ForwardReverseHoldingsAllocation.java

package org.drip.portfolioconstruction.allocator;

/*
 * -*- 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>ForwardReverseHoldingsAllocation</i> holds the Metrics that result from a Forward/Reverse Optimization
 * Run.
 *
 *  <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</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/portfolioconstruction/README.md">Portfolio Construction under Allocation Constraints</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/portfolioconstruction/allocator/README.md">MVO Based Portfolio Allocation Construction</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class ForwardReverseHoldingsAllocation extends
    org.drip.portfolioconstruction.allocator.HoldingsAllocation
{
    private double _riskAversion = java.lang.Double.NaN;
    private double[] _expectedAssetExcessReturnsArray = null;
    private double[][] _assetExcessReturnsCovarianceMatrix = null;

    /**
     * Construct an Instance of ForwardReverseHoldingsAllocation from a Standard Reverse Optimize Operation
     * 
     * @param equilibriumPortfolio The Equilibrium Portfolio
     * @param assetExcessReturnsCovarianceMatrix Pair-wse Asset Excess Returns Co-variance Matrix
     * @param riskAversion The Risk Aversion Parameter
     * 
     * @return The Instance of ForwardReverseHoldingsAllocation from a Standard Reverse Optimize Operation
     */

    public static final ForwardReverseHoldingsAllocation Reverse (
        final org.drip.portfolioconstruction.asset.Portfolio equilibriumPortfolio,
        final double[][] assetExcessReturnsCovarianceMatrix,
        final double riskAversion)
    {
        if (null == equilibriumPortfolio)
        {
            return null;
        }

        double[] assetWeightArray = equilibriumPortfolio.weightArray();

        int assetCount = assetWeightArray.length;

        double[] expectedAssetExcessReturnsArray = org.drip.numerical.linearalgebra.Matrix.Product (
            assetExcessReturnsCovarianceMatrix,
            assetWeightArray
        );

        if (null == expectedAssetExcessReturnsArray)
        {
            return null;
        }

        for (int assetIndex = 0; assetIndex < assetCount; ++assetIndex)
        {
            expectedAssetExcessReturnsArray[assetIndex] = expectedAssetExcessReturnsArray [assetIndex] *
                riskAversion;
        }

        return ForwardReverseHoldingsAllocation.Standard (
            equilibriumPortfolio,
            riskAversion,
            assetExcessReturnsCovarianceMatrix,
            expectedAssetExcessReturnsArray
        );
    }

    /**
     * Construct an Instance of ForwardReverseHoldingsAllocation from a Standard Forward Optimize Operation
     * 
     * @param assetIDArray The Array of the IDs of the Assets in the Portfolio
     * @param expectedAssetExcessReturnsArray Array of Expected Excess Returns
     * @param assetExcessReturnsCovarianceMatrix Excess Returns Co-variance Matrix
     * @param riskAversion The Risk Aversion Parameter
     * 
     * @return The Instance of ForwardReverseHoldingsAllocation from a Standard Forward Optimize Operation
     */

    public static final ForwardReverseHoldingsAllocation Forward (
        final java.lang.String[] assetIDArray,
        final double[] expectedAssetExcessReturnsArray,
        final double[][] assetExcessReturnsCovarianceMatrix,
        final double riskAversion)
    {
        if (null == assetIDArray)
        {
            return null;
        }

        int assetCount = assetIDArray.length;

        double[] assetWeightArray = org.drip.numerical.linearalgebra.Matrix.Product (
            org.drip.numerical.linearalgebra.Matrix.InvertUsingGaussianElimination (
                assetExcessReturnsCovarianceMatrix
            ),
            expectedAssetExcessReturnsArray
        );

        if (null == assetWeightArray || assetCount != assetWeightArray.length)
        {
            return null;
        }

        for (int assetIndex = 0; assetIndex < assetCount; ++assetIndex)
        {
            assetWeightArray[assetIndex] = assetWeightArray[assetIndex] / riskAversion;
        }

        return ForwardReverseHoldingsAllocation.Standard (
            org.drip.portfolioconstruction.asset.Portfolio.Standard (
                assetIDArray,
                assetWeightArray
            ),
            riskAversion,
            assetExcessReturnsCovarianceMatrix,
            expectedAssetExcessReturnsArray
        );
    }

