how to run optimisation problem

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]

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]

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.

Answer 1

[DAN TURMACU]

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]

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]

Now it is ok. I have to run fun script first.

Many thanks,

Dan

Answer 2

[Torsten]

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]

Thank you very much,

Dan

[DAN TURMACU]

I am searching for the max of Q.

I think I need to put objective function

f = @(x)sqrt(x'*sigma*x)/(R'*x)

for the min.

[Walter Roberson]

Use the negative of your problem to search for the maximum.

[DAN TURMACU]

How may I ? I do not know.

Thanks.

[Torsten]

f = @(x)-(R'*x)/sqrt(x'*sigma*x)

[DAN TURMACU]

Thanks.