- Global Frameworks: Basel III Market Risk Standards, GARP FRM Part 1 (Valuation and Risk Models).
1. Defining Value-at-Risk (VaR) Parameters
Value-at-Risk (VaR) is a standard statistical metric that quantifies the maximum potential financial loss an investment portfolio could suffer over a specified time horizon within a given confidence level under normal market conditions.
- Statement Example: “A portfolio’s 1-day VaR is $2.5 million at a 95% confidence level.” This means there is a 95% probability that the portfolio’s losses will not exceed $2.5 million over a single day, and a 5% probability that losses will be worse than $2.5 million.
2. Methodologies for Calculating VaR
Risk managers use three primary methods to estimate VaR:
- The Parametric (Variance-Covariance) Method: Assumes asset returns follow a standard normal distribution. VaR is calculated using the portfolio’s expected return (μ), standard deviation (σ), and the Z-score for the target confidence level:
VaR = −[μ − (Z × σ)] × Portfolio Value
- Flaw: Fails to account for “fat-tail” events or non-linear instruments like options, which do not follow a standard normal distribution.
- Historical Simulation Method: Re-prices the current portfolio using actual historical market price changes over a set historical window (e.g., the past 1,000 days). These simulated returns are ranked from worst to best, and the target percentile identifies the VaR limit. This method naturally accounts for real-world market distributions without assuming a normal curve.
- Monte Carlo Simulation Method: Uses algorithms to generate thousands of random future asset price paths based on specified statistical parameters. This method is highly flexible and excels at pricing complex, non-linear portfolios, but requires significant computational power.
3. Supplementary Risk Tools: Expected Shortfall (ES)
Because VaR only identifies the boundary where tail losses begin, it cannot measure how severe losses might be once that boundary is breached. To address this limitation, Basel III frameworks require institutions to use Expected Shortfall (ES)—also known as Conditional VaR. Expected Shortfall measures the average loss that occurs within the worst-case tail of the distribution (e.g., the average loss across the worst 5% of outcomes).
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