Re: [ojAlgo-user] Risk Parity on Markowitz model

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

As far as I can see that means you have quadratic constraints, and ojAlgo can't handle that. You'l have to reformulate the problem or write a cover algorithm that does what you want. If that's not possible then you'll have find another library that can handle quadratic constraints. /Anders


On 3 mar 2013, at 23:40, Matteo Baccan <mat...@gm...> wrote:

> Hi
> 
> I am performing some test on your ojalgo.finance.portfolio library based on Markowitz model, but I have a problem that I am not able to solve.
> 
>  
> Assuming a case of a two-asset portfolio. The input values for Markowitz model are: expected return, expected volatility and covariance matrix.
> 
>  
> Assets
> 
> Expected Return
> 
> Expected Volatility
> 
> Asset 1
> 
> μ1
> 
> σ1
> 
> Asset 2
> 
> μ2	σ2
>  
>  
>  
> Covariance Matrix
> 
> Asset 1
> 
> Asset 2
> 
> Asset 1
> 
> 
> σ1^2
> 
> σ2,1=σ1,2
> 
> Asset 2
> 
> σ1,2
> 
> σ2^2
> 
>  
>  
> The portfolio variance can be seen as the sum of the risk contribution of each asset class as following:
> 
>  
> Assets
> 
> Weights
> 
> Risk Contribution
> 
> Asset 1
> 
> X1
> 
> VP1=X1^2∙σ1^2+X1∙X2∙σ1,2
> 
> Asset 2
> 
> X2
> 
> 
> VP2=X2^2∙σ2^2+X1∙X2∙σ1,2
> 
>  
> Portfolio Variance = VP1+VP2
> 
>  
>  
> My goal is to calculate the asset allocation (sum weights =1) maximizing portfolio expected return and adding the following constraint:  VP1=VP2 (risk parity approach).
> 
>  
>  
> Considering n Assets, the logic is the same: maximizing portfolio return but adding the following constraint:
> 
>  VP1=VP2=⋯ =VPn
> 
>  
>  
> Could you give me some suggestion in order to solve this problem using your library?
> 
>  
> Best Regards,
> 
> 
> 
> -- 
> Matteo Baccan
> http://www.baccan.it
> 
> ------------------------------------------------------------------------------
> Everyone hates slow websites. So do we.
> Make your web apps faster with AppDynamics
> Download AppDynamics Lite for free today:
> http://p.sf.net/sfu/appdyn_d2d_feb_______________________________________________
> ojAlgo-user mailing list
> ojA...@li...
> https://lists.sourceforge.net/lists/listinfo/ojalgo-user