What is Value at Risk (VaR)?

Value at Risk (VaR) is a statistical measure that quantifies the potential loss of an investment or portfolio over a specific time period, given a certain confidence level. It answers the question: "What's the worst loss I can expect with X% confidence over Y days?"

How VaR Works

VaR is expressed as a dollar amount or percentage and consists of three components:
- Time horizon (e.g., 1 day, 10 days, 1 month)
- Confidence level (e.g., 95%, 99%)
- The potential loss amount

For example, a 1-day 95% VaR of $10,000 means: "There's a 95% chance that the portfolio won't lose more than $10,000 tomorrow."

VaR Calculation Methods

1. Historical Simulation
   - Uses historical price data to simulate potential losses
   - Simple but assumes past patterns will repeat
   - No distribution assumptions required

2. Parametric (Normal Distribution)
   - Assumes returns follow a normal distribution
   - Faster to calculate but may underestimate tail risks
   - Formula: VaR = μ - (Z × σ × √t)

3. Monte Carlo Simulation
   - Generates thousands of random scenarios
   - Most flexible but computationally intensive
   - Can model complex portfolios and dependencies

VaR Limitations

Critical weaknesses every trader should understand:

1. Tail Risk Blindness
   VaR tells you nothing about losses beyond the confidence level. A 99% VaR ignores the catastrophic 1% of scenarios.

2. Model Risk
   VaR is only as good as its underlying assumptions. Black swan events regularly violate these assumptions.

3. False Security
   VaR can create overconfidence. Just because you have a 95% VaR doesn't mean the other 5% won't bankrupt you.

4. Non-Additive
   Portfolio VaR ≠ Sum of individual position VaRs due to correlations and diversification effects.

Practical Applications

Risk Management:
- Set position sizing limits
- Determine portfolio exposure
- Stress test strategies
- Regulatory compliance (Basel III)

Trading Applications:
- Stop-loss level setting
- Capital allocation decisions
- Performance attribution
- Risk-adjusted returns calculation

VaR vs Other Risk Metrics

Expected Shortfall (ES):
- Measures average loss beyond VaR threshold
- Better for tail risk assessment
- More coherent risk measure

Maximum Drawdown:
- Historical worst peak-to-trough loss
- Backward-looking vs VaR's forward-looking nature
- Useful for understanding pain tolerance

Standard Deviation:
- Measures total volatility (up and down)
- VaR focuses only on downside risk
- Complementary metrics

Common VaR Mistakes

1. Over-reliance on historical data
2. Ignoring regime changes and structural breaks
3. Using inappropriate time horizons
4. Misunderstanding confidence intervals
5. Failing to backtest VaR models

Industry Standards

Typical confidence levels:
- 95% for internal risk management
- 99% for regulatory capital requirements
- 99.9% for extreme stress testing

Time horizons:
- 1-day for active trading
- 10-day for regulatory purposes
- Monthly/quarterly for strategic allocation

The MarketWizardry VaR Explorer

Our VaR calculator implements multiple methodologies and provides:
- Historical simulation with customizable lookback periods
- Parametric VaR with distribution fitting
- Portfolio-level risk aggregation
- Stress testing scenarios
- Risk decomposition by asset class

Try our free VaR Explorer tool: https://marketwizardry.org/var-explorer.html

Related Reading:
- What is Average True Range (ATR)? https://marketwizardry.org/blog/what-is-average-true-range-atr.html
- Understanding IQR Analysis: https://marketwizardry.org/blog/understanding-iqr-analysis.html
- VaR Rubber Band Effect on Darwinex: https://marketwizardry.org/blog/var-rubber-band-effect-darwinex.html

Remember: VaR is a tool, not a crystal ball. It provides estimates based on historical patterns and mathematical models. In volatile markets, these patterns can break down spectacularly.

The goal isn't to predict the future perfectly—it's to quantify uncertainty so you can make informed decisions about how much risk you're willing to accept for potential returns.

Use VaR as one input among many in your risk management framework. Combine it with stress testing, scenario analysis, and good old-fashioned common sense.

Because in the end, the market doesn't care about your VaR calculations when it decides to have a nervous breakdown.