Time Series Modelling with Python Master.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time Series Modelling\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We follow the notations of Tsay R. (2010) *Analysis of Financial Time Series*. John Wiley & Sons, Inc., Hoboken, New Jersey.\n",
    "\n",
    "The following notebook is an adaptation of Tsay's book except the codes are written in Python\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Characteristics of Time Series\n",
    "\n",
    "Price or returns: Campbell, Lo, and MacKinlay (1997) provided two reasons for using returns:\n",
    "1. Return of an asset provide complete information and it is also scale-free.        \n",
    "2. Return series have more attractive statistical properties."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "1.\n",
    "\n",
    "2.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[pandas-datareader](http://pandas-datareader.readthedocs.io/en/latest/index.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np  \n",
    "import pandas as pd  \n",
    "import matplotlib.pyplot as plt  \n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "from pandas_datareader import data, wb\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "start = datetime.datetime(2001, 1, 1)\n",
    "end = datetime.datetime(2010, 1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's download some data from Yahoo to play with. `^GSPC` is yahoo ticker code for S&P500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = data.DataReader(\"^GSPC\", 'yahoo', start, end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we start, let's convert the data frequency to annual.\n",
    "\n",
    "[pandas documentation](http://pandas.pydata.org/pandas-docs/stable/timeseries.html#up-and-downsampling)\n",
    "\n",
    "[stackoverflow example](https://stackoverflow.com/questions/17001389/pandas-resample-documentation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>1161.020020</td>\n",
       "      <td>1161.160034</td>\n",
       "      <td>1148.040039</td>\n",
       "      <td>1148.079956</td>\n",
       "      <td>1148.079956</td>\n",
       "      <td>9.436000e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.390015</td>\n",
       "      <td>881.929993</td>\n",
       "      <td>869.450012</td>\n",
       "      <td>879.820007</td>\n",
       "      <td>879.820007</td>\n",
       "      <td>1.088500e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1109.640015</td>\n",
       "      <td>1112.560059</td>\n",
       "      <td>1106.209961</td>\n",
       "      <td>1111.920044</td>\n",
       "      <td>1111.920044</td>\n",
       "      <td>1.027500e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1213.550049</td>\n",
       "      <td>1217.329956</td>\n",
       "      <td>1211.650024</td>\n",
       "      <td>1211.920044</td>\n",
       "      <td>1211.920044</td>\n",
       "      <td>7.869000e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1254.420044</td>\n",
       "      <td>1254.420044</td>\n",
       "      <td>1246.589966</td>\n",
       "      <td>1248.290039</td>\n",
       "      <td>1248.290039</td>\n",
       "      <td>1.443500e+09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Open         High          Low        Close    Adj Close  \\\n",
       "Date                                                                          \n",
       "2001-12-31  1161.020020  1161.160034  1148.040039  1148.079956  1148.079956   \n",
       "2002-12-31   879.390015   881.929993   869.450012   879.820007   879.820007   \n",
       "2003-12-31  1109.640015  1112.560059  1106.209961  1111.920044  1111.920044   \n",
       "2004-12-31  1213.550049  1217.329956  1211.650024  1211.920044  1211.920044   \n",
       "2005-12-30  1254.420044  1254.420044  1246.589966  1248.290039  1248.290039   \n",
       "\n",
       "                  Volume  \n",
       "Date                      \n",
       "2001-12-31  9.436000e+08  \n",
       "2002-12-31  1.088500e+09  \n",
       "2003-12-31  1.027500e+09  \n",
       "2004-12-31  7.869000e+08  \n",
       "2005-12-30  1.443500e+09  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = f.resample('BA').asfreq() # Resample to yearly data. Use last business day price\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Oaz45w5YDFdw3ycT8mb47JyHQ2umLTlc089rqQ8yalMGCmcO8+l6B3la+otrtIyGCxbnq\ny3x8sILkuGjmThukdjkBJSP5yh5IMgMp6EgoiJDU4XDxzsYSFAW+PXskkeH+OePNX0VHhpESH0NZ\nrQU/u9kg+khCQYSkD3eXUt1g5c7x6YwwxaldTkDKSjXSZnNQf7ld7VKEB0koiJBTXmtm494y4mMj\neeSOIWqXE7DkzObgJKEgQorT5eKdTSU4XQpPzBpJdGSvluoIrp6tUCqhEFQkFERI2bK/grIaM5NH\np5IzJEHtcgKaqWsPJNlGO6hIKIiQUdPYyvs7LxAbE87jd3t3GmUo0EeFk9gvirIasww2BxEJBRES\nXIrCOxtP0uFw8Y17R2CIDle7pKCQlWrE0tZBk9mmdinCQyQUREjYdqiKM5WXyR2exIQRSWqXEzRk\nG+3gI6Eggl7D5Tb+vP0cMZFhfPPe4XLesge5t9GWcYWgIaEggpqiKPzf5lPY7E4eu2sY/Q2RapcU\nVExXQkFmIAUPmY8ngpKiKJTXWthxpJpjFxoZPSieKbekql1W0InVRxBnjJSeQhCRUBBBQ1EUSmvM\nHCyp4+CpOuqbO1faxsaE861ZI+S2kZdkphg5fLaBZotNemJBQEJBBDSXonC+uoWDJXUUnarjUkvn\nLJjICB2TRiUzcWQyYwYnyN5GXpSV2hkK5bVmCYUgIKEgAo7LpXC26nJnEJyud0+HjI7UMXl0ChNG\nJDN6UDwREgQ+YfrcDKScIYkqVyP6SkJBBASXS+F0RTMHT9VRdKqey1Y7ADGRYUy5JZUJI5LJzoon\nPEzmTvhapgw2BxUJBeG3nC4XJeXNFJXUceh0PS2tHQAYosOZPjaNCSOSGZkZJ6elqay/IYJYfQTl\nMtgcFCQUhF9xOF2cLGviYEkdn51pwNLWGQSxMeHcMT6dCSOSGGHqj04rQeAvNBoNmSlGjp6/hLnV\njjEmQu2SRB9IKAjVdThcnChtdAdBq80BQD99BDNz05kwIpnhGf3RamX2kL/KTDVw9PwlymstjB4U\nr3Y5og8kFIQq7B1Ojl9o5OCpOg6fbaDN5gQgzhjJ7VfGCIYO7IdWppEGhMyUWKBzZbOEQmCTUBA+\nY+twcvTcJQ6eqqP43CVs9s4gSIiNYvrYAUwYkcygAbESBAEoM1XObA4WEgrCq9rtDo6cu8TBkjqO\nnL+EvcMFQFL/KCZcuTWUlWqUhWUBLiE2Cn1UmIRCEJBQEB7XZnNw+GwDB0vqOHahkQ5HZxCkxEUz\nYWQyE0YkY0oxSBAEEY1GQ2aqkROlTbS2dxATJVuTByoJBeExxy80suPvJzh0qhaHs/PQlQGJeiaM\nSGLCiGTSk/QSBEEsM6UzFMprLYzMjFO7HNFLEgrCI7YdqmTVltMowMAkAxNGJpE3Ipn0RL3apQkf\nyfzc8ZwSCoFLQkH0iaIovL/jAut3l2KMCecX37mNBL3cOghFmXJmc1Do0Qqg4uJi8vPzATh58iQL\nFy4kPz+f73znOzQ0NACwbt065s2bx/z589m2bRsAjY2NLFq0iIULF7J48WLa2tq8dBlCDU6Xiz9u\nPsX63aUk9Y9iSX4eI7NkOmKoSuofTXSkTgabA1y3obBixQqWLl2Kzda56diyZcv4+c9/zsqVK7nn\nnntYsWIF9fX1rFy5kjVr1vD2229TUFCA3W7nrbfeYs6cObz77rtkZ2ezdu1ar1+Q8A17h5P//Osx\nCourMaUYWPLNPFLiYtQuS6hIq9FgSjZSc6mVdrtD7XJEL3V7+8hkMrF8+XJ+8pOfAFBQUEBycjIA\nTqeTyMhIjhw5wvjx44mIiCAiIgKTyURJSQlFRUU89dRTAEyfPp2CggKefPLJG75fXFwMYWH+ubtl\nUpJR7RL8grnVzm/e3sfJ0kbGDktkyZOTrpltIu3UM8HYTiMHJXCqohmz3UVGuueuLxjbyl91Gwqz\nZs2isrLS/XVXIBw6dIhVq1axevVqduzYgdF49Yem1+uxWCxYLBb343q9HrO5+25lU1PrTV+ELyQl\nGamvl25xY0s7BeuKqW6wMmlUMt95IBuruR2rufNAG2mnngnWdkqO7TxPobikliSDZ/ZACta28jRP\nBWevBpo3btzI7373O37/+98THx+PwWDAarW6/91qtWI0Gt2PR0VFYbVaiY2N9UjRQh1VDVb+fd1h\nGlts3D1hII/dNUxWH4tryGBz4LvprSY/+OADVq1axcqVK8nIyAAgJyeHoqIibDYbZrOZc+fOMXz4\ncHJzc9m+fTsAhYWF5OXlebZ64TNnKy/z2qoiGltsPHLHEB6XQBBfITU+hohwLWU1FrVLEb10Uz0F\np9PJsmXLSEtL45lnngFg4sSJPPvss+Tn57Nw4UIUReG5554jMjKSp59+mhdeeIF169YRFxfHG2+8\n4ZWLEN51+EwD//XBMRxOhUX3j2JqTpraJQk/pdV2Djafr27B3uGU0+8CkEZRFEXtIj7PX+8dhup9\nzcLiav5v8ynCdBqefmgMY4fe+LjFUG2nmxXM7bR6y2k+OVTJ0icmMHhA328ZB3NbeZKnxhTkpBLx\nlRRFYf3uUv6wqYToSB0/fnx8t4EgBICpa8dUGVcISLKiWXyJy6Xw7j9Os/VQFQmxkTy/YBxpCbJd\nheiZrjObZRFbYJJQENfocLhYsf44B0/Vk56k5/n544gzRqpdlgggAxL1hOm00lMIUBIKwq213cGb\nfz1CSXkzwwf249lHcmQLZHHTwnRaMpL1VNRZcDhdhOnkLnUgkZ+WAKDZYuPf3j1ESXkzucOTeH7B\nOAkE0WuZKUYcToWqemv3TxZ+RXoKgprGVgrWHqbhcjt3jBvAN+8dgVYraxBE75k+t4ita0GbCAwS\nCiHuwsUW/n1dMZa2DuZOHcSDU7LkIBzRZ+7BZhlXCDgSCiHs2PlL/OffjmF3OHli1gjuGJ+udkki\nSAxM0qPTaiiXGUgBR0IhRO05VsP/bjyJRqPh+w/dQt6IJLVLEkEkPExHemLnYLPT5UKnleHLQCE/\nqRC0eV85Kz48QUS4jh8uGCuBILzClGrE7nBRc8k/dz4WX01CIYS4FIW1W8+wbttZ+hsi+Nk3chlh\nkrN0hXd0jSuUyi2kgOJ3ofDU659ytuqy2mUEHYfTxf98eIKP9leQlhDDkvw8BiYb1C5LBDHZRjsw\n+V0odDhcfLSvXO0ygkq73cFv/3yEvcdrGTIglp99M4/EftFqlyWCXEayAY0GGWwOMH430GxKMfDZ\nmQYaW9qJj41Su5yA12K18x/vFVNaYyZnSAJPzx1DZIRsZyy8LzJcx4AEPWV1FlyKIudvBAi/6ynM\nzB2IS1EoLK5Wu5SAV9fcxquriiitMTPlllR+MO8WCQThU6YUIza7k7qmNrVLET3kd6Fw66gUoiPD\n2F5cjcPpUrucgFVea+bVlUXUNbXxwORMFt0/SvagET7XNa5QWtOiciWip/zuf4nICB1TxqRy2WLn\n8JkGtcsJSCdLG3lt9SHMVjuP3z2Mh2cMkVXKQhWZKZ2TGcrleM6A4XehAHBnbufK2q2HKlWuJPDs\nP1nLv79XTIfDxVNzR3PPhAy1SxIhzCTbXQQcvwyFtAQ9ozLjKClvprpBdlnsqU+KKvnvD44TptPy\n3PyxTBqVonZJIsRFR4aREhdNWY0ZPzv5V1yHX4YCwJ1X9uH59LMqlSvxf4qi8Jft51j98WmM+ghe\nWJhLdla82mUJAXSOK7TaHDRcble7FNEDfhsK44Yl0s8Qwa5jF7HZnWqX47ecLhfvbCphw54ykvtH\nsyQ/T7YqFn7FvYhN1isEBL8NhTCdlhljB9Bmc7L3RI3a5fglW4eTN/9ylJ1HLpKZamRJfh7J/WVR\nmvAvso12YPHbUACYMS4drUbDtkNVcj/yCyxtHby+5jOKz11idFYcP3l8PLH6CLXLEuJL3IPNQdJT\n+P364/znX4+qXYbX+HUoxBkjGT8skfI6C+erZZ5zF4fTxa/fPcS5qhZuzU7hXx4dS3Sk3y1OFwIA\nQ3Q4if2iKKsN/MHmE6WN7D1eG9RrqPw6FODz01NlwLnLnuM1VNZbmTw6hf/va9myKE34vcwUI+bW\nDprMNrVL6TVFUfhr4XkA5k4bpHI13tOj/02Ki4vJz8+/5rFXX32VP/3pT+6v161bx7x585g/fz7b\ntm0DoLGxkUWLFrFw4UIWL15MW9vNL3UflRlHSnwMB0rqMLfab/r7g43LpbBxbzk6rYaHZwyR/WRE\nQAiGHVMPn23gfHULeSOSyEqNVbscr+k2FFasWMHSpUux2ToTvrGxke9+97ts3brV/Zz6+npWrlzJ\nmjVrePvttykoKMBut/PWW28xZ84c3n33XbKzs1m7du1NF6jRaLhzfDoOp4udRy/e9PcHm4On6qht\nbOX2MamyYaAIGIE+A8mlKPyt8DwaDTw0bbDa5XhVt6FgMplYvny5+2ur1cozzzzD3Llz3Y8dOXKE\n8ePHExERgdFoxGQyUVJSQlFREdOmTQNg+vTp7N69u1dFTrkllYgwLdsOVeEK8HuSfaEoChv2lKHR\nwP23ZapdjhA9FuiDzftP1lJZb+X20amkJ+rVLseruh2dnDVrFpWVV7ebyMjIICMjg8LCQvdjFosF\no/Hq3Hi9Xo/FYrnmcb1ej9nc/S9EXFwMYWHX7uSZBMzIHcjH+8upuNTGBJVW6iYlqTv//+DJWirq\nLEwfl86YEf67WlntdgoUodROSUmQ0C+Kinprr65bzbZyOF2s311GmE7Dkw+OISkhxEOhJwwGA1br\n1e0orFYrRqPR/XhUVBRWq5XY2O7vwzU1ffV5rpOzk/l4fzkffHqWzMQYT5R9U5KSjNTXq/cpR1EU\nVm86CcBduemq1nIjardToAjFdspIMnD4bANnLzTQzxDZ4+9Tu622H67iYoOVmbnp6Fwuv/25eSo4\nPTJtJScnh6KiImw2G2azmXPnzjF8+HByc3PZvn07AIWFheTl5fX6PbJSYxmUFkvx2QYamkNvb/bT\nFc2crbrM2CEJZMgxmiIAXR1sDpwdUzscTv6+q5SIMC1zbs9Suxyf8EgoJCUlkZ+fz8KFC/nWt77F\nc889R2RkJE8//TQbNmzgscce47PPPuOb3/xmn95nZm46CrA9BA/g2bCnDIAHQuQXUwSfQFzZvO1Q\nFU1mG3flDaT/TfRuAlmPbh8NHDiQdevWXfPYM888c83X8+fPZ/78+dc8lpiYyNtvv93HEq+aODKZ\nNZ+cYUdxNQ9OGUR4WGjMz79wsYVjFxoZaerP0PR+apcjRK8E2gykNpuDDXvLiI7UMTuEJnYE1P+q\nEeE6puak0dLaQdHpOrXL8ZmNXb2EyVnqFiJEH/Q3RBAbEx4wofCPgxWYWzuYNcmEITpc7XJ8JqBC\nAeCOK1tqbwuRFc5VDVaKTtczKM1Idlac2uUI0WsajQZTqpFLLe1Y2jrULueGLG0dbN5fjiE6POQO\nqgq4UEiJi2H0oHjOVF6msi5wBqx6a9Peq70EOVJTBLpAGVfYtK+MNpuTOZMzQ25fsYALBYCZXb2F\nID+Ap6G5jb3HaxmQqGfcsES1yxGiz7KujCuU+/EtpGaLjU8OVhJnjHTvvRZKAjIUcoYmEB8bye7j\nNbTZHGqX4zWb9pfjUhQeuC1T9jgSQSEQegof7i7F7nDxtSlZhH9hIW0oCMhQ0Gk7D+Cx2Z3sOR6c\nB/A0W2zsKL5IYr8oJmUnq12OEB6R0C8KfVQYpX7aU2hobmP74WqS+0cz9ZY0tctRRUCGAsD0sQPQ\naTVs+yw4D+DZcqACh9PF7Nsy0WkD9sckxDU0Gg2mFCN1TW20tvtfL/+DXRdwuhQemjYoZLekD9ir\n7meIJG9EElX1Vs5UXla7HI+ytHWw7bMq+hkimHpLqtrlCOFRXesVKur8q7dQ3WBl97EaBibpmZTt\nv3uLeVvAhgLAneO7DuCp7OaZgWVrUSU2u5NZE00heU9TBLdMP90x9f0d51EU+Pr0wSE9hhfQoTA8\noz/piXqKTtVz2RocB/C02x18fLACfVQYd4wfoHY5Qnhclh8euFNa08LBU/UMSotl3NDQnukX0KGg\n0Wi4Y3w6TpfCjiDZD2n74Wqs7Q7unpBBVERozY8WoSEpLpqoCJ1fbYzXdczmwzMGh/x6oIAOBYDb\nx6QSGa5j++EqXK7AHnDucDjZvL+cyHAdd+UNVLscIbxCe2Ww+eIlKza7U+1yOF3RzLHzjYzKjCM7\nK17tclQX8KEQHRnG5NEpXGpB6QfsAAAWc0lEQVSxceTcJbXL6ZNdR2u4bLFz5/j0kNprRYSezBQj\nigIVKu9KoCgKf9l+DoB504P7mM2eCvhQgKv7IW39LHAHnJ0uFxv3lhGm03LvpNDaa0WEnszUzjNB\n1B5XOHahkTOVlxk3NJEhsgMxECShYEoxMnRgP46db6TuOie3+bv9J+touNzOtJy0kNm3XYQuf5iB\n5LrSS9DQOeNIdAqKUICr01M/PRx4A84uRWHjnjK0Gg333WpSuxwhvC4tQU9EmFbVnsKhU/WU11qY\nlJ0ipxl+TtCEwoQRyRiiw9lRXI29Q/3Bq5tRfKaBqgYrt2ankNQ/Wu1yhPA6rVZDRoqB6gYrHQ7f\n/726XAp/23EerUbDQ1MH+fz9/VnQhEJ4mJbpYwdgbXdwoCRwDuBRFIUP95QCcP/k0DndSYjMFCNO\nl0JlvdXn773neA0XL7UyNSeNlPgYn7+/PwuaUAC4Y9wANATWltonypq4cNFM7vAk0hP1apcjhM+o\nNa7Q4XDx/o4LhOm0PDgly6fvHQiCKhQS+0dzy5AEzle3+N0S+uvZsLsUgAeklyBCTKZKK5sLi6u5\n1NLOzNx04mOjfPregSCoQgFgZm7XATz+Pz31bNVlSsqbGT0onkFpsWqXI4RPDUjUE6bT+PQDnM3u\nZP3uUiIjdHK79jqCLhTGDEogsV8Ue4/X0tru3+fAbtzTedTmHPnlFCEoTKdlYJKBynoLDqfLJ+/5\nyaFKWqx27pmQQWxMhE/eM9AEXShotZ37IdkdLnYd898DeCrqLBw+28DQ9H4Mz+ivdjlCqCIz1YjD\nqVDd4P3B5tb2DjbtLUMfFcZ9skD0uoIuFACm5qQRptOw7ZD/HsCzYU8p0DmWEOobcInQ5cvB5o/2\nV2BtdzD7tkxiomQbmesJylCIjYlg4shkahpbKSlrUrucL6ltbOVASR0DkwzkDElQuxwhVOOrweYW\nq50tByrop4/grlzZbPJGgjIUAO4c3/mD98fpqZv2laEoMOd26SWI0DYwSY9Oq/F6KGzcW4atw8mc\n27OIjJCDq26kR6FQXFxMfn4+AGVlZTz++OMsXLiQl156CZerc4DozTff5JFHHuGxxx7jyJEjN3yu\nLwxJjyUj2cCh0w00mW0+e9/uNLa0s+toDSlx0UwYkax2OUKoKjxMx4BEPRW1Fq9tfd/Y0s7WQ1Uk\n9otixjg5uKo73YbCihUrWLp0KTZb53+sv/rVr1i8eDHvvvsuiqLwySefcPz4cfbv3897771HQUEB\n//qv/3rd5/qKRqPhztx0XIpCoR8dwPPR/gqcLoX7b8tEq5VeghCZKUbsDhcXG72zmeXfd5XicLp4\ncMogwnRBe3PEY7ptIZPJxPLly91fHz9+nEmTJgEwffp0du/eTVFREVOnTkWj0TBgwACcTieNjY1f\n+Vxfui07haiIzgN4fDXl7UZaWu1sL64izhjJ5DGpapcjhF9wjyvUtHj8tWsbW9l55CJpCTFMHpPi\n8dcPRt2e9zhr1iwqK68uBFMUxX0fXK/XYzabsVgs9O9/dVpl1+Nf9dzuxMXFEObBw+rvnmjiw10X\nuFBn5facvnUdk5KMffr+zZtOYu9w8a0HhpGWGrx7t/e1nUKFtFOnsSNSWP3xaepabNdtk9621R8/\nOo1LUfjWA6NJTQnevzlPuulDgLXaq50Lq9VKbGwsBoMBq9V6zeNGo/Ern9udJg+fh3DrqGQ+3HWB\n9z89y7C03v8RJiUZqa/v/WBYa7uD9TvOY4gOJ3dIQp9ey5/1tZ1ChbTTVcYILRqg5ELjV7ZJb9uq\nos5C4WeVZKYYGZpmCPr29tSHjJu+wZadnc2+ffsAKCwsZMKECeTm5rJz505cLhfV1dW4XC7i4+O/\n8rm+lp6oZ0RGf06WNXHxku93Y+yy7bNK2mwO7p2YQWS4zH4QoktkhI7UhBjKa824PLiu6G+F51GA\neTMGo5VZfj1206HwwgsvsHz5chYsWEBHRwezZs1izJgxTJgwgQULFvDMM8/wi1/84rrPVcOdV/ZD\n+vQzdQacbR1OthyoIDpSx0yZIy3El2SlGmm3O6lvavPI652ruszhsw0MH9iPMYPiPfKaoUKj+NmS\nX2908RxOFz9+azd2h4uCf57Sq3nKfenuf1JUyeqPT/PA5EwenjGkV68RKOS2SM9IO11ry/5y1mw9\ny1MPjubW7GsHhHvTVr/502ecLGvip9/IDZltZFS7fRSIwnSdB/C02RzsO1nr0/d2OF1s2ldGRJiW\neybIfitCfBVPrmw+UdrIybImxgyOD5lA8KSQCAWAGeMGoNHg8/2Q9hyvobHFxvSxA4jVy66MQnyV\njGTP7IGkKAp/LTwPwLzpg/tcVygKmVCIj41i3NBEymrNXLjom267y6WwcW85Oq2G+241+eQ9hQhE\nMVFhJMdFU15r7tOHtsNnGzhf3cKEEUlkpcoZJb0RMqEAuAd5tx3yzQE8RafrqW1sZfKYVDnhSYhu\nZKUasbY7uHS5vVff77rSS9Bo4KFp0kvorZAKhVFZcSTHRbO/pA5Lm3cP4FEUhQ27S9Fo4IHb5BAd\nIbrj3ka7l+MK+0/UUlVv5fYxqQyQ8857LaRCQavRcOf4dDocLnYeuejV9zp6vpHyOgsTRyaTEh/j\n1fcSIhiYrgw2l/ZiXMHhdPH+jgvotBrmThnk6dJCSkiFAsCUW9IID9Py6WdVHl0o80Vdh+jcL70E\nIXqkLz2FnUcvUtfcxoxxA0jsH+3p0kJKyIWCITqcSaOSqWtu48SFRq+8x+mKZs5UXiZnSAKmFNnf\nRoieMESHkxAbRVnNzQ02dzicrN9VSkSYljm3Z3mvwBARcqEAnxtw9tIBPB/uLgVgzuQsr7y+EMEq\nM9WIubWDZou9x9+z7VAVTWYbd00YSH9DpBerCw0hGQqD0mLJSjVy+GxDr2c6XE9pTQvHLjQyIqM/\nQwfKroxC3Iyr22j37BZSm83Bh3vKiI7UMftWuVXrCSEZCgB3jk9HUWB7sWd7Cxv2lAFIN1aIXrjZ\ncYWPD1ZgaevgvkkmDNHh3iwtZIRsKEzKTiEmMozC4oseO4CnusHKoVP1ZKUayc6K88hrChFKbqan\nYGnr4KP95Riiw7lbtpDxmJANhchwHVNz0mix2jl0ut4jr7lpbxkK8MDkLPfhQkKInuunj6C/IaJH\nPYVNe8toszmZMzmT6MibPhpGXEfIhgLAHeM7t9Teeqjvt5AamtvYc7yWtIQYxg9P7PPrCRGqMlOM\nNJltXLZef7C52WLjk6JK4oyR7q3xhWeEdCikxseQnRXH6YpmquotfXqtTfvLcSkKD0zOlAM9hOiD\nrltI5TfoLXy4uxS7w8WDU7II9+DxvSLEQwHgzvF9n5562WJjR/FFEvtFMWmUHA4uRF90N65Q39zG\n9sPVJMdFM+WWNF+WFhJCPhTGDUsgzhjJ7mM1tNkcvXqNLQcqcDhdzL4tkzBdyDepEH3inoF0nVD4\n+84LOF0KD00bJH9vXhDyLarTapkxdgDtdid7T9z8ATzW9g62flZFP30EU29J9UKFQoSWOGMkxpjw\nrxxsrm6wsvt4DQOT9NIr95KQDwWAaWMHoNNqenUAzydFldjsTmZNMsm9TSE8QKPRkJlipOFy+5d2\nM35/x3kUBb4+fbCM3XmJhAKdn0zGD0+ist7C2arLPf6+druDjw9UoI8KY8a4AV6sUIjQ8lWDzaU1\nLRw8Vc/gAbGMGyoz/LxFQuGKO69MT912E9NTtx+uxtru4K68gTJPWggP+qqVzV3HbD48fbCsA/Ii\nCYUrRpr6k5YQw8FTdbTcYH50lw6Hi837y4kM18lqSiE87IszkE6VN3HsfCOjMuMYlRWvZmlBT0Lh\nCs2VA3gcToUdR6q7ff6uYxe5bLFz5/h02XNFCA9L7BdFTGSYexvtrl7CvBlyzKa3SSh8zu1j0ogI\n1/LpZ9W4XNcfcHa6XGzaW0aYTsO9k6SXIISnaTQaMlON1Da1sfNwNWcqLzNuaCJDBsjOw94mofA5\nMVFh3JadyqWWdo6ev3Td5x04WUd9cztTcwbI/u1CeEnXuMJ//qUYDZ0zjoT39SoU7HY7P/zhD5k/\nfz6LFi2itLSUw4cP8+ijj/LYY4/x5ptvAuByufjFL37BggULyM/Pp6yszKPFe8PMK/uoXG+Fs0tR\n2LC3DK1Gw323mnxZmhAhxZRqAMDa1sGt2SlkJBtUrig09GrKzLp164iJiWHdunWcP3+el19+mYaG\nBpYvX05GRgbf+973OH78OFVVVdjtdtauXcvhw4d57bXX+N3vfufpa/AoU4qRIemxHD13ibrmNpK/\ncN5r8ZkGquqtTB6d8qV/E0J4TlZqLABarYa50wapXE3o6FVP4ezZs0yfPh2AwYMHc/ToUex2OyaT\nCY1Gw9SpU9mzZw9FRUVMmzYNgHHjxnHs2DHPVe5Fd45PRwG2f6G3oCgKH145ROf+2+SUJyG8KTku\nmpwhCTx2zwhS4mLULidk9KqnMGrUKLZt28bdd99NcXExZrOZjIyrA656vZ6KigosFgsGw9Uun06n\nw+FwEBZ2/beNi4shTOWVwbOnxrB26zl2Havhu1/PISK8s56LzTYuXGxh8i1pjMuWjbiuJynJqHYJ\nAUHaqXvLvj9V7RJCTq9C4eGHH+bcuXM88cQT5ObmMnLkSNra2tz/brVaiY2Npb29HavV6n7c5XLd\nMBAAmppae1OSx029JZVN+8rZvPM8k8ekkpRkZPXmkwDcnZtOfX3PjgsMNUlJRmmbHpB26jlpq57x\n1IeMXt0+Onr0KHl5eaxcuZK7776brKwswsPDKS8vR1EUdu7cyYQJE8jNzaWwsBCAw4cPM3z4cI8U\n7QszxqejAbZ+VglASVkjJ8uaGJ0Vx6C0WHWLE0IIL+lVTyEzM5Pf/va3/O///i9Go5Fly5Zx8eJF\nfvSjH+F0Opk6dSpjx47llltuYdeuXTz22GMoisKrr77q6fq9Jrl/NGMGJ3D0/CXKa81s2l8BdB61\nKYQQwUqj3Oy2oF7mT93Ew2cb+P//fIQRGf05VdHMkPRYlnwzT/ZduQHp6veMtFPPSVv1jKq3j0JF\nzuAEEmKjOFXRDHT2EiQQhBDBTELhBrRaDXeM79wSOystlrFDElSuSAghvEv2e+7GHePTuXDRzPx7\nRkgvQQgR9KSn0A19VDg/mHcLowdLL0EIEfwkFIQQQrhJKAghhHCTUBBCCOEmoSCEEMJNQkEIIYSb\nhIIQQgg3CQUhhBBuEgpCCCHc/G5DPCGEEOqRnoIQQgg3CQUhhBBuEgpCCCHcJBSEEEK4SSgIIYRw\nk1AQQgjhJqEghBDCLaRPXuvo6GDJkiVUVVVht9t5+umnGTp0KD/96U/RaDQMGzaMl156Ca1Wy5tv\nvsmnn35KWFgYS5YsIScnh5MnT/Lyyy+j0+mIiIjg3/7t30hMTFT7sjyur+3UZf369axatYq1a9eq\neDXe1de2unTpEkuXLqWlpQWn08mvf/1rTCaT2pflcZ7423vppZfQ6XRkZWWxbNkytNrg+4x7M+0E\nUFZWxj//8z/z4YcfAtDY2MiPfvQj2tvbSU5O5le/+hXR0dE3flMlhP35z39WXnnlFUVRFKWxsVGZ\nMWOG8tRTTyl79+5VFEVRfv7znytbtmxRjh07puTn5ysul0upqqpS5s2bpyiKonzjG99QTpw4oSiK\novzpT39SXn31VXUuxMv62k6KoignTpxQnnjiCeXRRx9V5Rp8pa9t9cILLygbNmxQFEVR9uzZo2zb\ntk2V6/C2vrbT97//feXTTz9VFEVRnn/+eeWTTz5R50K8rKftpCiK8re//U35+te/rtx+++3u73/5\n5ZeVv/zlL4qiKMp///d/K++880637xl80XoT7rvvPv7lX/7F/bVOp+P48eNMmjQJgOnTp7N7926K\nioqYOnUqGo2GAQMG4HQ6aWxspKCggFGjRgHgdDqJjIxU5Tq8ra/t1NTUxOuvv86SJUvUugSf6Wtb\nHTp0iNraWp588knWr1/v/r5g09d2GjVqFM3NzSiKgtVqJSwsOG969LSdAPr168eqVauu+f6ioiKm\nTZv2pefeSEiHgl6vx2AwYLFYePbZZ1m8eDGKoqDRaNz/bjabsVgsGAyGa77PbDaTnJwMwKFDh1i1\nahVPPvmkGpfhdX1pp+bmZl588UWWLFmCXq9X6xJ8pq+/U1VVVcTGxvKHP/yBtLQ0VqxYodaleFVf\n26nrltHs2bO5dOkSt956q1qX4lU9bSeAO++8k5iYmGu+32KxYDQav/TcGwnpUAC4ePEiTzzxBHPn\nzuVrX/vaNfclrVYrsbGxGAwGrFbrNY93NfTGjRt56aWX+P3vf098fLzP6/eV3raTxWKhrKyMX/7y\nlzz//POcPXuWZcuWqXEJPtOX36n+/fszc+ZMAGbOnMmxY8d8Xr+v9KWdli1bxurVq9m8eTMPPfQQ\nr732mhqX4BM9aafr+Xz7dffcLiEdCg0NDSxatIgf//jHPPLIIwBkZ2ezb98+AAoLC5kwYQK5ubns\n3LkTl8tFdXU1LpeL+Ph4PvjgA1atWsXKlSvJyMhQ81K8qi/tlJOTw4YNG1i5ciUFBQUMHTqUF198\nUc3L8aq+/k7l5eWxfft2AA4cOMDQoUNVuxZv6ms79evXz92DSE5OpqWlRbVr8aaettP15Obmun+f\nCgsLycvL6/Y9Q3qX1FdeeYVNmzYxePBg92Mvvvgir7zyCh0dHQwePJhXXnkFnU7H8uXLKSwsxOVy\n8bOf/Yzx48czefJk0tLS3Ok7ceJEnn32WbUux2v60k6f/4WtrKzk+eefZ926dWpchk/0ta2qqqpY\nunQpbW1tGAwG3njjDfr166fiFXlHX9vp4MGDvP7664SFhREeHs7LL7/MwIEDVbwi77iZduoyZcoU\ndu3aBXSGygsvvIDVaiUuLo433njjS7eYviikQ0EIIcS1Qvr2kRBCiGtJKAghhHCTUBBCCOEmoSCE\nEMJNQkEIIYRbcK4NF+ImVFZWct999zFkyBAA2tvbyc3N5Yc//OENNzjMz89n5cqVvipTCJ+QnoIQ\ndC6A+uCDD/jggw/YvHkziYmJ3a452b9/v4+qE8J3JBSE+AKNRsMzzzzDmTNnKCkpYenSpSxYsIC7\n7rqL73//+7S3t/PKK68A8OijjwKdq0UfeeQRHnroIX7wgx/Q1NSk5iUI0WsSCkJ8hYiICDIzM/nH\nP/5BeHg4a9eu5eOPP8ZsNrN9+3aWLl0KwHvvvUdjYyNvvPEGb7/9Nu+//z5Tp07l9ddfV/kKhOgd\nGVMQ4jo0Gg3Z2dlkZGSwevVqzp8/T2lpKa2trdc8r7i42L1pGYDL5QrKrSlEaJBQEOIr2O12Lly4\nQEVFBb/97W954oknmDdvHk1NTXxxZxin00lubi7/9V//BYDNZrtmZ08hAoncPhLiC1wuF8uXL2fs\n2LFUVFQwe/ZsHn74YWJjY9m3bx9OpxPoPPDE4XAwduxYDh8+zIULFwB46623+PWvf63mJQjRa9JT\nEAKoq6tj7ty5QGcojBo1ioKCAmpqavjRj37Ehg0bCA8PJzc3l8rKSgDuuusu5s6dy1//+ldeffVV\nFi9ejMvlIiUlhd/85jdqXo4QvSa7pAohhHCT20dCCCHcJBSEEEK4SSgIIYRwk1AQQgjhJqEghBDC\nTUJBCCGEm4SCEEIIt/8HNeBU7V70/HUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x26fe6fb6518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df['Adj Close'].plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.0 Introduction to Time Series (Chapter 1)\n",
    "- Asset returns\n",
    "- Stylised facts of returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Asset Returns\n",
    "\n",
    "### One-Period Simple Return\n",
    "\n",
    "Buy and hold an asset from one period between  $t-1$ to date $t$, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2001-12-31    1148.079956\n",
       "2002-12-31     879.820007\n",
       "2003-12-31    1111.920044\n",
       "2004-12-31    1211.920044\n",
       "2005-12-30    1248.290039\n",
       "Freq: BA-DEC, Name: Adj Close, dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Adj Close'].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Gross Return:\n",
    "\n",
    "$$1 + R_t = \\frac{P_t}{P_{t-1}}$$\n",
    "\n",
    "-    $P_t$ is price of an asset at time $t$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the first two observations for the next section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2001-12-31    1148.079956\n",
       "2002-12-31     879.820007\n",
       "Freq: BA-DEC, Name: Adj Close, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Adj Close'].iloc[0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Simple Gross Return is 0.7663\n"
     ]
    }
   ],
   "source": [
    "print(\"The Simple Gross Return is {0:.4f}\".\n",
    "      format(df['Adj Close'].iloc[1] / df['Adj Close'].iloc[0])) # Simple Gross Return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Net Return:\n",
    "\n",
    "$$R_t = \\frac{P_t}{P_{t-1}} - 1$$\n",
    "\n",
    "-    $R_t$ is the simple net return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Simple Net Return is -0.2337\n"
     ]
    }
   ],
   "source": [
    "print(\"The Simple Net Return is {0:.4f}\".\n",
    "      format(df['Adj Close'].iloc[1] / df['Adj Close'].iloc[0] -1)) # Simple Net Return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiperiod Simple Return\n",
    "\n",
    "Buy and hold an asset for $k$ periods between $t-k$ to date $t$, \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compound Return:\n",
    "\n",
    "\\begin{align}\n",
    "1+R_t[k] = \\frac{P_t}{P_{t-k}} & = \\frac{P_t}{P_{t-1}}\\times\\frac{P_{t-1}}{P_{t-2}}\\times...\\times\\frac{P_{t-k+1}}{P_{t-k}} \\\\ & =(1+R_t)(1+R_{t-1})...(1+R_{t-k-1}) \\\\ & =\\prod^{k-1}_{j=0}(1+R_{t-j}) \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>1161.020020</td>\n",
       "      <td>1161.160034</td>\n",
       "      <td>1148.040039</td>\n",
       "      <td>1148.079956</td>\n",
       "      <td>1148.079956</td>\n",
       "      <td>9.436000e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.390015</td>\n",
       "      <td>881.929993</td>\n",
       "      <td>869.450012</td>\n",
       "      <td>879.820007</td>\n",
       "      <td>879.820007</td>\n",
       "      <td>1.088500e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1109.640015</td>\n",
       "      <td>1112.560059</td>\n",
       "      <td>1106.209961</td>\n",
       "      <td>1111.920044</td>\n",
       "      <td>1111.920044</td>\n",
       "      <td>1.027500e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1213.550049</td>\n",
       "      <td>1217.329956</td>\n",
       "      <td>1211.650024</td>\n",
       "      <td>1211.920044</td>\n",
       "      <td>1211.920044</td>\n",
       "      <td>7.869000e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1254.420044</td>\n",
       "      <td>1254.420044</td>\n",
       "      <td>1246.589966</td>\n",
       "      <td>1248.290039</td>\n",
       "      <td>1248.290039</td>\n",
       "      <td>1.443500e+09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Open         High          Low        Close    Adj Close  \\\n",
       "Date                                                                          \n",
       "2001-12-31  1161.020020  1161.160034  1148.040039  1148.079956  1148.079956   \n",
       "2002-12-31   879.390015   881.929993   869.450012   879.820007   879.820007   \n",
       "2003-12-31  1109.640015  1112.560059  1106.209961  1111.920044  1111.920044   \n",
       "2004-12-31  1213.550049  1217.329956  1211.650024  1211.920044  1211.920044   \n",
       "2005-12-30  1254.420044  1254.420044  1246.589966  1248.290039  1248.290039   \n",
       "\n",
       "                  Volume  \n",
       "Date                      \n",
       "2001-12-31  9.436000e+08  \n",
       "2002-12-31  1.088500e+09  \n",
       "2003-12-31  1.027500e+09  \n",
       "2004-12-31  7.869000e+08  \n",
       "2005-12-30  1.443500e+09  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pandas provides a neat function for us to calcuate percentage change very quickly.\n",
    "\n",
    "Note below that we have calculated **Simple Net Return** for all our data by using `pct_change()` in pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>returns</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>1148.079956</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.820007</td>\n",
       "      <td>-0.233660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1111.920044</td>\n",
       "      <td>0.263804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1211.920044</td>\n",
       "      <td>0.089935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1248.290039</td>\n",
       "      <td>0.030010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Adj Close   returns\n",
       "Date                             \n",
       "2001-12-31  1148.079956       NaN\n",
       "2002-12-31   879.820007 -0.233660\n",
       "2003-12-31  1111.920044  0.263804\n",
       "2004-12-31  1211.920044  0.089935\n",
       "2005-12-30  1248.290039  0.030010"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['returns'] = df['Adj Close'].pct_change()\n",
    "df = df[['Adj Close', 'returns']].copy()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's zoom into the first couple of periods with returns data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2001-12-31         NaN\n",
       "2002-12-31   -0.233660\n",
       "2003-12-31    0.263804\n",
       "2004-12-31    0.089935\n",
       "Freq: BA-DEC, Name: returns, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['returns'].iloc[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate multiperiod simple returns, \n",
    "\n",
    "\\begin{align}\n",
    "1+R_t[k] = \\frac{P_t}{P_{t-k}} & = \\frac{P_t}{P_{t-1}}\\times\\frac{P_{t-1}}{P_{t-2}}\\times...\\times\\frac{P_{t-k+1}}{P_{t-k}} \\\\ & =(1+R_t)(1+R_{t-1})...(1+R_{t-k-1}) \\\\ & =\\prod^{k-1}_{j=0}(1+R_{t-j}) \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the first two periods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Multiperiod Simple Returns is 0.9685\n"
     ]
    }
   ],
   "source": [
    "print(\"The Multiperiod Simple Returns is {0:.4f}\".\n",
    "      format((1 + df['returns'].iloc[1]) * (1 + df['returns'].iloc[2]))) # Multiperiod simple returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the first three periods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Multiperiod Simple Returns is 1.0556\n"
     ]
    }
   ],
   "source": [
    "print(\"The Multiperiod Simple Returns is {0:.4f}\".\n",
    "      format((1 + df['returns'].iloc[1]) * \\\n",
    "             (1 + df['returns'].iloc[2]) * \\\n",
    "             (1 + df['returns'].iloc[3]))) # Multiperiod simple returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we are only looking at period from 2002-12-31 until 2003-01-03. What if we want to calculate for the whole period, how do we do that?\n",
    "\n",
    "Again pandas library has nicely provided a function called `cumprod()` which stands for cummulative product, which is this part of the equation:\n",
    "\n",
    "$$(1+R_t)(1+R_{t-1})...(1+R_{t-k-1})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>returns</th>\n",
       "      <th>compound returns</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>1148.079956</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.820007</td>\n",
       "      <td>-0.233660</td>\n",
       "      <td>0.766340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1111.920044</td>\n",
       "      <td>0.263804</td>\n",
       "      <td>0.968504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1211.920044</td>\n",
       "      <td>0.089935</td>\n",
       "      <td>1.055606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1248.290039</td>\n",
       "      <td>0.030010</td>\n",
       "      <td>1.087285</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Adj Close   returns  compound returns\n",
       "Date                                               \n",
       "2001-12-31  1148.079956       NaN               NaN\n",
       "2002-12-31   879.820007 -0.233660          0.766340\n",
       "2003-12-31  1111.920044  0.263804          0.968504\n",
       "2004-12-31  1211.920044  0.089935          1.055606\n",
       "2005-12-30  1248.290039  0.030010          1.087285"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['compound returns'] = (df.returns + 1).cumprod()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the **Compound Returns** column."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple net return:\n",
    "\n",
    "\\begin{equation*}\n",
    "R_t[k]=\\frac{P_t-P_{t-k}}{P_{t-k}}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Multiperiod Simple Net Returns is -0.0315\n"
     ]
    }
   ],
   "source": [
    "print(\"The Multiperiod Simple Net Returns is {0:.4f}\".\n",
    "      format((1 + df['returns'].iloc[1]) * (1 + df['returns'].iloc[2]) - 1)) # Multiperiod simple returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Multiperiod Simple Returns is 0.0556\n"
     ]
    }
   ],
   "source": [
    "print(\"The Multiperiod Simple Returns is {0:.4f}\".\n",
    "      format((1 + df['returns'].iloc[1]) * \\\n",
    "             (1 + df['returns'].iloc[2]) * \\\n",
    "             (1 + df['returns'].iloc[3]) - 1)) # Multiperiod simple returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>returns</th>\n",
       "      <th>compound returns</th>\n",
       "      <th>simple net returns</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>1148.079956</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.820007</td>\n",
       "      <td>-0.233660</td>\n",
       "      <td>0.766340</td>\n",
       "      <td>-0.233660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1111.920044</td>\n",
       "      <td>0.263804</td>\n",
       "      <td>0.968504</td>\n",
       "      <td>-0.031496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1211.920044</td>\n",
       "      <td>0.089935</td>\n",
       "      <td>1.055606</td>\n",
       "      <td>0.055606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1248.290039</td>\n",