    /**
     * Construct a Standard Instance of ForwardReverseHoldingsAllocation
     * 
     * @param equilibriumPortfolio The Optimal Equilibrium Portfolio
     * @param riskAversion The Risk Aversion Parameter
     * @param assetExcessReturnsCovarianceMatrix Pair-wise Asset Excess Returns Co-variance Matrix
     * @param expectedAssetExcessReturnsArray Array of Expected Excess Returns
     * 
     * @return The Standard Instance of ForwardReverseHoldingsAllocation
     */

    public static final ForwardReverseHoldingsAllocation Standard (
        final org.drip.portfolioconstruction.asset.Portfolio equilibriumPortfolio,
        final double riskAversion,
        final double[][] assetExcessReturnsCovarianceMatrix,
        final double[] expectedAssetExcessReturnsArray)
    {
        if (null == equilibriumPortfolio || null == expectedAssetExcessReturnsArray)
        {
            return null;
        }

        double[] assetWeightArray = equilibriumPortfolio.weightArray();

        double portfolioExcessReturnsMean = 0.;
        int assetCount = assetWeightArray.length;
        double portfolioExcessReturnsVariance = 0.;

        if (assetCount != expectedAssetExcessReturnsArray.length)
        {
            return null;
        }

        double[] impliedBetaArray = org.drip.numerical.linearalgebra.Matrix.Product (
            assetExcessReturnsCovarianceMatrix,
            assetWeightArray
        );

        if (null == impliedBetaArray)
        {
            return null;
        }

        for (int assetIndexI = 0; assetIndexI < assetCount; ++assetIndexI)
        {
            portfolioExcessReturnsMean += assetWeightArray[assetIndexI] *
                expectedAssetExcessReturnsArray[assetIndexI];

            for (int assetIndexJ = 0; assetIndexJ < assetCount; ++assetIndexJ)
            {
                portfolioExcessReturnsVariance += assetWeightArray[assetIndexI] *
                    assetWeightArray[assetIndexJ] *
                    assetExcessReturnsCovarianceMatrix[assetIndexI][assetIndexJ];
            }
        }

        for (int assetIndex = 0; assetIndex < assetCount; ++assetIndex)
        {
            impliedBetaArray[assetIndex] = impliedBetaArray[assetIndex] / portfolioExcessReturnsVariance;
        }

        double portfolioExcessReturnsSigma = java.lang.Math.sqrt (portfolioExcessReturnsVariance);

        try
        {
            return new ForwardReverseHoldingsAllocation (
                equilibriumPortfolio,
                new org.drip.portfolioconstruction.asset.PortfolioMetrics (
                    portfolioExcessReturnsMean,
                    portfolioExcessReturnsVariance,
                    portfolioExcessReturnsSigma,
                    portfolioExcessReturnsMean / portfolioExcessReturnsSigma,
                    impliedBetaArray
                ),
                riskAversion,
                assetExcessReturnsCovarianceMatrix,
                expectedAssetExcessReturnsArray
            );
        }
        catch (java.lang.Exception e)
        {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * ForwardReverseHoldingsAllocation Constructor
     * 
     * @param optimalEquilibriumPortfolio The Optimal Equilibrium Portfolio
     * @param optimalEquilibriumPortfolioMetrics The Optimal Equilibrium Portfolio Metrics
     * @param riskAversion The Risk Aversion Parameter
     * @param assetExcessReturnsCovarianceMatrix Pair-wise Asset Excess Returns Co-variance Matrix
     * @param expectedAssetExcessReturnsArray Array of Expected Excess Returns
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public ForwardReverseHoldingsAllocation (
        final org.drip.portfolioconstruction.asset.Portfolio optimalEquilibriumPortfolio,
        final org.drip.portfolioconstruction.asset.PortfolioMetrics optimalEquilibriumPortfolioMetrics,
        final double riskAversion,
        final double[][] assetExcessReturnsCovarianceMatrix,
        final double[] expectedAssetExcessReturnsArray)
        throws java.lang.Exception
    {
        super (
            optimalEquilibriumPortfolio,
            optimalEquilibriumPortfolioMetrics
        );

