCovarianceMatrix
  402.                     )
  403.                 );

  405.             forwardReverseOptimizationOutputAdjusted = null == combinedDistribution ? null :
  406.                 org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation.Forward (
  407.                     assetIDArray,
  408.                     combinedDistribution.mean(),
  409.                     assetExcessReturnsCovarianceMatrix,
  410.                     riskAversion
  411.                 );
  412.         }

  414.         try
  415.         {
  416.             return null == forwardReverseOptimizationOutputAdjusted ? null :
  417.                 new org.drip.portfolioconstruction.bayesian.BlackLittermanOutput (
  418.                     forwardReverseOptimizationOutputAdjusted,
  419.                     allocationTiltArray (
  420.                         forwardReverseOptimizationOutputAdjusted
  421.                     )
  422.                 );
  423.         }
  424.         catch (java.lang.Exception e)
  425.         {
  426.             e.printStackTrace();
  427.         }

  429.         return null;
  430.     }

  432.     /**
  433.      * Compute the Idzorek Implied Projection Confidence Level
  434.      * 
  435.      * @return The Idzorek Implied Projection Confidence Level
  436.      */

  438.     public org.drip.portfolioconstruction.bayesian.ProjectionImpliedConfidenceOutput impliedConfidenceRun()
  439.     {
  440.         double[][] assetExcessReturnsCovarianceMatrix =
  441.             _forwardReverseOptimizationOutputUnadjusted.assetExcessReturnsCovarianceMatrix();

  443.         org.drip.portfolioconstruction.asset.Portfolio unadjustedPortfolio =
  444.             _forwardReverseOptimizationOutputUnadjusted.optimalPortfolio();

  446.         org.drip.measure.bayesian.ScopingProjectionVariateDistribution scopingProjectionVariateDistribution =
  447.             scopingProjectionVariateDistribution();

  449.         boolean useAlternateReferenceModel = _priorControlSpecification.useAlternateReferenceModel();

  451.         org.drip.measure.continuous.MultivariateMeta portfolioMeta = unadjustedPortfolio.meta();

  453.         double riskAversion = _forwardReverseOptimizationOutputUnadjusted.riskAversion();

  455.         java.lang.String[] assetIDArray = portfolioMeta.names();

  457.         if (null == scopingProjectionVariateDistribution)
  458.         {
  459.             return null;
  460.         }

  462.         org.drip.measure.bayesian.R1MultivariateConvolutionMetrics jointPosteriorMetrics =
  463.             org.drip.measure.bayesian.TheilMixedEstimationModel.GenerateComposite (
  464.                 scopingProjectionVariateDistribution,
  465.                 "VIEW",
  466.                 org.drip.measure.gaussian.R1MultivariateNormal.Standard (
  467.                     portfolioMeta,
  468.                     scopingProjectionVariateDistribution.scopingDistribution().mean(),
  469.                     assetExcessReturnsCovarianceMatrix
  470.                 )
  471.             );

  473.         if (null == jointPosteriorMetrics)
  474.         {
  475.             return null;
  476.         }

  478.         org.drip.measure.continuous.R1Multivariate posteriorDistribution = jointPosteriorMetrics.posterior();

  480.         org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation
  481.             forwardReverseOptimizationOutputCustomConfidence =
  482.                 org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation.Forward (
  483.                     assetIDArray,
  484.                     posteriorDistribution.mean(),
  485.                     useAlternateReferenceModel ? assetExcessReturnsCovarianceMatrix :
  486.                         ((org.drip.measure.gaussian.R1MultivariateNormal)
  487.                             posteriorDistribution).covariance().covarianceMatrix(),
  488.                     riskAversion
  489.                 );

  491.         if (null == forwardReverseOptimizationOutputCustomConfidence)
  492.         {
  493.             return null;
  494.         }

  496.         org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation
  497.             forwardReverseOptimizationOutputFullConfidence = null;

