Portfolio Value

$1,000M

Static VAR (95%)

$7.8M

GARCH VAR (95%)

$7.6M

CVaR (95%)

$10.6M

Static Volatility

7%

GARCH Volatility

7.4%

VAR Comparison: Traditional Methods
Static vs GARCH VAR Comparison
Returns Distribution
Volatility: Current vs Historical Average
GARCH Model Diagnostics (Top 10)
Instrument α+β AIC Status
Silver 1.009 −5.380 ✓ PASS
Natural Gas 1.005 −4.454 ✓ PASS
Copper 1.005 −5.611 ✓ PASS
Small Cap US 1.003 −5.644 ✓ PASS
Municipal Bonds 1.003 −8.558 ✓ PASS
US Treasury 10Y 1.003 −8.287 ⚠ CHECK
JPY/USD 1.002 −7.348 ✓ PASS
Corporate IG 1.002 −7.449 ✓ PASS
CHF/USD 1.002 −7.109 ✓ PASS
Gold 1.002 −5.980 ✓ PASS
Conditional Volatility Over Time (Top 5 Assets)
Forecasted Volatilities (Top 10)
Instrument Forecasted Vol (%)
Natural Gas 43.01
Crude Oil 34.66
Commodity Futures 32.33
Tech Sector 30.34
Emerging Markets 28.36
Equity Options 26.26
Small Cap US 24.56
Copper 23.85
Silver 21.81
Financial Sector 20.55
Top 10 Risk Contributors (Static VAR)
Instrument Class VAR ($M) % of Total
Emerging Markets equities −1.66 21.3
Small Cap US equities −1.21 15.5
Tech Sector equities −1.11 14.2
Financial Sector equities −0.78 10.0
European Equity equities −0.61 7.9
Large Cap US equities −0.45 5.7
International Bonds bonds −0.33 4.2
Corporate HY bonds −0.24 3.1
Corporate IG bonds −0.22 2.9
US Treasury 10Y bonds −0.22 2.8
Top 10 Risk Contributors (GARCH VAR)
Instrument Class VAR ($M) % of Total Vol (%)
Emerging Markets equities −1.51 21.1 28.4
Small Cap US equities −1.23 17.2 24.6
Tech Sector equities −1.02 14.2 30.3
Financial Sector equities −0.71 9.9 20.6
European Equity equities −0.57 7.9 19.5
Large Cap US equities −0.41 5.8 16.6
International Bonds bonds −0.28 3.9 8.6
Corporate HY bonds −0.20 2.8 12.7
Corporate IG bonds −0.19 2.6 9.9
US Treasury 10Y bonds −0.18 2.5 7.9
Component VAR Waterfall (Static)
Basel III Capital Requirements (Traditional vs GARCH)
Basel III Capital: Static vs GARCH
Internal Models Approach Comparison
Component Static ($M) GARCH ($M) Δ %
1-Day VAR (99%) 12.29 7.58 −38.4
10-Day VAR (99%) 38.87 33.54 −13.7
Multiplier 3.00 3.00 0.0
Capital Requirement 116.62 100.61 −13.7
% of Portfolio 11.66 10.06 −13.7
Model Choice Impact on Capital
Backtesting: Static vs GARCH Models
Metric Value
Days Analyzed 250
Exceptions (Static) 2
Exception Rate (Static) 0.8%
Basel Zone (Static) Green
Exceptions (GARCH) 3
Exception Rate (GARCH) 1.2%
Basel Zone (GARCH) Green
Expected Exceptions 2-3 (1%)
Preferred Model Static
Exception Visualization: Static vs GARCH
Regulatory Considerations & Model Comparison
Model Performance Summary
Metric Static Model GARCH Model Difference
Basel Zone Green Green -
Exception Count 2 3 +1
Exception Rate 0.80% 1.20% +0.40pp
Capital Required $116.6M $100.6M -16.0M
% of Portfolio 11.66% 10.06% -1.60pp
GARCH Model Benefits for Basel III

1. Time-Varying Risk Capture - Adapts dynamically to changing market conditions - More responsive to volatility spikes and regime changes
- Better reflects current risk environment vs. static lookback

2. Improved Backtesting Performance - Fewer exceptions during stressed periods - Better calibrated to actual realized risk - Maintains Green Zone status more consistently

3. Capital Efficiency - Lower capital requirements in calm markets - Appropriate capital increase during stress - Optimized risk-based capital allocation

4. Advanced Modeling Recognition - Demonstrates sophisticated risk management - May support lower multiplier (with supervisory approval) - Aligns with best practices in quantitative finance

Regulatory Requirements
Supervisory Approval

GARCH models require supervisory approval under Basel III IMA. Banks must demonstrate: - Robust model validation framework - Sound risk management processes
- Comprehensive backtesting program (250+ days) - Independent model review and governance

Current Status & Recommendation
Performance Analysis

Static Model: Green Zone (2 exceptions in 250 days)
GARCH Model: Green Zone (3 exceptions in 250 days)

Capital Impact: $16.0M (13.7%)

Recommendation: GARCH model recommended for capital efficiency

Methodology & Key Insights
VAR Calculation Methods

Traditional VAR (6 methods): - Historical, Parametric (Normal & t), Cornish-Fisher, Monte Carlo, CVaR

GARCH-Enhanced VAR: - Time-varying conditional volatility - GJR-GARCH for leverage effects - Student’s t-distribution for fat tails

Current Risk Assessment
Static vs GARCH Comparison
  • Static VAR (95%): $7.8M (0.78% of portfolio)
  • GARCH VAR (95%): $7.6M (0.76% of portfolio)
  • Difference: -3.1%
Volatility Status

Current GARCH volatility (7.4%) is ABOVE historical average (7.3%)

Model Diagnostics Summary
  • Total Instruments: 31
  • Historical Period: 900 days (~3.6 years)
  • GARCH Models Estimated: 31
  • Models Passed Diagnostics: 29 (93.5%)
When to Use Each Method

Use Static VAR when: - Regulatory reporting (Basel III) - Stable market conditions - Quick daily updates needed

Use GARCH VAR when: - Volatile market conditions - Forward-looking analysis - Early warning system needed - Volatility regime changes

Best Practice: Monitor both methods. Large divergences indicate changing risk environment.