Simple_n_log_returns.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from pandas_datareader import data as wb\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "PG = wb.DataReader('PG', 'quandl', '1995-01-01', '2018-01-01')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>Volume</th>\n",
       "      <th>ExDividend</th>\n",
       "      <th>SplitRatio</th>\n",
       "      <th>AdjOpen</th>\n",
       "      <th>AdjHigh</th>\n",
       "      <th>AdjLow</th>\n",
       "      <th>AdjClose</th>\n",
       "      <th>AdjVolume</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>1995-01-03</th>\n",
       "      <td>61.88</td>\n",
       "      <td>62.5000</td>\n",
       "      <td>61.7500</td>\n",
       "      <td>62.38</td>\n",
       "      <td>829600.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.952809</td>\n",
       "      <td>9.042510</td>\n",
       "      <td>8.934000</td>\n",
       "      <td>9.025149</td>\n",
       "      <td>3318400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-04</th>\n",
       "      <td>62.63</td>\n",
       "      <td>62.6300</td>\n",
       "      <td>61.2500</td>\n",
       "      <td>61.88</td>\n",
       "      <td>554700.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.061319</td>\n",
       "      <td>9.061319</td>\n",
       "      <td>8.861660</td>\n",
       "      <td>8.952809</td>\n",
       "      <td>2218800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-05</th>\n",
       "      <td>61.50</td>\n",
       "      <td>61.7500</td>\n",
       "      <td>60.8800</td>\n",
       "      <td>61.00</td>\n",
       "      <td>579900.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.897830</td>\n",
       "      <td>8.934000</td>\n",
       "      <td>8.808129</td>\n",
       "      <td>8.825490</td>\n",
       "      <td>2319600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-06</th>\n",
       "      <td>60.63</td>\n",
       "      <td>61.6300</td>\n",
       "      <td>60.6300</td>\n",
       "      <td>61.25</td>\n",
       "      <td>859500.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.771959</td>\n",
       "      <td>8.916639</td>\n",
       "      <td>8.771959</td>\n",
       "      <td>8.861660</td>\n",
       "      <td>3438000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-09</th>\n",
       "      <td>61.38</td>\n",
       "      <td>61.6300</td>\n",
       "      <td>60.7500</td>\n",
       "      <td>60.88</td>\n",
       "      <td>448800.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.880469</td>\n",
       "      <td>8.916639</td>\n",
       "      <td>8.789320</td>\n",
       "      <td>8.808129</td>\n",
       "      <td>1795200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-10</th>\n",
       "      <td>61.13</td>\n",
       "      <td>61.7500</td>\n",
       "      <td>60.7500</td>\n",
       "      <td>61.63</td>\n",
       "      <td>1091000.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.844299</td>\n",
       "      <td>8.934000</td>\n",
       "      <td>8.789320</td>\n",
       "      <td>8.916639</td>\n",
       "      <td>4364000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-11</th>\n",
       "      <td>62.38</td>\n",
       "      <td>62.3800</td>\n",
       "      <td>61.5000</td>\n",
       "      <td>61.50</td>\n",
       "      <td>934600.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.025149</td>\n",
       "      <td>9.025149</td>\n",
       "      <td>8.897830</td>\n",
       "      <td>8.897830</td>\n",
       "      <td>3738400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-12</th>\n",
       "      <td>61.50</td>\n",
       "      <td>62.0000</td>\n",
       "      <td>61.3800</td>\n",
       "      <td>62.00</td>\n",
       "      <td>826900.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.897830</td>\n",
       "      <td>8.970170</td>\n",
       "      <td>8.880469</td>\n",
       "      <td>8.970170</td>\n",
       "      <td>3307600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-13</th>\n",
       "      <td>62.38</td>\n",
       "      <td>63.3800</td>\n",
       "      <td>62.1300</td>\n",
       "      <td>62.50</td>\n",
       "      <td>998200.0</td>\n",
       "      <td>0.35</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.075690</td>\n",
       "      <td>9.221180</td>\n",
       "      <td>9.039317</td>\n",
       "      <td>9.093149</td>\n",
       "      <td>3992800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-16</th>\n",
       "      <td>63.63</td>\n",
       "      <td>63.7500</td>\n",
       "      <td>63.0000</td>\n",
       "      <td>63.00</td>\n",
       "      <td>919300.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.257553</td>\n",
       "      <td>9.275011</td>\n",
       "      <td>9.165894</td>\n",
       "      <td>9.165894</td>\n",
       "      <td>3677200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-17</th>\n",
       "      <td>62.88</td>\n",
       "      <td>63.2500</td>\n",
       "      <td>62.6300</td>\n",
       "      <td>63.25</td>\n",
       "      <td>609400.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.148435</td>\n",
       "      <td>9.202266</td>\n",
       "      <td>9.112062</td>\n",
       "      <td>9.202266</td>\n",
       "      <td>2437600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-18</th>\n",
       "      <td>62.75</td>\n",
       "      <td>63.0000</td>\n",
