{ "metadata": { "name": "", "signature": "sha256:f2c5aa586d64c13760b044d697532f8d2b3ea33463d294bcc4a76b8d66435177" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Power Law Analysis on Stock Markets\n", "Submitted as CSS 625 Assignment\n", "\n", "Analyst: [Talha OZ](https://twitter.com/tozCSS)\n", "\n", "Instructor: [Maksim Tsvetovat](https://twitter.com/maksim2042)\n", "###Assignment\n", "1. Get a stock market dataset of your choice -- pick an index\n", "2. Get historical data on a stock (or two) that is a part of that index\n", "3. Compute day over day, month over month and year over year delta. Try both absolute ($ value) and relative differences (%)\n", "4. Are deltas power-law distributed?\n", "5. Compute alphas for all of them\n", "6. Are the alphas similar? Where are the differences?\n", "7. Compute C for day over day distribution on an index\n", "8. Compute probability of a stock market crash (losing > 30% value)\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import plotly.plotly as py\n", "from plotly.graph_objs import *\n", "import urllib.request" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# 1. Get a stock market dataset of your choice -- pick an index\n", "# The New York Stock Exchange (NYSE) is by far the world's largest stock exchange\n", "# by market capitalization of its listed companies at US$16.6 trillion as of February 2015\n", "# urllib.request.urlretrieve(\"http://www1.nyse.com/indexes/nyahist.csv\", \"nyahist.csv\")\n", "# Read in the downloaded NYSE index history file as is\n", "df = pd.read_csv('nyahist.csv',skiprows=1,header=0,usecols=[0,1],names=['dt','price'],parse_dates=[0])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# 2. Get historical data on a stock (or two) that is a part of that index\n", "ibm = pd.read_csv('IBM_Exxon.csv',usecols=[0,1],names=['dt','price'],header=0,parse_dates=[0])\n", "exx = pd.read_csv('IBM_Exxon.csv',usecols=[0,2],names=['dt','price'],header=0,parse_dates=[0])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# 3. get daily,monthly and yearly absolute & relative deltas\n", "def get_deltas(df,delta='dy'):\n", " \"\"\"delta can be 'dy', 'mo' or 'yr'\"\"\"\n", " if delta=='mo':\n", " df = df.groupby(df.dt.dt.to_period('M'),as_index=False).nth(0).loc[:,['dt','price']]\n", " elif delta=='yr':\n", " df = df.groupby(df.dt.dt.to_period('Y'),as_index=False).nth(0).loc[:,['dt','price']]\n", " df._metadata = {'delta':delta}\n", " df.loc[df.index[0],'absolute'] = 0\n", " df.loc[df.index[1]:,'absolute'] = df.loc[df.index[1]:,'price'].values - df.loc[:df.index[-2],'price'].values\n", " df.absolute = df.absolute.abs()\n", " df['relative'] = df.absolute / df.price\n", " return df\n", "\n", "\n", "# get standard deviations for daily, monthly and yearly changes...\n", "def get_std(df):\n", " header = ['sample size','price std','abs std','rel std']\n", " return pd.DataFrame([[len(df),df.price.std(),df.absolute.std(),df.relative.std()]],\n", " index=[df._metadata['delta']],columns=header)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "# get deltas\n", "deltas=[]\n", "for delta in ('dy','mo','yr'):\n", " deltas.append(get_deltas(df,delta=delta))\n", "# expecting higher variance as sample size gets smaller\n", "std = pd.DataFrame()\n", "for delta in deltas:\n", " std = std.append(get_std(delta))\n", "std" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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sample sizeprice stdabs stdrel std
dy 9869 2311.920557 41.527595 0.007652
mo 472 2326.309189 166.941093 0.031725
yr 41 2433.346535 326.264125 0.086290
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ " sample size price std abs std rel std\n", "dy 9869 2311.920557 41.527595 0.007652\n", "mo 472 2326.309189 166.941093 0.031725\n", "yr 41 2433.346535 326.264125 0.086290" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# 4. Are deltas power-law distributed?\n", "# 5. Compute alphas for all of them\n", "# 6. Are the alphas similar? Where are the differences?\n", "# 7. Compute C for day over day distribution on an index\n", "def get_alphaC(df,absolute=True):\n", " \"\"\"header = ['sample size','\u03b1 using aggregation method','Normalization constant C for \u03b1>1']\"\"\"\n", " if absolute:\n", " alpha = 1 + len(df.absolute[df.absolute>0])/sum([np.log(x) for x in df.absolute[df.absolute>0]])\n", " C = (alpha-1)*(min(df.absolute[df.absolute>0])**(alpha-1))\n", " else:\n", " alpha = 1 + len(df.relative[df.relative>0])/sum([np.log(x) for x in df.relative[df.relative>0]])\n", " C = (alpha-1)*(min(df.relative[df.relative>0])**(alpha-1)) \n", " return pd.DataFrame([[alpha,C]], index=[df._metadata['delta']], columns=['alpha','C'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "print('NYSE index using absolute deltas:')\n", "alphaC = pd.DataFrame()\n", "for delta in deltas:\n", " alphaC = alphaC.append(get_alphaC(delta))\n", "alphaC " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "NYSE index using absolute deltas:\n" ] }, { "html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
alphaC
dy 1.567097 0.153660
mo 1.288382 0.148452
yr 1.205517 0.222761
