Value at Risk (VaR)

What it is

Value at Risk states a loss threshold and a probability over a horizon. A one-day 99 percent VaR of two million dollars means that on 99 days out of 100 the loss is expected to be smaller than two million. It became the standard portfolio risk summary because it compresses an entire book into one number expressed in currency.

How it works

There are three standard estimation methods. Historical simulation reprices the current portfolio across past return windows and reads the relevant percentile directly. The parametric or variance-covariance approach assumes a distribution, usually normal, and derives the quantile from the portfolio's volatility. Monte Carlo simulates return paths from a specified model. Horizons are often scaled by the square root of time, which is valid only under independent, identically distributed returns.

How traders use it

It is used to set desk limits, allocate risk budgets, satisfy regulatory reporting and compare exposure across otherwise incomparable positions. Its companion measure, Expected Shortfall or CVaR, averages the losses in the tail beyond the VaR threshold and is now preferred by regulators precisely because it describes the severity of the bad cases rather than only their frequency.

Where it breaks down

The well-known criticism is that VaR says nothing about how bad the remaining one percent is, so two portfolios with identical VaR can have wildly different tails. It is also not sub-additive in general, meaning a combined portfolio can report more VaR than the sum of its parts and diversification can look like it increases risk. Normal-distribution versions badly understate fat tails, and every version is estimated from a historical window that may not contain the relevant scenario. Validate it by counting exceptions against expectations, and never present it as a worst case.