Re: [ojAlgo-user] Markowitz Model Problem
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Re: [ojAlgo-user] Markowitz Model Problem
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From: Anders P. <an...@op...> - 2009-01-16 06:25:55
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On 16 jan 2009, at 02.28, Ruan Weichao wrote:
> Hi,
>
> Yes, that's the expected excess returns of my program.
>
> Is it right?
>
> Can the "expected excess returns" be negative?
I have no way of knowing what model/problem you want to solve...
In a general case excess returns (what you get for taking a risk)
should not be negative. If they are, you do not need to optimise
anything. Just invest everything in the risk free asset.
I'm not sure exactly why you get those negative (constraint breaking)
portfolio weights. I'm going to look into this, but later. Don't hold
your breath. For you, I think the solution is to work on your model.
/Anders
> On Thu, 15 Jan 2009 14:09:43 +0100, Anders Peterson wrote
>> Your expected excess returns matrix looks like this:
>>
>> class org.ojalgo.matrix.BigMatrix
>> {{-0.010638291263564232},
>> {-0.013500370827906071},
>> {-0.011390037735101773},
>> {-0.010385042339767682},
>> {-0.0003812208389845893},
>> {-0.002315505853720011},
>> {0}}
>>
>> Is that correct?
>>
>> Earlier you wrote "And i found that if i change the nagetive
>> ExceptedReturn to positive, the result will be fine."
>>
>> /Anders
>>
>> On 15 jan 2009, at 11.10, Ruan Weichao wrote:
>>
>>> Hi，i am using v25 and here's my code:
>>>
>>> /
>>> ********************************************************************
>>> **
>>> **********/
>>>
>>> import java.math.BigDecimal;
>>> import java.util.List;
>>>
>>> import org.ojalgo.finance.portfolio.MarketEquilibrium;
>>> import org.ojalgo.finance.portfolio.MarkowitzModel;
>>> import org.ojalgo.matrix.*;
>>> import org.ojalgo.matrix.store.BigDenseStore;
>>> import org.ojalgo.matrix.store.MatrixStore;
>>>
>>>
>>> public class TestMarkowitz {
>>>
>>> public double getCovarance(double[] value1, double[] value2){
>>>
>>> int n = value1.length;
>>> double averOne = 0;
>>> double averTwo = 0;
>>> for(int i=0;i<n;i++)
>>> {
>>> averOne+=value1[i];
>>> averTwo+=value2[i];
>>> }
>>> averOne /= n;
>>> averTwo /= n;
>>>
>>> double sum = 0;
>>> for(int i=0;i<n;i++)
>>> sum+=(value1[i]-averOne)*(value2[i]-averTwo);
>>>
>>> return sum / (n-1);
>>> }
>>>
>>> public BasicMatrix getACovariances(double[][] returns){
>>>
>>> int row = returns.length;
>>> int col = returns[0].length;
>>> MatrixStore<BigDecimal> a = BigDenseStore.FACTORY..makeZero(row,
>>> col);
>>> BasicMatrix covariances = new BigMatrix(a);
>>>
>>> for(int i=1;i<=row;i++){
>>> for(int j=i;j<=col;j++){
>>> double tmp = this.getCovarance(returns[i-1], returns[j-1]);
>>> covariances = covariances.set(i-1, j-1,tmp);
>>> covariances = covariances.set(j-1, i-1,tmp);
>>> }
>>> }
>>> return covariances;
>>> }
>>>
>>> public BasicMatrix getAnExpectedExcessReturns(double[][] returns){
>>>
>>> int row = returns.length;
>>> int col = returns[0].length;
>>>
>>> MatrixStore<BigDecimal> a = BigDenseStore.FACTORY..makeZero
>>> (row, 1);
>>> BasicMatrix expectedExcessReturns = new BigMatrix(a);
>>>
>>> double riskFreeReturn = 0;
>>> for(int i=1;i<=col;i++)
>>> riskFreeReturn+=returns[row-1][i-1];
>>> riskFreeReturn/=row;
