Optimization problem with constraints

Hi all. Supposing I've a matrix A(n,m) of daily returns where 'n' are daily observations and 'm' are number of assets and that SR(1,m) is a vector of Sharpe Ratios, calculated on the above matrix. My target is to find the optimal weights w(1,m) which maximize sum(SR.*w,2) given the constraints that the weigths sum up to 1 (sum(w,2)=1) and that all weights are >=0. It's pretty simple in Excel with the Solver tool but i'm not so familiar with the optimization functions in Matlab. Thank you very much in advance for your kind support. Regards

Answer 1

[Alan Weiss]

I am not familiar with the financial model you discuss. However, it is likely that fmincon can do what you want. If you have Optimization Toolbox, just follow the steps to shoehorn your problem into the syntax it expects. See the Getting Started example.

In particular, the constraint that the weights add up to 1 and are nonnegative are easily handled by a linear equality constraint and bounds respectively.

For examples, see the function reference page.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation