GARCH(1,1).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## importing all the important libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#importing all the libraries\n",
    "import pandas as pd\n",
    "import Quandl\n",
    "from scipy.stats import norm\n",
    "import datetime\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading data from Quandl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ftse_data = Quandl.get('YAHOO/HK_4337', trim_start=\"2009-01-01\", trim_end=\"2014-01-01\")\n",
    "ftse_data.columns = ['Open','High','Low','Close','Volume','AdjustedClose']\n",
    "returns = ftse_data.AdjustedClose.pct_change()\n",
    "returns.fillna(0)\n",
    "mean = returns.mean()\n",
    "std_dev = returns.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Getting data and setting parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ftse_data['log_returns'] = ftse_data['AdjustedClose']/ftse_data['AdjustedClose'].shift()\n",
    "ftse_data['log_returns'] = ftse_data.apply(lambda x: math.log(x['log_returns']), axis=1)\n",
    "ftse_data = ftse_data.fillna(0)\n",
    "ftse_data['mean'] = mean\n",
    "ftse_data['variance'] = std_dev**2\n",
    "omega = 0.000001 \n",
    "alpha = 0.047\n",
    "beta = 0.9466\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###populating residual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ftse_data['residual'] = ftse_data.apply(lambda x: (x['log_returns'] - x['mean']), axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Populating variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def populate_variance(row):\n",
    "    return (omega + alpha*row['residual']**2 + beta*row.shift(1)['variance'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ftse_data['variance'] = ftse_data.apply(populate_variance, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Populating volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ftse_data['volatility'] = ftse_data.apply(lambda x: math.sqrt(x['variance']), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\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>AdjustedClose</th>\n",
       "      <th>log_returns</th>\n",
       "      <th>mean</th>\n",
       "      <th>variance</th>\n",
       "      <th>residual</th>\n",
       "      <th>volatility</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2009-01-01</th>\n",
       "      <td> 4434.2</td>\n",
       "      <td> 4434.2</td>\n",
       "      <td> 4434.2</td>\n",
       "      <td> 4434.2</td>\n",
       "      <td>          0</td>\n",
       "      <td> 4434.2</td>\n",
       "      <td> 0.000000</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000385</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-02</th>\n",
       "      <td> 4434.2</td>\n",
       "      <td> 4561.8</td>\n",
       "      <td> 4430.0</td>\n",
       "      <td> 4561.8</td>\n",
       "      <td>  407295500</td>\n",
       "      <td> 4561.8</td>\n",
       "      <td> 0.028370</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000403</td>\n",
       "      <td> 0.027985</td>\n",
       "      <td> 0.020065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-05</th>\n",
       "      <td> 4561.8</td>\n",
       "      <td> 4618.1</td>\n",
       "      <td> 4520.8</td>\n",
       "      <td> 4579.6</td>\n",
       "      <td>  836676100</td>\n",
       "      <td> 4579.6</td>\n",
       "      <td> 0.003894</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.003509</td>\n",
       "      <td> 0.019141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-06</th>\n",
       "      <td> 4579.6</td>\n",
       "      <td> 4675.7</td>\n",
       "      <td> 4562.0</td>\n",
       "      <td> 4638.9</td>\n",
       "      <td> 1036086000</td>\n",
       "      <td> 4638.9</td>\n",
       "      <td> 0.012866</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000373</td>\n",
       "      <td> 0.012480</td>\n",
       "      <td> 0.019316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-07</th>\n",
       "      <td> 4638.9</td>\n",
       "      <td> 4638.9</td>\n",
       "      <td> 4478.0</td>\n",
       "      <td> 4507.5</td>\n",
       "      <td> 1059568400</td>\n",
       "      <td> 4507.5</td>\n",
       "      <td>-0.028735</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000406</td>\n",
       "      <td>-0.029120</td>\n",
       "      <td> 0.020141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-08</th>\n",
       "      <td> 4507.5</td>\n",
       "      <td> 4514.7</td>\n",
       "      <td> 4410.5</td>\n",
       "      <td> 4505.4</td>\n",
       "      <td>  923008000</td>\n",
       "      <td> 4505.4</td>\n",
       "      <td>-0.000466</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000851</td>\n",
       "      <td> 0.019127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-09</th>\n",
