How do I put a series of sum into a function?

Hi! I am trying to solve the optimization problem for a risk parity portfolio. To be precise:

w is a nx1 vector of portfolio weigths and C th nxn covariance matrix.

The variable port_size is a scalar that returns the number of assets invested in.

I tried to solve it with fmincon, but the first problem that is appearing is that apparently I cannot do the fun_rp = @(w_rp) with the for loop as MATLAB gives me the error: illegal use of reserved keyword "for".

w_mv0 = [0.25; 0.25; 0.25; 0.25];

Aeq = ones(1, port_size);
beq = 1;

lb = zeros(1, port_size);
ub = ones(1, port_size);


fun_rp = @(w_rp) for i = 1:port_size
    for j = 1: port_size
        (w(1,i)*(C*w(1,i)')-w(1,j)*(C*w(1,j)'))^2;
    end
end

w_rp = fmincon(fun_rp,w_rp0,[],[],Aeq,beq,lb,ub)

Does anybody know where my mistake is? I´d appriciate every help!

Best regards

Answer 1

[Alan Weiss]

I did not try to run your code, but I have several comments.

1. Use the appropriate solver for your objective. For a quadratic objective function with linear constraints, the Optimization Decision Table says to use quadprog.
2. Even if you decide to use fmincon as a solver, you cannot write an objective function using an anonymous function with a loop. Instead, write the loop in a function file, and call the function file with fmincon. For an example, see an introductory example on minimization.
3. Where do you define C? Or is that your name for your decision variable w_rp?

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation