Maximize expected return with constraints

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Marcel
Marcel 2014-11-14
评论： Marcel 2014-11-14
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.

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采纳的回答

Torsten
Torsten 2014-11-14
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.
  1 个评论
Marcel
Marcel 2014-11-14
Thank you Torsten. That's basically it. My failure was that I wrote the variable x into the function, which didn't work.

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更多回答（4 个）

John D'Errico
John D'Errico 2014-11-14
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.
Marcel
Marcel 2014-11-14
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.
Torsten
Torsten 2014-11-14
If the mean vector has the same entries at all positions, then the answer is correct ...
Best wishes
Torsten.
Marcel
Marcel 2014-11-14
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.

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