Value at Risk (VaR) is one of the most widely used risk metrics in finance. It answers a simple question: "What is the worst loss I can expect under normal market conditions?" While institutions have used VaR for decades, individual traders can also benefit from understanding and applying this concept.
What is Value at Risk?
VaR is a statistical measure that quantifies the maximum expected loss over a given time period at a specified confidence level.
Example VaR statement: "Our 1-day 95% VaR is $10,000."
This means: "We are 95% confident that we will not lose more than $10,000 in a single day."
Or equivalently: "On 5% of days (about 1 in 20), we could lose more than $10,000."
The Three Components of VaR
Every VaR measure has three parts:
- Time horizon: Usually 1 day or 10 days (longer for less liquid positions)
- Confidence level: Usually 95% or 99%
- Loss amount: The dollar (or percentage) value at risk
Interpreting VaR
- 1-day 95% VaR of $5,000: About once every 20 trading days, losses could exceed $5,000
- 1-day 99% VaR of $5,000: About once every 100 trading days, losses could exceed $5,000
- 10-day 95% VaR of $15,000: About once every 20 10-day periods, losses could exceed $15,000
Methods for Calculating VaR
1. Historical VaR
The simplest approach: look at what actually happened.
- Collect historical daily returns (e.g., last 252 trading days)
- Sort returns from worst to best
- For 95% VaR, find the 5th percentile worst return
- Multiply by current portfolio value
Historical VaR Example
Portfolio: $100,000. You have 250 days of returns.
- Sort all 250 daily returns
- 95% VaR = 13th worst day (250 x 5% = 12.5, round up)
- If 13th worst return was -2.3%
- 1-day 95% VaR = $100,000 x 2.3% = $2,300
2. Parametric (Variance-Covariance) VaR
Assumes returns follow a normal distribution:
- Calculate portfolio mean and standard deviation
- Use z-scores for confidence level (1.65 for 95%, 2.33 for 99%)
- VaR = Portfolio Value x z-score x Standard Deviation
Parametric VaR Example
- Portfolio: $100,000
- Daily standard deviation: 1.5%
- For 95% confidence, z-score = 1.65
- 1-day 95% VaR = $100,000 x 1.65 x 1.5% = $2,475
3. Monte Carlo VaR
Simulates thousands of possible scenarios:
- Define probability distributions for each asset
- Run thousands of simulations
- Calculate portfolio value for each simulation
- Find the 5th percentile of outcomes
More complex but handles non-normal distributions and complex portfolios.
VaR for a Stock Portfolio
For a portfolio of stocks, you need to account for correlations:
Two-Stock Portfolio VaR
$50,000 in Stock A (daily volatility 2%), $50,000 in Stock B (daily volatility 3%), correlation 0.5
- Portfolio variance = w1^2var1 + w2^2var2 + 2w1w2corrstd1*std2
- = 0.5^2*(0.02)^2 + 0.5^2*(0.03)^2 + 20.50.50.50.02*0.03
- = 0.0001 + 0.000225 + 0.00015 = 0.000475
- Portfolio std dev = sqrt(0.000475) = 2.18%
- 95% VaR = $100,000 x 1.65 x 2.18% = $3,597
VaR for Options Positions
Options require special treatment because their payoffs are non-linear:
- Delta-normal VaR uses delta to approximate option behavior
- Full revaluation simulates option prices at different underlying levels
- Monte Carlo is often used for complex options portfolios
Using VaR in Practice
Setting Position Limits
Use VaR to limit positions:
- Set a maximum 1-day 95% VaR (e.g., 5% of account)
- Size positions to stay within VaR limits
- Reduce positions when VaR exceeds limits
Comparing Risk Across Strategies
VaR lets you compare apples to apples:
- Strategy A has VaR of $5,000
- Strategy B has VaR of $8,000
- Strategy B is riskier (though may have higher return)
Risk Budgeting
Allocate VaR across strategies:
- Total VaR budget: $10,000
- Strategy 1 gets $4,000 VaR allocation
- Strategy 2 gets $3,000 VaR allocation
- Strategy 3 gets $3,000 VaR allocation
Limitations of VaR
VaR is useful but has serious limitations:
1. VaR Says Nothing About Tail Losses
95% VaR tells you the 5% threshold, not what happens beyond it. You could lose $10,000 or $100,000 - VaR does not distinguish.
2. VaR Assumes Normal Markets
VaR uses historical data from normal periods. During crises, correlations spike and volatility explodes, making VaR estimates too optimistic.
3. False Precision
A VaR of $4,723 sounds precise, but it is just an estimate with significant uncertainty.
4. VaR Can Be Gamed
Traders can construct portfolios that look safe by VaR but have hidden risks (e.g., selling far OTM options).
Important: VaR tells you what to expect under normal conditions. It does not protect you from crashes. Use Expected Shortfall (CVaR) for tail risk awareness.
VaR Calculation Example for Traders
Here is a simplified approach for individual traders:
Quick Historical VaR Method
- Export your daily P&L for the last 100+ days
- Sort from worst to best
- For 95% VaR: Look at the 5th worst day
- That P&L is approximately your daily VaR
If your 5th worst day was -$2,500 and portfolio is $100,000:
Your 1-day 95% VaR is approximately 2.5%
Track Your Daily P&L
Pro Trader Dashboard automatically tracks your daily profit and loss, giving you the data you need to calculate VaR and understand your risk exposure over time.
VaR vs Other Risk Measures
- Standard Deviation: Measures volatility, not worst-case loss
- Maximum Drawdown: Historical worst peak-to-trough, backward-looking
- Expected Shortfall (CVaR): Average loss beyond VaR, better for tail risk
- VaR: Threshold loss at confidence level, widely used but ignores tails
Summary
Value at Risk provides a standardized way to measure portfolio risk. It answers "how much could I lose on a normal bad day?" Use it for position sizing, risk limits, and comparing strategies. But remember its limitations - VaR does not protect you from extreme events. Complement VaR with Expected Shortfall and stress testing for a complete risk picture.
Learn about Expected Shortfall (CVaR) for tail-aware risk measurement or explore tail risk management for protecting against extreme events.