       "      <td>0.030010</td>\n",
       "      <td>1.087285</td>\n",
       "      <td>0.087285</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Adj Close   returns  compound returns  simple net returns\n",
       "Date                                                                   \n",
       "2001-12-31  1148.079956       NaN               NaN                 NaN\n",
       "2002-12-31   879.820007 -0.233660          0.766340           -0.233660\n",
       "2003-12-31  1111.920044  0.263804          0.968504           -0.031496\n",
       "2004-12-31  1211.920044  0.089935          1.055606            0.055606\n",
       "2005-12-30  1248.290039  0.030010          1.087285            0.087285"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['simple net returns'] = (df.returns + 1).cumprod() - 1\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How then is returns different from simple net returns?\n",
    "\n",
    "Returns is single period. From 2001-12-31 to 2002-12-31 for example.\n",
    "\n",
    "Multiple Simple Net Returns involves multiple-periods. Here are some examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Multiperiod Simple Returns from 2001-12-31 to 2002-12-31 is -0.2337\n"
     ]
    }
   ],
   "source": [
    "print(\"The Multiperiod Simple Returns from 2001-12-31 to 2002-12-31 is {0:.4f}\".\n",
    "      format(df['simple net returns'].iloc[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Multiperiod Simple Returns from 2002-12-31 to 2003-12-31 is -0.0315\n"
     ]
    }
   ],
   "source": [
    "print(\"The Multiperiod Simple Returns from 2002-12-31 to 2003-12-31 is {0:.4f}\".\n",
    "      format(df['simple net returns'].iloc[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Multiperiod Simple Returns from 2002-12-31 to 2004-12-31 is 0.0556\n"
     ]
    }
   ],
   "source": [
    "print(\"The Multiperiod Simple Returns from 2002-12-31 to 2004-12-31 is {0:.4f}\".\n",
    "      format(df['simple net returns'].iloc[3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Annualised Average Return \n",
    "\n",
    "Assume the asset was held for $k$ years, \n",
    "\n",
    "**the annualised (average) return** is:\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "Annualised\\{R_t[k]\\} & =\\Bigg[\\prod^{k-1}_{j=0}(1+R_{t-j})\\Bigg]^{\\frac{1}{k}}-1  \\\\ & = exp\\Bigg[{\\frac{1}{k}}\\sum^{k-1}_{j=0}ln(1+R_{t-j})\\Bigg]-1 \n",
    "\\end{align}\n",
    "\n",
    "NB: $exp$ is exponential function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will show both ways below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>returns</th>\n",
       "      <th>compound returns</th>\n",
       "      <th>simple net returns</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>1148.079956</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.820007</td>\n",
       "      <td>-0.233660</td>\n",
       "      <td>0.766340</td>\n",
       "      <td>-0.233660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1111.920044</td>\n",
       "      <td>0.263804</td>\n",
       "      <td>0.968504</td>\n",
       "      <td>-0.031496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1211.920044</td>\n",
       "      <td>0.089935</td>\n",
       "      <td>1.055606</td>\n",
       "      <td>0.055606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1248.290039</td>\n",
       "      <td>0.030010</td>\n",
       "      <td>1.087285</td>\n",
       "      <td>0.087285</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Adj Close   returns  compound returns  simple net returns\n",
       "Date                                                                   \n",
       "2001-12-31  1148.079956       NaN               NaN                 NaN\n",
       "2002-12-31   879.820007 -0.233660          0.766340           -0.233660\n",
       "2003-12-31  1111.920044  0.263804          0.968504           -0.031496\n",
       "2004-12-31  1211.920044  0.089935          1.055606            0.055606\n",
       "2005-12-30  1248.290039  0.030010          1.087285            0.087285"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Method 1: Multiplicative**\n",
    "\n",
    "\\begin{align}\n",
    "Annualised\\{R_t[k]\\} & =\\Bigg[\\prod^{k-1}_{j=0}(1+R_{t-j})\\Bigg]^{\\frac{1}{k}}-1  \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Annualised Average Returns from 2001-12-31 to 2005-12-31 (5 years) is 0.0169\n"
     ]
    }
   ],
   "source": [
    "print(\"The Annualised Average Returns from 2001-12-31 to 2005-12-31 (5 years) is {0:.4f}\".\n",
    "      format(df['compound returns'].iloc[4] ** (1/5) - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Method 2: Using Log**\n",
    "\n",
    "\\begin{align}\n",
    "Annualised\\{R_t[k]\\} & = exp\\Bigg[{\\frac{1}{k}}\\sum^{k-1}_{j=0}ln(1+R_{t-j})\\Bigg]-1 \n",
    "\\end{align}\n",
    "\n",
    "NB: $exp$ is exponential function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>returns</th>\n",
       "      <th>compound returns</th>\n",
       "      <th>simple net returns</th>\n",
       "      <th>log returns</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>1148.079956</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.820007</td>\n",
       "      <td>-0.233660</td>\n",
       "      <td>0.766340</td>\n",
       "      <td>-0.233660</td>\n",
       "      <td>-0.266129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1111.920044</td>\n",
       "      <td>0.263804</td>\n",
       "      <td>0.968504</td>\n",
       "      <td>-0.031496</td>\n",
       "      <td>0.234126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1211.920044</td>\n",
       "      <td>0.089935</td>\n",
       "      <td>1.055606</td>\n",
       "      <td>0.055606</td>\n",
       "      <td>0.086118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1248.290039</td>\n",
       "      <td>0.030010</td>\n",
       "      <td>1.087285</td>\n",
       "      <td>0.087285</td>\n",
       "      <td>0.029569</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Adj Close   returns  compound returns  simple net returns  \\\n",
       "Date                                                                      \n",
       "2001-12-31  1148.079956       NaN               NaN                 NaN   \n",
       "2002-12-31   879.820007 -0.233660          0.766340           -0.233660   \n",
       "2003-12-31  1111.920044  0.263804          0.968504           -0.031496   \n",
       "2004-12-31  1211.920044  0.089935          1.055606            0.055606   \n",
       "2005-12-30  1248.290039  0.030010          1.087285            0.087285   \n",
       "\n",
       "            log returns  \n",
       "Date                     \n",
       "2001-12-31          NaN  \n",
       "2002-12-31    -0.266129  \n",
       "2003-12-31     0.234126  \n",
       "2004-12-31     0.086118  \n",
       "2005-12-30     0.029569  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['log returns'] = np.log(df['returns'] + 1 )\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>returns</th>\n",
       "      <th>compound returns</th>\n",
       "      <th>simple net returns</th>\n",
       "      <th>log returns</th>\n",
       "      <th>log_rtns_cumsum</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>1148.079956</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.820007</td>\n",
       "      <td>-0.233660</td>\n",
       "      <td>0.766340</td>\n",
       "      <td>-0.233660</td>\n",
       "      <td>-0.266129</td>\n",
       "      <td>-0.266129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1111.920044</td>\n",
       "      <td>0.263804</td>\n",
       "      <td>0.968504</td>\n",
       "      <td>-0.031496</td>\n",
       "      <td>0.234126</td>\n",
       "      <td>-0.032003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1211.920044</td>\n",
       "      <td>0.089935</td>\n",
       "      <td>1.055606</td>\n",
       "      <td>0.055606</td>\n",
       "      <td>0.086118</td>\n",
       "      <td>0.054115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1248.290039</td>\n",
       "      <td>0.030010</td>\n",
       "      <td>1.087285</td>\n",
       "      <td>0.087285</td>\n",
       "      <td>0.029569</td>\n",
       "      <td>0.083684</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Adj Close   returns  compound returns  simple net returns  \\\n",
       "Date                                                                      \n",
       "2001-12-31  1148.079956       NaN               NaN                 NaN   \n",
       "2002-12-31   879.820007 -0.233660          0.766340           -0.233660   \n",
       "2003-12-31  1111.920044  0.263804          0.968504           -0.031496   \n",
       "2004-12-31  1211.920044  0.089935          1.055606            0.055606   \n",
       "2005-12-30  1248.290039  0.030010          1.087285            0.087285   \n",
       "\n",
       "            log returns  log_rtns_cumsum  \n",
       "Date                                      \n",
       "2001-12-31          NaN              NaN  \n",
       "2002-12-31    -0.266129        -0.266129  \n",
       "2003-12-31     0.234126        -0.032003  \n",
       "2004-12-31     0.086118         0.054115  \n",
       "2005-12-30     0.029569         0.083684  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['log_rtns_cumsum'] = df['log returns'].cumsum()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Annualised Average Returns from 2001-12-31 to 2005-12-31 (5 years) is 0.0169\n"
     ]
    }
   ],
   "source": [
    "print(\"The Annualised Average Returns from 2001-12-31 to 2005-12-31 (5 years) is {0:.4f}\".\n",
    "      format(np.exp(df['log_rtns_cumsum'].iloc[4] / 5) - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Continuous Compounding\n",
    "The net asset value $A$ of continuous compounding is:\n",
    "\\begin{equation*}\n",
    "A = Ce^{rn}\n",
    "\\end{equation*}\n",
    "\n",
    "-    $C$ is the initial capital\n",
    "\n",
    "-    $r$ is the interest rate per annum\n",
    "\n",
    "-    $n$ is the number of years\n",
    "\n",
    "-    $e$ is exponential function\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall earlier we calculate the annualised average returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Annualised Average Returns from 2001-12-31 to 2005-12-31 (5 years) is 0.0169\n"
     ]
    }
   ],
   "source": [
    "print(\"The Annualised Average Returns from 2001-12-31 to 2005-12-31 (5 years) is {0:.4f}\".\n",
    "      format(df['compound returns'].iloc[4] ** (1/5) - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's store that"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "aar = df['compound returns'].iloc[4] ** (1/5) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Annually Compounded Returns is 0.087285\n"
     ]
    }
   ],
   "source": [
    "print(\"The Annually Compounded Returns is {0:.6f}\".\n",
    "      format((1 + aar) ** 5 - 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Continuously Compounded Returns is 0.088051\n"
     ]
    }
   ],
   "source": [
    "ccr = 1 * np.exp(aar * 5) - 1\n",
    "print(\"The Continuously Compounded Returns is {0:.6f}\".\n",
    "      format(1 * np.exp(aar * 5) - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Present Value\n",
    "\\begin{equation*}\n",
    "C = Ae^{-rn}\n",
    "\\end{equation*}\n",
    "\n",
    "-    $C$ is the initial capital\n",
    "\n",
    "-    $r$ is the interest rate per annum\n",
    "\n",
    "-    $n$ is the number of years"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if we are given the number of periods, end price and returns, how do we calculate the Present Value?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Annualised Average Returns from 2001-12-31 to 2005-12-31 (5 years) is 0.0169\n"
     ]
    }
   ],
   "source": [
    "print(\"The Annualised Average Returns from 2001-12-31 to 2005-12-31 (5 years) is {0:.4f}\".\n",
    "      format(aar))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 5 # number of periods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Present Value is 0.999296\n"
     ]
    }
   ],
   "source": [
    "print(\"The Present Value is {0:.6f}\".\n",
    "      format(df['compound returns'].iloc[4] * np.exp(- aar * n)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Continuously Compounded Return\n",
    "\n",
    "Recall **Simple Gross Return**:\n",
    "\n",
    "$$1 + R_t = \\frac{P_t}{P_{t-1}}$$\n",
    "\n",
    "-    $P_t$ is price of an asset at time $t$\n",
    "\n",
    "\n",
    "The natural log of simple gross return is called **continuously compounded return**:\n",
    "\n",
    "\\begin{align}\n",
    "r_t &= ln(1+R_t) \\\\ &= ln\\frac{P_t}{P_{t-1}} \\\\ &= p_t-p_{t-1}\n",
    "\\end{align}\n",
    "\n",
    "- $r_t$ is the continuously compounded return or log return\n",
    "\n",
    "- $p_t = ln(P_t)$\n",
    "\n",
    "- $R_t$ is the simple net return\n",
    "\n",
    "Advantages of log return:\n",
    "\n",
    "1. Continuously compounded multiperiod return is the sum of continuously compounded one-period return\n",
    "\n",
    "2. Statistical log returns are more tractable\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>returns</th>\n",
       "      <th>compound returns</th>\n",
       "      <th>simple net returns</th>\n",
       "      <th>log returns</th>\n",
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       "    <tr>\n",
       "      <th>Date</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>2001-12-31</th>\n",
       "      <td>1148.079956</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>879.820007</td>\n",
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       "      <td>-0.266129</td>\n",
       "      <td>-0.266129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>1111.920044</td>\n",
       "      <td>0.263804</td>\n",
       "      <td>0.968504</td>\n",
       "      <td>-0.031496</td>\n",
       "      <td>0.234126</td>\n",
       "      <td>-0.032003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>1211.920044</td>\n",
       "      <td>0.089935</td>\n",
       "      <td>1.055606</td>\n",
       "      <td>0.055606</td>\n",
       "      <td>0.086118</td>\n",
       "      <td>0.054115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-30</th>\n",
       "      <td>1248.290039</td>\n",
       "      <td>0.030010</td>\n",
       "      <td>1.087285</td>\n",
       "      <td>0.087285</td>\n",
       "      <td>0.029569</td>\n",
       "      <td>0.083684</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Adj Close   returns  compound returns  simple net returns  \\\n",
       "Date                                                                      \n",