       "      <td> 4505.4</td>\n",
       "      <td> 4534.8</td>\n",
       "      <td> 4431.9</td>\n",
       "      <td> 4448.5</td>\n",
       "      <td>  979530100</td>\n",
       "      <td> 4448.5</td>\n",
       "      <td>-0.012710</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000374</td>\n",
       "      <td>-0.013095</td>\n",
       "      <td> 0.019335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-12</th>\n",
       "      <td> 4448.5</td>\n",
       "      <td> 4471.3</td>\n",
       "      <td> 4402.3</td>\n",
       "      <td> 4426.2</td>\n",
       "      <td>  785473900</td>\n",
       "      <td> 4426.2</td>\n",
       "      <td>-0.005026</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000367</td>\n",
       "      <td>-0.005411</td>\n",
       "      <td> 0.019162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-13</th>\n",
       "      <td> 4426.2</td>\n",
       "      <td> 4426.2</td>\n",
       "      <td> 4321.3</td>\n",
       "      <td> 4399.2</td>\n",
       "      <td>  928429000</td>\n",
       "      <td> 4399.2</td>\n",
       "      <td>-0.006119</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000368</td>\n",
       "      <td>-0.006504</td>\n",
       "      <td> 0.019178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-14</th>\n",
       "      <td> 4399.2</td>\n",
       "      <td> 4426.5</td>\n",
       "      <td> 4115.4</td>\n",
       "      <td> 4180.6</td>\n",
       "      <td> 1309107200</td>\n",
       "      <td> 4180.6</td>\n",
       "      <td>-0.050968</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000490</td>\n",
       "      <td>-0.051353</td>\n",
       "      <td> 0.022130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-15</th>\n",
       "      <td> 4180.6</td>\n",
       "      <td> 4199.4</td>\n",
       "      <td> 4090.9</td>\n",
       "      <td> 4121.1</td>\n",
       "      <td> 1247030300</td>\n",
       "      <td> 4121.1</td>\n",
       "      <td>-0.014335</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000376</td>\n",
       "      <td>-0.014720</td>\n",
       "      <td> 0.019390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-16</th>\n",
       "      <td> 4121.1</td>\n",
       "      <td> 4251.7</td>\n",
       "      <td> 4121.1</td>\n",
       "      <td> 4147.1</td>\n",
       "      <td> 1380947500</td>\n",
       "      <td> 4147.1</td>\n",
       "      <td> 0.006289</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000367</td>\n",
       "      <td> 0.005904</td>\n",
       "      <td> 0.019168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-19</th>\n",
       "      <td> 4147.1</td>\n",
       "      <td> 4251.9</td>\n",
       "      <td> 4032.4</td>\n",
       "      <td> 4108.5</td>\n",
       "      <td> 1879365200</td>\n",
       "      <td> 4108.5</td>\n",
       "      <td>-0.009351</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000370</td>\n",
       "      <td>-0.009737</td>\n",
       "      <td> 0.019242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-20</th>\n",
       "      <td> 4108.5</td>\n",
       "      <td> 4184.3</td>\n",
       "      <td> 4060.6</td>\n",
       "      <td> 4091.4</td>\n",
       "      <td> 2078463800</td>\n",
       "      <td> 4091.4</td>\n",
       "      <td>-0.004171</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000367</td>\n",
       "      <td>-0.004556</td>\n",
       "      <td> 0.019151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-21</th>\n",
       "      <td> 4091.4</td>\n",
       "      <td> 4112.8</td>\n",
       "      <td> 4001.4</td>\n",
       "      <td> 4059.9</td>\n",
       "      <td> 2068435600</td>\n",
       "      <td> 4059.9</td>\n",
       "      <td>-0.007729</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000369</td>\n",
       "      <td>-0.008114</td>\n",
       "      <td> 0.019206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-22</th>\n",
       "      <td> 4059.9</td>\n",
       "      <td> 4153.9</td>\n",
       "      <td> 4046.4</td>\n",
       "      <td> 4052.2</td>\n",
       "      <td> 1614858900</td>\n",
       "      <td> 4052.2</td>\n",
       "      <td>-0.001898</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.002284</td>\n",
       "      <td> 0.019132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-23</th>\n",
       "      <td> 4052.2</td>\n",
       "      <td> 4070.8</td>\n",
       "      <td> 3956.7</td>\n",
       "      <td> 4052.5</td>\n",
       "      <td> 1508583500</td>\n",
       "      <td> 4052.5</td>\n",
       "      <td> 0.000074</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000311</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-26</th>\n",
       "      <td> 4052.5</td>\n",
       "      <td> 4225.2</td>\n",
       "      <td> 4039.4</td>\n",
