83 lines
3.0 KiB
Python
83 lines
3.0 KiB
Python
import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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import scipy.optimize as sco
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import yfinance as yf
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# 下载资产历史数据
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assets = ['AAPL', 'MSFT', 'GOOGL', 'AMZN', 'TSLA'] # 资产代码
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data = yf.download(assets, start="2020-01-01", end="2023-01-01")['Adj Close']
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print(data)
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# 计算每日收益率
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returns = data.pct_change().dropna()
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print(returns)
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# 计算年化预期收益和协方差矩阵
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annual_returns = returns.mean() * 252
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cov_matrix = returns.cov() * 252
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print(annual_returns)
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print(cov_matrix)
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# 定义组合的预期收益和风险（方差）
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def portfolio_performance(weights, mean_returns, cov_matrix):
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returns = np.sum(weights * mean_returns)
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volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
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return returns, volatility
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# 定义目标函数：最小化风险（方差）
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def minimize_volatility(weights, mean_returns, cov_matrix):
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return portfolio_performance(weights, mean_returns, cov_matrix)[1]
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# 定义约束条件
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def constraint_sum(weights):
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return np.sum(weights) - 1
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# 初始化权重和边界（每个资产的权重在0-1之间）
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num_assets = len(assets)
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bounds = tuple((0, 1) for asset in range(num_assets))
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initial_weights = num_assets * [1. / num_assets] # 初始等权重
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# 定义约束条件：总权重为1
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constraints = ({'type': 'eq', 'fun': constraint_sum})
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# 优化组合，使得组合的方差最小
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opt_result = sco.minimize(minimize_volatility, initial_weights, args=(annual_returns, cov_matrix),
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method='SLSQP', bounds=bounds, constraints=constraints)
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# 提取最优权重
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optimal_weights = opt_result.x
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# 计算最优组合的收益和风险
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optimal_return, optimal_volatility = portfolio_performance(optimal_weights, annual_returns, cov_matrix)
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# 输出最优组合结果
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print("最优资产组合权重:")
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for i, asset in enumerate(assets):
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print(f"{asset}: {optimal_weights[i]:.2%}")
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print(f"\n最优组合的年化预期收益: {optimal_return:.2%}")
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print(f"最优组合的年化风险（标准差）: {optimal_volatility:.2%}")
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# 可视化有效前沿
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def plot_efficient_frontier(mean_returns, cov_matrix, num_portfolios=10000):
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results = np.zeros((3, num_portfolios))
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for i in range(num_portfolios):
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weights = np.random.random(num_assets)
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weights /= np.sum(weights)
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portfolio_return, portfolio_volatility = portfolio_performance(weights, mean_returns, cov_matrix)
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results[0, i] = portfolio_return
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results[1, i] = portfolio_volatility
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results[2, i] = results[0, i] / results[1, i] # 计算夏普比率
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plt.figure(figsize=(10, 6))
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plt.scatter(results[1, :], results[0, :], c=results[2, :], cmap='viridis')
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plt.colorbar(label='Sharpe Ratio')
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plt.scatter(optimal_volatility, optimal_return, c='red', marker='*', s=200) # 最优组合
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plt.title('Efficient Frontier')
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plt.xlabel('Volatility (Risk)')
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plt.ylabel('Return')
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plt.show()
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# 绘制有效前沿
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plot_efficient_frontier(annual_returns, cov_matrix) |