Maximization of a function with two constraints

Hi everyone, i'm new in matlab and i have a problem of coding it. I have to find the Wt that solves the following problem.

max Wt'*μt/sqrt(Wt'Σwt)

s.t. w'ti=1

0<=Wt<=0.25

i=1...N

i=ones(10,1)

That is, Wt is such that it maximizes the portfolio's Sharpe ratio with the constraint that all

weights have to be between 0 and 0.25. (Hint: you should use numerical optimization.)

Thank you in advance for your time!

[John D'Errico]

Note: this being a clear homework assignment, you should have tried it yourself.

Answer 1

[Ameer Hamza]

You can use fmincon() from optimization toolbox

mu = rand(10, 1); % example value
sigma = rand(10);

objFun = @(Wt) Wt'*mu/sqrt(Wt'*sigma*Wt);
x0 = zeros(10, 1); % initial guess
lb = zeros(1, 10);
ub = 0.25*ones(1, 10);
Aeq = ones(1, 10); Beq = 1; % wt'*i=1;
sol = fmincon(objFun, x0, [], [], ones(1, 10), 1, lb, ub);

[Andreas S]

Ameer Hamza thank you very much. It worked for me!

[Ameer Hamza]

I am glad to be of help!!!