       "      <td> 4209.0</td>\n",
       "      <td> 1524347800</td>\n",
       "      <td> 4209.0</td>\n",
       "      <td> 0.037891</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000432</td>\n",
       "      <td> 0.037506</td>\n",
       "      <td> 0.020782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-27</th>\n",
       "      <td> 4209.0</td>\n",
       "      <td> 4211.0</td>\n",
       "      <td> 4130.8</td>\n",
       "      <td> 4194.4</td>\n",
       "      <td> 1264648400</td>\n",
       "      <td> 4194.4</td>\n",
       "      <td>-0.003475</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.003860</td>\n",
       "      <td> 0.019144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-28</th>\n",
       "      <td> 4194.4</td>\n",
       "      <td> 4317.6</td>\n",
       "      <td> 4194.4</td>\n",
       "      <td> 4295.2</td>\n",
       "      <td> 1714540400</td>\n",
       "      <td> 4295.2</td>\n",
       "      <td> 0.023748</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000391</td>\n",
       "      <td> 0.023362</td>\n",
       "      <td> 0.019785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-29</th>\n",
       "      <td> 4295.2</td>\n",
       "      <td> 4295.2</td>\n",
       "      <td> 4147.7</td>\n",
       "      <td> 4190.1</td>\n",
       "      <td> 1387667200</td>\n",
       "      <td> 4190.1</td>\n",
       "      <td>-0.024774</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000396</td>\n",
       "      <td>-0.025159</td>\n",
       "      <td> 0.019888</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-30</th>\n",
       "      <td> 4190.1</td>\n",
       "      <td> 4228.0</td>\n",
       "      <td> 4125.2</td>\n",
       "      <td> 4149.6</td>\n",
       "      <td> 1496062700</td>\n",
       "      <td> 4149.6</td>\n",
       "      <td>-0.009713</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000371</td>\n",
       "      <td>-0.010098</td>\n",
       "      <td> 0.019251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-02</th>\n",
       "      <td> 4149.6</td>\n",
       "      <td> 4149.6</td>\n",
       "      <td> 4036.9</td>\n",
       "      <td> 4077.8</td>\n",
       "      <td>  929235800</td>\n",
       "      <td> 4077.8</td>\n",
       "      <td>-0.017454</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000381</td>\n",
       "      <td>-0.017840</td>\n",
       "      <td> 0.019513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-03</th>\n",
       "      <td> 4077.8</td>\n",
       "      <td> 4173.2</td>\n",
       "      <td> 4043.4</td>\n",
       "      <td> 4164.5</td>\n",
       "      <td> 1085343300</td>\n",
       "      <td> 4164.5</td>\n",
       "      <td> 0.021039</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000386</td>\n",
       "      <td> 0.020653</td>\n",
       "      <td> 0.019643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-04</th>\n",
       "      <td> 4164.5</td>\n",
       "      <td> 4262.7</td>\n",
       "      <td> 4160.4</td>\n",
       "      <td> 4228.6</td>\n",
       "      <td> 1196794000</td>\n",
       "      <td> 4228.6</td>\n",
       "      <td> 0.015275</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000376</td>\n",
       "      <td> 0.014889</td>\n",
       "      <td> 0.019396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-05</th>\n",
       "      <td> 4228.6</td>\n",
       "      <td> 4235.3</td>\n",
       "      <td> 4133.5</td>\n",
       "      <td> 4228.9</td>\n",
       "      <td> 1216188700</td>\n",
       "      <td> 4228.9</td>\n",
       "      <td> 0.000071</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000314</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-06</th>\n",
       "      <td> 4228.9</td>\n",
       "      <td> 4330.7</td>\n",
       "      <td> 4225.6</td>\n",
       "      <td> 4291.9</td>\n",
       "      <td> 1412522900</td>\n",
       "      <td> 4291.9</td>\n",
       "      <td> 0.014788</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000376</td>\n",
       "      <td> 0.014402</td>\n",
       "      <td> 0.019379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-09</th>\n",
       "      <td> 4291.9</td>\n",
       "      <td> 4334.0</td>\n",
       "      <td> 4244.0</td>\n",
       "      <td> 4307.6</td>\n",
       "      <td> 1158075200</td>\n",
       "      <td> 4307.6</td>\n",
       "      <td> 0.003651</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.003266</td>\n",
       "      <td> 0.019139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-10</th>\n",
       "      <td> 4307.6</td>\n",
       "      <td> 4309.5</td>\n",
       "      <td> 4210.5</td>\n",
       "      <td> 4213.1</td>\n",
       "      <td> 1113424800</td>\n",
       "      <td> 4213.1</td>\n",
