[ojAlgo-user] Risk Parity on Markowitz model

[Matteo B. <mat...@gm...>]

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