PriorPosteriorMetricsComparison.java

package org.drip.sample.idzorek;

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.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation;
import org.drip.portfolioconstruction.asset.*;
import org.drip.portfolioconstruction.bayesian.*;
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>PriorPosteriorMetricsComparison</i> reconciles the Prior-Posterior Black-Litterman Model Process
 * Metrics generated using the Idzorek Model. The References are:
 *  
 * <br><br>
 *  <ul>
 *      <li>
 *          He. G., and R. Litterman (1999): The Intuition behind the Black-Litterman Model Portfolios,
 *              Goldman Sachs Asset Management
 *      </li>
 *      <li>
 *          Idzorek, T. (2005): A Step-by-Step Guide to the Black-Litterman Model: Incorporating User
 *              Specified Confidence Levels, Ibbotson Associates, Chicago
 *      </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/idzorek/README.md">Idzorek (2005) User Confidence Setting</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class PriorPosteriorMetricsComparison
{

    private static final void ForwardOptimizationWeights (
        final ForwardReverseHoldingsAllocation forwardReverseOptimizationOutput,
        final double[] weightReconcilerArray,
        final int preDecimalDigits,
        final int postDecimalDigits,
        final String header)
    {
        Portfolio forwardReverseOptimizationPortfolio = forwardReverseOptimizationOutput.optimalPortfolio();

        AssetComponent highestWeightAsset = forwardReverseOptimizationPortfolio.highestWeightAsset();

        AssetComponent lowestWeightAsset = forwardReverseOptimizationPortfolio.lowestWeightAsset();

        String[] assetIDArray = forwardReverseOptimizationPortfolio.assetIDArray();

        double[] weightArray = forwardReverseOptimizationPortfolio.weightArray();

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

        System.out.println (header);

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

        System.out.println ("\t|                  ID               =>  CALC   | VERIFY  ||");

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

        for (int assetIndex = 0;
            assetIndex < weightArray.length;
            ++assetIndex)
        {
            System.out.println (
                "\t| [" + assetIDArray[assetIndex] + "] => " +
                FormatUtil.FormatDouble (weightArray[assetIndex], preDecimalDigits, postDecimalDigits, 100.)
                    + "% | " +
                FormatUtil.FormatDouble (
                    weightReconcilerArray[assetIndex], preDecimalDigits, postDecimalDigits, 100.
                ) + "% ||"
            );
        }

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

        System.out.println (
            "\t| HIGH  : " + highestWeightAsset.id() + " => " + FormatUtil.FormatDouble (
                highestWeightAsset.amount(), preDecimalDigits, postDecimalDigits, 100.
            ) + "%     ||"
        );

        System.out.println (
            "\t| LOW   : " + lowestWeightAsset.id() + " => " + FormatUtil.FormatDouble (
                lowestWeightAsset.amount(), preDecimalDigits, postDecimalDigits, 100.
            ) + "%     ||"
        );

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

        System.out.println (
            "\t| TOTAL :                                   " + FormatUtil.FormatDouble (
                forwardReverseOptimizationPortfolio.notional(), preDecimalDigits, postDecimalDigits, 100.
            ) + "%     ||"
        );

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

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

        double tau = 0.025;
        double riskAversion = 3.07;
        double riskFreeRate = 0.00;
        double[] assetSpaceJointReturnsReconcilerArray = new double[]
        {
            0.0007,
            0.0050,
            0.0650,
            0.0432,
            0.0759,
            0.0394,
            0.0493,
            0.0684
        };
        double[] posteriorPriorDeviationReconcilerArray = new double[]
        {
            -0.0002,
            -0.0017,
             0.0008,
             0.0024,
             0.0016,
             0.0023,
             0.0013,
             0.0024
        };
        double[] posteriorPortfolioWeightReconcilerArray = new double[]
        {
              0.2988,
              0.1559,
              0.0935,
              0.1482,
              0.0104,
              0.0165,
              0.2781,
              0.0349
        };
        double[] posteriorWeightDeviationReconcilerArray = new double[]
        {
              0.1054,
             -0.1054,
             -0.0273,
              0.0273,
             -0.0030,
              0.0030,
              0.0363,
              0.0000
        };
        String[] assetIDArray = new String[]
        {
            "US BONDS                       ",
            "INTERNATIONAL BONDS            ",
            "US LARGE GROWTH                ",
            "US LARGE VALUE                 ",
            "US SMALL GROWTH                ",
            "US SMALL VALUE                 ",
            "INTERNATIONAL DEVELOPED EQUITY ",
            "INTERNATIONAL EMERGING EQUITY  "
        };
        double[] assetEquilibriumWeightArray = new double[]
        {
            0.1934,
            0.2613,
            0.1209,
            0.1209,
            0.0134,
            0.0134,
            0.2418,
            0.0349
        };
        double[][] assetExcessReturnsCovarianceMatrix = new double[][]
        {
            { 0.001005,  0.001328, -0.000579, -0.000675,  0.000121,  0.000128, -0.000445, -0.000437},
            { 0.001328,  0.007277, -0.001307, -0.000610, -0.002237, -0.000989,  0.001442, -0.001535},
            {-0.000579, -0.001307,  0.059582,  0.027588,  0.063497,  0.023036,  0.032967,  0.048039},
            {-0.000675, -0.000610,  0.027588,  0.029609,  0.026572,  0.021465,  0.020697,  0.029854},
            { 0.000121, -0.002237,  0.063497,  0.026572,  0.102488,  0.042744,  0.039943,  0.065994},
            { 0.000128, -0.000989,  0.023036,  0.021465,  0.042744,  0.032056,  0.019881,  0.032235},
            {-0.000445,  0.001442,  0.032967,  0.020697,  0.039943,  0.019881,  0.028355,  0.035064},
            {-0.000437, -0.001535,  0.048039,  0.029854,  0.065994,  0.032235,  0.035064,  0.079958}
        };
        double[][] assetSpaceViewProjectionMatrix = new double[][]
        {
            {  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  1.00,  0.00},
            { -1.00,  1.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00},
            {  0.00,  0.00,  0.90, -0.90,  0.10, -0.10,  0.00,  0.00}
        };
        double[] projectionExpectedExcessReturnsArray = new double[]
        {
            0.0525,
            0.0025,
            0.0200
        };

