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Risk Measurement and Management (VaR): Quantifying Worst-Case Scenarios
Risk Measurement: How Much Can You Lose?
Risk management in financial markets is not just about saying something is “dangerous”; it’s the process of answering “Exactly how much can we lose?” with a numerical value. The most widely used metric for this is Value at Risk (VaR).
1. Definition and Three Elements of VaR
VaR represents the maximum loss amount that can occur over a specific holding period under normal market conditions, given a certain confidence level.
- Holding Period: The time unit for measuring risk (e.g., 1 day, 10 days).
- Confidence Level: The statistical degree of certainty (e.g., 95%, 99%).
- Maximum Loss: The threshold within that probability range.
Note
Saying “the 1-day 99% VaR is 1 million over the course of a single day.
2. Visualizing VaR: Probability Distribution and Thresholds
The chart below shows where VaR is located on a return distribution. The ‘tail’ area on the far left represents the loss interval we must be wary of.
Return Distribution and 95% VaR Threshold
The red bar area on the left represents extreme loss scenarios with a probability of 5% or less.
3. Three Methods to Calculate VaR
Financial institutions choose different calculation methods based on the nature of their data.
Comparison of VaR Calculation Methodologies
| Methodology | Key Characteristics | Pros | Cons |
|---|---|---|---|
| Historical Simulation | Uses historical return data directly | Easy to calculate, no distribution assumptions needed | Past performance does not guarantee future results |
| Delta-Normal Method | Uses normal distribution and sensitivity (Δ) | Very fast calculation speed | Weak for measuring non-linear products (options) |
| Monte Carlo | Generates tens of thousands of random scenarios | Most accurate, handles complex products | Requires significant calculation time |
💡 Professor’s Tip
VaR is an excellent tool, but its limitations are clear. VaR only tells you the threshold (2M? $10M?)** the loss could be once you enter that 1% tail. To supplement this, we often use ‘Expected Shortfall (ES)’ alongside VaR.