Maximize expected return with constraints

Hi guys, I need help for a really easy maximization.

Max E(r)=(mean vector)*(weight vector)'

I want to max the return by changing the weight vector (variable). The mean vector is constant.

The constraints are : (vector of 1's)*(weight vector)' = 1 %weights sum to 1

lb wi >= 0

ub wi =< 1

The solution should give me the Max E(r) and the corresponding (weight vector).

Thank you.

[Mikhail]

Isn't that a mathematical probmlem>?

Answer 1

[Torsten]

f=-[0.0055; 0.0063; 0.0080; 0.0060; 0.0037; 0.0035; -0.0028; 0.0071; 0.0055; 0.0028];

Aeq=[1 1 1 1 1 1 1 1 1 1];

beq=[1];

lb=zeros(10,1);

ub=ones(10,1);

x = linprog(f,[],[],Aeq,beq,lb,ub);

does not work ?

Best wishes

Torsten.

[Marcel]

Thank you Torsten. That's basically it. My failure was that I wrote the variable x into the function, which didn't work.

Answer 2

[John D'Errico]

You want to maximize a linear objective function of the weights, subject to a linear equality constraint (that the weights sum to 1) as well as lower (0) and upper (1) bound constraints.

This is just a linear programming problem, and a basic, virtually trivial one at that.

help linprog

If you lack the optimization toolbox, then you will find something on the file exchange.

Answer 3

[Marcel]

I know that it is very basic and trivial. When I put it in the Optimization toolbox it calculates E(r) with equal weights (that is 0,1 with 10 assets) and gives me wi=0,1.

But it should give me a weight vector(n=10) that maximizes E(r).

I just don't know how to program that.

Answer 4

[Torsten]

If the mean vector has the same entries at all positions, then the answer is correct ...

Best wishes

Torsten.

Answer 5

[Marcel]

That is right.

But: m = [0,0055 0,0063 0,0080 0,0060 0,0037 0,0035 -0,0028 0,0071 0,0055 0,0028] w = [w1 w2 w3 w4 w5 w6 w7 w8 w9 w10]

I know that the max E(r) is 0,0080 and the vector must be w=[0 0 1 0 0 0 0 0 0 0] , but I want Matlab to calculate that.