Long-Run Value-at-Risk Analysis Page — User Guide
See how potential losses evolve over 30 days or a full year for any security
Contents
Page Overview
Essential Concepts
Navigation Guide
Data Interpretation
Practical Applications
Understanding Data
Troubleshooting
Tips & Best Practices
Essential Concepts
These terms appear throughout the Long-Run VaR analysis and are essential for understanding the methodology:
Value-at-Risk (VaR)
The maximum cumulative loss expected at a given confidence level over a specified time horizon. 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 displays VaR as negative percentages. A value of -20% on a given date means that on that date, the model estimated a 20% potential loss for the selected horizon and percentile. Values closer to 0% indicate lower estimated risk.
Monte Carlo Simulation
A computational technique that generates thousands of possible future price paths by randomly sampling from estimated return distributions. V-Lab runs 10,000 simulations for each security.
Why it matters: Every VaR value comes from 10,000 simulated scenarios. This captures a wide range of possibilities, including extreme events, rather than assuming a single deterministic outcome.
Percentile (1st vs 5th)
The 1st percentile shows extreme tail risk (1-in-100 chance of worse outcome). The 5th percentile shows moderate tail risk (1-in-20 chance of worse outcome).
Why it matters: Use the Percentile dropdown to switch between them. Select both to see two lines on the chart and observe how much worse extreme events could be compared to moderate stress.
Volatility Clustering
The empirical tendency for high-volatility days to follow high-volatility days, and calm days to follow calm days. Markets exhibit regime-like behavior rather than random switching.
Why it matters: This explains why the chart line moves up and down over time. After volatile periods, the GJR model expects continued volatility. After calm periods, it expects lower risk.
Time Horizon (30 days vs 365 days)
The forward-looking period over which VaR is calculated. V-Lab offers 30-day and 365-day horizons for long-run risk assessment.
Why it matters: 30-day VaR reflects near-term risk. 365-day VaR includes the possibility that market conditions will change significantly over a year, often producing larger potential losses.
Tail Risk
The risk of extreme losses that fall in the far tails of the return distribution. These are rare events (1% or 5% probability) but can be devastating when they occur.
Why it matters: The 1st percentile captures tail risk. During crises like 2008 or 2020, this estimate drops sharply, showing the model's assessment of extreme potential losses.
Bootstrap Methodology
A resampling technique that creates synthetic return paths by randomly drawing from standardized historical residuals. This preserves the empirical distribution of shocks without assuming normality.
Why it matters: The bootstrap captures fat tails and asymmetries in real market data that parametric distributions would miss. This makes the VaR estimates more realistic during stress periods.
Data Interpretation
The VaR values shown are potential cumulative losses expressed as negative percentages. A value of -25% means the model estimated a 25% potential cumulative loss by the end of the selected horizon at the chosen percentile.
Comparing Risk Across Horizons
Different time horizons serve different purposes in risk assessment:
- Near-Term Focus (30 days)
Best for tactical decisions and short-term position sizing. Reflects current market conditions with limited time for regime changes.
- Strategic View (365 days)
Appropriate for long-term allocations and capital planning. Includes the possibility of volatility regime changes over the year.
- Comparing Both
The 365-day VaR is typically larger than 30-day VaR because more can happen over a year. When they are closer together during volatile periods, it suggests the model expects volatility to mean-revert downward.
Practical Applications
Strategic Asset Allocation
Use 365-day VaR to understand potential annual drawdowns when setting long-term portfolio allocations. Compare VaR across asset classes to assess relative risk contributions.
Risk Budgeting
Set position limits based on VaR estimates. Monitor how the VaR evolves over time to decide when to reduce exposure (rising VaR) or potentially increase it (falling VaR).
Research and Backtesting
Download historical VaR estimates to test trading strategies against realized outcomes. Analyze how well the model captured risk during past market events.
Understanding Data
Every data point results from a rigorous simulation process that runs daily for each security in the V-Lab database.
Daily Estimation Process
Each day, V-Lab fits a GJR-GARCH(1,1) model to all available historical returns, estimates the conditional volatility, and runs 10,000 bootstrap simulations to project returns over the selected horizon. VaR is taken from the resulting distribution.
Troubleshooting
Common Questions
Why did VaR suddenly increase?
VaR rises after volatile market days because the GJR-GARCH model detects increased risk. The model gives more weight to recent observations, so a large price move immediately raises the volatility estimate and the resulting VaR forecast.
How accurate are these VaR estimates?
A well-calibrated 1% VaR should be exceeded approximately 1% of the time. You can validate this yourself by downloading historical VaR estimates and comparing them to realized returns over the same periods.
Why does the chart show sudden jumps on certain dates?
Sharp moves correspond to days when markets experienced unusual volatility. Events like earnings surprises, geopolitical shocks, or macro announcements cause the model to rapidly revise its risk estimate.
Technical Questions
Questions from users about the methodology:
Why is 365-day VaR not simply 30-day VaR multiplied by √12?
The square-root-of-time rule assumes constant volatility and independent returns. The GJR model allows for mean reversion in volatility over longer horizons, so the 365-day VaR incorporates different dynamics than simple scaling would produce.
How do I know 10,000 simulations are enough?
With 10,000 paths, the 1st and 5th percentile estimates are generally stable. More simulations would marginally improve precision but significantly increase computation time. You can assess stability by comparing estimates across similar securities or time periods.
The VaR seems unrealistically high/low. Is something wrong?
VaR reflects the model's assessment based on recent volatility. If markets have been exceptionally volatile, VaR will be high. If markets have been calm, VaR will be low. Compare to historical periods with similar conditions.
How does the model perform during crises?
You can see for yourself by examining the historical VaR series during 2008, 2011, 2015, 2020, and other volatile periods. The GJR-GARCH model generally captures rising risk as volatility increases, though like all models, it responds to events rather than predicting them.
How do I download the VaR time series?
Use the Download option in the menu above the chart. You must be logged in with a V-Lab account. The download includes the historical VaR series for the selected security and parameters.
Tips & Best Practices
Follow these practices to get the most value from the Long-Run VaR analysis:
Recommended Workflow
1. Check the current VaR level relative to historical values on the chart 2. Compare 30-day vs 365-day horizons to assess short vs long-term risk 3. Look at both 1st and 5th percentiles to understand tail risk severity 4. Review how VaR behaved during past crises (2008, 2020) for context 5. Download data if you need to incorporate VaR into your own analysis
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