Table6Reconciler.java

package org.drip.sample.helitterman;

import org.drip.measure.bayesian.R1MultivariateConvolutionMetrics;
import org.drip.measure.continuous.MultivariateMeta;
import org.drip.measure.gaussian.*;
import org.drip.measure.statistics.MultivariateMoments;
import org.drip.numerical.common.FormatUtil;
import org.drip.portfolioconstruction.allocator.*;
import org.drip.portfolioconstruction.asset.*;
import org.drip.portfolioconstruction.bayesian.*;
import org.drip.portfolioconstruction.params.AssetUniverseStatisticalProperties;
import org.drip.service.env.EnvManager;

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

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
 *      credit, commodity, equity, FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Algorithm Support
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
 *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  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.
 */

/**
 * <i>Table6Reconciler</i> reconciles the First Set of Outputs (Table #6) of the Black-Litterman Model
 * Process as illustrated in the Following Paper:
 *  
 * <br><br>
 *  <ul>
 *      <li>
 *          He. G., and R. Litterman (1999): The Intuition behind the Black-Litterman Model Portfolios,
 *              Goldman Sachs Asset Management
 *      </li>
 *  </ul>
 *  
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AssetAllocationAnalyticsLibrary.md">Asset Allocation Analytics Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/helitterman/README.md">He and Litterman (1999) Reconcilers</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class Table6Reconciler
{

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv ("");

        String[] assetIDArray = new String[]
        {
            "AUS",
            "CAD",
            "FRA",
            "GER",
            "JPN",
            "UK ",
            "USA"
        };
        double[] assetEquilibriumWeightArray = new double[]
        {
            0.016,
            0.022,
            0.052,
            0.055,
            0.116,
            0.124,
            0.615
        };
        double[][] assetExcessReturnsCorrelationMatrix = new double[][]
        {
            {1.000, 0.488, 0.478, 0.515, 0.439, 0.512, 0.491},
            {0.488, 1.000, 0.664, 0.655, 0.310, 0.608, 0.779},
            {0.478, 0.664, 1.000, 0.861, 0.355, 0.783, 0.668},
            {0.515, 0.655, 0.861, 1.000, 0.354, 0.777, 0.653},
            {0.439, 0.310, 0.355, 0.354, 1.000, 0.405, 0.306},
            {0.512, 0.608, 0.783, 0.777, 0.405, 1.000, 0.652},
            {0.491, 0.779, 0.668, 0.653, 0.306, 0.652, 1.000}
        };
        double[] assetExcessReturnsVolatilityArray = new double[]
        {
            0.160,
            0.203,
            0.248,
            0.271,
            0.210,
            0.200,
            0.187
        };
        double[][] assetSpaceViewProjectionMatrix = new double[][]
        {
            {0.000,  0.000, -0.295,  1.000,  0.000, -0.705,  0.000},
            {0.000,  1.000,  0.000,  0.000,  0.000,  0.000, -1.000}
        };
        double tau = 0.05;
        double riskAversion = 2.5;
        double riskFreeRate = 0.0;
        double[] projectionExpectedExcessReturnsArray = new double[]
        {
            0.05,
            0.04
        };
        double[] assetSpaceJointReturnsReconcilerArray = new double[]
        {
            0.044,
            0.091,
            0.095,
            0.113,
            0.046,
            0.070,
            0.073
        };
        double[] posteriorOptimalWeightsReconcilerArray = new double[]
        {
             0.015,
             0.533,
            -0.033,
             0.331,
             0.110,
            -0.078,
             0.073
        };
        double[] posteriorOptimalDeviationReconcilerArray = new double[] {
             0.000,
             0.513,
            -0.082,
             0.278,
             0.000,
            -0.196,
            -0.513
        };
        double[] peLoadingsReconcilerArray = new double[]
        {
            0.292,
            0.538
        };

        double[][] projectionExcessReturnsCovarianceMatrix = new double[][]
        {
            {0.021 * tau, 0.000 * tau},
            {0.000 * tau, 0.017 * tau}
        };

