Re: [ojAlgo-user] Risk Aversion Factor Question

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

if/when you're using QuadraticModel you do not need to directly worry  
about the specifications of QuadraticSolver. Just model your problem  
the way you want it. Specifying a contribution weight makes that  
Variable or Expression part of the objective function. The size of a  
contribution weight only matters in relation to other contribution  
weights.

Why don't you use the org.ojalgo.finance.portfolio.MarkowitzModel  
class or at least look at how it is implemented.

/Anders


On 16 jun 2009, at 16.14, bru...@uk... wrote:

>
> Hi, when looking at the javadoc of the QuadraticSolver class, the  
> following can be read:
>
> QuadraticSolver solves optimisation problems of the form:
>
> min 1/2 [X]T[Q][X] - [C]T[X]
> when [AE][X] == [BE]
> and [AI][X] <= [BI]
>
>
> I wondered how it would be possible to optimise the following  
> problem with QuadraticSolver:
>
> min k*[X]T[Q][X] - (1-k)*[R]T[X] where R is the vector of the  
> returns and 0 <= k <= 1
> when [AE][X] == [BE]
> and [AI][X] <= [BI]
>
> Typically I want to either:
> - maximise the return for a target volatility [X]T[Q][X] = targetVol
> - minimise the volatility for a target return  [R]T[X]       =  
> targetReturn
>
> How can I do that with QuadraticSolver?
> Here is the code I wrote as an attempt to solve my problem. It gives  
> me weights but I am not sure if I have set the problem correctly.
>
>  public boolean solveProblem() {
>         Variable[] variables = new Variable[allReturns[0].length];
>
>         //R is the vector of the assets' returns
>         //Inequality constraints are between 0 and 1 for the weights
>
>         for (int i = 0; i < variables.length; i++) {
>             variables[i] = new Variable("w"+(i+1));
>             variables[i].setContributionWeight( R.toBigDecimal(i,  
> 0) );
>             variables[i].setLowerLimit("0" );
>             variables[i].setUpperLimit("1" );
>         }
>
>         QuadraticModel quadraticModel = new QuadraticModel(variables);
>
>          //Q is the correlation matrix of the assets' returns
>          //The question is: What do I do if I want to set a  
> volatility target? How do I specify it?
>          // How is it related to the contribution?
>
>         Expression expression =  
> quadraticModel.addCorrelationExpression("Variance", Q );
>         BigDecimal riskAversion = new BigDecimal("1");
>         expression.setContributionWeight(riskAversion.multiply(new  
> BigDecimal("0.5")));
>
>         // set balance expression, sum of weights equal to 1
>         expression =  
> quadraticModel.addSimpleWeightExpression("Balance");
>         expression.setLowerLimit(new BigDecimal("1"));
>         expression.setUpperLimit(new BigDecimal("1"));
>
>         res = quadraticModel.getDefaultSolver().solve();
>         solverState = res.getState();
>
>         return solverState == solverState.OPTIMAL;
>     }
>
>
> Regards
> BF
>
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