ExpectedExcessReturnsWeights.java

package org.drip.sample.idzorek;

import org.drip.numerical.common.FormatUtil;
import org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation;
import org.drip.portfolioconstruction.asset.*;
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>ExpectedExcessReturnsWeights</i> reconciles the Expected Returns and the corresponding Weights for
 * different Input Asset Distributions using the Black-Litterman Model Process. 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 ExpectedExcessReturnsWeights
{

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

        String[] assetIDArray = optimalPortfolio.assetIDArray();

        double[] weightArray = optimalPortfolio.weightArray();

        AssetComponent highestWeightAsset = optimalPortfolio.highestWeightAsset();

        AssetComponent lowestWeightAsset = optimalPortfolio.lowestWeightAsset();

        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|------------------------------------------------------||\n");
    }

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

        double riskAversion = 3.07;
        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[] assetSpaceHistoricalReturnsArray = new double[]
        {
             0.0315,
             0.0175,
            -0.0639,
            -0.0286,
            -0.0675,
            -0.0054,
            -0.0675,
            -0.0526
        };
        double[] assetSpaceCAPMReturnsArray = new double[]
        {
            0.0008,
            0.0067,
            0.0641,
            0.0408,
            0.0743,
            0.0370,
            0.0480,
            0.0660
        };
        double[] assetSpaceGSMIReturnsArray = new double[]
        {
             0.0002,
             0.0018,
             0.0557,
             0.0339,
             0.0659,
             0.0316,
             0.0392,
             0.0560
        };
        double[] historicalPortfolioWeightReconcilerArray = new double[]
        {
             11.4432,
             -1.0459,
              0.5459,
             -0.0529,
             -0.6052,
              0.8147,
             -1.0436,
              0.1459
        };
        double[] capmGSMIPortfolioWeightReconcilerArray = new double[]
        {
              0.2133,
              0.0519,
              0.1080,
              0.1082,
              0.0373,
             -0.0049,
              0.1710,
              0.0214
        };

        double[] impliedEquilibriumExcessReturnsArray = ForwardReverseHoldingsAllocation.Reverse (
            Portfolio.Standard (
                assetIDArray,
                assetEquilibriumWeightArray
            ),
            assetExcessReturnsCovarianceMatrix,
            riskAversion
        ).expectedAssetExcessReturnsArray();

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

        System.out.println ("\t|               STARTING RETURNS SOURCES RECONCILIATION               ||");

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

        System.out.println ("\t|                ID                 =>  HIST  | GSMI  | CAPM  | IMPL  ||");

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

        for (int assetIndex = 0;
            assetIndex < impliedEquilibriumExcessReturnsArray.length;
            ++assetIndex)
        {
            System.out.println (
                "\t| [" + assetIDArray[assetIndex] + "] => " +
                FormatUtil.FormatDouble (assetSpaceHistoricalReturnsArray[assetIndex], 1, 2, 100.) + "% |" +
                FormatUtil.FormatDouble (assetSpaceGSMIReturnsArray[assetIndex], 1, 2, 100.) + "% |" +
                FormatUtil.FormatDouble (assetSpaceCAPMReturnsArray[assetIndex], 1, 2, 100.) + "% |" +
                FormatUtil.FormatDouble (
                    riskAversion * impliedEquilibriumExcessReturnsArray[assetIndex], 1, 2, 100.
                ) + "% ||"
            );
        }

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

        ForwardOptimizationWeights (
            ForwardReverseHoldingsAllocation.Forward (
                assetIDArray,
                assetSpaceHistoricalReturnsArray,
                assetExcessReturnsCovarianceMatrix,
                riskAversion
            ),
            historicalPortfolioWeightReconcilerArray,
            4,
            0,
            "\t|             HISTORICAL WEIGHTS RECONCILER            ||"
        );

        ForwardOptimizationWeights (
            ForwardReverseHoldingsAllocation.Forward (
                assetIDArray,
                assetSpaceGSMIReturnsArray,
                assetExcessReturnsCovarianceMatrix,
                riskAversion
            ),
            capmGSMIPortfolioWeightReconcilerArray,
            2,
            1,
            "\t|              CAPM GSMI WEIGHTS RECONCILER            ||"
        );

        ForwardOptimizationWeights (
            ForwardReverseHoldingsAllocation.Forward (
                assetIDArray,
                assetSpaceCAPMReturnsArray,
                assetExcessReturnsCovarianceMatrix,
                riskAversion
            ),
            assetEquilibriumWeightArray,
            2,
            1,
            "\t|             EQUILIBRIUM WEIGHTS RECONCILER           ||"
        );

        EnvManager.TerminateEnv();
    }
}