        R1MultivariateNormal viewDistribution = R1MultivariateNormal.Standard (
            new MultivariateMeta (
                new String[]
                {
                    "PROJECTION #1",
                    "PROJECTION #2"
                }
            ),
            projectionExpectedExcessReturnsArray,
            projectionExcessReturnsCovarianceMatrix
        );

        double[][] assetExcessReturnsCovarianceMatrix = new double[assetIDArray.length][assetIDArray.length];

        for (int assetIDI = 0;
            assetIDI < assetIDArray.length;
            ++assetIDI)
        {
            for (int assetIDJ = 0;
                assetIDJ < assetIDArray.length;
                ++assetIDJ)
            {
                assetExcessReturnsCovarianceMatrix[assetIDI][assetIDJ] =
                    assetExcessReturnsCorrelationMatrix[assetIDI][assetIDJ] *
                    assetExcessReturnsVolatilityArray[assetIDI] *
                    assetExcessReturnsVolatilityArray[assetIDJ];
            }
        }

        BlackLittermanCombinationEngine blackLittermanCombinationEngine =
            new BlackLittermanCombinationEngine (
                ForwardReverseHoldingsAllocation.Reverse (
                    Portfolio.Standard (
                        assetIDArray,
                        assetEquilibriumWeightArray
                    ),
                    assetExcessReturnsCovarianceMatrix,
                    riskAversion
                ),
                new PriorControlSpecification (
                    false,
                    riskFreeRate,
                    tau
                ),
                new ProjectionSpecification (
                    viewDistribution,
                    assetSpaceViewProjectionMatrix
                )
            );

        R1MultivariateConvolutionMetrics jointPosteriorMetrics =
            blackLittermanCombinationEngine.customConfidenceRun().jointPosteriorMetrics();

        R1MultivariateNormal jointDistribution = (R1MultivariateNormal) jointPosteriorMetrics.joint();

        R1MultivariateNormal posteriorDistribution =
            (R1MultivariateNormal) jointPosteriorMetrics.posterior();

        double[] assetSpaceJointReturnsArray = jointDistribution.mean();

        double[][] assetSpaceJointCovarianceMatrix = jointDistribution.covariance().covarianceMatrix();

        double[][] assetSpacePosteriorCovarianceMatrix =
            posteriorDistribution.covariance().covarianceMatrix();

        AssetComponent[] assetComponentArray = new QuadraticMeanVarianceOptimizer().allocate (
            new HoldingsAllocationControl (
                assetIDArray,
                CustomRiskUtilitySettings.RiskAversion (riskAversion),
                EqualityConstraintSettings.Unconstrained()
            ),
            AssetUniverseStatisticalProperties.FromMultivariateMetrics (
                MultivariateMoments.Standard (
                    assetIDArray,
                    posteriorDistribution.mean(),
                    assetSpacePosteriorCovarianceMatrix
                )
            )
        ).optimalPortfolio().assetComponentArray();

        ProjectionExposure projectionExposure =
            blackLittermanCombinationEngine.projectionExposureAttribution();

        double[] interViewComponentArray = projectionExposure.interViewComponentArray();

        double[] intraViewComponentArray = projectionExposure.intraViewComponentArray();

        double[] priorViewComponentArray = projectionExposure.priorViewComponentArray();

        double[] cumulativeViewComponentLoadingArray =
            projectionExposure.cumulativeViewComponentLoadingArray();

        System.out.println ("\n\t|------------------------||");

        System.out.println ("\t| TAU   => " + FormatUtil.FormatDouble (tau, 1, 8, 1.) + "   ||");

        System.out.println ("\t| DELTA => " + FormatUtil.FormatDouble (riskAversion, 1, 8, 1.) + "   ||");

        System.out.println ("\t|------------------------||");

        System.out.println ("\n\t|------------------------||");

        System.out.println ("\t|  ASSET EXCESS RETURNS  ||");

        System.out.println ("\t|------------------------||");

        System.out.println ("\t|   ID  => EQ WT |  VOL  ||");

        System.out.println ("\t|------------------------||");

        for (int assetID = 0;
            assetID < assetSpaceJointReturnsReconcilerArray.length;
            ++assetID)
        {
            System.out.println (
                "\t| [" + assetIDArray[assetID] + "] =>" +
                FormatUtil.FormatDouble (assetEquilibriumWeightArray[assetID], 2, 1, 100.) + "% |" +
                FormatUtil.FormatDouble (assetExcessReturnsVolatilityArray[assetID], 2, 1, 100.) + "% ||"
            );
        }

        System.out.println ("\t|------------------------||");

