Maximization of a function with two constraints

Question

Andreas S 2020-10-7

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https://ww2.mathworks.cn/matlabcentral/answers/607511-maximization-of-a-function-with-two-constraints

评论： Ameer Hamza 2020-10-8

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!

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John D'Errico 2020-10-7

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

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Answer 1

Ameer Hamza 2020-10-7

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https://ww2.mathworks.cn/matlabcentral/answers/607511-maximization-of-a-function-with-two-constraints#answer_507866

编辑：Ameer Hamza 2020-10-7

在 MATLAB Online 中打开

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);