You should be aware that NZ has AML (Anti-Money Laundering Laws) & CRS (Common Reporting Standard). The reason is despite you have setup funds in the US, have you ever thought how those funds would end up - if they would be sent to NZ? How would you realise those profits and at the end of the day, how would you spend it or get access to it for consumption?

The AML basically means good record keeping for IRD. So when large amounts are wire transferred in or out of NZ, this is recorded and IRD will look to it in the case of a tax audit. CRS further enforces the tax requirement by foreign residents living in NZ. If you are a US citizen or green card holder, you would be under FACTA and the banks in NZ would be required for you to comply under FACTA - which is they report to the IRS of your bank balances etc (basically the same as CRS but for US citizens).

The term LTC seems interesting. When I studied tax in Canada, such an arrangement would hold no defense in the case of a tax audit. The key words is "control" - ie Cdn Controlled Private Corporation ; who are the directors, where were decisions made. There are also 'attribution' tax laws in Canada which prevents a person from moving funds from 1 hand to another via by gifting to a relative or spouse, without paying tax (the person that gifts the shares would still have to declare the dividend income on their tax return despite it being already gifted) - anyways, i'm not sure if NZ tax laws are that detailed but it's certainly something to think about it or talk with a NZ tax specialist.

If it can be proven you made trades via a company holding abroad, and the decisions made were made on NZ soil, it may be hard to dispute those profits were beyond your control and thus not taxable in NZ. In this day of age, tax depts have a wealth of resources they can go on, even looking at your ISP records and how and when you made those trades. It's scary as my wife was once audited some 15+ years ago and they knew she had a bank account in China and full record of her issued Visa card on all her purchases she made overseas while traveling. I'm certain information gathering is far more sophisticated today ; seeing how CRS and AML reinforces quite the evasive information gathering.

One thing certain, the US is not part of the CRS regime imposed by the OECD so privacy laws for US banks still hold.