Insight: Value-at-Risk- and Expectile-based Systemic Risk Measures an

Winners Consulting Services Co. Ltd. (積穗科研股份有限公司), Taiwan's expert in Enterprise Risk Management (ERM), presents a critical finding for corporate risk executives: a landmark 2024 study published on arXiv demonstrates that the widely used Value-at-Risk (VaR) metric systematically overestimates diversification benefits under systemic risk scenarios, while newly proposed Expectile-based systemic risk measures consistently yield more conservative and accurate tail-risk assessments—a distinction that carries direct consequences for how Taiwan's boards set risk appetite, design risk matrices, and calibrate Key Risk Indicators (KRIs) under ISO 31000 and COSO ERM frameworks.

About the Authors and This Research

This paper is the product of three quantitative risk researchers whose work sits at the intersection of actuarial science, financial mathematics, and enterprise risk management. Lead author Bingzhen Geng has established a focused research profile in asymptotic theory for systemic risk measures, achieving an h-index of 6 with over 90 cumulative citations—a meaningful footprint for a researcher operating in a highly technical sub-field. Co-author Yang Liu, with an h-index of 4 and 61 citations, specializes in heavy-tailed distributions and risk dependence structures, two modeling challenges that are central to understanding how losses propagate across interconnected corporate systems. Yimiao Zhao contributes expertise in the statistical quantification of diversification effects.

The paper's placement in the arXiv Enterprise Risk Management category is deliberate: while its methodology draws on advanced probability theory, its implications are explicitly framed for practitioners who must decide how to measure, report, and manage systemic risk within organizational governance structures. Published in 2024, the research employs the multivariate Sarmanov distribution framework combined with second-order regular variation—tools that allow the authors to model the realistic combination of heavy tails and mutual dependence that characterizes genuine market crises, as opposed to the simplified assumptions embedded in standard first-order asymptotic models.

Core Findings: Why Your Diversification Numbers May Be Telling the Wrong Story

The paper's central contribution is a rigorous, unified asymptotic analysis of two families of systemic risk measures, yielding findings that challenge common ERM assumptions about portfolio diversification under extreme conditions.

Finding One: Expectile-based measures consistently report higher risk than VaR-based measures under systemic stress

The authors introduce two new Expectile-based systemic risk measures: the Individual Conditional Expectile (ICE) and the Systemic Individual Conditional Expectile (SICE), proposed as alternatives to the Marginal Expected Shortfall (MES) and Systemic Expected Shortfall (SES) that currently dominate financial risk practice. Through second-order asymptotic analysis applied to a multivariate Sarmanov distribution with heavy-tailed marginals, the research demonstrates that Expectile-based measures consistently produce higher risk evaluations than their VaR-based counterparts when extreme system-wide events occur. This is not a marginal difference attributable to model calibration—it is a structural feature of how these two metric families respond to tail events. For enterprise risk managers, this means that if your ERM system relies exclusively on VaR-derived metrics, it is structurally predisposed to underreporting the severity of tail losses at the exact moments when accurate reporting matters most: during systemic crises.

Finding Two: VaR-based diversification benefits are systematically overstated; Expectile-based diversification benefits are systematically understated

Perhaps the most practically significant finding concerns diversification. The paper proves analytically that VaR-based systemic risk measures consistently overestimate diversification benefits, while Expectile-based measures consistently underestimate them. Translated into ERM practice: if your risk committee is using VaR-derived diversification metrics to justify the risk reduction achieved through spreading exposures across geographies, suppliers, or asset classes, those metrics are likely giving you an optimistic picture. The Expectile approach, by contrast, suggests that true diversification benefits in the tail are more limited than VaR implies—a conservative approximation that aligns better with the "prudent person" principle embedded in risk governance frameworks including COSO ERM and ISO 31000. Furthermore, the authors demonstrate that second-order asymptotic methods provide materially more accurate estimates than traditional first-order approaches, confirming through numerical simulation that the precision improvement is not merely theoretical.

Implications for Taiwan's Enterprise Risk Management (ERM) Practice

This research carries three layers of implication for Taiwan-based organizations implementing ERM frameworks.

ISO 31000 Adequacy Principle: ISO 31000's Section 6.4 on risk assessment requires that the methods chosen must be "adequate" for the risk context being evaluated. When a company faces systemic risk scenarios—supply chain disruption cascades, correlated financial market shocks, or sector-wide regulatory crises—the "adequacy" of VaR as the sole systemic risk metric is genuinely questionable under this standard. The 2024 research provides quantitative evidence that VaR's structural overoptimism about diversification constitutes a systematic adequacy gap when applied to interconnected, heavy-tailed risk environments.

COSO ERM Risk Appetite and Information Transparency: The COSO ERM framework's "Information, Communication, and Reporting" component requires that risk information presented to boards be sufficiently complete and accurate for governance decisions. If diversification benefit figures reported to the board are derived from VaR-based systemic measures—and are therefore structurally optimistic by an analytically demonstrable margin—the board's risk appetite calibration may be set too permissively. The Expectile-based approach provides a more conservative benchmark that better serves the spirit of COSO ERM's governance transparency requirements.

