{ "cells": [ { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "import pandas_datareader.data as web\n", "import datetime" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# We specify the timeframe and download the prices with Yahoo Finance\n", "start = datetime.datetime(2011, 1, 1)\n", "end = datetime.datetime(2014, 1, 27)\n", "coke_prices = web.DataReader(\"KO\", 'yahoo', start, end)\n", "pepsi_prices = web.DataReader(\"PEP\", 'yahoo', start, end)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Let us take a look at what we downloaded." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "
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OpenHighLowCloseVolumeAdj Close
Date
2011-01-0365.87999765.87999765.11000165.2200011894560027.033453
2011-01-0465.01999765.19000263.81000163.8699992794040026.473882
2011-01-0563.79000163.95000162.86000163.4900023437900026.316375
2011-01-0663.61999963.66000062.83000263.0299992171240026.125705
2011-01-0762.77999963.00000062.56000162.9199981659280026.080110
\n", "
" ], "text/plain": [ " Open High Low Close Volume Adj Close\n", "Date \n", "2011-01-03 65.879997 65.879997 65.110001 65.220001 18945600 27.033453\n", "2011-01-04 65.019997 65.190002 63.810001 63.869999 27940400 26.473882\n", "2011-01-05 63.790001 63.950001 62.860001 63.490002 34379000 26.316375\n", "2011-01-06 63.619999 63.660000 62.830002 63.029999 21712400 26.125705\n", "2011-01-07 62.779999 63.000000 62.560001 62.919998 16592800 26.080110" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coke_prices.head()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We are interested in the adjusted close. The close prices themselves do not work, because of stock splits." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "coke_close=coke_prices['Adj Close']\n", "pepsi_close=pepsi_prices['Adj Close']" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Let us do a scatterplot. If they are cointegrated, then we expect to see the points clustered around a line" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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vvAGYawrVzOcmezWiV4WFV949bVUXpiX1QGX2bi8ucl5YLk6V8Mlqqsbd4Cyq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\nbwOwB0AfgNOolC2er/Na56q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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.scatter(coke_close, pepsi_close)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We fit a line with linear regression\n", "So pepsi = slope * coke + intercept + error" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "slope: 2.1868969195\n", "intercept: -7.04139940461\n", "r-value: 0.896540328487\n", "p-value: 3.64783454604e-274\n", "std-err: 0.0389638534876\n" ] } ], "source": [ "from scipy import stats\n", "slope, intercept, r_value, p_value, std_err = stats.linregress(coke_close, pepsi_close)\n", "print(\"slope: \" + str(slope) +\n", " \"\\nintercept: \" + str(intercept) +\n", " \"\\nr-value: \" + str(r_value) +\n", " \"\\np-value: \" + str(p_value) +\n", " \"\\nstd-err: \" + str(std_err))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The p-value is small, which is good.\n", "Let us plot this thing with the fitted line" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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H+Oyuzxj1Obz4xUaWX+DDH9vRsMTkoT3YsvdEs1fevcjBg1ePjlklEn7upy9u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\nVM+Wwcln5QpYMHV8THEqr/C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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.scatter(coke_close, pepsi_close)\n", "x=[26,39]\n", "plt.plot(x,[slope*x_i+intercept for x_i in x], color='m')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Now we compute the term e, which is the residue or the error term.\n", "If the error is stationary, then Coke and Pepsi are cointegrated." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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4sxFOu4Q9uqxGIrc8s+4wABg6oYVkDpvEtJaXd199Em443Zg7YpekjIlzoNTi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\n+naKrskNNokhxCNF/u+fPB0nqWJSrIi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "error = pepsi_close - slope * coke_close - intercept\n", "plt.plot(error)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The plot looks okay, but it is not clear it if is really stationary.\n", "E.g., there is an upward trending segment in the middle.\n", "But we can test the error for stationarity." