Portfolio Capital Allocation & Performance Optimization

A comprehensive quantitative framework leveraging Value-at-Risk (VaR) for proactive capital allocation, risk-adjusted performance measurement, and regulatory compliance in a diversified investment portfolio.

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Project Overview: Strategic Financial Analysis

This project transitions a purely risk measurement tool (VaR) into a strategic financial planning instrument. By rigorously quantifying downside risk, it provides the foundation for setting optimal risk limits, determining necessary capital reserves (capital adequacy), and making data-driven investment decisions.

Key Deliverables & Business Impact:

• Capital Adequacy & Reserve Setting: Precisely quantifies the capital buffer required to absorb potential 99% confidence daily loss.
• Risk-Adjusted Performance: Provides the necessary risk metrics to calculate RAROC (Risk-Adjusted Return on Capital).
• Compliance: Implements industry-standard methodologies required by regulations (e.g., Basel III framework).
• Forecasting/Modeling: Utilizes Monte Carlo Simulation for scenario-based financial forecasting.

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Core Business Problem & Solution

Financial Challenge: How much capital is truly at risk, and how much reserve capital is required to ensure solvency and stability while maximizing investment efficiency?

Solution: Implement and validate three advanced VaR models to provide a definitive, statistically-validated answer to the question: "What is the maximum potential capital loss we must be prepared to absorb on a single, extremely volatile day (99% confidence)?"

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Methodology: Data-Driven Financial Modeling

The project employs a structured, three-step quantitative methodology.

1. Data & Pre-Analysis

• Data Set: 3 years of historical prices for 5 major assets (AAPL, MSFT, JPM, GLD, SPY) to simulate a real-world, diversified portfolio.
• Distribution Analysis: Performed normality tests (Jarque-Bera, Shapiro-Wilk) to inform the appropriate choice of VaR model.
• Correlation Mapping: Analyzed asset correlations to understand diversification benefits and concentration risk.

2. Capital-at-Risk Quantification (VaR Calculation)

Three distinct models were implemented to ensure estimate robustness and consensus:

• Historical Simulation: Non-parametric approach for a true, observed "worst-case" loss estimation.
• Variance-Covariance (Parametric): Fast and efficient method for quick daily capital estimates, assuming return normality.
• Monte Carlo Simulation: Scenario Analysis by generating 10,000 random market environments for flexible stress-testing and forecasting.

3. Model Validation & Capital Recommendation

• Backtesting Framework: A rigorous train (70%) and test (30%) split was used to check model accuracy against 225 days of actual market data.
• Statistical Validation: Employed Kupiec's POF Test to ensure the models' estimated 1% failure rate statistically aligned with the actual observed failure rate.

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Key Results & Financial Recommendation

Metric	Detail
Portfolio Value	$1,000,000
Confidence Level	99% (Expected Failure Rate: 1.00%)
Time Horizon	1-Day
Validation Status	100% Validation (All models passed Kupiec's POF Test)

Capital Reserve Requirement (VaR Estimates)

Method	Capital-at-Risk (%)	Recommended Daily Capital Reserve ($)
Historical Simulation	-2.16%	$21,577.69
Variance-Covariance	-2.07%	$20,673.91
Monte Carlo	-2.07%	$20,715.75

Conclusion: The project recommends setting the daily risk limit (Capital Reserve) at $21,578. This establishes a clear financial boundary for the trading desk and ensures the institution holds sufficient capital reserves to cover losses with 99% certainty.

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Technologies Used

• Python 3.x
• Data Processing: Pandas, NumPy
• Statistical Analysis: SciPy
• Financial Data: yfinance
• Environment: Jupyter Notebook

Project Structure

portfolio-analytics/
│
├── 01_data_setup.ipynb              # Data collection & analysis
├── 02_var_calculation.ipynb         # Risk quantification (3 methods)
├── 03_backtesting_validation.ipynb  # Model validation & testing
│
├── data/                            # Analysis outputs
│   ├── portfolio_returns.csv
│   ├── var_results.csv
│   └── backtest_results.csv
│
└── outputs/                         # Visualizations
    ├── 01_price_history.png
    ├── 02_return_distributions.png
    ├── 03_var_comparison_all_methods.png
    └── 04_backtesting_results.png

Running the Analysis

Requirements

pip install pandas numpy scipy matplotlib yfinance

Execution Steps

1. Run 01_data_setup.ipynb - Downloads and prepares data
2. Run 02_var_calculation.ipynb - Calculates risk estimates
3. Run 03_backtesting_validation.ipynb - Validates model accuracy

Outputs

• CSV files with detailed results in data/ folder
• Publication-ready charts in outputs/ folder
• Summary statistics for reporting

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