Function and Minimisation Problem

Hi here is my problem :

Create a function that solves for the efficient portfolio, given a set of stocks, their expected value, their variance-covariance matrix, and a target expected value of the investment. The function should use either the MATLAB minimisation procedure fmincon or quadprog.

Inputs:

            procedure                      a string containing the MATLAB procedure used to 
                                           perform  the minimization ('quadprog' or 'fmincon')
            Sigma                          Variance-covariance matrix (reminder: this is a                                                    
                                           positive semi-definite matrix!)
            mu                             vector of expected values for each stock
            mu_p_0                         expected return
            initial_guess                  for fmincon, you need to give an initial guess, 
                                           can be left  as [] if using quadprog
            optimisation_options           can be added, but otherwise set to default 
                                           by using [] as the value for this input
Outputs:
            x                  optimal shares for each stock
            fval               value of the optimisation
            expected_return    as a check, needs to be equal to mu_p_0

The objective function for the optimisation will be a local function called effportobj. This function takes as inputs: the optimal shares x, and the variance-covariance matrix Sigma. In the main function, when calling this objective function in the optimisation procedure (either quadprog or fmincon), use the function handle (starting with @).

I have attached a file showing the theory behind this model

I am having trouble with my code:

function [x, fval, expected_return] = effportfolio(fmincon, Sigma, mu, mu_p_0, initial_guess, optimisation_options)
% EFFPORTFOLIO  solves for the efficient portfolio.

A_eq = [2*Sigma, mu , 1; mu', 0, 0; 1', 0, 0];
B_eq = [0;mu_p_0;1];
optimisation_options = optimset('Display','iter');

[x, fval] = fmincon(@effportobj,initial_guess,[],[],A_eq,B_eq,[],[],[],optimisation_options,Sigma);
expected_return = mu_p_0 ;

end

function E = effportobj(x, Sigma)

E = x'* Sigma * x; 

end

Thanks very much

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html