Beyond Z-Score Levels: A Risk-Adjusted, Trend-Aware Index of Banking Stability

This paper introduces a Risk-Adjusted Stability Index (RASI) that summarizes banking-system stability from a single state variable, the banking Z-score, by integrating its level, trend, and risk dimensions. The index multiplies the mean Z-score by a concave, non-negative transformation of the estimated trend (geometric-mean log growth, with a Theil-Sen estimator in log space as a robustness alternative) and divides by dispersion in Z-score levels (baseline: population standard deviation; robustness: median absolute deviation × 1.4826, interquartile range / 1.349, and downside semi-deviation). Annual data for 2007-2021 are used with an inclusion rule of at least eight valid observations per country; an extended 2000-2021 window supports replication. Uncertainty is quantified via a within-country, over-years clustered bootstrap (B = 1000) that yields rank intervals and Top-1 leadership probabilities, complemented by a leave-one-year-out jackknife. Comparative summaries by continent and subregion show a persistent hierarchy: Africa’s median RASI exceeds Europe’s (e.g., 0.131 vs 0.046), Western > Eastern/Other Europe, and North Africa > Rest of Africa. These relations remain stable across trend estimators, risk normalizations, and subperiods. The framework enables transparent cross-country benchmarking with explicit rank-uncertainty and effect-size summaries, complementing market-based and structural models for counterfactual analysis.