Value at Risk (VaR)
1. Definition
Value at Risk (VaR) is a statistical risk measure that estimates the maximum potential loss in the value of a portfolio over a specific time horizon at a given confidence level.
Example: “1-day VaR of $2.5 million at 95% confidence” means there is a 5% chance the portfolio will lose more than $2.5 million in a single day.
2. Where to use VaR
- Banks & Financial Institutions – trading book risk, capital requirements.
- Investment Funds – portfolio risk reporting to investors.
- Corporate Risk Management – FX, commodities, interest rate exposures.
- Regulators (Basel, RBI, SEC) – capital adequacy norms.
3. Assumptions
- Returns follow a normal distribution.
- Markets remain stable (no extreme shocks).
- Past price data represents future risks.
- Short time horizon (usually 1–10 days).
4. Numerical Example
Portfolio Value = $100 million
Daily Volatility (σ) = 2% = $2 million
Confidence Level = 95% (Z = 1.65)
VaR = Z × Ïƒ × Portfolio Value
VaR = 1.65 × 2,000,000 = $3.3 million
Interpretation: With 95% confidence, the maximum 1-day loss will not exceed $3.3 million. There is a 5% chance the loss could be higher.
5. What VaR Tells Us
- Maximum loss at a chosen confidence level and horizon.
- Comparable single number to express risk.
- Useful for capital reserve estimation.
6. What VaR Does Not Tell Us
- Does not measure losses beyond the confidence interval.
- Ignores tail risk (extreme crisis events).
- Heavily dependent on historical data.
7. Pros
- Simple and intuitive – one number.
- Standardized across institutions.
- Flexible across assets and time horizons.
- Regulatory acceptance (Basel norms).
8. Cons
- Ignores extreme tail events.
- Assumes normal distribution (often unrealistic).
- Relies on historical data (backward-looking).
- Not additive across portfolios.
Quick Recap:
VaR = “At X% confidence, maximum loss over Y horizon is Z.”
✅ Good for: risk measurement, reporting, regulation.
❌ Weak in: crises, tail risk, systemic shocks.
VaR = “At X% confidence, maximum loss over Y horizon is Z.”
✅ Good for: risk measurement, reporting, regulation.
❌ Weak in: crises, tail risk, systemic shocks.