Financial Analysis Examples.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Financial Analysis Examples with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook will provide an overview of popular statistical packages in Python including NumPy, statsmodels and SciPy. During the session participants will gain experience in performing statistical analysis, linear regressions, time series forecasting and optimization. The session will also explore some more advanced functions in Pandas, including transforming time series data using the resample, aggregate and rolling functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color = 'blue'> **Section 1 - Importing Packages and Data** </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np #log, matrix calculation, random numbers\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import statsmodels.api as sm #Linear regression\n",
    "import statsmodels.tsa as tsa #time series analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp500 = pd.read_csv(\"StockData/SP500.csv\",parse_dates=['Date'],index_col=['Date'])\n",
    "aapl = pd.read_csv(\"StockData/AAPL.csv\",parse_dates=['Date'],index_col=['Date'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color = 'blue'> **Section 2 - Linear Regression Model** </font>\n",
    "- this example will calculate the Beta of Apple against S&P 500 using the CAPM model\n",
    "- CAPM: return on equity = risk free rate + beta * market risk premium\n",
    "- For simplicity, we will ignore in this example the risk free rate (assume it has been 0 for the period being analyzed) and perform a regression of AAPL's returns over S&P 500 returns\n",
    "- The slope of the line of best fit will represent AAPL's beta\n",
    "- Regression model will be run using OLS from statsmodels package"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Creating Calculated Fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%% Calculating Returns\n",
    "sp500['Returns'] = sp500['Close'] / sp500['Close'].shift(1) - 1\n",
    "    #daily return (Close/Prev Close) - 1\n",
    "\n",
    "aapl['Returns'] = aapl['Close'].pct_change()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Merging Data Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open_SP</th>\n",
       "      <th>High_SP</th>\n",
       "      <th>Low_SP</th>\n",
       "      <th>Close_SP</th>\n",
       "      <th>Adj Close_SP</th>\n",
       "      <th>Volume_SP</th>\n",
       "      <th>Returns_SP</th>\n",
       "      <th>Open_AAPL</th>\n",
       "      <th>High_AAPL</th>\n",
       "      <th>Low_AAPL</th>\n",
       "      <th>Close_AAPL</th>\n",
       "      <th>Adj Close_AAPL</th>\n",
       "      <th>Volume_AAPL</th>\n",
       "      <th>Returns_AAPL</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",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-10-02</th>\n",
       "      <td>1691.900024</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>1680.339966</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>3148600000</td>\n",
       "      <td>-0.000667</td>\n",
       "      <td>69.375717</td>\n",
       "      <td>70.257141</td>\n",
       "      <td>69.107140</td>\n",
       "      <td>69.937141</td>\n",
       "      <td>63.731426</td>\n",
       "      <td>72296000</td>\n",
       "      <td>0.003279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-03</th>\n",
       "      <td>1692.349976</td>\n",
       "      <td>1692.349976</td>\n",
       "      <td>1670.359985</td>\n",
       "      <td>1678.660034</td>\n",
       "      <td>1678.660034</td>\n",
       "      <td>3279650000</td>\n",
       "      <td>-0.008979</td>\n",
       "      <td>70.072861</td>\n",
       "      <td>70.335716</td>\n",
       "      <td>68.677139</td>\n",
       "      <td>69.058571</td>\n",
       "      <td>62.930801</td>\n",
       "      <td>80688300</td>\n",
       "      <td>-0.012562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-04</th>\n",
       "      <td>1678.790039</td>\n",
       "      <td>1691.939941</td>\n",
       "      <td>1677.329956</td>\n",
       "      <td>1690.500000</td>\n",
       "      <td>1690.500000</td>\n",
       "      <td>2880270000</td>\n",
       "      <td>0.007053</td>\n",
       "      <td>69.122856</td>\n",
       "      <td>69.228569</td>\n",
       "      <td>68.371429</td>\n",
       "      <td>69.004288</td>\n",
       "      <td>62.881340</td>\n",
       "      <td>64717100</td>\n",
       "      <td>-0.000786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-07</th>\n",
       "      <td>1687.150024</td>\n",
       "      <td>1687.150024</td>\n",
       "      <td>1674.699951</td>\n",
       "      <td>1676.119995</td>\n",
       "      <td>1676.119995</td>\n",
       "      <td>2678490000</td>\n",
       "      <td>-0.008506</td>\n",
       "      <td>69.508568</td>\n",
       "      <td>70.378571</td>\n",
       "      <td>69.335716</td>\n",
       "      <td>69.678574</td>\n",
       "      <td>63.495800</td>\n",
       "      <td>78073100</td>\n",
       "      <td>0.009772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-08</th>\n",
       "      <td>1676.219971</td>\n",
       "      <td>1676.790039</td>\n",
       "      <td>1655.030029</td>\n",
       "      <td>1655.449951</td>\n",
       "      <td>1655.449951</td>\n",
       "      <td>3569230000</td>\n",
       "      <td>-0.012332</td>\n",
       "      <td>69.991432</td>\n",
       "      <td>70.091431</td>\n",
       "      <td>68.648575</td>\n",
       "      <td>68.705711</td>\n",
       "      <td>62.609249</td>\n",
       "      <td>72729300</td>\n",
       "      <td>-0.013962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-24</th>\n",
       "      <td>2921.830078</td>\n",
       "      <td>2923.790039</td>\n",
       "      <td>2912.629883</td>\n",
       "      <td>2919.370117</td>\n",
       "      <td>2919.370117</td>\n",
       "      <td>3372210000</td>\n",
       "      <td>-0.003516</td>\n",
       "      <td>216.820007</td>\n",
       "      <td>221.259995</td>\n",
       "      <td>216.630005</td>\n",
       "      <td>220.789993</td>\n",
       "      <td>220.789993</td>\n",
       "      <td>27693400</td>\n",
       "      <td>0.014380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-25</th>\n",
       "      <td>2921.750000</td>\n",
       "      <td>2923.949951</td>\n",
       "      <td>2913.699951</td>\n",
       "      <td>2915.560059</td>\n",
       "      <td>2915.560059</td>\n",
       "      <td>3285480000</td>\n",
       "      <td>-0.001305</td>\n",
       "      <td>219.750000</td>\n",
       "      <td>222.820007</td>\n",
       "      <td>219.699997</td>\n",
       "      <td>222.190002</td>\n",
       "      <td>222.190002</td>\n",
       "      <td>24554400</td>\n",
       "      <td>0.006341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-26</th>\n",
       "      <td>2916.979980</td>\n",
       "      <td>2931.149902</td>\n",
       "      <td>2903.280029</td>\n",
       "      <td>2905.969971</td>\n",
       "      <td>2905.969971</td>\n",
       "      <td>3388620000</td>\n",
       "      <td>-0.003289</td>\n",
       "      <td>221.000000</td>\n",
       "      <td>223.750000</td>\n",
       "      <td>219.759995</td>\n",
       "      <td>220.419998</td>\n",
       "      <td>220.419998</td>\n",
       "      <td>23984700</td>\n",
       "      <td>-0.007966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-27</th>\n",
       "      <td>2911.649902</td>\n",
       "      <td>2927.219971</td>\n",
       "      <td>2909.270020</td>\n",
       "      <td>2914.000000</td>\n",
       "      <td>2914.000000</td>\n",
       "      <td>3060850000</td>\n",
       "      <td>0.002763</td>\n",
       "      <td>223.820007</td>\n",
       "      <td>226.440002</td>\n",
       "      <td>223.539993</td>\n",
       "      <td>224.949997</td>\n",
       "      <td>224.949997</td>\n",
       "      <td>30181200</td>\n",
       "      <td>0.020552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-28</th>\n",
       "      <td>2910.030029</td>\n",
       "      <td>2920.530029</td>\n",
       "      <td>2907.500000</td>\n",
       "      <td>2913.979980</td>\n",
       "      <td>2913.979980</td>\n",
       "      <td>3432300000</td>\n",
       "      <td>-0.000007</td>\n",
       "      <td>224.789993</td>\n",
       "      <td>225.839996</td>\n",
       "      <td>224.020004</td>\n",
       "      <td>225.740005</td>\n",
       "      <td>225.740005</td>\n",
       "      <td>22889300</td>\n",
       "      <td>0.003512</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1258 rows × 14 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Open_SP      High_SP       Low_SP     Close_SP  Adj Close_SP  \\\n",
       "Date                                                                           \n",
       "2013-10-02  1691.900024  1693.869995  1680.339966  1693.869995   1693.869995   \n",
       "2013-10-03  1692.349976  1692.349976  1670.359985  1678.660034   1678.660034   \n",
       "2013-10-04  1678.790039  1691.939941  1677.329956  1690.500000   1690.500000   \n",
       "2013-10-07  1687.150024  1687.150024  1674.699951  1676.119995   1676.119995   \n",
       "2013-10-08  1676.219971  1676.790039  1655.030029  1655.449951   1655.449951   \n",
       "...                 ...          ...          ...          ...           ...   \n",
       "2018-09-24  2921.830078  2923.790039  2912.629883  2919.370117   2919.370117   \n",
       "2018-09-25  2921.750000  2923.949951  2913.699951  2915.560059   2915.560059   \n",
       "2018-09-26  2916.979980  2931.149902  2903.280029  2905.969971   2905.969971   \n",
       "2018-09-27  2911.649902  2927.219971  2909.270020  2914.000000   2914.000000   \n",
       "2018-09-28  2910.030029  2920.530029  2907.500000  2913.979980   2913.979980   \n",
       "\n",
       "             Volume_SP  Returns_SP   Open_AAPL   High_AAPL    Low_AAPL  \\\n",
       "Date                                                                     \n",
       "2013-10-02  3148600000   -0.000667   69.375717   70.257141   69.107140   \n",
       "2013-10-03  3279650000   -0.008979   70.072861   70.335716   68.677139   \n",
       "2013-10-04  2880270000    0.007053   69.122856   69.228569   68.371429   \n",
       "2013-10-07  2678490000   -0.008506   69.508568   70.378571   69.335716   \n",
       "2013-10-08  3569230000   -0.012332   69.991432   70.091431   68.648575   \n",
       "...                ...         ...         ...         ...         ...   \n",
       "2018-09-24  3372210000   -0.003516  216.820007  221.259995  216.630005   \n",
       "2018-09-25  3285480000   -0.001305  219.750000  222.820007  219.699997   \n",
       "2018-09-26  3388620000   -0.003289  221.000000  223.750000  219.759995   \n",
       "2018-09-27  3060850000    0.002763  223.820007  226.440002  223.539993   \n",
       "2018-09-28  3432300000   -0.000007  224.789993  225.839996  224.020004   \n",
       "\n",
       "            Close_AAPL  Adj Close_AAPL  Volume_AAPL  Returns_AAPL  \n",
       "Date                                                               \n",
       "2013-10-02   69.937141       63.731426     72296000      0.003279  \n",
       "2013-10-03   69.058571       62.930801     80688300     -0.012562  \n",
       "2013-10-04   69.004288       62.881340     64717100     -0.000786  \n",
       "2013-10-07   69.678574       63.495800     78073100      0.009772  \n",
       "2013-10-08   68.705711       62.609249     72729300     -0.013962  \n",
       "...                ...             ...          ...           ...  \n",
       "2018-09-24  220.789993      220.789993     27693400      0.014380  \n",
       "2018-09-25  222.190002      222.190002     24554400      0.006341  \n",
       "2018-09-26  220.419998      220.419998     23984700     -0.007966  \n",
       "2018-09-27  224.949997      224.949997     30181200      0.020552  \n",
       "2018-09-28  225.740005      225.740005     22889300      0.003512  \n",
       "\n",
       "[1258 rows x 14 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mergedData = sp500.merge(aapl, how='inner',\n",
    "                         left_index=True, right_index=True,\n",
    "                         suffixes=(\"_SP\",\"_AAPL\"))  \n",
    "mergedData.dropna(inplace=True)\n",
    "    #same as: mergedData = mergedData.dropna()\n",
    "mergedData"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Regression Model\n",
    "Steps:\n",
    "- pick the model and the x/y variables\n",
    "- fit the model\n",
    "- look at the summary results and extract any important results (beta, r2, etc.)\n",
    "- predict new data set (out of sample), or test old data (in-sample)\n",
    "- plot predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%% Linear Regression Model\n",
    "#run the model\n",
    "#look at the summary results\n",
    "#predict new data set (out of sample), can test old data (in-sample, backtesting)\n",
    "\n",
    "#CAPM\n",
    "# cost of equity = risk free rate + beta * MRP\n",
    "    #MRP ---> market risk premium = excess returns of the market\n",
    "    # S&P 500 as a proxy for the market\n",
    "    \n",
    "    #simplify assumption --> risk free rate = 0\n",
    "    #return of AAPL = 0 + beta * MRP\n",
    "        #MRP = S&P returns - 0\n",
    "\n",
    "capm = sm.OLS(mergedData['Returns_AAPL'], mergedData['Returns_SP'])\n",
    "         #  OLS(dependent variable, independ variable)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>Returns_AAPL</td>   <th>  R-squared (uncentered):</th>      <td>   0.321</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.321</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   594.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 01 Oct 2021</td> <th>  Prob (F-statistic):</th>          <td>7.67e-108</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:15:19</td>     <th>  Log-Likelihood:    </th>          <td>  3810.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1258</td>      <th>  AIC:               </th>          <td>  -7618.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1257</td>      <th>  BIC:               </th>          <td>  -7613.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Returns_SP</th> <td>    1.0363</td> <td>    0.043</td> <td>   24.383</td> <td> 0.000</td> <td>    0.953</td> <td>    1.120</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>220.041</td> <th>  Durbin-Watson:     </th> <td>   1.935</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>3571.548</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.262</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>11.238</td>  <th>  Cond. No.          </th> <td>    1.00</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:           Returns_AAPL   R-squared (uncentered):                   0.321\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.321\n",
       "Method:                 Least Squares   F-statistic:                              594.5\n",
       "Date:                Fri, 01 Oct 2021   Prob (F-statistic):                   7.67e-108\n",
       "Time:                        12:15:19   Log-Likelihood:                          3810.0\n",
       "No. Observations:                1258   AIC:                                     -7618.\n",
       "Df Residuals:                    1257   BIC:                                     -7613.\n",