       "      <td>-0.022182</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000390</td>\n",
       "      <td>-0.022568</td>\n",
       "      <td> 0.019742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-11</th>\n",
       "      <td> 4213.1</td>\n",
       "      <td> 4244.5</td>\n",
       "      <td> 4182.1</td>\n",
       "      <td> 4234.3</td>\n",
       "      <td>  977770500</td>\n",
       "      <td> 4234.3</td>\n",
       "      <td> 0.005019</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000367</td>\n",
       "      <td> 0.004634</td>\n",
       "      <td> 0.019152</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-21</th>\n",
       "      <td> 6681.1</td>\n",
       "      <td> 6697.7</td>\n",
       "      <td> 6643.5</td>\n",
       "      <td> 6681.3</td>\n",
       "      <td>  483785600</td>\n",
       "      <td> 6681.3</td>\n",
       "      <td> 0.000030</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000355</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-22</th>\n",
       "      <td> 6681.3</td>\n",
       "      <td> 6711.0</td>\n",
       "      <td> 6661.0</td>\n",
       "      <td> 6674.3</td>\n",
       "      <td>  495703600</td>\n",
       "      <td> 6674.3</td>\n",
       "      <td>-0.001048</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.001434</td>\n",
       "      <td> 0.019128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-25</th>\n",
       "      <td> 6674.3</td>\n",
       "      <td> 6709.1</td>\n",
       "      <td> 6674.3</td>\n",
       "      <td> 6694.6</td>\n",
       "      <td>  465826500</td>\n",
       "      <td> 6694.6</td>\n",
       "      <td> 0.003037</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.002652</td>\n",
       "      <td> 0.019134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-26</th>\n",
       "      <td> 6694.6</td>\n",
       "      <td> 6697.0</td>\n",
       "      <td> 6636.2</td>\n",
       "      <td> 6636.2</td>\n",
       "      <td>  985378000</td>\n",
       "      <td> 6636.2</td>\n",
       "      <td>-0.008762</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000370</td>\n",
       "      <td>-0.009147</td>\n",
       "      <td> 0.019228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-27</th>\n",
       "      <td> 6636.2</td>\n",
       "      <td> 6664.1</td>\n",
       "      <td> 6635.7</td>\n",
       "      <td> 6649.5</td>\n",
       "      <td>  580621900</td>\n",
       "      <td> 6649.5</td>\n",
       "      <td> 0.002002</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.001617</td>\n",
       "      <td> 0.019129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-28</th>\n",
       "      <td> 6649.5</td>\n",
       "      <td> 6679.5</td>\n",
       "      <td> 6642.6</td>\n",
       "      <td> 6654.5</td>\n",
       "      <td>  462672900</td>\n",
       "      <td> 6654.5</td>\n",
       "      <td> 0.000752</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-29</th>\n",
       "      <td> 6654.5</td>\n",
       "      <td> 6681.6</td>\n",
       "      <td> 6648.5</td>\n",
       "      <td> 6650.6</td>\n",
       "      <td>  535923900</td>\n",
       "      <td> 6650.6</td>\n",
       "      <td>-0.000586</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000972</td>\n",
       "      <td> 0.019127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-02</th>\n",
       "      <td> 6650.6</td>\n",
       "      <td> 6657.4</td>\n",
       "      <td> 6595.2</td>\n",
       "      <td> 6595.3</td>\n",
       "      <td>  559055100</td>\n",
       "      <td> 6595.3</td>\n",
       "      <td>-0.008350</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000369</td>\n",
       "      <td>-0.008735</td>\n",
       "      <td> 0.019219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-03</th>\n",
       "      <td> 6595.3</td>\n",
       "      <td> 6595.5</td>\n",
       "      <td> 6531.3</td>\n",
       "      <td> 6532.4</td>\n",
       "      <td>  685375800</td>\n",
       "      <td> 6532.4</td>\n",
       "      <td>-0.009583</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000370</td>\n",
       "      <td>-0.009968</td>\n",
       "      <td> 0.019247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-04</th>\n",
       "      <td> 6532.4</td>\n",
       "      <td> 6544.7</td>\n",
       "      <td> 6479.7</td>\n",
       "      <td> 6510.0</td>\n",
       "      <td>  780322600</td>\n",
       "      <td> 6510.0</td>\n",
       "      <td>-0.003435</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.003820</td>\n",
       "      <td> 0.019144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-05</th>\n",
       "      <td> 6510.0</td>\n",
       "      <td> 6518.9</td>\n",
       "      <td> 6487.2</td>\n",
       "      <td> 6498.3</td>\n",
       "      <td>  558155700</td>\n",