       "      <td>61.7500</td>\n",
       "      <td>61.88</td>\n",
       "      <td>883800.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.129521</td>\n",
       "      <td>9.165894</td>\n",
       "      <td>8.984031</td>\n",
       "      <td>9.002944</td>\n",
       "      <td>3535200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-19</th>\n",
       "      <td>61.38</td>\n",
       "      <td>61.6300</td>\n",
       "      <td>61.3800</td>\n",
       "      <td>61.50</td>\n",
       "      <td>622800.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.930199</td>\n",
       "      <td>8.966572</td>\n",
       "      <td>8.930199</td>\n",
       "      <td>8.947658</td>\n",
       "      <td>2491200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-20</th>\n",
       "      <td>61.63</td>\n",
       "      <td>61.6300</td>\n",
       "      <td>61.0000</td>\n",
       "      <td>61.38</td>\n",
       "      <td>1282700.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.966572</td>\n",
       "      <td>8.966572</td>\n",
       "      <td>8.874913</td>\n",
       "      <td>8.930199</td>\n",
       "      <td>5130800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-23</th>\n",
       "      <td>60.75</td>\n",
       "      <td>62.0000</td>\n",
       "      <td>60.7500</td>\n",
       "      <td>62.00</td>\n",
       "      <td>786800.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8.838540</td>\n",
       "      <td>9.020403</td>\n",
       "      <td>8.838540</td>\n",
       "      <td>9.020403</td>\n",
       "      <td>3147200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-24</th>\n",
       "      <td>62.00</td>\n",
       "      <td>62.1300</td>\n",
       "      <td>61.5000</td>\n",
       "      <td>62.00</td>\n",
       "      <td>504100.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.020403</td>\n",
       "      <td>9.039317</td>\n",
       "      <td>8.947658</td>\n",
       "      <td>9.020403</td>\n",
       "      <td>2016400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-25</th>\n",
       "      <td>62.00</td>\n",
       "      <td>63.1300</td>\n",
       "      <td>61.7500</td>\n",
       "      <td>62.75</td>\n",
       "      <td>700600.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.020403</td>\n",
       "      <td>9.184807</td>\n",
       "      <td>8.984031</td>\n",
       "      <td>9.129521</td>\n",
       "      <td>2802400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-26</th>\n",
       "      <td>62.88</td>\n",
       "      <td>63.3800</td>\n",
       "      <td>62.7500</td>\n",
       "      <td>63.13</td>\n",
       "      <td>781000.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.148435</td>\n",
       "      <td>9.221180</td>\n",
       "      <td>9.129521</td>\n",
       "      <td>9.184807</td>\n",
       "      <td>3124000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-27</th>\n",
       "      <td>63.25</td>\n",
       "      <td>65.0000</td>\n",
       "      <td>62.5000</td>\n",
       "      <td>64.75</td>\n",
       "      <td>1561800.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.202266</td>\n",
       "      <td>9.456874</td>\n",
       "      <td>9.093149</td>\n",
       "      <td>9.420502</td>\n",
       "      <td>6247200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-30</th>\n",
       "      <td>64.50</td>\n",
       "      <td>66.2500</td>\n",
       "      <td>64.3800</td>\n",
       "      <td>65.75</td>\n",
       "      <td>1306600.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.384129</td>\n",
       "      <td>9.638737</td>\n",
       "      <td>9.366670</td>\n",
       "      <td>9.565992</td>\n",
       "      <td>5226400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>65.63</td>\n",
       "      <td>65.6300</td>\n",
       "      <td>65.2500</td>\n",
       "      <td>65.25</td>\n",
       "      <td>983700.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.548533</td>\n",
       "      <td>9.548533</td>\n",
       "      <td>9.493247</td>\n",
       "      <td>9.493247</td>\n",
       "      <td>3934800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-01</th>\n",
       "      <td>65.38</td>\n",
       "      <td>65.3800</td>\n",
       "      <td>63.7500</td>\n",
       "      <td>63.88</td>\n",
       "      <td>761800.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.512161</td>\n",
       "      <td>9.512161</td>\n",
       "      <td>9.275011</td>\n",
       "      <td>9.293925</td>\n",
       "      <td>3047200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-02</th>\n",
       "      <td>63.88</td>\n",
       "      <td>64.5000</td>\n",
       "      <td>63.5000</td>\n",
       "      <td>64.38</td>\n",
       "      <td>952600.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.293925</td>\n",
       "      <td>9.384129</td>\n",
       "      <td>9.238639</td>\n",
       "      <td>9.366670</td>\n",
       "      <td>3810400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-03</th>\n",
       "      <td>64.88</td>\n",
       "      <td>65.5000</td>\n",
       "      <td>64.7500</td>\n",
       "      <td>65.00</td>\n",
       "      <td>1110700.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.439416</td>\n",
       "      <td>9.529620</td>\n",
       "      <td>9.420502</td>\n",
       "      <td>9.456874</td>\n",
