Simple Hedge for Portfolio Risk Management

# INSTALL REQUIRED LIBRARIES
# pip3 install yfinance --upgrade
# pip3 install statsmodels.api --upgrade
# pip3 install matplotlib
# pip3 install nbconvert # to convert the article to md later.

# IMPORT LIBARIES
import yfinance as yf
import statsmodels.api as sm
import matplotlib.pyplot as plt

# Set to display plots in Jupyter Notebook
%matplotlib inline

# Define tickers for "Magnificent 7" tech stocks and benchmark
tickers = ['AAPL', 'MSFT', 'AMZN', 'NVDA', 'GOOG', 'META', 'TSLA', 'QQQ']
#print(tickers)

# Define time period
start_date = "2022-01-01"
end_date = "2023-12-31"

# Fetch adjusted closing prices from Yahoo Finance
data = yf.download(tickers, start=start_date, end=end_date)['Adj Close']
#data.head()

# Calculate benchmark returns Nasdaq-100 ETF (QQQ), then remove QQQ from the portfolio data
benchmark_returns = data.pop('QQQ').pct_change().dropna()

# Calculate portfolio returns (sum of daily percentage changes for remaining stocks
portfolio_returns = data.pct_change().dropna().sum(axis=1)
#benchmark_returns.head()
#portfolio_returns.head()

# Linear Regression function for return analysis
def linreg(x,y):
    """Perform linear regression using OLS and return the model."""
    x = sm.add_constant(x)
    model = sm.OLS(y, x).fit()
    return model

# Calculate alpha and beta for the unhedged portfolio
X = benchmark_returns.values.reshape(-1, 1)
Y = portfolio_returns.values.reshape(-1, 1)
model = linreg(X, Y)
alpha, beta = model.params[0], model.params[1]
#print(f'Alpha: ', alpha)
#print(f'Beta: ', beta)

# Create a hedged portfolio by adjusting portfolio returns with the beta
hedged_portfolio_returns = portfolio_returns - beta * benchmark_returns

# Calculate alpha and beta for the hedged portfolio
P = hedged_portfolio_returns.values
model_hedged = linreg(X, P)
alpha_hedged, beta_hedged = model_hedged.params[0], model_hedged.params[1]
#print(f'Alpha_Hedged: ', alpha_hedged)
#print(f'Beta_Hedged: ', beta_hedged)

# Print regression summaries
print("Unhedged Portfolio Regression Summary")
print(model.summary())
print('==============================================================================')
print(f'Unhedged Alpha: {alpha:.4f}, Unhedged Beta: {beta:.4f}\n')
print("Hedged Portfolio Regression Summary")
print(model_hedged.summary())
print('==============================================================================')
print(f'Hedged Alpha: {alpha_hedged:.4f}, Hedged Beta: {beta_hedged:.4f}\n')

# Calculate cumulative returns for both portfolios
cumulative_unhedged = (1 + portfolio_returns).cumprod() - 1
cumulative_hedged = (1 + hedged_portfolio_returns).cumprod() - 1

# Plotting the unhedged and hedged portfolio returns compared to the benchmark, 
# Cumulative returns to understand the overall impact of hedging

fig, axs = plt.subplots(3, 1, figsize=(12, 15), sharex=True)

# Plot 1: Unhedget Portfolio vs Benchmark Returns
axs[0].plot(portfolio_returns, color='orange', label='Unhedged Portfolio')
axs[0].plot(benchmark_returns, color='blue', label='Benchmark')
axs[0].set_title('Unhedged - Benchmark vs Portfolio Returns')
axs[0].set_xlabel('Date')
axs[0].set_ylabel('Daily Returns in %')
axs[0].set_ylim(-0.5 , 0.5)
axs[0].legend()
axs[0].grid(True)

# Annotate unhedged alpha and beta values
axs[0].text(0.05, 0.9, f'Unhedged Alpha: {alpha:.4f}\nUnhedged Beta: {beta:.4f}',
            transform=axs[0].transAxes, fontsize=10, color='red', verticalalignment='top',
            bbox=dict(boxstyle='round,pad=0.5', edgecolor='black', facecolor='white'))

# Plot 2: Hedget Portfolio vs Benchmark Returns
axs[1].plot(hedged_portfolio_returns, color='green', label='Hedged Portfolio')
axs[1].plot(benchmark_returns, color='blue', label='Benchmark')
axs[1].set_title('Hedged - Benchmark vs Portfolio Returns')
axs[1].set_xlabel('Date')
axs[1].set_ylabel('Daily Returns in %')
axs[1].set_ylim(-0.5 , 0.5)
axs[1].legend()
axs[1].grid(True)

# Annotate hedged alpha and beta values
axs[1].text(0.05, 0.9, f'Hedged Alpha: {alpha_hedged:.4f}\nHedged Beta: {beta_hedged:.4f}',
            transform=axs[1].transAxes, fontsize=10, color='red', verticalalignment='top',
            bbox=dict(boxstyle='round,pad=0.5', edgecolor='black', facecolor='white'))


# Plot 3: Cumulative Unhedged vs Hedged Portfolio Returns
axs[2].plot(cumulative_unhedged, color='orange', label='Cumulative Unhedged Portfolio')
axs[2].plot(cumulative_hedged, color='green', label='Cumulative Hedged Portfolio')
axs[2].set_title('Cumulative Returns - Unhedged vs Hedged Portfolio')
axs[2].set_xlabel('Date')
axs[2].set_ylabel('Cumulative Returns')
axs[2].legend()
axs[2].grid(True)

plt.tight_layout()
plt.show()

# Display the plot
plt.tight_layout()
plt.show()

# List of Sample Portfolios with their benchmarks provided for further testing, by assigning these portfolios to `tickers`
MAG7 =  ['MSFT', 'AAPL', 'GOOG', 'META', 'AMZN', 'NVDA', 'TSLA', 'QQQ']             
FAANG = ['META', 'AAPL', 'AMZN', 'NFLX', 'GOOG', 'SPY']                          
MANGA = ['MSFT', 'AAPL', 'NVDA', 'GOOG', 'AMZN', 'QQQ']                         
TAND =  ['TSLA', 'AAPL', 'NVDA', 'DIS', 'QQQ']                                
MAAN =  ['MSFT', 'AAPL', 'AMZN', 'NVDA', 'QQQ']                               
FANTASY=['META', 'AMZN', 'NFLX', 'TSLA', 'GOOG', 'CRM', 'ZM', 'ARKK']               
BAT =   ['BIDU', 'BABA', 'TCEHY', 'HSTECH'] 

# List of Sample benchmarks
benchmark_list = ['QQQ', 'SPY', 'ARKK', 'HSTECH']