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ " alpha C\n", "dy 1.567097 0.153660\n", "mo 1.288382 0.148452\n", "yr 1.205517 0.222761" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "ibm_d = []\n", "for delta in ('dy','mo','yr'):\n", " ibm_d.append(get_deltas(ibm,delta=delta))\n", "print('IBM stock absolute deltas:')\n", "alphaC = pd.DataFrame()\n", "for delta in ibm_d:\n", " alphaC = alphaC.append(get_alphaC(delta))\n", "alphaC" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "IBM stock absolute deltas:\n" ] }, { "html": [ "
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alphaC
dy-0.104839-179.050702
mo 2.469503 0.009002
yr 1.467852 0.196278
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ " alpha C\n", "dy -0.104839 -179.050702\n", "mo 2.469503 0.009002\n", "yr 1.467852 0.196278" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "exx_d = []\n", "for delta in ('dy','mo','yr'):\n", " exx_d.append(get_deltas(exx,delta=delta))\n", "print('Exxon stock absolute deltas:')\n", "alphaC = pd.DataFrame()\n", "for delta in exx_d:\n", " alphaC = alphaC.append(get_alphaC(delta))\n", "alphaC" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Exxon stock absolute deltas:\n" ] }, { "html": [ "
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alphaC
dy 0.406505 -32.129860
mo-0.933245-22981.841886
yr 2.004189 0.030879
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ " alpha C\n", "dy 0.406505 -32.129860\n", "mo -0.933245 -22981.841886\n", "yr 2.004189 0.030879" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "# 4. Using package https://pypi.python.org/pypi/powerlaw\n", "import powerlaw\n", "fit = []\n", "for delta in deltas:\n", " fit.append(powerlaw.Fit(delta.absolute[delta.absolute>0]))\n", "pd.DataFrame([fit[0].alpha,fit[1].alpha,fit[2].alpha],index=['dy','mo','yr'],columns=['alpha by pypi/powerlaw'])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Calculating best minimal value for power law fit\n", "Calculating best minimal value for power law fit" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Calculating best minimal value for power law fit" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
alpha by pypi/powerlaw
dy 3.716880
mo 2.933664
yr 1.791319
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ " alpha by pypi/powerlaw\n", "dy 3.716880\n", "mo 2.933664\n", "yr 1.791319" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "# 4.1 Plot CCDF & fitted power law\n", "fig = fit[0].plot_ccdf(color='b', linewidth=3, label='Empirical Daily')\n", "fit[1].plot_ccdf(ax=fig, color='g', linewidth=3, label='Empirical Monthly')\n", "fit[2].plot_ccdf(ax=fig, color='r', linewidth=3, label='Empirical Yearly')\n", "fit[0].power_law.plot_ccdf(ax=fig, color='b', linestyle='--', label='Power law fit dy')\n", "fit[1].power_law.plot_ccdf(ax=fig, color='g', linestyle='--', label='Power law fit mo')\n", "fit[2].power_law.plot_ccdf(ax=fig, color='r', linestyle='--', label='Power law fit yr')\n", "fig.set_ylabel(u'p(X\u2265x)')\n", "fig.set_xlabel(\"NYSE daily closing price absolute change frequency\")\n", "handles, labels = fig.get_legend_handles_labels()\n", "fig.legend(handles, labels, loc=3)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Bk5qkY0eTuunttz0Xnze7mXCTFQdWELU7imV/LiM+6c7MvAVyF6BH7R6E1w+n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\nYN++fbRv357ixYtTq1YtFixYYFnv9vK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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "# 8. Compute probability of a stock market crash (losing > 30% value)\n", "# prob_down = len(df.absolute[df.absolute>0]) /len(df.absolute)\n", "alphaC = pd.DataFrame()\n", "for delta in deltas:\n", " alphaC = alphaC.append(get_alphaC(delta))\n", "alpha = alphaC.loc['dy','alpha']\n", "C = alphaC.loc['dy','C']\n", "prob_crash= (C/(alpha-1))*(0.3**(-(alpha-1)))\n", "print('Probability of crash (>30% value loss):',prob_crash)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Probability of crash (>30% value loss): 0.536322373735\n" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "# 3.1 Plot daily changes \n", "y,x = np.histogram(df.absolute, bins=len(df)/50)\n", "trace1 = Scatter(x=x,y=y,name='absolute')\n", "y2,x2 = np.histogram(df.relative, bins=len(df)/50)\n", "trace2 = Scatter(x=x2,y=y2,name='relative')\n", "data = Data([trace1,trace2])\n", "layout = Layout(\n", " title='NYSE Daily Closing Price Change',\n", " xaxis=XAxis(type='log',autorange=True,title='Daily price change'),\n", " yaxis=YAxis(type='log',autorange=True,title='Frequency'))\n", "fig = Figure(data=data, layout=layout)\n", "py.iplot(fig, filename='NYSE-daily-absolute-changes')" ], "language": "python", "metadata": {}, "outputs": [ { "application/pdf": "%PDF-1.4\n%\ufffd\ufffd\ufffd\ufffd\n4 0 obj\n<<\n/Producer (Apache FOP Version 1.0beta2: PDF Transcoder for Batik)\n/CreationDate (D:20150224021141Z)\n>>\nendobj\n6 0 obj\n<< /Length 7 0 R\n/Filter /FlateDecode 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F/wB9in7E/uL+VGxP7i/lQAz7Vbf8/EX/AH2Khu7i3aEh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\nQavXiJJGkcihlaRQykZBGehrxf4Exz/Dvx54z+B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N2UbKg7l4yBkZqeFPiZ4K8bXsth4b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\nDz5v+fKb/vpP/iqPPm/58pv++k/+KoAnqC8/1B/3k/8AQhR583/PlN/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CEV7+NTJXdXkaKn5Sn4WwuI1bDbh944orrtCr2XGlmeOwIPGv3bk6yVteCeQHsXjaNG5b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