VaR

Value at Risk (VaR) is a statistical measure used in finance to estimate the potential loss on a portfolio over a specified time horizon with a given confidence level. For example, a 1-day VaR at 99% confidence might indicate that there is a 1% chance the portfolio could lose more than a certain amount in one day. VaR is widely used in risk management, governance, and capital allocation to summarize downside risk in a single number.

VaR can be estimated using several methods. Historical simulation uses past market moves to construct the loss distribution; variance-covariance (or parametric) methods rely on assuming a distribution, typically normal, and computing VaR from the portfolio’s mean and standard deviation; Monte Carlo simulation generates many hypothetical scenarios to model potential losses. VaR can be reported for a single asset, a portfolio, and across different horizons (commonly 1 day or 10 days) and confidence levels (such as 95% or 99%). It is often backtested by comparing forecast VaR to actual losses to assess accuracy.

Limitations of VaR include that it does not quantify losses beyond the VaR threshold, is not a coherent risk measure in all cases, and can be sensitive to model, data, and assumptions. It may understate risk in extreme events or fail to capture diversification effects if not calculated correctly. As a result, many institutions supplement VaR with other measures such as Expected Shortfall (CVaR) and stress testing. Regulatory frameworks have historically used VaR for market risk, though some areas now emphasize tail-risk measures like Expected Shortfall.