       "Df Model:                           1                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Returns_SP     1.0363      0.043     24.383      0.000       0.953       1.120\n",
       "==============================================================================\n",
       "Omnibus:                      220.041   Durbin-Watson:                   1.935\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             3571.548\n",
       "Skew:                           0.262   Prob(JB):                         0.00\n",
       "Kurtosis:                      11.238   Cond. No.                         1.00\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = capm.fit()\n",
    "r2 = results.rsquared\n",
    "results.summary() \n",
    "    #look at the r2\n",
    "    #beta --> coefficient\n",
    "    #look for p-stat to be less than 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Returns_SP    1.036313\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.params #just the coefficients or betas\n",
    "# coefficients = results.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.036313306900059"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Just the beta\n",
    "beta = results.params[0]\n",
    "beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Predicting New Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open_SP</th>\n",
       "      <th>High_SP</th>\n",
       "      <th>Low_SP</th>\n",
       "      <th>Close_SP</th>\n",
       "      <th>Adj Close_SP</th>\n",
       "      <th>Volume_SP</th>\n",
       "      <th>Returns_SP</th>\n",
       "      <th>Open_AAPL</th>\n",
       "      <th>High_AAPL</th>\n",
       "      <th>Low_AAPL</th>\n",
       "      <th>Close_AAPL</th>\n",
       "      <th>Adj Close_AAPL</th>\n",
       "      <th>Volume_AAPL</th>\n",
       "      <th>Returns_AAPL</th>\n",
       "      <th>Predictions</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",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></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>2013-10-02</th>\n",
       "      <td>1691.900024</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>1680.339966</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>3148600000</td>\n",
       "      <td>-0.000667</td>\n",
       "      <td>69.375717</td>\n",
       "      <td>70.257141</td>\n",
       "      <td>69.107140</td>\n",
       "      <td>69.937141</td>\n",
       "      <td>63.731426</td>\n",
       "      <td>72296000</td>\n",
       "      <td>0.003279</td>\n",
       "      <td>-0.000691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-03</th>\n",
       "      <td>1692.349976</td>\n",
       "      <td>1692.349976</td>\n",
       "      <td>1670.359985</td>\n",
       "      <td>1678.660034</td>\n",
       "      <td>1678.660034</td>\n",
       "      <td>3279650000</td>\n",
       "      <td>-0.008979</td>\n",
       "      <td>70.072861</td>\n",
       "      <td>70.335716</td>\n",
       "      <td>68.677139</td>\n",
       "      <td>69.058571</td>\n",
       "      <td>62.930801</td>\n",
       "      <td>80688300</td>\n",
       "      <td>-0.012562</td>\n",
       "      <td>-0.009305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-04</th>\n",
       "      <td>1678.790039</td>\n",
       "      <td>1691.939941</td>\n",
       "      <td>1677.329956</td>\n",
       "      <td>1690.500000</td>\n",
       "      <td>1690.500000</td>\n",
       "      <td>2880270000</td>\n",
       "      <td>0.007053</td>\n",
       "      <td>69.122856</td>\n",
       "      <td>69.228569</td>\n",
       "      <td>68.371429</td>\n",
       "      <td>69.004288</td>\n",
       "      <td>62.881340</td>\n",
       "      <td>64717100</td>\n",
       "      <td>-0.000786</td>\n",
       "      <td>0.007309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-07</th>\n",
       "      <td>1687.150024</td>\n",
       "      <td>1687.150024</td>\n",
       "      <td>1674.699951</td>\n",
       "      <td>1676.119995</td>\n",
       "      <td>1676.119995</td>\n",
       "      <td>2678490000</td>\n",
       "      <td>-0.008506</td>\n",
       "      <td>69.508568</td>\n",
       "      <td>70.378571</td>\n",
       "      <td>69.335716</td>\n",
       "      <td>69.678574</td>\n",
       "      <td>63.495800</td>\n",
       "      <td>78073100</td>\n",
       "      <td>0.009772</td>\n",
       "      <td>-0.008815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-08</th>\n",
       "      <td>1676.219971</td>\n",
       "      <td>1676.790039</td>\n",
       "      <td>1655.030029</td>\n",
       "      <td>1655.449951</td>\n",
       "      <td>1655.449951</td>\n",
       "      <td>3569230000</td>\n",
       "      <td>-0.012332</td>\n",
       "      <td>69.991432</td>\n",
       "      <td>70.091431</td>\n",
       "      <td>68.648575</td>\n",
       "      <td>68.705711</td>\n",
       "      <td>62.609249</td>\n",
       "      <td>72729300</td>\n",
       "      <td>-0.013962</td>\n",
       "      <td>-0.012780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-24</th>\n",
       "      <td>2921.830078</td>\n",
       "      <td>2923.790039</td>\n",
       "      <td>2912.629883</td>\n",
       "      <td>2919.370117</td>\n",
       "      <td>2919.370117</td>\n",
       "      <td>3372210000</td>\n",
       "      <td>-0.003516</td>\n",
       "      <td>216.820007</td>\n",
       "      <td>221.259995</td>\n",
       "      <td>216.630005</td>\n",
       "      <td>220.789993</td>\n",
       "      <td>220.789993</td>\n",
       "      <td>27693400</td>\n",
       "      <td>0.014380</td>\n",
       "      <td>-0.003643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-25</th>\n",
       "      <td>2921.750000</td>\n",
       "      <td>2923.949951</td>\n",
       "      <td>2913.699951</td>\n",
       "      <td>2915.560059</td>\n",
       "      <td>2915.560059</td>\n",
       "      <td>3285480000</td>\n",
       "      <td>-0.001305</td>\n",
       "      <td>219.750000</td>\n",
       "      <td>222.820007</td>\n",
       "      <td>219.699997</td>\n",
       "      <td>222.190002</td>\n",
       "      <td>222.190002</td>\n",
       "      <td>24554400</td>\n",
       "      <td>0.006341</td>\n",
       "      <td>-0.001352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-26</th>\n",
       "      <td>2916.979980</td>\n",
       "      <td>2931.149902</td>\n",
       "      <td>2903.280029</td>\n",
       "      <td>2905.969971</td>\n",
       "      <td>2905.969971</td>\n",
       "      <td>3388620000</td>\n",
       "      <td>-0.003289</td>\n",
       "      <td>221.000000</td>\n",
       "      <td>223.750000</td>\n",
       "      <td>219.759995</td>\n",
       "      <td>220.419998</td>\n",
       "      <td>220.419998</td>\n",
       "      <td>23984700</td>\n",
       "      <td>-0.007966</td>\n",
       "      <td>-0.003409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-27</th>\n",
       "      <td>2911.649902</td>\n",
       "      <td>2927.219971</td>\n",
       "      <td>2909.270020</td>\n",
       "      <td>2914.000000</td>\n",
       "      <td>2914.000000</td>\n",
       "      <td>3060850000</td>\n",
       "      <td>0.002763</td>\n",
       "      <td>223.820007</td>\n",
       "      <td>226.440002</td>\n",
       "      <td>223.539993</td>\n",
       "      <td>224.949997</td>\n",
       "      <td>224.949997</td>\n",
       "      <td>30181200</td>\n",
       "      <td>0.020552</td>\n",
       "      <td>0.002864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-28</th>\n",
       "      <td>2910.030029</td>\n",
       "      <td>2920.530029</td>\n",
       "      <td>2907.500000</td>\n",
       "      <td>2913.979980</td>\n",
       "      <td>2913.979980</td>\n",
       "      <td>3432300000</td>\n",
       "      <td>-0.000007</td>\n",
       "      <td>224.789993</td>\n",
       "      <td>225.839996</td>\n",
       "      <td>224.020004</td>\n",
       "      <td>225.740005</td>\n",
       "      <td>225.740005</td>\n",
       "      <td>22889300</td>\n",
       "      <td>0.003512</td>\n",
       "      <td>-0.000007</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1258 rows × 15 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Open_SP      High_SP       Low_SP     Close_SP  Adj Close_SP  \\\n",
       "Date                                                                           \n",
       "2013-10-02  1691.900024  1693.869995  1680.339966  1693.869995   1693.869995   \n",
       "2013-10-03  1692.349976  1692.349976  1670.359985  1678.660034   1678.660034   \n",
       "2013-10-04  1678.790039  1691.939941  1677.329956  1690.500000   1690.500000   \n",
       "2013-10-07  1687.150024  1687.150024  1674.699951  1676.119995   1676.119995   \n",
       "2013-10-08  1676.219971  1676.790039  1655.030029  1655.449951   1655.449951   \n",
       "...                 ...          ...          ...          ...           ...   \n",
       "2018-09-24  2921.830078  2923.790039  2912.629883  2919.370117   2919.370117   \n",
       "2018-09-25  2921.750000  2923.949951  2913.699951  2915.560059   2915.560059   \n",
       "2018-09-26  2916.979980  2931.149902  2903.280029  2905.969971   2905.969971   \n",
       "2018-09-27  2911.649902  2927.219971  2909.270020  2914.000000   2914.000000   \n",
       "2018-09-28  2910.030029  2920.530029  2907.500000  2913.979980   2913.979980   \n",
       "\n",
       "             Volume_SP  Returns_SP   Open_AAPL   High_AAPL    Low_AAPL  \\\n",
       "Date                                                                     \n",
       "2013-10-02  3148600000   -0.000667   69.375717   70.257141   69.107140   \n",
       "2013-10-03  3279650000   -0.008979   70.072861   70.335716   68.677139   \n",
       "2013-10-04  2880270000    0.007053   69.122856   69.228569   68.371429   \n",
       "2013-10-07  2678490000   -0.008506   69.508568   70.378571   69.335716   \n",
       "2013-10-08  3569230000   -0.012332   69.991432   70.091431   68.648575   \n",
       "...                ...         ...         ...         ...         ...   \n",
       "2018-09-24  3372210000   -0.003516  216.820007  221.259995  216.630005   \n",
       "2018-09-25  3285480000   -0.001305  219.750000  222.820007  219.699997   \n",
       "2018-09-26  3388620000   -0.003289  221.000000  223.750000  219.759995   \n",
       "2018-09-27  3060850000    0.002763  223.820007  226.440002  223.539993   \n",
       "2018-09-28  3432300000   -0.000007  224.789993  225.839996  224.020004   \n",
       "\n",
       "            Close_AAPL  Adj Close_AAPL  Volume_AAPL  Returns_AAPL  Predictions  \n",
       "Date                                                                            \n",
       "2013-10-02   69.937141       63.731426     72296000      0.003279    -0.000691  \n",
       "2013-10-03   69.058571       62.930801     80688300     -0.012562    -0.009305  \n",
       "2013-10-04   69.004288       62.881340     64717100     -0.000786     0.007309  \n",
       "2013-10-07   69.678574       63.495800     78073100      0.009772    -0.008815  \n",
       "2013-10-08   68.705711       62.609249     72729300     -0.013962    -0.012780  \n",
       "...                ...             ...          ...           ...          ...  \n",
       "2018-09-24  220.789993      220.789993     27693400      0.014380    -0.003643  \n",
       "2018-09-25  222.190002      222.190002     24554400      0.006341    -0.001352  \n",
       "2018-09-26  220.419998      220.419998     23984700     -0.007966    -0.003409  \n",
       "2018-09-27  224.949997      224.949997     30181200      0.020552     0.002864  \n",
       "2018-09-28  225.740005      225.740005     22889300      0.003512    -0.000007  \n",
       "\n",
       "[1258 rows x 15 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#In-Sample forecast / \"Backtesting\"\n",
    "mergedData['Predictions'] = results.predict(mergedData['Returns_SP'])\n",
    "\n",
    "#Out-of sample forecast --> give your own data set to predict\n",
    "mergedData"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% Visualize\n",
    "plt.plot(mergedData['Returns_SP'],mergedData['Predictions'],'red')\n",
    "plt.scatter(mergedData['Returns_SP'],mergedData['Returns_AAPL'],alpha=0.5)\n",
    "plt.title(\"Linear Regression SP500 vs AAPL\")\n",
    "plt.xlabel(\"S&P 500 Daily Returns\")\n",
    "plt.ylabel(\"AAPL Daily Returns\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Beta using Monthly Data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open_SP</th>\n",
       "      <th>Close_SP</th>\n",
       "      <th>Volume_SP</th>\n",
       "      <th>High_SP</th>\n",
       "      <th>Low_SP</th>\n",
       "      <th>Returns_SP</th>\n",
       "      <th>Open_AAPL</th>\n",
       "      <th>Close_AAPL</th>\n",
       "      <th>Volume_AAPL</th>\n",
       "      <th>High_AAPL</th>\n",
       "      <th>Low_AAPL</th>\n",
       "      <th>Returns_AAPL</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",
       "      <th></th>\n",
       "      <th></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>2013-11-30</th>\n",
       "      <td>1758.699951</td>\n",
       "      <td>1805.810059</td>\n",
       "      <td>63628190000</td>\n",
       "      <td>1813.550049</td>\n",
       "      <td>1746.199951</td>\n",
       "      <td>0.028049</td>\n",
       "      <td>74.860001</td>\n",
       "      <td>79.438568</td>\n",
       "      <td>1.306289e+09</td>\n",
       "      <td>79.761429</td>\n",
       "      <td>73.197144</td>\n",
       "      <td>0.063842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-31</th>\n",
       "      <td>1806.550049</td>\n",
       "      <td>1848.359985</td>\n",
       "      <td>64958820000</td>\n",
       "      <td>1849.439941</td>\n",
       "      <td>1767.989990</td>\n",
       "      <td>0.023563</td>\n",
       "      <td>79.714287</td>\n",
       "      <td>80.145714</td>\n",
       "      <td>1.764349e+09</td>\n",
       "      <td>82.162857</td>\n",
       "      <td>76.971428</td>\n",
       "      <td>0.008902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-01-31</th>\n",
       "      <td>1845.859985</td>\n",
       "      <td>1782.589966</td>\n",
       "      <td>75871910000</td>\n",
       "      <td>1850.839966</td>\n",
       "      <td>1770.449951</td>\n",
       "      <td>-0.035583</td>\n",
       "      <td>79.382858</td>\n",
       "      <td>71.514282</td>\n",
       "      <td>2.191489e+09</td>\n",
       "      <td>80.028572</td>\n",
       "      <td>70.507141</td>\n",
       "      <td>-0.107697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-02-28</th>\n",
       "      <td>1782.680054</td>\n",
       "      <td>1859.449951</td>\n",
       "      <td>69725590000</td>\n",
       "      <td>1867.920044</td>\n",
       "      <td>1737.920044</td>\n",
       "      <td>0.043117</td>\n",
       "      <td>71.801430</td>\n",
       "      <td>75.177139</td>\n",
       "      <td>1.470092e+09</td>\n",
       "      <td>78.741432</td>\n",
       "      <td>71.328575</td>\n",
       "      <td>0.051219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-03-31</th>\n",
       "      <td>1857.680054</td>\n",
       "      <td>1872.339966</td>\n",
       "      <td>71885030000</td>\n",
       "      <td>1883.969971</td>\n",
       "      <td>1834.439941</td>\n",
