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Quinta
2024-06-28 17:55:26 +02:00
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.idea/.gitignore
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.idea/MonteCarlo.iml
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README.md
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# MonteCarlo
## Monte Carlo Simulation to Estimate Pi
This program uses a Monte Carlo simulation to estimate the value of Pi. The program generates random points within a square of side length 2, centered at the origin, and calculates how many of those points fall inside a unit circle. The ratio of the points inside the circle to the total number of points is used to estimate Pi.
### How to Run
1. Make sure you have `numpy` and `matplotlib` installed, if not you can install them using the following command:
```bash
pip install requirements.txt
```
2. Save the script as `pi.py`.
3. Run the script using the command `python pi.py` or `py pi.py` if you have installed python from the microsoft store.
### Output
The output is an animation of the Monte Carlo simulation and a GIF file named PI.gif saved in the same directory.
## Portfolio Analysis with Real Stock Data
This program performs a Monte Carlo simulation to analyze the potential future returns of a portfolio composed of real stocks. Historical data is fetched from Yahoo Finance.
### How to Run
1. Make sure you have `numpy`, `pandas`, `matplotlib`, and `yfinance` installed, just as before if dont have them installed you can install them with the following command:
```bash
pip install requirements.txt
```
2. Save the script as `portfolio.py`.
3. Run the script using the command `python portfolio.py` or `py pi.py` if you have installed python from the microsoft store.
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# Sample historical return data (in real use, replace with actual data)
data = {
'Asset1': np.random.normal(0.01, 0.02, 1000),
'Asset2': np.random.normal(0.015, 0.025, 1000),
'Asset3': np.random.normal(0.02, 0.03, 1000),
}
returns = pd.DataFrame(data)
# Calculate mean returns and covariance matrix
mean_returns = returns.mean()
cov_matrix = returns.cov()
# Portfolio weights (assuming an equally weighted portfolio)
weights = np.array([1 / 3, 1 / 3, 1 / 3])
# Number of simulations
num_simulations = 100000
# 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%}")
pi.py
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import numpy as np
from numpy.random import uniform
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation, PillowWriter
num_of_frames = 50
num_of_samples = 150_000
x = uniform(low=-1.0, high=1.0, size=num_of_samples)
y = uniform(low=-1.0, high=1.0, size=num_of_samples)
radius = 1.0
theta = np.linspace(0, 2 * np.pi, 1000)
x_circle = radius * np.cos(theta)
y_circle = radius * np.sin(theta)
fig, ax = plt.subplots(figsize=(4.8, 4.8))
def animate(i):
ax.clear()
x_samples = x[:int(num_of_samples * (i + 1) / num_of_frames)]
y_samples = y[:int(num_of_samples * (i + 1) / num_of_frames)]
inside_circle = np.sqrt(x_samples ** 2 + y_samples ** 2) <= 1
x_inside = x_samples[inside_circle]
x_outside = x_samples[~inside_circle]
y_inside = y_samples[inside_circle]
y_outside = y_samples[~inside_circle]
ax.scatter(x_inside, y_inside, 1, c='b', alpha=0.5)
ax.scatter(x_outside, y_outside, 1, c='r', alpha=0.5)
ax.plot(x_circle, y_circle, 'k')
ax.axis('equal')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_title(fr'$n = ${len(x_samples):,} $\pi \approx {4 * len(x_inside) / len(x_samples):.4f}$')
return ax
# Create animation object
ani = FuncAnimation(fig, animate, frames=num_of_frames, interval=200, blit=False)
# Display the animation in a window
plt.show()
# Save the animation as a GIF
ani.save("PI.gif", dpi=300, writer=PillowWriter(fps=60))
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%}")
requirements.txt
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