       "2001-12-31  1148.079956       NaN               NaN                 NaN   \n",
       "2002-12-31   879.820007 -0.233660          0.766340           -0.233660   \n",
       "2003-12-31  1111.920044  0.263804          0.968504           -0.031496   \n",
       "2004-12-31  1211.920044  0.089935          1.055606            0.055606   \n",
       "2005-12-30  1248.290039  0.030010          1.087285            0.087285   \n",
       "\n",
       "            log returns  log_rtns_cumsum  \n",
       "Date                                      \n",
       "2001-12-31          NaN              NaN  \n",
       "2002-12-31    -0.266129        -0.266129  \n",
       "2003-12-31     0.234126        -0.032003  \n",
       "2004-12-31     0.086118         0.054115  \n",
       "2005-12-30     0.029569         0.083684  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simple Gross Return = 0.766340\n"
     ]
    }
   ],
   "source": [
    "sgr = df['Adj Close'].iloc[1] / df['Adj Close'].iloc[0]\n",
    "print(\"Simple Gross Return = {0:.6f}\".\n",
    "      format(df['Adj Close'].iloc[1] / df['Adj Close'].iloc[0])) # Simple Gross Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.76634036018306728"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Continuously Compounded Return = -0.266129\n"
     ]
    }
   ],
   "source": [
    "print(\"Continuously Compounded Return = {0:.6f}\".\n",
    "      format(np.log(sgr))) # Continuously Compounded Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Continuously Compounded Return = -0.266129\n"
     ]
    }
   ],
   "source": [
    "print(\"Continuously Compounded Return = {0:.6f}\".\n",
    "      format(np.log(df['Adj Close'].iloc[1] / df['Adj Close'].iloc[0]))) # Continuously Compounded Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Continuously Compounded Return = -0.266129\n"
     ]
    }
   ],
   "source": [
    "print(\"Continuously Compounded Return = {0:.6f}\".\n",
    "      format(np.log(df['Adj Close'].iloc[1]) - np.log(df['Adj Close'].iloc[0]))) # Continuously Compounded Return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Portfolio Return\n",
    "\n",
    "Simple net return of $N$ asset in portfolio $p$\n",
    "\n",
    "\\begin{align}\n",
    "R_{p,t}=\\sum^N_{i=1}w_iR_{it}\n",
    "\\end{align}\n",
    "\n",
    "-    $w_t$ is capital allocation of asset $i$ in the portfolio\n",
    "\n",
    "-    $R_{it}$ is the return of asset $i$ at time $t$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "symbols_list = ['ORCL', 'TSLA', 'IBM', 'YELP', 'MSFT']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = {}\n",
    "for ticker in symbols_list:\n",
    "    d[ticker] = data.DataReader(ticker, \"yahoo\", '2014-12-01')\n",
    "pan = pd.Panel(d)\n",
    "df1 = pan.minor_xs('Adj Close')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>IBM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>ORCL</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>YELP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-12-01</th>\n",
       "      <td>145.063065</td>\n",
       "      <td>45.061207</td>\n",
       "      <td>40.221016</td>\n",
       "      <td>231.639999</td>\n",
       "      <td>55.130001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-02</th>\n",
       "      <td>146.077820</td>\n",
       "      <td>44.912918</td>\n",
       "      <td>40.316593</td>\n",
       "      <td>231.429993</td>\n",
       "      <td>55.169998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-03</th>\n",
       "      <td>147.739166</td>\n",
       "      <td>44.560738</td>\n",
       "      <td>40.201897</td>\n",
       "      <td>229.300003</td>\n",
       "      <td>54.770000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-04</th>\n",
       "      <td>147.317078</td>\n",
       "      <td>45.265102</td>\n",
       "      <td>40.039402</td>\n",
       "      <td>228.279999</td>\n",
       "      <td>55.139999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-05</th>\n",
       "      <td>146.616638</td>\n",
       "      <td>44.875847</td>\n",
       "      <td>40.077637</td>\n",
       "      <td>223.710007</td>\n",
       "      <td>53.840000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   IBM       MSFT       ORCL        TSLA       YELP\n",
       "Date                                                               \n",
       "2014-12-01  145.063065  45.061207  40.221016  231.639999  55.130001\n",
       "2014-12-02  146.077820  44.912918  40.316593  231.429993  55.169998\n",
       "2014-12-03  147.739166  44.560738  40.201897  229.300003  54.770000\n",
       "2014-12-04  147.317078  45.265102  40.039402  228.279999  55.139999\n",
       "2014-12-05  146.616638  44.875847  40.077637  223.710007  53.840000"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert to percentage returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>IBM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>ORCL</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>YELP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-12-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-02</th>\n",
       "      <td>0.006995</td>\n",
       "      <td>-0.003291</td>\n",
       "      <td>0.002376</td>\n",
       "      <td>-0.000907</td>\n",
       "      <td>0.000726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-03</th>\n",
       "      <td>0.011373</td>\n",
       "      <td>-0.007841</td>\n",
       "      <td>-0.002845</td>\n",
       "      <td>-0.009204</td>\n",
       "      <td>-0.007250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-04</th>\n",
       "      <td>-0.002857</td>\n",
       "      <td>0.015807</td>\n",
       "      <td>-0.004042</td>\n",
       "      <td>-0.004448</td>\n",
       "      <td>0.006756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-05</th>\n",
       "      <td>-0.004755</td>\n",
       "      <td>-0.008599</td>\n",
       "      <td>0.000955</td>\n",
       "      <td>-0.020019</td>\n",
       "      <td>-0.023576</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 IBM      MSFT      ORCL      TSLA      YELP\n",
       "Date                                                        \n",
       "2014-12-01       NaN       NaN       NaN       NaN       NaN\n",
       "2014-12-02  0.006995 -0.003291  0.002376 -0.000907  0.000726\n",
       "2014-12-03  0.011373 -0.007841 -0.002845 -0.009204 -0.007250\n",
       "2014-12-04 -0.002857  0.015807 -0.004042 -0.004448  0.006756\n",
       "2014-12-05 -0.004755 -0.008599  0.000955 -0.020019 -0.023576"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = df1.pct_change()\n",
    "df2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's assumed we have an **equally weighted** portfolio.\n",
    "\n",
    "First of all, let's take a look at the returns for a specific date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The date is 02-12-2014\n"
     ]
    }
   ],
   "source": [
    "idx = 1\n",
    "print(\"The date is {0:%d-%m-%Y}\".format(df2.iloc[idx].name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "IBM     0.006995\n",
       "MSFT   -0.003291\n",
       "ORCL    0.002376\n",
       "TSLA   -0.000907\n",
       "YELP    0.000726\n",
       "Name: 2014-12-02 00:00:00, dtype: float64"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.iloc[idx][0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The portfolio average returns is 0.001180\n"
     ]
    }
   ],
   "source": [
    "print(\"The portfolio average returns is {0:.6f}\".format(df2.iloc[idx][0:5].mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate for everyday"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>IBM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>ORCL</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>YELP</th>\n",
       "      <th>portfolio_rtns</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-12-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-02</th>\n",
       "      <td>0.006995</td>\n",
       "      <td>-0.003291</td>\n",
       "      <td>0.002376</td>\n",
       "      <td>-0.000907</td>\n",
       "      <td>0.000726</td>\n",
       "      <td>0.001180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-03</th>\n",
       "      <td>0.011373</td>\n",
       "      <td>-0.007841</td>\n",
       "      <td>-0.002845</td>\n",
       "      <td>-0.009204</td>\n",
       "      <td>-0.007250</td>\n",
       "      <td>-0.003153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-04</th>\n",
       "      <td>-0.002857</td>\n",
       "      <td>0.015807</td>\n",
       "      <td>-0.004042</td>\n",
       "      <td>-0.004448</td>\n",
       "      <td>0.006756</td>\n",
       "      <td>0.002243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-05</th>\n",
       "      <td>-0.004755</td>\n",
       "      <td>-0.008599</td>\n",
       "      <td>0.000955</td>\n",
       "      <td>-0.020019</td>\n",
       "      <td>-0.023576</td>\n",
       "      <td>-0.011199</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 IBM      MSFT      ORCL      TSLA      YELP  portfolio_rtns\n",
       "Date                                                                        \n",
       "2014-12-01       NaN       NaN       NaN       NaN       NaN             NaN\n",
       "2014-12-02  0.006995 -0.003291  0.002376 -0.000907  0.000726        0.001180\n",
       "2014-12-03  0.011373 -0.007841 -0.002845 -0.009204 -0.007250       -0.003153\n",
       "2014-12-04 -0.002857  0.015807 -0.004042 -0.004448  0.006756        0.002243\n",
       "2014-12-05 -0.004755 -0.008599  0.000955 -0.020019 -0.023576       -0.011199"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2['portfolio_rtns'] = df2.mean(axis=1)\n",
    "df2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is we have a different portfolio construction?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Floating Point Arithmetic: Issues and Limitations](https://docs.python.org/3.6/tutorial/floatingpoint.html)\n",
    "\n",
    "[Floating point arithmetic issues in Python 3](https://www.ploggingdev.com/2016/11/floating-point-arithmetic-issues-in-python-3/)\n",
    "\n",
    "[decimal — Fixed and Floating Point Math](https://pymotw.com/3/decimal/)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "from decimal import Decimal"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "w = [Decimal(0.10), Decimal(0.20), Decimal(0.30), Decimal(0.20), Decimal(0.20)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = [0.10, 0.20, 0.30, 0.20, 0.20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Portfolio combined weight 1.0000\n"
     ]
    }
   ],
   "source": [
    "print(\"Portfolio combined weight {0:.4f}\".format(np.sum(w)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>IBM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>ORCL</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>YELP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-12-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-02</th>\n",
       "      <td>0.006995</td>\n",
       "      <td>-0.003291</td>\n",
       "      <td>0.002376</td>\n",
       "      <td>-0.000907</td>\n",
       "      <td>0.000726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-03</th>\n",
       "      <td>0.011373</td>\n",
       "      <td>-0.007841</td>\n",
       "      <td>-0.002845</td>\n",
       "      <td>-0.009204</td>\n",
       "      <td>-0.007250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-04</th>\n",
       "      <td>-0.002857</td>\n",
       "      <td>0.015807</td>\n",
       "      <td>-0.004042</td>\n",
       "      <td>-0.004448</td>\n",
       "      <td>0.006756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-05</th>\n",
       "      <td>-0.004755</td>\n",
       "      <td>-0.008599</td>\n",
       "      <td>0.000955</td>\n",
       "      <td>-0.020019</td>\n",
       "      <td>-0.023576</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 IBM      MSFT      ORCL      TSLA      YELP\n",
       "Date                                                        \n",
       "2014-12-01       NaN       NaN       NaN       NaN       NaN\n",
       "2014-12-02  0.006995 -0.003291  0.002376 -0.000907  0.000726\n",
       "2014-12-03  0.011373 -0.007841 -0.002845 -0.009204 -0.007250\n",
       "2014-12-04 -0.002857  0.015807 -0.004042 -0.004448  0.006756\n",
       "2014-12-05 -0.004755 -0.008599  0.000955 -0.020019 -0.023576"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = df2.iloc[:, 0:5]\n",
    "df3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(758, 5)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "IBM     0.006995\n",
       "MSFT   -0.003291\n",
       "ORCL    0.002376\n",
       "TSLA   -0.000907\n",
       "YELP    0.000726\n",
       "Name: 2014-12-02 00:00:00, dtype: float64"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3.iloc[idx][0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can make use of matrix multiplication. Pandas has the built in function called `dot` for this exact purpose "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The portfolio average returns is 0.000718\n"
     ]
    }
   ],
   "source": [
    "print(\"The portfolio average returns is {0:.6f}\".format(df2.iloc[idx][0:5].dot(w)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>IBM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>ORCL</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>YELP</th>\n",
       "      <th>portfolio_rtns</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-12-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-02</th>\n",
       "      <td>0.006995</td>\n",
       "      <td>-0.003291</td>\n",
       "      <td>0.002376</td>\n",
       "      <td>-0.000907</td>\n",
       "      <td>0.000726</td>\n",
       "      <td>0.000718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-03</th>\n",
       "      <td>0.011373</td>\n",
       "      <td>-0.007841</td>\n",
       "      <td>-0.002845</td>\n",
       "      <td>-0.009204</td>\n",
       "      <td>-0.007250</td>\n",
       "      <td>-0.004575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-04</th>\n",
       "      <td>-0.002857</td>\n",
       "      <td>0.015807</td>\n",
       "      <td>-0.004042</td>\n",
       "      <td>-0.004448</td>\n",
       "      <td>0.006756</td>\n",
       "      <td>0.002125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-05</th>\n",
       "      <td>-0.004755</td>\n",
       "      <td>-0.008599</td>\n",
       "      <td>0.000955</td>\n",
       "      <td>-0.020019</td>\n",
       "      <td>-0.023576</td>\n",
       "      <td>-0.010628</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 IBM      MSFT      ORCL      TSLA      YELP  portfolio_rtns\n",