>>>
>>> for(int i=1;i<=row;i++){
>>>
>>> double tmp = 0;
>>> for(int j=1;j<=col;j++)
>>> tmp+=returns[i-1][j-1];
>>> tmp/=col;
>>>
>>> expectedExcessReturns = expectedExcessReturns.set(i-1, 0, tmp-
>>> riskFreeReturn);
>>> }
>>>
>>> return expectedExcessReturns;
>>> }
>>>
>>> public static void main(String[] args)
>>> {
>>> int assetNum=7;
>>> double[][] assets_return={
>>> {-1.5905837442343828E-4, -0.03062360801781757,
>>> -0.029857534032853142, -0.011811692726036832,
>>> -0.017972310602803136, 0.017338003502626997, 0.0},
>>> {-0.02757158006362653, -0.02562704471101405,
>>> -0.011751538891997735, -0.024915062287655786, -0.01684088269454123,
>>> 0.013585351447135364, 0.0},
>>> {-0.00699300699300693, -0.033802816901408676,
>>> -0.04675196850393671, -0.021166752710376546, -0.007911392405063583,
>>> 0.03827751196172254, 0.0},
>>> {-0.007626310772164015, 0.0038424591738713027,
>>> 0.02488038277511978, 0.025210084033613675, -0.02003642987249557,
>>> -0.09758364312267642, 0.0},
>>> {-0.03965053763440893, 0.021693491952414375,
>>> 0.01643835616438392, -0.007412398921833087, 0.01765105227427014,
>>> -0.010006671114076025, 0.0},
>>> {-0.017821782178217872, 0.005040322580645311,
>>> 0.006018054162487363, 9.008107296569024E-4, 0.002999999999999824,
>>> -0.01196410767696908, 0.0},
>>> {2.630552127527583E-4, 2.5867028174649627E-4,
>>> 2.3866431891514327E-4, 1.9564035993080523E-4, 2.351016690966669E-4,
>>> 1.9070675120065465E-4, 0.0}
>>> };
>>>
>>> TestMarkowitz tm = new TestMarkowitz();
>>> BasicMatrix covariances = tm.getACovariances(assets_return);
>>> BasicMatrix expectedExcessReturns = tm.getAnExpectedExcessReturns
>>> (assets_return);
>>> BigDecimal riskAversion = new BigDecimal(1.0);
>>>
>>> MarketEquilibrium marketEquilibrium = new MarketEquilibrium
>>> (covariances,riskAversion);
>>> MarkowitzModel markowitzModel = new MarkowitzModel
>>> (marketEquilibrium,expectedExcessReturns);
>>>
>>> for(int i=0;i<assetNum;i++){
>>> markowitzModel.setLowerLimit(i, new BigDecimal(0.0));
>>> markowitzModel.setUpperLimit(i, new BigDecimal(1.0));
>>> }
>>> List<BigDecimal> re = markowitzModel.getWeights();
>>>
>>> System.out.println("=======result====================");
>>> for(int i=0;i<re.size();i++)
>>> System.out.println(re.get(i));
>>>
>>> return;
>>> }
>>>
>>> }
>>>
>>> /
>>> ********************************************************************
>>> **
>>> **********/
>>>
>>> and the result turn out as:
>>>
>>> -0.25
>>> -0.25
>>> -0.25
>>> -0.25
>>> 0.75
>>> 0.75
>>> 0.75
>>>
>>> /
>>> ********************************************************************
>>> **
>>> ******/
>>>
>>> If you find out any problem, just let me know , thanks a lot!
>>>
>>> On Thu, 15 Jan 2009 09:20:52 +0100, Anders Peterson wrote
>>>> You have to send code (snippets) that I can execute.
>>>>
>>>> Are you using v25 or the latest from cvs?
>>>>
>>>> How do you instantiate the ActiveSetSolver?
>>>>
>>>> What's the correct solution?
>>>>
>>>> You say that if you change the sign of "C" you get an ok result.
>>>> What does this mean? Did you make a mistake with the sign, or do
>>>> you suspect there is a bug in ojAlgo?
>>>>
>>>> I need better info regarding what you do, and what the problem is!
>>>>
>>>> /Anders
>>>>
>>>> On 15 jan 2009, at 06.14, Ruan Weichao wrote:
>>>>
>>>>>
>>>>> Thank you for your response.
