📊 Portfolio Optimization and Risk Simulation

This project applies Modern Portfolio Theory (MPT) to analyze the trade-off between risk and return across a portfolio of assets.
Using Monte Carlo simulation and numerical optimization, it identifies the maximum Sharpe ratio and minimum variance portfolios, visualizing the efficient frontier that represents optimal investment strategies.

---

🧠 Overview

• Goal: Model and optimize investment portfolios using historical stock data.
• Approach:
  • Simulate thousands of random portfolios to explore possible risk–return combinations.
  • Apply optimization techniques (scipy.optimize) to find portfolios with the best risk-adjusted return and the lowest volatility.
• Core Concepts:
  • Monte Carlo Simulation
  • Covariance-based Risk Modeling
  • Efficient Frontier Visualization
  • Sharpe Ratio Maximization
  • Modern Portfolio Theory (MPT)

---

🧰 Technologies Used

Category	Tools
Programming	Python
Libraries	NumPy, Pandas, Matplotlib, SciPy, yFinance
Optimization	scipy.optimize.minimize (SLSQP)
Data	Historical daily prices from Yahoo Finance

---

📈 Methodology

1. Data Collection

• Downloaded 5 years of daily closing prices for AAPL, MSFT, GOOG, and AMZN using yfinance.

2. Return Calculation

• Computed daily and annualized returns.
• Calculated the covariance matrix to represent asset co-movements.

3. Monte Carlo Simulation

• Generated 10,000+ random portfolios with randomized weights.
• Calculated each portfolio’s expected return, volatility, and Sharpe ratio.

4. Optimization

• Used Sequential Least Squares Programming (SLSQP) to:
  • Maximize Sharpe ratio, identifying the optimal risk-adjusted portfolio.
  • Minimize variance, finding the most stable allocation.

5. Visualization

• Plotted the efficient frontier showing portfolios that yield the highest return for each level of risk.
• Highlighted:
  • 🔴 Max Sharpe Ratio Portfolio
  • 🟢 Minimum Variance Portfolio

---

🧮 Results

---

🖥️ How to Run

1. Clone and run this repository

   git clone https://github.com/evy004/PortfolioSimulation.git
   cd PortfolioSimulation
   pip install -r requirements.txt
   python main.py