My mother is not a resident of USA. she has some money to invest. I would like to help her to open an account with IB. is it legal for me to manage her account, e.g., log into her account and buy stocks for her?
One of the questions from your mothers application the FCM will ask is: Does somebody else trade your account? If your mother says YES, she will have to fill and sign a POA and mention who will trade her account. Should normally be no problem.
