Minimize turnover for combined portfolio

wh408 · April 4th, 2017, 9:44 am

Assume I have M portfolios, each of them can be represented as a T by N matrix, where N represents number of stocks traded and T represents number of days. For each portfolio matrix, each row is under the following constraints:

Absolute values for each row entries sum up to one which represents the weight of money allocation.
Sum of all entries on each row is zero which means a dollar neutral portfolio.

My question is that is there a mathematical solution of finding weights
w_1, w_2, ... w_M
such that
w_i>=0 for i in 1,2, ... M
and
w_1 + w_2 + ... + w_M = 1
such that the combined portfolio has minimum overall turnover.

Alan · April 4th, 2017, 6:51 pm

This is quite vague. First what is the overall objective function? Second, try to express "minimum overall turnover" mathematically.

wh408 · April 5th, 2017, 10:32 am

Hi Alan, sorry I did not make it clearly enough. The math expression of turnover is position changes for each stocks on each day. If I use python DataFrame with dates as index and stocks as columns to represent a portfolio (entries are money allocated to each stock on each day), then the turnover is simply df.diff(). Overall turnover simply means the sum of all entries of the turnover matrix. Thanks!

Alan · April 5th, 2017, 3:46 pm

Sorry, but that is English, not math. Use the LaTeX. Unless you can express your problem mathematically and clearly, you have no hope of solving it.

Minimize turnover for combined portfolio

Minimize turnover for combined portfolio

Re: Minimize turnover for combined portfolio

Re: Minimize turnover for combined portfolio

Re: Minimize turnover for combined portfolio