       "      <td>4442800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-06</th>\n",
       "      <td>65.13</td>\n",
       "      <td>66.5000</td>\n",
       "      <td>65.1300</td>\n",
       "      <td>66.50</td>\n",
       "      <td>1000900.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.475788</td>\n",
       "      <td>9.675110</td>\n",
       "      <td>9.475788</td>\n",
       "      <td>9.675110</td>\n",
       "      <td>4003600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-07</th>\n",
       "      <td>66.25</td>\n",
       "      <td>66.3800</td>\n",
       "      <td>65.6300</td>\n",
       "      <td>66.38</td>\n",
       "      <td>595100.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.638737</td>\n",
       "      <td>9.657651</td>\n",
       "      <td>9.548533</td>\n",
       "      <td>9.657651</td>\n",
       "      <td>2380400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-08</th>\n",
       "      <td>66.38</td>\n",
       "      <td>66.3800</td>\n",
       "      <td>65.6300</td>\n",
       "      <td>65.63</td>\n",
       "      <td>620300.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.657651</td>\n",
       "      <td>9.657651</td>\n",
       "      <td>9.548533</td>\n",
       "      <td>9.548533</td>\n",
       "      <td>2481200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-09</th>\n",
       "      <td>65.75</td>\n",
       "      <td>65.8800</td>\n",
       "      <td>65.2500</td>\n",
       "      <td>65.63</td>\n",
       "      <td>535900.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.565992</td>\n",
       "      <td>9.584906</td>\n",
       "      <td>9.493247</td>\n",
       "      <td>9.548533</td>\n",
       "      <td>2143600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-10</th>\n",
       "      <td>65.38</td>\n",
       "      <td>65.6300</td>\n",
       "      <td>64.6300</td>\n",
       "      <td>65.50</td>\n",
       "      <td>611400.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.512161</td>\n",
       "      <td>9.548533</td>\n",
       "      <td>9.403043</td>\n",
       "      <td>9.529620</td>\n",
       "      <td>2445600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-13</th>\n",
       "      <td>65.25</td>\n",
       "      <td>65.8800</td>\n",
       "      <td>65.2500</td>\n",
       "      <td>65.88</td>\n",
       "      <td>431600.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.493247</td>\n",
       "      <td>9.584906</td>\n",
       "      <td>9.493247</td>\n",
       "      <td>9.584906</td>\n",
       "      <td>1726400.0</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-16</th>\n",
       "      <td>89.84</td>\n",
       "      <td>89.9000</td>\n",
       "      <td>88.7710</td>\n",
       "      <td>89.25</td>\n",
       "      <td>7082826.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>89.840000</td>\n",
       "      <td>89.900000</td>\n",
       "      <td>88.771000</td>\n",
       "      <td>89.250000</td>\n",
       "      <td>7082826.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-17</th>\n",
       "      <td>88.95</td>\n",
       "      <td>89.0900</td>\n",
       "      <td>88.0800</td>\n",
       "      <td>88.43</td>\n",
       "      <td>5919864.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>88.950000</td>\n",
       "      <td>89.090000</td>\n",
       "      <td>88.080000</td>\n",
       "      <td>88.430000</td>\n",
       "      <td>5919864.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-20</th>\n",
       "      <td>88.43</td>\n",
       "      <td>88.5550</td>\n",
       "      <td>87.7100</td>\n",
       "      <td>88.27</td>\n",
       "      <td>4920032.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>88.430000</td>\n",
       "      <td>88.555000</td>\n",
       "      <td>87.710000</td>\n",
       "      <td>88.270000</td>\n",
       "      <td>4920032.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-21</th>\n",
       "      <td>88.18</td>\n",
       "      <td>89.2100</td>\n",
       "      <td>88.0200</td>\n",
       "      <td>88.72</td>\n",
       "      <td>5919107.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>88.180000</td>\n",
       "      <td>89.210000</td>\n",
       "      <td>88.020000</td>\n",
       "      <td>88.720000</td>\n",
       "      <td>5919107.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-22</th>\n",
       "      <td>88.50</td>\n",
       "      <td>88.9100</td>\n",
       "      <td>88.0600</td>\n",
       "      <td>88.33</td>\n",
       "      <td>5786078.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>88.500000</td>\n",
       "      <td>88.910000</td>\n",
       "      <td>88.060000</td>\n",
       "      <td>88.330000</td>\n",
       "      <td>5786078.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-24</th>\n",
       "      <td>88.59</td>\n",
       "      <td>88.9600</td>\n",
       "      <td>88.4200</td>\n",
       "      <td>88.45</td>\n",
       "      <td>2196665.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>88.590000</td>\n",
       "      <td>88.960000</td>\n",
       "      <td>88.420000</td>\n",
       "      <td>88.450000</td>\n",
       "      <td>2196665.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-27</th>\n",
       "      <td>88.33</td>\n",
       "      <td>89.0950</td>\n",
       "      <td>88.1500</td>\n",
       "      <td>88.96</td>\n",
