Re: [ojAlgo-user] 答复: ojAlgo-user Digest, Vol 79, Issue 3

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

Think of it this way. The optimisation algorithm tries to maximise expected return and minimise variance and the same time - there are 2 terms in the optimisation objective function. To balance those 2 terms they need to be weighted somehow. The risk aversion factor/parameter scales the variance term to match the return term.

For a more theoretical explanation you may read Appendix 2 of this document:

http://kth.diva-portal.org/smash/get/diva2:10311/FULLTEXT01


/Anders



> On 11 May 2017, at 02:46, lvz...@gt... wrote:
> 
> 
> Hi, 
> What is the definition of risk aversion factor? 
> 
> Lvzifeng
> 
> 
> 
> oja...@li...
> 2017/05/10 20:05
> 请答复 给
> oja...@li...
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> ojAlgo-user Digest, Vol 79, Issue 3
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> Today's Topics:
> 
>   1. ??:  Report A Bug Of ojalgo finace library (yifa wang)
>   2. Re: ??:  Report A Bug Of ojalgo finace library (Anders Peterson)
>   3. Re: Report A Bug Of ojalgo finace library (Anders Peterson)
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Tue, 9 May 2017 15:15:36 +0000
> From: yifa wang <fag...@ho...>
> Subject: [ojAlgo-user] ??:  Report A Bug Of ojalgo finace library
> To: "oja...@li..."
>                 <oja...@li...>
> Message-ID:
>                 <SG2...@SG...>
>                 
> Content-Type: text/plain; charset="gb2312"
> 
> hi,
> 
> 
> I try to use ojalgo to do a portfolio optimization. The target is find an efficient frontier for 15 securities or more. I generate random returns for simulation. However, when I run the program, I get the state as "UNEXPLORED". Usually, we get OPTIMAL.  What does this mean? Is it possible to get the optimal weight for more than 50 securities?
> 
> 
> Thanks.
> 
> Jerry
> 
> 
> 
> 
> 
> ________________________________
> ???: lvz...@gt... <lvz...@gt...>
> ????: 2017?5?8? ?? 8:20:21
> ???: oja...@li...
> ??: [ojAlgo-user] Report A Bug Of ojalgo finace library
> 
> 
> Hi,
>      I have a problem when calculate best invest group by using markowitzModel in ojalgo with code below(for test);
> 
> 
> 
> 
>          for(int j = 0; j < 100; j ++)
>         { Builder<PrimitiveMatrix> tmpBuilder = PrimitiveMatrix.FACTORY.getBuilder(2, 2);
>    tmpBuilder.add(0, 0, 0.040000);
>    tmpBuilder.add(0, 1, 0.1000);
>    tmpBuilder.add(1, 0, 0.1000);
>    tmpBuilder.add(1, 1, 0.250000);
>        BasicMatrix covariances = tmpBuilder.build();
>        tmpBuilder = PrimitiveMatrix.FACTORY.getBuilder(2);
>        tmpBuilder.add(0, 0.20000);
>        tmpBuilder.add(1, 0.40000);
>        BasicMatrix expectedExcessReturns = tmpBuilder.build();
> 
>       MarketEquilibrium equilibrium = new MarketEquilibrium(covariances);
>        MarkowitzModel markowitzModel = new MarkowitzModel(equilibrium, expectedExcessReturns);
>        markowitzModel.setShortingAllowed(false);
>       // markowitzModel.optimiser().validate(true);
>        markowitzModel.setTargetReturn(new BigDecimal(0.2 + (0.002 * j)));
>        for (int i = 0; i < 2; i++) {
>            markowitzModel.setLowerLimit(i, new BigDecimal(0.00000));
>            markowitzModel.setUpperLimit(i, new BigDecimal(1.00000));
>        }
>        System.out.println(0.2 + (0.002 * j) + "," + markowitzModel.getReturnVariance() + " , "  +  markowitzModel.getMeanReturn()  + "," + markowitzModel.getWeights());