        System.out.println ("\n\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\t|                           PRIOR CROSS ASSET CORRELATION MATRIX                                 ||");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        String header = "\t|     |";

        for (int assetID = 0;
            assetID < assetIDArray.length;
            ++assetID)
        {
            header += "    " + assetIDArray[assetID] + "     |";
        }

        System.out.println (header + "|");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        for (int assetIDI = 0;
            assetIDI < assetIDArray.length;
            ++assetIDI)
        {
            String dump = "\t| " + assetIDArray[assetIDI] + " ";

            for (int assetIDJ = 0;
                assetIDJ < assetIDArray.length;
                ++assetIDJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    assetExcessReturnsCorrelationMatrix[assetIDI][assetIDJ], 1, 8, 1.
                ) + " ";
            }

            System.out.println (dump + "||");
        }

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\n\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\t|                           PRIOR CROSS ASSET COVARIANCE MATRIX                                  ||");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        header = "\t|     |";

        for (int assetID = 0;
            assetID < assetIDArray.length;
            ++assetID)
        {
            header += "    " + assetIDArray[assetID] + "     |";
        }

        System.out.println (header + "|");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        for (int assetIDI = 0;
            assetIDI < assetIDArray.length;
            ++assetIDI)
        {
            String dump = "\t| " + assetIDArray[assetIDI] + " ";

            for (int assetIDJ = 0;
                assetIDJ < assetIDArray.length;
                ++assetIDJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    assetExcessReturnsCovarianceMatrix[assetIDI][assetIDJ], 1, 8, 1.
                ) + " ";
            }

            System.out.println (dump + "||");
        }

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\n\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\t|                          VIEW SCOPING ASSET PROJECTION LOADING                                 ||");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        header = "\t|     |";

        for (int assetID = 0;
            assetID < assetIDArray.length;
            ++assetID)
        {
            header += "    " + assetIDArray[assetID] + "     |";
        }

        System.out.println (header + "|");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        for (int viewIndex = 0;
            viewIndex < assetSpaceViewProjectionMatrix.length;
            ++viewIndex)
        {
            String dump = "\t|  #" + viewIndex + " ";

            for (int assetID = 0;
                assetID < assetIDArray.length;
                ++assetID)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    assetSpaceViewProjectionMatrix[viewIndex][assetID], 1, 8, 1.
                ) + " ";
            }

            System.out.println (dump + "||");
        }

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\n\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        for (int viewIndexI = 0;
            viewIndexI < assetSpaceViewProjectionMatrix.length;
            ++viewIndexI)
        {
            String dump = "\t|  #" + viewIndexI + " ";

            for (int viewIndexJ = 0;
                viewIndexJ < assetSpaceViewProjectionMatrix.length;
                ++viewIndexJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    projectionExcessReturnsCovarianceMatrix[viewIndexI][viewIndexJ], 1, 8, 1.
                ) + " ";
            }

            System.out.println (
                dump + "|" + FormatUtil.FormatDouble (
                    projectionExpectedExcessReturnsArray[viewIndexI], 1, 2, 100.
                ) + "%"
            );
        }

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\n\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\t|                           JOINT CROSS ASSET COVARIANCE MATRIX                                  ||");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        header = "\t|     |";

        for (int assetID = 0;
            assetID < assetIDArray.length;
            ++assetID)
        {
            header += "    " + assetIDArray[assetID] + "     |";
        }

        System.out.println (header + "|");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        for (int assetIDI = 0;
            assetIDI < assetIDArray.length;
            ++assetIDI)
        {
            String dump = "\t| " + assetIDArray[assetIDI] + " ";

            for (int assetIDJ = 0;
                assetIDJ < assetIDArray.length;
                ++assetIDJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    assetSpaceJointCovarianceMatrix[assetIDI][assetIDJ], 1, 8, 1.
                ) + " ";
            }

            System.out.println (dump + "||");
        }

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\n\t|------------------------------------------------------------------------------------------------||");

        System.out.println ("\t|                         POSTERIOR CROSS ASSET COVARIANCE MATRIX                                ||");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        header = "\t|     |";

        for (int assetID = 0;
            assetID < assetIDArray.length;
            ++assetID)
        {
            header += "    " + assetIDArray[assetID] + "     |";
        }

        System.out.println (header + "|");