       "Date                                                                        \n",
       "2014-12-01       NaN       NaN       NaN       NaN       NaN             NaN\n",
       "2014-12-02  0.006995 -0.003291  0.002376 -0.000907  0.000726        0.000718\n",
       "2014-12-03  0.011373 -0.007841 -0.002845 -0.009204 -0.007250       -0.004575\n",
       "2014-12-04 -0.002857  0.015807 -0.004042 -0.004448  0.006756        0.002125\n",
       "2014-12-05 -0.004755 -0.008599  0.000955 -0.020019 -0.023576       -0.010628"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3['portfolio_rtns'] = df3.dot(w)\n",
    "df3.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dividend Payment\n",
    "\n",
    "Simple net return at time t:\n",
    "\\begin{align}\n",
    "R_{t} &=\\frac{P_t+D_t}{P_{t-1}}-1 \n",
    "\\end{align}\n",
    "\n",
    "Continuously compounded return at time t:\n",
    "\\begin{align}\n",
    "r_t & = ln(P_t+D_t)-ln(P_{t-1})\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Excess Return\n",
    "\n",
    "Simple excess return:\n",
    "\\begin{align}\n",
    "Z_t=R_t-R_{0t}\n",
    "\\end{align}\n",
    "\n",
    "Log excess return:\n",
    "\\begin{align}\n",
    "z_t=r_t-r_{0t}\n",
    "\\end{align}\n",
    "\n",
    "**Excess return**: the payoff on an arbitrage portfolio that goes long in an asset and short in the reference asset with no net initial investment.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Distribution Properties of Asset Returns\n",
    "\n",
    "The objective is to understand the behaviour of the returns across assets and over time.\n",
    "\n",
    "Consider a collection of $N$ assets held for $T$ time periods, say, $t=1, ..., T$. For each asset $i$, let $r_{it}$ be its log return at time $t$.\n",
    "\n",
    "The **log returns** under study are:\n",
    "\\begin{align}\n",
    "\\{r_{it}: i=1, ..., N; t=1, ...,T\\}\n",
    "\\end{align}\n",
    "\n",
    "One can also consider the **simple returns**:\n",
    "\\begin{align}\n",
    "\\{R_{it}: i=1, ..., N; t=1, ...,T\\}\n",
    "\\end{align}\n",
    "\n",
    "And the **log excess returns**:\n",
    "\\begin{align}\n",
    "\\{z_{it}: i=1, ..., N; t=1, ...,T\\}\n",
    "\\end{align}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Random Variable](https://en.wikipedia.org/wiki/Random_variable)\n",
    "\n",
    "The definition of random variable, accoring to Wikipedia is:\n",
    "\n",
    "In probability and statistics, a **random variable**, random quantity, or stochastic variable is a **variable** quantity whose possible values depend, in **random** manner, on a set of **random outcomes** events.\n",
    "\n",
    "A univariate distribution of a random variable $X$ describes the probability of different values. \n",
    "\n",
    "If $f(x)$ is the probability density function (PDF), then the probability that $X$ is between $A$ and $B$ is calculated by:\n",
    "\n",
    "\\begin{align}\n",
    "Pr(A<=X<B)=\\int^B_Af(x)dx\n",
    "\\end{align}\n",
    "\n",
    "The cumulative distribution function (CDF) for the random variable is:\n",
    "\n",
    "\\begin{align}\n",
    "F(x)=Pr(X<x)=\\int^x_{-\\infty}f(u)du\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not covered:\n",
    "\n",
    "- Joint distribution\n",
    "- Marginal distribution\n",
    "- Conditional distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moments\n",
    "\n",
    "#### The $\\ell$-th moment:\n",
    "The $\\ell$-th moment of a continuous random variable $X$ is defined as:\n",
    "\n",
    "\\begin{align}\n",
    "m^{'}_{\\ell}=E(X^{\\ell})=\\int^{\\infty}_{-\\infty}x^{\\ell}f(x)dx\n",
    "\\end{align}\n",
    "\n",
    "-    $E$ stands for expectation\n",
    "\n",
    "-    $f(x)$ is the probability density function of $X$\n",
    "\n",
    "#### First Moment: Mean\n",
    "The first moment is called the *mean* or *expectation* of $X$. It measures the central location of the distribution. We normally denote the mean of $X$ by $\\mu_x$.\n",
    "\n",
    "\\begin{align}\n",
    "E(x) = \\mu_x\n",
    "\\end{align}\n",
    "\n",
    "#### Second Central Moment: Variance\n",
    "The second central moment, denoted by $\\sigma^2_x$ is called the *variance* of $X$ and it measures the variability of $X$. We obtain *standard deviation*, $\\sigma_x$, of $X$ by taking square root of the variance.\n",
    "\n",
    "The first two moments - mean and variance - of a random variable are sufficient to describe a normal distribution. For other distributions, you would need to utilise higher moments.\n",
    "\n",
    "\\begin{align}\n",
    "Var(X) = \\sigma^2_X=E(X-\\mu_X)^2\n",
    "\\end{align}\n",
    "\n",
    "#### The $\\ell$-th central moment:\n",
    "The $\\ell$-th central moment of a continuous random variable $X$ is defined as:\n",
    "\n",
    "\\begin{align}\n",
    "m^{'}_{\\ell}=E(X-\\mu_X)^{\\ell}=\\int^{\\infty}_{-\\infty}(x-\\mu_X)^{\\ell}f(x)dx\n",
    "\\end{align}\n",
    "\n",
    "#### Third Central Moment:\n",
    "Measures the symmetry of random variable $X$ with respect to its mean. **Skewness**, which is normalised third central moments, is frequently used in statistics. Skewness:\n",
    "\n",
    "\\begin{align}\n",
    "S(x)=E\\bigg[\\frac{(x-\\mu_x)^3}{\\sigma^3_x}\\bigg]\n",
    "\\end{align}\n",
    "\n",
    "#### Forth Central Moment:\n",
    "Measures the tail behaviour of $X$. **Kurtosis** is normalised forth central moment. Kurtosis:\n",
    "\n",
    "\\begin{align}\n",
    "K(x)=E\\bigg[\\frac{(x-\\mu_x)^4}{\\sigma^4_x}\\bigg]\n",
    "\\end{align}\n",
    "\n",
    "#### Excess Kurtosis\n",
    "Excess Kurtosis, $K(x)-3$, is frequently used to measure the peakedness of a distribution. 3 is used because the kurtosis of a normal distribution is 3. \n",
    "\n",
    "A distribution with a positive excess kurtosis, *leptokurtic*, is said to have heavy tails, i.e., more mass on the tails than a normal distribution. In practice, it implies greater occurences of extreme values from such distribution.\n",
    "\n",
    "A distribution with negative excess kurtosis, *platykurtic*, has short tail.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample Moments\n",
    "\n",
    "Let ${x_1, x_2, ..., x_T}$ be a random sample of $X$ with $T$ observations.\n",
    "\n",
    "#### Sample Mean:\n",
    "\n",
    "\\begin{align}\n",
    "\\hat\\mu_x=\\frac{1}{T}\\sum^T_{t=1}x_t\n",
    "\\end{align}\n",
    "\n",
    "#### Sample Variance:\n",
    "\n",
    "\\begin{align}\n",
    "\\hat\\sigma^2_x=\\frac{1}{T-1}\\sum^T_{t=1}(x_t-\\hat\\mu_x)^2\n",
    "\\end{align}\n",
    "\n",
    "#### Sample Skewness:\n",
    "\\begin{align}\n",
    "\\hat S(x)=\\frac{1}{(T-1)\\hat\\sigma^3_x}\\sum^T_{t=1}(x_t-\\hat\\mu_x)^3\n",
    "\\end{align}\n",
    "\n",
    "#### Sample Kurtosis:\n",
    "\\begin{align}\n",
    "\\hat K(x)=\\frac{1}{(T-1)\\hat\\sigma^4_x}\\sum^T_{t=1}(x_t-\\hat\\mu_x)^4\n",
    "\\end{align}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normality Test, Jarque and Bera (1987) (JB)\n",
    "\n",
    "Asset return series $\\{r_1,r_2,...,r_t\\}$\n",
    "\n",
    "$H_0: JB(r)=0$\n",
    "\n",
    "$H_a: JB(r) \\neq 0$\n",
    "\n",
    "The test statistic is\n",
    "\n",
    "\\begin{align}\n",
    "JB=\\frac{\\hat{S}^2(r)}{6/T}+\\frac{[\\hat{K}(r)-3]^2}{24/T}\n",
    "\\end{align}\n",
    "\n",
    "Decision rule: One rejects $H_0$ of normality if the $p$ value of the JB statistic is less than the significance level, $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method 1: SciPy\n",
    "\n",
    "[reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.jarque_bera.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "JB Value is \t 4.2301 \n",
      "p-value is \t 0.1206\n"
     ]
    }
   ],
   "source": [
    "print(\"JB Value is \\t {0[0]:.4f} \\np-value is \\t {0[1]:.4f}\".\n",
    "      format(stats.jarque_bera(np.random.normal(0, 1, 1000000))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember the decision rule is to reject $H_0$ of normality if the $p$-value of the JB statistic is less than the significance level, $\\alpha$.\n",
    "\n",
    "Normally the $p$-value is set a 0.05. If the $p$-value is below 0.05, then we can reject the null hypothesis, $H_0$, of normality.\n",
    "\n",
    "Now, let's apply this to our stocks returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IBM\n",
      "JB Value is \t 1546.9368 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "MSFT\n",
      "JB Value is \t 3806.0309 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "ORCL\n",
      "JB Value is \t 3718.3573 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "TSLA\n",
      "JB Value is \t 117.2708 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "YELP\n",
      "JB Value is \t 15334.4969 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "portfolio_rtns\n",
      "JB Value is \t 275.8945 \n",
      "p-value is \t 0.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for k, v in enumerate(df3):\n",
    "    print(v)\n",
    "    print(\"JB Value is \\t {0[0]:.4f} \\np-value is \\t {0[1]:.4f}\\n\".\n",
    "          format(stats.jarque_bera(df3[v].dropna())))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DescribeResult(nobs=757, minmax=(-0.092533429805476297, 0.10452251880743901), mean=0.00092804921972187862, variance=0.00020309560006109872, skewness=0.566353570755845, kurtosis=10.926286682028808)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.describe(df3.iloc[:, 1].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no obs = 757 \n",
      "min -0.0925 \n",
      "max = 0.1045\n",
      "mean = 0.0009        \n",
      "nvariance = 0.0002 \n",
      "skewness = 0.5664 \n",
      "kurtosis = 10.9263\n"
     ]
    }
   ],
   "source": [
    "print(\"no obs = {0[0]} \\nmin {0[1][0]:.4f} \\nmax = {0[1][1]:.4f}\\nmean = {0[2]:.4f} \\\n",
    "       \\nnvariance = {0[3]:.4f} \\nskewness = {0[4]:.4f} \\nkurtosis = {0[5]:.4f}\".\n",
    "      format(stats.describe(df3.iloc[:, 1].dropna())))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method 2: StatsModels\n",
    "\n",
    "[doc](http://www.statsmodels.org/dev/generated/statsmodels.stats.stattools.jarque_bera.html)\n",
    "\n",
    "[source code](http://www.statsmodels.org/dev/_modules/statsmodels/stats/stattools.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.stattools import jarque_bera"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "JB Value is \t 5.0468 \n",
      "p-value is \t 0.0802 \n",
      "skew is \t 0.0019 \n",
      "kurtosis is \t 3.0103\n"
     ]
    }
   ],
   "source": [
    "print(\"JB Value is \\t {0[0]:.4f} \\np-value is \\t {0[1]:.4f} \\nskew is \\t {0[2]:.4f} \\nkurtosis is \\t {0[3]:.4f}\".\n",
    "      format(jarque_bera(np.random.normal(0, 1, 1000000))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NB: For normally distributed data, skewness is 0, kurtosis is 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normal Distribution\n",
    "\n",
    "\n",
    "A traditional assumption made in financial study is that the simple returns ${R_{it} | t = 1, . . . , T }$ are independently and identically distributed as normal with fixed mean and variance. This assumption makes statistical properties of asset returns tractable. But it encounters several difficulties. \n",
    "\n",
    "* The lower bound of a simple return is −1. Yet the normal distribution may assume any value in the real line and, hence, has no lower bound. \n",
    "* If $R_{it}$ is normally distributed, then the multiperiod simple return $R_{it}[k]$ is not normally distributed because it is a product of one-period returns. \n",
    "* The normality assumption is not supported by many empirical asset returns, which tend to have a positive excess kurtosis.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lognormal Distribution\n",
    "\n",
    "Another commonly used assumption is that the log returns $r_t$ of an asset are independent and identically distributed (iid) as normal with mean $\\mu$ and variance $\\sigma^2$. The simple returns are then iid lognormal random variables with mean and variance given by\n",
    "\n",
    "\\begin{align}\n",
    "E(R_t) & = \\text{exp}(\\mu+\\frac{\\sigma^2}{2})-1 \\\\ \n",
    "\\text{Var}(R_t) & =\\text{exp}(2\\mu+\\sigma^2)[\\text{exp}(\\sigma^2)-1] \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These two equations are useful in studying asset returns (e.g., in forecasting using models built for log returns)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, let $m_1$ and $m_2$ be the mean and variance of the simple return $R_t$ , which is lognormally distributed. Then the mean and variance of the corresponding log return $r_t$ are"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "E(r_t) & = ln\\bigg[ \\frac{m_1+1}{\\sqrt{1+ \\frac{m_2}{(1+m_1)^2}}}\\bigg] \\\\ \n",
    "\\text{Var}(r_t) & =ln\\bigg[ 1 + \\frac{m_2}{(1 + m_1)^2}\\bigg] \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the sum of a finite number of iid normal random variables is normal, $r_t[k]$ is also normally distributed under the normal assumption for ${r_t}$. In addition, there is no lower bound for $r_t$ , and the lower bound for $R_t$ is satisfied using\n",
    "$1 + R_t = \\text{exp}(r_t)$. However, the lognormal assumption is not consistent with all the properties of historical stock returns. In particular, many stock returns exhibit a positive excess kurtosis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>IBM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>ORCL</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>YELP</th>\n",
       "      <th>portfolio_rtns</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-12-02</th>\n",
       "      <td>0.006971</td>\n",
       "      <td>-0.003296</td>\n",
       "      <td>0.002373</td>\n",
       "      <td>-0.000907</td>\n",
       "      <td>0.000725</td>\n",
       "      <td>0.000718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-03</th>\n",
       "      <td>0.011309</td>\n",
       "      <td>-0.007872</td>\n",
       "      <td>-0.002849</td>\n",
       "      <td>-0.009246</td>\n",
       "      <td>-0.007277</td>\n",
       "      <td>-0.004586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-04</th>\n",
       "      <td>-0.002861</td>\n",
       "      <td>0.015683</td>\n",
       "      <td>-0.004050</td>\n",
       "      <td>-0.004458</td>\n",
       "      <td>0.006733</td>\n",
       "      <td>0.002122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-05</th>\n",
       "      <td>-0.004766</td>\n",
       "      <td>-0.008637</td>\n",
       "      <td>0.000954</td>\n",
       "      <td>-0.020222</td>\n",
       "      <td>-0.023859</td>\n",