       "      <td> 6498.3</td>\n",
       "      <td>-0.001799</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.002184</td>\n",
       "      <td> 0.019132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-06</th>\n",
       "      <td> 6498.3</td>\n",
       "      <td> 6555.7</td>\n",
       "      <td> 6496.3</td>\n",
       "      <td> 6552.0</td>\n",
       "      <td>  564649300</td>\n",
       "      <td> 6552.0</td>\n",
       "      <td> 0.008230</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000369</td>\n",
       "      <td> 0.007844</td>\n",
       "      <td> 0.019201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-09</th>\n",
       "      <td> 6552.0</td>\n",
       "      <td> 6568.4</td>\n",
       "      <td> 6534.7</td>\n",
       "      <td> 6559.5</td>\n",
       "      <td>  506215400</td>\n",
       "      <td> 6559.5</td>\n",
       "      <td> 0.001144</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.000759</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-10</th>\n",
       "      <td> 6559.5</td>\n",
       "      <td> 6571.9</td>\n",
       "      <td> 6519.0</td>\n",
       "      <td> 6523.3</td>\n",
       "      <td>  553693100</td>\n",
       "      <td> 6523.3</td>\n",
       "      <td>-0.005534</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000367</td>\n",
       "      <td>-0.005919</td>\n",
       "      <td> 0.019169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-11</th>\n",
       "      <td> 6523.3</td>\n",
       "      <td> 6555.6</td>\n",
       "      <td> 6507.7</td>\n",
       "      <td> 6507.7</td>\n",
       "      <td>  524482100</td>\n",
       "      <td> 6507.7</td>\n",
       "      <td>-0.002394</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.002780</td>\n",
       "      <td> 0.019135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-12</th>\n",
       "      <td> 6507.7</td>\n",
       "      <td> 6507.7</td>\n",
       "      <td> 6436.0</td>\n",
       "      <td> 6445.3</td>\n",
       "      <td>  663531400</td>\n",
       "      <td> 6445.3</td>\n",
       "      <td>-0.009635</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000371</td>\n",
       "      <td>-0.010020</td>\n",
       "      <td> 0.019249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-13</th>\n",
       "      <td> 6445.3</td>\n",
       "      <td> 6462.8</td>\n",
       "      <td> 6433.5</td>\n",
       "      <td> 6440.0</td>\n",
       "      <td>  694450900</td>\n",
       "      <td> 6440.0</td>\n",
       "      <td>-0.000823</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.001208</td>\n",
       "      <td> 0.019127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-16</th>\n",
       "      <td> 6440.0</td>\n",
       "      <td> 6531.2</td>\n",
       "      <td> 6422.2</td>\n",
       "      <td> 6522.2</td>\n",
       "      <td>  653797800</td>\n",
       "      <td> 6522.2</td>\n",
       "      <td> 0.012683</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000373</td>\n",
       "      <td> 0.012298</td>\n",
       "      <td> 0.019311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-17</th>\n",
       "      <td> 6522.2</td>\n",
       "      <td> 6522.2</td>\n",
       "      <td> 6482.6</td>\n",
       "      <td> 6486.2</td>\n",
       "      <td>  584054600</td>\n",
       "      <td> 6486.2</td>\n",
       "      <td>-0.005535</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000367</td>\n",
       "      <td>-0.005920</td>\n",
       "      <td> 0.019169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-18</th>\n",
       "      <td> 6486.2</td>\n",
       "      <td> 6524.5</td>\n",
       "      <td> 6486.2</td>\n",
       "      <td> 6492.1</td>\n",
       "      <td>  529477900</td>\n",
       "      <td> 6492.1</td>\n",
       "      <td> 0.000909</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.000524</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-19</th>\n",
       "      <td> 6492.1</td>\n",
       "      <td> 6584.7</td>\n",
       "      <td> 6492.1</td>\n",
       "      <td> 6584.7</td>\n",
       "      <td>  648648400</td>\n",
       "      <td> 6584.7</td>\n",
       "      <td> 0.014163</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000375</td>\n",
       "      <td> 0.013777</td>\n",
       "      <td> 0.019357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-20</th>\n",
       "      <td> 6584.7</td>\n",
       "      <td> 6616.8</td>\n",
       "      <td> 6576.8</td>\n",
       "      <td> 6606.6</td>\n",
       "      <td> 1096668200</td>\n",
       "      <td> 6606.6</td>\n",
       "      <td> 0.003320</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.002935</td>\n",
       "      <td> 0.019136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-23</th>\n",
       "      <td> 6606.6</td>\n",