  499.         if (useAlternateReferenceModel)
  500.         {
  501.             forwardReverseOptimizationOutputFullConfidence =
  502.                 org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation.Forward (
  503.                     assetIDArray,
  504.                     org.drip.measure.bayesian.TheilMixedEstimationModel.ProjectionInducedScopingMean (
  505.                         scopingProjectionVariateDistribution,
  506.                         "VIEW"
  507.                     ),
  508.                     assetExcessReturnsCovarianceMatrix,
  509.                     riskAversion
  510.                 );
  511.         }
  512.         else
  513.         {
  514.             org.drip.measure.gaussian.R1MultivariateNormal combinedDistribution =
  515.                 org.drip.measure.bayesian.TheilMixedEstimationModel.ProjectionInducedScopingDistribution (
  516.                     scopingProjectionVariateDistribution,
  517.                     "VIEW",
  518.                     org.drip.measure.gaussian.R1MultivariateNormal.Standard (
  519.                         portfolioMeta,
  520.                         scopingProjectionVariateDistribution.scopingDistribution().mean(),
  521.                         assetExcessReturnsCovarianceMatrix
  522.                     )
  523.                 );

  525.             forwardReverseOptimizationOutputFullConfidence = null == combinedDistribution ? null :
  526.                 org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation.Forward (
  527.                     assetIDArray,
  528.                     combinedDistribution.mean(),
  529.                     assetExcessReturnsCovarianceMatrix,
  530.                     riskAversion
  531.                 );
  532.         }

  534.         try
  535.         {
  536.             return new org.drip.portfolioconstruction.bayesian.ProjectionImpliedConfidenceOutput (
  537.                 unadjustedPortfolio.weightArray(),
  538.                 new org.drip.portfolioconstruction.bayesian.BlackLittermanCustomConfidenceOutput (
  539.                     forwardReverseOptimizationOutputCustomConfidence,
  540.                     allocationTiltArray (
  541.                         forwardReverseOptimizationOutputCustomConfidence
  542.                     ),
  543.                     jointPosteriorMetrics
  544.                 ), new org.drip.portfolioconstruction.bayesian.BlackLittermanOutput (
  545.                     forwardReverseOptimizationOutputFullConfidence,
  546.                     allocationTiltArray (
  547.                         forwardReverseOptimizationOutputFullConfidence
  548.                     )
  549.                 )
  550.             );
  551.         }
  552.         catch (java.lang.Exception e)
  553.         {
  554.             e.printStackTrace();
  555.         }

  557.         return null;
  558.     }

  560.     /**
  561.      * Compute the Exposure Loadings Attribution on a per-Projection Basis
  562.      * 
  563.      * @return The Exposure Loadings Attribution on a per-Projection Basis
  564.      */

  566.     public org.drip.portfolioconstruction.bayesian.ProjectionExposure projectionExposureAttribution()
  567.     {
  568.         org.drip.measure.bayesian.ScopingProjectionVariateDistribution scopingProjectionVariateDistribution =
  569.             scopingProjectionVariateDistribution();

  571.         if (null == scopingProjectionVariateDistribution)
  572.         {
  573.             return null;
  574.         }

  576.         double[] intraViewComponentArray =
  577.             org.drip.measure.bayesian.TheilMixedEstimationModel.ProjectionPrecisionMeanProduct (
  578.                 scopingProjectionVariateDistribution,
  579.                 "VIEW"
  580.             );

  582.         if (null == intraViewComponentArray)
  583.         {
  584.             return null;
  585.         }

  587.         double tau = _priorControlSpecification.tau();

  589.         double riskAversion = _forwardReverseOptimizationOutputUnadjusted.riskAversion();

  591.         double[][] assetSpaceLoadingMatrix = _projectionSpecification.assetSpaceLoadingMatrix();

  593.         double[][] assetExcessReturnsCovarianceMatrix =
  594.             _forwardReverseOptimizationOutputUnadjusted.assetExcessReturnsCovarianceMatrix();

  596.         double projectionConfidenceScaler = 1. / tau;
  597.         int viewCount = intraViewComponentArray.length;
  598.         double assetConfidenceScaler = 1. / (1. + tau);
  599.         int assetCount = assetExcessReturnsCovarianceMatrix.length;
  600.         double[][] compositeConfidenceCovarianceMatrix = new double[viewCount][viewCount];

