python-pour-finance/09-Python-Finance-Fondamentaux/.ipynb_checkpoints/03-CAPM-Capital-Asset-Pricing-Model-checkpoint.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CAPM - Capital Asset Pricing Model \n",
    "\n",
    "Watch the video for the full overview.\n",
    "\n",
    "Portfolio Returns:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $r_p(t) = \\sum\\limits_{i}^{n}w_i r_i(t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Market Weights:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $ w_i = \\frac{MarketCap_i}{\\sum_{j}^{n}{MarketCap_j}} $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CAPM of a portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## $ r_p(t) = \\beta_pr_m(t) + \\sum\\limits_{i}^{n}w_i \\alpha_i(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Model CAPM as a simple linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function linregress in module scipy.stats._stats_mstats_common:\n",
      "\n",
      "linregress(x, y=None)\n",
      "    Calculate a linear least-squares regression for two sets of measurements.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    x, y : array_like\n",
      "        Two sets of measurements.  Both arrays should have the same length.\n",
      "        If only x is given (and y=None), then it must be a two-dimensional\n",
      "        array where one dimension has length 2.  The two sets of measurements\n",
      "        are then found by splitting the array along the length-2 dimension.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    slope : float\n",
      "        slope of the regression line\n",
      "    intercept : float\n",
      "        intercept of the regression line\n",
      "    rvalue : float\n",
      "        correlation coefficient\n",
      "    pvalue : float\n",
      "        two-sided p-value for a hypothesis test whose null hypothesis is\n",
      "        that the slope is zero.\n",
      "    stderr : float\n",
      "        Standard error of the estimated gradient.\n",
      "    \n",
      "    See also\n",
      "    --------\n",
      "    :func:`scipy.optimize.curve_fit` : Use non-linear\n",
      "     least squares to fit a function to data.\n",
      "    :func:`scipy.optimize.leastsq` : Minimize the sum of\n",
      "     squares of a set of equations.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> import matplotlib.pyplot as plt\n",
      "    >>> from scipy import stats\n",
      "    >>> np.random.seed(12345678)\n",
      "    >>> x = np.random.random(10)\n",
      "    >>> y = np.random.random(10)\n",
      "    >>> slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)\n",
      "    \n",
      "    To get coefficient of determination (r_squared)\n",
      "    \n",
      "    >>> print(\"r-squared:\", r_value**2)\n",
      "    ('r-squared:', 0.080402268539028335)\n",
      "    \n",
      "    Plot the data along with the fitted line\n",
      "    \n",
      "    >>> plt.plot(x, y, 'o', label='original data')\n",
      "    >>> plt.plot(x, intercept + slope*x, 'r', label='fitted line')\n",
      "    >>> plt.legend()\n",
      "    >>> plt.show()\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(stats.linregress)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas_datareader as web"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "spy_etf = web.DataReader('SPY','google')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 1897 entries, 2010-01-04 to 2017-07-18\n",
      "Data columns (total 5 columns):\n",
      "Open      1879 non-null float64\n",
      "High      1879 non-null float64\n",
      "Low       1879 non-null float64\n",
      "Close     1897 non-null float64\n",
      "Volume    1897 non-null int64\n",
      "dtypes: float64(4), int64(1)\n",
      "memory usage: 88.9 KB\n"
     ]
    }
   ],
   "source": [
    "spy_etf.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2010-01-04</th>\n",
       "      <td>112.37</td>\n",
       "      <td>113.39</td>\n",
       "      <td>111.51</td>\n",
       "      <td>113.33</td>\n",
       "      <td>118944541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-05</th>\n",
       "      <td>113.26</td>\n",
       "      <td>113.68</td>\n",
       "      <td>112.85</td>\n",
       "      <td>113.63</td>\n",
       "      <td>111579866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-06</th>\n",
       "      <td>113.52</td>\n",
       "      <td>113.99</td>\n",
       "      <td>113.43</td>\n",
       "      <td>113.71</td>\n",
       "      <td>116074402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-07</th>\n",
       "      <td>113.50</td>\n",
       "      <td>114.33</td>\n",
       "      <td>113.18</td>\n",