       "      <td>6196621.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>88.330000</td>\n",
       "      <td>89.095000</td>\n",
       "      <td>88.150000</td>\n",
       "      <td>88.960000</td>\n",
       "      <td>6196621.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-28</th>\n",
       "      <td>89.48</td>\n",
       "      <td>89.5200</td>\n",
       "      <td>88.9100</td>\n",
       "      <td>89.40</td>\n",
       "      <td>4346159.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>89.480000</td>\n",
       "      <td>89.520000</td>\n",
       "      <td>88.910000</td>\n",
       "      <td>89.400000</td>\n",
       "      <td>4346159.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-29</th>\n",
       "      <td>89.40</td>\n",
       "      <td>89.8100</td>\n",
       "      <td>89.0300</td>\n",
       "      <td>89.38</td>\n",
       "      <td>5085899.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>89.400000</td>\n",
       "      <td>89.810000</td>\n",
       "      <td>89.030000</td>\n",
       "      <td>89.380000</td>\n",
       "      <td>5085899.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-30</th>\n",
       "      <td>89.35</td>\n",
       "      <td>90.3700</td>\n",
       "      <td>89.2100</td>\n",
       "      <td>89.99</td>\n",
       "      <td>8864870.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>89.350000</td>\n",
       "      <td>90.370000</td>\n",
       "      <td>89.210000</td>\n",
       "      <td>89.990000</td>\n",
       "      <td>8864870.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-01</th>\n",
       "      <td>90.18</td>\n",
       "      <td>90.5300</td>\n",
       "      <td>89.1200</td>\n",
       "      <td>90.36</td>\n",
       "      <td>7840491.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>90.180000</td>\n",
       "      <td>90.530000</td>\n",
       "      <td>89.120000</td>\n",
       "      <td>90.360000</td>\n",
       "      <td>7840491.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-04</th>\n",
       "      <td>90.17</td>\n",
       "      <td>91.9100</td>\n",
       "      <td>89.8300</td>\n",
       "      <td>91.41</td>\n",
       "      <td>8972682.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>90.170000</td>\n",
       "      <td>91.910000</td>\n",
       "      <td>89.830000</td>\n",
       "      <td>91.410000</td>\n",
       "      <td>8972682.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-05</th>\n",
       "      <td>91.52</td>\n",
       "      <td>91.8400</td>\n",
       "      <td>91.0700</td>\n",
       "      <td>91.40</td>\n",
       "      <td>8200560.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.520000</td>\n",
       "      <td>91.840000</td>\n",
       "      <td>91.070000</td>\n",
       "      <td>91.400000</td>\n",
       "      <td>8200560.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-06</th>\n",
       "      <td>91.50</td>\n",
       "      <td>91.7800</td>\n",
       "      <td>91.0700</td>\n",
       "      <td>91.25</td>\n",
       "      <td>6728731.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.500000</td>\n",
       "      <td>91.780000</td>\n",
       "      <td>91.070000</td>\n",
       "      <td>91.250000</td>\n",
       "      <td>6728731.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-07</th>\n",
       "      <td>91.05</td>\n",
       "      <td>91.0650</td>\n",
       "      <td>89.8900</td>\n",
       "      <td>90.10</td>\n",
       "      <td>7261029.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.050000</td>\n",
       "      <td>91.065000</td>\n",
       "      <td>89.890000</td>\n",
       "      <td>90.100000</td>\n",
       "      <td>7261029.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-08</th>\n",
       "      <td>90.02</td>\n",
       "      <td>90.3700</td>\n",
       "      <td>89.5800</td>\n",
       "      <td>90.37</td>\n",
       "      <td>5580725.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>90.020000</td>\n",
       "      <td>90.370000</td>\n",
       "      <td>89.580000</td>\n",
       "      <td>90.370000</td>\n",
       "      <td>5580725.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-11</th>\n",
       "      <td>90.23</td>\n",
       "      <td>90.3300</td>\n",
       "      <td>89.7499</td>\n",
       "      <td>90.23</td>\n",
       "      <td>4819223.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>90.230000</td>\n",
       "      <td>90.330000</td>\n",
       "      <td>89.749900</td>\n",
       "      <td>90.230000</td>\n",
       "      <td>4819223.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-12</th>\n",
       "      <td>90.45</td>\n",
       "      <td>90.5100</td>\n",
       "      <td>89.8200</td>\n",
       "      <td>89.85</td>\n",
       "      <td>6555457.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>90.450000</td>\n",
       "      <td>90.510000</td>\n",
       "      <td>89.820000</td>\n",
       "      <td>89.850000</td>\n",
       "      <td>6555457.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-13</th>\n",
       "      <td>90.02</td>\n",
       "      <td>91.4100</td>\n",
       "      <td>89.9650</td>\n",
       "      <td>90.88</td>\n",
       "      <td>7062236.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>90.020000</td>\n",
       "      <td>91.410000</td>\n",
       "      <td>89.965000</td>\n",
       "      <td>90.880000</td>\n",