  602.         for (int viewIndex = 0; viewIndex < viewCount; ++viewIndex)
  603.         {
  604.             intraViewComponentArray[viewIndex] = intraViewComponentArray[viewIndex] * tau / riskAversion;
  605.         }

  607.         double[][] projectionSpaceAssetLoadingsMatrix = org.drip.numerical.linearalgebra.Matrix.Product (
  608.             org.drip.numerical.linearalgebra.Matrix.Product (
  609.                 assetSpaceLoadingMatrix,
  610.                 assetExcessReturnsCovarianceMatrix
  611.             ),
  612.             org.drip.numerical.linearalgebra.Matrix.Transpose (
  613.                 assetSpaceLoadingMatrix
  614.             )
  615.         );

  617.         if (null == projectionSpaceAssetLoadingsMatrix)
  618.         {
  619.             return null;
  620.         }

  622.         double[][] projectionCovarianceMatrix =
  623.             _projectionSpecification.excessReturnsDistribution().covariance().covarianceMatrix();

  625.         for (int viewIndexI = 0; viewIndexI < viewCount; ++viewIndexI)
  626.         {
  627.             for (int viewIndexJ = 0; viewIndexJ < viewCount; ++viewIndexJ)
  628.             {
  629.                 compositeConfidenceCovarianceMatrix[viewIndexI][viewIndexJ] =
  630.                     projectionCovarianceMatrix[viewIndexI][viewIndexJ] * projectionConfidenceScaler +
  631.                     projectionSpaceAssetLoadingsMatrix[viewIndexI][viewIndexJ] * assetConfidenceScaler;
  632.             }
  633.         }

  635.         double[][] compositePrecisionProjectionScoping = org.drip.numerical.linearalgebra.Matrix.Product (
  636.             org.drip.numerical.linearalgebra.Matrix.Product (
  637.                 org.drip.numerical.linearalgebra.Matrix.InvertUsingGaussianElimination (
  638.                     compositeConfidenceCovarianceMatrix
  639.                 ),
  640.                 assetSpaceLoadingMatrix
  641.             ),
  642.             assetExcessReturnsCovarianceMatrix
  643.         );

  645.         if (null == compositePrecisionProjectionScoping)
  646.         {
  647.             return null;
  648.         }

  650.         for (int viewIndexI = 0; viewIndexI < viewCount; ++viewIndexI)
  651.         {
  652.             for (int viewIndexJ = 0; viewIndexJ < assetCount; ++viewIndexJ)
  653.             {
  654.                 compositePrecisionProjectionScoping[viewIndexI][viewIndexJ] = -1. * assetConfidenceScaler *
  655.                     compositePrecisionProjectionScoping[viewIndexI][viewIndexJ];
  656.             }
  657.         }

  659.         try
  660.         {
  661.             return new org.drip.portfolioconstruction.bayesian.ProjectionExposure (
  662.                 intraViewComponentArray,
  663.                 org.drip.numerical.linearalgebra.Matrix.Product (
  664.                     compositePrecisionProjectionScoping,
  665.                     _forwardReverseOptimizationOutputUnadjusted.optimalPortfolio().weightArray()
  666.                 ),
  667.                 org.drip.numerical.linearalgebra.Matrix.Product (
  668.                     org.drip.numerical.linearalgebra.Matrix.Product (
  669.                         compositePrecisionProjectionScoping,
  670.                         org.drip.numerical.linearalgebra.Matrix.Transpose (
  671.                             assetSpaceLoadingMatrix
  672.                         )
  673.                     ),
  674.                     intraViewComponentArray
  675.                 ),
  676.                 compositeConfidenceCovarianceMatrix
  677.             );
  678.         }
  679.         catch (java.lang.Exception e)
  680.         {
  681.             e.printStackTrace();
  682.         }

  684.         return null;
  685.     }

  687.     /**
  688.      * Compute the Idzorek Implied Tilt Matrix from the User Projection Confidence Level
  689.      * 
  690.      * @param userSpecifiedProjectionConfidenceArray Array of User-specified Projection Confidence
  691.      * 
  692.      * @return The Idzorek Implied Tilt Matric from the Projection Confidence Level
  693.      */

