DualConstrainedEllipsoidVariance.java
package org.drip.sample.semidefinite;
import org.drip.function.definition.RdToR1;
import org.drip.function.rdtor1.*;
import org.drip.function.rdtor1descent.LineStepEvolutionControl;
import org.drip.function.rdtor1solver.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
*
* This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
* libraries targeting analysts and developers
* https://lakshmidrip.github.io/DRIP/
*
* DRIP is composed of four main libraries:
*
* - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
* - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
* - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
* - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
*
* - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
* Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
* Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
* Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
* Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
*
* - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
* Incorporator, Holdings Constraint, and Transaction Costs.
*
* - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
*
* - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
*
* 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.
*/
/**
* DualConstrainedEllipsoidVariance demonstrates the Application of the Interior Point Method for Minimizing
* the Variance Across The Specified Ellipsoid under both Normalization and first Moment Constraints.
*
* @author Lakshmi Krishnamurthy
*/
public class DualConstrainedEllipsoidVariance
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
String[] entityNameArray = new String[]
{
"IBM",
"ATT",
"ALU",
"QCO",
"INT",
"MSF",
"VER"
};
double[] entityReturnsArray = new double[]
{
0.0264,
0.0332,
0.0400,
0.0468,
0.0536,
0.0604,
0.0672
};
double entityDesignReturn = 0.0468;
double[][] entityCovarianceMatrix = new double[][]
{
{1.00, 0.76, 0.80, 0.38, 0.60, 0.61, 0.51},
{0.76, 1.00, 0.65, 0.35, 0.56, 0.43, 0.40},
{0.80, 0.65, 1.00, 0.68, 0.74, 0.40, 0.51},
{0.38, 0.35, 0.68, 1.00, 0.72, 0.02, 0.57},
{0.60, 0.56, 0.74, 0.72, 1.00, 0.31, 0.67},
{0.61, 0.43, 0.40, 0.02, 0.31, 1.00, 0.39},
{0.51, 0.40, 0.51, 0.57, 0.67, 0.39, 1.00}
};
InteriorPointBarrierControl interiorPointBarrierControl = InteriorPointBarrierControl.Standard();
System.out.println ("\n\n\t|------------------------------------------------------||");
String header = "\t| |";
for (int entityIndex = 0;
entityIndex < entityNameArray.length;
++entityIndex)
{
header += " " + entityNameArray[entityIndex] + " |";
}
System.out.println (header + "|");
System.out.println ("\t|------------------------------------------------------||");
for (int entityIndexI = 0;
entityIndexI < entityNameArray.length;
++entityIndexI)
{
String dump = "\t| " + entityNameArray[entityIndexI] + " ";
for (int entityIndexJ = 0;
entityIndexJ < entityNameArray.length;
++entityIndexJ)
{
dump += "|" + FormatUtil.FormatDouble (
entityCovarianceMatrix[entityIndexI][entityIndexJ], 1, 2, 1.
) + " ";
}
System.out.println (dump + "||");
}
System.out.println ("\t|------------------------------------------------------||\n\n");
double equalityConstraintConstant = -1.;
int entityCount = entityCovarianceMatrix.length;
RdToR1[] equalityConstraintFunctionArray = new RdToR1[]
{
new AffineMultivariate (
ObjectiveConstraintVariateSet.Unitary (
entityCount
),
equalityConstraintConstant
),
new AffineMultivariate (
entityReturnsArray,
-1. * entityDesignReturn
)
};
int equalityConstraintCount = equalityConstraintFunctionArray.length;
LagrangianMultivariate lagrangianMultivariate = new LagrangianMultivariate (
new CovarianceEllipsoidMultivariate (
entityCovarianceMatrix
),
equalityConstraintFunctionArray
);
double[] optimalVariateArray = new BarrierFixedPointFinder (
lagrangianMultivariate,
new RdToR1[]
{
new AffineBoundMultivariate (
false,
0,
entityCount + equalityConstraintCount,
0.05
),
new AffineBoundMultivariate (
true,
0,
entityCount + equalityConstraintCount,
0.65
),
new AffineBoundMultivariate (false, 1, entityCount + equalityConstraintCount, 0.05),
new AffineBoundMultivariate (true, 1, entityCount + equalityConstraintCount, 0.65),
new AffineBoundMultivariate (false, 2, entityCount + equalityConstraintCount, 0.05),
new AffineBoundMultivariate (true, 2, entityCount + equalityConstraintCount, 0.65),
new AffineBoundMultivariate (false, 3, entityCount + equalityConstraintCount, 0.05),
new AffineBoundMultivariate (true, 3, entityCount + equalityConstraintCount, 0.65),
new AffineBoundMultivariate (false, 4, entityCount + equalityConstraintCount, 0.05),
new AffineBoundMultivariate (true, 4, entityCount + equalityConstraintCount, 0.65),
new AffineBoundMultivariate (false, 5, entityCount + equalityConstraintCount, 0.05),
new AffineBoundMultivariate (true, 5, entityCount + equalityConstraintCount, 0.65),
new AffineBoundMultivariate (false, 6, entityCount + equalityConstraintCount, 0.05),
new AffineBoundMultivariate (true, 6, entityCount + equalityConstraintCount, 0.65)
},
interiorPointBarrierControl,
LineStepEvolutionControl.NocedalWrightStrongWolfe (
false
)
).solve (
ObjectiveConstraintVariateSet.Uniform (
entityCount,
lagrangianMultivariate.constraintFunctionDimension()
)
).variateArray();
System.out.println ("\t|----------------------||");
System.out.println ("\t| OPTIMAL ENTITIES ||");
System.out.println ("\t|----------------------||");
double expectedReturn = 0.;
for (int entityIndex = 0;
entityIndex < entityCount;
++entityIndex)
{
System.out.println (
"\t| " + entityNameArray[entityIndex] + " => " + FormatUtil.FormatDouble (
optimalVariateArray[entityIndex], 2, 2, 100.
) + "% ||"
);
expectedReturn += optimalVariateArray[entityIndex] * entityReturnsArray[entityIndex];
}
System.out.println ("\t|----------------------||\n");
System.out.println ("\t|------------------------------||");
System.out.println (
"\t| DESIGN RETURN => " + FormatUtil.FormatDouble (
entityDesignReturn, 1, 5, 1.
) + " ||"
);
System.out.println (
"\t| EXPECTED RETURN => " + FormatUtil.FormatDouble (
expectedReturn, 1, 5, 1.
) + " ||"
);
System.out.println (
"\t| OPTIMAL VARIANCE => " + FormatUtil.FormatDouble (
lagrangianMultivariate.evaluate (
optimalVariateArray
), 1, 5, 1.
) + " ||"
);
System.out.println ("\t|------------------------------||\n");
}
}