Value at Risk (VaR)
A statistical measure that estimates the maximum potential loss of a portfolio over a given time period at a specified confidence level. VaR answers the question: "What's the worst I should expect to lose?"
Quick Summary
- Formula: VaR = Portfolio Value x z-score x σ x √t (parametric method)
- Measures: Maximum expected loss at a given confidence level over a time period
- Key numbers: "95% daily VaR of $5,000" means: 95% of the time, daily losses won't exceed $5,000
- Key insight: VaR doesn't tell you what happens in the worst 5% — that's where Conditional VaR comes in
What Is Value at Risk?
VaR became the industry standard risk measure after JP Morgan published its RiskMetrics framework in the 1990s. Banks, hedge funds, and regulators use it daily to quantify market risk. In plain English: if you have a 95% daily VaR of $5,000, it means on 19 out of 20 trading days, your portfolio's loss will not exceed $5,000. On that 20th day (the 5% tail), losses could be anything — $6,000, $20,000, or more. This is both VaR's strength (simple, intuitive) and its limitation (it doesn't describe tail risk).
VaR has three components: a confidence level (typically 95% or 99%), a time horizon (1 day, 1 week, 1 month), and the loss amount in dollars or percentage.
VaR relies on the concept of standard deviation to quantify how returns vary, and complements backward-looking measures like maximum drawdown by providing a forward-looking estimate of potential losses.
How to Calculate VaR: Three Methods
Method 1: Historical VaR
The simplest approach — use actual past returns to estimate future risk:
Step 1: Collect actual past returns (e.g., 500 daily returns)
Step 2: Sort from worst to best
Step 3: At 95% confidence, VaR = the 25th worst return (5% of 500)
Example: $100K portfolio, sorted returns, 25th worst day was -2.1%, so 95% daily VaR = $2,100
Pro: No distribution assumptions. Con: Assumes the past repeats.
Method 2: Parametric (Variance-Covariance) VaR
Where z = 1.65 for 95% confidence, 2.33 for 99%, σ is the portfolio standard deviation, and t is the time period in days.
Example: $100K portfolio, daily σ = 1.2%
95% 1-day VaR = $100,000 x 1.65 x 0.012 = $1,980
Scale to other periods: multiply by √t
10-day VaR = $1,980 x √10 = $6,261
Pro: Fast, easy to compute. Con: Assumes normal distribution (underestimates tail risk).
Method 3: Monte Carlo VaR
The most flexible approach — simulate thousands of possible futures:
Step 1: Simulate thousands (10,000+) of possible future return scenarios
Step 2: Use historical volatility and correlations as inputs
Step 3: Sort simulated outcomes, find the cutoff at the desired confidence level
Pro: Handles any distribution, non-linear instruments, correlations. Con: Computationally intensive, model-dependent.
Method Comparison
| Feature | Historical | Parametric | Monte Carlo |
|---|---|---|---|
| Assumptions | None (uses actual data) | Normal distribution | Model-dependent |
| Tail risk | Captures if in sample | Underestimates | Flexible |
| Speed | Fast | Very fast | Slow |
| Best for | Simple portfolios | Quick estimates | Complex / non-linear |
| Data needed | Long history | Mean, std dev, correlations | Parameters + simulation engine |
How to Interpret VaR
VaR vs Maximum Drawdown
Both measure risk, but from very different angles. Use them together for a complete picture:
| Feature | Value at Risk | Maximum Drawdown |
|---|---|---|
| Time frame | Short (daily/weekly) | Full investment period |
| Direction | Forward-looking estimate | Backward-looking fact |
| What it measures | Expected loss at confidence level | Actual worst peak-to-trough loss |
| Distribution assumption | Yes (parametric) or No (historical) | None |
| Tail risk | Doesn't measure beyond threshold | Captures actual worst case |
| Best for | Day-to-day risk monitoring | Evaluating total investment experience |
Use both: VaR for daily risk management, max drawdown for evaluating overall strategy quality. Together they answer different but equally important questions about your portfolio's risk.
Conditional VaR (Expected Shortfall)
CVaR (also called Expected Shortfall) answers a question VaR cannot: "When losses exceed VaR, how bad is it on average?"
