financial portfolio optimization using fmincon?

Hi y'all. I'm struggling to solve a portfolio optimization problem. I know other ways to do it but I am curious about how to solve it with fmincon. Here is what I've come up with

function[weight,psd,sharpe]= poptim(mu,sigma,mutarget)

function[sigmap] = psigma(weight,sigma)

sigmap = weight.'* sigma *weight ;

end

x0 = [1/3;1/3;1/3];

Aeq = [1 1 1; mu];

beq = [1;mutarget] ;

options=optimset(Algorithm ,'sqp');

[weight,fval]= fmincon(@psigma,x0,[],[],Aeq,beq);

psd = sqrt(fval);

sharpe = (mu * weight)/ psd ;

end

because fmincon requires a function to work with therefore I have to write a function within a function. Problems: the first sigma is unused, making the whole thing stuck

Anyone has any idea how to rearrange them so that it could work?

Thank you!

Answer 1

[Akiva Gordon]

If you want the sigma passed into POPTIM to be also passed into PSIGMA, you do not need to specify sigma as an input parameter to PSIGMA, since the scope of PSIGMA includes the scope of POPTIM due to the fact that PSIGMA is a nested function of POPTIM.

[Yang]

Akiva:

Thank you for your input! However when do I input sigma (covariance matrix among assets) now?

[Akiva Gordon]

sigma is an input to POPTIM, isn't it? Perhaps I am not understanding your question...

[Yang]

Nevermind. Thank you for your input!

For later viewers:

If you are trying to solve a Markowitz portfolio optimization problem, use quadprog instead of fmincon!