UserConfidenceProjectionCalibration.java

package org.drip.sample.idzorek;

import org.drip.function.definition.R1ToR1;
import org.drip.measure.bayesian.ProjectionDistributionLoading;
import org.drip.measure.continuous.MultivariateMeta;
import org.drip.measure.gaussian.R1MultivariateNormal;
import org.drip.numerical.common.FormatUtil;
import org.drip.portfolioconstruction.allocator.ForwardReverseHoldingsAllocation;
import org.drip.portfolioconstruction.asset.Portfolio;
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>UserConfidenceProjectionCalibration</i> calibrates the Black Litterman Projection Variance using the
 * Implied Allocation Tilts. 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 UserConfidenceProjectionCalibration
{

    private static final void IdzorekImpliedProjectionConfidence (
        final BlackLittermanCombinationEngine blackLittermanCombinationEngine,
        final int viewIndex,
        final double[] impliedTiltArray,
        final double projectionUserConfidence)
        throws Exception
    {
        System.out.println ("\t|-----------------------------||");

        System.out.println (
            "\t|            VIEW #" + viewIndex + "          ||"
        );

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

        System.out.println (
            "\t|     CONFIDENCE =>" +
            FormatUtil.FormatDouble (projectionUserConfidence, 2, 2, 100.) + "%    ||"
        );

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

        R1ToR1 tiltDepartureFunction = blackLittermanCombinationEngine.tiltDepartureR1ToR1 (
            impliedTiltArray,
            viewIndex,
            false
        );

        R1ToR1 tiltDepartureFunctionDerivative = blackLittermanCombinationEngine.tiltDepartureR1ToR1 (
            impliedTiltArray,
            viewIndex,
            true
        );

        for (int tiltDepartureIndex = 1;
            tiltDepartureIndex <= 15;
            ++tiltDepartureIndex)
        {
            System.out.println ("\t| " +
                FormatUtil.FormatDouble (0.01 * tiltDepartureIndex, 2, 2, 100.) + "% | " +
                FormatUtil.FormatDouble (
                    tiltDepartureFunction.evaluate (
                        0.01 * tiltDepartureIndex
                    ), 2, 2, 100.
                ) + "% | " +
                FormatUtil.FormatDouble (
                    tiltDepartureFunctionDerivative.evaluate (
                        0.01 * tiltDepartureIndex
                    ), 2, 2, 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;
        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[] userSpecifiedProjectionConfidenceArray = new double[]
        {
            0.25,
            0.50,
            0.65
        };

        BlackLittermanCombinationEngine blackLittermanCombinationEngine =
            new BlackLittermanCombinationEngine (
                ForwardReverseHoldingsAllocation.Reverse (
                    Portfolio.Standard (
                        assetIDArray,
                        assetEquilibriumWeightArray
                    ),
                    assetExcessReturnsCovarianceMatrix,
                    riskAversion
                ),
                new PriorControlSpecification (
                    true,
                    riskFreeRate,
                    tau
                ),
                new ProjectionSpecification (
                    R1MultivariateNormal.Standard (
                        new MultivariateMeta (
                            new String[]
                            {
                                "PROJECTION #1",
                                "PROJECTION #2",
                                "PROJECTION #3"
                            }
                        ),
                        projectionExpectedExcessReturnsArray,
                        ProjectionDistributionLoading.ProjectionCovariance (
                            assetExcessReturnsCovarianceMatrix,
                            assetSpaceViewProjectionMatrix,
                            tau
                        )
                    ),
                    assetSpaceViewProjectionMatrix
                )
            );

        double[][] projectionTiltArray = blackLittermanCombinationEngine.userConfidenceProjectionTitMatrix (
            userSpecifiedProjectionConfidenceArray
        );

        System.out.println ("\n\n");

        for (int userSpecifiedProjectionConfidenceArrayIndex = 0;
            userSpecifiedProjectionConfidenceArrayIndex < userSpecifiedProjectionConfidenceArray.length;
            ++userSpecifiedProjectionConfidenceArrayIndex)
        {
            IdzorekImpliedProjectionConfidence (
                blackLittermanCombinationEngine,
                userSpecifiedProjectionConfidenceArrayIndex,
                projectionTiltArray[userSpecifiedProjectionConfidenceArrayIndex],
                userSpecifiedProjectionConfidenceArray[userSpecifiedProjectionConfidenceArrayIndex]
            );
        }

        EnvManager.TerminateEnv();
    }
}