       "      <td>0.006932</td>\n",
       "      <td>74.774284</td>\n",
       "      <td>76.677139</td>\n",
       "      <td>1.250425e+09</td>\n",
       "      <td>78.428574</td>\n",
       "      <td>74.687141</td>\n",
       "      <td>0.019953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-04-30</th>\n",
       "      <td>1873.959961</td>\n",
       "      <td>1883.949951</td>\n",
       "      <td>71595810000</td>\n",
       "      <td>1897.280029</td>\n",
       "      <td>1814.359985</td>\n",
       "      <td>0.006201</td>\n",
       "      <td>76.822861</td>\n",
       "      <td>84.298569</td>\n",
       "      <td>1.608765e+09</td>\n",
       "      <td>85.632858</td>\n",
       "      <td>73.047142</td>\n",
       "      <td>0.099396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-05-31</th>\n",
       "      <td>1884.390015</td>\n",
       "      <td>1923.569946</td>\n",
       "      <td>63623630000</td>\n",
       "      <td>1924.030029</td>\n",
       "      <td>1859.790039</td>\n",
       "      <td>0.021030</td>\n",
       "      <td>84.571426</td>\n",
       "      <td>90.428574</td>\n",
       "      <td>1.433917e+09</td>\n",
       "      <td>92.024284</td>\n",
       "      <td>82.904289</td>\n",
       "      <td>0.072718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-06-30</th>\n",
       "      <td>1923.869995</td>\n",
       "      <td>1960.229980</td>\n",
       "      <td>63283380000</td>\n",
       "      <td>1968.170044</td>\n",
       "      <td>1915.979980</td>\n",
       "      <td>0.019058</td>\n",
       "      <td>90.565712</td>\n",
       "      <td>92.930000</td>\n",
       "      <td>1.206935e+09</td>\n",
       "      <td>95.050003</td>\n",
       "      <td>88.928574</td>\n",
       "      <td>0.027662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-07-31</th>\n",
       "      <td>1962.290039</td>\n",
       "      <td>1930.670044</td>\n",
       "      <td>66524690000</td>\n",
       "      <td>1991.390015</td>\n",
       "      <td>1930.670044</td>\n",
       "      <td>-0.015080</td>\n",
       "      <td>93.519997</td>\n",
       "      <td>95.599998</td>\n",
       "      <td>1.035086e+09</td>\n",
       "      <td>99.440002</td>\n",
       "      <td>92.570000</td>\n",
       "      <td>0.028731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-08-31</th>\n",
       "      <td>1929.800049</td>\n",
       "      <td>2003.369995</td>\n",
       "      <td>58131140000</td>\n",
       "      <td>2005.040039</td>\n",
       "      <td>1904.780029</td>\n",
       "      <td>0.037655</td>\n",
       "      <td>94.900002</td>\n",
       "      <td>102.500000</td>\n",
       "      <td>9.370770e+08</td>\n",
       "      <td>102.900002</td>\n",
       "      <td>93.279999</td>\n",
       "      <td>0.072176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-09-30</th>\n",
       "      <td>2004.069946</td>\n",
       "      <td>1972.290039</td>\n",
       "      <td>66706000000</td>\n",
       "      <td>2019.260010</td>\n",
       "      <td>1964.040039</td>\n",
       "      <td>-0.015514</td>\n",
       "      <td>103.059998</td>\n",
       "      <td>100.750000</td>\n",
       "      <td>1.526420e+09</td>\n",
       "      <td>103.739998</td>\n",
       "      <td>96.139999</td>\n",
       "      <td>-0.017073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-10-31</th>\n",
       "      <td>1971.439941</td>\n",
       "      <td>2018.050049</td>\n",
       "      <td>93714040000</td>\n",
       "      <td>2018.189941</td>\n",
       "      <td>1820.660034</td>\n",
       "      <td>0.023201</td>\n",
       "      <td>100.589996</td>\n",
       "      <td>108.000000</td>\n",
       "      <td>1.360280e+09</td>\n",
       "      <td>108.040001</td>\n",
       "      <td>95.180000</td>\n",
       "      <td>0.071960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-11-30</th>\n",
       "      <td>2018.209961</td>\n",
       "      <td>2067.560059</td>\n",
       "      <td>63600190000</td>\n",
       "      <td>2075.760010</td>\n",
       "      <td>2001.010010</td>\n",
       "      <td>0.024534</td>\n",
       "      <td>108.220001</td>\n",
       "      <td>118.930000</td>\n",
       "      <td>8.204082e+08</td>\n",
       "      <td>119.750000</td>\n",
       "      <td>107.720001</td>\n",
       "      <td>0.101204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-31</th>\n",
       "      <td>2065.780029</td>\n",
       "      <td>2058.899902</td>\n",
       "      <td>80743820000</td>\n",
       "      <td>2093.550049</td>\n",
       "      <td>1972.560059</td>\n",
       "      <td>-0.004189</td>\n",
       "      <td>118.809998</td>\n",
       "      <td>110.379997</td>\n",
       "      <td>1.073595e+09</td>\n",
       "      <td>119.250000</td>\n",
       "      <td>106.260002</td>\n",
       "      <td>-0.071891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-31</th>\n",
       "      <td>2058.899902</td>\n",
       "      <td>1994.989990</td>\n",
       "      <td>77330040000</td>\n",
       "      <td>2072.360107</td>\n",
       "      <td>1988.119995</td>\n",
       "      <td>-0.031041</td>\n",
       "      <td>111.389999</td>\n",
       "      <td>117.160004</td>\n",
       "      <td>1.304644e+09</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>104.629997</td>\n",
       "      <td>0.061424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-28</th>\n",
       "      <td>1996.670044</td>\n",
       "      <td>2104.500000</td>\n",
       "      <td>68775560000</td>\n",
       "      <td>2119.590088</td>\n",
       "      <td>1980.900024</td>\n",
       "      <td>0.054893</td>\n",
       "      <td>118.050003</td>\n",
       "      <td>128.460007</td>\n",
       "      <td>1.136535e+09</td>\n",
       "      <td>133.600006</td>\n",
       "      <td>116.080002</td>\n",
       "      <td>0.096449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-03-31</th>\n",
       "      <td>2105.229980</td>\n",
       "      <td>2067.889893</td>\n",
       "      <td>76675850000</td>\n",
       "      <td>2117.520020</td>\n",
       "      <td>2039.689941</td>\n",
       "      <td>-0.017396</td>\n",
       "      <td>129.250000</td>\n",
       "      <td>124.430000</td>\n",
       "      <td>1.138642e+09</td>\n",
       "      <td>130.279999</td>\n",
       "      <td>121.629997</td>\n",
       "      <td>-0.031372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-30</th>\n",
       "      <td>2067.629883</td>\n",
       "      <td>2085.510010</td>\n",
       "      <td>72060940000</td>\n",
       "      <td>2125.919922</td>\n",
       "      <td>2048.379883</td>\n",
       "      <td>0.008521</td>\n",
       "      <td>124.820000</td>\n",
       "      <td>125.150002</td>\n",
       "      <td>9.961355e+08</td>\n",
       "      <td>134.539993</td>\n",
       "      <td>123.099998</td>\n",
       "      <td>0.005786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-05-31</th>\n",
       "      <td>2087.379883</td>\n",
       "      <td>2107.389893</td>\n",
       "      <td>65187730000</td>\n",
       "      <td>2134.719971</td>\n",
       "      <td>2067.929932</td>\n",
       "      <td>0.010491</td>\n",
       "      <td>126.099998</td>\n",
       "      <td>130.279999</td>\n",
       "      <td>9.541521e+08</td>\n",
       "      <td>132.970001</td>\n",
       "      <td>123.360001</td>\n",
       "      <td>0.040991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-30</th>\n",
       "      <td>2108.639893</td>\n",
       "      <td>2063.110107</td>\n",
       "      <td>73213980000</td>\n",
       "      <td>2129.870117</td>\n",
       "      <td>2056.320068</td>\n",
       "      <td>-0.021012</td>\n",
       "      <td>130.279999</td>\n",
       "      <td>125.430000</td>\n",
       "      <td>8.785126e+08</td>\n",
       "      <td>131.389999</td>\n",
       "      <td>124.480003</td>\n",
       "      <td>-0.037228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-07-31</th>\n",
       "      <td>2067.000000</td>\n",
       "      <td>2103.840088</td>\n",
       "      <td>77920590000</td>\n",
       "      <td>2132.820068</td>\n",
       "      <td>2044.020020</td>\n",
       "      <td>0.019742</td>\n",
       "      <td>126.900002</td>\n",
       "      <td>121.300003</td>\n",
       "      <td>1.057507e+09</td>\n",
       "      <td>132.970001</td>\n",
       "      <td>119.220001</td>\n",
       "      <td>-0.032927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-08-31</th>\n",
       "      <td>2104.489990</td>\n",
       "      <td>1972.180054</td>\n",
       "      <td>84626790000</td>\n",
       "      <td>2112.659912</td>\n",
       "      <td>1867.010010</td>\n",
       "      <td>-0.062581</td>\n",
       "      <td>121.500000</td>\n",
       "      <td>112.760002</td>\n",
       "      <td>1.605978e+09</td>\n",
       "      <td>122.570000</td>\n",
       "      <td>92.000000</td>\n",
       "      <td>-0.070404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-09-30</th>\n",
       "      <td>1970.089966</td>\n",
       "      <td>1920.030029</td>\n",
       "      <td>79989370000</td>\n",
       "      <td>2020.859985</td>\n",
       "      <td>1871.910034</td>\n",
       "      <td>-0.026443</td>\n",
       "      <td>110.150002</td>\n",
       "      <td>110.300003</td>\n",
       "      <td>1.206547e+09</td>\n",
       "      <td>116.889999</td>\n",
       "      <td>107.360001</td>\n",
       "      <td>-0.021816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-10-31</th>\n",
       "      <td>1919.650024</td>\n",
       "      <td>2079.360107</td>\n",
       "      <td>85844900000</td>\n",
       "      <td>2094.320068</td>\n",
       "      <td>1893.699951</td>\n",
       "      <td>0.082983</td>\n",
       "      <td>109.070000</td>\n",
       "      <td>119.500000</td>\n",
       "      <td>1.112323e+09</td>\n",
       "      <td>121.220001</td>\n",
       "      <td>107.309998</td>\n",
       "      <td>0.083409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-11-30</th>\n",
       "      <td>2080.760010</td>\n",
       "      <td>2080.409912</td>\n",
       "      <td>75943590000</td>\n",
       "      <td>2116.479980</td>\n",
       "      <td>2019.390015</td>\n",
       "      <td>0.000505</td>\n",
       "      <td>120.800003</td>\n",
       "      <td>118.300003</td>\n",
       "      <td>7.506406e+08</td>\n",
       "      <td>123.820000</td>\n",
       "      <td>111.000000</td>\n",
       "      <td>-0.010042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>2082.929932</td>\n",
       "      <td>2043.939941</td>\n",
       "      <td>83649260000</td>\n",
       "      <td>2104.270020</td>\n",
       "      <td>1993.260010</td>\n",
       "      <td>-0.017530</td>\n",
       "      <td>118.750000</td>\n",
       "      <td>105.260002</td>\n",
       "      <td>9.215297e+08</td>\n",
       "      <td>119.860001</td>\n",
       "      <td>104.820000</td>\n",
       "      <td>-0.110228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-31</th>\n",
       "      <td>2038.199951</td>\n",
       "      <td>1940.239990</td>\n",
       "      <td>92409770000</td>\n",
       "      <td>2038.199951</td>\n",
       "      <td>1812.290039</td>\n",
       "      <td>-0.050735</td>\n",
       "      <td>102.610001</td>\n",
       "      <td>97.339996</td>\n",
       "      <td>1.271024e+09</td>\n",
       "      <td>105.849998</td>\n",
       "      <td>92.389999</td>\n",
       "      <td>-0.075242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-02-29</th>\n",
       "      <td>1936.939941</td>\n",
       "      <td>1932.229980</td>\n",
       "      <td>93049560000</td>\n",
       "      <td>1962.959961</td>\n",
       "      <td>1810.099976</td>\n",
       "      <td>-0.004128</td>\n",
       "      <td>96.470001</td>\n",
       "      <td>96.690002</td>\n",
       "      <td>8.108626e+08</td>\n",
       "      <td>98.889999</td>\n",
       "      <td>92.589996</td>\n",
       "      <td>-0.006678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-03-31</th>\n",
       "      <td>1937.089966</td>\n",
       "      <td>2059.739990</td>\n",
       "      <td>92639420000</td>\n",
       "      <td>2072.209961</td>\n",
       "      <td>1937.089966</td>\n",
       "      <td>0.065991</td>\n",
       "      <td>97.650002</td>\n",
       "      <td>108.989998</td>\n",
       "      <td>7.460496e+08</td>\n",
       "      <td>110.419998</td>\n",
       "      <td>97.419998</td>\n",
       "      <td>0.127211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-04-30</th>\n",
       "      <td>2056.620117</td>\n",
       "      <td>2065.300049</td>\n",
       "      <td>81124990000</td>\n",
       "      <td>2111.050049</td>\n",
       "      <td>2033.800049</td>\n",
       "      <td>0.002699</td>\n",
       "      <td>108.779999</td>\n",
       "      <td>93.739998</td>\n",
       "      <td>8.723962e+08</td>\n",
       "      <td>112.389999</td>\n",
       "      <td>92.510002</td>\n",
       "      <td>-0.139921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-05-31</th>\n",
       "      <td>2067.169922</td>\n",
       "      <td>2096.949951</td>\n",
       "      <td>78883600000</td>\n",
       "      <td>2103.479980</td>\n",
       "      <td>2025.910034</td>\n",
       "      <td>0.015325</td>\n",
       "      <td>93.970001</td>\n",
       "      <td>99.860001</td>\n",
       "      <td>9.003181e+08</td>\n",
       "      <td>100.730003</td>\n",
       "      <td>89.470001</td>\n",
       "      <td>0.065287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-06-30</th>\n",
       "      <td>2093.939941</td>\n",
       "      <td>2098.860107</td>\n",
       "      <td>86852700000</td>\n",
       "      <td>2120.550049</td>\n",
       "      <td>1991.680054</td>\n",
       "      <td>0.000911</td>\n",
       "      <td>99.019997</td>\n",
       "      <td>95.599998</td>\n",
       "      <td>7.790557e+08</td>\n",
       "      <td>101.889999</td>\n",
       "      <td>91.500000</td>\n",
       "      <td>-0.042660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-07-31</th>\n",
       "      <td>2099.340088</td>\n",
       "      <td>2173.600098</td>\n",
       "      <td>69530250000</td>\n",
       "      <td>2177.090088</td>\n",
       "      <td>2074.020020</td>\n",
       "      <td>0.035610</td>\n",
       "      <td>95.489998</td>\n",
       "      <td>104.209999</td>\n",
       "      <td>6.857796e+08</td>\n",
       "      <td>104.550003</td>\n",
       "      <td>94.370003</td>\n",
       "      <td>0.090063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-31</th>\n",
       "      <td>2173.149902</td>\n",
       "      <td>2170.949951</td>\n",
       "      <td>75610310000</td>\n",
       "      <td>2193.810059</td>\n",
       "      <td>2147.580078</td>\n",
       "      <td>-0.001219</td>\n",
       "      <td>104.410004</td>\n",
       "      <td>106.099998</td>\n",
       "      <td>6.301285e+08</td>\n",
       "      <td>110.230003</td>\n",
       "      <td>104.000000</td>\n",
       "      <td>0.018136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-09-30</th>\n",
       "      <td>2171.330078</td>\n",
       "      <td>2168.270020</td>\n",
       "      <td>77270240000</td>\n",
       "      <td>2187.870117</td>\n",
       "      <td>2119.120117</td>\n",
       "      <td>-0.001234</td>\n",
       "      <td>106.139999</td>\n",
