limited number of Assets in a universe, with constraints.

Hi,

I was wondering if someone could help me regarding portfolio construction and constraints.

Linear inequalities are quite straigtforward, however I cannot figure out how to limit the number of asset selected.

Building constraints, if I get 10 columns each representing an asset, is there a way to specify that the asset weight can only be 0 or between 0.2 and 0.5? (which would limit the number of asset to be selected)

Thank you

Answer 1

[Matt J]

You could solve the 2^10 separate problems corresponding to the different combinations of assets, each time deleting the corresponding columns from your problem data.

2^10 is not such a big number to loop over.

[Johan]

Thank you for your answer, but the objective is to select 50 assets in a universe of 1500...

[Matt J]

It's going to be a difficult global search. You might have to move to the Global Optimization Toolbox and formulate as a mixed integer program with constraint

 A*(e.*w)<=b

 sum(e)<=50

where w(i) are your weights and e(i) are binary variables.

[Johan]

Thank you, it is a bit were I am going, I just hoped I missed it somwhere in the finanical toolbox.

Answer 2

[Shashank Prasanna]

Are you using the Financial Toolbox? If you are then you can create a portfolio object and set bounds for each of the assets:

http://www.mathworks.com/help/finance/portfolio.setbounds.html

Answer 3

[owr]

As stated, that's a very difficult problem. There are roughly 9e93 different ways to select a subset of 50 assets from a universe of 1500. If a good quadratic optimizer takes 1 second to find the optimal combination of each subset of 50, you'll still be waiting a long time to test every combination...

More generally, one approach to this type of problem is to use a hybrid optimization, use an integer based optimization (genetic algorithm) to choose which assets to include, and then a standard quadratic type optimizer within the objective to find the optimal combination of weights.

This webinar may give you some ideas - though it was written before the Global Optimization Toolbox was able to handle integer problems - so Id suggest adapting the ideas to the latest capabiliites:

http://www.mathworks.com/company/events/webinars/wbnr30357.html?id=30357&p1=56449&p2=56450

Again though - this is going to be useless for a problem of the scale you're suggesting. Id try breaking your problem into subsets of assets by sector, industry group, etc. There is so much noise that goes into the usual expected returns/covariance calculation that I'd be skeptical of any results you get on a problem of this dimension.

Good luck!

[Johan]

Thank you very much! I like your opinion. I am not a big fan of optimisation by weight on big universe, especially when they have to vary from 3 to 2%... I am going your way, and it looks very interesting!