        System.out.println ("\t|------------------------------------------------------------------------------------------------||");

        for (int assetIDI = 0;
            assetIDI < assetIDArray.length;
            ++assetIDI)
        {
            String dump = "\t| " + assetIDArray[assetIDI] + " ";

            for (int assetIDJ = 0;
                assetIDJ < assetIDArray.length;
                ++assetIDJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    assetSpacePosteriorCovarianceMatrix[assetIDI][assetIDJ], 1, 8, 1.
                ) + " ";
            }

            System.out.println (dump + "||");
        }

        System.out.println ("\t|------------------------------------------------------------------------------------------------||\n");

        System.out.println ("\t|------------------------||");

        System.out.println ("\t| JOINT/POSTERIOR RETURN ||");

        System.out.println ("\t|------------------------||");

        System.out.println ("\t|   ID  => RIOC  | HL99  ||");

        System.out.println ("\t|------------------------||");

        for (int assetID = 0;
            assetID < assetSpaceJointReturnsReconcilerArray.length;
            ++assetID)
        {
            System.out.println (
                "\t| [" + assetIDArray[assetID] + "] =>" +
                FormatUtil.FormatDouble (assetSpaceJointReturnsArray[assetID], 2, 1, 100.) + "% |" +
                FormatUtil.FormatDouble (assetSpaceJointReturnsReconcilerArray[assetID], 2, 1, 100.) + "% ||"
            );
        }

        System.out.println ("\t|------------------------||");

        System.out.println ("\n\t|------------------------||");

        System.out.println ("\t| OPTIMAL POSTERIOR WTS. ||");

        System.out.println ("\t|------------------------||");

        System.out.println ("\t|   ID  => RIOC  | HL99  ||");

        System.out.println ("\t|------------------------||");

        for (int assetID = 0;
            assetID < assetComponentArray.length;
            ++assetID)
        {
            System.out.println (
                "\t| [" + assetIDArray[assetID] + "] =>" +
                FormatUtil.FormatDouble (assetComponentArray[assetID].amount(), 2, 1, 100.) + "% |" +
                FormatUtil.FormatDouble (posteriorOptimalWeightsReconcilerArray[assetID], 2, 1, 100.) + "% ||"
            );
        }

        System.out.println ("\t|------------------------||");

        System.out.println ("\n\t|------------------------||");

        System.out.println ("\t|   POSTERIOR DEVIATION  ||");

        System.out.println ("\t|------------------------||");

        System.out.println ("\t|   ID  => RIOC  | HL99  ||");

        System.out.println ("\t|------------------------||");

        for (int assetID = 0;
            assetID < assetComponentArray.length;
            ++assetID)
        {
            System.out.println (
                "\t| [" + assetIDArray[assetID] + "] =>" +
                FormatUtil.FormatDouble (assetComponentArray[assetID].amount() - (assetEquilibriumWeightArray[assetID]) / (1. + tau), 2, 1, 100.) + "% |" +
                FormatUtil.FormatDouble (posteriorOptimalDeviationReconcilerArray[assetID], 2, 1, 100.) + "% ||"
            );
        }

        System.out.println ("\t|------------------------||\n");

        System.out.println ("\t|-----------------------------------------------------------------||");

        System.out.println ("\t|              POSTERIOR DEVIATION WEIGHTS ATTRIBUTION            ||");

        System.out.println ("\t|-----------------------------------------------------------------||");

        System.out.println ("\t| VIEW NUM =>  INTRA |  INTER |  PRIOR |  CUMUL |  RECON |  BAYES ||");

        System.out.println ("\t|-----------------------------------------------------------------||");

        for (int viewIndex = 0; viewIndex < interViewComponentArray.length; ++viewIndex)
        {
            System.out.println (
                "\t| VIEW  #" + (viewIndex + 1) + " => " +
                FormatUtil.FormatDouble (interViewComponentArray[viewIndex], 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (intraViewComponentArray[viewIndex], 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (priorViewComponentArray[viewIndex], 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (cumulativeViewComponentLoadingArray[viewIndex], 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (peLoadingsReconcilerArray[viewIndex], 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (
                    cumulativeViewComponentLoadingArray[viewIndex] / (1. + tau), 1, 3, 1.
                ) + " ||"
            );
        }

        System.out.println ("\t|-----------------------------------------------------------------||");

        EnvManager.TerminateEnv();
    }
}