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import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

import seaborn as sns

import yfinance as yf

def plot_risk_and_returns(annual_returns, annual_risk):

    # Summarize the results

    summary = pd.DataFrame({

        'Annual Return (%)': annual_returns,

        'Annual Risk (%)': annual_risk

    })

    # Plotting the results

    plt.figure(figsize=(10, 6))

    plt.scatter(summary['Annual Risk (%)'], summary['Annual Return (%)'], color='blue')

    for i, txt in enumerate(summary.index):

        plt.annotate(txt, (summary['Annual Risk (%)'][i], summary['Annual Return (%)'][i]), fontsize=12)

    plt.title('Annual Return vs. Annual Risk')

    plt.xlabel('Annual Risk (%)')

    plt.ylabel('Annual Return (%)')

    plt.grid(True)

    plt.xlim(0, summary['Annual Risk (%)'].max() * 1.1)  # Extend x-axis slightly

    plt.ylim(0, summary['Annual Return (%)'].max() * 1.1)  # Extend y-axis slightly

    plt.savefig("risk_and_returns.png")

def plot_cov_matrix(cov_matrix):

    # Display the covariance matrix as a heatmap

    plt.figure(figsize=(10, 8))

    sns.heatmap(cov_matrix, annot=True, fmt=".6f", cmap='coolwarm', linewidths=.5)

    plt.title('Covariance Matrix Heatmap')

    plt.savefig("cov_matrix.png")

# Define the tickers

tickers = ['VTI', 'BND','GLDM']

# Fetch historical data for the past 10 years

data = yf.download(tickers, start='2014-05-31', end='2024-05-31')['Adj Close']

returns = data.pct_change().dropna()

# Calculate annual returns and risk

annual_returns = returns.mean() * 252

annual_risk = returns.std() * np.sqrt(252)

plot_risk_and_returns(annual_returns, annual_risk)

# Calculate covariance matrix

cov_matrix = returns.cov() * 252

plot_cov_matrix(cov_matrix)

# Monte Carlo simulation

num_portfolios = 100000

results = np.zeros((3 + len(tickers), num_portfolios))

for i in range(num_portfolios):

    weights = np.random.random(len(tickers))

    weights /= np.sum(weights)

   

    portfolio_return = np.dot(weights, annual_returns)

    portfolio_risk = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))

   

    results[0, i] = portfolio_return

    results[1, i] = portfolio_risk

    results[2, i] = portfolio_return / portfolio_risk

    for j in range(len(tickers)):

        results[3 + j, i] = weights[j]

# Create DataFrame

columns = ['Return', 'Risk', 'Sharpe Ratio'] + tickers

results_frame = pd.DataFrame(results.T, columns=columns)

# Find the portfolio with the maximum Sharpe Ratio

max_sharpe_idx = results_frame['Sharpe Ratio'].idxmax()

max_sharpe_portfolio = results_frame.loc[max_sharpe_idx]

# Plot efficient frontier

plt.figure(figsize=(10, 6))

plt.scatter(results_frame['Risk'], results_frame['Return'], c=results_frame['Sharpe Ratio'], cmap='viridis')

plt.colorbar(label='Sharpe Ratio')

plt.xlabel('Risk')

plt.ylabel('Return')

plt.title('Efficient Frontier')

plt.scatter(max_sharpe_portfolio['Risk'], max_sharpe_portfolio['Return'], color='red', marker='*', s=100)  # Max Sharpe Ratio point

plt.xlim(0, results_frame['Risk'].max() * 1.1)  # Extend x-axis slightly

plt.ylim(0, results_frame['Return'].max() * 1.1)  # Extend y-axis slightly

plt.savefig("mvo.png")

# Output the portfolio with the maximum Sharpe Ratio

max_sharpe_weights = max_sharpe_portfolio[tickers]

print(f"Max Sharpe Ratio Portfolio Weights:\n{max_sharpe_weights}")

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Pythonで学ぶモダンポートフォリオ理論：平均分散最適化の考え方 - Otama's Playground