       "      <td> 6678.6</td>\n",
       "      <td> 6606.2</td>\n",
       "      <td> 6678.6</td>\n",
       "      <td>  351999300</td>\n",
       "      <td> 6678.6</td>\n",
       "      <td> 0.010839</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000371</td>\n",
       "      <td> 0.010454</td>\n",
       "      <td> 0.019259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-24</th>\n",
       "      <td> 6678.6</td>\n",
       "      <td> 6712.1</td>\n",
       "      <td> 6672.2</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td>  101669600</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 0.002333</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.001948</td>\n",
       "      <td> 0.019130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-25</th>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td>          0</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 0.000000</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000385</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-26</th>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td>          0</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 0.000000</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000385</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-27</th>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 6754.1</td>\n",
       "      <td> 6694.2</td>\n",
       "      <td> 6750.9</td>\n",
       "      <td>  291262200</td>\n",
       "      <td> 6750.9</td>\n",
       "      <td> 0.008434</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000369</td>\n",
       "      <td> 0.008049</td>\n",
       "      <td> 0.019205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-30</th>\n",
       "      <td> 6750.9</td>\n",
       "      <td> 6768.4</td>\n",
       "      <td> 6718.2</td>\n",
       "      <td> 6731.3</td>\n",
       "      <td>  295360600</td>\n",
       "      <td> 6731.3</td>\n",
       "      <td>-0.002908</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td> 0.019139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-31</th>\n",
       "      <td> 6731.3</td>\n",
       "      <td> 6757.0</td>\n",
       "      <td> 6731.3</td>\n",
       "      <td> 6749.1</td>\n",
       "      <td>  153445200</td>\n",
       "      <td> 6749.1</td>\n",
       "      <td> 0.002641</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td> 0.002256</td>\n",
       "      <td> 0.019132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-01-01</th>\n",
       "      <td> 6749.1</td>\n",
       "      <td> 6749.1</td>\n",
       "      <td> 6749.1</td>\n",
       "      <td> 6749.1</td>\n",
       "      <td>          0</td>\n",
       "      <td> 6749.1</td>\n",
       "      <td> 0.000000</td>\n",
       "      <td> 0.000385</td>\n",
       "      <td> 0.000366</td>\n",
       "      <td>-0.000385</td>\n",
       "      <td> 0.019126</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1305 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              Open    High     Low   Close      Volume  AdjustedClose  \\\n",
       "Date                                                                    \n",
       "2009-01-01  4434.2  4434.2  4434.2  4434.2           0         4434.2   \n",
       "2009-01-02  4434.2  4561.8  4430.0  4561.8   407295500         4561.8   \n",
       "2009-01-05  4561.8  4618.1  4520.8  4579.6   836676100         4579.6   \n",
       "2009-01-06  4579.6  4675.7  4562.0  4638.9  1036086000         4638.9   \n",
       "2009-01-07  4638.9  4638.9  4478.0  4507.5  1059568400         4507.5   \n",
       "2009-01-08  4507.5  4514.7  4410.5  4505.4   923008000         4505.4   \n",
       "2009-01-09  4505.4  4534.8  4431.9  4448.5   979530100         4448.5   \n",
       "2009-01-12  4448.5  4471.3  4402.3  4426.2   785473900         4426.2   \n",
       "2009-01-13  4426.2  4426.2  4321.3  4399.2   928429000         4399.2   \n",
       "2009-01-14  4399.2  4426.5  4115.4  4180.6  1309107200         4180.6   \n",
       "2009-01-15  4180.6  4199.4  4090.9  4121.1  1247030300         4121.1   \n",
       "2009-01-16  4121.1  4251.7  4121.1  4147.1  1380947500         4147.1   \n",
       "2009-01-19  4147.1  4251.9  4032.4  4108.5  1879365200         4108.5   \n",
       "2009-01-20  4108.5  4184.3  4060.6  4091.4  2078463800         4091.4   \n",
       "2009-01-21  4091.4  4112.8  4001.4  4059.9  2068435600         4059.9   \n",
       "2009-01-22  4059.9  4153.9  4046.4  4052.2  1614858900         4052.2   \n",
       "2009-01-23  4052.2  4070.8  3956.7  4052.5  1508583500         4052.5   \n",
       "2009-01-26  4052.5  4225.2  4039.4  4209.0  1524347800         4209.0   \n",
       "2009-01-27  4209.0  4211.0  4130.8  4194.4  1264648400         4194.4   \n",
       "2009-01-28  4194.4  4317.6  4194.4  4295.2  1714540400         4295.2   \n",