Regulatory and ESG Disclosure Trends: Taiwan's Financial Supervisory Commission (FSC) has been progressively strengthening requirements for systemic risk disclosure among listed companies and financial institutions, particularly in the context of climate-related financial risk (TCFD) and supply chain concentration risk. The Expectile-based measures introduced in this research offer a more defensible quantitative basis for conservative systemic risk disclosure, aligning well with the direction of regulatory expectations post-2024.

How Winners Consulting Services Co. Ltd. Helps Taiwan Enterprises Act on These Insights

Winners Consulting Services Co. Ltd. (積穗科研股份有限公司) supports Taiwan enterprises in implementing ISO 31000 and COSO ERM frameworks, building risk matrices and KRI systems, and strengthening board-level risk governance. In response to the systemic risk quantification challenges identified in this research, we recommend three concrete actions:

1. Conduct a Risk Metrics Audit: Review your current ERM framework to identify the degree to which systemic risk assessments rely on VaR-based measures. Map specific risk scenarios—such as supply chain concentration, cross-market financial contagion, or correlated operational failures—where the heavy-tail and mutual dependence conditions studied in this paper are most likely to apply. Benchmark your current metrics against the ISO 31000 Section 6.4 adequacy criterion and document where gaps exist.
2. Introduce Conservative Scenario Columns in the Risk Matrix: Based on the paper's findings, add a "conservative systemic scenario" dimension to your existing risk matrix. For risk factors exhibiting mutual dependence or heavy-tail characteristics, recalculate KRI thresholds using more conservative diversification benefit assumptions consistent with the Expectile framework's findings. Present board reports that explicitly show the estimation gap between VaR-based and conservative-scenario diversification figures, enabling more informed risk appetite decisions.
3. Strengthen Assumption Transparency in Board Risk Reporting: Aligned with COSO ERM's Information and Communication component, update board risk report templates to explicitly disclose the quantitative methodology underpinning systemic risk assessments, including the known directional bias of each tool (e.g., VaR tends to overestimate diversification benefits). This "assumption transparency" practice ensures that board members can calibrate risk appetite with full awareness of measurement uncertainty, rather than treating risk numbers as objective facts.

Frequently Asked Questions

Is VaR really insufficient for measuring systemic risk in an ERM framework?

VaR remains a valuable and widely accepted risk metric, but this 2024 study demonstrates a specific structural limitation: in systemic risk scenarios characterized by heavy-tailed and mutually dependent losses—which represent the conditions of genuine market crises—VaR-based systemic measures consistently overestimate diversification benefits. This is not a calibration error but an analytically proven structural bias. For ERM purposes, VaR should not be abandoned but should be supplemented with more conservative Expectile-based measures, particularly for scenarios involving correlated systemic shocks. The parallel reporting of both approaches provides boards with a more complete picture of the range between optimistic and conservative risk estimates.

What compliance requirements do Taiwan enterprises face regarding systemic risk disclosure?

Taiwan's listed companies are required to disclose material risk factors in annual reports and material information filings under FSC regulations. Financial institutions face additional capital adequacy requirements under Basel III/IV for systemic risk. Since 2023, the FSC has progressively required larger listed companies to publish sustainability reports incorporating TCFD-aligned climate risk disclosures, which include quantitative systemic risk dimensions. The Expectile-based measures in this research provide a more conservative quantitative basis for such disclosures, supporting compliance with the FSC's trend toward more rigorous systemic risk transparency requirements post-2024.

Does ISO 31000 require specific mathematical tools, and does this research align with ISO 31000?

ISO 31000 is a principles-based framework that does not mandate specific mathematical tools. However, its Section 6.4 on risk assessment explicitly requires that chosen methods must be "adequate" for the risk context—meaning tools must be appropriate for the type and severity of risks being evaluated. For systemic risks characterized by heavy tails and mutual dependence, this research provides evidence that Expectile-based measures satisfy the adequacy criterion more robustly than VaR alone. COSO ERM similarly emphasizes "rigor" in risk quantification methodology. Enterprises can reference this research as justification for incorporating Expectile-based metrics into their ISO 31000 and COSO ERM toolkits as a complement or conservative alternative to VaR.

How long does it take to upgrade a systemic risk measurement framework, and what are the steps?

Based on Winners Consulting Services Co. Ltd.'s implementation experience, a systemic risk metrics upgrade for a mid-to-large Taiwan enterprise typically requires 90 to 120 days across four phases. Phase 1 (approximately 2 weeks): Current-state diagnostic—inventory existing ERM risk quantification tools and assess VaR dependency. Phase 2 (approximately 3–4 weeks): Framework design—develop a revised risk matrix incorporating conservative scenario dimensions, redesign KRI thresholds aligned with ISO 31000 adequacy requirements. Phase 3 (approximately 6–8 weeks): Implementation—staff training, system updates (Excel/BI tool revision), board report template redesign. Phase 4 (ongoing): Monitoring and optimization—establish quarterly KRI review cycles to ensure metrics continue to reflect the current risk environment and regulatory expectations.

Why engage Winners Consulting Services Co. Ltd. for Enterprise Risk Management (ERM) matters?

Winners Consulting Services Co. Ltd. (積穗科研股份有限公司) is one of Taiwan's few consultancies combining frontier academic research monitoring with hands-on ERM implementation expertise. We systematically track publications on arXiv, SSRN, and leading academic journals, translating cutting-edge