Re: [ojAlgo-user] Markowitz Problem

[Anders P. <an...@op...>]

I've tweaked the underlying optimization algorithm so that it now produces {0.5, 0.5} as the optimal solution for the case with target return 0.11.

Your covariance matrix looks like this:

 0.0036 0.0018
 0.0018 0.0009

and thus the correlations matrix is:

 1 1
 1 1

Is this intended/expected?


/Anders


On 31 mar 2013, at 11:38, Anders Peterson <an...@op...> wrote:

> Yes, ojAlgo seems to have a problem solving that. I'll have to look into exactly what goes on.
> 
> The covariance matrix is positive semidefinite, right? That should be enough, but positive definite would be better.
> 
> You should always check the optimisation state. In this case it is APPROXIMATE. Suppose it should be FAILED or something, but anything less that OPTIMAL would indicate a problem with the underlying optimisation algorithm.
> 
> Regarding how to create matrices; I think you should read this:
> http://code.google.com/p/ojalgo/wiki/GettingStartedLinearAlgebra
> 
> /Anders
> 
> 
> On 29 mar 2013, at 13:19, Matteo Baccan <mat...@gm...> wrote:
> 
>> Hi
>> 
>> we have a problem with MarkowitzModel.
>> I have produced a little source that explain the problem.
>> 
>> We have set 3 different TargetReturn on the same data..
>> 
>> With targets near to the best end worst target return, the MarkowitzModel works fine.
>> With targets within the interval of best and worst return, seem that the MarkowitzModel 
>> is not able to find a correct list of weights.
>> 
>> If you try this program and use target of 0.08 or 0.13 or 0.12 you can see a correct solution.
>> With a target of 0.10 MarkowitzModel is not able to find a valid solution.
>> 
>> It's a OJAlgo bug or is a problem in my implementation?
>> 
>> All the best
>> Matteo Baccan
>> 
>> 
>> 
>> import java.math.BigDecimal;
>> import java.util.List;
>> 
>> import org.ojalgo.access.AccessUtils;
>> import org.ojalgo.constant.BigMath;
>> import org.ojalgo.finance.portfolio.MarketEquilibrium;
>> import org.ojalgo.finance.portfolio.MarkowitzModel;
>> import org.ojalgo.matrix.BasicMatrix;
>> import org.ojalgo.matrix.BigMatrix;
>> import org.ojalgo.matrix.PrimitiveMatrix;
>> import org.ojalgo.matrix.store.BigDenseStore;
>> import org.ojalgo.matrix.store.MatrixStore;
>> import org.ojalgo.matrix.store.PrimitiveDenseStore;
>> import org.ojalgo.optimisation.Optimisation;
>> import org.ojalgo.optimisation.quadratic.QuadraticSolver;
>> 
>> public class MarkowitzProblems
>> {
>> 
>>    public static void main(String[] args)
>>    {
>> 
>> //BigDecimal nTarget = new BigDecimal("0.08"); // OK
>> // 0.0
>> // 1.0
>> 
>> BigDecimal nTarget = new BigDecimal("0.10"); // ERROR
>> // -0.9999
>> // 1.9999
>> 
>> //BigDecimal nTarget = new BigDecimal("0.13"); // OK
>> // 0.8333
>> // 0.1667
>> 
>> double[][] cm=
>> {{0.00360000,    0.001800000000},
>> {0.001800000000,    0.00090000}}
>> ;
>> 
>>      int assetNum = cm.length;
>> 
>>      final int row = cm.length;
>>      if (row > 0) {
>>         final int col = cm[0].length;
>>         final MatrixStore<BigDecimal> a = BigDenseStore.FACTORY.makeZero(row, col);
>>         BasicMatrix covariances = BigMatrix.FACTORY.copy(a);
>> 
>>         for (int i = 0; i < row; i++) {
>>            for (int j = 0; j < col; j++) {
>>               covariances = covariances.replace(i, j, cm[i][j]);
>>            }
>>         }
>> 
>>         double nRisk = 1000.0;
>>         final BigDecimal riskAversion = new BigDecimal(nRisk);
>>         final MarketEquilibrium marketEquilibrium = new MarketEquilibrium(covariances, riskAversion);
>> 
>>         final MatrixStore<BigDecimal> ret_matrix = BigDenseStore.FACTORY.makeZero(assetNum, 1);
>>         BasicMatrix expectedExcessReturns1 = BigMatrix.FACTORY.copy(ret_matrix);
>> 
>> expectedExcessReturns1 = expectedExcessReturns1.replace(0, 0, 0.1400);
>> expectedExcessReturns1 = expectedExcessReturns1.replace(1, 0, 0.0800);
>> 
>>         final MarkowitzModel markowitzModel = new MarkowitzModel(marketEquilibrium, expectedExcessReturns1);
>> 
>> markowitzModel.setLowerLimit(0, new BigDecimal(0.0000));
>> markowitzModel.setUpperLimit(0, new BigDecimal(1.0000));
>> markowitzModel.setLowerLimit(1, new BigDecimal(0.0000));
>> markowitzModel.setUpperLimit(1, new BigDecimal(1.0000));
>> 
>>         boolean bShort = false;
>>         markowitzModel.setShortingAllowed(bShort);
>>         markowitzModel.setTargetReturn(nTarget);
>> 
>>         final List<BigDecimal> re = markowitzModel.getWeights();
>>         for (int nn = 0; nn < re.size(); nn++) {
>>            System.out.println( re.get(nn) );
>>         }
>>      }
>>    }
>> 
>> }
>> 
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> 
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