Having fun with statistics

portfolio.py

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+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+import yfinance as yf
+
+# Define the list of stock tickers and the portfolio weights
+tickers = ['AAPL', 'MSFT', 'GOOGL']
+weights = np.array([0.3, 0.4, 0.3])  # Example weights, should sum to 1
+
+# Fetch historical data for the tickers
+data = yf.download(tickers, start="2020-01-01", end="2023-01-01")['Adj Close']
+
+# Calculate daily returns
+returns = data.pct_change().dropna()
+
+# Calculate mean returns and covariance matrix
+mean_returns = returns.mean()
+cov_matrix = returns.cov()
+
+# Number of simulations
+num_simulations = 10000
+
+# Time horizon (e.g., 252 trading days in a year)
+time_horizon = 252
+
+# Initialize arrays to store simulation results
+simulated_portfolio_returns = np.zeros(num_simulations)
+
+# Run Monte Carlo simulations
+for i in range(num_simulations):
+    # Generate random returns for each asset
+    random_returns = np.random.multivariate_normal(mean_returns, cov_matrix, time_horizon)
+
+    # Calculate portfolio return for each time period
+    portfolio_returns = np.dot(random_returns, weights)
+
+    # Calculate cumulative return over the time horizon
+    cumulative_return = np.prod(1 + portfolio_returns) - 1
+
+    # Store the cumulative return in the results array
+    simulated_portfolio_returns[i] = cumulative_return
+
+# Plot the distribution of simulated portfolio returns
+plt.hist(simulated_portfolio_returns, bins=50, edgecolor='k', alpha=0.7)
+plt.title('Distribution of Simulated Portfolio Returns')
+plt.xlabel('Cumulative Return')
+plt.ylabel('Frequency')
+plt.show()
+
+# Summary statistics
+mean_simulated_return = np.mean(simulated_portfolio_returns)
+std_dev_simulated_return = np.std(simulated_portfolio_returns)
+var_95 = np.percentile(simulated_portfolio_returns, 5)
+
+print(f"Mean Simulated Return: {mean_simulated_return:.2%}")
+print(f"Standard Deviation of Simulated Return: {std_dev_simulated_return:.2%}")
+print(f"Value at Risk (95% confidence level): {var_95:.2%}")