Week 11: Portfolio Optimization

Learn how to implement Modern Portfolio Theory (MPT) and optimize investment portfolios using Python.

Learning Objectives:

1. Foundations of Portfolio Optimization

Start with these fundamental resources:

Optimization: Background and Foundations - Essential video lecture
Portfolio Optimization - Comprehensive overview

import numpy as np
import pandas as pd
import yfinance as yf

# Download stock data
tickers = ['AAPL', 'MSFT', 'GOOGL', 'AMZN']
data = pd.DataFrame()
for ticker in tickers:
    data[ticker] = yf.download(ticker)['Adj Close']

# Calculate returns and covariance
returns = data.pct_change()
cov_matrix = returns.cov() * 252  # Annualized covariance

2. Practical Implementation

Learn how to implement portfolio optimization in Python:

Efficient Frontier & Portfolio Optimization in Python - Step-by-step tutorial
Extended Reading: Scientific Python - Advanced concepts

from scipy.optimize import minimize

def portfolio_stats(weights, returns, cov):
    portfolio_return = np.sum(returns.mean() * weights) * 252
    portfolio_std = np.sqrt(np.dot(weights.T, np.dot(cov, weights)))
    return portfolio_return, portfolio_std

# Minimize negative Sharpe Ratio
def neg_sharpe_ratio(weights):
    p_ret, p_std = portfolio_stats(weights, returns, cov_matrix)
    return -(p_ret - risk_free_rate) / p_std  # Negative SR for minimization

💡 ChatGPT Learning Tips

Use these prompts to enhance your understanding of portfolio optimization:

"Explain Modern Portfolio Theory and its key assumptions"
"Show me how to calculate portfolio risk and return in Python"
"Write code to implement the Efficient Frontier using scipy.optimize"
"How can I incorporate risk-free rate in portfolio optimization?"
"What are the limitations of MPT and how can we address them?"

📚 Research Tip: Use Perplexity.ai to search for "Modern Portfolio Theory Python implementation" or "portfolio optimization techniques"

Weekly Project: Portfolio Optimization Tool

Create a comprehensive portfolio optimization tool that includes:

Data collection and preprocessing for a set of stocks
Risk and return calculations
Efficient frontier visualization
Optimal portfolio weights calculation
Performance comparison with benchmark indices

Use the video lecture and provided resources as references for your implementation.