       "      <td>114.19</td>\n",
       "      <td>131091048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-08</th>\n",
       "      <td>113.89</td>\n",
       "      <td>114.62</td>\n",
       "      <td>113.66</td>\n",
       "      <td>114.57</td>\n",
       "      <td>126402764</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Open    High     Low   Close     Volume\n",
       "Date                                                 \n",
       "2010-01-04  112.37  113.39  111.51  113.33  118944541\n",
       "2010-01-05  113.26  113.68  112.85  113.63  111579866\n",
       "2010-01-06  113.52  113.99  113.43  113.71  116074402\n",
       "2010-01-07  113.50  114.33  113.18  114.19  131091048\n",
       "2010-01-08  113.89  114.62  113.66  114.57  126402764"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spy_etf.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "start = pd.to_datetime('2010-01-04')\n",
    "end = pd.to_datetime('2017-07-18')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "aapl = web.DataReader('AAPL','google',start,end)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2010-01-04</th>\n",
       "      <td>30.49</td>\n",
       "      <td>30.64</td>\n",
       "      <td>30.34</td>\n",
       "      <td>30.57</td>\n",
       "      <td>123432050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-05</th>\n",
       "      <td>30.66</td>\n",
       "      <td>30.80</td>\n",
       "      <td>30.46</td>\n",
       "      <td>30.63</td>\n",
       "      <td>150476004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-06</th>\n",
       "      <td>30.63</td>\n",
       "      <td>30.75</td>\n",
       "      <td>30.11</td>\n",
       "      <td>30.14</td>\n",
       "      <td>138039594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-07</th>\n",
       "      <td>30.25</td>\n",
       "      <td>30.29</td>\n",
       "      <td>29.86</td>\n",
       "      <td>30.08</td>\n",
       "      <td>119282324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-08</th>\n",
       "      <td>30.04</td>\n",
       "      <td>30.29</td>\n",
       "      <td>29.87</td>\n",
       "      <td>30.28</td>\n",
       "      <td>111969081</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "             Open   High    Low  Close     Volume\n",
       "Date                                             \n",
       "2010-01-04  30.49  30.64  30.34  30.57  123432050\n",
       "2010-01-05  30.66  30.80  30.46  30.63  150476004\n",
       "2010-01-06  30.63  30.75  30.11  30.14  138039594\n",
       "2010-01-07  30.25  30.29  29.86  30.08  119282324\n",
       "2010-01-08  30.04  30.29  29.87  30.28  111969081"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aapl.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c4e9221cf8>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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SAxSUChgsyyQhdQZaDy2j1aw+Cfdqudu1xARaztqARZ4uRWe9xj98DK16V+99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\n8/j5Q/ng5olNOlaqx+i31e5g3zG9yHHt/pXT+qfywiUjXfc/uW0SF43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E3TcoDvgTuAeUqpcON11mnU93rSNK0CeAcYBfxe07RzgKXAXOP6dSoNXCcL+gjyv4DvNE2bCzwI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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c4e910cdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aapl['Close'].plot(label='AAPL',figsize=(10,8))\n",
    "spy_etf['Close'].plot(label='SPY Index')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare Cumulative Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "aapl['Cumulative'] = aapl['Close']/aapl['Close'].iloc[0]\n",
    "spy_etf['Cumulative'] = spy_etf['Close']/spy_etf['Close'].iloc[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1c4e97460b8>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ElLwkSUJDuyMhU3NaIXhQpqnvQdPlS74BAEweLHfUqW6Jzoo8Cvb1/nq88M0h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\nTQCAG08biXnjijEwz4JjrTb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9NuGl5GZ1uIKO6XUCORZjxN25/YMmb+uCaUPyg8713QMv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8TPDxq3l5/xHziXwoNMw+WlSQmEyAQYfHvZx0nqI+UEjmyAM589/vNSSimlVL1So0HTnaPaM6pT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c4e9634ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aapl['Cumulative'].plot(label='AAPL',figsize=(10,8))\n",
    "spy_etf['Cumulative'].plot(label='SPY Index')\n",
    "plt.legend()\n",
    "plt.title('Cumulative Return')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get Daily Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "aapl['Daily Return'] = aapl['Close'].pct_change(1)\n",
