ATLASExpected shortfall (CVaR)
Investing glossary · Risk and statistics
The average loss in the worst cases, those that go beyond the value-at-risk threshold.
Definition
Expected shortfall (ES), also called conditional value at risk (CVaR), answers the question VaR leaves open: when things go worse than the VaR threshold, how bad is it on average? A 95% ES is the average loss across the worst 5% of outcomes.
Because it looks into the tail, expected shortfall is always at least as large as VaR at the same confidence, and it is more sensitive to extreme events. Regulators have moved toward it for this reason. For a bell curve the ES is about 25% larger than the 95% VaR; for fat-tailed returns the gap is wider.
Formula
ES(95%) ≈ σ × φ(1.645) ÷ 0.05 ≈ 2.06 × σ (normal approximation)
φ(1.645) is the standard normal density at the 95% point; 0.05 is the tail probability; σ is the volatility over the horizon. The result is for a normal distribution.
Worked example
For a position of $10,000 in NVIDIA (NVDA), the simple 95% one-month VaR is $1,568. The expected shortfall at the same confidence is $1,966: if the month ends in the worst 5% of cases, the average loss would be about that.
The gap between the two numbers is the answer to "how bad can the bad months be?".
How ATLAS uses it
ATLAS reports expected shortfall in the same scenario analytics as VaR, from the same simulated outcomes, so both come from one consistent model.
Related in ATLAS: Scenario simulation →Browse all ATLAS tools →See it on a real stock
The example above uses these companies. Open their pages for the full numbers:
Frequently asked questions
Why is expected shortfall better than VaR?
It measures the size of losses in the tail, not just the threshold, and it behaves more sensibly when you combine positions into a portfolio.
Is CVaR the same as expected shortfall?
In practice yes. Both names are used for the average loss beyond the VaR level.
Related terms
Put the idea to work on your own stocks
Open any company in ATLAS to see its fair value, its odds of rising and its risk numbers side by side.
Try ATLAS →Not investment advice. ATLAS estimates are produced by statistical models from public data; they can be wrong and past performance does not predict future results. Consider your own situation before investing. Disclaimer