I have a finite amount of 26 assets, the total amount of these assets needs to be allocated to 9 portfolios. Each portfolio has its own required return which needs to be met, using a min-variance approach.
This is the optimization problem, subject to:
- Each asset should be 100% allocated
- Asset 1 and 2 are held constant (the sub-portfolios already holds some amount of these 26 assets)
- Asset 3 must not weigh more than 20% within each portfolio
- Asset 4 must not weigh more than 25% within each portfolio
- Each portfolio has a given AuM which the new allocation must equal
- No assets can have negative weight (long-only)
I have a dataset holding the 26 assets, expected returns and a covariance matrix.
I am able to optimize a single portfolio, the trick is when i want to optimize across the 9 portfolios.
I have been looking into quadratic programming as a means to this problem, if anyone are able to point me in the right direction, maybe some useful links or something. I am coding in Python, so Python solutions is a plus, but i also have access to R and MatLab.