Glossary/Risk

Value at Risk

Also known as VaR, Value-at-Risk

Value at Risk, or VaR, estimates a loss threshold that should not be exceeded over a stated horizon at a stated confidence level under a specified model. It summarizes ordinary downside exposure in one number but does not describe how severe losses may be beyond the threshold.

Editorially reviewed 2026-07-29

Why value at risk matters

VaR gives trading desks, asset managers, banks, and boards a common language for market risk. It can aggregate different positions, support risk limits, compare portfolios, and inform regulatory capital. A single figure is operationally convenient, but its meaning is precise only when horizon, confidence, currency, data, and methodology are disclosed. Used responsibly, it is a monitoring tool rather than a claim about the worst possible loss.

How it is applied

Parametric VaR uses estimated volatility, correlations, and a return distribution. Historical simulation reapplies observed market moves to current positions. Monte Carlo simulation generates many modeled scenarios and revalues the portfolio. The relevant loss percentile becomes VaR. Nonlinear instruments require full revaluation or suitable approximations. Firms usually calculate several confidence levels and horizons, backtest exceptions, run stress scenarios, and pair VaR with expected shortfall and concentration limits.

Formula

VaRα = quantileα of the portfolio loss distribution
VaRα
Loss threshold at confidence level α
α
Selected confidence level, such as 95% or 99%
Loss distribution
Historical or modeled portfolio losses over the chosen horizon

Portfolio example

A one-day 95% VaR of $2 million means the model estimates a 5% chance that the portfolio will lose more than $2 million over one day. It does not mean the portfolio can lose at most $2 million, nor that such a breach will occur exactly once every 20 trading days. During a liquidity shock, losses might be much larger and positions may not be tradable at modeled prices.

How to interpret it

Larger VaR generally indicates more modeled market risk, but comparisons require the same horizon, confidence, currency, and method. VaR can fall because positions are smaller or better diversified, but also because recent markets were calm. Backtesting counts days when actual loss exceeds VaR and helps identify poor calibration. Even a well-calibrated 99% VaR intentionally says little about the size of losses in the worst 1% of outcomes.

Limitations and common misconceptions

VaR is model-dependent and vulnerable to unstable correlations, limited histories, regime shifts, and incorrect distributions. It can reward positions that earn small steady gains while retaining rare catastrophic losses. Scaling across horizons may fail, especially for illiquid assets. A portfolio can be optimized to the metric rather than genuinely safer. Expected shortfall, stress tests, scenario analysis, gross exposure, liquidity, and qualitative review are necessary complements.

Sources and further reading

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