Long-Run VaR Welcome Page — User Guide
See how much a security could lose over the next 30 days, with models that account for changing market conditions
Contents
Page Overview
Essential Concepts
Getting Started
Key Features
Available Tools
Understanding the Data
Common Questions
Next Steps
Essential Concepts
These terms appear in the chart and throughout the Long-Run VaR pages:
VaR (Value-at-Risk)
The maximum cumulative loss you would expect with a certain probability over a given time period. A 30-day 1% VaR of 15% means there is only a 1% chance of cumulatively losing more than 15% by the end of 30 days.
Why it matters: The chart shows VaR as negative percentages. A value of -20% on a given date means the model estimated a 20% potential cumulative loss by the end of the selected horizon. Values closer to 0% indicate lower estimated risk.
Long-Run VaR
VaR calculated over extended periods (30 days or longer) that accounts for how volatility itself changes over time. Unlike daily VaR, it does not assume today's volatility will persist.
Why it matters: The Welcome page shows 30-day Long-Run VaR. During calm periods, the lines are closer to 0%. During crises like 2008 or 2020, they dropped to -40% or lower.
GJR-GARCH Model
A volatility model that captures two key patterns: volatility clustering (high volatility tends to follow high volatility) and asymmetry (markets react more strongly to bad news than to good news of the same magnitude).
Why it matters: The blue line on the chart uses this model. It is available for all securities with sufficient trading history. Named after Glosten, Jagannathan, and Runkle who developed it.
Implied Volatility
The market's expectation of future volatility, derived from options prices. When options are expensive, implied volatility is high, meaning the market expects large price moves.
Why it matters: The red line on the chart incorporates implied volatility from options markets. When it diverges from the blue line, the options market sees different risk than historical patterns suggest.
Mean Reversion
The tendency of volatility to return toward its long-term average over time. Extremely high or low volatility rarely persists indefinitely.
Why it matters: This is why Long-Run VaR differs from daily VaR. The model accounts for the fact that even during calm markets, volatility will eventually increase, and during volatile periods, it will eventually subside.
Percentile (1st vs 5th)
The 1st percentile represents extreme tail risk (1-in-100 chance of worse outcome). The 5th percentile represents moderate tail risk (1-in-20 chance). Lower percentiles capture more extreme scenarios.
Why it matters: This page shows the 1st percentile, the most extreme estimate. On individual Analysis pages, you can switch between 1st and 5th percentile to see different risk levels.
Bootstrap Simulation
A resampling technique that generates 10,000 possible future scenarios by randomly drawing from standardized historical residuals. Each simulation path represents one possible way cumulative returns might evolve.
Why it matters: Every VaR value on this chart comes from 10,000 simulations. The 1st percentile means only 100 of those 10,000 simulations showed worse cumulative outcomes.
Getting Started
Reading the Chart
The chart shows 30-day Long-Run VaR at the 1st percentile for the S&P 500 Index. Here is how to interpret what you see:
What the Two Lines Mean
The chart compares two different models for estimating Long-Run VaR:
- Blue Line: GJR-GARCH Model
Uses only historical return data to estimate future volatility. Available for any security with sufficient trading history. This is the baseline model.
- Red Line: GJR with Options
Adds implied volatility from options prices to the model. Due to data limitations, only available for a few major indices.
- When Lines Converge or Diverge
When the lines are close, historical patterns and options markets agree on future risk. When they diverge significantly, options traders see different risk than historical patterns suggest.
Key Features
Dual Model Comparison
The Welcome page lets you compare two approaches to estimating Long-Run VaR:
- Base Model (Blue Line)
The GJR-GARCH model estimates volatility using only historical return data. It captures volatility clustering and asymmetric responses to gains versus losses.
- Options-Enhanced Model (Red Line)
Incorporates forward-looking information from options prices. When available, it can detect market expectations that historical patterns might miss.
30-Day Risk Horizon
The Welcome page focuses on 30-day risk. Here is what this means:
- Why 30 Days?
Thirty days is long enough for volatility dynamics to matter but short enough to be actionable. It is a common horizon for risk management and regulatory purposes.
- 1st Percentile Shown
The chart shows the 1st percentile, meaning only 1% of simulated scenarios resulted in worse cumulative losses. This represents extreme tail risk.
- Mean Reversion Included
Unlike daily VaR, the 30-day estimate accounts for the tendency of volatility to revert toward its long-term average over longer horizons.
Available Tools
Comparing the Two Models
The two lines on the chart offer different perspectives on risk:
- When Models Agree
If the blue and red lines are close together, historical volatility patterns and options market expectations are aligned. This increases confidence in the risk estimate.
- When Models Disagree
Large gaps between the lines suggest uncertainty. The options market may be pricing in events (earnings, policy changes) that historical patterns cannot capture.
