Package org.drip.portfolioconstruction.bayesian

Class BlackLittermanCombinationEngine

java.lang.Object

org.drip.portfolioconstruction.bayesian.BlackLittermanCombinationEngine

public class BlackLittermanCombinationEngine
extends java.lang.Object

BlackLittermanCombinationEngine implements the Engine that generates the Combined/Posterior Distributions from the Prior and the Conditional Joint R¹ Multivariate Normal Distributions. The References are:

• He. G., and R. Litterman (1999): The Intuition behind the Black-Litterman Model Portfolios Goldman Sachs Asset Management
• Idzorek, T. (2005): A Step-by-Step Guide to the Black-Litterman Model: Incorporating User-Specified Confidence Levels Ibbotson Associates Chicago, IL

• Module = Portfolio Core Module
• Library = Asset Allocation Analytics
• Project = Portfolio Construction under Allocation Constraints
• Package = Black Litterman Bayesian Portfolio Construction

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
BlackLittermanCombinationEngine(ForwardReverseHoldingsAllocation forwardReverseOptimizationOutputUnadjusted, PriorControlSpecification priorControlSpecification, ProjectionSpecification projectionSpecification)	BlackLittermanCombinationEngine Construction

Method Summary

Modifier and Type	Method	Description
BlackLittermanCustomConfidenceOutput	customConfidenceRun()	Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator Using the specified Confidence Level
BlackLittermanOutput	fullConfidenceRun()	Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator For 100% Confidence in the Projection
ProjectionImpliedConfidenceOutput	impliedConfidenceRun()	Compute the Idzorek Implied Projection Confidence Level
BlackLittermanOutput	noConfidenceRun()	Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator for 0% Confidence in the Projection
ProjectionExposure	projectionExposureAttribution()	Compute the Exposure Loadings Attribution on a per-Projection Basis
R1ToR1	tiltDepartureR1ToR1(double[] userConfidenceProjectionTiltArray, int projectionIndex, boolean generateDerivative)	Generate the Squared Tilt Departure R1 To R1
double	tiltMismatchSquared(double[] userConfidenceProjectionTiltArray, int projectionIndex, double projectionVariance)	Compute the Mismatch between the User Specified Projection and the Custom Confidence Implied Tilts
double[][]	userConfidenceProjectionTitMatrix(double[] userSpecifiedProjectionConfidenceArray)	Compute the Idzorek Implied Tilt Matrix from the User Projection Confidence Level

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

BlackLittermanCombinationEngine

public BlackLittermanCombinationEngine(ForwardReverseHoldingsAllocation forwardReverseOptimizationOutputUnadjusted,
PriorControlSpecification priorControlSpecification,
ProjectionSpecification projectionSpecification)
                                throws java.lang.Exception

BlackLittermanCombinationEngine Construction

Parameters:

forwardReverseOptimizationOutputUnadjusted - The Unadjusted Instance of ForwardReverseOptimizationOutput

priorControlSpecification - The Prior Control Specification Instance

projectionSpecification - The View Projection Specification Settings

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

noConfidenceRun

public BlackLittermanOutput noConfidenceRun()

Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator for 0% Confidence in the Projection

Returns:

Output of the Black Litterman Run

customConfidenceRun

public BlackLittermanCustomConfidenceOutput customConfidenceRun()

Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator Using the specified Confidence Level

Returns:

Output of the Black Litterman Run

fullConfidenceRun

public BlackLittermanOutput fullConfidenceRun()

Conduct a Black Litterman Run using a Theil-like Mixed Model Estimator For 100% Confidence in the Projection

Returns:

Output of the Black Litterman Run

impliedConfidenceRun

public ProjectionImpliedConfidenceOutput impliedConfidenceRun()

Compute the Idzorek Implied Projection Confidence Level

Returns:

The Idzorek Implied Projection Confidence Level

projectionExposureAttribution

public ProjectionExposure projectionExposureAttribution()

Compute the Exposure Loadings Attribution on a per-Projection Basis

Returns:

The Exposure Loadings Attribution on a per-Projection Basis

userConfidenceProjectionTitMatrix

public double[][] userConfidenceProjectionTitMatrix(double[] userSpecifiedProjectionConfidenceArray)

Compute the Idzorek Implied Tilt Matrix from the User Projection Confidence Level

Parameters:

userSpecifiedProjectionConfidenceArray - Array of User-specified Projection Confidence

Returns:

The Idzorek Implied Tilt Matric from the Projection Confidence Level

tiltMismatchSquared

public double tiltMismatchSquared(double[] userConfidenceProjectionTiltArray,
int projectionIndex,
double projectionVariance)
                           throws java.lang.Exception

Compute the Mismatch between the User Specified Projection and the Custom Confidence Implied Tilts

Parameters:

userConfidenceProjectionTiltArray - Array of the User Confidence induced Projection Tilts

projectionIndex - The Index into the Projection Meta

projectionVariance - The Projection Variance

Returns:

The Squared Mismatch

Throws:

java.lang.Exception - Thrown if the Squared Mismatch cannot be calculated

tiltDepartureR1ToR1

public R1ToR1 tiltDepartureR1ToR1(double[] userConfidenceProjectionTiltArray,
int projectionIndex,
boolean generateDerivative)

Generate the Squared Tilt Departure R¹ To R¹

Parameters:

userConfidenceProjectionTiltArray - Array of the User Confidence induced Projection Tilts

projectionIndex - The Index into the Projection Meta

generateDerivative - TRUE - Generate the Derivative of the Tilt Departure

Returns:

The Squared Tilt Departure R¹ To R¹