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PORTFOLIO VALUE AT RISK (VaR)
Parametric & Simulation-Based VaR with Confidence Intervals
               
PARAMETRIC VALUE AT RISK (VARIANCE-COVARIANCE METHOD)
Parameter Value Unit Description
Portfolio Value $50,000,000 $ Total portfolio value from Assumptions
Expected Return (μ) 10.00% % Mean annual return
Volatility (σ) 15.00% % Annualized standard deviation
Z-Score (95%) 1.6449   Normal quantile for 95% confidence
Z-Score (99%) 2.3263   Normal quantile for 99% confidence
VaR (95%) - 1 Day $777,120 $ Max loss at 95% confidence (daily)
VaR (99%) - 1 Day $1,099,096 $ Max loss at 99% confidence (daily)
VaR (95%) - Annual $12,336,402 $ Max loss at 95% confidence (annual)
VaR (99%) - Annual $17,447,609 $ Max loss at 99% confidence (annual)
Expected Shortfall (CVaR 95%) $15,470,346 $ Average loss beyond VaR threshold
SIMULATION-BASED VaR (HISTORICAL SIMULATION METHOD)
Metric Value Unit Interpretation
Simulated Mean Return 9.64% % Average simulated portfolio return
Simulated Volatility 14.87% % Standard deviation of simulated returns
Simulated Skewness 0.136   Negative = left tail risk
Simulated Kurtosis -0.143   Excess kurtosis (>0 = fat tails)
Sim VaR (95%) - Return -13.63% % 5th percentile return (worst 5%)
Sim VaR (99%) - Return -21.84% % 1st percentile return (worst 1%)
Sim VaR (95%) - $ Amount $6,816,262 $ Maximum loss at 95% confidence
Sim VaR (99%) - $ Amount $10,918,414 $ Maximum loss at 99% confidence
Sim CVaR (95%) - $ Amount $9,619,712 $ Expected loss in worst 5% scenarios
Sim CVaR (99%) - $ Amount $13,000,221 $ Expected loss in worst 1% scenarios
Max Drawdown (Simulated) 32.77% % Worst single scenario return
Sharpe Ratio (Simulated) 0.38 Ratio Risk-adjusted return measure
VaR METHOD COMPARISON
Metric Parametric VaR Simulation VaR Difference Difference %
VaR (95%) - Annual $12,336,402 $6,816,262 ($5,520,140) -44.7%
VaR (99%) - Annual $17,447,609 $10,918,414 ($6,529,195) -37.4%
CVaR / ES (95%) $15,470,346 $9,619,712 ($5,850,634) -37.8%
PORTFOLIO RETURN CONFIDENCE INTERVALS
Confidence Level Lower Bound (%) Upper Bound (%) Lower Bound ($) Upper Bound ($) Width ($) Interpretation
90% Confidence -13.63% 35.02% $43,183,738 $67,509,165 $24,325,427 90% of outcomes fall within this range
95% Confidence -18.79% 39.10% $40,604,976 $69,552,369 $28,947,393 95% of outcomes fall within this range
99% Confidence -24.81% 48.18% $37,595,784 $74,091,905 $36,496,121 99% of outcomes fall within this range
NOTES
• Parametric VaR assumes normal distribution; Simulation VaR uses actual Monte Carlo outcomes
• CVaR (Conditional VaR / Expected Shortfall) captures average loss beyond VaR threshold
• Daily VaR = Annual VaR / √252 (252 trading days per year)
• Differences between methods indicate non-normality in return distribution