Value-at-Risk (VaR) Estimator

Understanding Value at Risk (VaR)

Value at Risk (VaR) is a statistical technique used to measure and quantify the level of financial risk within a firm, portfolio, or position over a specific timeframe. This metric is most commonly used by investment and commercial banks to determine the extent and occurrence ratio of potential losses in their institutional portfolios.

The standard mathematical formula for parametric VaR is:
VaR = Portfolio Value × Z-Score × Volatility × √(Time Horizon / 252)

In this formula, the Z-Score corresponds to your chosen confidence level (e.g., 1.645 for 95% confidence). The Volatility is the annualized standard deviation of the portfolio's returns. The Time Horizon represents the number of days over which the risk is being assessed, adjusted by the trading days in a year (typically 252).

Essentially, if a portfolio has a 10-day 95% VaR of $100,000, it means that there is a 95% confidence that the portfolio will not lose more than $100,000 in a 10-day period. Conversely, there is a 5% chance that losses will exceed this amount. The interactive area chart above visually approximates this concept using a normal distribution curve, highlighting the "tail risk" zone that falls below the VaR threshold.

While VaR is incredibly useful for standard risk assessment, it does not predict the maximum possible loss during extreme black swan events. To complement VaR, consider looking at historical drawdowns with our Max Drawdown Calculator or assess collateral requirements via the Over-Collateralization Ratio Calculator.