1. Defining Value at Risk (VaR)
Value at Risk (VaR) is a foundational quantitative risk metric that estimates the maximum potential financial loss an investment portfolio or corporation could incur over a specified time horizon at a given statistical confidence level under normal market conditions.
  • Standard Expression Statement: “The firm’s 1-day VaR is €2.5 Million at a 95% Confidence Level.” This means there is a 95% mathematical probability that the firm’s losses tomorrow will not exceed €2.5 Million, and a 5% probability that losses will be worse than €2.5 Million.

2. The Three Primary Methodologies for Computing VaR
  • The Parametric (Variance-Covariance) Method: Assumes that financial asset returns follow a normal statistical distribution. VaR is calculated using the mean return (μ), standard deviation (σ), and a standardized Z-score matching the target confidence level:
    \(\text{VaR}=\left[\text{Portfolio\ Value}\times \left(Z_{\alpha }\times \sigma -\mu \right)\right]\)
  • Historical Simulation Method: Relies on real historical data. The analyst takes actual price movements over the last 500 days, applies those percentage changes to the current portfolio, ranks the resulting profits and losses chronologically, and identifies the target percentile cutoff point. It makes no assumptions about normal distributions.
  • Monte Carlo Simulation Method: The most computationally advanced approach. A computer algorithm runs thousands of automated trials using random variables derived from defined probability distributions to model potential future portfolio values.

3. Structural Limitations of VaR and Expected Shortfall (ES)
While VaR is an effective high-level risk communication metric, it features a critical blind spot: it completely ignores tail risk. VaR indicates the threshold where a 5% worst-case scenario begins, but it fails to quantify how severe the losses could be within that 5% distribution tail.
To resolve this limitation, regulators (such as European Basel capital frameworks) mandate Expected Shortfall (ES)—also known as Conditional VaR—which calculates the mathematical average of all losses that occur beyond the VaR cutoff point.
 
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