       "      <td>113.050003</td>\n",
       "      <td>9.680156e+08</td>\n",
       "      <td>116.180000</td>\n",
       "      <td>102.529999</td>\n",
       "      <td>0.065504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-10-31</th>\n",
       "      <td>2164.330078</td>\n",
       "      <td>2126.149902</td>\n",
       "      <td>73196630000</td>\n",
       "      <td>2169.600098</td>\n",
       "      <td>2114.719971</td>\n",
       "      <td>-0.019426</td>\n",
       "      <td>112.709999</td>\n",
       "      <td>113.540001</td>\n",
       "      <td>6.869143e+08</td>\n",
       "      <td>118.690002</td>\n",
       "      <td>112.279999</td>\n",
       "      <td>0.004334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-11-30</th>\n",
       "      <td>2128.679932</td>\n",
       "      <td>2198.810059</td>\n",
       "      <td>88299760000</td>\n",
       "      <td>2214.100098</td>\n",
       "      <td>2083.790039</td>\n",
       "      <td>0.034175</td>\n",
       "      <td>113.459999</td>\n",
       "      <td>110.519997</td>\n",
       "      <td>7.213055e+08</td>\n",
       "      <td>113.769997</td>\n",
       "      <td>104.080002</td>\n",
       "      <td>-0.026599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>2200.169922</td>\n",
       "      <td>2238.830078</td>\n",
       "      <td>75251240000</td>\n",
       "      <td>2277.530029</td>\n",
       "      <td>2187.439941</td>\n",
       "      <td>0.018201</td>\n",
       "      <td>110.370003</td>\n",
       "      <td>115.820000</td>\n",
       "      <td>6.087717e+08</td>\n",
       "      <td>118.019997</td>\n",
       "      <td>108.250000</td>\n",
       "      <td>0.047955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-31</th>\n",
       "      <td>2251.570068</td>\n",
       "      <td>2278.870117</td>\n",
       "      <td>70483180000</td>\n",
       "      <td>2300.989990</td>\n",
       "      <td>2245.129883</td>\n",
       "      <td>0.017884</td>\n",
       "      <td>115.800003</td>\n",
       "      <td>121.349998</td>\n",
       "      <td>5.631220e+08</td>\n",
       "      <td>122.440002</td>\n",
       "      <td>114.760002</td>\n",
       "      <td>0.047746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-02-28</th>\n",
       "      <td>2285.590088</td>\n",
       "      <td>2363.639893</td>\n",
       "      <td>69162420000</td>\n",
       "      <td>2371.540039</td>\n",
       "      <td>2271.649902</td>\n",
       "      <td>0.037198</td>\n",
       "      <td>127.029999</td>\n",
       "      <td>136.990005</td>\n",
       "      <td>5.749686e+08</td>\n",
       "      <td>137.479996</td>\n",
       "      <td>127.010002</td>\n",
       "      <td>0.128883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-03-31</th>\n",
       "      <td>2380.129883</td>\n",
       "      <td>2362.719971</td>\n",
       "      <td>81547770000</td>\n",
       "      <td>2400.979980</td>\n",
       "      <td>2322.250000</td>\n",
       "      <td>-0.000389</td>\n",
       "      <td>137.889999</td>\n",
       "      <td>143.660004</td>\n",
       "      <td>5.616284e+08</td>\n",
       "      <td>144.500000</td>\n",
       "      <td>137.050003</td>\n",
       "      <td>0.048690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-04-30</th>\n",
       "      <td>2362.340088</td>\n",
       "      <td>2384.199951</td>\n",
       "      <td>65265670000</td>\n",
       "      <td>2398.159912</td>\n",
       "      <td>2328.949951</td>\n",
       "      <td>0.009091</td>\n",
       "      <td>143.710007</td>\n",
       "      <td>143.649994</td>\n",
       "      <td>3.733041e+08</td>\n",
       "      <td>145.460007</td>\n",
       "      <td>140.059998</td>\n",
       "      <td>-0.000070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-31</th>\n",
       "      <td>2388.500000</td>\n",
       "      <td>2411.800049</td>\n",
       "      <td>79607170000</td>\n",
       "      <td>2418.709961</td>\n",
       "      <td>2352.719971</td>\n",
       "      <td>0.011576</td>\n",
       "      <td>145.100006</td>\n",
       "      <td>152.759995</td>\n",
       "      <td>6.539818e+08</td>\n",
       "      <td>156.649994</td>\n",
       "      <td>144.270004</td>\n",
       "      <td>0.063418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-30</th>\n",
       "      <td>2415.649902</td>\n",
       "      <td>2423.409912</td>\n",
       "      <td>81002490000</td>\n",
       "      <td>2453.820068</td>\n",
       "      <td>2405.699951</td>\n",
       "      <td>0.004814</td>\n",
       "      <td>153.169998</td>\n",
       "      <td>144.020004</td>\n",
       "      <td>6.841781e+08</td>\n",
       "      <td>155.979996</td>\n",
       "      <td>142.199997</td>\n",
       "      <td>-0.057214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-07-31</th>\n",
       "      <td>2431.389893</td>\n",
       "      <td>2470.300049</td>\n",
       "      <td>63169400000</td>\n",
       "      <td>2484.040039</td>\n",
       "      <td>2407.699951</td>\n",
       "      <td>0.019349</td>\n",
       "      <td>144.880005</td>\n",
       "      <td>148.729996</td>\n",
       "      <td>4.220119e+08</td>\n",
       "      <td>153.990005</td>\n",
       "      <td>142.410004</td>\n",
       "      <td>0.032704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-08-31</th>\n",
       "      <td>2477.100098</td>\n",
       "      <td>2471.649902</td>\n",
       "      <td>70616030000</td>\n",
       "      <td>2490.870117</td>\n",
       "      <td>2417.350098</td>\n",
       "      <td>0.000546</td>\n",
       "      <td>149.100006</td>\n",
       "      <td>164.000000</td>\n",
       "      <td>6.610690e+08</td>\n",
       "      <td>164.520004</td>\n",
       "      <td>148.410004</td>\n",
       "      <td>0.102669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-30</th>\n",
       "      <td>2474.419922</td>\n",
       "      <td>2519.360107</td>\n",
       "      <td>66337980000</td>\n",
       "      <td>2519.439941</td>\n",
       "      <td>2446.550049</td>\n",
       "      <td>0.019303</td>\n",
       "      <td>164.800003</td>\n",
       "      <td>154.119995</td>\n",
       "      <td>6.803741e+08</td>\n",
       "      <td>164.940002</td>\n",
       "      <td>149.160004</td>\n",
       "      <td>-0.060244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-31</th>\n",
       "      <td>2521.199951</td>\n",
       "      <td>2575.260010</td>\n",
       "      <td>70871570000</td>\n",
       "      <td>2582.979980</td>\n",
       "      <td>2520.399902</td>\n",
       "      <td>0.022188</td>\n",
       "      <td>154.259995</td>\n",
       "      <td>169.039993</td>\n",
       "      <td>5.042913e+08</td>\n",
       "      <td>169.649994</td>\n",
       "      <td>152.460007</td>\n",
       "      <td>0.096808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-30</th>\n",
       "      <td>2583.209961</td>\n",
       "      <td>2647.580078</td>\n",
       "      <td>73173260000</td>\n",
       "      <td>2657.739990</td>\n",
       "      <td>2557.449951</td>\n",
       "      <td>0.028083</td>\n",
       "      <td>169.869995</td>\n",
       "      <td>171.850006</td>\n",
       "      <td>6.006634e+08</td>\n",
       "      <td>176.240005</td>\n",
       "      <td>165.279999</td>\n",
       "      <td>0.016623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-31</th>\n",
       "      <td>2645.100098</td>\n",
       "      <td>2673.610107</td>\n",
       "      <td>65251190000</td>\n",
       "      <td>2694.969971</td>\n",
       "      <td>2605.520020</td>\n",
       "      <td>0.009832</td>\n",
       "      <td>169.949997</td>\n",
       "      <td>169.229996</td>\n",
       "      <td>5.308335e+08</td>\n",
       "      <td>177.199997</td>\n",
       "      <td>166.460007</td>\n",
       "      <td>-0.015246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-31</th>\n",
       "      <td>2683.729980</td>\n",
       "      <td>2823.810059</td>\n",
       "      <td>76860120000</td>\n",
       "      <td>2872.870117</td>\n",
       "      <td>2682.360107</td>\n",
       "      <td>0.056179</td>\n",
       "      <td>170.160004</td>\n",
       "      <td>167.429993</td>\n",
       "      <td>6.594873e+08</td>\n",
       "      <td>180.100006</td>\n",
       "      <td>164.699997</td>\n",
       "      <td>-0.010636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-28</th>\n",
       "      <td>2816.449951</td>\n",
       "      <td>2713.830078</td>\n",
       "      <td>79579410000</td>\n",
       "      <td>2835.959961</td>\n",
       "      <td>2532.689941</td>\n",
       "      <td>-0.038947</td>\n",
       "      <td>167.169998</td>\n",
       "      <td>178.119995</td>\n",
       "      <td>9.278943e+08</td>\n",
       "      <td>180.619995</td>\n",
       "      <td>150.240005</td>\n",
       "      <td>0.063848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-03-31</th>\n",
       "      <td>2715.219971</td>\n",
       "      <td>2640.870117</td>\n",
       "      <td>76369800000</td>\n",
       "      <td>2801.899902</td>\n",
       "      <td>2585.889893</td>\n",
       "      <td>-0.026884</td>\n",
       "      <td>178.539993</td>\n",
       "      <td>167.779999</td>\n",
       "      <td>7.130109e+08</td>\n",
       "      <td>183.500000</td>\n",
       "      <td>164.940002</td>\n",
       "      <td>-0.058051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-04-30</th>\n",
       "      <td>2633.449951</td>\n",
       "      <td>2648.050049</td>\n",
       "      <td>69648590000</td>\n",
       "      <td>2717.489990</td>\n",
       "      <td>2553.800049</td>\n",
       "      <td>0.002719</td>\n",
       "      <td>166.639999</td>\n",
       "      <td>165.259995</td>\n",
       "      <td>6.660579e+08</td>\n",
       "      <td>178.940002</td>\n",
       "      <td>160.630005</td>\n",
       "      <td>-0.015020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-05-31</th>\n",
       "      <td>2642.959961</td>\n",
       "      <td>2705.270020</td>\n",
       "      <td>75617280000</td>\n",
       "      <td>2742.239990</td>\n",
       "      <td>2594.620117</td>\n",
       "      <td>0.021608</td>\n",
       "      <td>166.410004</td>\n",
       "      <td>186.869995</td>\n",
       "      <td>6.209763e+08</td>\n",
       "      <td>190.369995</td>\n",
       "      <td>165.270004</td>\n",
       "      <td>0.130764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-30</th>\n",
       "      <td>2718.699951</td>\n",
       "      <td>2718.370117</td>\n",
       "      <td>77439710000</td>\n",
       "      <td>2791.469971</td>\n",
       "      <td>2691.989990</td>\n",
       "      <td>0.004842</td>\n",
       "      <td>187.990005</td>\n",
       "      <td>185.110001</td>\n",
       "      <td>5.276245e+08</td>\n",
       "      <td>194.199997</td>\n",
       "      <td>180.729996</td>\n",
       "      <td>-0.009418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-07-31</th>\n",
       "      <td>2704.949951</td>\n",
       "      <td>2816.290039</td>\n",
       "      <td>64542170000</td>\n",
       "      <td>2848.030029</td>\n",
       "      <td>2698.949951</td>\n",
       "      <td>0.036022</td>\n",
       "      <td>183.820007</td>\n",
       "      <td>190.289993</td>\n",
       "      <td>3.936914e+08</td>\n",
       "      <td>195.960007</td>\n",
       "      <td>183.419998</td>\n",
       "      <td>0.027983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-08-31</th>\n",
       "      <td>2821.169922</td>\n",
       "      <td>2901.520020</td>\n",
       "      <td>69238220000</td>\n",
       "      <td>2916.500000</td>\n",
       "      <td>2796.340088</td>\n",
       "      <td>0.030263</td>\n",
       "      <td>199.130005</td>\n",
       "      <td>227.630005</td>\n",
       "      <td>7.003189e+08</td>\n",
       "      <td>228.869995</td>\n",
       "      <td>197.309998</td>\n",
       "      <td>0.196227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-30</th>\n",
       "      <td>2896.959961</td>\n",
       "      <td>2913.979980</td>\n",
       "      <td>62492080000</td>\n",
       "      <td>2940.909912</td>\n",
       "      <td>2864.120117</td>\n",
       "      <td>0.004294</td>\n",
       "      <td>228.410004</td>\n",
       "      <td>225.740005</td>\n",
       "      <td>6.789319e+08</td>\n",
       "      <td>229.669998</td>\n",
       "      <td>215.300003</td>\n",
       "      <td>-0.008303</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Open_SP     Close_SP    Volume_SP      High_SP       Low_SP  \\\n",
       "Date                                                                          \n",
       "2013-11-30  1758.699951  1805.810059  63628190000  1813.550049  1746.199951   \n",
       "2013-12-31  1806.550049  1848.359985  64958820000  1849.439941  1767.989990   \n",
       "2014-01-31  1845.859985  1782.589966  75871910000  1850.839966  1770.449951   \n",
       "2014-02-28  1782.680054  1859.449951  69725590000  1867.920044  1737.920044   \n",
       "2014-03-31  1857.680054  1872.339966  71885030000  1883.969971  1834.439941   \n",
       "2014-04-30  1873.959961  1883.949951  71595810000  1897.280029  1814.359985   \n",
       "2014-05-31  1884.390015  1923.569946  63623630000  1924.030029  1859.790039   \n",
       "2014-06-30  1923.869995  1960.229980  63283380000  1968.170044  1915.979980   \n",
       "2014-07-31  1962.290039  1930.670044  66524690000  1991.390015  1930.670044   \n",
       "2014-08-31  1929.800049  2003.369995  58131140000  2005.040039  1904.780029   \n",
       "2014-09-30  2004.069946  1972.290039  66706000000  2019.260010  1964.040039   \n",
       "2014-10-31  1971.439941  2018.050049  93714040000  2018.189941  1820.660034   \n",
       "2014-11-30  2018.209961  2067.560059  63600190000  2075.760010  2001.010010   \n",
       "2014-12-31  2065.780029  2058.899902  80743820000  2093.550049  1972.560059   \n",
       "2015-01-31  2058.899902  1994.989990  77330040000  2072.360107  1988.119995   \n",
       "2015-02-28  1996.670044  2104.500000  68775560000  2119.590088  1980.900024   \n",
       "2015-03-31  2105.229980  2067.889893  76675850000  2117.520020  2039.689941   \n",
       "2015-04-30  2067.629883  2085.510010  72060940000  2125.919922  2048.379883   \n",
       "2015-05-31  2087.379883  2107.389893  65187730000  2134.719971  2067.929932   \n",
       "2015-06-30  2108.639893  2063.110107  73213980000  2129.870117  2056.320068   \n",
       "2015-07-31  2067.000000  2103.840088  77920590000  2132.820068  2044.020020   \n",
       "2015-08-31  2104.489990  1972.180054  84626790000  2112.659912  1867.010010   \n",
       "2015-09-30  1970.089966  1920.030029  79989370000  2020.859985  1871.910034   \n",
       "2015-10-31  1919.650024  2079.360107  85844900000  2094.320068  1893.699951   \n",
       "2015-11-30  2080.760010  2080.409912  75943590000  2116.479980  2019.390015   \n",
       "2015-12-31  2082.929932  2043.939941  83649260000  2104.270020  1993.260010   \n",
       "2016-01-31  2038.199951  1940.239990  92409770000  2038.199951  1812.290039   \n",
       "2016-02-29  1936.939941  1932.229980  93049560000  1962.959961  1810.099976   \n",
       "2016-03-31  1937.089966  2059.739990  92639420000  2072.209961  1937.089966   \n",
       "2016-04-30  2056.620117  2065.300049  81124990000  2111.050049  2033.800049   \n",
