tech.nmfin.algoquant.demo.model.portfoliooptimization

Class SOCPMarkowitzComparisonDemo

java.lang.Object

tech.nmfin.algoquant.demo.model.portfoliooptimization.SOCPMarkowitzComparisonDemo

@Demo
public class SOCPMarkowitzComparisonDemo
extends Object

We compare the results from a QP solver (Markowitz) and from an SOCP solver. They should give more or less the same results given only QP constraints, subject to numerical differences. The portfolio optimization problem is:

 max r*w-q*w'*Sigma*w
 s.t. sum(w)=1, w_i=1 for i in the black list.
 

We assume that the last index of w is in the black list.

Using this example. Compares quadratic and second-order-cone formulations using the same inputs and constraints. Numerical solver tolerances can produce different weights; inspect the existing TODO about correlated inputs rather than assuming universal agreement.

Model and publication. Related theory and the scope of this example are distinguished below.

Implementation in this tutorial. Compares QP and SOCP representations under the configured constraints and data. Equality of mathematical formulations does not imply bit-identical numerical solutions; inspect the existing correlated-input TODO and solver tolerances.

See Also:

H. Markowitz (1952), Portfolio Selection, Journal of Finance 7(1), 77–91

Constructor Summary

Constructors

Constructor and Description
SOCPMarkowitzComparisonDemo(int n, dev.nm.algebra.linear.vector.doubles.Vector r_bar, dev.nm.algebra.linear.matrix.doubles.Matrix Sigma, double riskAverseCoeff)

Method Summary

Modifier and Type	Method and Description
dev.nm.algebra.linear.vector.doubles.Vector	getMarkowitzSolution()
dev.nm.algebra.linear.vector.doubles.Vector	getSOCPSolution()
double	getUtilityValue(dev.nm.algebra.linear.vector.doubles.Vector x) Computes the utility value given the optimal weights.
static void	main(String[] args)
static dev.nm.algebra.linear.matrix.doubles.Matrix	randomNormalReturnMatrix(int N, int T) Generates a random return matrix, whose entries follow the standard Normal distribution.

Methods inherited from class java.lang.Object

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

Constructor Detail

SOCPMarkowitzComparisonDemo

public SOCPMarkowitzComparisonDemo(int n,
                                   dev.nm.algebra.linear.vector.doubles.Vector r_bar,
                                   dev.nm.algebra.linear.matrix.doubles.Matrix Sigma,
                                   double riskAverseCoeff)

Method Detail

main

public static void main(String[] args)
                 throws Exception

Throws:

Exception

getSOCPSolution

public dev.nm.algebra.linear.vector.doubles.Vector getSOCPSolution()
                                                            throws Exception

Throws:

Exception

getMarkowitzSolution

public dev.nm.algebra.linear.vector.doubles.Vector getMarkowitzSolution()
                                                                 throws dev.nm.solver.multivariate.constrained.convex.sdp.socp.qp.QPInfeasible

Throws:

dev.nm.solver.multivariate.constrained.convex.sdp.socp.qp.QPInfeasible

getUtilityValue

public double getUtilityValue(dev.nm.algebra.linear.vector.doubles.Vector x)

Computes the utility value given the optimal weights.

Parameters:

x - the optimal weights

Returns:

the value of the utility function

randomNormalReturnMatrix

public static dev.nm.algebra.linear.matrix.doubles.Matrix randomNormalReturnMatrix(int N,
                                                                                   int T)

Generates a random return matrix, whose entries follow the standard Normal distribution.

Parameters:

N - the number of stocks

T - the number of observations

Returns:

a random return matrix