> 
> 
> }
> 
> 
>      when TargetReturn equal to 0.206,Variance equal to 0.04 , weights equal to [1.0, 0.0]
>      when TargetReturn  equal to  0.208, Variance equal to 0.25,weights equal to [0.0, 1.0]
>      Below  Relationship of TargetReturn And Target Variance?Y-Axis TargetReturn,X-AXis standard deviation?
> 
> 
> 
> ???
> 
> -------------- next part --------------
> An HTML attachment was scrubbed...
> 
> ------------------------------
> 
> Message: 2
> Date: Tue, 9 May 2017 22:34:46 +0200
> From: Anders Peterson <an...@op...>
> Subject: Re: [ojAlgo-user] ??:  Report A Bug Of ojalgo finace library
> To: oja...@li...
> Message-ID: <9FD...@op...>
> Content-Type: text/plain; charset=utf-8
> 
> UNEXPLORED would mean the optimisation has not been executed (since you last modified the model). How did you get that?
> 
> /Anders
> 
> 
> 
> 
> > On 9 May 2017, at 17:15, yifa wang <fag...@ho...> wrote:
> > 
> > hi,
> > 
> > I try to use ojalgo to do a portfolio optimization. The target is find an efficient frontier for 15 securities or more. I generate random returns for simulation. However, when I run the program, I get the state as "UNEXPLORED". Usually, we get OPTIMAL.  What does this mean? Is it possible to get the optimal weight for more than 50 securities?
> > 
> > Thanks. 
> > Jerry 
> > 
> > 
> > 
> > 
> > ???: lvz...@gt... <lvz...@gt...>
> > ????: 2017?5?8? ?? 8:20:21
> > ???: oja...@li...
> > ??: [ojAlgo-user] Report A Bug Of ojalgo finace library
> >  
> > 
> > Hi,
> >       I have a problem when calculate best invest group by using markowitzModel in ojalgo with code below(for test);
> > 
> > 
> > 
> > 
> >           for(int j = 0; j < 100; j ++)
> >          { Builder<PrimitiveMatrix> tmpBuilder = PrimitiveMatrix.FACTORY.getBuilder(2, 2);
> >     tmpBuilder.add(0, 0, 0.040000);
> >     tmpBuilder.add(0, 1, 0.1000);
> >     tmpBuilder.add(1, 0, 0.1000);
> >     tmpBuilder.add(1, 1, 0.250000);
> >         BasicMatrix covariances = tmpBuilder.build();
> >         tmpBuilder = PrimitiveMatrix.FACTORY.getBuilder(2);
> >         tmpBuilder.add(0, 0.20000);
> >         tmpBuilder.add(1, 0.40000);
> >         BasicMatrix expectedExcessReturns = tmpBuilder.build(); 
> >         
> >        MarketEquilibrium equilibrium = new MarketEquilibrium(covariances);
> >         MarkowitzModel markowitzModel = new MarkowitzModel(equilibrium, expectedExcessReturns);
> >         markowitzModel.setShortingAllowed(false);
> >        // markowitzModel.optimiser().validate(true);
> >         markowitzModel.setTargetReturn(new BigDecimal(0.2 + (0.002 * j)));
> >         for (int i = 0; i < 2; i++) {
> >             markowitzModel.setLowerLimit(i, new BigDecimal(0.00000));
> >             markowitzModel.setUpperLimit(i, new BigDecimal(1.00000));
> >         }
> >         System.out.println(0.2 + (0.002 * j) + "," + markowitzModel.getReturnVariance() + " , "  +  markowitzModel.getMeanReturn()  + "," + markowitzModel.getWeights());
> > 
> > 
> > }
> > 
> >      
> >       when TargetReturn equal to 0.206,Variance equal to 0.04 , weights equal to [1.0, 0.0]
> >       when TargetReturn  equal to  0.208, Variance equal to 0.25,weights equal to [0.0, 1.0]
> >       Below  Relationship of TargetReturn And Target Variance?Y-Axis TargetReturn,X-AXis standard deviation? 
> > 
> > 
> > 
> > ???
> > 
> > ------------------------------------------------------------------------------