       "2016-05-31  2067.169922  2096.949951  78883600000  2103.479980  2025.910034   \n",
       "2016-06-30  2093.939941  2098.860107  86852700000  2120.550049  1991.680054   \n",
       "2016-07-31  2099.340088  2173.600098  69530250000  2177.090088  2074.020020   \n",
       "2016-08-31  2173.149902  2170.949951  75610310000  2193.810059  2147.580078   \n",
       "2016-09-30  2171.330078  2168.270020  77270240000  2187.870117  2119.120117   \n",
       "2016-10-31  2164.330078  2126.149902  73196630000  2169.600098  2114.719971   \n",
       "2016-11-30  2128.679932  2198.810059  88299760000  2214.100098  2083.790039   \n",
       "2016-12-31  2200.169922  2238.830078  75251240000  2277.530029  2187.439941   \n",
       "2017-01-31  2251.570068  2278.870117  70483180000  2300.989990  2245.129883   \n",
       "2017-02-28  2285.590088  2363.639893  69162420000  2371.540039  2271.649902   \n",
       "2017-03-31  2380.129883  2362.719971  81547770000  2400.979980  2322.250000   \n",
       "2017-04-30  2362.340088  2384.199951  65265670000  2398.159912  2328.949951   \n",
       "2017-05-31  2388.500000  2411.800049  79607170000  2418.709961  2352.719971   \n",
       "2017-06-30  2415.649902  2423.409912  81002490000  2453.820068  2405.699951   \n",
       "2017-07-31  2431.389893  2470.300049  63169400000  2484.040039  2407.699951   \n",
       "2017-08-31  2477.100098  2471.649902  70616030000  2490.870117  2417.350098   \n",
       "2017-09-30  2474.419922  2519.360107  66337980000  2519.439941  2446.550049   \n",
       "2017-10-31  2521.199951  2575.260010  70871570000  2582.979980  2520.399902   \n",
       "2017-11-30  2583.209961  2647.580078  73173260000  2657.739990  2557.449951   \n",
       "2017-12-31  2645.100098  2673.610107  65251190000  2694.969971  2605.520020   \n",
       "2018-01-31  2683.729980  2823.810059  76860120000  2872.870117  2682.360107   \n",
       "2018-02-28  2816.449951  2713.830078  79579410000  2835.959961  2532.689941   \n",
       "2018-03-31  2715.219971  2640.870117  76369800000  2801.899902  2585.889893   \n",
       "2018-04-30  2633.449951  2648.050049  69648590000  2717.489990  2553.800049   \n",
       "2018-05-31  2642.959961  2705.270020  75617280000  2742.239990  2594.620117   \n",
       "2018-06-30  2718.699951  2718.370117  77439710000  2791.469971  2691.989990   \n",
       "2018-07-31  2704.949951  2816.290039  64542170000  2848.030029  2698.949951   \n",
       "2018-08-31  2821.169922  2901.520020  69238220000  2916.500000  2796.340088   \n",
       "2018-09-30  2896.959961  2913.979980  62492080000  2940.909912  2864.120117   \n",
       "\n",
       "            Returns_SP   Open_AAPL  Close_AAPL   Volume_AAPL   High_AAPL  \\\n",
       "Date                                                                       \n",
       "2013-11-30    0.028049   74.860001   79.438568  1.306289e+09   79.761429   \n",
       "2013-12-31    0.023563   79.714287   80.145714  1.764349e+09   82.162857   \n",
       "2014-01-31   -0.035583   79.382858   71.514282  2.191489e+09   80.028572   \n",
       "2014-02-28    0.043117   71.801430   75.177139  1.470092e+09   78.741432   \n",
       "2014-03-31    0.006932   74.774284   76.677139  1.250425e+09   78.428574   \n",
       "2014-04-30    0.006201   76.822861   84.298569  1.608765e+09   85.632858   \n",
       "2014-05-31    0.021030   84.571426   90.428574  1.433917e+09   92.024284   \n",
       "2014-06-30    0.019058   90.565712   92.930000  1.206935e+09   95.050003   \n",
       "2014-07-31   -0.015080   93.519997   95.599998  1.035086e+09   99.440002   \n",
       "2014-08-31    0.037655   94.900002  102.500000  9.370770e+08  102.900002   \n",
       "2014-09-30   -0.015514  103.059998  100.750000  1.526420e+09  103.739998   \n",
       "2014-10-31    0.023201  100.589996  108.000000  1.360280e+09  108.040001   \n",
       "2014-11-30    0.024534  108.220001  118.930000  8.204082e+08  119.750000   \n",
       "2014-12-31   -0.004189  118.809998  110.379997  1.073595e+09  119.250000   \n",
       "2015-01-31   -0.031041  111.389999  117.160004  1.304644e+09  120.000000   \n",
       "2015-02-28    0.054893  118.050003  128.460007  1.136535e+09  133.600006   \n",
       "2015-03-31   -0.017396  129.250000  124.430000  1.138642e+09  130.279999   \n",
       "2015-04-30    0.008521  124.820000  125.150002  9.961355e+08  134.539993   \n",
       "2015-05-31    0.010491  126.099998  130.279999  9.541521e+08  132.970001   \n",
       "2015-06-30   -0.021012  130.279999  125.430000  8.785126e+08  131.389999   \n",
       "2015-07-31    0.019742  126.900002  121.300003  1.057507e+09  132.970001   \n",
       "2015-08-31   -0.062581  121.500000  112.760002  1.605978e+09  122.570000   \n",
       "2015-09-30   -0.026443  110.150002  110.300003  1.206547e+09  116.889999   \n",
       "2015-10-31    0.082983  109.070000  119.500000  1.112323e+09  121.220001   \n",
       "2015-11-30    0.000505  120.800003  118.300003  7.506406e+08  123.820000   \n",
       "2015-12-31   -0.017530  118.750000  105.260002  9.215297e+08  119.860001   \n",
       "2016-01-31   -0.050735  102.610001   97.339996  1.271024e+09  105.849998   \n",
       "2016-02-29   -0.004128   96.470001   96.690002  8.108626e+08   98.889999   \n",
       "2016-03-31    0.065991   97.650002  108.989998  7.460496e+08  110.419998   \n",
       "2016-04-30    0.002699  108.779999   93.739998  8.723962e+08  112.389999   \n",
       "2016-05-31    0.015325   93.970001   99.860001  9.003181e+08  100.730003   \n",
       "2016-06-30    0.000911   99.019997   95.599998  7.790557e+08  101.889999   \n",
       "2016-07-31    0.035610   95.489998  104.209999  6.857796e+08  104.550003   \n",
       "2016-08-31   -0.001219  104.410004  106.099998  6.301285e+08  110.230003   \n",
       "2016-09-30   -0.001234  106.139999  113.050003  9.680156e+08  116.180000   \n",
       "2016-10-31   -0.019426  112.709999  113.540001  6.869143e+08  118.690002   \n",
       "2016-11-30    0.034175  113.459999  110.519997  7.213055e+08  113.769997   \n",
       "2016-12-31    0.018201  110.370003  115.820000  6.087717e+08  118.019997   \n",
       "2017-01-31    0.017884  115.800003  121.349998  5.631220e+08  122.440002   \n",
       "2017-02-28    0.037198  127.029999  136.990005  5.749686e+08  137.479996   \n",
       "2017-03-31   -0.000389  137.889999  143.660004  5.616284e+08  144.500000   \n",
       "2017-04-30    0.009091  143.710007  143.649994  3.733041e+08  145.460007   \n",
       "2017-05-31    0.011576  145.100006  152.759995  6.539818e+08  156.649994   \n",
       "2017-06-30    0.004814  153.169998  144.020004  6.841781e+08  155.979996   \n",
       "2017-07-31    0.019349  144.880005  148.729996  4.220119e+08  153.990005   \n",
       "2017-08-31    0.000546  149.100006  164.000000  6.610690e+08  164.520004   \n",
       "2017-09-30    0.019303  164.800003  154.119995  6.803741e+08  164.940002   \n",
       "2017-10-31    0.022188  154.259995  169.039993  5.042913e+08  169.649994   \n",
       "2017-11-30    0.028083  169.869995  171.850006  6.006634e+08  176.240005   \n",
       "2017-12-31    0.009832  169.949997  169.229996  5.308335e+08  177.199997   \n",
       "2018-01-31    0.056179  170.160004  167.429993  6.594873e+08  180.100006   \n",
       "2018-02-28   -0.038947  167.169998  178.119995  9.278943e+08  180.619995   \n",
       "2018-03-31   -0.026884  178.539993  167.779999  7.130109e+08  183.500000   \n",
       "2018-04-30    0.002719  166.639999  165.259995  6.660579e+08  178.940002   \n",
       "2018-05-31    0.021608  166.410004  186.869995  6.209763e+08  190.369995   \n",
       "2018-06-30    0.004842  187.990005  185.110001  5.276245e+08  194.199997   \n",
       "2018-07-31    0.036022  183.820007  190.289993  3.936914e+08  195.960007   \n",
       "2018-08-31    0.030263  199.130005  227.630005  7.003189e+08  228.869995   \n",
       "2018-09-30    0.004294  228.410004  225.740005  6.789319e+08  229.669998   \n",
       "\n",
       "              Low_AAPL  Returns_AAPL  \n",
       "Date                                  \n",
       "2013-11-30   73.197144      0.063842  \n",
       "2013-12-31   76.971428      0.008902  \n",
       "2014-01-31   70.507141     -0.107697  \n",
       "2014-02-28   71.328575      0.051219  \n",
       "2014-03-31   74.687141      0.019953  \n",
       "2014-04-30   73.047142      0.099396  \n",
       "2014-05-31   82.904289      0.072718  \n",
       "2014-06-30   88.928574      0.027662  \n",
       "2014-07-31   92.570000      0.028731  \n",
       "2014-08-31   93.279999      0.072176  \n",
       "2014-09-30   96.139999     -0.017073  \n",
       "2014-10-31   95.180000      0.071960  \n",
       "2014-11-30  107.720001      0.101204  \n",
       "2014-12-31  106.260002     -0.071891  \n",
       "2015-01-31  104.629997      0.061424  \n",
       "2015-02-28  116.080002      0.096449  \n",
       "2015-03-31  121.629997     -0.031372  \n",
       "2015-04-30  123.099998      0.005786  \n",
       "2015-05-31  123.360001      0.040991  \n",
       "2015-06-30  124.480003     -0.037228  \n",
       "2015-07-31  119.220001     -0.032927  \n",
       "2015-08-31   92.000000     -0.070404  \n",
       "2015-09-30  107.360001     -0.021816  \n",
       "2015-10-31  107.309998      0.083409  \n",
       "2015-11-30  111.000000     -0.010042  \n",
       "2015-12-31  104.820000     -0.110228  \n",
       "2016-01-31   92.389999     -0.075242  \n",
       "2016-02-29   92.589996     -0.006678  \n",
       "2016-03-31   97.419998      0.127211  \n",
       "2016-04-30   92.510002     -0.139921  \n",
       "2016-05-31   89.470001      0.065287  \n",
       "2016-06-30   91.500000     -0.042660  \n",
       "2016-07-31   94.370003      0.090063  \n",
       "2016-08-31  104.000000      0.018136  \n",
       "2016-09-30  102.529999      0.065504  \n",
       "2016-10-31  112.279999      0.004334  \n",
       "2016-11-30  104.080002     -0.026599  \n",
       "2016-12-31  108.250000      0.047955  \n",
       "2017-01-31  114.760002      0.047746  \n",
       "2017-02-28  127.010002      0.128883  \n",
       "2017-03-31  137.050003      0.048690  \n",
       "2017-04-30  140.059998     -0.000070  \n",
       "2017-05-31  144.270004      0.063418  \n",
       "2017-06-30  142.199997     -0.057214  \n",
       "2017-07-31  142.410004      0.032704  \n",
       "2017-08-31  148.410004      0.102669  \n",
       "2017-09-30  149.160004     -0.060244  \n",
       "2017-10-31  152.460007      0.096808  \n",
       "2017-11-30  165.279999      0.016623  \n",
       "2017-12-31  166.460007     -0.015246  \n",
       "2018-01-31  164.699997     -0.010636  \n",
       "2018-02-28  150.240005      0.063848  \n",
       "2018-03-31  164.940002     -0.058051  \n",
       "2018-04-30  160.630005     -0.015020  \n",
       "2018-05-31  165.270004      0.130764  \n",
       "2018-06-30  180.729996     -0.009418  \n",
       "2018-07-31  183.419998      0.027983  \n",
       "2018-08-31  197.309998      0.196227  \n",
       "2018-09-30  215.300003     -0.008303  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp500 = pd.read_csv(\"StockData/SP500.csv\",parse_dates=['Date'],index_col=['Date'])\n",
    "aapl = pd.read_csv(\"StockData/AAPL.csv\",parse_dates=['Date'],index_col=['Date'])\n",
    "\n",
    "rules = {'Open':'first', 'Close':'last', 'Volume':'sum', 'High':'max', 'Low':'min'}\n",
    "sp500_mo = sp500.resample('M').agg(rules)\n",
    "aapl_mo = aapl.resample('M').agg(rules)\n",
    "\n",
    "aapl_mo['Returns'] = aapl_mo['Close'].pct_change()\n",
    "sp500_mo['Returns'] = sp500_mo['Close'].pct_change()\n",
    "\n",
    "monthly_data = sp500_mo.merge(aapl_mo, how='outer',\n",
    "                         left_index=True, right_index=True,\n",
    "                         suffixes=(\"_SP\",\"_AAPL\")) \n",
    "\n",
    "monthly_data.dropna(inplace=True)\n",
    "monthly_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Returns_SP', ylabel='Returns_AAPL'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "monthly_data.plot.scatter(x='Returns_SP', y='Returns_AAPL')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>Returns_AAPL</td>   <th>  R-squared (uncentered):</th>      <td>   0.339</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.328</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   29.77</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 24 Sep 2021</td> <th>  Prob (F-statistic):</th>          <td>1.05e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>02:21:41</td>     <th>  Log-Likelihood:    </th>          <td>  85.738</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    59</td>      <th>  AIC:               </th>          <td>  -169.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    58</td>      <th>  BIC:               </th>          <td>  -167.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Returns_SP</th> <td>    1.4207</td> <td>    0.260</td> <td>    5.457</td> <td> 0.000</td> <td>    0.900</td> <td>    1.942</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.727</td> <th>  Durbin-Watson:     </th> <td>   2.487</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.695</td> <th>  Jarque-Bera (JB):  </th> <td>   0.202</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.010</td> <th>  Prob(JB):          </th> <td>   0.904</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.286</td> <th>  Cond. No.          </th> <td>    1.00</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:           Returns_AAPL   R-squared (uncentered):                   0.339\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.328\n",
       "Method:                 Least Squares   F-statistic:                              29.77\n",
       "Date:                Fri, 24 Sep 2021   Prob (F-statistic):                    1.05e-06\n",
       "Time:                        02:21:41   Log-Likelihood:                          85.738\n",
       "No. Observations:                  59   AIC:                                     -169.5\n",
       "Df Residuals:                      58   BIC:                                     -167.4\n",
       "Df Model:                           1                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Returns_SP     1.4207      0.260      5.457      0.000       0.900       1.942\n",
       "==============================================================================\n",
       "Omnibus:                        0.727   Durbin-Watson:                   2.487\n",
       "Prob(Omnibus):                  0.695   Jarque-Bera (JB):                0.202\n",
       "Skew:                           0.010   Prob(JB):                        0.904\n",
       "Kurtosis:                       3.286   Cond. No.                         1.00\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "capm_mo = sm.OLS(monthly_data['Returns_AAPL'], monthly_data['Returns_SP']).fit()\n",
    "monthly_data['Predictions'] = capm_mo.predict(monthly_data['Returns_SP'])\n",
    "capm_mo.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "monthly_data.plot.scatter(x='Returns_SP', y='Returns_AAPL')\n",
    "plt.plot(monthly_data['Returns_SP'],monthly_data['Predictions'],'red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color = 'blue'> **Section 3 - Time Series Regression** </font>\n",