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(-1.9345595231989032,\n", " 0.31598188286172724,\n", " 0,\n", " 770,\n", " {'1%': -3.4388710830827125,\n", " '10%': -2.568772659807725,\n", " '5%': -2.8653008652386576},\n", " 1257.1859133786406)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import statsmodels.tsa.stattools as ts\n", "ts.adfuller(error,1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Remember the null hypothesis is, that there is a unit root.\n", "Having a unit root, means that the process is not stationary.\n", "The p-value is 0.31, so we cannot reject the null hypothesis.\n", "\n", "Thus, Coke and Pepsi are not useful for pairs trading with the setup I described. There may be other setups, where it works. Maybe the timeframe is not useful. Maybe the error time series is not an AR(1)-process.\n", "\n", "Let us take another example.\n", "There is an iShares MSCI Australia and an iShares MSCI Canada. These are two ETFs which track the economy of Australia, respectively Canada. Their ticker symbols are EWA and EWC.\n", "We will test their cointegration.\n", "\n", "First, we define the timeframe and download the data from yahoo finance." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "import pandas_datareader.data as web\n", "import datetime\n", "\n", "start = datetime.datetime(2003, 1, 1)\n", "end = datetime.datetime(2008, 1, 27)\n", "ewa_prices = web.DataReader(\"EWA\", 'yahoo', start, end)\n", "ewc_prices = web.DataReader(\"EWC\", 'yahoo', start, end)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we need to trade on the adjusted closes. Let us plot the two charts." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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UWLTu2ObtbiEB9myK4VXM21JZrrb120hAF8IVjrMDXfGuPTOhLeHVnsX2/WkJ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\nvEJeW7SLd5ftA+xfCAu3JXHbp/ZEaD1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ewa_close=ewa_prices['Adj Close']\n", "ewc_close=ewc_prices['Adj Close']\n", "\n", "import matplotlib.pyplot as plt\n", "ewa_close.plot(label='ewa', legend=True)\n", "ewc_close.plot(label='ewc', legend=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that they have common jumps, so we can go on to the next step: drawing a scatterplot." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.scatter(ewa_close, ewc_close)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This fairly looks like a line. Perfect. So we fit a line." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "slope: 1.27629111076\n", "intercept: 1.79841662559\n", "r-value: 0.989386266306\n", "p-value: 0.0\n", "std-err: 0.00525367636547\n" ] } ], "source": [ "from scipy import stats\n", "slope, intercept, r_value, p_value, std_err = stats.linregress(ewa_close, ewc_close)\n", "print(\"slope: \" + str(slope) +\n", " \"\\nintercept: \" + str(intercept) +\n", " \"\\nr-value: \" + str(r_value) +\n", " \"\\np-value: \" + str(p_value) +\n", " \"\\nstd-err: \" + str(std_err))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(ewa_close, ewc_close)\n", "x=[4,22]\n", "plt.plot(x,[slope*x_i+intercept for x_i in x], color='m')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks great. Now we compute the error and test if it is mean-reverting." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9whUchdvsrKGdcfnY2kwNLesROmfnX59yUh8AqRf2EAcYFGEXc0OxYgw7Fti5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\nbqvGOMZldqIuWism2jD7V2cMiGk745m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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "error = ewc_close - slope * ewa_close - intercept\n", "plt.plot(error)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-3.3459094549609389,\n", " 0.012946959495104054,\n", " 1,\n", " 1273,\n", " {'1%': -3.4354973175106842,\n", " '10%': -2.5679802172809003,\n", " '5%': -2.8638130956084464},\n", " -845.44796472685812)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import statsmodels.tsa.stattools as ts\n", "ts.adfuller(error,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We got a p-value of 0.0129. That means we are statistically significant. So we could go on to build a trading strat by trading on the error. The interesting part is that it is only significant, since I chose the timeframe appropriately. For other timeframes the cointegration relationship interestingly does not hold." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": 2 }