Risk Measurement and Stress Testing

Overview

Systematic risk-measurement methodology covering VaR/CVaR calculation, Monte Carlo simulation, stress-test design, and tail-risk analysis. It provides risk evaluation for backtest results and risk-control constraints for asset allocation.

The measures below are implemented once, with tests, in src/quantlib/risk.py. Call them; do not retype the formulas, because a hand-retyped VaR is where the sign convention silently flips.

from src.quantlib.risk import (
    historical_var, parametric_var, historical_cvar,
    max_drawdown_analysis, monte_carlo_gbm, analyze_mc_results, fit_gpd_tail,
)

Sign convention

A loss is a positive number, uniformly, across every function in the module:

Value	Reads as
historical_var(...) == 0.028	a 2.8% loss
historical_cvar(...) == 0.042	a 4.2% average loss in the tail
max_drawdown_analysis(...)["max_drawdown"] == 0.325	a 32.5% peak-to-trough decline
analyze_mc_results(...)["var"] == 0.224	a 22.4% loss

Quantities that are returns rather than losses keep their natural sign and are named *_return (mean_return, worst_5pct_return, best_5pct_return), so a bad outcome there is negative. Report VaR to the user with the sign the user expects, but never re-derive it, flip it at the presentation layer only.

cvar >= var holds by construction whenever both come from the same sample at the same confidence level. If you ever compute a CVaR below its VaR, the tail mask is wrong.

This is not cvar >= var >= 0. The magnitudes are never clipped, so a sample whose tail contains no actual loss reports a negative loss, a gain. That is deliberate and informative; do not assert non-negativity on a VaR and do not clip it, or you destroy the distinction between "small loss" and "no loss at all".

Risk Measurement Methods

1. VaR (Value at Risk)