        double[][] projectionExcessReturnsCovarianceMatrix =
            ProjectionDistributionLoading.ProjectionCovariance (
                assetExcessReturnsCovarianceMatrix,
                assetSpaceViewProjectionMatrix,
                tau
            );

        R1MultivariateNormal viewDistribution = R1MultivariateNormal.Standard (
            new MultivariateMeta (
                new String[]
                {
                    "PROJECTION #1",
                    "PROJECTION #2",
                    "PROJECTION #3"
                }
            ),
            projectionExpectedExcessReturnsArray,
            projectionExcessReturnsCovarianceMatrix
        );

        R1MultivariateConvolutionMetrics jointPosteriorMetrics = new BlackLittermanCombinationEngine (
            ForwardReverseHoldingsAllocation.Reverse (
                Portfolio.Standard (
                    assetIDArray,
                    assetEquilibriumWeightArray
                ),
                assetExcessReturnsCovarianceMatrix,
                riskAversion
            ),
            new PriorControlSpecification (
                true,
                riskFreeRate,
                tau
            ),
            new ProjectionSpecification (
                viewDistribution,
                assetSpaceViewProjectionMatrix
            )
        ).customConfidenceRun().jointPosteriorMetrics();

        R1MultivariateNormal priorDistribution = (R1MultivariateNormal) jointPosteriorMetrics.prior();

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

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

        double[] assetSpacePriorReturnsArray = priorDistribution.mean();

        double[] assetSpaceJointReturnsArray = jointDistribution.mean();

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

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

        ForwardReverseHoldingsAllocation posteriorForwardReverseOptimizationOutput =
            ForwardReverseHoldingsAllocation.Forward (
                assetIDArray,
                assetSpaceJointReturnsArray,
                assetExcessReturnsCovarianceMatrix,
                riskAversion
            );

        double[] posteriorWeightArray =
            posteriorForwardReverseOptimizationOutput.optimalPortfolio().weightArray();

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

        System.out.println ("\t| TAU            => " + FormatUtil.FormatDouble (tau, 1, 4, 1.) + " ||");

        System.out.println (
            "\t| RISK AVERSION  => " + FormatUtil.FormatDouble (riskAversion, 1, 4, 1.) + " ||"
        );

        System.out.println (
            "\t| RISK FREE RATE => " + FormatUtil.FormatDouble (riskFreeRate, 1, 4, 1.) + " ||"
        );

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

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

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

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

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

            for (int assetIndexJ = 0;
                assetIndexJ < assetIDArray.length;
                ++assetIndexJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    assetExcessReturnsCovarianceMatrix[assetIndexI][assetIndexJ], 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|---------------------------------------------------------------------------------------------||");

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

            for (int assetIndex = 0;
                assetIndex < assetIDArray.length;
                ++assetIndex)
            {
                dump += "| " + FormatUtil.FormatDouble (
                    assetSpaceViewProjectionMatrix[viewIndex][assetIndex], 1, 5, 1.
                ) + " ";
            }

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

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

        System.out.println ("\n\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, 6, 1.
                ) + " ";
            }

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

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

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

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

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

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

            for (int assetIndexJ = 0;
                assetIndexJ < assetIDArray.length;
                ++assetIndexJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    aadblAssetSpaceJointCovariance[assetIndexI][assetIndexJ], 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|-----------------------------------------------------------------------------------------------------------------------------------------||");

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

            for (int assetIndexJ = 0;
                assetIndexJ < assetIDArray.length;
                ++assetIndexJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    aadblAssetSpacePosteriorCovariance[assetIndexI][assetIndexJ], 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                => DROP  | IDZO  ||");

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

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

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

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

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

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

        System.out.println ("\t|                 ID                => DROP  | IDZO  ||");

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

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

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

        ForwardOptimizationWeights (
            posteriorForwardReverseOptimizationOutput,
            posteriorPortfolioWeightReconcilerArray,
            2,
            2,
            "\t|               POSTERIOR WEIGHTS RECONCILER             ||"
        );

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

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

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

        System.out.println ("\t|                 ID                =>   DROP  |   IDZO  ||");

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

        for (int assetIndex = 0;
            assetIndex < assetEquilibriumWeightArray.length;
            ++assetIndex)
        {
            System.out.println (
                "\t| [" + assetIDArray[assetIndex] + "] => " +
                FormatUtil.FormatDouble (
                    posteriorWeightArray[assetIndex] - assetEquilibriumWeightArray[assetIndex], 2, 2, 100.
                ) + "% | " +
                FormatUtil.FormatDouble (posteriorWeightDeviationReconcilerArray[assetIndex], 2, 2, 100.)
                    + "% ||"
            );
        }

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

        EnvManager.TerminateEnv();
    }
}