    "- this example will run a regression using S&P 500 SMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\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>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>sma</th>\n",
       "      <th>sma_1</th>\n",
       "      <th>sma_5</th>\n",
       "      <th>sma_20</th>\n",
       "      <th>sma_100</th>\n",
       "      <th>sma_42</th>\n",
       "      <th>sma_252</th>\n",
       "      <th>ema_20</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",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></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>2013-09-30</th>\n",
       "      <td>1687.260010</td>\n",
       "      <td>1687.260010</td>\n",
       "      <td>1674.989990</td>\n",
       "      <td>1681.550049</td>\n",
       "      <td>1681.550049</td>\n",
       "      <td>3308630000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1681.550049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-01</th>\n",
       "      <td>1682.410034</td>\n",
       "      <td>1696.550049</td>\n",
       "      <td>1682.069946</td>\n",
       "      <td>1695.000000</td>\n",
       "      <td>1695.000000</td>\n",
       "      <td>3238690000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1681.550049</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1688.611273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-02</th>\n",
       "      <td>1691.900024</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>1680.339966</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>3148600000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1695.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1690.542244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-03</th>\n",
       "      <td>1692.349976</td>\n",
       "      <td>1692.349976</td>\n",
       "      <td>1670.359985</td>\n",
       "      <td>1678.660034</td>\n",
       "      <td>1678.660034</td>\n",
       "      <td>3279650000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1693.869995</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1687.112034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-04</th>\n",
       "      <td>1678.790039</td>\n",
       "      <td>1691.939941</td>\n",
       "      <td>1677.329956</td>\n",
       "      <td>1690.500000</td>\n",
       "      <td>1690.500000</td>\n",
       "      <td>2880270000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1678.660034</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1687.931554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-07</th>\n",
       "      <td>1687.150024</td>\n",
       "      <td>1687.150024</td>\n",
       "      <td>1674.699951</td>\n",
       "      <td>1676.119995</td>\n",
       "      <td>1676.119995</td>\n",
       "      <td>2678490000</td>\n",
       "      <td>1687.916016</td>\n",
       "      <td>1690.500000</td>\n",
       "      <td>1687.916016</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1685.439855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-08</th>\n",
       "      <td>1676.219971</td>\n",
       "      <td>1676.790039</td>\n",
       "      <td>1655.030029</td>\n",
       "      <td>1655.449951</td>\n",
       "      <td>1655.449951</td>\n",
       "      <td>3569230000</td>\n",
       "      <td>1685.950012</td>\n",
       "      <td>1676.119995</td>\n",
       "      <td>1686.830005</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1679.769506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-09</th>\n",
       "      <td>1656.989990</td>\n",
       "      <td>1662.469971</td>\n",
       "      <td>1646.469971</td>\n",
       "      <td>1656.400024</td>\n",
       "      <td>1656.400024</td>\n",
       "      <td>3577840000</td>\n",
       "      <td>1681.592861</td>\n",
       "      <td>1655.449951</td>\n",
       "      <td>1678.919995</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1675.729974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-10</th>\n",
       "      <td>1660.880005</td>\n",
       "      <td>1692.560059</td>\n",
       "      <td>1660.880005</td>\n",
       "      <td>1692.560059</td>\n",
       "      <td>1692.560059</td>\n",
       "      <td>3362300000</td>\n",
       "      <td>1678.443756</td>\n",
       "      <td>1656.400024</td>\n",
       "      <td>1671.426001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1678.429602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-11</th>\n",
       "      <td>1691.089966</td>\n",
       "      <td>1703.439941</td>\n",
       "      <td>1688.520020</td>\n",
       "      <td>1703.199951</td>\n",
       "      <td>1703.199951</td>\n",
       "      <td>2944670000</td>\n",
       "      <td>1680.012234</td>\n",
       "      <td>1692.560059</td>\n",
       "      <td>1674.206006</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1682.159802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-14</th>\n",
       "      <td>1699.859985</td>\n",
       "      <td>1711.030029</td>\n",
       "      <td>1692.130005</td>\n",
       "      <td>1710.140015</td>\n",
       "      <td>1710.140015</td>\n",
       "      <td>2580580000</td>\n",
       "      <td>1682.331006</td>\n",
       "      <td>1703.199951</td>\n",
       "      <td>1676.745996</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1686.152377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-15</th>\n",
       "      <td>1709.170044</td>\n",
       "      <td>1711.569946</td>\n",
       "      <td>1695.930054</td>\n",
       "      <td>1698.060059</td>\n",
       "      <td>1698.060059</td>\n",
       "      <td>3327740000</td>\n",
       "      <td>1684.859098</td>\n",
       "      <td>1710.140015</td>\n",
       "      <td>1683.550000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1687.774539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-16</th>\n",
       "      <td>1700.489990</td>\n",
       "      <td>1721.760010</td>\n",
       "      <td>1700.489990</td>\n",
       "      <td>1721.540039</td>\n",
       "      <td>1721.540039</td>\n",
       "      <td>3486180000</td>\n",
       "      <td>1685.959178</td>\n",
       "      <td>1698.060059</td>\n",
       "      <td>1692.072022</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1692.193228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-17</th>\n",
       "      <td>1720.170044</td>\n",
       "      <td>1733.449951</td>\n",
       "      <td>1714.119995</td>\n",
       "      <td>1733.150024</td>\n",
       "      <td>1733.150024</td>\n",
       "      <td>3453590000</td>\n",
       "      <td>1688.696167</td>\n",
       "      <td>1721.540039</td>\n",
       "      <td>1705.100025</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1697.368621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-18</th>\n",
       "      <td>1736.719971</td>\n",
       "      <td>1745.310059</td>\n",
       "      <td>1735.739990</td>\n",
       "      <td>1744.500000</td>\n",
       "      <td>1744.500000</td>\n",
       "      <td>3664890000</td>\n",
       "      <td>1691.871443</td>\n",
       "      <td>1733.150024</td>\n",
       "      <td>1713.218018</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1703.144480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-21</th>\n",
       "      <td>1745.199951</td>\n",
       "      <td>1747.790039</td>\n",
       "      <td>1740.670044</td>\n",
       "      <td>1744.660034</td>\n",
       "      <td>1744.660034</td>\n",
       "      <td>3052710000</td>\n",
       "      <td>1695.380013</td>\n",
       "      <td>1744.500000</td>\n",
       "      <td>1721.478027</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1708.096880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-22</th>\n",
       "      <td>1746.479980</td>\n",
       "      <td>1759.329956</td>\n",
       "      <td>1746.479980</td>\n",
       "      <td>1754.670044</td>\n",
       "      <td>1754.670044</td>\n",
       "      <td>3850840000</td>\n",
       "      <td>1698.460014</td>\n",
       "      <td>1744.660034</td>\n",
       "      <td>1728.382031</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1713.522116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-23</th>\n",
       "      <td>1752.270020</td>\n",
       "      <td>1752.270020</td>\n",
       "      <td>1740.500000</td>\n",
       "      <td>1746.380005</td>\n",
       "      <td>1746.380005</td>\n",
       "      <td>3713380000</td>\n",
       "      <td>1701.766487</td>\n",
       "      <td>1754.670044</td>\n",
       "      <td>1739.704028</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1717.270036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-24</th>\n",
       "      <td>1747.479980</td>\n",
       "      <td>1753.939941</td>\n",
       "      <td>1745.500000</td>\n",
       "      <td>1752.069946</td>\n",
       "      <td>1752.069946</td>\n",
       "      <td>3671700000</td>\n",
       "      <td>1704.245015</td>\n",
       "      <td>1746.380005</td>\n",
       "      <td>1744.672021</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1721.166122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-25</th>\n",
       "      <td>1756.010010</td>\n",
       "      <td>1759.819946</td>\n",
       "      <td>1752.449951</td>\n",
       "      <td>1759.770020</td>\n",
       "      <td>1759.770020</td>\n",
       "      <td>3175720000</td>\n",
       "      <td>1706.762117</td>\n",
       "      <td>1752.069946</td>\n",
       "      <td>1748.456006</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1725.417021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-28</th>\n",
       "      <td>1759.420044</td>\n",
       "      <td>1764.989990</td>\n",
       "      <td>1757.670044</td>\n",
       "      <td>1762.109985</td>\n",
       "      <td>1762.109985</td>\n",
       "      <td>3282300000</td>\n",
       "      <td>1709.412512</td>\n",
       "      <td>1759.770020</td>\n",
       "      <td>1751.510010</td>\n",
       "      <td>1709.412512</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1729.398264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-29</th>\n",
       "      <td>1762.930054</td>\n",
       "      <td>1772.089966</td>\n",
       "      <td>1762.930054</td>\n",
       "      <td>1771.949951</td>\n",
       "      <td>1771.949951</td>\n",
       "      <td>3358460000</td>\n",
       "      <td>1713.440509</td>\n",
       "      <td>1762.109985</td>\n",
       "      <td>1755.000000</td>\n",
       "      <td>1713.440509</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1733.954753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-30</th>\n",
       "      <td>1772.270020</td>\n",
       "      <td>1775.219971</td>\n",
       "      <td>1757.239990</td>\n",
       "      <td>1763.310059</td>\n",
       "      <td>1763.310059</td>\n",
       "      <td>3523040000</td>\n",
       "      <td>1717.288007</td>\n",
       "      <td>1771.949951</td>\n",
       "      <td>1758.455981</td>\n",
       "      <td>1717.288007</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1737.061364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-31</th>\n",
       "      <td>1763.239990</td>\n",
       "      <td>1768.530029</td>\n",
       "      <td>1755.719971</td>\n",
       "      <td>1756.540039</td>\n",
       "      <td>1756.540039</td>\n",
       "      <td>3826530000</td>\n",
       "      <td>1720.760010</td>\n",
       "      <td>1763.310059</td>\n",
       "      <td>1761.841992</td>\n",
       "      <td>1720.760010</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1739.101151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-01</th>\n",
       "      <td>1758.699951</td>\n",
       "      <td>1765.670044</td>\n",
       "      <td>1752.699951</td>\n",
       "      <td>1761.640015</td>\n",
       "      <td>1761.640015</td>\n",
       "      <td>3686290000</td>\n",
       "      <td>1724.654010</td>\n",
       "      <td>1756.540039</td>\n",
       "      <td>1762.736011</td>\n",
       "      <td>1724.654010</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1741.439231</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Open         High          Low        Close    Adj Close  \\\n",
       "Date                                                                          \n",
       "2013-09-30  1687.260010  1687.260010  1674.989990  1681.550049  1681.550049   \n",
       "2013-10-01  1682.410034  1696.550049  1682.069946  1695.000000  1695.000000   \n",
       "2013-10-02  1691.900024  1693.869995  1680.339966  1693.869995  1693.869995   \n",
       "2013-10-03  1692.349976  1692.349976  1670.359985  1678.660034  1678.660034   \n",
       "2013-10-04  1678.790039  1691.939941  1677.329956  1690.500000  1690.500000   \n",
       "2013-10-07  1687.150024  1687.150024  1674.699951  1676.119995  1676.119995   \n",
       "2013-10-08  1676.219971  1676.790039  1655.030029  1655.449951  1655.449951   \n",
       "2013-10-09  1656.989990  1662.469971  1646.469971  1656.400024  1656.400024   \n",
       "2013-10-10  1660.880005  1692.560059  1660.880005  1692.560059  1692.560059   \n",
       "2013-10-11  1691.089966  1703.439941  1688.520020  1703.199951  1703.199951   \n",
       "2013-10-14  1699.859985  1711.030029  1692.130005  1710.140015  1710.140015   \n",
       "2013-10-15  1709.170044  1711.569946  1695.930054  1698.060059  1698.060059   \n",
       "2013-10-16  1700.489990  1721.760010  1700.489990  1721.540039  1721.540039   \n",
       "2013-10-17  1720.170044  1733.449951  1714.119995  1733.150024  1733.150024   \n",
       "2013-10-18  1736.719971  1745.310059  1735.739990  1744.500000  1744.500000   \n",
       "2013-10-21  1745.199951  1747.790039  1740.670044  1744.660034  1744.660034   \n",
       "2013-10-22  1746.479980  1759.329956  1746.479980  1754.670044  1754.670044   \n",
       "2013-10-23  1752.270020  1752.270020  1740.500000  1746.380005  1746.380005   \n",
       "2013-10-24  1747.479980  1753.939941  1745.500000  1752.069946  1752.069946   \n",
       "2013-10-25  1756.010010  1759.819946  1752.449951  1759.770020  1759.770020   \n",
       "2013-10-28  1759.420044  1764.989990  1757.670044  1762.109985  1762.109985   \n",
       "2013-10-29  1762.930054  1772.089966  1762.930054  1771.949951  1771.949951   \n",
       "2013-10-30  1772.270020  1775.219971  1757.239990  1763.310059  1763.310059   \n",
       "2013-10-31  1763.239990  1768.530029  1755.719971  1756.540039  1756.540039   \n",
       "2013-11-01  1758.699951  1765.670044  1752.699951  1761.640015  1761.640015   \n",
       "\n",
       "                Volume          sma        sma_1        sma_5       sma_20  \\\n",
       "Date                                                                         \n",
       "2013-09-30  3308630000          NaN          NaN          NaN          NaN   \n",
       "2013-10-01  3238690000          NaN  1681.550049          NaN          NaN   \n",
       "2013-10-02  3148600000          NaN  1695.000000          NaN          NaN   \n",
       "2013-10-03  3279650000          NaN  1693.869995          NaN          NaN   \n",
       "2013-10-04  2880270000          NaN  1678.660034          NaN          NaN   \n",
       "2013-10-07  2678490000  1687.916016  1690.500000  1687.916016          NaN   \n",
       "2013-10-08  3569230000  1685.950012  1676.119995  1686.830005          NaN   \n",
       "2013-10-09  3577840000  1681.592861  1655.449951  1678.919995          NaN   \n",