  695.     public double[][] userConfidenceProjectionTitMatrix (
  696.         final double[] userSpecifiedProjectionConfidenceArray)
  697.     {
  698.         if (null == userSpecifiedProjectionConfidenceArray)
  699.         {
  700.             return null;
  701.         }

  703.         double[][] assetSpaceLoadingMatrix = _projectionSpecification.assetSpaceLoadingMatrix();

  705.         int assetCount = assetSpaceLoadingMatrix[0].length;
  706.         int projectionCount = assetSpaceLoadingMatrix.length;
  707.         double[][] userConfidenceProjectionTitMatrix = new double[projectionCount][assetCount];

  709.         if (projectionCount != userSpecifiedProjectionConfidenceArray.length)
  710.         {
  711.             return null;
  712.         }

  714.         org.drip.portfolioconstruction.bayesian.BlackLittermanOutput fullConfidenceOutput =
  715.             fullConfidenceRun();

  717.         if (null == fullConfidenceOutput)
  718.         {
  719.             return null;
  720.         }

  722.         double[] fullConfidenceWeightsDeviationArray = fullConfidenceOutput.allocationAdjustmentTiltArray();

  724.         for (int projectionIndex = 0; projectionIndex < projectionCount; ++projectionIndex)
  725.         {
  726.             for (int assetIndex = 0; assetIndex < assetCount; ++assetIndex)
  727.             {
  728.                 userConfidenceProjectionTitMatrix[projectionIndex][assetIndex] =
  729.                     fullConfidenceWeightsDeviationArray[assetIndex] *
  730.                     assetSpaceLoadingMatrix[projectionIndex][assetIndex] *
  731.                     userSpecifiedProjectionConfidenceArray[projectionIndex];
  732.             }
  733.         }

  735.         return userConfidenceProjectionTitMatrix;
  736.     }

  738.     /**
  739.      * Compute the Mismatch between the User Specified Projection and the Custom Confidence Implied Tilts
  740.      * 
  741.      * @param userConfidenceProjectionTiltArray Array of the User Confidence induced Projection Tilts
  742.      * @param projectionIndex The Index into the Projection Meta
  743.      * @param projectionVariance The Projection Variance
  744.      * 
  745.      * @return The Squared Mismatch
  746.      * 
  747.      * @throws java.lang.Exception Thrown if the Squared Mismatch cannot be calculated
  748.      */

  750.     public double tiltMismatchSquared (
  751.         final double[] userConfidenceProjectionTiltArray,
  752.         final int projectionIndex,
  753.         final double projectionVariance)
  754.         throws java.lang.Exception
  755.     {
  756.         if (null == userConfidenceProjectionTiltArray ||
  757.             !org.drip.numerical.common.NumberUtil.IsValid (
  758.                 projectionVariance
  759.             ))
  760.         {
  761.             throw new java.lang.Exception
  762.                 ("BlackLittermanCombinationEngine::tiltMismatchSquared => Invalid Inputs");
  763.         }

  765.         org.drip.measure.gaussian.R1MultivariateNormal totalExcessReturnsDistribution =
  766.             _projectionSpecification.excessReturnsDistribution();

  768.         org.drip.measure.gaussian.R1MultivariateNormal projectionDistribution =
  769.             org.drip.measure.gaussian.R1MultivariateNormal.Standard (
  770.                 new java.lang.String[] {
  771.                     totalExcessReturnsDistribution.meta().names()[projectionIndex]
  772.                 },
  773.                 new double[] {
  774.                     totalExcessReturnsDistribution.mean()[projectionIndex]
  775.                 },
  776.                 new double[][]
  777.                 {
  778.                     {
  779.                         projectionVariance
  780.                     }
  781.                 }
  782.             );

  784.         if (null == projectionDistribution)
  785.         {
  786.             throw new java.lang.Exception
  787.                 ("BlackLittermanCombinationEngine::tiltMismatchSquared => Invalid Inputs");
  788.         }

