Risk

Risk numbers are computed from joint sample paths of a forecast and carry that forecast's calibration status. A number is never presented as more trustworthy than the forecast under it.

Measures (tycheon.risk)

• VaR and Expected Shortfall at several levels (default 90, 95, 97.5, 99%) with a bootstrap standard error, the number of tail paths, a reliable flag (at least 10 tail paths) and a calibrated flag (true only when the tail lies within the calibrated level range).
• Probability of drawdown beyond X (max drawdown over the horizon, peak includes the start) and of ending the horizon down more than X, each with a Wilson interval.
• Volatility forecast: cross-path horizon volatility per bar and annualised, per-path realised volatility quantiles, and the model's own conditional sigma when it has one.
• Tested against closed forms: Gaussian and lognormal VaR/ES, and Brownian-motion expected drawdown with the discrete-monitoring correction.

Calibration for risk only widens

The service layer calibrates a risk run with widen_only=True: calibration may move the tails outward, never inward, and never shifts the median. A calibrator that has just seen a calm or rising stretch would otherwise shrink VaR and ES on the strength of a few dozen past forecasts, which is the wrong direction to be wrong in. With the same seed, a calibrated risk figure is at least the uncalibrated one. The response says so in its warnings. Forecast intervals are still calibrated in both directions. See ADR 0011.

Portfolios and the dependence assumption

aggregate_portfolio values a buy-and-hold portfolio along joint paths. Assets are forecast separately, so their dependence is an assumption: a shrunk correlation of daily log returns estimated from data known at as_of, imposed with a Gaussian copula by rank reordering (Iman-Conover), which leaves each asset's marginal paths untouched.

Coupling	Keeps	Understates
terminal (default)	each path's own shape and serial dependence	co-movement before the end of the horizon (step-k correlation is about rho * k / H), so interim drawdowns
stepwise	the stated correlation at every step	serial dependence within each path

A multi-asset portfolio is therefore always uncalibrated, with the reason in its notes and in the report warnings. A single-asset portfolio needs no dependence assumption and keeps its calibration. Gaussian dependence has no tail dependence: the lower tail in a crash is likely understated. stress_correlation raises correlations to show the sensitivity.

Stress scenarios

Historical replay of a named window, the worst windows in the history, user shocks, and the model-implied tail (what the model's own worst 5% of paths look like). None of the historical or shock scenarios has a probability; the model-implied one is labelled uncalibrated unless the forecast is.

The report

build_risk_report produces a RiskReport: to_json() and a self-contained to_html() (inline SVG, no scripts, no external resources, light and dark themes, all dynamic text escaped). It opens with the warnings that apply to this particular report. Run examples/risk_report.py to produce one for a synthetic three-asset portfolio.

For research and risk analytics. Not investment advice.