What Is Value at Risk?¶
Value at Risk (VaR) answers a deceptively simple question: “What is the maximum loss I can expect over a given time horizon at a given confidence level?”
For example, a 1-day 95% VaR of $50,000 means:
There is a 95% probability that your portfolio will not lose more than $50,000 in a single trading day.
Or equivalently: on 5% of trading days (roughly once a month), losses may exceed $50,000.
VaR has become the standard risk metric across the financial industry since J.P. Morgan popularized it with their RiskMetrics framework in the 1990s. Regulators require it, risk committees report it, and portfolio managers use it daily.
Three Approaches to Calculating VaR¶
1. Parametric (Variance-Covariance) VaR¶
The simplest approach assumes returns follow a normal distribution.
Formula:
$$VaR = \mu - z_\alpha \cdot \sigma$$
Where: - $\mu$ is the expected portfolio return - $z_\alpha$ is the z-score for the confidence level (1.645 for 95%, 2.326 for 99%) - $\sigma$ is the portfolio standard deviation
Pros: - Fast computation - Easy to decompose by asset - Works well for liquid, linear portfolios
Cons: - Assumes normal distribution (fat tails are ignored) - Poor for portfolios with options or non-linear instruments - Correlation assumptions may break down in crises
2. Historical Simulation VaR¶
Uses actual historical returns rather than distributional assumptions.
Process: 1. Collect N days of historical returns for each asset 2. Apply those returns to today’s portfolio weights 3. Sort the resulting portfolio returns 4. The VaR is the return at the (1 - confidence) percentile
Pros: - No distributional assumptions - Captures fat tails naturally - Includes actual correlation structure
Cons: - Only as good as the historical window chosen - Cannot capture regime changes not in the data - Computationally heavier than parametric
3. Monte Carlo Simulation VaR¶
Generates thousands of random scenarios based on estimated return distributions and correlations.
Process: 1. Estimate the mean return vector and covariance matrix 2. Generate N random portfolio return scenarios (typically 10,000+) 3. Sort scenarios and find the percentile corresponding to the confidence level
Pros: - Handles non-linear instruments (options, structured products) - Flexible - can incorporate any distributional assumption - Can model complex dependency structures
Cons: - Computationally expensive - Results depend on model assumptions - Requires careful calibration
Beyond VaR: Conditional VaR (CVaR)¶
VaR tells you the threshold loss, but nothing about what happens beyond it. Conditional VaR (CVaR) - also called Expected Shortfall - answers the question:
“If losses exceed VaR, what is the expected loss?”
CVaR is the average of all losses beyond the VaR threshold. It’s a more conservative and coherent risk measure, and is increasingly preferred by regulators.
Backtesting: Does Your Model Work?¶
A VaR model is only useful if it’s accurate. Backtesting compares predicted VaR against actual portfolio returns:
- Too few exceptions (actual losses exceeding VaR): your model is too conservative, potentially leaving returns on the table
- Too many exceptions: your model underestimates risk - dangerous
The Basel traffic light system categorizes backtesting results:
| Zone | Exceptions (250 days, 99% VaR) | Status |
|---|---|---|
| Green | 0-4 | Model is acceptable |
| Yellow | 5-9 | Needs investigation |
| Red | 10+ | Model must be revised |
VaR in Genesis RM¶
Genesis RM provides all three VaR methodologies through the risk analytics widget:
- Real-time VaR calculation as your portfolio changes
- Backtesting dashboard with traffic light visualization
- Customizable parameters: confidence level, time horizon, lookback window
- Component VaR: see which assets contribute most to portfolio risk
Getting Started
Open the Command Palette (Ctrl+K) and search for “VaR Calculator” to add the widget to your workspace.
Key Takeaways¶
- VaR is a starting point, not the final word on risk. Always complement with stress testing and scenario analysis.
- Choose the right method for your portfolio: parametric for simple equity portfolios, Monte Carlo for complex instruments.
- Backtest regularly - a model that passed last year may fail this year.
- CVaR is increasingly important - it tells you about tail risk that VaR ignores.
Want to explore VaR calculations hands-on? Sign up for Genesis RM and try the risk analytics suite with your own portfolio data.