Value at risk
Family III · Risk
Not to be confused with forex risk, correlation risk, gap risk.
Value at risk (VaR) is a forward-looking risk measure that condenses portfolio exposure into a single monetary figure: the loss threshold that is expected to be exceeded only a stated percentage of the time. It is expressed with two parameters, a holding period and a confidence level, and is used for internal limits, regulatory capital and risk reporting. VaR says nothing about the size of losses beyond the threshold.
Calculation methods
Three approaches are common, and they can produce materially different numbers on the same portfolio.
- Historical simulation revalues the current portfolio against actual past market moves, making no distributional assumption.
- Variance-covariance assumes returns are normally distributed and scales a standard deviation by a confidence factor.
- Monte Carlo simulation generates many hypothetical price paths from a chosen model and takes the relevant percentile of the resulting profit-and-loss distribution.
Confidence levels and holding periods are conventions that vary by firm, regulator and instrument; a 95% one-day figure and a 99% ten-day figure are not comparable without conversion.
Worked example
The interpretation is that on roughly one trading day in twenty, losses are expected to exceed $19,740 if market conditions remain within the model's assumptions. The figure is silent on how far beyond that threshold a loss might run.
Limitations
VaR is a quantile, not a worst case. It does not describe the tail beyond the confidence level, so two portfolios with identical VaR can have very different extreme-loss profiles; expected shortfall is often reported alongside it for that reason. The measure also relies on historical data and distributional assumptions that can understate risk when correlations shift or markets become illiquid, and it can be gamed by positions whose risks are not captured in the model's inputs.
Often confused with
- forex risk
- Forex risk is the exposure of a position or firm to adverse movements in currency exchange rates, which may or may not be the dominant driver of a given VaR figure; the visible sign is whether the loss estimate changes when only FX rates are shocked.
- correlation risk
- Correlation risk is the danger that the historical relationships between assets used in a VaR model break down, causing diversification benefits to vanish; the visible sign is a VaR estimate that rises sharply when assumed correlations are set to one.
- gap risk
- Gap risk is the possibility that a price jumps discontinuously between trades, so no execution is possible at the level implied by a continuous model; the visible sign is a realised loss that exceeds the VaR threshold without any intermediate prices being traded.