       "2013-10-10  3362300000  1678.443756  1656.400024  1671.426001          NaN   \n",
       "2013-10-11  2944670000  1680.012234  1692.560059  1674.206006          NaN   \n",
       "2013-10-14  2580580000  1682.331006  1703.199951  1676.745996          NaN   \n",
       "2013-10-15  3327740000  1684.859098  1710.140015  1683.550000          NaN   \n",
       "2013-10-16  3486180000  1685.959178  1698.060059  1692.072022          NaN   \n",
       "2013-10-17  3453590000  1688.696167  1721.540039  1705.100025          NaN   \n",
       "2013-10-18  3664890000  1691.871443  1733.150024  1713.218018          NaN   \n",
       "2013-10-21  3052710000  1695.380013  1744.500000  1721.478027          NaN   \n",
       "2013-10-22  3850840000  1698.460014  1744.660034  1728.382031          NaN   \n",
       "2013-10-23  3713380000  1701.766487  1754.670044  1739.704028          NaN   \n",
       "2013-10-24  3671700000  1704.245015  1746.380005  1744.672021          NaN   \n",
       "2013-10-25  3175720000  1706.762117  1752.069946  1748.456006          NaN   \n",
       "2013-10-28  3282300000  1709.412512  1759.770020  1751.510010  1709.412512   \n",
       "2013-10-29  3358460000  1713.440509  1762.109985  1755.000000  1713.440509   \n",
       "2013-10-30  3523040000  1717.288007  1771.949951  1758.455981  1717.288007   \n",
       "2013-10-31  3826530000  1720.760010  1763.310059  1761.841992  1720.760010   \n",
       "2013-11-01  3686290000  1724.654010  1756.540039  1762.736011  1724.654010   \n",
       "\n",
       "            sma_100  sma_42  sma_252       ema_20  \n",
       "Date                                               \n",
       "2013-09-30      NaN     NaN      NaN  1681.550049  \n",
       "2013-10-01      NaN     NaN      NaN  1688.611273  \n",
       "2013-10-02      NaN     NaN      NaN  1690.542244  \n",
       "2013-10-03      NaN     NaN      NaN  1687.112034  \n",
       "2013-10-04      NaN     NaN      NaN  1687.931554  \n",
       "2013-10-07      NaN     NaN      NaN  1685.439855  \n",
       "2013-10-08      NaN     NaN      NaN  1679.769506  \n",
       "2013-10-09      NaN     NaN      NaN  1675.729974  \n",
       "2013-10-10      NaN     NaN      NaN  1678.429602  \n",
       "2013-10-11      NaN     NaN      NaN  1682.159802  \n",
       "2013-10-14      NaN     NaN      NaN  1686.152377  \n",
       "2013-10-15      NaN     NaN      NaN  1687.774539  \n",
       "2013-10-16      NaN     NaN      NaN  1692.193228  \n",
       "2013-10-17      NaN     NaN      NaN  1697.368621  \n",
       "2013-10-18      NaN     NaN      NaN  1703.144480  \n",
       "2013-10-21      NaN     NaN      NaN  1708.096880  \n",
       "2013-10-22      NaN     NaN      NaN  1713.522116  \n",
       "2013-10-23      NaN     NaN      NaN  1717.270036  \n",
       "2013-10-24      NaN     NaN      NaN  1721.166122  \n",
       "2013-10-25      NaN     NaN      NaN  1725.417021  \n",
       "2013-10-28      NaN     NaN      NaN  1729.398264  \n",
       "2013-10-29      NaN     NaN      NaN  1733.954753  \n",
       "2013-10-30      NaN     NaN      NaN  1737.061364  \n",
       "2013-10-31      NaN     NaN      NaN  1739.101151  \n",
       "2013-11-01      NaN     NaN      NaN  1741.439231  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp500 = pd.read_csv(\"StockData/SP500.csv\",parse_dates=['Date'],index_col=['Date'])\n",
    "\n",
    "\n",
    "#Simple Moving Averages\n",
    "sp500['sma'] = sp500['Close'].shift(1).rolling(window = 20, min_periods = 5).mean()\n",
    "\n",
    "sp500['sma_1'] = sp500['Close'].shift(1)\n",
    "sp500['sma_5'] = sp500['sma_1'].rolling(window = 5, min_periods = 5).mean()\n",
    "sp500['sma_20'] = sp500['sma_1'].rolling(window = 20, min_periods = 20).mean()\n",
    "sp500['sma_100'] = sp500['sma_1'].rolling(window = 100, min_periods = 100).mean()\n",
    "sp500['sma_42'] = sp500['sma_1'].rolling(window = 42, min_periods = 42).mean()\n",
    "sp500['sma_252'] = sp500['sma_1'].rolling(window = 252, min_periods = 252).mean()\n",
    "\n",
    "#Exponential Moving Averages\n",
    "sp500['ema_20'] = sp500['Close'].ewm(span=20).mean()\n",
    "\n",
    "sp500.head(25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Date'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sp500[['Close','sma_42','sma_252']].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>Close</td>      <th>  R-squared (uncentered):</th>      <td>   0.999</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.999</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>9.637e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 24 Sep 2021</td> <th>  Prob (F-statistic):</th>           <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>02:22:06</td>     <th>  Log-Likelihood:    </th>          <td> -5428.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1008</td>      <th>  AIC:               </th>          <td>1.086e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1006</td>      <th>  BIC:               </th>          <td>1.087e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sma_42</th>  <td>    1.0543</td> <td>    0.024</td> <td>   44.745</td> <td> 0.000</td> <td>    1.008</td> <td>    1.101</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sma_252</th> <td>   -0.0474</td> <td>    0.025</td> <td>   -1.931</td> <td> 0.054</td> <td>   -0.096</td> <td>    0.001</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>110.395</td> <th>  Durbin-Watson:     </th> <td>   0.117</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 165.538</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.782</td>  <th>  Prob(JB):          </th> <td>1.13e-36</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.222</td>  <th>  Cond. No.          </th> <td>    64.9</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                  Close   R-squared (uncentered):                   0.999\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.999\n",
       "Method:                 Least Squares   F-statistic:                          9.637e+05\n",
       "Date:                Fri, 24 Sep 2021   Prob (F-statistic):                        0.00\n",
       "Time:                        02:22:06   Log-Likelihood:                         -5428.5\n",
       "No. Observations:                1008   AIC:                                  1.086e+04\n",
       "Df Residuals:                    1006   BIC:                                  1.087e+04\n",
       "Df Model:                           2                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sma_42         1.0543      0.024     44.745      0.000       1.008       1.101\n",
       "sma_252       -0.0474      0.025     -1.931      0.054      -0.096       0.001\n",
       "==============================================================================\n",
       "Omnibus:                      110.395   Durbin-Watson:                   0.117\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              165.538\n",
       "Skew:                          -0.782   Prob(JB):                     1.13e-36\n",
       "Kurtosis:                       4.222   Cond. No.                         64.9\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp500.dropna(inplace=True)\n",
    "\n",
    "# add constant to dataframe\n",
    "sp500['alpha'] = 1\n",
    "#regts = sm.OLS(sp500['Close'], sp500[['alpha','sma_1', 'sma_5', 'sma_20','sma_100','ema_20']]).fit()\n",
    "#regts = sm.OLS(sp500['Close'], sp500[['sma_20', 'ema_20']]).fit()\n",
    "regts = sm.OLS(sp500['Close'], sp500[['sma_42', 'sma_252']]).fit()\n",
    "regts.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sp500.index, sp500['Close'])\n",
    "# plt.plot(sp500.index, regts.predict(sp500[['sma_20', 'ema_20']]))\n",
    "plt.plot(sp500.index, regts.predict(sp500[['sma_42', 'sma_252']]))\n",
    "plt.legend(['Close','TSA'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color = 'blue'> **Section 4 - Optimization - SciPy** </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import Optimization Packages\n",
    "#from scipy.optimize import minimize, Bounds, LinearConstraint #Only for scipy version >1.0\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.6.2'"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#check version of scipy\n",
    "import scipy\n",
    "scipy.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Optimization Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optw(w, V):\n",
    "    # Function returns the variance of the portfolio given weights and covar matrix\n",
    "    return(np.matmul(np.matmul(w,V),w))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Preparing Data Set\n",
    "Load all the stock data except for the S&P500 data.\n",
    "- Resample to Monthly frequency.\n",
    "- Calculate simple returns for each stock using the adjusted close.\n",
    "- Combine the returns into a data frame where the index is date time and the columns are the individual stock returns.\n",
    "- Drop any na rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['AAPL.csv',\n",
       " 'AXP.csv',\n",
       " 'BA.csv',\n",
       " 'CAT.csv',\n",
       " 'CSCO.csv',\n",
       " 'CVX.csv',\n",
       " 'DIS.csv',\n",
       " 'DWDP.csv',\n",
       " 'GE.csv',\n",
       " 'GS.csv',\n",
       " 'HD.csv',\n",
       " 'IBM.csv',\n",
       " 'INTC.csv',\n",
       " 'JNJ.csv',\n",
       " 'JPM.csv',\n",
       " 'KO.csv',\n",
       " 'MCD.csv',\n",
       " 'MMM.csv',\n",
       " 'NKE.csv',\n",
       " 'PFE.csv',\n",
       " 'PG.csv',\n",
       " 'TRV.csv',\n",
       " 'UNH.csv',\n",
       " 'UTX.csv',\n",
       " 'V.csv',\n",
       " 'VZ.csv',\n",
       " 'WMT.csv',\n",
       " 'XOM.csv']"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "stockdatalist = []\n",
    "for file in os.listdir(\"StockData/\"):\n",
    "    if file.endswith(\".csv\"):\n",
    "        stockdatalist.append(file)\n",
    "\n",
    "# Remove SP500\n",
    "stockdatalist.remove('SP500.csv')\n",
    "#stockdatalist\n",
    "stockdatalist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>AXP</th>\n",
       "      <th>BA</th>\n",
       "      <th>CAT</th>\n",
       "      <th>CSCO</th>\n",
       "      <th>CVX</th>\n",
       "      <th>DIS</th>\n",
       "      <th>DWDP</th>\n",
       "      <th>GE</th>\n",
       "      <th>GS</th>\n",
       "      <th>...</th>\n",
       "      <th>NKE</th>\n",
       "      <th>PFE</th>\n",
       "      <th>PG</th>\n",
       "      <th>TRV</th>\n",
       "      <th>UNH</th>\n",
       "      <th>UTX</th>\n",
       "      <th>V</th>\n",
       "      <th>VZ</th>\n",
       "      <th>WMT</th>\n",
       "      <th>XOM</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",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></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>2013-11-30</th>\n",
       "      <td>0.070053</td>\n",
       "      <td>0.048900</td>\n",
       "      <td>0.032485</td>\n",
       "      <td>0.014875</td>\n",
       "      <td>-0.058067</td>\n",
       "      <td>0.029244</td>\n",
       "      <td>0.028430</td>\n",
       "      <td>-0.010388</td>\n",
       "      <td>0.019893</td>\n",
       "      <td>0.053679</td>\n",
       "      <td>...</td>\n",
       "      <td>0.044614</td>\n",
       "      <td>0.041892</td>\n",
       "      <td>0.042972</td>\n",
       "      <td>0.051448</td>\n",
       "      <td>0.091122</td>\n",
       "      <td>0.049149</td>\n",
       "      <td>0.042941</td>\n",
       "      <td>-0.017620</td>\n",
       "      <td>0.055505</td>\n",
       "      <td>0.050168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-31</th>\n",
       "      <td>0.008902</td>\n",
       "      <td>0.057459</td>\n",
       "      <td>0.016685</td>\n",
       "      <td>0.073404</td>\n",
       "      <td>0.055530</td>\n",
       "      <td>0.020173</td>\n",
       "      <td>0.096445</td>\n",
       "      <td>0.144879</td>\n",
       "      <td>0.059895</td>\n",
       "      <td>0.049248</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000072</td>\n",
       "      <td>-0.034667</td>\n",
       "      <td>-0.033365</td>\n",
       "      <td>0.003503</td>\n",
       "      <td>0.014864</td>\n",
       "      <td>0.026520</td>\n",
       "      <td>0.094466</td>\n",
       "      <td>-0.009673</td>\n",
       "      <td>-0.022984</td>\n",
       "      <td>0.082584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-01-31</th>\n",
       "      <td>-0.107697</td>\n",
       "      <td>-0.060516</td>\n",
       "      <td>-0.082277</td>\n",
       "      <td>0.047728</td>\n",
       "      <td>-0.015723</td>\n",
       "      <td>-0.106317</td>\n",
       "      <td>-0.049607</td>\n",
       "      <td>0.025000</td>\n",
       "      <td>-0.103461</td>\n",
       "      <td>-0.074128</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.073627</td>\n",
       "      <td>-0.007509</td>\n",
       "      <td>-0.051724</td>\n",
       "      <td>-0.102275</td>\n",
       "      <td>-0.040106</td>\n",
       "      <td>0.001933</td>\n",
       "      <td>-0.032558</td>\n",
       "      <td>-0.012172</td>\n",
       "      <td>-0.050960</td>\n",
       "      <td>-0.089328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-02-28</th>\n",
       "      <td>0.057511</td>\n",
       "      <td>0.073630</td>\n",
       "      <td>0.035024</td>\n",
       "      <td>0.032584</td>\n",
       "      <td>-0.005021</td>\n",
       "      <td>0.042322</td>\n",
       "      <td>0.112932</td>\n",
       "      <td>0.070314</td>\n",
       "      <td>0.022385</td>\n",
       "      <td>0.017620</td>\n",
       "      <td>...</td>\n",
       "      <td>0.081430</td>\n",
       "      <td>0.065058</td>\n",
       "      <td>0.026625</td>\n",
       "      <td>0.031496</td>\n",
       "      <td>0.069037</td>\n",
       "      <td>0.031700</td>\n",
       "      <td>0.056388</td>\n",
       "      <td>-0.009163</td>\n",
       "      <td>0.000268</td>\n",
       "      <td>0.051995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-03-31</th>\n",
       "      <td>0.019953</td>\n",
       "      <td>-0.013694</td>\n",
       "      <td>-0.026606</td>\n",
       "      <td>0.024750</td>\n",
       "      <td>0.028441</td>\n",
       "      <td>0.031041</td>\n",
       "      <td>-0.009157</td>\n",
       "      <td>0.005060</td>\n",
       "      <td>0.016490</td>\n",
       "      <td>-0.015620</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.056705</td>\n",
       "      <td>0.000311</td>\n",
       "      <td>0.024663</td>\n",
       "      <td>0.021080</td>\n",
       "      <td>0.064918</td>\n",
       "      <td>-0.001538</td>\n",
       "      <td>-0.044614</td>\n",
       "      <td>-0.000210</td>\n",
       "      <td>0.029760</td>\n",
       "      <td>0.014646</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 28 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL       AXP        BA       CAT      CSCO       CVX  \\\n",
       "Date                                                                     \n",
       "2013-11-30  0.070053  0.048900  0.032485  0.014875 -0.058067  0.029244   \n",
       "2013-12-31  0.008902  0.057459  0.016685  0.073404  0.055530  0.020173   \n",
       "2014-01-31 -0.107697 -0.060516 -0.082277  0.047728 -0.015723 -0.106317   \n",
       "2014-02-28  0.057511  0.073630  0.035024  0.032584 -0.005021  0.042322   \n",