  790.         BlackLittermanCombinationEngine projectionEngine =
  791.             new BlackLittermanCombinationEngine (
  792.                 _forwardReverseOptimizationOutputUnadjusted,
  793.                 _priorControlSpecification,
  794.                 new org.drip.portfolioconstruction.bayesian.ProjectionSpecification (
  795.                     projectionDistribution,
  796.                     new double[][]
  797.                     {
  798.                         _projectionSpecification.assetSpaceLoadingMatrix()[projectionIndex]
  799.                     }
  800.                 )
  801.             );

  803.         org.drip.portfolioconstruction.bayesian.BlackLittermanCustomConfidenceOutput customConfidenceOuput =
  804.             projectionEngine.customConfidenceRun();

  806.         if (null == customConfidenceOuput)
  807.         {
  808.             throw new java.lang.Exception
  809.                 ("BlackLittermanCombinationEngine::tiltMismatchSquared => Invalid Inputs");
  810.         }

  812.         double[] posteriorTiltArray = customConfidenceOuput.allocationAdjustmentTiltArray();

  814.         int assetCount = posteriorTiltArray.length;
  815.         double tiltMismatchSquared = 0.;

  817.         if (assetCount != userConfidenceProjectionTiltArray.length)
  818.         {
  819.             throw new java.lang.Exception
  820.                 ("BlackLittermanCombinationEngine::tiltMismatchSquared => Invalid Inputs");
  821.         }

  823.         for (int assetIndex = 0; assetIndex < assetCount; ++assetIndex)
  824.         {
  825.             if (!org.drip.numerical.common.NumberUtil.IsValid (
  826.                 userConfidenceProjectionTiltArray[assetIndex]
  827.             ))
  828.             {
  829.                 throw new java.lang.Exception
  830.                     ("BlackLittermanCombinationEngine::tiltMismatchSquared => Invalid Inputs");
  831.             }

  833.             double dblAssetTiltGap = posteriorTiltArray[assetIndex] -
  834.                 userConfidenceProjectionTiltArray[assetIndex];
  835.             tiltMismatchSquared = tiltMismatchSquared + dblAssetTiltGap * dblAssetTiltGap;
  836.         }

  838.         return tiltMismatchSquared;
  839.     }

  841.     /**
  842.      * Generate the Squared Tilt Departure R<sup>1</sup> To R<sup>1</sup>
  843.      * 
  844.      * @param userConfidenceProjectionTiltArray Array of the User Confidence induced Projection Tilts
  845.      * @param projectionIndex The Index into the Projection Meta
  846.      * @param generateDerivative TRUE - Generate the Derivative of the Tilt Departure
  847.      * 
  848.      * @return The Squared Tilt Departure R<sup>1</sup> To R<sup>1</sup>
  849.      */

  851.     public org.drip.function.definition.R1ToR1 tiltDepartureR1ToR1 (
  852.         final double[] userConfidenceProjectionTiltArray,
  853.         final int projectionIndex,
  854.         final boolean generateDerivative)
  855.     {
  856.         final org.drip.function.definition.R1ToR1 tiltDepartureFunction =
  857.             new org.drip.function.definition.R1ToR1 (
  858.                 null
  859.             )
  860.         {
  861.             @Override public double evaluate (
  862.                 final double projectionVariance)
  863.                 throws java.lang.Exception
  864.             {
  865.                 return tiltMismatchSquared (
  866.                     userConfidenceProjectionTiltArray,
  867.                     projectionIndex,
  868.                     projectionVariance
  869.                 );
  870.             }
  871.         };

  873.         if (!generateDerivative)
  874.         {
  875.             return tiltDepartureFunction;
  876.         }

  878.         return new org.drip.function.definition.R1ToR1 (
  879.             null
  880.         )
  881.         {
  882.             @Override public double evaluate (
  883.                 final double projectionVariance)
  884.                 throws java.lang.Exception
  885.             {
  886.                 return tiltDepartureFunction.derivative (
  887.                     projectionVariance,
  888.                     1
  889.                 );
  890.             }
  891.         };
  892.     }
  893. }
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