Informative Risk Measures in the Banking Industry: A Proposal based on the Magnitude-Propensity Approach

ArXiv ID: 2511.21556 “View on arXiv”

Authors: Michele Bonollo, Martino Grasselli, Gianmarco Mori, Havva Nilsu Oz

Abstract

Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a poor informative value as they miss the intrinsic multivariate nature of risk.To contribute to a paradigmatic enhancement, and building on recent theoretical work by Faugeras and Pagés (2024), we propose a novel multivariate representation of risk that better reflects the structure of potential portfolio losses, while maintaining desirable properties of interpretability and analytical coherence. The proposed framework extends the classical frequency-severity approach and provides a more comprehensive characterization of extreme events. Several empirical applications based on real-world data demonstrate the feasibility, robustness and practical relevance of the methodology, suggesting its potential for both regulatory and managerial applications.

Keywords: Multivariate Risk Measures, Value-at-Risk (VaR), Expected Shortfall, Frequency-Severity Approach, Risk Management, Portfolio

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper proposes a novel, multivariate risk framework with advanced mathematical foundations (e.g., quantization, stochastic processes) and extensive theoretical derivations, but the empirical applications are described at a high level without providing code, specific datasets, or detailed backtesting results.

  flowchart TD
    A["Research Goal<br>Develop a multivariate risk measure<br>that overcomes limitations of scalar metrics<br>like VaR and Expected Shortfall"] --> B

    subgraph B ["Methodology: Magnitude-Propensity Approach"]
        B1["Frequency Component<br>Model probability of extreme events"] --> B2
        B2["Magnitude Component<br>Model severity of potential losses"] --> B3
        B3["Integration<br>Combine components via<br>Faugeras & Pagés (2024) framework"]
    end

    B --> C["Data & Inputs<br>Real-world portfolio data<br>Market risk indicators"]

    C --> D["Computational Process<br>Estimate joint distribution<br>Calculate multivariate risk measures"]

    D --> E["Key Findings & Outcomes"]
    subgraph E [" "]
        E1["Enhanced Interpretability<br>Multivariate structure reveals hidden dependencies"]
        E2["Regulatory & Managerial Utility<br>Robust framework for risk oversight<br>and capital allocation"]
    end