> > Check out the vibrant tech community on one of the world's most
> > engaging tech sites, Slashdot.org! http://sdm.link/slashdot_______________________________________________
> > ojAlgo-user mailing list
> > ojA...@li...
> > https://lists.sourceforge.net/lists/listinfo/ojalgo-user
> 
> 
> 
> 
> ------------------------------
> 
> Message: 3
> Date: Tue, 9 May 2017 23:32:47 +0200
> From: Anders Peterson <an...@op...>
> Subject: Re: [ojAlgo-user] Report A Bug Of ojalgo finace library
> To: oja...@li...
> Message-ID: <A20...@op...>
> Content-Type: text/plain; charset=utf-8
> 
> Haven?t fully understood yet why that small/simple model is so problematic. The covariance matrix is not positive definite, Strictly speaking it needs to be, but most of the time semidefinite is ok. 
> 
> Setting a target return or variance is not the best way to use ojAlgo?s MarkowitzModel class. Work directly with the risk aversion factor instead. 
> 
> If what you want to do is to calculate the efficient frontier then it?s better to use the EfficientFrontier class rather than the MarkowitzModel class.
> 
> /Anders
> 
> 
> > On 8 May 2017, at 14:20, lvz...@gt... wrote:
> > 
> > 
> > Hi,
> >       I have a problem when calculate best invest group by using markowitzModel in ojalgo with code below(for test);
> > 
> > 
> > 
> > 
> >           for(int j = 0; j < 100; j ++)
> >          { Builder<PrimitiveMatrix> tmpBuilder = PrimitiveMatrix.FACTORY.getBuilder(2, 2);
> >     tmpBuilder.add(0, 0, 0.040000);
> >     tmpBuilder.add(0, 1, 0.1000);
> >     tmpBuilder.add(1, 0, 0.1000);
> >     tmpBuilder.add(1, 1, 0.250000);
> >         BasicMatrix covariances = tmpBuilder.build();
> >         tmpBuilder = PrimitiveMatrix.FACTORY.getBuilder(2);
> >         tmpBuilder.add(0, 0.20000);
> >         tmpBuilder.add(1, 0.40000);
> >         BasicMatrix expectedExcessReturns = tmpBuilder.build(); 
> >         
> >        MarketEquilibrium equilibrium = new MarketEquilibrium(covariances);
> >         MarkowitzModel markowitzModel = new MarkowitzModel(equilibrium, expectedExcessReturns);
> >         markowitzModel.setShortingAllowed(false);
> >        // markowitzModel.optimiser().validate(true);
> >         markowitzModel.setTargetReturn(new BigDecimal(0.2 + (0.002 * j)));
> >         for (int i = 0; i < 2; i++) {
> >             markowitzModel.setLowerLimit(i, new BigDecimal(0.00000));
> >             markowitzModel.setUpperLimit(i, new BigDecimal(1.00000));
> >         }
> >         System.out.println(0.2 + (0.002 * j) + "," + markowitzModel.getReturnVariance() + " , "  +  markowitzModel.getMeanReturn()  + "," + markowitzModel.getWeights());
> > 
> > 
> > }
> > 
> >      
> >       when TargetReturn equal to 0.206,Variance equal to 0.04 , weights equal to [1.0, 0.0]
> >       when TargetReturn  equal to  0.208, Variance equal to 0.25,weights equal to [0.0, 1.0]
> >       Below  Relationship of TargetReturn And Target Variance?Y-Axis TargetReturn,X-AXis standard deviation? 
> > 
> > 
> > 
> > ???
> > 
> > <1.jpg>------------------------------------------------------------------------------
> > Check out the vibrant tech community on one of the world's most
> > engaging tech sites, Slashdot.org! http://sdm.link/slashdot_______________________________________________
> > ojAlgo-user mailing list
> > ojA...@li...
> > https://lists.sourceforge.net/lists/listinfo/ojalgo-user
> 
> 
> 
> 
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