       "      <td>-0.010685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-08</th>\n",
       "      <td>-0.008674</td>\n",
       "      <td>-0.014981</td>\n",
       "      <td>-0.013446</td>\n",
       "      <td>-0.042694</td>\n",
       "      <td>-0.044047</td>\n",
       "      <td>-0.025135</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 IBM      MSFT      ORCL      TSLA      YELP  portfolio_rtns\n",
       "Date                                                                        \n",
       "2014-12-02  0.006971 -0.003296  0.002373 -0.000907  0.000725        0.000718\n",
       "2014-12-03  0.011309 -0.007872 -0.002849 -0.009246 -0.007277       -0.004586\n",
       "2014-12-04 -0.002861  0.015683 -0.004050 -0.004458  0.006733        0.002122\n",
       "2014-12-05 -0.004766 -0.008637  0.000954 -0.020222 -0.023859       -0.010685\n",
       "2014-12-08 -0.008674 -0.014981 -0.013446 -0.042694 -0.044047       -0.025135"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df4 = np.log(df3.dropna() + 1)\n",
    "df4.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IBM\n",
      "JB Value is \t 1440.8865 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "MSFT\n",
      "JB Value is \t 3463.0338 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "ORCL\n",
      "JB Value is \t 3156.5231 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "TSLA\n",
      "JB Value is \t 132.8359 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "YELP\n",
      "JB Value is \t 17501.0231 \n",
      "p-value is \t 0.0000\n",
      "\n",
      "portfolio_rtns\n",
      "JB Value is \t 276.2527 \n",
      "p-value is \t 0.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for k, v in enumerate(df4):\n",
    "    print(v)\n",
    "    print(\"JB Value is \\t {0[0]:.4f} \\np-value is \\t {0[1]:.4f}\\n\".\n",
    "          format(stats.jarque_bera(df4[v].dropna())))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stable Distribution\n",
    "\n",
    "The stable distributions are a natural generalization of normal in that they are stable under addition, which meets the need of continuously compounded returns $r_t$. Furthermore, stable distributions are capable of capturing excess kurtosis shown\n",
    "by historical stock returns. However, nonnormal stable distributions do not have a finite variance, which is in conflict with most finance theories. In addition, statistical modeling using nonnormal stable distributions is difficult. An example of\n",
    "nonnormal stable distributions is the Cauchy distribution, which is symmetric with respect to its median but has infinite variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scale Mixture of Normal Distributions\n",
    "\n",
    "Recent studies of stock returns tend to use scale mixture or finite mixture of normal distributions. Under the assumption of scale mixture of normal distributions, the log return $r_t$ is normally distributed with mean $\\mu$ and variance $\\sigma^2$ [i.e., $r_t ∼ N(\\mu, \\sigma^2)$]. However, $\\sigma^2$ is a random variable that follows a positive distribution (e.g., $\\sigma^{-2}$ follows a gamma distribution). An example of finite mixture of normal distributions is\n",
    "\n",
    "$$r_t ∼ (1-X)N(\\mu,\\sigma_1^2)+XN(\\mu,\\sigma_2^2)$$\n",
    "\n",
    "where $X$ is a Bernoulli random variable such that $P(X = 1) = \\alpha$ and $P(X = 0) = 1 − \\alpha$ with $0 < \\alpha < 1$, $\\sigma_1^2$ is small, and $\\sigma_2^2$ is relatively large. For instance, with $\\alpha = 0.05$, the finite mixture says that 95% of the returns follow $N(\\mu, \\sigma_1^2)$ and 5% follow $N(\\mu, \\sigma_2^2)$. The large value of $\\sigma_2^2$ enables the mixture to put more mass at the tails of its distribution. The low percentage of returns that are from $N(\\mu, \\sigma_2^2)$ says\n",
    "that the majority of the returns follow a simple normal distribution. Advantages of mixtures of normal include that they maintain the tractability of normal, have finite higher order moments, and can capture the excess kurtosis. Yet it is hard to\n",
    "estimate the mixture parameters (e.g., the $\\alpha$ in the finite-mixture case).\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Jake VanderPlas - Kernel Density Estimation in Python](https://jakevdp.github.io/blog/2013/12/01/kernel-density-estimation/)\n",
    "\n",
    "[Jake VanderPlas - Kernel Density Estimation in Python Notebook](http://nbviewer.jupyter.org/url/jakevdp.github.com/downloads/notebooks/KDEBench.ipynb)\n",
    "\n",
    "[Michael Lerner - Histograms and kernel density estimation KDE 2](https://mglerner.github.io/posts/histograms-and-kernel-density-estimation-kde-2.html?p=28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pcWIT23GCxuv1KjNzjIqKCrVgQY7tOACA41CAAYTMhx9OldQwP/x2vNGjx0qSPvqIaRAA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x26fe4dd1710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %matplotlib notebook\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(12,6))\n",
    "sns.distplot(df4['IBM'], bins=50, fit=stats.norm, kde=False);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2Ad8Cq4E1pmmuAN4DGhiG8Q0wivxlFiIiAePz+Zg9eyYA/foNxBboPYGLyb5n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x26fe7914a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12,6))\n",
    "x = np.linspace(-4, 4, 100)\n",
    "line1, = ax.plot(x, stats.norm.pdf(x), 'k-', lw=2, alpha=0.8, label='normal pdf')\n",
    "line2, = ax.plot(x, stats.cauchy.pdf(x), 'r-', lw=2, alpha=0.8, label='cauchy pdf')\n",
    "plt.legend([line1, line2], [\"Normal\", \"Cauchy\"]);"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "from sklearn.neighbors import KernelDensity\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "ax.grid(color='white', linestyle='-', linewidth=2)\n",
    "X_src = np.zeros((1, 1))\n",
    "x_grid = np.linspace(-4, 4, 1000)\n",
    "log_dens = KernelDensity(kernel='gaussian').fit(X_src).score_samples(x_grid[:, None])\n",
    "ax.plot(x_grid, np.exp(log_dens), lw=3, alpha=0.5, label='gaussian');"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "from sklearn.mixture import GaussianMixture"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "gmm = GaussianMixture(n_components=2, max_iter=1000, \n",
    "                      weights_init = [0.9, 0.1],\n",
    "                      init_params='random')\n",
    "\n",
    "samples_1 = np.random.normal(0, 1, 10000)\n",
    "samples_2 = np.random.normal(0, 2, 10000)\n",
    "X = np.concatenate((samples_1, samples_2))\n",
    "\n",
    "gmm = gmm.fit(X.reshape(-1,1))\n",
    "gmm_x = np.linspace(-4, 4, 1000)\n",
    "gmm_y = np.exp(gmm.score_samples(gmm_x.reshape(-1, 1)))\n",
    "plt.plot(gmm_x, gmm_y);"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "def gen_mix(x, mu, sigma, weights):\n",
    "    gmm = GaussianMixture(n_components=2, max_iter=1000, \n",
    "                          weights_init = weights,\n",
    "                          covariance_type = 'full',\n",
    "                          init_params = 'random')\n",
    "\n",
    "    samples_1 = np.random.normal(mu[0], sigma[0], 100000)\n",
    "    samples_2 = np.random.normal(mu[1], sigma[1], 100000)\n",
    "    print(mu[1], sigma[1])\n",
    "    X = np.concatenate((samples_1, samples_2))\n",
    "\n",
    "    gmm = gmm.fit(X.reshape(-1, 1))\n",
    "    gmm_x = np.linspace(-4, 4, 1000)\n",
    "    gmm_y = np.exp(gmm.score_samples(gmm_x.reshape(-1, 1)))\n",
    "    \n",
    "    return gmm_x, gmm_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "def std_norm_pdf(x):\n",
    "    return 1 / np.sqrt(2 * math.pi) * np.exp(-x ** 2 / 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "def norm_pdf(mu, sigma, x):\n",
    "    return 1 / (sigma * np.sqrt(2 * math.pi)) * np.exp(- 1 / 2 * ((x - mu) / sigma) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu = [0, 0]\n",
    "sigma = [1, 2]\n",
    "alpha = 0.05\n",
    "length = 100000\n",
    "\n",
    "x = np.linspace(-4, 4, length)\n",
    "\n",
    "samples_1 = np.random.normal(mu[0], sigma[0], length)\n",
    "samples_2 = np.random.normal(mu[1], sigma[1], length)\n",
    "ind = np.random.rand(length)\n",
    "res = []\n",
    "for k, v in enumerate(ind):\n",
    "    if v >= alpha:\n",
    "        res.append(samples_1[k])\n",
    "    else:\n",
    "        res.append(samples_2[k])\n",
    "mm_mean = np.mean(res)\n",
    "mm_std = np.std(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9fXOlrWsso8ZCCGchhbEQIkdZv34Nt27dpHRphZo1a6W9fvbWGdadWcOwqq9q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eYa6y4C5VcsH1o2pmi0CL9/fE/HTy+rp+XMJExMfIbv8tTITn2M6Bs+fKbvcj/X/KYfn+kb8Ylo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\nAKQwFkIIIYQQAoD/B23551Xd9Cb1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x26fe7b66908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12,6))\n",
    "x = np.linspace(-4, 4, length)\n",
    "y = norm_pdf(mm_mean, mm_std, x)\n",
    "\n",
    "line1, = ax.plot(x, stats.norm.pdf(x), 'k-', lw=2, alpha=0.8, label='Nrmal')\n",
    "line2, = ax.plot(x, stats.cauchy.pdf(x), 'r-', lw=2, alpha=0.8, label='Cauchy')\n",
    "line3, = ax.plot(x, y, 'g-', lw=1, alpha=0.8, label='Mixture')\n",
    "plt.legend([line1, line2, line3], [\"Normal\", \"Cauchy\", \"Mixture\"]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Returns\n",
    "\n",
    "Joint distribution \n",
    "\n",
    "How conditional expectation and conditional covariance matrix evolve over time\n",
    "\n",
    "Random Vector $X = (X_1, ..., X_p)$\n",
    "\n",
    "$E(X)=\\mu_x=[E(X_1), ..., E(X_p)]^\\prime$\n",
    "\n",
    "$Cov(X)=\\sum_x=E[(X - \\mu_x)(X - \\mu_x)^\\prime]$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Likelihood Function of Returns\n",
    "\n",
    "Some financial theories such as the capital asset pricing model (CAPM) of Sharpe (1964) focus on the joint distribution of $N$ returns at a **single time index $t$** (i.e., the distribution of ${r_{1t}, ..., r_{Nt}}$). In this, we are looking at the returns of all the different assets, $1, ..., N$, at time $T$ only.\n",
    "\n",
    "\n",
    "Other theories emphasize the **dynamic structure** of individual asset returns (i.e., the distribution of {$r_{i1}, ..., r_{iT}$} for a given asset $i$). Here are only looking at the returns of asset $i$ across time, $1, ..., T$.\n",
    "\n",
    "In univariate analysis, our main concern is the joint distribution of {$r_{it}$}$^T_{t=1}$ for asset $i$. To this end, it is useful to partition the joint distribution as\n",
    "\n",
    "\\begin{align}\n",
    "F(r_{i1}, ...r_{iT}; \\theta) & = F(r_{i1}; \\theta)F(r_{i2}|r_{i1}; \\theta)...F(r_{iT}|r_{i, T-1}, ...,r_{i1}; \\theta) \\\\ \n",
    "& = F(r_{i1}; \\theta)\\prod_{t=2}^TF(r_{it}|r_{i,t-1}, ..., r_{i1}; \\theta) \\\\\n",
    "\\end{align}\n",
    "\n",
    "This partition highlights the temporal dependencies of the log return $r_{it}$.\n",
    "\n",
    "The above equation can be used to obtain the likelihood function of the log returns {$r_1, ..., r_T$} of an asset.\n",
    "\n",
    "If the conditional distribution $f(r_t|r_{t-1}, ..., r_1, \\theta)$ is normal with mean $\\mu_t$ and variance $\\sigma_t^2$, when $\\theta$ consists of the parameters in $\\mu_t$ and $\\sigma_t^2$ and the likelihood function of the data is:\n",
    "\n",
    "\n",
    "$$f(r_1, ..., r_T;\\theta)=f(r_1;\\theta)\\prod_{t=2}^T\\frac{1}{\\sqrt{2\\pi}\\sigma_t}exp\\bigg[\\frac{-(r_t-\\mu_t)^2}{2\\sigma_t^2}\\bigg]$$\n",
    "\n",
    "where $f(r_1; θ)$ is the marginal density function of the first observation $r_1$. The value of $\\theta$ that maximizes this likelihood function is the maximum-likelihood estimate (MLE) of $\\theta$. Since the log function is monotone, the MLE can be obtained by maximizing the log-likelihood function,\n",
    "\n",
    "$$ln\\  f(r_1, ..., r_T;\\theta)=ln\\ f(r_1;\\theta) - \\frac{1}{2} \\sum_{t=2}^T\\bigg[ln(2\\pi)+ln(\\sigma_t^2)+\\frac{(r_t-\\mu_t)^2}{\\sigma_t^2}\\bigg]$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Empirical Properties of Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "start = datetime.datetime(1975, 1, 1)\n",
    "end = datetime.datetime(2015, 1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = data.DataReader(\"IBM\", 'yahoo', start, end)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = f.resample('M').asfreq().ffill()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1974-12-31</th>\n",
       "      <td>10.375000</td>\n",
       "      <td>10.554688</td>\n",
       "      <td>10.375000</td>\n",
       "      <td>10.500000</td>\n",
       "      <td>3.329909</td>\n",
       "      <td>782400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-01-31</th>\n",
       "      <td>11.453125</td>\n",
       "      <td>11.812500</td>\n",
       "      <td>11.453125</td>\n",
       "      <td>11.765625</td>\n",
       "      <td>3.731280</td>\n",
       "      <td>1542400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-02-28</th>\n",
       "      <td>13.265625</td>\n",
       "      <td>13.484375</td>\n",
       "      <td>13.242188</td>\n",
       "      <td>13.468750</td>\n",
       "      <td>4.303698</td>\n",
       "      <td>1094400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-03-31</th>\n",
       "      <td>12.968750</td>\n",
       "      <td>13.031250</td>\n",
       "      <td>12.859375</td>\n",
       "      <td>12.914063</td>\n",
       "      <td>4.126455</td>\n",
       "      <td>796800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-04-30</th>\n",
       "      <td>12.640625</td>\n",
       "      <td>13.125000</td>\n",
       "      <td>12.609375</td>\n",
       "      <td>13.117188</td>\n",
       "      <td>4.191364</td>\n",
       "      <td>1099200.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Open       High        Low      Close  Adj Close     Volume\n",
       "Date                                                                        \n",
       "1974-12-31  10.375000  10.554688  10.375000  10.500000   3.329909   782400.0\n",
       "1975-01-31  11.453125  11.812500  11.453125  11.765625   3.731280  1542400.0\n",
       "1975-02-28  13.265625  13.484375  13.242188  13.468750   4.303698  1094400.0\n",
       "1975-03-31  12.968750  13.031250  12.859375  12.914063   4.126455   796800.0\n",
       "1975-04-30  12.640625  13.125000  12.609375  13.117188   4.191364  1099200.0"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        text-align: right;\n",
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       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Simple Return</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1974-12-31</th>\n",
       "      <td>10.375000</td>\n",
       "      <td>10.554688</td>\n",
       "      <td>10.375000</td>\n",
       "      <td>10.500000</td>\n",
