Maximum Diversified Porfolio (MDP) fmincon optimization problem doesn't work

Goodmorning to all,

I have to solve the following problem (image) with fmincon: x is the portfolio weight vector, sigma the std. dev. of returns, omega cov matrix. I tried as follow but doesn't work. Thanks to everyone!

Aeq = ones(1,n_asset);
beq = 1;
x0 = zeros(1,n_asset);
lb = zeros(1,n_asset);
ub = ones(1,n_asset);

fun = @(x) -(x)*(sqrt(variance))./sqrt((x')*Cov(x))

w = -fmincon(fun,x0,[],[],Aeq,beq,lb,ub)

[Alan Weiss]

What was the error that fmincon returned? What are the dimensions of x, variance, and Cov? Is Cov(x) a function, or did you mean to write x*Cov*x'?

Alan Weiss

MATLAB mathematical toolbox documentation

[Leonardo Coccia]

Hi, the error is in the screenshot. x is the portfolio that has 12 assets weights (12zx1), variance is 12x1, Cov is a 12x12 covariance matrix and Cov(x) is Cov*x but doesn't work even if I delete parenthesis. And yes, I meant x*Cov*x' but doesn't work. I don't know even how to set x0 ...

Thanks in advance!

Answer 1

[Alan Weiss]

You say that x is 12-by-1, yet you write x0 as 1-by-12. That could be the problem. Try

x0 = zeros(n_asset,1); % Now x0 is 12-by-1, and so is x

You then need to change your definition of the objective.

fun = @(x) -(sqrt(variance)'*x)/sqrt(x'*Cov*x);

Alan Weiss

MATLAB mathematical toolbox documentation

[Leonardo Coccia]

Thanks very much Alan! Now it seems to work properly. Thanks again

[Alan Weiss]

I'm glad that my suggestions helped. Please accept the answer.

Alan Weiss

MATLAB mathematical toolbox documentation