Re: [ojAlgo-user] Markowitz optimisation

[Arthur M. <art...@be...>]

Hi Anders,

Here's the test case for zero weightings at default risk aversion factor.
Changing the RAF to "1" works although I'm wondering whether a better solut=
ion would be with the 0.35% and 0.25% weights swapped round.  All other ass=
ets get a 0.05% weight.

regards
Arthur

public void testEfficientFrontier2()
	{
		// create expected returns matrix
		PrimitiveMatrix expectedReturnsMatrix =3D new PrimitiveMatrix(new double[=
][] { {10.003264}, {9.989771}, {9.987513}, {9.988449}, {9.996579}, {9.99069=
0}, {9.994904}, {9.994514}, {9.984064}, {9.987534}});
		// create covariance matrix
		PrimitiveMatrix covarianceMatrix =3D new PrimitiveMatrix(new double[][] {=
{6.483565230120298E-4,	-1.3344603795915894E-4,	-4.610345510893708E-4,	-7.33=
4405624030001E-4,	1.1551383115707195E-5,	-0.00104145662863434,	-1.072589668=
5568462E-4,	-1.221384153392056E-4,	-4.173413644389791E-4,	-2.48610438949469=
35E-4},
				{-1.3344603795915894E-4,	0.0026045957224784455,	0.0012394355327235707,	=
9.243919166568456E-4,	-8.653805945112411E-5,	8.100239312410631E-4,	4.215960=
274481846E-4,	5.243272007211247E-4,	0.0013062718630332956,	1.47664502933954=
05E-4},
				{-4.610345510893708E-4,	0.0012394355327235707,	0.002361436913752224,	0.=
0020101714731002238,	-1.4236763916609785E-5,	0.002120395905829043,	5.399158=
658928662E-4,	5.048790842067473E-4,	0.0014855261720730444,	4.84145810618139=
6E-4},
				{-7.334405624030001E-4,	9.243919166568456E-4,	0.0020101714731002238,	0.=
0028542819089926895,	-4.311102526746861E-6,	0.0028465650900869476,	6.242643=
883624462E-4,	4.086484048798765E-4,	0.001647437646316569,	7.58419663970477E=
-4},
				{1.1551383115707195E-5,	-8.653805945112411E-5,	-1.4236763916609785E-5,	=
-4.311102526746861E-6,	1.213366124417227E-4,	-9.027529241741836E-5,	7.24138=
9994693716E-6,	-3.166855950737129E-5,	-1.2445276374560802E-5,	-5.3976919759=
028745E-5},
				{-0.00104145662863434,	8.100239312410631E-4,	0.002120395905829043,	0.00=
28465650900869476,	-9.027529241741836E-5,	0.0064756879298965295,	2.80762775=
64885113E-4,	3.6082073553997553E-4,	0.001945238279500792,	0.001242113234298=
8626},
				{-1.0725896685568462E-4,	4.215960274481846E-4,	5.399158658928662E-4,	6.=
242643883624462E-4,	7.241389994693716E-6,	2.8076277564885113E-4,	0.00101215=
00024739688,	8.206099676659543E-5,	1.6129237403855146E-4,	7.550465994733837=
E-4},
				{-1.221384153392056E-4,	5.243272007211247E-4,	5.048790842067473E-4,	4.0=
86484048798765E-4,	-3.166855950737129E-5,	3.6082073553997553E-4,	8.20609967=
6659543E-5,	4.504461842318998E-4,	4.7980942831718363E-4,	-4.763223568683059=
E-5},
				{-4.173413644389791E-4,	0.0013062718630332956,	0.0014855261720730444,	0=
.001647437646316569,	-1.2445276374560802E-5,	0.001945238279500792,	1.612923=
7403855146E-4,	4.7980942831718363E-4,	0.002228245076175045,	3.2083564921169=
634E-4},
				{-2.4861043894946935E-4,	1.4766450293395405E-4,	4.841458106181396E-4,	7=
.58419663970477E-4,	-5.3976919759028745E-5,	0.0012421132342988626,	7.550465=
994733837E-4,	-4.763223568683059E-5,	3.2083564921169634E-4,	0.0017093327832=
123186}});

		MarketEquilibrium myMarket =3D new MarketEquilibrium(covarianceMatrix);

		// create asset variables - cost and weighting constraints
		Variable[] tmpVariables =3D new Variable[expectedReturnsMatrix.getRowDim(=
)];
		for (int i =3D 0; i < tmpVariables.length; i++)
		{
			tmpVariables[i] =3D new Variable("");
			tmpVariables[i].setCost(expectedReturnsMatrix.toBigDecimal(i, 0).negate(=
));
			// set the constraints on the asset weights
			// require at least a 2% allocation to each asset
			tmpVariables[i].setLowerLimit(new BigDecimal("0.05"));
			// require no more than 80% allocation to each asset
			tmpVariables[i].setUpperLimit(new BigDecimal("0.35"));
		}

		QuadraticModel quadModel =3D new QuadraticModel(tmpVariables);

		Expression tmpExpr =3D quadModel.addCorrelationExpression("Variance", cov=
arianceMatrix.toBigStore().toArray());
		BigDecimal tmpRiskAversion =3D myMarket.getRiskAversion();
		tmpExpr.setCost(tmpRiskAversion.multiply(BigMath.HALF));

		// set balance expression
		tmpExpr =3D quadModel.addSimpleWeightExpression("Balance");
		tmpExpr.setLowerLimit(BigMath.ONE);
		tmpExpr.setUpperLimit(BigMath.ONE);

		// exception here...
		BasicMatrix bm =3D BigMatrix.FACTORY.buildColumnVector(quadModel.getDefau=
ltSolver().getSolution());
=09
		System.out.print(bm.toString());
	}


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