       "2009-01-29  4295.2  4295.2  4147.7  4190.1  1387667200         4190.1   \n",
       "2009-01-30  4190.1  4228.0  4125.2  4149.6  1496062700         4149.6   \n",
       "2009-02-02  4149.6  4149.6  4036.9  4077.8   929235800         4077.8   \n",
       "2009-02-03  4077.8  4173.2  4043.4  4164.5  1085343300         4164.5   \n",
       "2009-02-04  4164.5  4262.7  4160.4  4228.6  1196794000         4228.6   \n",
       "2009-02-05  4228.6  4235.3  4133.5  4228.9  1216188700         4228.9   \n",
       "2009-02-06  4228.9  4330.7  4225.6  4291.9  1412522900         4291.9   \n",
       "2009-02-09  4291.9  4334.0  4244.0  4307.6  1158075200         4307.6   \n",
       "2009-02-10  4307.6  4309.5  4210.5  4213.1  1113424800         4213.1   \n",
       "2009-02-11  4213.1  4244.5  4182.1  4234.3   977770500         4234.3   \n",
       "...            ...     ...     ...     ...         ...            ...   \n",
       "2013-11-21  6681.1  6697.7  6643.5  6681.3   483785600         6681.3   \n",
       "2013-11-22  6681.3  6711.0  6661.0  6674.3   495703600         6674.3   \n",
       "2013-11-25  6674.3  6709.1  6674.3  6694.6   465826500         6694.6   \n",
       "2013-11-26  6694.6  6697.0  6636.2  6636.2   985378000         6636.2   \n",
       "2013-11-27  6636.2  6664.1  6635.7  6649.5   580621900         6649.5   \n",
       "2013-11-28  6649.5  6679.5  6642.6  6654.5   462672900         6654.5   \n",
       "2013-11-29  6654.5  6681.6  6648.5  6650.6   535923900         6650.6   \n",
       "2013-12-02  6650.6  6657.4  6595.2  6595.3   559055100         6595.3   \n",
       "2013-12-03  6595.3  6595.5  6531.3  6532.4   685375800         6532.4   \n",
       "2013-12-04  6532.4  6544.7  6479.7  6510.0   780322600         6510.0   \n",
       "2013-12-05  6510.0  6518.9  6487.2  6498.3   558155700         6498.3   \n",
       "2013-12-06  6498.3  6555.7  6496.3  6552.0   564649300         6552.0   \n",
       "2013-12-09  6552.0  6568.4  6534.7  6559.5   506215400         6559.5   \n",
       "2013-12-10  6559.5  6571.9  6519.0  6523.3   553693100         6523.3   \n",
       "2013-12-11  6523.3  6555.6  6507.7  6507.7   524482100         6507.7   \n",
       "2013-12-12  6507.7  6507.7  6436.0  6445.3   663531400         6445.3   \n",
       "2013-12-13  6445.3  6462.8  6433.5  6440.0   694450900         6440.0   \n",
       "2013-12-16  6440.0  6531.2  6422.2  6522.2   653797800         6522.2   \n",
       "2013-12-17  6522.2  6522.2  6482.6  6486.2   584054600         6486.2   \n",
       "2013-12-18  6486.2  6524.5  6486.2  6492.1   529477900         6492.1   \n",
       "2013-12-19  6492.1  6584.7  6492.1  6584.7   648648400         6584.7   \n",
       "2013-12-20  6584.7  6616.8  6576.8  6606.6  1096668200         6606.6   \n",
       "2013-12-23  6606.6  6678.6  6606.2  6678.6   351999300         6678.6   \n",
       "2013-12-24  6678.6  6712.1  6672.2  6694.2   101669600         6694.2   \n",
       "2013-12-25  6694.2  6694.2  6694.2  6694.2           0         6694.2   \n",
       "2013-12-26  6694.2  6694.2  6694.2  6694.2           0         6694.2   \n",
       "2013-12-27  6694.2  6754.1  6694.2  6750.9   291262200         6750.9   \n",
       "2013-12-30  6750.9  6768.4  6718.2  6731.3   295360600         6731.3   \n",
       "2013-12-31  6731.3  6757.0  6731.3  6749.1   153445200         6749.1   \n",
       "2014-01-01  6749.1  6749.1  6749.1  6749.1           0         6749.1   \n",
       "\n",
       "            log_returns      mean  variance  residual  volatility  \n",
       "Date                                                               \n",
       "2009-01-01     0.000000  0.000385  0.000366 -0.000385    0.019126  \n",
       "2009-01-02     0.028370  0.000385  0.000403  0.027985    0.020065  \n",
       "2009-01-05     0.003894  0.000385  0.000366  0.003509    0.019141  \n",
       "2009-01-06     0.012866  0.000385  0.000373  0.012480    0.019316  \n",
       "2009-01-07    -0.028735  0.000385  0.000406 -0.029120    0.020141  \n",
       "2009-01-08    -0.000466  0.000385  0.000366 -0.000851    0.019127  \n",
       "2009-01-09    -0.012710  0.000385  0.000374 -0.013095    0.019335  \n",
       "2009-01-12    -0.005026  0.000385  0.000367 -0.005411    0.019162  \n",
       "2009-01-13    -0.006119  0.000385  0.000368 -0.006504    0.019178  \n",
       "2009-01-14    -0.050968  0.000385  0.000490 -0.051353    0.022130  \n",
       "2009-01-15    -0.014335  0.000385  0.000376 -0.014720    0.019390  \n",
       "2009-01-16     0.006289  0.000385  0.000367  0.005904    0.019168  \n",
       "2009-01-19    -0.009351  0.000385  0.000370 -0.009737    0.019242  \n",
       "2009-01-20    -0.004171  0.000385  0.000367 -0.004556    0.019151  \n",
       "2009-01-21    -0.007729  0.000385  0.000369 -0.008114    0.019206  \n",