       "      <td>7062236.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-14</th>\n",
       "      <td>90.97</td>\n",
       "      <td>91.4300</td>\n",
       "      <td>90.9000</td>\n",
       "      <td>91.00</td>\n",
       "      <td>5820716.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>90.970000</td>\n",
       "      <td>91.430000</td>\n",
       "      <td>90.900000</td>\n",
       "      <td>91.000000</td>\n",
       "      <td>5820716.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-15</th>\n",
       "      <td>91.60</td>\n",
       "      <td>92.2700</td>\n",
       "      <td>91.4800</td>\n",
       "      <td>91.89</td>\n",
       "      <td>14857992.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.600000</td>\n",
       "      <td>92.270000</td>\n",
       "      <td>91.480000</td>\n",
       "      <td>91.890000</td>\n",
       "      <td>14857992.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-18</th>\n",
       "      <td>91.89</td>\n",
       "      <td>93.1400</td>\n",
       "      <td>91.8100</td>\n",
       "      <td>91.88</td>\n",
       "      <td>7368839.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.890000</td>\n",
       "      <td>93.140000</td>\n",
       "      <td>91.810000</td>\n",
       "      <td>91.880000</td>\n",
       "      <td>7368839.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-19</th>\n",
       "      <td>91.96</td>\n",
       "      <td>92.1306</td>\n",
       "      <td>91.5800</td>\n",
       "      <td>91.68</td>\n",
       "      <td>5619300.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.960000</td>\n",
       "      <td>92.130600</td>\n",
       "      <td>91.580000</td>\n",
       "      <td>91.680000</td>\n",
       "      <td>5619300.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-20</th>\n",
       "      <td>91.87</td>\n",
       "      <td>91.9700</td>\n",
       "      <td>91.3500</td>\n",
       "      <td>91.53</td>\n",
       "      <td>6541762.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.870000</td>\n",
       "      <td>91.970000</td>\n",
       "      <td>91.350000</td>\n",
       "      <td>91.530000</td>\n",
       "      <td>6541762.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-21</th>\n",
       "      <td>91.86</td>\n",
       "      <td>92.0800</td>\n",
       "      <td>91.5300</td>\n",
       "      <td>91.67</td>\n",
       "      <td>4368974.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.860000</td>\n",
       "      <td>92.080000</td>\n",
       "      <td>91.530000</td>\n",
       "      <td>91.670000</td>\n",
       "      <td>4368974.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-22</th>\n",
       "      <td>91.77</td>\n",
       "      <td>92.4318</td>\n",
       "      <td>91.7200</td>\n",
       "      <td>92.13</td>\n",
       "      <td>4907370.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.770000</td>\n",
       "      <td>92.431800</td>\n",
       "      <td>91.720000</td>\n",
       "      <td>92.130000</td>\n",
       "      <td>4907370.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-26</th>\n",
       "      <td>92.35</td>\n",
       "      <td>92.7700</td>\n",
       "      <td>92.1500</td>\n",
       "      <td>92.48</td>\n",
       "      <td>3429407.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>92.350000</td>\n",
       "      <td>92.770000</td>\n",
       "      <td>92.150000</td>\n",
       "      <td>92.480000</td>\n",
       "      <td>3429407.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-27</th>\n",
       "      <td>92.49</td>\n",
       "      <td>92.7500</td>\n",
       "      <td>91.9300</td>\n",
       "      <td>92.10</td>\n",
       "      <td>4186932.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>92.490000</td>\n",
       "      <td>92.750000</td>\n",
       "      <td>91.930000</td>\n",
       "      <td>92.100000</td>\n",
       "      <td>4186932.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-28</th>\n",
       "      <td>92.30</td>\n",
       "      <td>92.5400</td>\n",
       "      <td>91.9100</td>\n",
       "      <td>92.07</td>\n",
       "      <td>2994628.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>92.300000</td>\n",
       "      <td>92.540000</td>\n",
       "      <td>91.910000</td>\n",
       "      <td>92.070000</td>\n",
       "      <td>2994628.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-29</th>\n",
       "      <td>92.24</td>\n",
       "      <td>92.4600</td>\n",
       "      <td>91.8800</td>\n",
       "      <td>91.88</td>\n",
       "      <td>4309461.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>92.240000</td>\n",
       "      <td>92.460000</td>\n",
       "      <td>91.880000</td>\n",
       "      <td>91.880000</td>\n",
       "      <td>4309461.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5790 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Open     High      Low  Close      Volume  ExDividend  \\\n",
       "Date                                                                 \n",
       "1995-01-03  61.88  62.5000  61.7500  62.38    829600.0        0.00   \n",
       "1995-01-04  62.63  62.6300  61.2500  61.88    554700.0        0.00   \n",
       "1995-01-05  61.50  61.7500  60.8800  61.00    579900.0        0.00   \n",
       "1995-01-06  60.63  61.6300  60.6300  61.25    859500.0        0.00   \n",
       "1995-01-09  61.38  61.6300  60.7500  60.88    448800.0        0.00   \n",
