#Optimal Portfolio Allocation using Modern Portfolio Theory -This project implements a portfolio optimization algorithm based on Modern Portfolio Theory (MPT). It analyzes historical data to allocate weights across a selection of assets in a way that maximizes the Sharpe Ratio, balancing expected return against risk.

#Overview -Assets considered: SPY, BND, GLD, QQQ, VTI -Data source: Historical price data via yfinance

#Methodology: -Computes log returns from adjusted closing prices -Annualizes return and covariance to evaluate performance -Uses Sharpe Ratio as the optimization objective -Solves the constrained optimization using SLSQP

#Features -Pulls 8 years of price data -Calculates expected return, volatility, and risk -Prevents short selling and overexposure via constraints -Visualizes the optimal allocation using a bar chart

#Installation -Make sure you have Python 3.x installed. Then install the required libraries:

#bash pip install numpy pandas yfinance scipy matplotlib

#Running the Script -bash python app.py

---You’ll see the optimal weights printed in the console along with the expected return, volatility, and Sharpe ratio. A bar chart will also display the final portfolio allocation.

#Example Output yaml Optimal Weights: SPY: 0.2010 BND: 0.2391 GLD: 0.1573 QQQ: 0.3026 VTI: 0.1000

Expected Annual Return: 0.1364 Expected Volatility: 0.1497 Sharpe Ratio: 0.7776

#Notes -The weights are subject to constraints: -Must sum to 1 (fully invested) -No short positions (minimum weight = 0) -Maximum 40% allocation to any single asset -The risk-free rate is assumed to be 2% for Sharpe Ratio calculations -You can modify the tickers list or adjust constraints to experiment with other asset mixes