DaJagannathan2005a.java

package org.drip.sample.blacklitterman;

import org.drip.measure.bayesian.*;
import org.drip.measure.continuous.MultivariateMeta;
import org.drip.measure.gaussian.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * 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 analytics/risk, transaction cost analytics,
 *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
 *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
 *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
 *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
 *      and computational support.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
 * 
 *  DROP Product Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Loan Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Asset Liability Management Analytics
 *  - Capital Estimation Analytics
 *  - Exposure Analytics
 *  - Margin Analytics
 *  - XVA Analytics
 * 
 *  DROP Computational Core implements libraries for the following:
 *  - Algorithm Support
 *  - Computation Support
 *  - Function Analysis
 *  - Model Validation
 *  - Numerical Analysis
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Statistical Learning
 * 
 *  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>DaJagannathan2005a</i> reconciles the Outputs of the Black-Litterman Model Process. The References are:
 *  
 * <br><br>
 *  <ul>
 *      <li>
 *          Da, Z., and R. Jagannathan (2005): https://www3.nd.edu/~zda/TeachingNote_Black-Litterman.pdf
 *      </li>
 *      <li>
 *          He. G., and R. Litterman (1999): <i>The Intuition behind the Black-Litterman Model Portfolios</i>
 *              <b>Goldman Sachs Asset Management</b>
 *      </li>
 *  </ul>
 *  
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/blacklitterman/README.md">Canonical Black Litterman and Extensions</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class DaJagannathan2005a {

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

        String[] astrAssetID = new String[] {
            "A",
            "B",
            "C"
        };

        double[] adblAssetExcessReturns = new double[] {
            0.01,
            0.01,
            0.01
        };

        double[][] aadblAssetExcessReturnsCovariance = new double[][] {
            {0.00091, 0.00030, 0.00060},
            {0.00030, 0.00011, 0.00020},
            {0.00060, 0.00020, 0.00041}
        };

        double[][] aadblAssetSpaceViewProjection = new double[][] {
            {1.000, -1.000,  0.000}
        };

        double dblTau = 1.00;
        double dblDelta = 1.00;

        double[] adblProjectionExpectedExcessReturns = new double[] {
            0.02
        };

        double[][] aadblProjectionExcessReturnsCovariance = new double[][] {
            {0.0001}
        };

        double[] adblAssetSpaceJointReturnsReconciler = new double[] {
            0.0335,
            0.0173,
            0.0254
        };

        R1MultivariateNormal viewDistribution = R1MultivariateNormal.Standard (
            new MultivariateMeta (new String[] {"DJVIEW"}),
            adblProjectionExpectedExcessReturns,
            aadblProjectionExcessReturnsCovariance
        );

        R1MultivariateNormal r1mnScoping = R1MultivariateNormal.Standard (
            new MultivariateMeta (astrAssetID),
            adblAssetExcessReturns,
            aadblAssetExcessReturnsCovariance
        );

        ScopingProjectionVariateDistribution spvd = new ScopingProjectionVariateDistribution (r1mnScoping);

        spvd.addProjectionDistributionLoading (
            "VIEW",
            new ProjectionDistributionLoading (
                viewDistribution,
                aadblAssetSpaceViewProjection
            )
        );

        R1MultivariateConvolutionMetrics jpm = TheilMixedEstimationModel.GenerateComposite (
            spvd,
            "VIEW",
            r1mnScoping
        );

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

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

        double[] adblAssetSpaceJointReturns = jointDistribution.mean();

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

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

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

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

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

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

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

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

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

        String strHeader = "\t|     |";

        for (int i = 0; i < astrAssetID.length; ++i)
            strHeader += "    " + astrAssetID[i] + "     |";

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

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

        for (int i = 0; i < astrAssetID.length; ++i) {
            String strDump = "\t| " + astrAssetID[i] + " ";

            for (int j = 0; j < astrAssetID.length; ++j)
                strDump += "|" + FormatUtil.FormatDouble (aadblAssetExcessReturnsCovariance[i][j], 1, 8, 1.) + " ";

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

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

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

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

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

        strHeader = "\t|     |";

        for (int i = 0; i < astrAssetID.length; ++i)
            strHeader += "    " + astrAssetID[i] + "     |";

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

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

        for (int i = 0; i < aadblAssetSpaceViewProjection.length; ++i) {
            String strDump = "\t|  #" + i + " ";

            for (int j = 0; j < astrAssetID.length; ++j)
                strDump += "|" + FormatUtil.FormatDouble (aadblAssetSpaceViewProjection[i][j], 1, 8, 1.) + " ";

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

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

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

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

        for (int i = 0; i < aadblAssetSpaceViewProjection.length; ++i) {
            String strDump = "\t|  #" + i + " ";

            for (int j = 0; j < aadblAssetSpaceViewProjection.length; ++j)
                strDump += "|" + FormatUtil.FormatDouble (aadblProjectionExcessReturnsCovariance[i][j], 1, 8, 1.) + " ";

            System.out.println (strDump + "|" + FormatUtil.FormatDouble (adblProjectionExpectedExcessReturns[i], 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|------------------------------------------------------------------------------------------------||");

        strHeader = "\t|     |";

        for (int i = 0; i < astrAssetID.length; ++i)
            strHeader += "    " + astrAssetID[i] + "     |";

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

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

        for (int i = 0; i < astrAssetID.length; ++i) {
            String strDump = "\t| " + astrAssetID[i] + " ";

            for (int j = 0; j < astrAssetID.length; ++j)
                strDump += "|" + FormatUtil.FormatDouble (aadblAssetSpaceJointCovariance[i][j], 1, 8, 1.) + " ";

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

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

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

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

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

        strHeader = "\t|     |";

        for (int i = 0; i < astrAssetID.length; ++i)
            strHeader += "    " + astrAssetID[i] + "     |";

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

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

        for (int i = 0; i < astrAssetID.length; ++i) {
            String strDump = "\t| " + astrAssetID[i] + " ";

            for (int j = 0; j < astrAssetID.length; ++j)
                strDump += "|" + FormatUtil.FormatDouble (aadblAssetSpacePosteriorCovariance[i][j], 1, 8, 1.) + " ";

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

        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  | DJ05  ||");

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

        for (int i = 0; i < adblAssetSpaceJointReturnsReconciler.length; ++i) {
            System.out.println (
                "\t|  [" + astrAssetID[i] + "] => " +
                FormatUtil.FormatDouble (adblAssetSpaceJointReturns[i], 1, 2, 100.) + "% |" +
                FormatUtil.FormatDouble (adblAssetSpaceJointReturnsReconciler[i], 1, 2, 100.) + "% ||"
            );
        }

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

        EnvManager.TerminateEnv();
    }
}