       "1995-01-10  61.13  61.7500  60.7500  61.63   1091000.0        0.00   \n",
       "1995-01-11  62.38  62.3800  61.5000  61.50    934600.0        0.00   \n",
       "1995-01-12  61.50  62.0000  61.3800  62.00    826900.0        0.00   \n",
       "1995-01-13  62.38  63.3800  62.1300  62.50    998200.0        0.35   \n",
       "1995-01-16  63.63  63.7500  63.0000  63.00    919300.0        0.00   \n",
       "1995-01-17  62.88  63.2500  62.6300  63.25    609400.0        0.00   \n",
       "1995-01-18  62.75  63.0000  61.7500  61.88    883800.0        0.00   \n",
       "1995-01-19  61.38  61.6300  61.3800  61.50    622800.0        0.00   \n",
       "1995-01-20  61.63  61.6300  61.0000  61.38   1282700.0        0.00   \n",
       "1995-01-23  60.75  62.0000  60.7500  62.00    786800.0        0.00   \n",
       "1995-01-24  62.00  62.1300  61.5000  62.00    504100.0        0.00   \n",
       "1995-01-25  62.00  63.1300  61.7500  62.75    700600.0        0.00   \n",
       "1995-01-26  62.88  63.3800  62.7500  63.13    781000.0        0.00   \n",
       "1995-01-27  63.25  65.0000  62.5000  64.75   1561800.0        0.00   \n",
       "1995-01-30  64.50  66.2500  64.3800  65.75   1306600.0        0.00   \n",
       "1995-01-31  65.63  65.6300  65.2500  65.25    983700.0        0.00   \n",
       "1995-02-01  65.38  65.3800  63.7500  63.88    761800.0        0.00   \n",
       "1995-02-02  63.88  64.5000  63.5000  64.38    952600.0        0.00   \n",
       "1995-02-03  64.88  65.5000  64.7500  65.00   1110700.0        0.00   \n",
       "1995-02-06  65.13  66.5000  65.1300  66.50   1000900.0        0.00   \n",
       "1995-02-07  66.25  66.3800  65.6300  66.38    595100.0        0.00   \n",
       "1995-02-08  66.38  66.3800  65.6300  65.63    620300.0        0.00   \n",
       "1995-02-09  65.75  65.8800  65.2500  65.63    535900.0        0.00   \n",
       "1995-02-10  65.38  65.6300  64.6300  65.50    611400.0        0.00   \n",
       "1995-02-13  65.25  65.8800  65.2500  65.88    431600.0        0.00   \n",
       "...           ...      ...      ...    ...         ...         ...   \n",
       "2017-11-16  89.84  89.9000  88.7710  89.25   7082826.0        0.00   \n",
       "2017-11-17  88.95  89.0900  88.0800  88.43   5919864.0        0.00   \n",
       "2017-11-20  88.43  88.5550  87.7100  88.27   4920032.0        0.00   \n",
       "2017-11-21  88.18  89.2100  88.0200  88.72   5919107.0        0.00   \n",
       "2017-11-22  88.50  88.9100  88.0600  88.33   5786078.0        0.00   \n",
       "2017-11-24  88.59  88.9600  88.4200  88.45   2196665.0        0.00   \n",
       "2017-11-27  88.33  89.0950  88.1500  88.96   6196621.0        0.00   \n",
       "2017-11-28  89.48  89.5200  88.9100  89.40   4346159.0        0.00   \n",
       "2017-11-29  89.40  89.8100  89.0300  89.38   5085899.0        0.00   \n",
       "2017-11-30  89.35  90.3700  89.2100  89.99   8864870.0        0.00   \n",
       "2017-12-01  90.18  90.5300  89.1200  90.36   7840491.0        0.00   \n",
       "2017-12-04  90.17  91.9100  89.8300  91.41   8972682.0        0.00   \n",
       "2017-12-05  91.52  91.8400  91.0700  91.40   8200560.0        0.00   \n",
       "2017-12-06  91.50  91.7800  91.0700  91.25   6728731.0        0.00   \n",
       "2017-12-07  91.05  91.0650  89.8900  90.10   7261029.0        0.00   \n",
       "2017-12-08  90.02  90.3700  89.5800  90.37   5580725.0        0.00   \n",
       "2017-12-11  90.23  90.3300  89.7499  90.23   4819223.0        0.00   \n",
       "2017-12-12  90.45  90.5100  89.8200  89.85   6555457.0        0.00   \n",
       "2017-12-13  90.02  91.4100  89.9650  90.88   7062236.0        0.00   \n",
       "2017-12-14  90.97  91.4300  90.9000  91.00   5820716.0        0.00   \n",
       "2017-12-15  91.60  92.2700  91.4800  91.89  14857992.0        0.00   \n",
       "2017-12-18  91.89  93.1400  91.8100  91.88   7368839.0        0.00   \n",
       "2017-12-19  91.96  92.1306  91.5800  91.68   5619300.0        0.00   \n",
       "2017-12-20  91.87  91.9700  91.3500  91.53   6541762.0        0.00   \n",
       "2017-12-21  91.86  92.0800  91.5300  91.67   4368974.0        0.00   \n",
       "2017-12-22  91.77  92.4318  91.7200  92.13   4907370.0        0.00   \n",
       "2017-12-26  92.35  92.7700  92.1500  92.48   3429407.0        0.00   \n",
       "2017-12-27  92.49  92.7500  91.9300  92.10   4186932.0        0.00   \n",
       "2017-12-28  92.30  92.5400  91.9100  92.07   2994628.0        0.00   \n",
       "2017-12-29  92.24  92.4600  91.8800  91.88   4309461.0        0.00   \n",
       "\n",
       "            SplitRatio    AdjOpen    AdjHigh     AdjLow   AdjClose   AdjVolume  \n",
       "Date                                                                            \n",
       "1995-01-03         1.0   8.952809   9.042510   8.934000   9.025149   3318400.0  \n",
       "1995-01-04         1.0   9.061319   9.061319   8.861660   8.952809   2218800.0  \n",
       "1995-01-05         1.0   8.897830   8.934000   8.808129   8.825490   2319600.0  \n",
       "1995-01-06         1.0   8.771959   8.916639   8.771959   8.861660   3438000.0  \n",
       "1995-01-09         1.0   8.880469   8.916639   8.789320   8.808129   1795200.0  \n",
       "1995-01-10         1.0   8.844299   8.934000   8.789320   8.916639   4364000.0  \n",
       "1995-01-11         1.0   9.025149   9.025149   8.897830   8.897830   3738400.0  \n",
