Having fun with statistics

.idea/.gitignore

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+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml

.idea/MonteCarlo.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="jdk" jdkName="Python 3.11" jdkType="Python SDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+  <component name="PackageRequirementsSettings">
+    <option name="versionSpecifier" value="Greater or equal (&gt;=x.y.z)" />
+    <option name="removeUnused" value="true" />
+  </component>
+</module>

.idea/git_toolbox_blame.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="GitToolBoxBlameSettings">
+    <option name="version" value="2" />
+  </component>
+</project>

.idea/inspectionProfiles/Project_Default.xml

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+<component name="InspectionProjectProfileManager">
+  <profile version="1.0">
+    <option name="myName" value="Project Default" />
+    <inspection_tool class="Eslint" enabled="true" level="WARNING" enabled_by_default="true" />
+    <inspection_tool class="PyPackageRequirementsInspection" enabled="true" level="WARNING" enabled_by_default="true">
+      <option name="ignoredPackages">
+        <value>
+          <list size="11">
+            <item index="0" class="java.lang.String" itemvalue="notebook_shim" />
+            <item index="1" class="java.lang.String" itemvalue="jupyter_server" />
+            <item index="2" class="java.lang.String" itemvalue="jupyterlab_widgets" />
+            <item index="3" class="java.lang.String" itemvalue="automium_web" />
+            <item index="4" class="java.lang.String" itemvalue="jupyterlab_pygments" />
+            <item index="5" class="java.lang.String" itemvalue="jupyter_client" />
+            <item index="6" class="java.lang.String" itemvalue="typing_extensions" />
+            <item index="7" class="java.lang.String" itemvalue="jupyter_server_terminals" />
+            <item index="8" class="java.lang.String" itemvalue="prometheus_client" />
+            <item index="9" class="java.lang.String" itemvalue="jupyter_core" />
+            <item index="10" class="java.lang.String" itemvalue="jupyterlab_server" />
+          </list>
+        </value>
+      </option>
+    </inspection_tool>
+    <inspection_tool class="PyShadowingBuiltinsInspection" enabled="true" level="WEAK WARNING" enabled_by_default="true">
+      <option name="ignoredNames">
+        <list>
+          <option value="id" />
+        </list>
+      </option>
+    </inspection_tool>
+    <inspection_tool class="PyUnresolvedReferencesInspection" enabled="true" level="WARNING" enabled_by_default="true">
+      <option name="ignoredIdentifiers">
+        <list>
+          <option value="statsmodels.tsa.arima.model.*" />
+        </list>
+      </option>
+    </inspection_tool>
+  </profile>
+</component>

.idea/inspectionProfiles/profiles_settings.xml

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+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/misc.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Black">
+    <option name="sdkName" value="Python 3.11" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.11" project-jdk-type="Python SDK" />
+</project>

.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/MonteCarlo.iml" filepath="$PROJECT_DIR$/.idea/MonteCarlo.iml" />
+    </modules>
+  </component>
+</project>

.idea/other.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="PySciProjectComponent">
+    <option name="PY_INTERACTIVE_PLOTS_SUGGESTED" value="true" />
+  </component>
+</project>

.idea/vcs.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="" vcs="Git" />
+  </component>
+</project>

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.

fictportfolio.py

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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%}")