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Per-Asset Beta to a Benchmark Portfolio

Basel IRB Risk-Weighted Asset for a Corporate Exposure

Basel VaR Backtest Traffic-Light Zones

Analytical Binomial Credit-Loss VaR for a Uniform-PD Homogeneous Portfolio

Brinson-Hood-Beebower Three-Effect Attribution

Calmar Ratio — Annualized Return over Maximum Drawdown

Implied Default Probability from a CDS Spread

Choueifaty Diversification Ratio of a Gaussian Portfolio

Christoffersen Independence Test for VaR Breach Clustering

Sample from a Clayton Copula

Component VaR Decomposition (Euler Allocation)

Component VaR Decomposition for a Gaussian Portfolio

Compound-Poisson Aggregate-Loss Variance for an Operational-Risk LDA Period

Conditional Drawdown at Risk

Empirical Copula Tail-Dependence Coefficients

Cornish-Fisher VaR

Cornish-Fisher VaR Adjusted for Skewness and Excess Kurtosis

Aggregate Multi-Desk VaR from Standalone VaRs and a Loss-Correlation Matrix

Correlated Factor-Shock Monte-Carlo for Stress P&L

Credit Portfolio Expected Loss and Naive Unexpected Loss

Credit Portfolio MC Loss Distribution (Single-Factor Gaussian Copula)

Empirical Copula via Per-Column Uniform Rank Transform

Empirical Mean Excess Function for POT Threshold Selection

Empirical Upper-Tail-Dependence Coefficient from Bivariate Samples

Euler Risk Allocation for Portfolio Volatility

Fit a Gumbel (GEV, ξ=0) to Block Maxima by Method of Moments

Hill Estimator for the Tail Index

Peaks-Over-Threshold GPD Fit by Method of Moments

Rolling Historical Expected Shortfall (CVaR)

Per-Factor Risk Attribution Under a Linear Factor Model

Factor-Shock Scenario P&L on a Linear Factor Model

Sample from a Gaussian Copula

GPD Tail-VaR Extrapolation under the POT Framework

Hill Estimator for the Tail Index of a Heavy-Tailed Loss Distribution

Historical Stress Loss Replay

Historical VaR for a Long-Only Portfolio

Rolling Historical VaR Track

Component VaR per Asset (Euler Decomposition)

Incremental VaR of a Candidate Trade

Information Ratio of an Active-Return Series

Kendall's Tau-a Rank Correlation on a Bivariate Sample

Kupiec Proportion-of-Failures (POF) Test Statistic

Basel III Liquidity Coverage Ratio with HQLA Caps

Basel III Leverage Ratio

LGD Aggregation with Collateral Recovery Cascade

Marginal VaR by Asset (Closed-Form Gradient)

Marginal VaR Sensitivity for a Gaussian Portfolio

Maximum Drawdown Duration on the Equity Curve

Modigliani M-Squared — Vol-Rescaled Risk-Adjusted Return

Monte-Carlo VaR for a Multi-Asset Portfolio

Basel III Net Stable Funding Ratio (NSFR)

Omega Ratio of a Return Series at a Threshold

Parametric Gaussian Expected Shortfall from Caller-Supplied Moments

Rolling Parametric VaR (Normal)

Pareto Tail VaR via Hill-Estimator Extrapolation

Multi-Period Default Probability from a Rating-Transition Matrix

Multi-Asset Portfolio Parametric VaR (w^T Σ w)

Spearman Rho and Kendall Tau-b: Dual Rank-Correlation Diagnostic for the Copula Pipeline

Realized-Volatility Jump Test (Barndorff-Nielsen and Shephard)

Reverse Stress Test — Solve for Shock Magnitude Hitting a Target Loss

Risk-Budget Allocation via Iterative Fixed-Point

Rolling-Window Variance Ratio Test (Lo-MacKinlay)

Semi-Deviation of a Return Series Around the Sample Mean

Sortino Ratio of a Return Series with Target Return

Spectral Risk Measure (Acerbi 2002)

Stress Coverage Ratios Against Available Capital

Stress-Loss Aggregation by Bucket

Systematic-vs-Idiosyncratic Variance Decomposition (Factor Model)

Tracking-Error Variance Contribution by Sector

Scalar Tracking Error of an Active-Return Series

Treynor Ratio — Systematic-Risk-Adjusted Excess Return

Up-Capture and Down-Capture Ratios versus a Benchmark

Count and Timestamp VaR Breaches

Vasicek ASRF Loss Rate