VaR is a threshold for a specified horizon and distribution

VaR is a quantile of a loss distribution at a specified horizon and confidence level. A one-day 99% VaR means the modeled tail probability of exceeding that threshold is about 1%. It is not maximum possible loss, average daily loss, or exactly one event every 100 days. Comparing numbers with different horizons or confidence levels can mislead.

Calculate a simple normal example

Illustrative portfolio value:1,000,000 units; mean daily return 0; daily volatility 1%; linear profit and loss with a normal distribution. Using the 99% z-score≈2.32635 gives one-day VaR =1,000,000×0.01×2.32635≈23,263.50 units. Zero assumed mean removes a drift term. This is not a loss cap.

If the same holdings respond linearly to a specified −5% shock, the scenario loss is 50,000. It answers a different question from 99% VaR; it establishes neither the probability of that shock nor maximum future loss. With options, FX or spread exposure, reprice under the scenario instead of relying on simple multiplication.

Distinguish estimation methods from tail-loss measures

A linear-normal variance-covariance approximation is fast but can miss nonlinear payoffs and fat tails. Historical simulation depends on its sample and does not automatically include unobserved shocks. Monte Carlo depends on the generated distribution and pricing model; random draws alone do not ensure realism.

Expected Shortfall(ES) measures average loss in a selected tail region and supplements VaR's threshold. The Basel Committee's explanation of its 2019 market-risk standard describes ES in the internal-model approach for bank trading books. That is the scope of an international standard, not a statement of every country's effective date or a common rule for personal accounts.

Check the date and scope of supervisory guidance

As checked on October12,2026, the Federal Reserve FRRS guidance dated April 17,2026, SR-26-2 addresses model development, validation, monitoring and governance. Do not cite the earlier SR 11-7 alone as current guidance. This is U.S. banking model-risk guidance, not a guarantee of VaR forecasts.

Record valuation date, currency, horizon, confidence, data window and repricing method. Compare actual P&L with the frequency and size of exceedances. Stress results need their assumed shocks recorded alongside them. Verifying arithmetic does not establish that inputs and models remain suitable in the future.