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