Value at Risk (VaR): A Comprehensive Guide
Everything you need to know about VaR — parametric, historical simulation, Monte Carlo, backtesting, Expected Shortfall, and the strengths and weaknesses of each approach.
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Loss Tail Versus Expected Loss
Valuation and risk-model questions often hinge on the difference between a normal day and a stressed tail outcome.
Why it matters
Value at Risk gives a cutoff; expected shortfall tells you what happens after the cutoff is breached.
Value at Risk (VaR): A Comprehensive Guide
What Is VaR?
Value at Risk is a statistical measure that estimates the maximum potential loss on a portfolio over a specified time period, at a given confidence level.
Definition: "The VaR at the X% confidence level is the loss that will be exceeded only (100−X)% of the time."
Example: A 10-day 99% VaR of $5 million means: "There is a 1% probability that the portfolio will lose more than $5 million over the next 10 trading days."
VaR Has Three Parameters
- Confidence level (typically 95% or 99%)
- Time horizon (1 day, 10 days, etc.)
- The portfolio being measured
Why VaR Became Standard
- Single number summarizing risk — easy for executives and boards to understand
- Comparable across asset classes and business units
- Required by regulators (Basel framework uses VaR for market risk capital)
- Can be aggregated across portfolios (with correlation assumptions)
Parametric (Variance-Covariance) VaR
The simplest approach. Assumes portfolio returns are normally distributed.
Formula
VaR = z_α × σ_P × √T
Where:
- z_α = standard normal quantile at confidence level α (e.g., 2.326 for
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