How do I generate all possible weights for a constraint

While I was working on my portfolio optimization I wanted to perform a numerical analysis and I wanted to generate several combinations of weights that all sum to 1. in the case of 3 assets I had this code:

for i= 0:0.1:1 for j = 0:0.1:(1-i) w_Consmr = i; w_Manuf = j; w_HiTec = 1-j-i; a = a+1; w(a,:) = [w_Consmr w_Manuf w_HiTec] ; end end

However, now I want to do this for lets say, 50 assets and making 50 for loops seems quite cumbersome, is there another way to make this more efficient ?

Sincerely, Stephan

[Matt J]

for i= 0:0.1:1 
  for j = 0:0.1:(1-i) 
    w_Consmr = i; 
    w_Manuf = j; 
    w_HiTec = 1-j-i; 
    a = a+1; 
    w(a,:) = [w_Consmr w_Manuf w_HiTec] ; 
 end 
 end

[Matt J]

What do you mean by "several"? For 50 assets, the number of combinations can be intractably large, depending on whether you'd still be using increments of 0.1 or something else. If 0.1, then at most 10 of the weights can be non-zero. Is that what you want?

[stef]

What I wanted to try to do is to have all possible combinations for my weights under those restrictions. I already knew that in this exact way the amount of combinations would take too much time to compute and thus I was wondering if there was a different and more efficient algorithm to this approach, but after some more thinking and searching I think this would be the only way to do it, other than just randomizing weights.

So I think I will just use random weights as you proposed since it would indeed be too big to compute the weights for 50 assets this way

Thank you for your time and help.

Answer 1

[Matt J]

Why not do something like the following?

w=rand(1,50);
w=w/sum(w);