Finding Securities to Analyze
- Popular Analyses Tabs
Below the chart, see trending securities in the weekly and monthly popular analyses lists. Click any link to go directly to that security's full Long-Run VaR analysis page.
- V-Lab Search
Use the search bar in the main navigation to find any security by name or ticker symbol. Each security has its own dedicated analysis page.
Understanding the Simulation
- 10,000 Scenarios
Every VaR value results from simulating 10,000 possible future paths. The bootstrap method samples from standardized historical residuals to generate realistic scenarios.
- Daily Updates
The models are refitted each day using all available historical data. Risk estimates evolve as new market information arrives.
Understanding the Data
How the Numbers Are Calculated
Every data point on the chart represents the result of a rigorous daily simulation process:
The GJR-GARCH Model (Blue Line)
The base model captures key patterns from historical returns:
- Volatility Clustering
High-volatility days tend to be followed by more high-volatility days. The model uses recent volatility to predict near-term risk, then allows it to revert over longer horizons.
- Asymmetric Response
Markets react more strongly to losses than to gains of the same size. A 3% drop increases the volatility estimate more than a 3% rally decreases it (the leverage effect).
The Options-Enhanced Model (Red Line)
When available, the enhanced model adds forward-looking market expectations:
- Forward-Looking Information
Options prices reflect what traders expect to happen. If options are expensive, it suggests traders expect larger price moves ahead.
- Volatility Term Structure
Uses options at different expiration dates to build a picture of expected volatility across multiple time horizons, not just immediate expectations.
- Limited Availability
Due to data limitations, only available for a few major indices.
Common Questions
Understanding the Chart
Why are there two lines on the chart?
The blue line uses only historical return data (GJR-GARCH model). The red line adds forward-looking information from options markets. Comparing them shows when historical patterns and market expectations agree or disagree about future risk.
Why do the lines sometimes diverge?
When the red line differs significantly from the blue line, options traders expect different volatility than historical patterns suggest. This often happens before major events or during periods of unusual market stress.
What do the negative percentages mean?
The y-axis shows potential cumulative losses. A value of -25% means there is a 1% chance of cumulatively losing 25% or more by the end of 30 days. Values closer to 0% indicate calmer markets; values at -40% or below indicate crisis conditions.
About the Methodology
Why use Long-Run VaR instead of daily VaR?
Daily VaR assumes today's volatility continues unchanged. Long-Run VaR recognizes that volatility changes over time, tending to spike during stress and subside afterward. For any position held more than a few days, this distinction matters significantly.
Why is the red line not available for all securities?
Due to data limitations, V-Lab only has options data for a few major indices. The options-enhanced model (red line) is not available for most securities.
Using V-Lab Effectively
Common questions about navigating and using Long-Run VaR analysis:
How do I analyze a specific security?
Use the search bar in the top navigation to find any security by name or ticker. Or click on any link in the Popular Analyses section to go directly to that security's analysis page.
Can I change the time horizon from 30 days?
Yes, but not on this Welcome page. Click through to an individual security's analysis page where you can select different horizons (30 days or 365 days).
Can I download the data?
Yes. On individual analysis pages, you can download the historical VaR data. The Welcome page chart is for orientation; detailed downloads are available on security-specific pages.
What does the 1st percentile mean in practice?
If the chart shows -30% at the 1st percentile, there is a 1-in-100 chance of cumulatively losing 30% or more by the end of 30 days. It is the 100th-worst outcome out of 10,000 simulated scenarios.
How often is the data updated?
The models are refitted daily using all available historical data through the previous trading day. The chart updates each morning with new risk estimates.
Next Steps
Quick Start: First 60 Seconds
- 1. Look at the Chart
The two lines show risk estimates for the S&P 500 over time. More negative values mean higher estimated risk. Notice how risk spiked during 2008, 2020, and other volatile periods.
- 2. Compare the Lines
When blue and red lines are close, historical patterns and options markets agree. Large gaps suggest the options market sees different risk than historical patterns indicate.
- 3. Check Popular Analyses
Scroll down to see which securities other users are analyzing in the weekly and monthly popular analyses lists. Click any link to explore that security's full analysis.
- 4. Search for a Security
Use the search bar in the main navigation to find a specific stock, index, or ETF you are interested in analyzing.
What You Can Do on Analysis Pages
- Change the Time Horizon
Select 30-day or 365-day periods to see how risk estimates differ across holding periods.
- Switch Percentiles
Toggle between 1st percentile (extreme tail risk) and 5th percentile (more moderate stress scenarios) depending on your needs.
- Download Data
Export historical Long-Run VaR values for your own analysis or record-keeping. Login required.
- Compare Securities
Open multiple analysis pages in separate tabs to compare risk estimates across different securities in your portfolio.
- Review Historical Crises
Examine how VaR behaved during past events (2008, 2020) to understand how the model responds to extreme market conditions.
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