       "1995-01-12         1.0   8.897830   8.970170   8.880469   8.970170   3307600.0  \n",
       "1995-01-13         1.0   9.075690   9.221180   9.039317   9.093149   3992800.0  \n",
       "1995-01-16         1.0   9.257553   9.275011   9.165894   9.165894   3677200.0  \n",
       "1995-01-17         1.0   9.148435   9.202266   9.112062   9.202266   2437600.0  \n",
       "1995-01-18         1.0   9.129521   9.165894   8.984031   9.002944   3535200.0  \n",
       "1995-01-19         1.0   8.930199   8.966572   8.930199   8.947658   2491200.0  \n",
       "1995-01-20         1.0   8.966572   8.966572   8.874913   8.930199   5130800.0  \n",
       "1995-01-23         1.0   8.838540   9.020403   8.838540   9.020403   3147200.0  \n",
       "1995-01-24         1.0   9.020403   9.039317   8.947658   9.020403   2016400.0  \n",
       "1995-01-25         1.0   9.020403   9.184807   8.984031   9.129521   2802400.0  \n",
       "1995-01-26         1.0   9.148435   9.221180   9.129521   9.184807   3124000.0  \n",
       "1995-01-27         1.0   9.202266   9.456874   9.093149   9.420502   6247200.0  \n",
       "1995-01-30         1.0   9.384129   9.638737   9.366670   9.565992   5226400.0  \n",
       "1995-01-31         1.0   9.548533   9.548533   9.493247   9.493247   3934800.0  \n",
       "1995-02-01         1.0   9.512161   9.512161   9.275011   9.293925   3047200.0  \n",
       "1995-02-02         1.0   9.293925   9.384129   9.238639   9.366670   3810400.0  \n",
       "1995-02-03         1.0   9.439416   9.529620   9.420502   9.456874   4442800.0  \n",
       "1995-02-06         1.0   9.475788   9.675110   9.475788   9.675110   4003600.0  \n",
       "1995-02-07         1.0   9.638737   9.657651   9.548533   9.657651   2380400.0  \n",
       "1995-02-08         1.0   9.657651   9.657651   9.548533   9.548533   2481200.0  \n",
       "1995-02-09         1.0   9.565992   9.584906   9.493247   9.548533   2143600.0  \n",
       "1995-02-10         1.0   9.512161   9.548533   9.403043   9.529620   2445600.0  \n",
       "1995-02-13         1.0   9.493247   9.584906   9.493247   9.584906   1726400.0  \n",
       "...                ...        ...        ...        ...        ...         ...  \n",
       "2017-11-16         1.0  89.840000  89.900000  88.771000  89.250000   7082826.0  \n",
       "2017-11-17         1.0  88.950000  89.090000  88.080000  88.430000   5919864.0  \n",
       "2017-11-20         1.0  88.430000  88.555000  87.710000  88.270000   4920032.0  \n",
       "2017-11-21         1.0  88.180000  89.210000  88.020000  88.720000   5919107.0  \n",
       "2017-11-22         1.0  88.500000  88.910000  88.060000  88.330000   5786078.0  \n",
       "2017-11-24         1.0  88.590000  88.960000  88.420000  88.450000   2196665.0  \n",
       "2017-11-27         1.0  88.330000  89.095000  88.150000  88.960000   6196621.0  \n",
       "2017-11-28         1.0  89.480000  89.520000  88.910000  89.400000   4346159.0  \n",
       "2017-11-29         1.0  89.400000  89.810000  89.030000  89.380000   5085899.0  \n",
       "2017-11-30         1.0  89.350000  90.370000  89.210000  89.990000   8864870.0  \n",
       "2017-12-01         1.0  90.180000  90.530000  89.120000  90.360000   7840491.0  \n",
       "2017-12-04         1.0  90.170000  91.910000  89.830000  91.410000   8972682.0  \n",
       "2017-12-05         1.0  91.520000  91.840000  91.070000  91.400000   8200560.0  \n",
       "2017-12-06         1.0  91.500000  91.780000  91.070000  91.250000   6728731.0  \n",
       "2017-12-07         1.0  91.050000  91.065000  89.890000  90.100000   7261029.0  \n",
       "2017-12-08         1.0  90.020000  90.370000  89.580000  90.370000   5580725.0  \n",
       "2017-12-11         1.0  90.230000  90.330000  89.749900  90.230000   4819223.0  \n",
       "2017-12-12         1.0  90.450000  90.510000  89.820000  89.850000   6555457.0  \n",
       "2017-12-13         1.0  90.020000  91.410000  89.965000  90.880000   7062236.0  \n",
       "2017-12-14         1.0  90.970000  91.430000  90.900000  91.000000   5820716.0  \n",
       "2017-12-15         1.0  91.600000  92.270000  91.480000  91.890000  14857992.0  \n",
       "2017-12-18         1.0  91.890000  93.140000  91.810000  91.880000   7368839.0  \n",
       "2017-12-19         1.0  91.960000  92.130600  91.580000  91.680000   5619300.0  \n",
       "2017-12-20         1.0  91.870000  91.970000  91.350000  91.530000   6541762.0  \n",
       "2017-12-21         1.0  91.860000  92.080000  91.530000  91.670000   4368974.0  \n",
       "2017-12-22         1.0  91.770000  92.431800  91.720000  92.130000   4907370.0  \n",
       "2017-12-26         1.0  92.350000  92.770000  92.150000  92.480000   3429407.0  \n",
       "2017-12-27         1.0  92.490000  92.750000  91.930000  92.100000   4186932.0  \n",
       "2017-12-28         1.0  92.300000  92.540000  91.910000  92.070000   2994628.0  \n",
       "2017-12-29         1.0  92.240000  92.460000  91.880000  91.880000   4309461.0  \n",
       "\n",
       "[5790 rows x 12 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PG = PG.iloc[::-1]\n",
    "PG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Date\n",
      "1995-01-03         NaN\n",
      "1995-01-04   -0.008015\n",
      "1995-01-05   -0.014221\n",
      "1995-01-06    0.004098\n",
      "1995-01-09   -0.006041\n",
      "1995-01-10    0.012319\n",
      "1995-01-11   -0.002109\n",
