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Private Banking vs. Wealth Management: What's the Difference?
Wealth management is a broader category that involves dealing with the optimization of a client's portfolio, taking into account their aversion to, or comfort with, risk, and investing financial assets according to their plans and goals. Wealth management can be practiced on a portfolio of any size, though, as the name implies, it is geared toward the well-off.
Private banking, by comparison, typically refers to an envelope solution for high-net-worth individuals (HNWIs) wherein a public or private financial institution employs staff members to offer high-net-worth clients personalized care and management of their finances .
https://www.investopedia.com/articles/professionals/111715/private-banking-vs-wealth-management-not-quite-same.asp