A comprehensive financial analysis project that implements Modern Portfolio Theory (MPT) using historical stock data from 2000-2023. This project analyzes 27 selected stocks and the S&P 500 index to construct optimal portfolios based on mean-variance optimization principles.

This project demonstrates the application of Harry Markowitz's Modern Portfolio Theory to real financial data, focusing on:

• Risk-Return Analysis: Statistical analysis of individual stocks and market indices
• Portfolio Optimization: Construction of efficient portfolios using mean-variance optimization
• Risk Management: Value at Risk (VaR) calculations and risk assessment
• Efficient Frontier: Visualization of optimal risk-return combinations

• Descriptive Statistics: Mean, standard deviation, skewness, and kurtosis for all assets
• Annualized Returns: Conversion of monthly returns to annual metrics
• Risk Metrics: 5% Value at Risk (VaR) calculations
• Distribution Analysis: Assessment of return distribution characteristics

• Global Minimum Variance Portfolio (GMVP): Portfolio with the lowest possible risk
• Mean-Variance Frontier: Complete efficient frontier construction
• Optimal Asset Allocation: Risk-averse investor portfolio optimization

• Equal-Weighted Index Performance: Historical performance tracking (2000-2023)
• Efficient Frontier Plot: Risk-return trade-off visualization
• Statistical Distribution Analysis: Return distribution characteristics

• Monthly Mean Return: 0.68%
• Annualized Return: 8.45%
• Annualized Volatility: 15.4%
• 5% VaR: -6.65% (monthly)
• Skewness: -0.46 (left-skewed, indicating higher probability of extreme losses)
• Kurtosis: 0.70 (platykurtic, fewer extreme outliers than normal distribution)

1. Market Characteristics: S&P 500 shows negative skewness, indicating higher probability of extreme losses
2. Diversification Benefits: Portfolio optimization significantly reduces risk compared to individual stocks
3. Risk Management: VaR provides practical risk assessment for portfolio management
4. Optimal Allocation: Risk-averse investors should allocate approximately 46% to risky assets