Value at Risk (VaR) is one of the most important concepts in the FRM exam and in risk management practice. This guide covers everything you need to know about VaR for both Parts 1 and 2.

What Is VaR?

Value at Risk answers: "What is the maximum loss over a given time period at a specified confidence level?"

For example, a 1-day 99% VaR of $10 million means there is a 1% probability of losing more than $10 million in a single day.

Three Key Parameters

  1. Confidence Level: Typically 95% or 99%
  2. Time Horizon: Usually 1-day (trading) or 10-day (regulatory)
  3. Loss Amount: In dollar terms or as a percentage

VaR Calculation Methods

1. Parametric (Variance-Covariance) Method

  • Assumes normally distributed returns
  • VaR = μ - z_α × σ × √T
  • Fast and simple but fails for non-normal distributions and non-linear positions

2. Historical Simulation

  • Uses actual historical returns to build a loss distribution
  • No distributional assumptions needed
  • Limited by the historical period chosen (may miss extreme events)

3. Monte Carlo Simulation

  • Generates thousands of random scenarios based on specified models
  • Most flexible — can handle any distribution and non-linear payoffs
  • Most computationally intensive

VaR Limitations

VaR has well-known shortcomings:

  • Does NOT tell you how much you could lose beyond VaR (use Expected Shortfall for this)
  • Not subadditive — portfolio VaR can exceed the sum of individual VaRs
  • Highly sensitive to assumptions (distribution, correlation, time period)
  • Can give false sense of security

Expected Shortfall (ES) vs VaR

Expected Shortfall (also called CVaR) measures the average loss in the tail beyond VaR. It is a coherent risk measure (unlike VaR) and has been adopted as the primary market risk measure under FRTB.

Backtesting VaR

Comparing VaR predictions with actual P&L outcomes is essential for model validation:

  • Kupiec Test: Tests whether the number of exceptions is consistent with the confidence level
  • Christoffersen Test: Tests for independence of exceptions (no clustering)
  • Basel Traffic Light: Green (0-4 exceptions/250 days), Yellow (5-9), Red (10+)

Practice with our VaR questions to master this critical topic!