Often an in-specie custody transfer is cleaner. But first you need to know whether your existing broker accepts Swiss residents.
Step 1: ask the current broker what changes after Swiss residence
Some international brokers serve Swiss residents without difficulty. Others restrict products, stop new purchases or close accounts. US persons face an additional layer because FATCA and US securities rules can limit the choices of both Swiss and foreign institutions.
For the surrounding context, see Swiss banking hub.
Get the policy in writing before the move.
Step 2: decide Swiss broker or foreign broker
A Swiss broker simplifies Swiss tax documents and withholding-tax processes, but can be more expensive and can bring Swiss securities transfer stamp duty into transactions where a Swiss securities dealer is involved.
A foreign broker can be cheaper and may avoid Swiss stamp duty in some structures, but you assume more of the tax-reporting work yourself.
If this decision changes the viability or sequence of your move, a Swiss relocation strategy consultation can apply it to your own facts.
If the move has not happened yet, neither option is open on Swiss terms. FreedomBanking compares brokers for people without a Swiss address.
Step 3: transfer assets rather than crystallising gains unnecessarily
An in-specie transfer normally preserves the investment rather than creating a disposal merely to move custody. The tax treatment in the country you are leaving still matters: some jurisdictions have exit taxes, deemed disposals or fund-specific rules.
For the surrounding context, see opening a Swiss bank account.
Preserve the original acquisition dates and costs even though Swiss taxation of private capital gains generally does not rely on cost basis in the same way as a capital-gains-tax country. You may need the records for your former country, a future move or professional-trader analysis.
Step 4: rebuild the tax file for Switzerland
Swiss residents declare securities and income annually. Foreign dividends can suffer source-country withholding; treaty relief and the Swiss DA-1 credit/reclaim process may recover part of it where the conditions are met.
Step 5: do not convert currencies automatically
Moving USD or EUR securities into a Swiss account does not require converting the portfolio into CHF. Custody location and investment currency are separate decisions.
For the surrounding context, see choosing a Swiss bank.
Move the relationship. Do not rebuild the portfolio unless there is an investment reason to do so.
General information on Swiss law and practice, not individual legal, tax or investment advice.