>>>>>
>>>>> Here's my model's detail:
>>>>>
>>>>> [AE]={1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
>>> 1.0}
>>>>>
>>>>>
>>>>> [be]={1.0}
>>>>>
>>>>>
>>>>> [Q]={3.048907897157133E-4, 1.6671472561019247E-4,
>>>>> 4.4500080981934345E-4, -5.389129745055723E-4,
>>>>> -2.6090705011393183E-4, -1.2633284900760366E-4,
>>>>> -6.485428846447651E-7},
>>>>> {1.6671472561019247E-4, 2.341985572849691E-4,
>>>>> 2.9113916450678265E-4, -4.5760873539850514E-4,
>>>>> 1.3078636134987255E-5, -2.354289901013046E-5,
>>> -7.578030042426654E-7},
>>>>> {4.4500080981934345E-4, 2.9113916450678265E-4,
>>> 7.46023915996829E-4,
>>>>> -0.0010247176498305568, -2.6745504327902895E-4,
>>>>> -1.6563544154823496E-4, -8.293698990696063E-7},
>>>>> {-5.389129745055723E-4, -4.5760873539850514E-4,
>>>>> -0.0010247176498305568, 0.001754169535149865,
>>>>> 2.0293065310212377E-4, 2.1401092557826588E-4,
>>> 1.0252846778608953E-7},
>>>>> {-2.6090705011393183E-4, 1.3078636134987255E-5,
>>>>> -2.6745504327902895E-4, 2.0293065310212377E-4,
>>>>> 4.632320892679136E-4, 1.7969731066037214E-4,
>>> 2.4953495129362833E-8},
>>>>> {-1.2633284900760366E-4, -2.354289901013046E-5,
>>>>> -1.6563544154823496E-4, 2.1401092557826588E-4,
>>>>> 1.7969731066037214E-4, 8..346410612364995E-5,
>>> -7.02099350897589E-8},
>>>>> {-6.485428846447651E-7, -7.578030042426654E-7,
>>>>> -8.293698990696063E-7, 1.0252846778608953E-7,
>>>>> 2.4953495129362833E-8, -7.02099350897589E-8,
>>> 8.367244992498656E-9}}
>>>>>
>>>>> [c]={{0.010638291263564232},
>>>>> {0.013500370827906071},
>>>>> {0.011390037735101773},
>>>>> {0.010385042339767682},
>>>>> {3.812208389845893E-4},
>>>>> {0.002315505853720011},
>>>>> {0.0}}
>>>>>
>>>>>
>>>>> [AI]={{1.0, 0.0, 0.0, 0.0, 0.0,
>>> 0.0, 0.0},
>>>>> {0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
>>>>> {0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
>>>>> {0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
>>>>> {0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
>>>>> {0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
>>>>> {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0},
>>>>> {-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
>>>>> {0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
>>>>> {0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0},
>>>>> {0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0},
>>>>> {0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0},
>>>>> {0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0},
>>>>> {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0}}
>>>>>
>>>>> [bi]={{1.0},
>>>>> {1.0},
>>>>> {1.0},
>>>>> {1.0},
>>>>> {1.0},
>>>>> {1.0},
>>>>> {1.0},
>>>>> {0.0},
>>>>> {0.0},
>>>>> {0.0},
>>>>> {0.0},
>>>>> {0.0},
>>>>> {0.0},
>>>>> {0.0}}
>>>>>
>>>>> And here's the result:
>>>>>
>>>>> -0.25
>>>>> -0.25
>>>>> -0.25
>>>>> -0.25
>>>>> 0.75
>>>>> 0.75
>>>>> 0.75
>>>>>
>>>>> And i found that if i change the nagetive ExceptedReturn to
>>>>> positive, the result will be fine.
>>>>>
>>>>>
>>>>> On Wed, 14 Jan 2009 09:27:53 +0100, Anders Peterson wrote
>>>>>> How small are the negative values?
>>>>>>
>>>>>> Give me a unit test (something that I can easily integrate
>>> with the
>>>>>> existing junit tests) that shows what you do, and where/how you
>>>>>> think it goes wrong.
>>>>>>
>>>>>> /Anders
>>>>>>
>>>>>> On 14 jan 2009, at 03.58, Ruan Weichao wrote:
>>>>>>
>>>>>>>
>>>>>>> Hi,
>>>>>>>
>>>>>>> I use the Markowitz model to calculate the optimize some
>>> assets'
>>>>>>> weights,
>>>>>>>
>>>>>>> and set all the assets' lowerlimit with Zero and set all the
>>>>>>> upperlimits with
>>>>>>>
>>>>>>> One, but it turns out with some negative value which are
>>> little
>>>>>>> than Zero, it
>>>>>>>
>>>>>>> seems that the lowerlimit does not work.
>>>>>>>
>>>>>>> So I want to ask what should I do it to confirm the
>>> lowerlimit?
>>>>>>>
>>>>>>> --
>>>>>>> Best regards
>>>>>>>
>>>>>>> weichao
>>>>>>>
>>>>>>>
>>>>>
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>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>>>
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>>>>>
>>>>>
>>>>> --
>>>>> Best regards
>>>>>
>>>>>
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