95% VaR = $5,000
On the worst 5% of days, losses exceed $5,000 — but by how much? VaR doesn't say.
95% CVaR = $8,000
When you do have a bad day (the worst 5%), you lose $8,000 on average. CVaR tells the rest of the story.
CVaR is always greater than or equal to VaR. The Basel III framework requires banks to use Expected Shortfall instead of VaR because ES captures the severity of tail losses, not just their probability.
For individual investors, CVaR gives a more honest picture of tail risk. If your 95% VaR is $5,000 but your CVaR is $15,000, the tail is very heavy — and you should plan accordingly.
Real-World Example: $200,000 Diversified Portfolio
Consider a $200,000 diversified portfolio and its VaR using the parametric method:
| Asset Class | Weight | Annual σ |
|---|---|---|
| Stocks | 60% | 16% |
| Bonds | 30% | 5% |
| Gold | 10% | 15% |
Portfolio σ (accounting for correlations): ≈ 10%
Daily σ: 10% / √252 ≈ 0.63%
95% daily VaR:
$200,000 x 1.65 x 0.0063 = $2,079
99% daily VaR:
$200,000 x 2.33 x 0.0063 = $2,936
Meaning: on 95% of trading days, this portfolio loses less than ~$2,100. On the worst 1 in 100 days, losses could exceed ~$2,900. These numbers help set realistic expectations for daily portfolio fluctuations.
How Portfolio Genius Calculates VaR
Portfolio Genius automatically calculates Value at Risk for every portfolio, giving you instant visibility into your potential downside:
- •Automated VaR calculation — VaR computed for every portfolio using historical return data, updated as positions change
- •Multiple confidence levels — View both 95% and 99% VaR to understand your risk at different thresholds
- •AI-powered risk alerts — Get notified when VaR exceeds your risk tolerance, with recommendations for reducing exposure
- •Complete risk dashboard — VaR displayed alongside Sharpe ratio, beta, and maximum drawdown for comprehensive risk analysis
Understanding your portfolio's VaR helps you answer a critical daily question: how much could I lose today, and am I comfortable with that number?
Common Mistakes to Avoid
- •Treating VaR as the worst case — It's NOT the worst case; it's the boundary of the normal zone. A 95% VaR of $5,000 means losses exceed $5,000 about once a month — and on those days, the actual loss could be $10,000, $20,000, or more.
- •Ignoring VaR's distribution assumptions — Parametric VaR assumes returns follow a normal distribution. Real markets have fat tails — extreme events occur far more often than the bell curve predicts. This means parametric VaR systematically underestimates tail risk.
- •Using VaR alone without Conditional VaR — VaR tells you where the cliff is; CVaR tells you how far you fall. A portfolio can have a low VaR but catastrophic CVaR if tail losses are extreme. Always look at both numbers together.
- •Comparing VaR across different confidence levels — 95% VaR and 99% VaR are very different numbers. A portfolio with 95% VaR of $5,000 might have a 99% VaR of $8,000+. Always ensure you're comparing the same confidence level and time horizon.
- •Not scaling VaR correctly — To convert daily VaR to t-day VaR, multiply by √t, not by t directly. A daily VaR of $1,000 becomes a 10-day VaR of $3,162 (√10 ≈ 3.162), not $10,000. The square root scaling reflects how volatility grows slower than time.
Frequently Asked Questions
What does '95% daily VaR of $5,000' mean?
Which VaR method is best?
What is Conditional VaR (Expected Shortfall)?
How is VaR different from standard deviation?
Can VaR be used for individual stocks?
Why do regulators require Expected Shortfall instead of VaR?
Related Terms
Maximum Drawdown
The largest peak-to-trough decline in portfolio value. Shows worst-case loss scenario.
Standard Deviation
A measure of how spread out returns are from the average. Higher means more volatile.
Sortino Ratio
A variation of Sharpe ratio that only penalizes downside volatility, not upside gains.
Downside Deviation (D*)
Measures volatility of returns below a target rate using semivariance. Lower values indicate less downside risk.
Sharpe Ratio
A measure of risk-adjusted return that compares excess return to volatility. Higher is better.
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