Optimizing Tail-Risk Hedging via Model Hybridization: Integrating Strategic Asset Allocation with Regime Detection

Modern Portfolio Theory (MPT) relies on diversification benefits governed by covariance matrices. However, during systemic liquidity crises and market shocks (VIX > 30), crossasset correlations asymptotically tend toward unity, causing systemic variance to surge and nullifying diversification when downside protection is most needed. This paper presents an end-to-end quantitative framework developed at GEFIP that hybridizes a long-term strategic asset allocation model (GPS) with high-frequency statistical and machine learning regimedetection algorithms (CASSANDRE and AEGIS). We demonstrate the operational pitfalls of naive binary overlay links (whipsaw costs) and solve the critical "cash drag" dilemma by replacing asymmetric drawdown measures with a symmetric "Underwater / Run-up" profile (the Lifeboat project) trained via penalized Ridge regressions. Furthermore, we develop an Antifragile Asset Allocation Model (AAAM) and an industrial-grade options overlay engine (AEGIS) leveraging Hidden Markov Models (HMM) and Radial Basis Function (RBF) volatility surface reconstruction. Empirical out-of-sample backtests (2004-2026) show that a discrete, trend-filtered, geographically differentiated overlay backed by a remunerated cash and convex safe-haven sleeve consistently mitigates Maximum Drawdown (from -33.92% to -16.74%) while enhancing risk-adjusted returns (Sharpe ratio rising from 0.63 to 0.70). Finally, we discuss the transition into live institutional production, including cross-asset credit overlays, multi-horizon FX forecasting (Project Hécate), and empirical bond curve baseline calibrations.