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...> - 2009-01-20 10:20:31
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On 16 jan 2009, at 07.25, Anders Peterson wrote:
> 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.
This is fixed in CVS now. Your model does not get those constraint
breaking portfolio weights anymore. The solution I get is 100% of the
last instrument (the one with 0.0 excess return) which seems reasonable.
/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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