        if (null == (_assetExcessReturnsCovarianceMatrix = assetExcessReturnsCovarianceMatrix) ||
            !org.drip.numerical.common.NumberUtil.IsValid (_riskAversion = riskAversion) ||
            null == (_expectedAssetExcessReturnsArray = expectedAssetExcessReturnsArray))
        {
            throw new java.lang.Exception ("ForwardReverseHoldingsAllocation Constructor => Invalid Inputs");
        }
    }

    /**
     * Retrieve the Excess Returns Co-variance Matrix between each Pair-wise Asset
     * 
     * @return The Excess Returns Co-variance Matrix between each Pair-wise Asset
     */

    public double[][] assetExcessReturnsCovarianceMatrix()
    {
        return _assetExcessReturnsCovarianceMatrix;
    }

    /**
     * Retrieve the Risk Aversion Coefficient
     * 
     * @return The Risk Aversion Coefficient
     */

    public double riskAversion()
    {
        return _riskAversion;
    }

    /**
     * Retrieve the Array of Expected Excess Returns Array for each Asset
     * 
     * @return The Array of Expected Excess Returns Array for each Asset
     */

    public double[] expectedAssetExcessReturnsArray()
    {
        return _expectedAssetExcessReturnsArray;
    }

    /**
     * Compute the Portfolio Relative Metrics using the specified Benchmark
     * 
     * @param benchmarkPortfolioMetrics The Benchmark Metrics
     * 
     * @return The Portfolio Relative Metrics using the specified Benchmark
     */

    public org.drip.portfolioconstruction.asset.PortfolioBenchmarkMetrics benchmarkMetrics (
        final org.drip.portfolioconstruction.asset.PortfolioMetrics benchmarkPortfolioMetrics)
    {
        if (null == benchmarkPortfolioMetrics)
        {
            return null;
        }

        org.drip.portfolioconstruction.asset.PortfolioMetrics portfolioMetrics = optimalMetrics();

        try
        {
            double beta = org.drip.numerical.linearalgebra.Matrix.DotProduct (
                optimalPortfolio().weightArray(),
                benchmarkPortfolioMetrics.impliedBeta()
            );

            double activeBeta = beta - 1.;

            double portfolioExcessReturnsMean = portfolioMetrics.excessReturnsMean();

            double benchmarkExcessReturnsMean = benchmarkPortfolioMetrics.excessReturnsMean();

            double benchmarkExcessReturnsVariance = benchmarkPortfolioMetrics.excessReturnsVariance();

            double residualRisk = java.lang.Math.sqrt (
                portfolioMetrics.excessReturnsVariance() - beta * beta * benchmarkExcessReturnsVariance
            );

            return new org.drip.portfolioconstruction.asset.PortfolioBenchmarkMetrics (
                beta,
                activeBeta,
                java.lang.Math.sqrt (
                    residualRisk * residualRisk + activeBeta * activeBeta * benchmarkExcessReturnsVariance
                ),
                portfolioExcessReturnsMean - benchmarkExcessReturnsMean,
                residualRisk,
                portfolioExcessReturnsMean - beta * benchmarkExcessReturnsMean
            );
        }
        catch (java.lang.Exception e)
        {
            e.printStackTrace();
        }

        return null;
    }
}