    "spy_etf['Daily Return'] = spy_etf['Close'].pct_change(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c4ea1ec518>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0dGWYTPWF56c27TTr3YgffbjClZUuUSrxHQvHMgllhpGmyCxvn9mNUn784Spp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\nAzZT+3HNlTMbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c4ea187e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(aapl['Daily Return'],spy_etf['Daily Return'],alpha=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c4ea1a4908>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c4ea212e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aapl['Daily Return'].hist(bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c4e97c9cc0>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvSQ1zqCXpMYZ9JLUuP8HoSgEoEgZcKcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c4e963a7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "spy_etf['Daily Return'].hist(bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta,alpha,r_value,p_value,std_err = stats.linregress(aapl['Daily Return'].iloc[1:],spy_etf['Daily Return'].iloc[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19423150396392763"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00026461336993233316"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33143080741409325"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What if our stock was completely related to SP500?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2010-01-04         NaN\n",
       "2010-01-05    0.002647\n",
       "2010-01-06    0.000704\n",
       "2010-01-07    0.004221\n",
       "2010-01-08    0.003328\n",
       "Name: Daily Return, dtype: float64"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spy_etf['Daily Return'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = np.random.normal(0,0.001,len(spy_etf['Daily Return'].iloc[1:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00089285,  0.00056301, -0.00022182, ..., -0.00075069,\n",
       "       -0.00017751, -0.00034175])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2010-01-05    0.003540\n",
       "2010-01-06    0.001267\n",
       "2010-01-07    0.003999\n",
       "2010-01-08    0.003744\n",
       "2010-01-11    0.002430\n",
       "2010-01-12   -0.008178\n",
       "2010-01-13    0.006244\n",
       "2010-01-14    0.003002\n",
       "2010-01-15   -0.010593\n",
       "2010-01-19    0.012289\n",
       "2010-01-20   -0.010683\n",
       "2010-01-21   -0.019239\n",
       "2010-01-22   -0.022449\n",
       "2010-01-25    0.003428\n",
       "2010-01-26   -0.003510\n",
       "2010-01-27    0.004741\n",
       "2010-01-28   -0.011874\n",
       "2010-01-29   -0.010649\n",
       "2010-02-01    0.015995\n",
       "2010-02-02    0.011317\n",
       "2010-02-03   -0.006852\n",
       "2010-02-04   -0.029828\n",
       "2010-02-05    0.000845\n",
       "2010-02-08   -0.007362\n",
       "2010-02-09    0.010399\n",
       "2010-02-10   -0.000745\n",
       "2010-02-11    0.008745\n",
       "2010-02-12   -0.001782\n",
       "2010-02-16    0.016414\n",
       "2010-02-17    0.003658\n",
       "                ...   \n",
       "2017-06-06   -0.001963\n",
       "2017-06-07    0.003158\n",
       "2017-06-08   -0.000087\n",
       "2017-06-09   -0.000582\n",
       "2017-06-12   -0.001564\n",
       "2017-06-13    0.006079\n",
       "2017-06-14   -0.002911\n",
       "2017-06-15   -0.001163\n",
       "2017-06-16   -0.004836\n",
       "2017-06-19    0.008102\n",
       "2017-06-20   -0.008464\n",
       "2017-06-21   -0.000669\n",
       "2017-06-22   -0.000532\n",
       "2017-06-23    0.002970\n",
       "2017-06-26    0.001098\n",
       "2017-06-27   -0.009717\n",
       "2017-06-28    0.008961\n",
       "2017-06-29   -0.010516\n",
       "2017-06-30    0.001965\n",
       "2017-07-03    0.001218\n",
       "2017-07-05    0.003210\n",
       "2017-07-06   -0.008497\n",
       "2017-07-07    0.005798\n",
       "2017-07-10    0.000335\n",
       "2017-07-11   -0.001653\n",
       "2017-07-12    0.008218\n",
       "2017-07-13    0.003311\n",
       "2017-07-14    0.003913\n",
       "2017-07-17   -0.000300\n",
       "2017-07-18    0.000188\n",
       "Name: Daily Return, Length: 1896, dtype: float64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spy_etf['Daily Return'].iloc[1:] + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta,alpha,r_value,p_value,std_err = stats.linregress(spy_etf['Daily Return'].iloc[1:]+noise,spy_etf['Daily Return'].iloc[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9902145894162997"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4861814214210613e-05"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like our understanding is correct!"
   ]
  }
 ],
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