A risk number is actionable only when loss definition, horizon, confidence level, unit, model, and validation status stay attached.

Base R; PerformanceAnalytics, rugarch, and evir are optional.

VaR_p = quantile_p(loss); ES_p = mean(loss | loss >= VaR_p)

1. Step 1Define every variable and unit.
2. Step 2Check assumptions and information timing.
3. Step 3Calculate, verify, and interpret in context.

Variable

2,400 seeded Student-t losses, in percent.

Model choice

Losses are positive in this convention, so upper quantiles measure risk.

Calculation

The live simulation reports monotone 95%/99% VaR and ES; the book's GARCH sample produced 95% VaR 2.037% and ES 2.775%.

Interpretation

Expected shortfall is larger because it averages losses beyond the VaR threshold.

Reasonableness check

Simulation choice, tail distribution, liquidity, horizon, and threshold uncertainty remain; this is not investment or regulatory advice.

Expected shortfall is larger because it averages losses beyond the VaR threshold. Limitation: Simulation choice, tail distribution, liquidity, horizon, and threshold uncertainty remain; this is not investment or regulatory advice.

Expected shortfall exceeds VaR, and higher confidence moves farther into the tail.

Run the self-contained starter code in the protected STATLAB R runner. The code prints an auditable result and avoids network or unrestricted file access.

Compare your result with the definition, units, and model assumptions—not only with a target number.

Complete these without looking at the selected solutions. More than one defensible program may exist.

These are compact solution routes. Confirm dimensions, units, and any changed modelling choices.

Define loss consistently, estimate tail risk, backtest prior-only forecasts, and qualify extreme-value extrapolation.

Name the assumption, evidence you would seek, and how the recommendation might change.

Reach 70% to complete the chapter. Explanations appear after submission.