Project Overview
This project explores portfolio optimization techniques for constructing efficient portfolios under long-only constraints. Using modern portfolio theory and numerical optimization, we analyze risk-return trade-offs in real-world investing scenarios where short selling is not permitted.
The analysis combines Monte Carlo simulation, Markowitz mean-variance optimization, and Sequential Least Squares Programming (SLSQP) to construct efficient frontiers under various practical constraints including minimum/maximum weights and sector limitations.
💰 Key Finance Concepts
Efficient Frontier: The set of optimal portfolios offering the highest expected return for each level of risk.
Sharpe Ratio: A measure of risk-adjusted return, calculated as excess return per unit of volatility.
Capital Market Line (CML): The line connecting the risk-free asset to the market portfolio, representing optimal risk-return combinations.
Long-Only Constraints: Investment restrictions that prevent short selling, requiring all portfolio weights to be non-negative.
🎯 Project Objectives
- Implement Markowitz mean-variance optimization
- Apply real-world long-only investment constraints
- Compare Monte Carlo vs. analytical optimization
- Analyze the impact of weight constraints on efficiency
- Visualize efficient frontiers and optimal allocations
🔧 Optimization Methods
- Monte Carlo simulation of random portfolios
- Sequential Least Squares Programming (SLSQP)
- Constrained quadratic programming
- Sharpe ratio maximization
- Minimum variance portfolio construction
📊 Analysis Features
- Efficient frontier construction and visualization
- Portfolio allocation pie charts
- Risk-return scatter plots
- Constraint impact analysis
- Capital Market Line identification
📈 Key Visualizations
SLSQP Optimization vs Random Portfolios
Impact of Minimum Weight Constraints
⚠️ Current Limitations
- Based on historical mean returns and covariances
- Assumes normally distributed returns
- No transaction costs or turnover constraints
- Static optimization (single-period model)
- Limited to publicly available market data