Optimal portfolio weights maximizing the expected utility function?

Hi all, I am a MSc student and I am new to Matlab. I have written the following function, which I need to maximize:

function EU=expectedutility(x,blockP1,gamma)

   U=zeros(18,1);

      for j=1:18

         U(j,1)=((1+x(1)*blockP1(j,2)+x(2)*blockP1(j,3))^(1-gamma))/(1-gamma) 

      end

   EU=mean(U)

end

Now I need to find x(1) and x(2) such that they maximize such average (i.e. EU), subject to the following constraints on x(1) and x(2):

• x(1) + x(2)=1;
• -3<=x(1)<=+3;
• -3<=x(2)<=+3;

blockP1(j,2) and blockP1(j,3) refer to the 18x3 matrix blockP1, already defined in my main code.

The function EU is defined correctly as I tested it with x(1)=1, x(2)=1 and gamma=5 in the following way:

expectedutility([1 1],blockP1,5)

and it correctly returned EU.

In my case however I do not need to set x(1) and x(2) but a "solver function" needs to give me those values so that EU is maximum (gamma=5 still holds).

After defining the function above, I have tried to run the optimization in my main code as follows:

ObjectFunction= @expectedutility;

lb=[-3 -3];
ub=[3 3];

Aeq=[1 1]; 
beq=1;

[x,fval]= linprog(ObjectFunction,[],[], Aeq, beq, lb, ub)

but it gives me the error:

Error using linprog (line 144)
LINPROG requires the following inputs to be of data type double: 'f'.

Error in optimization (line 72)
[x,fval]= linprog(ObjectFunction,[],[], Aeq, beq, lb, ub)

Could you kindly help me out with this?

Any help would be very much appreciated.

Thanks in advance,

Federico

Answer 1

[Alan Weiss]

You simply need to change your objective function reference to

ObjectFunction = @(x)expectedutility(x,blockP1,gamma)

This means that blockP1 and gamma are constants (make sure that these variables are in your Workspace before defining fun), and the function is a function of x alone. For more information, see Passing Extra Parameters.

Alan Weiss

MATLAB mathematical toolbox documentation

[Federico Rendina]

Thanks a lot Alan. I finally got it working following your advice!

Have a nice day!