Abstract

This study investigates the dynamic, non-linear relationship between private sector credit expansion and operational risk within financial institutions. Utilizing 2025 monthly loan data, the research proposes an integrative quantitative framework coupling Standard Score (Z-score) Probability Density Functions with the Weighted Expected Present Value (EPVw) model, incorporating a 0.995644 discount factor. Empirical results reveal a critical decoupling between credit volume and risk magnitude. While the loan portfolio expanded continuously from 6,742 billion in January to a peak of 7,318 billion in December, calculated risk (EPVw) followed a parabolic, bell-shaped distribution. Maximum risk exposure converged mid-year (June–August), driven by the highest statistical probability density as loan values hovered around the annual mean (μ = 6,997 billion). Conversely, despite peak volumes in December, year-end capital risk collapsed to its lowest point (377 billion) due to an extreme right-tail distribution shift (Z = 2.02) minimizing probability density weights (0.051). These findings challenge traditional linear risk assumptions, proving volatility concentrates within normal baselines rather than volume peaks. This study provides a vital framework for asset-liability management, ensuring capital reserves are optimally calibrated against market extremes, aligned with Clean Surplus Relation principles.

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