       "2009-01-22    -0.001898  0.000385  0.000366 -0.002284    0.019132  \n",
       "2009-01-23     0.000074  0.000385  0.000366 -0.000311    0.019126  \n",
       "2009-01-26     0.037891  0.000385  0.000432  0.037506    0.020782  \n",
       "2009-01-27    -0.003475  0.000385  0.000366 -0.003860    0.019144  \n",
       "2009-01-28     0.023748  0.000385  0.000391  0.023362    0.019785  \n",
       "2009-01-29    -0.024774  0.000385  0.000396 -0.025159    0.019888  \n",
       "2009-01-30    -0.009713  0.000385  0.000371 -0.010098    0.019251  \n",
       "2009-02-02    -0.017454  0.000385  0.000381 -0.017840    0.019513  \n",
       "2009-02-03     0.021039  0.000385  0.000386  0.020653    0.019643  \n",
       "2009-02-04     0.015275  0.000385  0.000376  0.014889    0.019396  \n",
       "2009-02-05     0.000071  0.000385  0.000366 -0.000314    0.019126  \n",
       "2009-02-06     0.014788  0.000385  0.000376  0.014402    0.019379  \n",
       "2009-02-09     0.003651  0.000385  0.000366  0.003266    0.019139  \n",
       "2009-02-10    -0.022182  0.000385  0.000390 -0.022568    0.019742  \n",
       "2009-02-11     0.005019  0.000385  0.000367  0.004634    0.019152  \n",
       "...                 ...       ...       ...       ...         ...  \n",
       "2013-11-21     0.000030  0.000385  0.000366 -0.000355    0.019126  \n",
       "2013-11-22    -0.001048  0.000385  0.000366 -0.001434    0.019128  \n",
       "2013-11-25     0.003037  0.000385  0.000366  0.002652    0.019134  \n",
       "2013-11-26    -0.008762  0.000385  0.000370 -0.009147    0.019228  \n",
       "2013-11-27     0.002002  0.000385  0.000366  0.001617    0.019129  \n",
       "2013-11-28     0.000752  0.000385  0.000366  0.000366    0.019126  \n",
       "2013-11-29    -0.000586  0.000385  0.000366 -0.000972    0.019127  \n",
       "2013-12-02    -0.008350  0.000385  0.000369 -0.008735    0.019219  \n",
       "2013-12-03    -0.009583  0.000385  0.000370 -0.009968    0.019247  \n",
       "2013-12-04    -0.003435  0.000385  0.000366 -0.003820    0.019144  \n",
       "2013-12-05    -0.001799  0.000385  0.000366 -0.002184    0.019132  \n",
       "2013-12-06     0.008230  0.000385  0.000369  0.007844    0.019201  \n",
       "2013-12-09     0.001144  0.000385  0.000366  0.000759    0.019126  \n",
       "2013-12-10    -0.005534  0.000385  0.000367 -0.005919    0.019169  \n",
       "2013-12-11    -0.002394  0.000385  0.000366 -0.002780    0.019135  \n",
       "2013-12-12    -0.009635  0.000385  0.000371 -0.010020    0.019249  \n",
       "2013-12-13    -0.000823  0.000385  0.000366 -0.001208    0.019127  \n",
       "2013-12-16     0.012683  0.000385  0.000373  0.012298    0.019311  \n",
       "2013-12-17    -0.005535  0.000385  0.000367 -0.005920    0.019169  \n",
       "2013-12-18     0.000909  0.000385  0.000366  0.000524    0.019126  \n",
       "2013-12-19     0.014163  0.000385  0.000375  0.013777    0.019357  \n",
       "2013-12-20     0.003320  0.000385  0.000366  0.002935    0.019136  \n",
       "2013-12-23     0.010839  0.000385  0.000371  0.010454    0.019259  \n",
       "2013-12-24     0.002333  0.000385  0.000366  0.001948    0.019130  \n",
       "2013-12-25     0.000000  0.000385  0.000366 -0.000385    0.019126  \n",
       "2013-12-26     0.000000  0.000385  0.000366 -0.000385    0.019126  \n",
       "2013-12-27     0.008434  0.000385  0.000369  0.008049    0.019205  \n",
       "2013-12-30    -0.002908  0.000385  0.000366 -0.003293    0.019139  \n",
       "2013-12-31     0.002641  0.000385  0.000366  0.002256    0.019132  \n",
       "2014-01-01     0.000000  0.000385  0.000366 -0.000385    0.019126  \n",
       "\n",
       "[1305 rows x 11 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ftse_data # Reviewing data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Actual calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value at Risk is $44461.52\n"
     ]
    }
   ],
   "source": [
    "confidence_level = 0.99\n",
    "quantile= 1.0 - confidence_level\n",
    "volwindow = 10 # 10 day volatility\n",
    "varwindow = 21 # we need 21 day rolling VaR\n",
    "#21 day rolling VaR \n",
    "unnormedquantileR = pd.rolling_quantile(ftse_data['volatility'],varwindow,quantile)\n",
    "\n",
    "returns_2=ftse_data['volatility'].shift(-1)\n",
    "\n",
    "all_data_frame=pd.DataFrame({'returns':returns_2,\n",
    "              'Rolling quantiles':unnormedquantileR\n",
    "              })\n",
    "\n",
    "portfolio_value = 1e6\n",
    "concidence_level = 0.99\n",
    "alpha = norm.ppf(1- concidence_level, mean, returns_2.mean())\n",
    "var = portfolio_value - portfolio_value*(alpha + 1)\n",
    "print \"Value at Risk is $%0.2f\" % var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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