Package tech.nmfin.portfoliooptimization.corvalan2005

Class Corvalan2005

java.lang.Object

tech.nmfin.portfoliooptimization.corvalan2005.Corvalan2005

public class Corvalan2005
extends Object

This paper tackles the corner solution problem of many portfolio optimizers, by optimizing the portfolio diversification with some relaxation on the volatility σ and the expected return R of a given optimized (but non-diversified) portfolio. This implementation generalizes this framework as the following optimization problem: \[ \max_{w} D(w) \quad \text{s.t.} \\ \begin{aligned} \sqrt{w' \Sigma w} & \le \sigma^* (1 + \Delta \sigma) \\ R^* (1 - \Delta R) & \le w'r \\ w' 1 & = 1 \\ ... & \text{some extra constraints} \end{aligned} \] where \( ( \sigma^* , R^* ) = ( \sqrt{w^{*'} \Sigma w^*} , w^{*'} r ) \), \(w^*\) is the original optimal weights, \(\Delta \sigma, \Delta R\) are the relaxation tolerance parameters, and \(D(w)\) is a defined measure for portfolio diversification (DiversificationMeasure).

See Also:

Well Diversified Efficient Portfolios

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static interface	Corvalan2005.WeightsConstraint	Constraints on weights which are defined by a set of less-than constraints.

Constructor Summary

Constructors

Constructor	Description
Corvalan2005(double deltaSigma, double deltaR)	Constructs an instance of the Corvalan model.
Corvalan2005(Minimizer<? super ConstrainedOptimProblem,IterativeSolution<Vector>> minimizer, DiversificationMeasure diversificationMeasure, double deltaSigma, double deltaR)	Constructs an instance of the Corvalan model.

Method Summary

Modifier and Type	Method	Description
Vector	getDiversifiedWeights(Corvalan2005.WeightsConstraint constraint, Vector weights0, Matrix sigma, Vector r)	Finds the optimal weights for a diversified portfolio.
Vector	getDiversifiedWeights(Corvalan2005.WeightsConstraint constraint, Vector weights0, Matrix sigma, Vector r, EqualityConstraints extraEqualityConstraints, LessThanConstraints extraLessThanConstraints)	Finds the optimal weights for a diversified portfolio.

Methods inherited from class java.lang.Object

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

Constructor Detail

Corvalan2005

public Corvalan2005(double deltaSigma,
                    double deltaR)

Constructs an instance of the Corvalan model.

Parameters:

deltaSigma - the relaxation of portfolio volatility

deltaR - the relaxation of portfolio return

Corvalan2005

public Corvalan2005(Minimizer<? super ConstrainedOptimProblem,IterativeSolution<Vector>> minimizer,
                    DiversificationMeasure diversificationMeasure,
                    double deltaSigma,
                    double deltaR)

Constructs an instance of the Corvalan model.

Parameters:

minimizer - the optimizer

diversificationMeasure - the diversification measure

deltaSigma - the relaxation of portfolio volatility

deltaR - the relaxation of portfolio return

Method Detail

getDiversifiedWeights

public Vector getDiversifiedWeights(Corvalan2005.WeightsConstraint constraint,
                                    Vector weights0,
                                    Matrix sigma,
                                    Vector r)
                             throws Exception

Finds the optimal weights for a diversified portfolio.

Parameters:

constraint - the weight constraints

weights0 - the original optimal weights

sigma - the covariance matrix of asset returns

r - the expected asset returns

Returns:

the diversified weights

Throws:

Exception - when the optimizer fails to find a solution

getDiversifiedWeights

public Vector getDiversifiedWeights(Corvalan2005.WeightsConstraint constraint,
                                    Vector weights0,
                                    Matrix sigma,
                                    Vector r,
                                    EqualityConstraints extraEqualityConstraints,
                                    LessThanConstraints extraLessThanConstraints)
                             throws Exception

Finds the optimal weights for a diversified portfolio.

Parameters:

constraint - the weight constraints

weights0 - the original optimal weights

sigma - the covariance matrix of asset returns

r - the expected asset returns

extraEqualityConstraints - the additional equality constraints

extraLessThanConstraints - the additional less-than constraints

Returns:

the diversified weights

Throws:

Exception - when the optimizer fails to find a solution