dailybagel wrote:I am sure it is O(N), to use "big O" notation. Is this the same problem as putting an NxN matrix in reduced row-echelon form?
Sorry to geek out on you.
Epsilon Delta wrote:I'm pretty sure the answer is (N-1).
It is certainly a lower bound, attained if one fund goes down and the other (N-1) go up.
I believe it is also an upper bound. If you look at each holding if you need to increase M of them you need to decrease at most N-M. As above if M is 1 you need at most N-1 trades and you can establish the result for all M by induction.
umfundi wrote:fd, I do not understand your distinction. If the amount in each fund within an allocation class does not matter, why have multiple funds in that class?