Value at Risk (VaR)
Value at Risk (Historical, Parametric, Monte Carlo) · Also known as: VaR, value-at-risk, delta-normal VaR, historical simulation VaR, Riske Maruz Değer (VaR — Historical, Parametric, MC)
Value at Risk is a financial risk measure that estimates the maximum loss a position or portfolio could suffer over a fixed holding period at a given confidence level. It is the standard benchmark in risk management and regulatory capital calculations, developed in the textbook tradition of Jorion (2007) and the Basel market-risk framework.
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When to use it
Use VaR when you hold a continuous-valued financial position over time and need a single, interpretable summary of downside risk for risk management or capital requirements. It needs a reasonable history of returns — at least about 100 observations, and ideally 250 or more — and the series should be stationary. The parametric form is quick but assumes normality and so understates tail risk; historical and Monte Carlo forms relax that. VaR is unreliable on short data histories and on non-stationary series, where differencing or a simpler volatility measure is preferable.
Strengths & limitations
- Produces a single, intuitive number — the threshold loss at a stated confidence level and horizon — that managers and regulators readily understand.
- Offers three complementary estimation routes (historical, parametric delta-normal, Monte Carlo) so the assumptions can be matched to the data.
- Is the established standard in market-risk management and Basel regulatory capital calculations.
- VaR is not sub-additive: the VaR of a combined portfolio can exceed the sum of the parts, so it is not a coherent risk measure — CVaR (expected shortfall) is the coherent alternative.
- It says nothing about the size of losses beyond the threshold, hiding tail severity.
- The parametric (normal) form systematically understates tail risk; estimates are unreliable on short histories (n < 250) and non-stationary series.
Frequently asked
What is the difference between historical, parametric, and Monte Carlo VaR?
Historical simulation reads the loss quantile directly from past returns and makes no distributional assumption. Parametric (delta-normal) VaR assumes returns are normal and uses the mean and standard deviation, which is fast but understates fat tails. Monte Carlo simulates many return paths from a model and takes the tail quantile, flexibly handling complex positions at higher computational cost.
Why is VaR not a coherent risk measure?
A coherent measure must be sub-additive — diversifying should never increase measured risk. VaR can violate this: the VaR of a combined portfolio can exceed the sum of the individual VaRs. Conditional Value at Risk (CVaR / expected shortfall) is sub-additive and therefore coherent.
How much data do I need to estimate VaR?
At least about 100 return observations, and ideally 250 or more. On shorter histories the tail quantile is unstable and a simpler realized-volatility measure is preferable.
What is backtesting and why does it matter?
Backtesting checks how often realised losses actually breach the estimated VaR over time. If breaches occur far more or far less often than the confidence level implies, the model is miscalibrated. Backtesting is what validates a VaR model before it is trusted.
Sources
- Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk (3rd ed.). McGraw-Hill. ISBN: 978-0071464956
- Basel Committee on Banking Supervision (2019). Minimum Capital Requirements for Market Risk. Bank for International Settlements. link ↗
How to cite this page
ScholarGate. (2026, June 1). Value at Risk (Historical, Parametric, Monte Carlo). ScholarGate. https://scholargate.app/en/finance/value-at-risk
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- ARIMAEconometrics↔ compare
- Conditional Value-at-RiskFinance↔ compare
- GARCHEconometrics↔ compare
- MONTE-CARLO-SIMULATIONDecision-making↔ compare
- Realized VolatilityFinance↔ compare