{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# EE16B: Discussion 10A" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# import necessary libraries\n", "import numpy as np\n", "import scipy.io as spio\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Financial Analysis with PCA\n", "\n", "You have recently joined the new hedge fund \"Berkeley Hathaway Partners\" as a quantitative analyst. Your job is to find a (small) basis that corresponds to the market, and to find the main stocks that make up this basis, eg. what stocks track the market best. \n", "\n", "Here, we have the [log return](https://quantivity.wordpress.com/2011/02/21/why-log-returns/) of 77 Fortune 500 stocks. We want to find the principal components of the market using our newly acquired knowledge of PCA." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Load stock data\n", "stock_data = spio.loadmat('77Stocks.mat')\n", "log_return = stock_data['LogReturn']\n", "ticker = stock_data['StockTicker']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 0: investigate the data\n", "What is the shape of data? How many stocks are there? And how many timestamps? \n", "Plot the data. Can you interpret any other information from the plot?" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "shape of log return: (77, 503)\n", "number of stocks: 77\n", "number of timestamps: 503\n" ] }, { "data": { "image/png": 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FTCkiF/ySDkdi9r0AR07GOz6x3Aa6+6L49sTl2Lz/cHA7IqIBI5cuSqGWrM3w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PUtDuwRJMiQnH6ysfYcXySnpm/J2yA8+RXd3MTtcq1rW/wZktpYSAy5rPYfzK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\nx6PZs2dz0kkn9byjlxle2ERrLtGnxZKj2XbqrpS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# investigate the shape\n", "print(\"shape of log return:\", log_return.shape)\n", "num_stocks, num_timestamps = log_return.shape\n", "print(\"number of stocks:\", num_stocks)\n", "print(\"number of timestamps:\", num_timestamps)\n", "\n", "# plot a few data slices\n", "idx = [0, 7, 14, 21]\n", "plt.figure(1, figsize=(20, 5))\n", "for i, j in enumerate(idx):\n", " plt.subplot(141+i)\n", " plt.xlim([0, num_timestamps])\n", " plt.xlabel(\"timestamps\")\n", " plt.ylabel(\"log return\")\n", " plt.title(\"stock #%d\"%(j))\n", " plt.plot(log_return[j]);\n", " \n", "\n", "# Plot all log returns\n", "plt.figure(2)\n", "plt.xlabel(\"timestamps\")\n", "plt.ylabel(\"log return\")\n", "plt.title(\"all stocks\")\n", "plt.plot(log_return.T);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 1: zero-center the data\n", "Since we are interested in the trend of each stock, we are interested in **rows** of the matrix." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(77, 503)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "log_return.shape" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.73984248358e-17\n" ] } ], "source": [ "### your code here ###\n", "log_return_centered = log_return - np.mean(log_return, axis=0)\n", "\n", "# verify that the data is zero-centered\n", "# the mean should be now zero (less than e-16)\n", "print(np.linalg.norm(np.mean(log_return_centered, axis=0)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 2: Calculate the Covariance matrix" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Compute the covariance matrix S\n", "### your code here ###\n", "S = " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 3: compute eigen-decomposition, and compare eigenvalues\n", "Plot the eigenvalues in one plot. What can you say about the plot? We want to decide how many basis vectors are really needed to explain the data. How many significant dimensions are there in the data? " ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#compute eigenvalues and eigenvectors of S\n", "### your code here ###\n", "D, P = \n", "\n", "#sort eigenvectors and eigenvalues so that larger eigenvalues come first\n", "Dinds = D.argsort()\n", "D = D[Dinds[::-1]]\n", "P = P[:,Dinds[::-1]]\n", "\n", "#plot eigenvalues in descending order\n", "plt.plot(D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Extra: \n", "Another way to show how much variance the Principal components capture is to plot the cumulative sum of eigenvalues" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the cumulative sum of singular values squared\n", "total_explained_variance = np.cumsum(D) / np.sum(D)\n", "\n", "plt.plot(total_explained_variance);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this graph, we can tell that we can capture more than 70% of the variance of the dataset with a basis of 10 rather than 77. This justifies the idea of \"the market average moves the market\". " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 4: transform the data matrix\n", "The (1st) principal component is the direction that captures most of the variance of data. In our case, the largest right singular vector captures most of the variance of stock trends. Project the data matrix along this direction and plot the result. What do you see? Is the vector relatively even across all of the stocks, or do a few stocks hold the majority of the weight?" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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S3+6hutiaCI0tYueJdowxvVoyh4XbNkTXunv9wUgVTabo9PrJ70dFT9hQ9+tJ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\ny6aVEzSw7kD/Nt94/AH+/rc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "### your code here ###\n", "v_1 = \n", "projection = \n", "plt.plot(np.abs(projection))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, what are the stocks that make up the majority of the largest singular vector? Find the top 5 stocks of the largest singular vector." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([[array(['FTU'], \n", " dtype='What do all of these stocks have in common? Look up the stock ticker symbols, they should all be of the same industry**" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.3" } }, "nbformat": 4, "nbformat_minor": 1 }