how to run optimisation problem

DAN TURMACU (view profile)

on 20 Mar 2019
Latest activity Commented on by DAN TURMACU

on 21 Mar 2019

DAN TURMACU (view profile)

Hello!
How can I run such kind of optimization :
max Q subject to x = x1,..., xn, where = Rp / σp
and constraints :
Rp = R' * x
σp^2 =x' * Σ * x
sum(x) = 1
Can someone help me about how to write down my objective function ...and the rest of the constraints. What type of sover I need to use ?
Best regards,

Walter Roberson

Walter Roberson (view profile)

on 21 Mar 2019
I think part of the equations got lost?
What is Q?
You say "where = " but what needs to equal that?
Why do you say "subject to" and list variable names?
In Rp / op is that matrix division (least squared fitting) or is it element-by-element division ?
DAN TURMACU

DAN TURMACU (view profile)

on 21 Mar 2019
yes.
Q = Rp / σp
Rp - Return of portfolio it is a number
σp - Risk of portfolio it is a number
but R' , Σ are matrix
The constraint is sum(x) = 1.

R2008a

DAN TURMACU (view profile)

on 21 Mar 2019

Dear Torsten,
I have another unexpected problem.
When I run x = fmincon(fun,x0,A,b,Aeq,beq) in Command Window, I receive the error message:
Undefined function or variable 'returns'.
Error in @(x)-(x'*returns)/sqrt(x'*sigma*x)
Error in fmincon (line 564)
initVals.f = feval(funfcn{3},X,varargin{:});
Caused by:
Failure in initial user-supplied objective function evaluation. FMINCON
cannot continue.
I do not understand. I provided with returns and sigma matrixes in Workspace Window.
Thank you.

Torsten

Torsten (view profile)

on 21 Mar 2019
Write a .m file and load it into matlab.
BTW: "returns" must be a vector of the same length as x, not a matrix.
DAN TURMACU

DAN TURMACU (view profile)

on 21 Mar 2019
Now it is ok. I have to run fun script first.
Many thanks,
Dan

Torsten (view profile)

on 21 Mar 2019
Edited by Torsten

Torsten (view profile)

on 21 Mar 2019

Use fmincon with objective function
f = @(x)(R'*x)/sqrt(x'*sigma*x)
and linear constraint
Aeq = ones(size(x))
beq = 1
Best wishes
Torsten.

DAN TURMACU

DAN TURMACU (view profile)

on 21 Mar 2019
How may I ? I do not know.
Thanks.
Torsten

Torsten (view profile)

on 21 Mar 2019
f = @(x)-(R'*x)/sqrt(x'*sigma*x)
DAN TURMACU

on 21 Mar 2019
Thanks.