       "2014-03-31  0.019953 -0.013694 -0.026606  0.024750  0.028441  0.031041   \n",
       "\n",
       "                 DIS      DWDP        GE        GS  ...       NKE       PFE  \\\n",
       "Date                                                ...                       \n",
       "2013-11-30  0.028430 -0.010388  0.019893  0.053679  ...  0.044614  0.041892   \n",
       "2013-12-31  0.096445  0.144879  0.059895  0.049248  ... -0.000072 -0.034667   \n",
       "2014-01-31 -0.049607  0.025000 -0.103461 -0.074128  ... -0.073627 -0.007509   \n",
       "2014-02-28  0.112932  0.070314  0.022385  0.017620  ...  0.081430  0.065058   \n",
       "2014-03-31 -0.009157  0.005060  0.016490 -0.015620  ... -0.056705  0.000311   \n",
       "\n",
       "                  PG       TRV       UNH       UTX         V        VZ  \\\n",
       "Date                                                                     \n",
       "2013-11-30  0.042972  0.051448  0.091122  0.049149  0.042941 -0.017620   \n",
       "2013-12-31 -0.033365  0.003503  0.014864  0.026520  0.094466 -0.009673   \n",
       "2014-01-31 -0.051724 -0.102275 -0.040106  0.001933 -0.032558 -0.012172   \n",
       "2014-02-28  0.026625  0.031496  0.069037  0.031700  0.056388 -0.009163   \n",
       "2014-03-31  0.024663  0.021080  0.064918 -0.001538 -0.044614 -0.000210   \n",
       "\n",
       "                 WMT       XOM  \n",
       "Date                            \n",
       "2013-11-30  0.055505  0.050168  \n",
       "2013-12-31 -0.022984  0.082584  \n",
       "2014-01-31 -0.050960 -0.089328  \n",
       "2014-02-28  0.000268  0.051995  \n",
       "2014-03-31  0.029760  0.014646  \n",
       "\n",
       "[5 rows x 28 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initalize an empty dataframe\n",
    "rtns = pd.DataFrame()\n",
    "ohlc_rule = {'Open':'first', 'High':'max',\n",
    "                'Low':'min', 'Close':'last', 'Volume':'sum', 'Adj Close':'last'}\n",
    "\n",
    "# Load the stock data, resample freq, calc simple returns, store in a df by ticker\n",
    "for fileName in stockdatalist:\n",
    "    ticker = fileName.replace(\".csv\",\"\")\n",
    "    filepath = \"StockData/{}\".format(fileName) \n",
    "    temp = pd.read_csv(filepath, index_col=0, parse_dates=True)\n",
    "    temp = temp.resample('M').agg(ohlc_rule)\n",
    "    temp = temp['Adj Close'].pct_change()\n",
    "    rtns[ticker] = temp \n",
    "\n",
    "rtns.dropna(inplace=True)\n",
    "rtns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Look at specific companies:\n",
    "rtns = rtns[['PG','JNJ','IBM','AAPL','MCD','WMT','KO','NKE']]\n",
    "#rtns = rtns.iloc[:,0:5].copy() #look at first 5 companies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Covariance Matrix and Avg Returns\n",
    "- Calculate the covariance matrix of the stocks.\n",
    "- Calculate the mean return of the stocks.\n",
    "- Scale the mean and covariance matrix by 100 and 10,000 respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# of tickers 8\n",
      "PG      0.384247\n",
      "JNJ     0.976907\n",
      "IBM     0.146776\n",
      "AAPL    2.276223\n",
      "MCD     1.283820\n",
      "WMT     0.705751\n",
      "KO      0.607143\n",
      "NKE     1.672362\n",
      "dtype: float64\n",
      "PG      3.845095\n",
      "JNJ     3.537908\n",
      "IBM     4.899611\n",
      "AAPL    6.729445\n",
      "MCD     3.899057\n",
      "WMT     5.314936\n",
      "KO      3.772647\n",
      "NKE     5.282574\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "V = np.cov(rtns, rowvar=False) * 10000\n",
    "mu = np.mean(rtns, axis=0) * 100\n",
    "n = mu.shape[0]\n",
    "\n",
    "print(\"# of tickers\",n)\n",
    "print(mu)\n",
    "print(np.std(rtns)*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Correlation Matrix\n",
    "# rtns.corr()\n",
    "#Covariance Matrix\n",
    "#rtns.cov() * 10000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set up Constraints and Bounds\n",
    "- Set initial values for the weights and define the expected return.\n",
    "- Set up investment weights and returns constraints.\n",
    "- Set up bounds for the weights (if no short selling allowed)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set initial values for the weights and define the expected return\n",
    "w = np.matrix([1/n] * n).T #initial guess equal weights\n",
    "expect_return = 5\n",
    "\n",
    "#lower/upper limits for the weights\n",
    "#setting to 0<w<100% to restrict for short selling\n",
    "bound = (0.0,1.0)\n",
    "bounds = tuple(bound for asset in range(n))\n",
    "\n",
    "#The following are Constraints using new Scipy (version >= 1.0)\n",
    "# Weight constraint\n",
    "#A = np.matrix([1]*n)\n",
    "#constraint_1 = LinearConstraint(A, 1, 1)\n",
    "\n",
    "# for the return constraint, the asset returns are the coefficients\n",
    "#constraint_2 = LinearConstraint(mu, expect_return, np.inf)\n",
    "\n",
    "#Constraints using older scipy version\n",
    "    #x represents the variables in the opimization that are being sensitized\n",
    "    #in this case they represent the weights in each security\n",
    "\n",
    "constraint_1 = {'type': 'eq', 'fun': lambda x: np.sum(x) - 1}\n",
    "constraint_2 = {'type': 'ineq', 'fun': lambda x: np.sum(x * mu ) - expect_return}\n",
    "    #eq --> means the fun has to be exactly equal to 0\n",
    "    #ineq --> means the fun has to be positive\n",
    "    #for constraint 2 using ineq to allow for returns to be > expect_return if possible"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Run Optimization Model\n",
    "- Set initial values for the weights and define the expected return.\n",
    "- Set up investment weights and returns constraints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "At an expected return of 5.00% the minimum variance is 46.07\n"
     ]
    }
   ],
   "source": [
    "#Negative weights allowed (short selling)\n",
    "#weight = minimize(optw, w, (V), constraints=(constraint_1,constraint_2), options={'maxiter':1000})\n",
    "\n",
    "#No negative weights (no short selling) by adding boundaries\n",
    "weight = minimize(optw, w, (V), constraints=(constraint_1,constraint_2),bounds=bounds,options={'maxiter':1000})\n",
    "\n",
    "\n",
    "#weight\n",
    "# weight.x.shape\n",
    "weight.fun #calculated minimum variance at given expected return\n",
    "weight.x #calculated optimal weights for each ticker\n",
    "print(\"At an expected return of {:.2%} the minimum variance is {:.2f}\".format(expect_return/100,weight.fun))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = []\n",
    "variances = []\n",
    "\n",
    "for expect_return in np.linspace(0,5, 11):\n",
    "    #constraint_2 = LinearConstraint(mu, expect_return, np.inf)\n",
    "    constraint_2 = {'type': 'ineq', 'fun': lambda x: np.sum(x * mu ) - expect_return}\n",
    "    \n",
    "    #Run one of the next two lines (comment out the other)\n",
    "        #Short-selling allowed:\n",
    "    weight = minimize(optw, w, (V), constraints=(constraint_1,constraint_2), options={'maxiter':1000})\n",
    "        #No short-selling:\n",
    "    #weight = minimize(optw, w, (V), constraints=(constraint_1,constraint_2), bounds=bounds, options={'maxiter':1000})\n",
    "    \n",
    "    if weight.success == True:\n",
    "        weights.append(weight.x)\n",
    "        variances.append(weight.fun)\n",
    "    else:\n",
    "        print(\"no solution for return of \", expect_return)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find the portfolio returns and variences\n",
    "portmu = []\n",
    "portvar = []\n",
    "\n",
    "for w in weights:\n",
    "    portmu.append(w @ mu)\n",
    "    portvar.append(w @ V @ w)\n",
    "    \n",
    "portstd = np.sqrt(portvar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PG</th>\n",
       "      <th>JNJ</th>\n",
       "      <th>IBM</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MCD</th>\n",
       "      <th>WMT</th>\n",
       "      <th>KO</th>\n",
       "      <th>NKE</th>\n",
       "      <th>Returns</th>\n",
       "      <th>Variances</th>\n",
       "      <th>STD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.259062</td>\n",
       "      <td>0.133906</td>\n",
       "      <td>0.216893</td>\n",
       "      <td>-0.004799</td>\n",
       "      <td>0.245993</td>\n",
       "      <td>0.007640</td>\n",
       "      <td>0.013216</td>\n",
       "      <td>0.128090</td>\n",
       "      <td>0.794708</td>\n",
       "      <td>6.862309</td>\n",
       "      <td>2.619601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.259060</td>\n",
       "      <td>0.133907</td>\n",
       "      <td>0.216892</td>\n",
       "      <td>-0.004799</td>\n",
       "      <td>0.245995</td>\n",
       "      <td>0.007640</td>\n",
       "      <td>0.013217</td>\n",
       "      <td>0.128088</td>\n",
       "      <td>0.794709</td>\n",
       "      <td>6.862309</td>\n",
       "      <td>2.619601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.189059</td>\n",
       "      <td>0.183191</td>\n",
       "      <td>0.165527</td>\n",
       "      <td>0.046952</td>\n",
       "      <td>0.277939</td>\n",
       "      <td>0.010735</td>\n",
       "      <td>-0.038591</td>\n",
       "      <td>0.165190</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>7.102923</td>\n",
       "      <td>2.665131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.018619</td>\n",
       "      <td>0.303111</td>\n",
       "      <td>0.040419</td>\n",
       "      <td>0.173003</td>\n",
       "      <td>0.355795</td>\n",
       "      <td>0.018265</td>\n",
       "      <td>-0.164764</td>\n",
       "      <td>0.255553</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>9.702313</td>\n",
       "      <td>3.114854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.151912</td>\n",
       "      <td>0.423331</td>\n",
       "      <td>-0.084694</td>\n",
       "      <td>0.299038</td>\n",
       "      <td>0.433488</td>\n",
       "      <td>0.025803</td>\n",
       "      <td>-0.290973</td>\n",
       "      <td>0.345918</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>15.156352</td>\n",
       "      <td>3.893116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.322399</td>\n",
       "      <td>0.543395</td>\n",
       "      <td>-0.209802</td>\n",
       "      <td>0.425081</td>\n",
       "      <td>0.511268</td>\n",
       "      <td>0.033338</td>\n",
       "      <td>-0.417164</td>\n",
       "      <td>0.436282</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>23.465039</td>\n",
       "      <td>4.844073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.492776</td>\n",
       "      <td>0.663263</td>\n",
       "      <td>-0.334963</td>\n",
       "      <td>0.551154</td>\n",
       "      <td>0.589076</td>\n",
       "      <td>0.040861</td>\n",
       "      <td>-0.543266</td>\n",
       "      <td>0.526650</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>34.628375</td>\n",
       "      <td>5.884588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.663373</td>\n",
       "      <td>0.783524</td>\n",
       "      <td>-0.460021</td>\n",
       "      <td>0.677167</td>\n",
       "      <td>0.666826</td>\n",
       "      <td>0.048408</td>\n",
       "      <td>-0.669540</td>\n",
       "      <td>0.617010</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>48.646359</td>\n",
       "      <td>6.974694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.833860</td>\n",
       "      <td>0.903588</td>\n",
       "      <td>-0.585130</td>\n",
       "      <td>0.803210</td>\n",
       "      <td>0.744606</td>\n",
       "      <td>0.055943</td>\n",
       "      <td>-0.795730</td>\n",
       "      <td>0.707373</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>65.518991</td>\n",
       "      <td>8.094380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-1.004346</td>\n",
       "      <td>1.023653</td>\n",
       "      <td>-0.710239</td>\n",
       "      <td>0.929253</td>\n",
       "      <td>0.822387</td>\n",
       "      <td>0.063477</td>\n",
       "      <td>-0.921919</td>\n",
       "      <td>0.797736</td>\n",
       "      <td>4.500000</td>\n",
       "      <td>85.246273</td>\n",
       "      <td>9.232891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-1.174834</td>\n",
       "      <td>1.143717</td>\n",
       "      <td>-0.835348</td>\n",
       "      <td>1.055295</td>\n",
       "      <td>0.900168</td>\n",
       "      <td>0.071011</td>\n",
       "      <td>-1.048108</td>\n",
       "      <td>0.888099</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>107.828202</td>\n",
       "      <td>10.384036</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          PG       JNJ       IBM      AAPL       MCD       WMT        KO  \\\n",
       "0   0.259062  0.133906  0.216893 -0.004799  0.245993  0.007640  0.013216   \n",
       "1   0.259060  0.133907  0.216892 -0.004799  0.245995  0.007640  0.013217   \n",
       "2   0.189059  0.183191  0.165527  0.046952  0.277939  0.010735 -0.038591   \n",
       "3   0.018619  0.303111  0.040419  0.173003  0.355795  0.018265 -0.164764   \n",
       "4  -0.151912  0.423331 -0.084694  0.299038  0.433488  0.025803 -0.290973   \n",
       "5  -0.322399  0.543395 -0.209802  0.425081  0.511268  0.033338 -0.417164   \n",
       "6  -0.492776  0.663263 -0.334963  0.551154  0.589076  0.040861 -0.543266   \n",
       "7  -0.663373  0.783524 -0.460021  0.677167  0.666826  0.048408 -0.669540   \n",
       "8  -0.833860  0.903588 -0.585130  0.803210  0.744606  0.055943 -0.795730   \n",
       "9  -1.004346  1.023653 -0.710239  0.929253  0.822387  0.063477 -0.921919   \n",
       "10 -1.174834  1.143717 -0.835348  1.055295  0.900168  0.071011 -1.048108   \n",
       "\n",
       "         NKE   Returns   Variances        STD  \n",
       "0   0.128090  0.794708    6.862309   2.619601  \n",
       "1   0.128088  0.794709    6.862309   2.619601  \n",
       "2   0.165190  1.000000    7.102923   2.665131  \n",
       "3   0.255553  1.500000    9.702313   3.114854  \n",
       "4   0.345918  2.000000   15.156352   3.893116  \n",
       "5   0.436282  2.500000   23.465039   4.844073  \n",
       "6   0.526650  3.000000   34.628375   5.884588  \n",
       "7   0.617010  3.500000   48.646359   6.974694  \n",
       "8   0.707373  4.000000   65.518991   8.094380  \n",
       "9   0.797736  4.500000   85.246273   9.232891  \n",
       "10  0.888099  5.000000  107.828202  10.384036  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tickers = rtns.columns\n",
    "results = pd.DataFrame(data=weights, columns=tickers)\n",
    "results['Returns'] = portmu\n",
    "results['Variances'] = portvar\n",
    "results['STD'] = portstd\n",
    "\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot of Portfolio Efficient Frontier\n",
    "plt.scatter(rtns.std() * 100, rtns.mean() * 100)\n",
    "plt.scatter(portstd, portmu)\n",
    "plt.plot(portstd, portmu, linestyle='-.', color='black')\n",
    "plt.title('Portfolio Frontier')\n",
    "plt.xlim([0,10])\n",
    "plt.ylim([0,5])\n",
    "for x, y, ticker in zip(rtns.std()*100,rtns.mean()*100,rtns.mean().index):\n",
    "    plt.text(x+0.2, y, ticker, ha='left')\n",
    "plt.xlabel('Portfolio Risk (STD %)')\n",
    "plt.ylabel('Portfolio Expected Return (%)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}