Portfolio Optimization & Quantitative Analysis
Institutional-grade quantitative analysis with Monte Carlo simulation, distribution fitting, factor decomposition, and extreme value theory.
Example: Diversified Growth Portfolio
$100,000 portfolio across 15 holdings with auto-detected sectors
| Ticker | Company | Sector | Allocation |
|---|---|---|---|
| AAPL | Apple Inc | Technology | 12% |
| MSFT | Microsoft | Technology | 12% |
| GOOGL | Alphabet | Technology | 10% |
| AMZN | Amazon | Consumer | 8% |
| NVDA | NVIDIA | Technology | 7% |
| JPM | JPMorgan Chase | Financials | 7% |
| JNJ | Johnson & Johnson | Healthcare | 6% |
| V | Visa | Financials | 6% |
| PG | Procter & Gamble | Consumer Staples | 5% |
| UNH | UnitedHealth | Healthcare | 5% |
| HD | Home Depot | Consumer | 5% |
| MA | Mastercard | Financials | 5% |
| LLY | Eli Lilly | Healthcare | 5% |
| KO | Coca-Cola | Consumer Staples | 5% |
| PEP | PepsiCo | Consumer Staples | 3% |
Sector Allocation
Quantitative Analysis Results
Example Diversified Portfolio
Analysis computed: 2026-02-15 | Period: 2y | 15 assets
Ann. Return
14.7%
Geometric mean
Volatility
14.8%
Annualized σ
Max Drawdown
-17.5%
179 days
Sharpe Ratio
0.66
Risk-adjusted
Sortino
0.88
Downside adj.
Beta
0.85
vs S&P 500
Alpha
-0.3%
Annualized
CVaR (95%)
-2.1%
Expected Shortfall
Portfolio Holdings
| Ticker | Sector | Weight | Price |
|---|---|---|---|
| AAPL | Technology | 12.0% | $255.78 |
| MSFT | Technology | 12.0% | $401.32 |
| GOOGL | Technology | 10.0% | $305.72 |
| AMZN | Consumer Discretionary | 8.0% | $198.79 |
| NVDA | Technology | 7.0% | $182.81 |
| JPM | Financials | 7.0% | $302.55 |
| JNJ | Healthcare | 6.0% | $243.45 |
| V | Financials | 6.0% | $314.08 |
| PG | Consumer Staples | 5.0% | $160.07 |
| UNH | Healthcare | 5.0% | $293.19 |
| HD | Consumer Discretionary | 5.0% | $391.05 |
| MA | Financials | 5.0% | $518.36 |
| LLY | Healthcare | 5.0% | $1040.00 |
| KO | Consumer Staples | 5.0% | $78.68 |
| PEP | Consumer Staples | 2.0% | $165.94 |
Asset Allocation
Return Distribution Analysis & Normality Tests
Jarque-Bera Test
Normality
4664.51
Non-Normal ✗
Skewness
Asymmetry
0.614
Kurtosis
Tail heaviness
15.060
Distribution Fitting (AIC Criteria)
| Distribution | Mean | Std Dev | VaR 95% | AIC |
|---|---|---|---|---|
| Normal | 0.0006 | 0.0093 | -1.47% | -3263 |
| Student-t (Best) | 0.0009 | 0.0090 | -1.24% | -3397 |
| Laplace | 0.0008 | 0.0089 | -1.36% | -3381 |
Non-Normal Distribution Detected: Returns follow a Student-t distribution better than Normal. This indicates fat tails - extreme returns occur more frequently than a normal distribution would predict.
Monte Carlo Simulation (5,000 Paths, 1 Year Horizon)
Probability of Profit
74.8%
Mean Final Value
$107,655
Median Final Value
$107,053
VaR 95% (1 Year)
$91,339
95% Confidence Interval
$89,430 - $131,115
Value at Risk (VaR) Analysis
Historical VaR (95%)
Empirical percentile
-1.3%
Historical VaR (99%)
Extreme tail risk
-2.4%
CVaR / ES (95%)
Expected Shortfall
-2.1%
Risk-Adjusted Performance Metrics
Sortino Ratio
0.88
Downside risk
Calmar Ratio
0.84
Return / Max DD
Omega Ratio
1.21
Gain/Loss ratio
Information Ratio
-0.38
vs Benchmark
Drawdown Analysis
Rolling Volatility (63-day)
Mean-Variance Optimization (Markowitz Efficient Frontier)
Portfolio Performance vs Benchmarks
Risk Contribution Analysis
Effective N (Diversification)
1.0
Uncorrelated bets
Concentration (HHI)
100.2%
Lower is better
Diversification Ratio
0.00
Portfolio vs weighted avg
Rolling Statistics (63-day) with 95% Confidence Bands
Rolling Beta (63-day)
Volatility Clustering (ARCH Effects)
Volatility of Volatility
--%
Volatility Persistence
--
Half-Life (days)
--
ARCH Effects
DETECTED
Principal Component Analysis (PCA)
Explained Variance
Factor Loadings (PC1, PC2, PC3)
Condition Number
--
Effective Rank
--
Rolling Correlation Analysis
Monthly Returns Heatmap
Factor Exposure Analysis (Fama-French 5-Factor Model)
Market (β)
0.85
Systematic risk
Size (SMB)
-0.002
Small cap premium
Value (HML)
-0.131
Value premium
Alpha (α)
16.20%
Excess return
R²
88.2%
Model fit
Advanced Risk Metrics
Modified VaR (95%)
-1.1%
Modified VaR (99%)
-4.2%
Ulcer Index
0.040
Pain Ratio
6.04
Tail Ratio (95/5)
0.95
Kappa-3
15.09
Kelly Fraction
6.81
Half-Kelly
3.40
Risk Matrix
| Risk Factor | Value | Risk Level | Interpretation |
|---|
Stress Test Scenarios
AI Quantitative Analysis Report
Asset Correlation Matrix
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