Value at risk
What is Value at risk?
Value at risk estimates a loss threshold for a portfolio over a stated horizon and confidence level under a specified model and set of market conditions.
What value at risk means
A one-day 95% VaR of $1 million means the model estimates that losses will exceed $1 million on about 5% of comparable days. It does not mean $1 million is the maximum possible loss. VaR compresses portfolio exposures into a common measure that can support limits, aggregation, and comparison when assumptions are clearly stated.
How it is calculated
Historical simulation revalues the portfolio under observed market moves, parametric VaR applies an assumed distribution and estimated covariance, and Monte Carlo VaR simulates risk-factor paths. Full revaluation handles nonlinear positions better but requires more computation. Results depend on horizon, confidence, lookback period, weighting, return model, and treatment of liquidity.
Example
A portfolio reports ten-day 99% VaR of $8 million. Under the model, only about 1% of comparable ten-day outcomes are expected to lose more than that threshold. The figure says nothing about the average or worst loss inside that 1%. Expected shortfall is designed to describe the severity beyond the VaR boundary.
How to interpret it
Always display currency, horizon, confidence, methodology, valuation date, and whether the number is absolute or relative. Compare VaR with limits, capital, liquidity, stress loss, and realized profit and loss. Backtesting counts exceptions and investigates their causes, but a passing backtest does not prove that future tail behavior is captured.
Limitations
VaR can encourage false precision and may reward positions whose rare losses sit beyond the selected quantile. Normal-distribution assumptions can understate fat tails and nonlinear exposure. Historical methods cannot include events absent from the sample. VaR is not coherent under every formulation and should never be described as the maximum amount that can be lost.
Practical checklist
Use more than one estimation method, reconcile risk-factor mappings, and test sensitivity to window and confidence choices. Backtest against clean profit and loss while investigating data and model changes. Pair VaR with expected shortfall, stress testing, concentration, liquidity, and scenario analysis. Escalation should focus on the exposure driving the number, not merely on whether a limit is breached.
Also known as: VaR
Sources and further reading
- Measuring and Managing Market Risk, CFA Institute