59 lines
1.9 KiB
Python
59 lines
1.9 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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# Sample historical return data (in real use, replace with actual data)
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data = {
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'Asset1': np.random.normal(0.01, 0.02, 1000),
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'Asset2': np.random.normal(0.015, 0.025, 1000),
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'Asset3': np.random.normal(0.02, 0.03, 1000),
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}
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returns = pd.DataFrame(data)
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# Calculate mean returns and covariance matrix
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mean_returns = returns.mean()
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cov_matrix = returns.cov()
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# Portfolio weights (assuming an equally weighted portfolio)
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weights = np.array([1 / 3, 1 / 3, 1 / 3])
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# Number of simulations
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num_simulations = 100000
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# Time horizon (e.g., 252 trading days in a year)
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time_horizon = 252
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# Initialize arrays to store simulation results
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simulated_portfolio_returns = np.zeros(num_simulations)
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# Run Monte Carlo simulations
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for i in range(num_simulations):
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# Generate random returns for each asset
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random_returns = np.random.multivariate_normal(mean_returns, cov_matrix, time_horizon)
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# Calculate portfolio return for each time period
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portfolio_returns = np.dot(random_returns, weights)
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# Calculate cumulative return over the time horizon
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cumulative_return = np.prod(1 + portfolio_returns) - 1
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# Store the cumulative return in the results array
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simulated_portfolio_returns[i] = cumulative_return
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# Plot the distribution of simulated portfolio returns
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plt.hist(simulated_portfolio_returns, bins=50, edgecolor='k', alpha=0.7)
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plt.title('Distribution of Simulated Portfolio Returns')
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plt.xlabel('Cumulative Return')
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plt.ylabel('Frequency')
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plt.show()
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# Summary statistics
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mean_simulated_return = np.mean(simulated_portfolio_returns)
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std_dev_simulated_return = np.std(simulated_portfolio_returns)
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var_95 = np.percentile(simulated_portfolio_returns, 5)
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print(f"Mean Simulated Return: {mean_simulated_return:.2%}")
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print(f"Standard Deviation of Simulated Return: {std_dev_simulated_return:.2%}")
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print(f"Value at Risk (95% confidence level): {var_95:.2%}")
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