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();
}
}