352 lines
8.3 KiB
Plaintext
352 lines
8.3 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "301963b1",
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"metadata": {},
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"source": [
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"<div style=\"background-color:#000;\"><img src=\"pqn.png\"></img></div>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "667b85b6",
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"metadata": {},
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"source": [
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"This code performs Principal Component Analysis (PCA) on a portfolio of stocks to identify principal components driving the returns. It retrieves historical stock data, calculates daily returns, and applies PCA to these returns. The explained variance and principal components are visualized, and the factor returns and exposures are computed. These statistical risk factors help in understanding how much of the portfolio's returns arise from unobservable features. This is useful for portfolio management, risk assessment, and diversification analysis."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "71d0282c",
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"metadata": {},
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"outputs": [],
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"source": [
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"import yfinance as yf"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "746b91c7",
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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"from sklearn.decomposition import PCA\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2863a52a",
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"metadata": {},
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"source": [
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"Define a list of stock symbols to retrieve historical data for"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "4f98bfc4",
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"metadata": {},
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"outputs": [],
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"source": [
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"symbols = [\n",
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" 'IBM',\n",
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" 'MSFT',\n",
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" 'META',\n",
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" 'INTC',\n",
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" 'NEM',\n",
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" 'AU',\n",
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" 'AEM',\n",
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" 'GFI'\n",
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"]"
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]
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},
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{
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"cell_type": "markdown",
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"id": "02e922c9",
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"metadata": {},
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"source": [
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"Download historical adjusted close prices for the defined stock symbols within the specified date range"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "a563405d",
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"metadata": {},
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"outputs": [],
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"source": [
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"data = yf.download(symbols, start=\"2020-01-01\", end=\"2022-11-30\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1f52f786",
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"metadata": {},
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"source": [
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"Calculate daily returns for the portfolio by computing percentage change and dropping NaN values"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "0b26bb2f",
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"metadata": {},
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"outputs": [],
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"source": [
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"portfolio_returns = data['Adj Close'].pct_change().dropna()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d6a1198c",
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"metadata": {},
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"source": [
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"Apply Principal Component Analysis (PCA) to the portfolio returns to identify key components"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "a9c1ac8b",
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"metadata": {},
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"outputs": [],
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"source": [
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"pca = PCA(n_components=3)\n",
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"pca.fit(portfolio_returns)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7dea06ae",
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"metadata": {},
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"source": [
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"Retrieve the explained variance ratio and the principal components from the PCA model"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "3ed0fced",
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"metadata": {},
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"outputs": [],
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"source": [
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"pct = pca.explained_variance_ratio_\n",
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"pca_components = pca.components_"
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]
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},
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{
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"cell_type": "markdown",
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"id": "91fe5bfd",
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"metadata": {},
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"source": [
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"Calculate the cumulative explained variance for visualization and create an array for component indices"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "4b40fb20",
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"metadata": {},
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"outputs": [],
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"source": [
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"cum_pct = np.cumsum(pct)\n",
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"x = np.arange(1, len(pct) + 1, 1)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a58e88c7",
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"metadata": {},
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"source": [
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"Plot the percentage contribution of each principal component and the cumulative contribution"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "184bb55c",
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"metadata": {},
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"outputs": [],
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"source": [
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"plt.subplot(1, 2, 1)\n",
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"plt.bar(x, pct * 100, align=\"center\")\n",
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"plt.title('Contribution (%)')\n",
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"plt.xlabel('Component')\n",
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"plt.xticks(x)\n",
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"plt.xlim([0, 4])\n",
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"plt.ylim([0, 100])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "9fbd347d",
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"metadata": {},
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"outputs": [],
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"source": [
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"plt.subplot(1, 2, 2)\n",
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"plt.plot(x, cum_pct * 100, 'ro-')\n",
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"plt.title('Cumulative contribution (%)')\n",
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"plt.xlabel('Component')\n",
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"plt.xticks(x)\n",
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"plt.xlim([0, 4])\n",
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"plt.ylim([0, 100])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5b0a4722",
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"metadata": {},
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"source": [
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"Construct statistical risk factors using the principal components and portfolio returns"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "027a88cf",
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"metadata": {},
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"outputs": [],
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"source": [
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"X = np.asarray(portfolio_returns)\n",
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"factor_returns = X.dot(pca_components.T)\n",
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"factor_returns = pd.DataFrame(\n",
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" columns=[\"f1\", \"f2\", \"f3\"], \n",
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" index=portfolio_returns.index,\n",
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" data=factor_returns\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3ba5fc5f",
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"metadata": {},
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"source": [
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"Display the first few rows of the factor returns DataFrame"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "3f7ee295",
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"metadata": {},
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"outputs": [],
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"source": [
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"factor_returns.head()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ae7022ed",
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"metadata": {},
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"source": [
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"Calculate and display the factor exposures by transposing the principal components matrix"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "69a1609b",
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"metadata": {},
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"outputs": [],
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"source": [
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"factor_exposures = pd.DataFrame(\n",
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" index=[\"f1\", \"f2\", \"f3\"], \n",
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" columns=portfolio_returns.columns,\n",
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" data=pca_components\n",
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").T"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "406e4727",
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"metadata": {},
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"outputs": [],
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"source": [
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"factor_exposures"
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]
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},
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{
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"cell_type": "markdown",
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"id": "73a266c3",
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"metadata": {},
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"source": [
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"Sort and plot the factor exposures for the first principal component (f1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "7ff5ca2a",
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"metadata": {},
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"outputs": [],
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"source": [
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"factor_exposures.f1.sort_values().plot.bar()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "65c58ba2",
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"metadata": {},
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"source": [
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"Scatter plot to visualize factor exposures of the first two principal components (f1 and f2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "6fd70496",
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"metadata": {},
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"outputs": [],
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"source": [
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"labels = factor_exposures.index\n",
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"data = factor_exposures.values\n",
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"plt.scatter(data[:, 0], data[:, 1])\n",
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"plt.xlabel('factor exposure of PC1')\n",
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"plt.ylabel('factor exposure of PC2')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "789e384f",
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"metadata": {},
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"outputs": [],
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"source": [
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"for label, x, y in zip(labels, data[:, 0], data[:, 1]):\n",
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" plt.annotate(\n",
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" label,\n",
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" xy=(x, y), \n",
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" xytext=(-20, 20),\n",
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" textcoords='offset points',\n",
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" arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0')\n",
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" )"
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]
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},
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{
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"cell_type": "markdown",
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"id": "425b0e57",
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"metadata": {},
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"source": [
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"<a href=\"https://pyquantnews.com/\">PyQuant News</a> is where finance practitioners level up with Python for quant finance, algorithmic trading, and market data analysis. Looking to get started? Check out the fastest growing, top-selling course to <a href=\"https://gettingstartedwithpythonforquantfinance.com/\">get started with Python for quant finance</a>. For educational purposes. Not investment advise. Use at your own risk."
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]
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "-all",
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"main_language": "python",
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"notebook_metadata_filter": "-all"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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