Conditional Value at Risk (CVaR95)

Gold definitionUpdated Apr 2, 2026

Definition

Conditional Value at Risk (CVaR95) is a risk-sensitive metric that quantifies the expected loss given that the loss exceeds the 95th percentile. It characterizes worst-case model behavior and tail exposure, particularly crucial for evaluating high-stakes AI systems where rare but severe failures can occur.

At a glance

Executive summary

Conditional Value at Risk (CVaR95) is a statistical tool used to measure the average severity of the worst 5% of outcomes. It helps identify and quantify extreme risks in AI models, especially in critical applications where rare but serious failures are a major concern, even if average performance looks good.

TL;DR

CVaR95 measures the average of the worst-case outcomes to help understand and manage extreme risks in AI systems.

Key points

Quantifies the expected loss given that the loss exceeds a specified percentile (e.g., 95th percentile).
Solves the problem of evaluating and mitigating rare but severe failures in high-stakes AI applications.
Used by researchers and ML engineers in AI safety, responsible AI, and robust LLM evaluation.
More robust and coherent than Value at Risk (VaR) because it averages losses in the tail, not just a threshold.
Growing importance in AI safety and responsible AI for understanding and mitigating extreme risks in large models.

Use cases

Evaluating LLM safety: Identifying models prone to severe social harm or ethical failures in sensitive prompts.
Financial risk management: Assessing potential losses in investment portfolios during extreme market conditions.
Autonomous driving safety: Quantifying the risk of severe accidents that occur rarely but have high impact.
Healthcare AI deployment: Measuring the expected impact of critical diagnostic errors that fall into the worst-case scenarios.
Infrastructure resilience: Analyzing the expected cost of failures in critical systems under extreme stress events.

Also known as

CVaR, Expected Shortfall, ES, Average Value at Risk, AVaR