Conditional VaR / Expected Shortfall
The risk metric that addresses VaR's tail-blindness — and what regulators chose for the post-2008 era
Two portfolios have identical 99% one-day VaR of $1 million. Portfolio A's loss distribution beyond the 1% threshold is bounded — the worst-case daily loss in the past decade was $1.5 million, and even the simulated tail beyond VaR rarely strays past $2 million.
Portfolio B's loss distribution beyond the threshold is fat-tailed — the worst-case daily loss in the past decade was $20 million, and the simulated tail past VaR has a substantial probability mass at $5-10 million. By VaR alone, the two portfolios look identical. By any reasonable measure of how badly things go when they go badly, Portfolio B is dramatically more dangerous.
Conditional VaR (also called Expected Shortfall, ES) is the metric that addresses this. Where VaR specifies the loss threshold at the alpha confidence level, CVaR specifies the EXPECTED loss conditional on the loss exceeding that threshold.
That is the opening. Finishing a lesson is where it stops being interesting and starts being useful: the full lesson runs to 8 sections and ends with 6 practice questions. A free account is what opens the rest, and the other 255 lessons in the Academy with it. No card.
What this lesson covers
- 1Why Basel switched from 99% VaR to 97.5% Expected Shortfall
- 2CVaR optimization — Rockafellar-Uryasev's tractable formulation
- 3VaR vs CVaR Visualizer
- 4CVaR in closed form (Gaussian) and via simulation (general)
- 5VaR vs. CVaR comparison — same Gaussian portfolio at three confidence levels
- 6Basel FRTB January 2019 — the regulatory shift to Expected Shortfall
- 7Where to see this on the platform
- 8Summary