Advisor Successions Are xi-Stable iff Post-Transition xi_c ≤ max(xi_{pre}, xi_{successor-baseline}) + ε: A Formal Criterion for Protocol-Quality in Private-Bank Advisor Turnover

Imagine you've worked with a trusted financial advisor for years — they know your risk tolerance, your family situation, your anxiety threshold when markets wobble. Now they leave. What happens to your financial wellbeing during the transition? This hypothesis borrows a powerful concept from the mathematics of rare, extreme events (think: flood-risk modeling and insurance catastrophe pricing) and applies it to the surprisingly understudied world of high-net-worth client handoffs at private banks. The core idea uses something called a 'tail index' — a number that captures how likely a person is to experience extreme, unexpected financial losses. Think of it as a measure of how fat the tail of bad outcomes is in someone's financial life. The hypothesis proposes a formal rule: a transition from one advisor to another is 'stable' if the client's tail index after the switch doesn't get meaningfully worse than what you'd expect from either the old advisor or the new one acting independently. If the handoff process itself introduces chaos — say, an abrupt cold transfer during a market crisis — it creates a whole new source of extreme-loss risk that wasn't in either advisor's profile. That's the danger zone. The math from extreme value theory actually predicts this: when you mix two risk profiles, the worst tail dominates. A bad handoff is like adding a third, much heavier tail to the mix. The practical upshot is a testable three-protocol comparison: a warm, overlapping transition with shared client narrative; a clean but cold document transfer; and a forced switch during a turbulent market period. The hypothesis predicts only the first is mathematically 'stable,' and that the others will show measurable spikes in clients' financial stress and loss patterns.

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