Regime labels are not representation-invariant: Implications for model risk governance

Background and gap: Regime models underpin capital, risk-limit, and hedging decisions, yet existing literature evaluates one fitted specification at a time. Basel IV and SR 11-7 require structural stability across admissible specifications. Contribution: We provide the first systematic audit of representation invariance for discrete-state regime models, measuring partition agreement by ARI and coarse risk-ordering agreement by a matching-free rank-aligned metric calibrated against a 1 / K null. Method: We test four single-asset case studies under four model classes (HMM, GMM, k-means, spectral) at K ∈ { 2,3,4,5 } . Eight representations (seven for all assets, one VIX-based for S&P 500 only) vary in standardisation, feature subset, rolling horizon, volatility estimator, and information source. A step-size sweep separates regime persistence from window overlap. Findings: Cross-representation ARI is 0.34–0.43 across all assets under HMM and GMM (with non-parametric robustness benchmarks confirming the same pattern at 0.29–0.47), well below the 0.65 poor-recovery threshold; disagreement persists under k-means and at non-overlapping windows. Top-1 ordering Jaccard at K = 3 is 0.47 against a 1 / K = 0.20 null, a 2.4 × excess comparable to the partition signal. Significance: Representation-conditional CVaR diverges by 39–73% of the unconditional CVaR on average and approaches 300% in COVID-19 stress (BTC-USD HMM peak 299%). We recommend a cross-representation envelope as a diagnostic complement to temporal backtesting; the registered admissible class (Supplementary Section ??) is narrow, so the reported ARI is a conservative upper bound.