      "1995-01-12    0.008130\n",
      "1995-01-13    0.013710\n",
      "1995-01-16    0.008000\n",
      "1995-01-17    0.003968\n",
      "1995-01-18   -0.021660\n",
      "1995-01-19   -0.006141\n",
      "1995-01-20   -0.001951\n",
      "1995-01-23    0.010101\n",
      "1995-01-24    0.000000\n",
      "1995-01-25    0.012097\n",
      "1995-01-26    0.006056\n",
      "1995-01-27    0.025661\n",
      "1995-01-30    0.015444\n",
      "1995-01-31   -0.007605\n",
      "1995-02-01   -0.020996\n",
      "1995-02-02    0.007827\n",
      "1995-02-03    0.009630\n",
      "1995-02-06    0.023077\n",
      "1995-02-07   -0.001805\n",
      "1995-02-08   -0.011299\n",
      "1995-02-09    0.000000\n",
      "1995-02-10   -0.001981\n",
      "1995-02-13    0.005802\n",
      "                ...   \n",
      "2017-11-16    0.011561\n",
      "2017-11-17   -0.009188\n",
      "2017-11-20   -0.001809\n",
      "2017-11-21    0.005098\n",
      "2017-11-22   -0.004396\n",
      "2017-11-24    0.001359\n",
      "2017-11-27    0.005766\n",
      "2017-11-28    0.004946\n",
      "2017-11-29   -0.000224\n",
      "2017-11-30    0.006825\n",
      "2017-12-01    0.004112\n",
      "2017-12-04    0.011620\n",
      "2017-12-05   -0.000109\n",
      "2017-12-06   -0.001641\n",
      "2017-12-07   -0.012603\n",
      "2017-12-08    0.002997\n",
      "2017-12-11   -0.001549\n",
      "2017-12-12   -0.004211\n",
      "2017-12-13    0.011464\n",
      "2017-12-14    0.001320\n",
      "2017-12-15    0.009780\n",
      "2017-12-18   -0.000109\n",
      "2017-12-19   -0.002177\n",
      "2017-12-20   -0.001636\n",
      "2017-12-21    0.001530\n",
      "2017-12-22    0.005018\n",
      "2017-12-26    0.003799\n",
      "2017-12-27   -0.004109\n",
      "2017-12-28   -0.000326\n",
      "2017-12-29   -0.002064\n",
      "Name: simple_return, Length: 5790, dtype: float64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "PG['simple_return']=(PG['AdjClose']/PG['AdjClose'].shift(1))-1\n",
    "print(PG['simple_return'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b22ef1de80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PG['simple_return'].plot(figsize=(8, 5))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0005028949365714817"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "avg_d = PG['simple_return'].mean()\n",
    "avg_d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.3933 %\n"
     ]
    }
   ],
   "source": [
    "avg_a = (((avg_d+1)**250)-1)*100\n",
    "print(str(round(avg_a,5)) + ' %')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Date\n",
      "1995-01-03         NaN\n",
      "1995-01-04   -0.008048\n",
      "1995-01-05   -0.014323\n",
      "1995-01-06    0.004090\n",
      "1995-01-09   -0.006059\n",
      "1995-01-10    0.012244\n",
      "1995-01-11   -0.002112\n",
      "1995-01-12    0.008097\n",
      "1995-01-13    0.013617\n",
      "1995-01-16    0.007968\n",
      "1995-01-17    0.003960\n",
      "1995-01-18   -0.021898\n",
      "1995-01-19   -0.006160\n",
      "1995-01-20   -0.001953\n",
      "1995-01-23    0.010050\n",
      "1995-01-24    0.000000\n",
      "1995-01-25    0.012024\n",
      "1995-01-26    0.006038\n",
      "1995-01-27    0.025338\n",
      "1995-01-30    0.015326\n",
      "1995-01-31   -0.007634\n",
      "1995-02-01   -0.021220\n",
      "1995-02-02    0.007797\n",
      "1995-02-03    0.009584\n",
      "1995-02-06    0.022815\n",
      "1995-02-07   -0.001806\n",
      "1995-02-08   -0.011363\n",
      "1995-02-09    0.000000\n",
      "1995-02-10   -0.001983\n",
      "1995-02-13    0.005785\n",
      "                ...   \n",
      "2017-11-16    0.011494\n",
      "2017-11-17   -0.009230\n",
      "2017-11-20   -0.001811\n",
      "2017-11-21    0.005085\n",
      "2017-11-22   -0.004406\n",
      "2017-11-24    0.001358\n",
      "2017-11-27    0.005749\n",
      "2017-11-28    0.004934\n",
      "2017-11-29   -0.000224\n",
      "2017-11-30    0.006802\n",
      "2017-12-01    0.004103\n",
      "2017-12-04    0.011553\n",
      "2017-12-05   -0.000109\n",
      "2017-12-06   -0.001642\n",
      "2017-12-07   -0.012683\n",
      "2017-12-08    0.002992\n",
      "2017-12-11   -0.001550\n",
      "2017-12-12   -0.004220\n",
      "2017-12-13    0.011398\n",
      "2017-12-14    0.001320\n",
      "2017-12-15    0.009733\n",
      "2017-12-18   -0.000109\n",
      "2017-12-19   -0.002179\n",
      "2017-12-20   -0.001637\n",
      "2017-12-21    0.001528\n",
      "2017-12-22    0.005005\n",
      "2017-12-26    0.003792\n",
      "2017-12-27   -0.004117\n",
      "2017-12-28   -0.000326\n",
      "2017-12-29   -0.002066\n",
      "Name: log_returns, Length: 5790, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "PG['log_returns'] = np.log(PG['AdjClose']/PG['AdjClose'].shift(1))\n",
    "print(PG['log_returns'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x187bc01c710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PG['log_returns'].plot(figsize=(8, 5))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.04 %\n"
     ]
    }
   ],
   "source": [
    "daily_l = PG['log_returns'].mean()\n",
    "print(str(round(daily_l,5) *100) + ' %')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.53811 %\n"
     ]
    }
   ],
   "source": [
    "annual_l = (((daily_l+1)**250)-1)*100\n",
    "print(str(round(annual_l,5)) + ' %')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}