portfolio optimization using fmincon

I am trying to predict the weights for my stocks that optimize my portfolio by reducing variance. My equation that I am using to predict the variance is

>>function f = varmin(x,VCV) >>f = ((x' * VCV) * x);

where x is the weights and VCV is the variance covariance matrix. Every time I run the program fmincon, I get an error relating to my function "varmin" saying

>>Not enough input arguments.

>>Error in varmin (line 2) >>f = ((x' * VCV) * x);

>>error in fmincon (line 536) >> initVals.f = feval(funfcn{3},X,varargin{:});

>>Caused by: >> Failure in initial objective function evaluation. FMINCON cannot >>continue.

this is what the fmincon equation looks like

>>w = fmincon('varmin',x,a,b,Aeq,Beq,MinWt,MaxWt);

if anyone has any advice that would be greatly appreciated.

[nadia meftah]

what means a,b, x . so defined that

Answer 1

[Alan Weiss]

If VCV is a given matrix in your workspace, take

fun = @(x)x'*VCV*x;

and then call

w = fmincon(fun,x,a,b,Aeq,Beq,MinWt,MaxWt);

Make sure that your initial x (which I would call x0) is a column vector.

Alan Weiss

MATLAB mathematical toolbox documentation

[Nathaniel Comar]

That did not work. My objective function is now

function f = varmin(x0,VCV)

    f = @(x0)x0'*VCV*x0;

And the fmincon equation is

w = fmincon(varmin,x0,a,b,Aeq,Beq,MinWt,MaxWt);

And i received the error

Error: File: varmin.m Line: 2 Column: 8
Unexpected MATLAB expression.

Error in fmincon (line 536)
      initVals.f = feval(funfcn{3},X,varargin{:});

Caused by:
    Failure in initial objective function evaluation. FMINCON cannot continue.

[Alan Weiss]

Please read my previous answer and use it verbatim.

Alan Weiss

MATLAB mathematical toolbox documentation

[Nathaniel Comar]

I believe I did. I do not see the discrepency you are referring to. Could you please tell me?

[Alan Weiss]

I'm sorry that I was not clear.

Please try the following. Do not use your varmin function. Instead, once you have the VCV matrix in your workspace, at the MATLAB command line issue the command

fun = @(x)x'*VCV*x;

Then, once you have all the other relevant inputs in your workspace (such as x, a, b, etc.), issue the command

w = fmincon(fun,x,a,b,Aeq,Beq,MinWt,MaxWt);

Alan Weiss

MATLAB mathematical toolbox documentation

[Nathaniel Comar]

Ah thank you for clarifying. I got it to work. Thank you for your help

[Muhammad Zain Razak]

Hi

Does the VCV is the 3x3 matrix?