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Value at Risk (VaR)

The maximum expected loss at a given confidence level — but doesn't tell you how bad the tail is.

VaR estimates the worst-case loss over a time horizon at a specified confidence level. For example, a 95% 1-day VaR of $100,000 means there's a 5% chance of losing more than $100,000 tomorrow. Critical limitation: VaR tells you the threshold, but not how severe losses beyond that threshold could be. A portfolio with $100k VaR could lose $101k or $1 million in the worst 5% of outcomes — VaR doesn't distinguish. This is why CVaR (Expected Shortfall) is often used alongside VaR — it measures the average loss in the tail. VaR is widely used for regulatory capital (Basel III), risk limits, and reporting, but should never be the only risk metric. Use it with stress tests, max drawdown, and scenario analysis.

Formula
P(Loss>VaRα)=1−αP(\text{Loss} > \text{VaR}_{\alpha}) = 1 - \alpha
Where
α\alpha=Confidence level (e.g. 95%)
Variables
\text{VaR}_{\alpha}Value at Risk at α confidence (e.g., 95%)
\alphaConfidence level (0.95 or 0.99)
1-\alphaLeft tail percentile (5% or 1%)
Assumptions
  • Simulated returns from Monte Carlo paths
  • VaR reported as positive loss amount
  • Horizon-specific (not scaled by square-root of time)
  • Does not indicate severity beyond VaR threshold
vs. Industry Tools
Basel III/IV — Requires historical simulation or internal models
RiskMetrics — Also offers parametric VaR using delta-normal method
Related Terms

CVaR / Expected Shortfall

The average loss in the worst-case scenarios beyond VaR.

Monte Carlo Simulation

Generating thousands of possible future scenarios through random sampling.

Stress Test (Rate Shock)

Estimates impact of large yield moves using duration and convexity.

Key Rate Duration

Sensitivity to rate changes at specific maturity points on the curve.