What are the main methodologies for aggregating risks across different risk types and business units?

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AcadiFi · Accepted Answer

Risk aggregation combines risks across silos to produce enterprise-level measures reflecting diversification and concentration. The challenge: different risk types use different methodologies, horizons, and confidence levels — aggregation must harmonize these.

Main approaches: (1) Simple summation — add individual risk capital numbers. Conservative but overstates risk by ignoring diversification. (2) Variance-covariance — assume joint normality with a correlation matrix: Total_Capital = sqrt(w' Σ w). Captures linear diversification but misses tail dependence. (3) Copula-based aggregation — use copulas (Gaussian, t, Clayton) to model joint tail behavior. More realistic but calibration-heavy. (4) Full Monte Carlo — simulate joint loss distributions across all risk types and take the 99.9% quantile. Most flexible but computationally expensive.

For Keystone Banking Corp aggregating credit, market, operational, and business risk with a total standalone capital of $12B, a moderate correlation assumption (0.4 across types) might produce a diversified enterprise capital of $9B — a 25% diversification benefit. Regulators scrutinize diversification claims; Basel II explicitly rejected aggregation benefits across risk types, requiring simple summation for regulatory capital. Economic capital models used internally can claim diversification but must justify correlations with empirical evidence and stress test assumption breakdown.

Key challenges: time horizon harmonization (market risk 10-day, credit 1-year), confidence level alignment, correlation instability during crises (correlations approach 1 in tail), and integration of stress test results with statistical aggregation. Best-practice frameworks combine quantitative aggregation with qualitative overlays and reverse stress testing to identify vulnerabilities the statistical model misses.

What are the main methodologies for aggregating risks across different risk types and business units?

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