Matlab Rounding as Portfolio Constraint

Hi there,

I am optimizing a portfolio using the mean-CVaR optimization function in Matlab. One of the constraints I would like to set is that the portfolio weights for each asset class should be rounded to the nearest 0.05.

I have defined the rounding constraint as

round(x/5,2)*5

which works fine. However, I am wondering now how I can include this as a constraint in the optimization instead of just rounding the weights after the optimization.

Here is the code I am using for the portfolio optimization

pmc = PortfolioCVaR; 
pmc = pmc.setAssetList(IndexList);          % select index names 
pmc = pmc.setScenarios(returns);            % select return series
pmc = pmc.setProbabilityLevel(0.95);        % cVaR confidence level
pmc = pmc.setDefaultConstraints;            % Constraint 1: only positive
weights that sum to 1
pmc = pmc.setBounds(0.01, 0.1);             % Constraint 2: min/max weights

I would be happy about any hints!

Thanks a lot, Carolin

Answer 1

[John D'Errico]

This becomes essentially an integer programming problem, since you are trying to force the parameters to be discrete values. So unless the optimization tool allows that as an option, you will need to use a different tool for the optimization.

[Carolin Brueckmann]

Hi John,

thanks a lot for the Hint. The default solver for the mean-cVaR optimization ('fmincon') does not support integer programming problems. The solver option in the PortfolioCVaR object can be changed to the ‘cuttingplane’ solver, which is a mixed integer programming technique and thus would suit my need. Unfortunately, I am struggling with the implementation of the 2 decimals constraint. I believe that I have to run the ‘cuttingplane’ solver under the 'intlinprog' algorithm and adjust the number of decimals using ‘TolInteger’. The latter two however it seems cannot be combined.

Here is the code I am trying to run: pmc = pmc.setSolver('cuttingplane','MasterSolverOptions', options); options = optimoptions('intlinprog', 'TolInteger', 1e-3)

Would you have any Tips on how to set the decimal places under this approach?

Many thanks in advance!

Best, Carolin