Value at Risk — Smart Financial Analysis
Calculate potential portfolio losses at 95% or 99% confidence using the parametric VaR formula.
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Parametric VaR uses the formula: VaR = Portfolio × Z-score × σ × √t. 95% is common for internal reporting and daily risk monitoring. VaR does not measure the severity of losses beyond the threshold (tail risk). Banks use VaR for regulatory capital (Basel III).
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Why: Value at Risk (VaR) is a statistical measure that estimates the maximum potential loss of a portfolio over a given time horizon at a specified confidence level. For example, a 9...
How: Enter Portfolio Value, Annual Volatility (%), Confidence Level to get instant results. Try the preset examples to see how different scenarios affect the outcome, then adjust to match your situation.
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📊 VaR at 95% / 99% / 99.9%
Risk comparison by confidence level
🍩 At-Risk vs Safe Portion
Portfolio composition by VaR
📈 VaR by Confidence Level
Line chart across confidence levels
📊 VaR by Time Horizon
1 / 5 / 10 / 30 day horizons
Value at Risk (VaR)
With 95% confidence, maximum loss over 1 day(s) will not exceed $15,544, which is 1.55% of portfolio value.
For educational purposes only — not financial advice. Consult a qualified advisor before making decisions.
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Value at Risk (VaR) estimates the maximum potential loss of a portfolio over a given time horizon at a specified confidence level. The parametric formula is VaR = P × Z × σ × √t, where P is portfolio value, Z is the Z-score (95% = 1.645, 99% = 2.326), σ is volatility, and t is the time horizon. Basel III requires banks to report VaR for regulatory capital. JP Morgan RiskMetrics popularized VaR in the 1990s.
Sources: Basel Committee, CFA Institute, JP Morgan RiskMetrics.
Key Takeaways
- • VaR answers: "What is the maximum loss I could face with X% confidence?"
- • Higher confidence (99% vs 95%) yields larger VaR estimates.
- • Longer time horizons increase VaR via the √t scaling factor.
- • VaR assumes normal distribution; fat tails can cause underestimation.
Did You Know?
How Does VaR Work?
Parametric (Variance-Covariance) Method
Assumes returns follow a normal distribution. VaR = P × Z × σ × √t. Fast and simple but underestimates tail risk.
Historical Simulation
Uses actual historical returns to build a distribution. No distribution assumption but past may not predict future.
Monte Carlo Simulation
Runs thousands of random scenarios. Flexible for complex portfolios but computationally intensive.
Expert Tips
VaR by Confidence Level
| Confidence | Z-Score | Interpretation |
|---|---|---|
| 90% | 1.282 | 10% chance of exceeding VaR |
| 95% | 1.645 | 5% chance of exceeding VaR |
| 99% | 2.326 | 1% chance of exceeding VaR (Basel) |
| 99.9% | 3.09 | 0.1% chance of exceeding VaR |
Frequently Asked Questions
What is Value at Risk?
Value at Risk (VaR) is a statistical measure that estimates the maximum potential loss of a portfolio over a given time horizon at a specified confidence level. For example, a 95% 1-day VaR of $25,000 means there is a 5% chance losses could exceed $25,000 in one day. VaR is widely used by banks, hedge funds, and regulators for risk management.
How is VaR calculated?
Parametric VaR uses the formula: VaR = Portfolio × Z-score × σ × √t. Z-scores map confidence levels (95% = 1.645, 99% = 2.326). σ is the portfolio standard deviation (volatility). t is the time horizon in days. Annual volatility is converted to daily by dividing by √252 (trading days).
What confidence level should I use?
95% is common for internal reporting and daily risk monitoring. 99% is required by Basel III for regulatory capital. 99.9% captures extreme tail risk. Higher confidence = larger VaR estimate but more conservative. Most institutions use 95% or 99% depending on regulatory requirements.
VaR limitations?
VaR does not measure the severity of losses beyond the threshold (tail risk). It assumes normal distribution, which underestimates fat tails. VaR is not sub-additive (portfolio VaR can exceed sum of component VaRs). It also fails during market stress when correlations break down. Use CVaR and stress testing alongside VaR.
VaR vs CVaR?
VaR answers: "What is the maximum loss at confidence level X?" CVaR (Conditional VaR, or Expected Shortfall) answers: "What is the average loss when we exceed VaR?" CVaR captures tail risk severity. Basel III now prefers CVaR for some risk metrics because it is coherent and sub-additive.
Who uses VaR?
Banks use VaR for regulatory capital (Basel III). Hedge funds and asset managers use it for position limits and risk reporting. Corporate treasuries use it for FX and commodity exposure. Regulators require VaR for market risk. JP Morgan popularized VaR in the 1990s with RiskMetrics.
Key Statistics
Official Data Sources
⚠️ Disclaimer: This calculator is for educational purposes only. Parametric VaR assumes normal distribution and may underestimate tail risk. Professional risk management requires additional methods (historical, Monte Carlo, stress testing). Not financial advice.
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