Yes, this migration will have no impact upon the cost basis of your positions.
Will the current cost basis of positions be carried over when my account is migrated due to Brexit?
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Will the current cost basis of positions be carried over if I transfer positions between Interactive Brokers accounts?
Do you send Cost basis information to the receiving institution for an outbound Free of Payment Transfer of Global Securities transfer?
Are periodic IRA distributions allowed?
Will I have access to the same trading platform or be subject to any software changes following Brexit migration?