The Advisor xi-Ledger: Expected ES-Reduction Per Client-Year Achieved via xi-Attenuation — Integrating H1-H4 Into Private-Bank P&L Under FTG-Universality Accounting

For each advisor-client-year triple (a, c, t), define the xi-Ledger entry Delta_ES_{a,c}(t) = [ES_q(xi^{baseline}) - ES_q(xi^{observed}_{a,c,t})] × AUM_c, where ES_q follows the EVT-based formula ES_q = [VaR_q + beta - xi u]/(1-xi) (McNeil-Frey-Embrechts 2015 GROUNDED; Acerbi-Tasche 2002 GROUNDED), and xi^{observed}_{a,c,t} is estimated via four complementary channels: (i) H1 retention-exceedance POT/GPD xi; (ii) H2 subjective-loss Hill estimator (triangulated via behavioral proxies for overprecision-bias mitigation); (iii) H3 transition xi-stability pre/post; (iv) H4 regime-aware dynamic Hill. TRIANGULATION ARGUMENT: all four channels are tail-shape estimates of the same latent subjective-loss process L^{sub}_{a,c}(t) under different sampling regimes (H1 observes exceedances of action threshold; H2 elicits distributional percentiles; H3 observes pre/post transition samples; H4 observes market-mediated crisis exposure). Under the assumption that these four sampling regimes all probe a common tail structure, their Hill estimates should correlate at rho ≥ 0.5 — formally motivated by regular variation: if the underlying L^{sub}_{a,c} is regularly varying with index -1/xi, all four sampling regimes inherit this index asymptotically (modulo sampling bias). FTG universality (Fisher-Tippett 1928 GROUNDED; Gnedenko 1943) implies xi is the necessary tail-shape parameter for characterizing heavy-tailed losses; mean-based P&L (AUM-growth, fee-revenue) is insufficient for heavy-tailed client subjective-loss distributions because the mean may diverge at xi ≥ 1 or be dominated by extreme observations at xi > 0. [CORRECTION from QG: xi is the necessary tail-shape parameter, NOT a Fisher-Neyman sufficient statistic — GEV has three parameters μ,σ,xi; xi is the distributional-type indicator.] The xi-Ledger aggregate at institution level: EUR 500M/year on a Banca Generali-scale book (calibrated to Vanguard Advisor's Alpha 150bps behavioral-coaching benchmark).