!pip install yfinance numpy pandas !pip install pandas_datareader import yfinance as yf import numpy as np import pandas as pd from scipy.optimize import minimize import pandas_datareader.data as web stocks = ['AAPL', 'TSLA', 'PDD', 'XPEV', 'ASML'] start_date = '2018-09-07' end_date = '2023-09-07' data = yf.download(stocks, start=start_date, end=end_date) returns = data['Adj Close'].pct_change().dropna() def negative_sharpe_ratio(weights): portfolio_return = np.dot(returns.mean(), weights) portfolio_std = np.sqrt(np.dot(weights.T, np.dot(returns.cov(), weights))) return -portfolio_return / portfolio_std constraints = ({'type': 'eq', 'fun': lambda weights: np.sum(weights) - 1}) stock_bounds = tuple((0, 1) for stock in range(len(stocks))) solution_sharpe = minimize(negative_sharpe_ratio, [1./len(stocks)]*len(stocks), method='SLSQP', bounds=stock_bounds, constraints=constraints) weights_sharpe = solution_sharpe.x returns_sharpe = (returns * weights_sharpe).sum(axis=1) fama_french = web.DataReader('F-F_Research_Data_5_Factors_2x3_daily', 'famafrench', start=start_date, end=end_date)[0] fama_french = fama_french.div(100) # Convert to percentage fama_french.index = pd.to_datetime(fama_french.index, format='%Y%m%d') merged_data = pd.merge(pd.DataFrame(returns_sharpe, columns=['Max Sharpe Daily']), fama_french, left_index=True, right_index=True, how='inner') print(merged_data)

!pip install seaborn import seaborn as sns import matplotlib.pyplot as plt correlation_matrix = merged_data.corr() factors = ['Mkt-RF', 'SMB', 'HML', 'RMW', 'CMA'] for factor in factors: plt.figure(figsize=(8, 6)) sns.scatterplot(x='Max Sharpe Daily', y=factor, data=merged_data) plt.title(f'Scatter Plot of Max Sharpe Daily Returns vs. {factor} Returns') plt.xlabel('Max Sharpe Daily Returns') plt.ylabel(f'{factor} Returns') plt.grid(True) plt.show() plt.figure(figsize=(10, 8)) sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', vmin=-1, vmax=1) plt.title('Correlation Heatmap') plt.show()

!pip install statsmodels import statsmodels.api as sm results = {} for factor in factors: X = merged_data[factor] y = merged_data['Max Sharpe Daily'] - merged_data['RF'] # deducting risk-free rate from portfolio returns X = sm.add_constant(X) model = sm.OLS(y, X).fit() coefficient = model.params[factor] t_value_alpha = model.tvalues['const'] results[factor] = {'Coefficient': coefficient, 'T-Value (Alpha)': t_value_alpha} results_df = pd.DataFrame(results).T print(results_df) alpha_significance = results_df['T-Value (Alpha)'].apply(lambda x: "Significant" if abs(x) > 1.96 else "Not Significant") print("\nIntercept (Alpha) Significance at 5% level:") print(alpha_significance)

X = merged_data[factors] y = merged_data['Max Sharpe Daily'] - merged_data['RF'] # deducting risk-free rate from portfolio returns X = sm.add_constant(X) model = sm.OLS(y, X).fit() coefficients = model.params t_value_alpha = model.tvalues['const'] print("Portfolio's Sensitivity to Factors:") print(coefficients) alpha_significance = "Significant" if abs(t_value_alpha) > 1.96 else "Not Significant" print("\nIntercept (Alpha) Significance at 5% level:", alpha_significance)