       "      <td>3.329909</td>\n",
       "      <td>782400.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-01-31</th>\n",
       "      <td>11.453125</td>\n",
       "      <td>11.812500</td>\n",
       "      <td>11.453125</td>\n",
       "      <td>11.765625</td>\n",
       "      <td>3.731280</td>\n",
       "      <td>1542400.0</td>\n",
       "      <td>0.120535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-02-28</th>\n",
       "      <td>13.265625</td>\n",
       "      <td>13.484375</td>\n",
       "      <td>13.242188</td>\n",
       "      <td>13.468750</td>\n",
       "      <td>4.303698</td>\n",
       "      <td>1094400.0</td>\n",
       "      <td>0.153411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-03-31</th>\n",
       "      <td>12.968750</td>\n",
       "      <td>13.031250</td>\n",
       "      <td>12.859375</td>\n",
       "      <td>12.914063</td>\n",
       "      <td>4.126455</td>\n",
       "      <td>796800.0</td>\n",
       "      <td>-0.041184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-04-30</th>\n",
       "      <td>12.640625</td>\n",
       "      <td>13.125000</td>\n",
       "      <td>12.609375</td>\n",
       "      <td>13.117188</td>\n",
       "      <td>4.191364</td>\n",
       "      <td>1099200.0</td>\n",
       "      <td>0.015730</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Open       High        Low      Close  Adj Close     Volume  \\\n",
       "Date                                                                           \n",
       "1974-12-31  10.375000  10.554688  10.375000  10.500000   3.329909   782400.0   \n",
       "1975-01-31  11.453125  11.812500  11.453125  11.765625   3.731280  1542400.0   \n",
       "1975-02-28  13.265625  13.484375  13.242188  13.468750   4.303698  1094400.0   \n",
       "1975-03-31  12.968750  13.031250  12.859375  12.914063   4.126455   796800.0   \n",
       "1975-04-30  12.640625  13.125000  12.609375  13.117188   4.191364  1099200.0   \n",
       "\n",
       "            Simple Return  \n",
       "Date                       \n",
       "1974-12-31            NaN  \n",
       "1975-01-31       0.120535  \n",
       "1975-02-28       0.153411  \n",
       "1975-03-31      -0.041184  \n",
       "1975-04-30       0.015730  "
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Simple Return'] = df['Adj Close'].pct_change()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Simple Return</th>\n",
       "      <th>Log Return</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1974-12-31</th>\n",
       "      <td>10.375000</td>\n",
       "      <td>10.554688</td>\n",
       "      <td>10.375000</td>\n",
       "      <td>10.500000</td>\n",
       "      <td>3.329909</td>\n",
       "      <td>782400.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-01-31</th>\n",
       "      <td>11.453125</td>\n",
       "      <td>11.812500</td>\n",
       "      <td>11.453125</td>\n",
       "      <td>11.765625</td>\n",
       "      <td>3.731280</td>\n",
       "      <td>1542400.0</td>\n",
       "      <td>0.120535</td>\n",
       "      <td>0.113806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-02-28</th>\n",
       "      <td>13.265625</td>\n",
       "      <td>13.484375</td>\n",
       "      <td>13.242188</td>\n",
       "      <td>13.468750</td>\n",
       "      <td>4.303698</td>\n",
       "      <td>1094400.0</td>\n",
       "      <td>0.153411</td>\n",
       "      <td>0.142723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-03-31</th>\n",
       "      <td>12.968750</td>\n",
       "      <td>13.031250</td>\n",
       "      <td>12.859375</td>\n",
       "      <td>12.914063</td>\n",
       "      <td>4.126455</td>\n",
       "      <td>796800.0</td>\n",
       "      <td>-0.041184</td>\n",
       "      <td>-0.042056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-04-30</th>\n",
       "      <td>12.640625</td>\n",
       "      <td>13.125000</td>\n",
       "      <td>12.609375</td>\n",
       "      <td>13.117188</td>\n",
       "      <td>4.191364</td>\n",
       "      <td>1099200.0</td>\n",
       "      <td>0.015730</td>\n",
       "      <td>0.015608</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Open       High        Low      Close  Adj Close     Volume  \\\n",
       "Date                                                                           \n",
       "1974-12-31  10.375000  10.554688  10.375000  10.500000   3.329909   782400.0   \n",
       "1975-01-31  11.453125  11.812500  11.453125  11.765625   3.731280  1542400.0   \n",
       "1975-02-28  13.265625  13.484375  13.242188  13.468750   4.303698  1094400.0   \n",
       "1975-03-31  12.968750  13.031250  12.859375  12.914063   4.126455   796800.0   \n",
       "1975-04-30  12.640625  13.125000  12.609375  13.117188   4.191364  1099200.0   \n",
       "\n",
       "            Simple Return  Log Return  \n",
       "Date                                   \n",
       "1974-12-31            NaN         NaN  \n",
       "1975-01-31       0.120535    0.113806  \n",
       "1975-02-28       0.153411    0.142723  \n",
       "1975-03-31      -0.041184   -0.042056  \n",
       "1975-04-30       0.015730    0.015608  "
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Log Return'] = np.log(df['Simple Return'] + 1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
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LJb+znwD4rBoriyG1MJEnYdVz+xqAO4UQT8Ov6am2vN9CCui1nHT9KoD3qefyB0gHee1b\ntQ+AXsMsqOv+J0h/yIeFEC9CPvPPWMo25xwX4XOTWfZiSJeD5yE1Y5eoTcE9kPMWQR6eOQRSSItz\n4lhzFuQhji+qd2CZEEJvai6CFP6egxQwL9P+Z2EQ0Z2QfrePCiEIciN1etQ1zMyQcF3besowtaO0\nML+iKuJEMRIhxD6QE+3bqbJzPsPMKoQQH4EUpuL4ezJM28EhMRimRRBCfBry9Ni3WCBj9jSEDJGx\nCFKzyzCMBdaUMQzDMAzDtADsU8YwDMMwDNMCsFDG1IwQ4kohxFcsn48JGfV7j0QIcZgQYszy+YFC\nRuyvpqxvCCE2CSEaHshRCPEbIdO1NKKss4UQv2pEWSHlf1MIMevNWkKIY4XMlBD83Dpm9kTCxooQ\n4nNCiLJAqRHlzBNCPCqEeEEIEQy0HLeMGet3IcSlQohqY/MxbQ77lDFMgyCZU+4tVV72H5BpaR6p\n+Mvq6zObciy2Qp5QpolQIGl2DKrJk9qKTEc+VWYPg4UypmkobdnDkDGY3gwZsPB0IloshDgb8oj4\nwZDxspZBpqcZEUK8DDKJ8CGQMbauI6IfqPLMHI3vICMHpnIkfgbA2yCPyF9NRN9S330d0sG4G/Ko\n+VdI5nI8W5V1AGSwx60APkpE28PqUaG9OidgxRyRQog/QKZHuUwI8U3IqOFlORdjtPvDkAEqdTDI\nrxLRX1R//AoyxMYDkLG2joF8778JGeX8cPX9v6h2Wp9XoN6x+kX4cx9eBBkX7OeQqbAykDGlvqrq\nYeYJ/TvVjz9R5Vyp/620UE9CpgH6OmSokishU4IdAuAqIjpLyFQ3V0DGjnIgw398NiqMiaghLyQR\nOUIGUP0SZA7Mijkohczj+VNV56Jqz5cgBfRjiOhj6jcDkKl+rhBCvA3AeUT0ZiHEByCfdwdk0Nav\nENHjaiwfDxlM9Dki+qhxz8MQ/i7uByk87AeZU3MjZD7NPtXfZf2ryrTWI6LdZwPYh4hOV332OciI\n/FOQz+ZF47cCgTypkDHRfPlUSSbhDm13nH4nmUfzryGffQdkuIlDVfkPBcrYAP/4ewr2uer78OdT\nPQfyRPoNqpyH9L9FeS7bRyDDyPwt5Lz0Y5J5M/eHfIf2UdX5s34WzJ4Dmy+ZZnMIgIdVpPkzIaOo\n62Cm74BMoHs4ZPDGb6rPrwZwOcn8hG8C8DdCiH9S33k5GimQlFwhIBfOowH8sxDiFCHEoZA5J99J\nMpfdNwB8x7jmBMh8lYejlGS6Uj0qUTFHJBH9M0o5F/+AkJyLMdp9LoDPk8yFeBbs6WBeDjmJHwsp\nXPwcUhB7nWr/cep3Uc9LU02/6NyHv4QUoJaq694IubicQfY8oVGsIKK/Mn7bS0QnQGopvyJkjsIP\nAZir2qEDxL7CUpZJ1XkhhRBHQaaseTsR/TX8aX/C+D/IBftI9V8S8hneBBl0Nwm5sRiH1LYAMlDq\njUKIV0Oe0NV5FT8DGQ9OB509FMAbQwSTsGf7EQCPE9HxkH00AX9cwbL+jVGPUIQMono+gJNUn/1a\ntdeDiAhGnlTVrrJ8qkKIeTHarbH2u5CJ6m+CjO93BGQ8r6MiyjHHn/VdoPJ8qlF4uWyJaAlkyq5d\nRPQWyNRRPxNCdEGmqFpHREdDvrOvFjK4MbMHwUIZUw9hWockSuk7BonoWsALYFiEXNQA4Hoi2qm0\nF5dBLkhzIIW176od8hOQi4meJIM5GoNcQkR5ktkDrgdwIhFthIzKfpoQ4keQQpeZi+4hKuUgfBbA\nXjHqUYk4OSI9RHTOxUrtvg7AzUKI30CmnrGlocpDBroEpCbgMSIaIRlVfRtK+feinhdq6BdTy3YK\nZKDRZZCaqzdBas2qZXHg37eq+m6FzLG5F6S24XVKI3EmgPOJKDIDA9WWF/I9kHlid6jf/DpG/U8G\ncLEapzp91MlEtAky0bROcP9DyACwCSihDFJIOwDA/aofr4F8D7WJ7wnyp8sysT5bIvo5ZD7bMyAj\n7r8+0G5b/1aqRygko8hfr+75K8iMAcFE80Eq5VONarfG2u9QY1D1CYjoQcisGGEsBmp6F6KwjmlI\nzX8npHb/LgB/L4S4A1K7fCZVH5CZaXFYKGPqYRekmcdDyHQjXSjlwwxOlKbAVrB8noI0rbyF/Lkc\ntXksW2HyLStTCHE0pEAzDzLa9jmonO+vUj0ioXg5Ik2ici4CEe1Wu/K3QWqbPo5AhH1FjvyZF8Ky\nBUQ9L6D6fgnmd/xH47o3wx5VPCpHZ7BMwPL8iGg9pIDwQ8jnfp8yt4UiassLicBvKgkGgD3PpX7O\nN0NqVv8WMkXQRsicjpNEtFZdez+V5zrVQkSUU7v12QohzoHUHPdDCpX3IN77EVWPSJRG6wOQwu2Z\nkH0dRaV8lHGc+cP6vYDydy8q/ZCZdzbuu1DTmDbe2QQRPQ2p8f41pBvDU3yQYM+DhTKmHu4E8E9C\niAMBL//cf0Pm7NOTzCIhxEnq+w9ACgPa7+bvhBDzlbnm05CaiBHIHecZ6poFkL5WcU/mfVQIkRRC\nLIQ0jf4JMm/dEiL6KaRfzamokO+v3nqIeDkizftF5VyMuk9a+bn0kHSk/jyAI4TM/1kLUc+r3n65\nG8CXRCk/6W0oCWVmnlAzR+eBkNqIqlAC1hWQWqz/Ufc+usJlteSFvAfA3xoC98djVO8uAP8pZM7E\nJOQz18/5Jsj0ZUmSB0fugdR83qi+v1/d73DVzvdBpvnpjnHfsGd7IqQm8WpI7dN7UbndNddDCLGP\nEGIzgAEiOh/SrGjLZxu834mivnyqYf2+EkDW6ButwY0M4hnjXQgb06+FoX2Oi9Lyn0VEtwD4L8iU\nUJw1ZQ+DhTKmZpSa/xwAdyj1/SpIHyUzYfEUgI8JmSvxGwBOpVIS3J0A7oCcFIdR2mH+K4DjhMw7\n9yRkHshrYlarG9L59gkAFxLR/ZC78H2EzCn4IuSudC+l1YuinnpUzBFpwZpzMeoCpT37bwDXCiGe\ngTQLfZJqT2Qd9bw0tfbLFyHNMMshF/DlKJlazTyhvwRwgJA5+q6APKRQLVdBChYvCiGWApgP6SsE\nIcQdQogPWq6pJS/kcsi8kPcLmU+zK0bdvgeZG3YZ5NjPQC6yOm+oi1Ji7bshhY8bje8/A+A69Yy+\nC+CDxiYoirBn+x0AP1Htvg3S9Fup3TXXg2Te2+9B9tlSSKf2T8e4X735VK39rt6hvwdwthDiWcjk\n9jsgNaaViHoXzHyq34MUYldA9nelucDG+QCOUmUsAbAe0nWB2YPgiP5M0xDGaUTLd2dDncRq4P0e\ngnHCiamOqOe1JyFkOqvNRHTXTNdlumiXZ1srQohzAfyEiHYKIQ6GTPb9CuWbyjDTBofEYBim3Sig\npIliGED67t0vhMhD+n59igUyZiZgTRnDMAzDMEwLwD5lDMMwDMMwLQALZQzDMAzDMC0AC2UMwzAM\nwzAtAAtlDMMwDMMwLQALZQzDMAzDMC0AC2UMwzAMwzAtAAtlDMMwDMMwLQALZQzDMAzDMC0AC2UM\nwzAMwzAtAAtlDMMwDMMwLQALZQzDMAzDMC0AC2UMwzAMwzAtAAtlDMMwDMMwLQALZQzDMAzDMC0A\nC2UMwzAMwzAtAAtlDMMwDMMwLQALZQzDMAzDMC0AC2UMwzAMwzAtAAtlDMMwDMMwLQALZQzDMAzD\nMC0AC2UMwzAMwzAtAAtlDMMwDMMwLQALZQzDMAzDMC0AC2UMwzAMwzAtAAtlDMMwDMMwLQALZQzD\nMAzDMC0AC2UMwzAMwzAtAAtlDMMwDMMwLQALZQzDMAzDMC0AC2UMwzAMwzAtAAtlDMMwDMMwLQAL\nZQzDMAzDMC0AC2UMwzAMwzAtAAtlDMMwDMMwLUB6pitQL/39o241v1+4sAeDgxPNqk5L085tB9q7\n/e3cdqC92z/b2/7VCx+D47o47wtvren62d7+emjntgOt2/5Fi+Ymwr5rO01ZOp2a6SrMGO3cdqC9\n29/ObQfau/2zve0uXDhuVXtvH7O9/fXQzm0HZmf7204oYxiGYWYPriv/Y5h2gIUyhmEYpmVxXBeO\nw1IZ0x6wUMYwDMO0LFJTxkIZ0x6wUMYwDMO0Lq4LVpQx7QILZQzDMEzL4rCmjGkjWChjGIZhWhbX\nre/0JcPMJlgoYxiGYVoWPn3JtBMslDEMwzAtiwvw6UumbWChjGEYhmlZXNdlTRnTNrBQxjAMw7Qs\nrgv2KWPaBhbKGIZhmJZFn7zkE5hMOzCtCcmFEEkAFwI4EkAWwKeIaI3x/RcAfBzSjeA7RHT7dNaP\nYRiGaS20KOa4LlKJ0DzODLNHMN2aslMBdBHR8QDOBHCe/kIIsQ+AzwN4C4D3ALhICMFvIMMwTBtT\n0pTNcEUYZhqYbqHsbQDuAgAiegLAsfoLItoF4EgiygPYH8AQEfFryDAM08ZoYYxPYDLtwLSaLwHM\nAzBs/LsohEgTUQEAiKgghDgdwLcB/CJOgQsX9iCdTlVViUWL5lb1+z2Jdm470N7tb+e2A+3d/tnc\ndq0p23vvXnR11rZkzeb210s7tx2Yfe2fbqFsBIDZQ0ktkGmI6FdCiF8DuFMI8S4iejCqwMHBiaoq\nsGjRXPT3j1Z1zZ5CO7cdaO/2t3PbgfZu/2xvu9aU9fWPorsGoWy2t78e2rntQOu2P0pQnG7z5aMA\n3gcAQojjACzXXwjJTcqPLA95EMCZ5voxDLOH4LouFj+3DYOj2ZmuClMjrut6jv58+pJpB6ZbKLsZ\nwJQQ4jEAPwPwJSHEGUKIDxIRAXgOwOMAHgPwBBE9PM31YxhmD2HrrnFccecq3Ld080xXZUZ44oUd\n+OWNz6M4i32xzJrP4mYwTGym1XxJRA6AzwU+XmV8/21IfzKGYZi6yOUd3//bjV//6UUAwKYdI+jN\nzM6QlKZ2jAPIMu3A7HxTGYZhKqBP67X7qb3Z3H5TDnNncTsYJi4slDEMs0eiNSuz2XzXCGazgsms\ne5s/RqZNYKGMYZg9Ek9TNpulkgYwm9tvmi/Z0Z9pB1goYxhmj0QLI7PZfNcIZrMw49eUzd52MExc\nWChjGGaPhIUyiTOLzzm4MB39Z7AiDDNNsFDGMC1CNl9EoTiLV9AWQwsj7e5TNps1TD5H/1ncDoaJ\nCwtlDNMifOfKp3HJrS/MdDX2GFhTJpnN7feFxJjF7WCYuEx3miWGYULoH5pEJs37pEbhsqM/AMxq\n7avj05TNXD0YZrrgFYBhWgTHYVNbI+GQGJI9pf3tLlwz7QELZQzTAriuC8d1USzywtMotCzS7mav\n2a0pM0NizGBFGGaaYKGMYVoAlwWIhqP7ck/RFNXKbBbKfCEx2vw5Mu0BC2UM0wIUPQFi9i6grQY7\n+ksKs1j76gsei9nbDoaJCwtlDNMCsP9T4/E0ZW1u9yoUZq+g79eUzVw9GGa6YKGMYVoANrU1Hi3o\ntnsia5v2dXA0i+9ftQRrtg7PQI3iw2mWmHaDhTKGaQHY1NZ4WNCV2MyXG3eOYu22EdCmwRmoUXw4\nzRLTbrBQxjAtgBYcCm0uQDQSPn0psTn6ezHcWrxvXD59ybQZLJQxTAswWxbJ2QT7lEmKFqGsOEu0\niGbt+N1g2gEWyhimBfAWyVl8Uq7VYJOwxGa+9PqmxQVW9ilj2g0WyhimBTAXSV58GoM7S7RBzcZm\nvpwt/nZ+n7KZqwfDTBcslDFMC2Bqc1p9oZwtsE+ZxCaUFWeJudxhTRnTZrBQxjAtgLk2slDWGGaL\nia7ZWM2Xs0RTZtLuz5FpD1goY5gWwFwcW117MVuYjYJHM7A6+s8SfzuHzZdMm8FCGcM0iNseWY9f\n3/ZCTde6bL5sOOzoL9ljQmK0eF0ZphGkp/NmQogkgAsBHAkgC+BTRLTG+P5LAD6i/nkHEX17OuvH\nMPXw7Eu7sHXXOD5Tw7VFFsoajjNLBI9mYzNfej5lLW4SZEd/pt2Ybk3ZqQC6iOh4AGcCOE9/IYR4\nBYDTALwFwPEA/lYIccQ0149haqboODULAObiaDM3MdXjOfq3uODRbKbr9KUtnVO9cEgMpt2YVk0Z\ngLcBuAsAiOgJIcSxxnebAZxEREUAEEJkAExVKnDhwh6k06mqKrFo0dyqfr8n0c5tB5rb/kQyAcd1\nsc8+vUgkElVdOzCR9/6ev6AHi/ae0+jqtd2z7+7OACgJZ+3Wfk2h6JS1vbunAwCQ6Ug3pF+y+SL+\n4czb8c5jDsKX//WYusvTjGSn4wlVAAAgAElEQVSL3t+9c7tqrmu7PnugvdsOzL72T7dQNg+AmQG3\nKIRIE1GBiPIAdgkhEgDOBfAsEa2uVODg4ERVFVi0aC76+0erumZPoZ3bDjS//bmcXED6+kaRTFYn\nlO3ePe79vWvXGFIN1jq047MfG8sCKGke2639mmLRLWv7yKjc705M5BrSLzt2y3n4oaVb8G/vfU3d\n5Wl2D5bei6HhiZrq2o5jX9PObQdat/1RguJ0my9HAJi1SRJRQf9DCNEF4Br1m89Pc92YFsd1Xfzo\nmmdw01/WznRVrNSTusY0e3L+y8agzZbt6KNnmmyjzJeN8rdrlt+eabFk6yXTDky3puxRAB8A8Ech\nxHEAlusvlIbsVgAPENE501wvZhbguC5Wbx5qiu9KI6gnIKd5Tbs7pjcK/Txct/361CfkT0Puy2b5\ne/kc/dvsGTLtyXQLZTcDeK8Q4jEACQCfEEKcAWANgBSAdwDoFEKcrH7/v0T0+DTXkWlR9KSczbW2\nUFbLQmcmzW5VoXO24Rrd2G7O/q7v4Igt96X6f6OEsoaUYinX5+jfpJswTAsxrUIZETkAPhf4eJXx\nd9c0VoeZJQyPZTG3p8M72p/NFypcMTM4dYQZMOWwdjS3NQPzObSblsUcT3lDU9Y3NImbHl6LTEp6\nrhQbJOk0S2Dyh8Ror2fItCccPLaJrN8+gide2DHT1ZjVDI9l8eULHsPtj2/whJVsvjU1SVrDVa9P\nmU2zwVSPL8xICwpl5/7+WVz/0JrKP6yBsBArK9YN4KmVfXhhw24AtQVk3bRzFGdd9iS27io54TfL\nfMm5L5l2g4WyJnLL4vW49PYXrT4dTDyGx3NwXBe7R7Il82W+WOGqmaEun7I21uo0i1ZO8u66LlZu\nHARtGrJ+Xyg6GBzN1ly+2d6CpR/yhdo3EGu3jWBr/zg2bB/xPpsOLVaLPUKGaQoslDWRbL4I12XN\nRz3oRaNQdLy/c7liS+6aSwE5qxfCW1mAmK3EDcj76PLt+Okfl02rMKzrViiU6rVm6zCeX7sLAPCL\nG57Hly94FAPDFUM1RpYfvIcTEMpqabPeZE5HFgoOHsu0GyyUNZF6zFmMRC8AhaLjLawuSotKK6GF\n73o1Zezo3xjMbox6Js++tAsr1u3GyERuGmol0WPF9Pf6/X2r8ZvbVwIAVqyX5sWBkdqEMn8u1XKh\nLKc1ZTUIOrrupqDbLIHWl5Cc51GmDWChrIl4izTv8GpG92Gh6PoWkKkWM2E6ruudQKvp9CVryhqO\nqVmJege1cDEdGu2+oUkUio53aMW8Zy7vlJnmOzPVZSvRmEPIzH0ZHFv1aMp8ZtEm9R2fvmTaDRbK\nmog38fIiWzM+86W5gOVaSygz61ZvnDI2dzcGv/nS36fZXBFTOXmK1xtjTdZQ7h6ZwpkXP447ntjo\naa9MTVnRccv8T2vd0IXFKQvORbXMTQWLENs086XxN29umXaAhbIm4pkv2dG/ZnQfmj5lQOs5+9fr\nE+YLHsuLT0OIeibn/XEZzv39swBME3lz+314XJpHh8Zyvs1GqY6ODHTbgFOjYf50jdCUleLxhZfb\nKFhT1hi29I3hyxc8ijVbhiv/mJlRWCiLwdb+Mfz+vpeq9vWp5zQeIzHNl45PKGstQdfnt1NLnLIK\nwT6Z6jFfu+C7u3tkCrvV6UZPyGjy5snzIysUjXEd7oRfbZ2uuGMlrrv/JVmWMZ7yhXAtbiVhamwy\nj+0D477P7I7+/nqu2jiIrf1jseseBscpaww3L16HwdEsfncPzXRVmAqwUBaDsy57Cvcu2Yyl1F/V\ndZ5DLE8mNWMumKZ5KZtrrQCy9fqE8enLxhPVp6aQXyj6/98sTI1cSQNcXketUQOqy4O6+PntuOfp\nzQCCbQ93yK9U/NcuegzfuPRJ5AzNtM0fLljuL258Htfcuzp23cPg05eNIZlMAOC5ZTbAQlkVpJLV\ndZcWIlpFUzY4MoU1W2eX+rpg+N6Yi0CracrqzV0ZpdVhaiMq9lux6JSFMGl2v3smy0LJ0b9QcDxh\nQ9dnyIhPVqv2Lr6jf3T5U8p3M2fR3oVtRFzXxVSuiMls/S4GnPuyMaRYKJs1sFBWBT2d1Z2EKlp2\nlDPJ5be/gHOuecZzcJ4NmH3oN1+2lk9ZsU6hjE9fNp4o3yyprfIfxJkuTVne8I90jfvr/w+NmUJZ\nbXUyQ2LYTKRh/w7Df3DA4lNmEfwaIeSaQhkrympHa8rYBNz6THdC8llNtWbIehJUN4OxiTyKjots\n3kFXx0zXJh5eBPIWd/Rn82XrEaW9LBQdT3tQMsdNj6YsX3B8Akuh6CCdSnoL5tBYruyaarjqrlV4\nZHkpvZvjuHBcF8lEomwOi1u+P0NA9OlLm89ZrcQNazJbuObe1Xj1QfPxpr/ab1rvm0oooYznlpaH\nNWUVcCNMIJXQE2+rTCY6svdsOg1aiiHlX8iyrRYSo87Tk+zo33jCwoy4rtSS6T4vxjx9uWnnaF3j\nzh8I2aZ5KteUxU3RZrb1oWXbyq4rBTZ2Qq+LwpwzbKF+bCcxGzGOfcFjZ/lrMZUr4P6lW7D4+e3T\nfm/2KZs9sFBWgfGpkqmv2kmmaJm8ZpJ8A3ew00XB05S5s0ZTVm+cslqF+E07RzE6jVHpW50wP72g\nBjuOuW33yBTOvuJp3PbYepx33bO4d8lm6+8GR7NY9tIu63d+TZlFs1S0+JTF1mRFC29h2UVq0ZSV\nfMrsITFs5s1a2ZMc/U0/wumGzZezh4rmSyFEGsCJAPYCkNCfE9FVTaxXy+Dz76hisdW7caB1NFOF\nOpIQzxRmShe/o39jhbLh8RxGx3M4aN/emq6PigUVB8ey6FXDxFQBZ1/xNHo60/jVl95e9fV7ImE+\nZXoc6ZhgcTRloxN5AMDW/nG8sGEQL2wYxHuPPbjsd1++4FEAwHlfeCsWzu30fWdqykxNViGQh7KW\nOaeSli8sPE/cRbpg05SFmC+9/mzwPDPbBQod6qTZQYpteJoy45k9vaoPh+4/F/su6J72+jDhxNGU\nXQvgmwDeA+Bd6r93NrFOLcXwmHk83f4yua6L869/Dnc+udH7rF7NSTPIG6bA2YIZ+byZmrKr7yZ8\n/+qlNT+rqJN+cajXJ21sSgoNE9nZc4ij2bghfVoIhIiwBXINor+bijBfmlpK22Gakn+kX+ubLzq+\nNF2D5pwT812t9Luw7CK1CH3WOGW27xtivjQ0ZbNn2rIS10zeDJIBn7KR8RwuumUF/vTI+mmvCxNN\nHEf/I4jo8KbXpEUxd61hi22+4OD5tQPI5oo4+c2HAghMWC2yw/N2arPIZyn09GWDfcpGxnPI5ovI\nFxx0dlSfb7BuR/86o7i3iqA9NpnHnK40EolE5R83mTBB2Rz/juPGSoemBY2JqXCh14xjaHvHiob5\nyqdlCozt8cl82TWVqDRm9PgoP30Zq3ifIGvThPkPLjTObWNPCh7bCpti3YeTatMw2WK+uUw8TdlK\nIcQBTa9JixLneLpplrD9tlU0ZY08FTVd6Im/6Li+PIGN1pTlCrK8fI0TZiNzX9Zyfa4F4rYNj2Xx\npV8+gjue2Fj5x9OAKXCEmYeLjhnINbwP9bgYn8qH/ualLUPe37ay9H3zgUMrQS2wqY2Lr8mqoCkL\nOQke39Hf1DSWu2XYcm022qdstgtlXkaHGdgUB83XeoOenwH/NiaaOJqyHgAkhFgBYEp/SETvblqt\nWohD95vr/R02Qea9l82fx877u0U0U42cLKcL34lLQxBrtBBS0iLWGKxzhjVlrXDwYXAsi6Ljon9o\nqvKPpwF/nxqanMCzihNPUGt/ooQyc0zaFjszeGzQ0T8sgXil8bhp5yj2md9dcY6xBXwFZB+5rltR\ns2mrU5h2uJGnL80SZrlMNqOasuDzr3e+Y5pHHKHsXADhM9EezutfsTf+89TX46JbVoQulgWLWTAq\nivZMkfdCYrRGfeJg1tVM9dJwTZlaUGs9GdXQ4LE1PJ8oX6dGQZsGsX77KE568yHW7wsFPeHPvIAI\nRDn6+wUM/U2UA7YeF1GbgXwFYSo0JEZASDOJmjvGp/L4zpVL8I43Hoh3H31Q6O/kPe2O/oDsp1RF\noax8fIYKZcb3cQS+KPZETdlMCELe83cDmjIWylqOOELZj4no6KbXpIXRTpLhmrLyBb3eBNW1sHXX\nOPZd0I1M2m6VbuTpyyWr+rCE+vCZD7zOO9nTDPzO/aU+bbQQogWJWk+M1etDaDox13J9bho0Zedc\n+ywA4G1HHIDe7kzZ9/o9aBWTSFicMlPAMNMHRflaxllI84VooczUUvg0T44bIZSF33d8Mg/HdTE6\nnquofYlyXXAcF6kKjizBYLdA+InjQuDzdKoeocz+92zEWydmxHwp7637sNXeVaZEHJ+yHUKIE4QQ\nnZV/umeSSmmhzD6AC5Zdx3Snzdk5OIGzfvMk7n5qU+hvGmm+vPCWFXhqZR/6hibrLisKn1CWM82X\njfYpKxes120bwTcufQLbdo1XvD4q6XMcTEGsFvPGdGjKNGH10+Mr1yITvT/wqF1oyBvjKKrf42gU\nfOVa+kAvxi4CwmDBCR0zUQu45zZh5NIM0pFJ+upju0+c+Skq2G3Z9yHxy2qh3lPNrUTR0JRON8Hx\nkc/PXF2YaOJoyv4awMMAIITQn7lEVPURNSFEEsCFAI4EkAXwKSJaE/jNIgCPAXgDEbWEc0raEuPF\nJG952YKnq5qNDt1hhvAI0sij6tOFuVBmI8yXoxM5DI3lcHCNccZs6vy1W4exfWACG3eO4sB95kRe\nX7dPWZ3mz0rm3ImpPNZsGcarDppfddlBwgSUVnMedkOEBvP5+BJtR/R7nHfGbLetj0zB3QyZEXT8\nj3tfczMYdn1nJoVc3in5M1nUTXHGm1+zV651CzvdWiy6QLlSNT4+TVnz5616za1RzKSmzHx+rus2\nXFN29d2EQ/efi7cfeWBDymtnKmrKiGgRESUD/1UfM0ByKoAuIjoewJkAzjO/FEKcCOAeANObGKwC\nXjTk0N1suVDmSwLsutjaP4YbH17btN1eSaiwL86OG+/ofxwmjVhYzV6ACzF9yn50zTP41uVPYfdI\n9XJ80Sn59JjPTZ/IjONn1siI/s1w9D/rksfwg98txYYdI1WXHSRsUSm0mEkkjk+ZOabinL6Mwh8Q\ntryPzH7LBu4bNmaitNrmwhr2TDozKe83QJhPWegtjDpafMZ8gm7IhrROrbxZtWa7gaxYP4D/OOdB\nrNo42JTyzUDYQQFzzZZhPNLE9EvBNFmeu0YDNGWFooMHn92KK+9cVXdZTLyI/t+0fU5E36nhfm8D\ncJe6/gkhxLGB7x0AfwNgadwCFy7sQTpdnYy4aNHcyj8y2HtEhsXo7MpYr92mTpsViq73/ZARz6in\npwNPr96FPz++Ee897jC88qAFVd0/Dj190sSWSqesdTSdr3vmdFbdByZrNpeO/s/pra+sSmQypWfr\nGjvYXMHx3Xf7wAQAYDhbhIioj62uE8aJujm9Xd5v0h3y9ejq6ajYxjmbSn3S3V3590E6OkuvYjpj\nf4ZRpIx3wHbtalW/qWL14z9I79wuaxndajFzQuowkzhOabxs2V0yuXfPKXllZDrSofXu6ipX9wR/\nawo3tjHT0VF6xolU6Xl193Ri/oIe32+TyQQcx42s0/ZhOe+4iQR6e7usv+npzgDDU+jpke+pzf9z\nwcIeLJxrv75Ux1J7tICbSCa8zzJG2+YYfbpg4RzsNS+67CjMsjo77fNvHOJcd+d1ywAAdz29GScc\naz/MUg/d6h10Aey1dy/ShiPfL25cjufW9OP9b38lOjK16jzsLFo0F0ljvM2b342u7g4A8lnW+64O\nG2GjWu29B1qzTlHEMV+ab3EGwEkAnqzxfvMADBv/Lgoh0kRUAAAiuhfwmUkrMjg4UVUFFi2ai/7+\n0aquGR2Vk9/I2JT12l0DUiDKFxz09Y0gkUh4nwHA8MgUhkbkQrCjbxTzOhv70gFA/8CYrOt4DstW\n7sD8OR0+Z2xTuzU4NFF1H5i8uLYUJLN/1xj26qnHPhHN+GTJHDs6Ll/+VDKBbK6InX0j3iEMzdqN\nu/HyRXZTY9izHxkv3WPXwDj6F8hFZGhYPrPBocmK/aV/CwAjo/ZxEsWEEQ1+YjJf9fWDxv31GLQx\nHjKGK2FqKfr6x9CbKVey71bv4uRU9fU3cV0XT6/qw18duhBzezpqLifo46nrNLC79G72G/6CY2PZ\n0Hqbz9e7NvDbbC76HdPjV34/6fvtrl3+dnZlUpjIFjA2Hl4nPcdMTuUxMGj3e9SnKgd2j6O/355Q\nvb9/DIWIUB+AbL+uh9a6ZXMF77NxY/yadenrG0UxW/vh/ZHRkuZ7YjJX07iKO+e7SqtXy/sXh93G\nWrVjx4gvSPXIeBauC2zcMogFvY1z39ZtnzSe77YdI15dcvli3W01/Yqb0W/1UMt6Px1ECYoVhTIi\n+rb5byHEdyFNjLUwAsCsTVILZK1MKqb5EiidNvKdTCo6nu9Ks0w7utzB0Smc9ZsnsXBuJ877wltD\n61gPWitl3rdZ2PJd9nSlMTqRRy5fRJfaoadTCRSKLnburv7gQa5gN2GVnlllJ/q6zZcNdPSPOvFW\n60lZczEP9kfRcbB83W4vxVO9Y2LTzjFcfOsL+OBbD8OpJ7yi5nJC0ywZYyrve/blz21L3xi+eflT\nOGDvnrLvguR9zvAWnzLj+ynTfGkJidHZIYWyyCwDxpwSNmY6taN/SER/IJ6JUZfvGrlCw/z08j4/\nvTrnB19C8so/d1wXS6kfrz1sIeZYtJtRZJS2uZKpevvAOIqOi4MW9cJxXd88FIV5srvgOOhESSjT\noVbGJ/MNFcq8+wXcMkqm7xoOJTkOnnhhJ4569T6Y05XBFKd2ayhxTl8G6QVQq273UQDvAwAhxHEA\nltdYzrSSquDobzt1FQyRoE+75JoUw0nfV2t9Bkezvu8bGTdth6EFbPZJO9vpyx5l6jNDZGgTybaB\nyiclg4SFMtD+RnEcc+s9bVtvSI24vlGpGoUynx9hoPx7nt6MX9zwPK5/cK2sS41jYmQih6vuJmzu\nk1rfevN4+k5fhqQEylUQIO5buhmAfyMShm8cWYPHGodWTCG3WC6UdSktSvTpy8o+ZR0Bn7KwkBg2\nfCdWdUR4I0en348srE/rPX1ZuZ4m67eN4KJbVuDBZ7ZWfa8OFUqokg/pRbe8gAtukkvXtfeuxtcu\nejzWRqTgm2cCpyHVujA22ZyQoH7fXMd3+rLaAxSrNw3hsj+vxOLnpA/cdJ78bgfi+JStR8nfMglg\nIWRA2Vq4GcB7hRCPQZpFPyGEOAPAGiK6rcYym44nlIXFKbNMQsH8etOlKZvM2l+QYMDMejAnjqZr\nyiwR/Xu60r5/A/DMdbUIZWGR2KuJeu1LOVODUBUWUysu5sQYtZAHzb1xiTrcsdrwp7N9H5ebHl6H\nvzy3DQ89KxfUek+phR2eKPo0ZeELJeAX/IMET+r5NmcRuS8Bv6kzmPsSKAllkWE6CqZQFn760vxt\nNSExbFkGfAGyQ/rX1D7We9Lb9WnK/GWNTeaxcecoXnfYXt5nOuNCLcJNOu0PHxLG6GTOE7C2D0xg\nbDKPiWwB89PRpnYzVEhQ8NPrw3hEbtV68G9EioFAxy4y6fjzgq7jhDJLT7KmrKHE8Sl7p/G3C2CI\niGo6wkVEDoDPBT4uO7JBRIfVUn6zSCmHzDBVfN6qKfMLanqialY6HK2BC0uY7POvqXOiNNswveZL\nea9urSmzmNSGx3KYmMqjpwrTRbimLL4gXW9Ii0aGxIiqb62ai8kIoS8YcLfWiP4TAb+mejMDhKZZ\nquL0ZVTiezMSvuu6yBccpFNJFIqOVdtilj9VQVOmhak4SdJt1wfL0X1pm8NCNWUWk28xZB4JN1/6\ny35sxXbc/Jf1+N+PHh3rAIA/Ibn/uzuf2Ig7n9yEH372OOy3UJqX9TtbyzybSflNvWHk8kWvP3Ro\nkzj382nKHAcTUwUUHQdzezq8PhuvUVNGmwYxOpHHsYfva793YF4Lbj7DAo7b0GuN7uvJHAtljSTO\nk/gpEW1U/20iohEhxP1Nr1kLkaygKStYFvVgnLJaNGVjk3mMToTHHTPxdsIhwRYbeUzdr1lqrJDp\nui52GU7VBZumrLNcU2bWaWSiuoktF+JXlKvi2HgxJPxCXMxL6g2JEVXfmoUyn6bM/8yDAkih6Nak\nLQz6u9WtKTPfhRANTyVTW9RiaxNKejrD/ZLCko7bQmJoH6U4mrJCpE+Zro9bVgdbvcI+L1o0ZWEm\n+3xA+DC5+p7VGBiZwu2Px0tab9YsqCkbUXPjqPG+6+cVJUyH30uWX2mO1kKN47rec4wTzDqYhu/0\n8/+C//rFI/J69U7Vqim77oE1uOLOlbHuncsXK2afiCIo+E4Z1pnpiCW3pxOqKRNC3ATgKAAHCiHW\nGV9lAISHjd8DSVcSyiwOvj7Hb9f1BnI1ibS/+PPFAIDLz6yc+902kYxN5TFPnV5rZJTtZmrKbnh4\nLe58YhO+/tFj8KqD5vtzX2qfMqUFC6tHtRNyLrBr9D6vIuq1Wc/aNGXyHgnUKJTlplMoCwph5ffL\nFxxPIIhLKunfI9aah1RjygNhaYDCDnl430cJZRZBpKszjZGJfGTuSyDo6O+W+RHqk3nRmrKSoBXm\nx9fR4feTso3NsHXUnwVBu2XYffCcMEE3IFi/4oB5WLlxEM+v3QWg8il7N2STCZTGvG9zpu5di59T\nnODHBUMrmS843n1iacoCh780ruFzHJXwPoqpbAGT2SIc17W6KATHqs1NIy66rfrdMDVl9abVYqI1\nZR8H8G4AdwN4l/HfcQDe0fSatRCVHP2rMV82K1mz7cUyd5C24I+14hNiGpym484npLy/cac8xmxO\nJvovrSnTQprrur7FtVrTRdhpsZz3zCr3l08rWYtPmbokk07WpMmMbb6s8Xn5zG2B8m1joBZhPXgI\nod6xFZbM2p/kvnSPLX0ywLPNj9GGb6Er+k3rdkd/U1NWWsgKTrmmLJNOIplIROZiNeeSMCGkK4aj\nfyxNmeoTnx+Zb06xa8+D400L6rtHsrECPftyXwa+0+4MOUv6tVrMl3E2Ybm8/176OeZiCIG+U78B\nny79Ta3mSz0nh20igplR/PevVlMWMF9m4809TDxChTIiGiGiDUT0dwAOAnAygO0AXjkbwlg0Eu1T\nFhoSwxiI45N5ZHNFhDn613IyLY5K2LaAjRrxt/zJ0uMLDbRpENsDzvO5ELNhvfQZcXy0j4Otrt3K\n0V9rG4qO65u8q52QcyECTTWaMnOxqin3pbomk07WdH1cR/9qNWWrNg5izZZhn69icKzZ7leTUBbY\nYdc7wTuO6wXoDDPfmwLEyEQef358I5ZSKQ5ftPnSWNhUXfWGwfY+Bk/AmdcGn0smlUQqEFoniHmY\nIMzZumS+lO2wmZVr9ilzXG9uiutTZvbnxh0xYodFasrK/bn0u1ybpsycT+x9Yh78yOUNTVmc05ch\n/nhmf41VMF86jovL71iJF9bv9n1eEkbt9fC7ZTj+Oa9aoUzHqSvovp6+DC/tQEWfMiHEfwH4HoAz\nIGOMXSKE+EqzK9ZKaHVwuPmyNBDPvW4Zfn7Dc2WnvfLeTqb6QRvHt8ZW7qix6/KbL+PVwXVdnHPt\ns/jGpU/6PsvlHU+r0UhN2bKXdnl/68nOtigFfcqCbddmjbgTRNgJvGpSkdSd+1KZHdKpZE0Tm81h\nfeuucaze7D8ZWW3dLr39RVxx58rIidemFaol9EsjNWWuCt2gT5WFxSmzbZLM9kUt7pGaMtvpy4iD\nQkHtdTqVRCqZ8H0+Mp7D969egnXbRtQ9zHraF/OOjjiaMnu9/D6p5T5lQEnIC/cpCxfKdsQI/B3l\nU5a1OPV7AkMtmrIYz90c12OTeW8zGM+nzBTo7Jr9Spqy/qFJPPL8dix+fpu17mHtDt7bZt2Jizfv\n5sp9ylgoq584jv4fB3AigHEiGoBMUP7JZlaq1dA7+KDTqiY4ELcPTPh3lG5JKKvFfBlngrFqyoxD\nAtWYLwtFBxfctNynMTDLcVwXc1S2gEa+hEOGZk/vgm2LiA6JkfOEL3//ZPNFLF83gM/95KFYu/Gc\nTygz1fzqmcXxKQvxr4mL47hIJqVPUrW7fFMTC5Tqe9ZvnsSPrnnGt5hVa74cnchhXB351wSFVKv5\nsobNR5mjfx1jSwsLacvJadsJWxOtpXVcF+OT4ZqLgkUQ6fbii1nMl6FxDssPRqTTUkA3x/9LW4ax\ndusIlq8b8N0TCBciOtMxcl/G0ZR5oX787SoWy4WyKJ8ycy6LE+jZb4L2fzdl0Q6VHP2rN+aY/Rl2\nit303TTn12p9ykyHflPLaQplNmFZP2fzfXSM9cVmRnVdt+yQie1w2rX3rsblfw4/LKDxHP0LDmjT\nIAYMM3Sz4nACcpN5y+J1Tc+BOtPEEcqKRGQeAZwC0FbR4qoJHgtIx8fgySXvGHENC03YLtgkb5kU\nfD5lVZgvX9oyjKWr+3HhLSvKvtPtmKMEo0b6yJmRofWEa1vcyjRlqm16Mc3mi9i0cxQugC39YxXv\na7bBFDCmOyF5MplAd0eq6iPmwQUhWN+4ps0g+YI0w0/mipG7YZtgXouWK+igXE88Pb2elYSyEJ8y\ny/jV10xMFSIXAFvsP60ps/VJmH+YdB73/z6jNGU2bZhexM3vwuITxgkeG+YDaX5uO1VulueEaMqC\n7crmiujtziABYOfuypoys7plmjJtvjTeFy0w1OPoD4Q73Jvz97CxiYxjATHNzWb5PqFMff7Qs1vx\n6R8/hE07A6m81LvucycwDzlZ1gH9jPScPZktWB3971u6BY8s315x/tLvzKYdozjn2mex0kjgHrVJ\nz+WLeGnLUOj3lXjgmS247dEN2Lyz8pxeiRXrB/DTPy5rWoiqeogjlD0shPgJgDlCiFMB3AbggeZW\nq7WolGYpuADl8k7ZifA00/MAACAASURBVD5PzV2TUFabpmzE1JRVYb6MCvquJ5/eJmjKzFhYekdq\n9Snr9PuU6T7Vdcrmit5OMk7fBf17AP+JqDgCRt3mS0eaL7s708jlS4v09oFxLH5uW+S1wTYWio5v\n0vbvvuPXTS/0+YITGjDYdV2rViGOOSdI8P2qZ2yVNGXl7675LtgWUy2AVApHYzPZdXakkECYpizM\n36fc0T+tfcqMzye9MV2ezips49bZUYq95biu9aRlHE2ZFsbKNGVag1aFT1lvdwZ7z+/Czjjmyyif\nMs98Wb6Rqs18WbomTFNmjuuRKjVl5vM330lTKNM+ZVfdTQCAJQFrRc4ilIWZQkv3VUKZmh+ncn6h\nLPhMByocwNBzs23URM2VDzyzFT/83TNYv708zOmKdQMV3zfdZ3GD1fYNTWJwZAr3LdmM+5du8X33\n0z88hxXrduPplX2xyppO4gSP/SqATwN4DsC/AbgDwEXNrFSrkUgkkEwkQhc0m/bBfOl8J9diThbm\nZBQnxINN2DM1ZcG4aVGkIwIJ6gmgKUKZqSnzfMr8dU0kStHOczm/SXhudwaDo1lk80VPoIjzAtsm\nqELR8SadQoXTl7l80TcZ1pr7MpVMeG3L5oro6Up6/nyvfNl8HLiPPdF6MB1Rvuj4Yr2NTUWbRMIw\n+263kRg6aDazaZNqGRdBTVJ9mjK/+TIsZp9N06vrXikqvFmOFuYzqSTSabtfYFScw+B36VQS6WTS\nJyjo5zGRLdcih20+OtIpJBLyHmHjMs7pS++9CIyfUh7McsFIfl4ulO01twt7z+vECxsGMZUrROeN\nNC437+y6rj0khnc4x0Wh6HjPPw7mHBqW4su814hPUxY+R7uui9se3YANhiuFab407yUPiZXqMX+O\nP0uAzXyZs5hvTfQzm9udQd/gJCazQZ8yf0aJnYMTWLSgO7Q9UYqFKKuCFsJ3DEzg5QfM8z5fu3UY\nP/3jczh43158+5NvCr1er6lxtaBnXvy4799vP/LAsiC5s05TJoToBZAiokuI6B+J6MMALgXwtWmp\nXQshd60hO11bjLCQnVBcTZm50E3FGDjWOGXGzsN3BNpxsXzdAH5xw/PWRSmBcFWZHsQ62W8jhbKp\nwOQEyIXBrI1PcAk4+s/tKcUv02XFMQXmfOZLV30WvpMM8rnzHsajy3d4/64192UikfAWqKA5Kqqf\nJ9UEP09N4MWii13DJSHKHIvVhEMxJ/7dI6Vcqnmf2Swkg0QtQlmZr1rtviP6/dGTcFgIANv7WNKU\nVRDKLI7+mXTSi+ofVq4mkZDCV96SZimTtmjKPMfqck1Z2HNIJhLIpFNSUxaqEfP/e8mqPjy1cqdV\n+xvcgHrmS9cUdO1aeR2vsbMjhf32khH4K/mVmeW6ASFRf2c7fRn8PA6+U/Rh5kszSPV4edBaG1v6\nx3HrI+t9+YjDNGWA/30NmtdL5ss8vnHpE7jqbvKHA7IILPqZ6Y30ZEBTli8WfZrWvsHoZxIlgEat\nb8Njcj0aGvPnZdap8XTO2zC0IDuVrzyn294/m4aumT5wtRIqlAkhPgtgN4CdQoij1Wf/AGA1gNOm\np3qtQyoZrimzqWzHQjRlcQeBP09ejUKZ4aQcjCn01Is7sWzNLmzbVW5CiNKmBM2X9SYkX7ttGLcs\nXgfXlb5LehEthbtwvECagAwwqo/56wlKt71XBcr1mS9DfG18bTIFMMsp2Wr9o2rKfenKMdatIsIH\nhUl92GQqV8Di57b5Jka9gOhAwVJTZghlpm9hVeZLw6wymS+duPUtXiFmHvWbjTtGY8WjAsrNe3WZ\nLz0/GjlOzUUwGN08iL6v6TNkwx9ao6SZy6QSFXNfAnIsZ9Iy7EW5+TJRdvoyuNHIx9CUJZIy0Xbe\noo3TBMfrhbeswMW3voBNhu9OwaIRA0rjKSzEg+8AgOrrzkwKe8+XKZZMDayNsDRL/tAUIUJZHUGk\nJ6s0X0b5lI1YzHJ+R39/PU2NWtCMqu9fKLrYPjCBdduGK2rK9DPr7kojmUhgKlsMzHmubwNWSVCO\namvUO6vfJ1M4rXSNiZ7n4jxXm6Zz1abBss9qOZDUbKI0ZV9D6aTlmUKIXwP4FYAfADhyGurWUkQJ\nZTap3G++NJwyYw4C817xhDL/b1LJhG+354/E7XpCo80XJUqbomPTdHWmkEwkvB140CE1Lt+/aql0\n3uwbw2S2gN7uDFLJRElTVnR9QlkymfCcl0uO/n6TqjRfxteU2cyXlSK9R1GbT5kjHf21v1xgotaL\n9i2L1+OKO1fhhofWet/pCWh+r8reUHCwa8gwX1Y40RVGcAe/QJXvP6Vm1yhIP0oXP7r2GVx5V1l6\nWytlOTXrMV+qouaohciM2ecPEFx+Dy3saGEyzATmE0RUHLBMOolMOmnPfek46DDMJ1LwSiJfdMqE\nZelTlvSZC/Vz1ou4eY8wn7JkIoGOTLRQFjYmfn//S6W6ez5lAU2ZJYOJTyiz5K7tzCTRkU6VfW/D\nNeyXPutBrlyrDvjjhVXj7O8aJxiB8M2mKfSYYypKU2bzlTJdCvRz1Ruy1ZtKzvDBdzAYh2x8Mh8I\nnB2uoU2nkujuTFk0ZY5PMKzk6xelWNDlPvTsVtz+2AbfdyPjUhgLasrihonSAmqc52rzCSSjX/Wh\nokYHP28EUULZOBE9R0S3QEbynwfgNcqU2Xo6vyYT3LWaWKPph2rKqhfKTPPl8HgOjy7fXnYSKViH\nhXM7o4Uy9d2kTd0dqSmTv+9Ip5BRO/DHVuzA2Vc8XRYTqxqmclKQ6ulMozOTkr5KjpyStbAFyOfg\nacoC8chK5kun5BQdR1NmifFlc/63YRMcajt9KScKbZoNCpN6POgTa6uNU0x6AvJSajXIfBncwc/v\n7VTlm0JZmPlS+pplc0Wf6XNwNIutISdig31ZUIJdLehnkEwmMKc77VsYfcKUbRFTz3tA9eH+ytQW\nxOdzZWjKwsyXxaLrPV9AjuVMOml19M+kk0gHNWU5v59kMJeijVQygXSI+TLsAJN5Sq9U95Kvpa6f\n2QehITHMzaWhKfPCDFVYFH0R/UP8bMPMl5O5Ai64eTnufHxD5D2A0hyiheawedp3+nIink+ZzQxu\nM18uUO8XbQ4XyoLC99hkobJPWbE0Nrs60pgKnL4sFBzffeoxX+pyr7qbcNNf1nkCv+u6GFbm3sGx\noKas8hztGAeK4igpbPHe1m4d9sZ6JqOe8yzTlJktHwTwMSIqN8q2CalUePqbSpqySV/gzbjmS/su\n+N6nN+OyP6/EuoB93CaUycS5JXW3WbaOvzRlUfPaFm69S80Zu10tlO1QgsKO3RMqoGK8hdRc0Ecn\ncpjKFdHVmUJnRwpTuYLXr/PndEBHS0ilElJblk6WmS/neqcvCyVNWYivjemTEtw1AnY/MxvVOHRH\n4bgqTpnyKbOdqARKJ6jM8aW1VVpTFnT0N2NtVXf60t9383rkc/BHIA8PHaAnQFMg+vIFj+Ksy56y\njpFg3dwq6+u7VpWfSibQ253xFsbn1+7yvTtRmrKBkSkkEsB+C6XTczCXp898qbUR6QTS6XKhTMeK\n0ppQQM4p6VRCximzacqUdl63Jer0ZRjJRCLUfJkOyZph6/NCQPjSfVGKU2aacu1aZh1Dq7MjhbTK\nc1opRIvPfGk01xabDPAvsn27J7GU+vHwM/6Tdzb0ONDvV5jgkfNpykyfsvBnMWYTyixxyhbOlUKZ\n6VsV3BiVBcrOF32bb1u99TPQ7hETWf9hAqkpK9Wnf2gy0gUj2Na953Xh9S/fS5YVWN/0hmwyW5rP\nhwLmS933lpSdHpPZgqczNZUUYZtCm1tFruCgT1kQSsJ36+mXooQy86mMEVFtSbn2EJKJRHhIDMvp\nvHHfkWVzAintHPT/71uyuSxmT5j5clipgE3tg6yD/0XRu67xqQKuf2gNbn1kva/ssYiTLNZYRp4G\nSWnKMlpTVvQW3WUv7cIXf77YF5k/iq27SpPPwEhWLlodaXR1pJDNF0uph1JJT+DSu/uOTKosTpn2\nmcjmHe+Ems186TguPnPuQzj/+ud813ekk94i4dOURezmbYu6HicPPrsV37j0iVgnQGWcsmTJpyxb\nCAR99ftImelYxoOasoLfHOE/fVn+bCem8liyqq/stGGw3r3dGU8Q1+gTaMEkxKYQMDaZL5vkrbHN\nYn4WB09TlkhgTncGYxM5OK6L869/3ufTYnXIV+/z7pEpLJzb6QlSWhOrsZ++TCnnfX+5ui8W9HZ6\nB1dSyYSnVbOdvkwFYqzpZzqlEk/HMe8mkgl0pFPIW05fZkLSx1mFsoCmzBPKLD5lvg2gRePfmUl5\n4yVKKw/4tWOmKdOMTWYLiQGUzHCDMXwa9TgrxV+sbL40x3Sk+dKitbFpyrRQ5tdE+6+13cdcC2xa\nJP0M0qkEujrT3v30XFooOGVJxaNOHgcFv//51zfiXW98GQDZb2YdtBBk+mcOjeUCpuiS9SUMWzSD\nFesGcPr5fwFZfMXCDmpsUQKvFsrihteYTqKEslcLIR4QQjxg/m181lakUuHJgavxfckXHKzdNoxP\n/fhB0KZBbBuYwLX3vYQ7n9zkL9O417aBCazZMgygtDMw7fIyIXepDh3ppGfyG5/Me0m+S/V1vUEb\nVyjzhJVCaVLWC7TWQqxQ+diCWrwwthg7wn6lMu/qVEJZriSUpVJJzFUnC/VE0qmEspv+shZXq5g+\nHekUOjuSmMoVPA2gzXypJ4gV62R984ViyRdIPUtfQFnDjLZ++4j/O8skqSec59bswvaBCe90URRF\nx0UyAXRrTVm24A/66uidvAqcmyviu79dgvXbR8p9ygLBSP3mS/9Y3do/htPPX4wLb1mBO5/c6Psu\n6Cw7pzuNTEDgGBqVfRk8Qm9qyly3fEcb5ZBsEtfnY/fIFO58YqN3T/0MEskEersycFx/CIMopEDp\nYHA0h73mdaFDmTr2md+Fz5/6epz05kNkfa2nLxPIpJJlYVS00NKRSaG3p7TB0EJZucCU8Ex8JaFM\n9qEL+fzjacqkqSZfcMqCxHqZC4JCWcQhBT0PaD9PPc7Cw22Ua7SkUFaek9SGX1NW7p8G+AURn6ZM\nCQRBx3Ib+YBfapgGJczcpQUV2jSIb13+lG9+tvmU2eLPaaEMKPl/6c3lxFQB3/3tEjy1cmdZWWb7\nouKUpVNJb34BjEDHhk+ZFkr1SckgTmCtAeRm2DzlbJp1tSnULK/ouBibyKNQlFYWLXAFw1WYmEoO\nLZBrM+/67eX+zMH5Rj9XHUw8owTAsNAnM0lUnLJTpq0Ws4Aon7JqhLJcoYiXNg/DdYHVm4cgDlkI\noHzBMBeoJav6sGRVHy740tu9AWwO8qAJIJNOeou3TY07auRsszkI29qTLzroRuml71Dmy/HJvDfp\n6Ovinrbb3F8SVvQE2t2RQmcmhVzB8RadVDKBeT0d2Ipxr97zezuwcccobn+sJEh0pJPoyKQwMpH3\n9tQ2TVlwkh6fKqC7I4VEImE9fQnIiWTt1iGcc+2zOPo1i3D6h98AoDwRsZkaR/t17R7J4pUHyu+z\nuSKuf2gNTnrTIdjHEGTcQJyyyVzRt4vTz9jcTa7fPoLL/rzS83nSITHyRcc3JkzzSVDgNjWoOwb8\n2trgLnJOV7mmTC8++y3swfaBCXSkk8ip3bJ5r9GJnC+3pTVoq20zEFNTds/Tm3HP05tx6P5z8drD\n9vIc/aWmTL4LQe1yGPmig6FRuZvfe16X1+fpdBLHHr6vJ+SaWh5fnLJUAo7roug4SCX9aZ5SyQTm\nz+nE6ETe8z/LF9yy55JSccoAtahm/O/qZLYQS2BNKk1Z0XHLhN50QOgD5Di0ma50W/UBks5MqW7a\n99OGL3uCYb70BM5KPmUw61b63AyLoOckmZfX0JSpU4ST2QKyuaLvwFAQLWj0dGnzZbTwFUTX4bm1\nA9jcN4ZVmwZx3Gv3B1A5tIoWiBb2loSy+XM64ML13sEl1GcN6QD4T7Dafcr85ktNT1caY5N55AuO\nt4ndf+8erN06gqGxLA7et7esLNtGoKsjVRLKCo7vAITebA8bGvVC0cWqTYO4/I6Vvn7Wmx8bpuZL\nb1a3q/nKJnQHfcpefsA8LF834JmGdUq3sFO2M0moUEZED09nRVqdVDIZO6J/FK4L9Ct/n13DUzhY\nvQzB3ZTdzFTAeLZcUxa043dkUiUzl0UNbQqAVk2ZRfgsCSslVXNHQFOmibMzBYBthsO3J5R1pj2/\nKq26T6USnsChhcxD9u31EjNrMukkujIp7DQcVW3pZwaNScxxXAwMT+Gw/ediaCxnPX0JwOc798zq\nfpz1myfx9iMPxKsPnh+ogzRzu67r+XWZQuqND6/FA89sxZa+MZz50WO8z6WmTJoXACks3f1UScOp\nn0lwwezpSnv9ZDr6h2rKjHG1pW8MS6kfh+4/F9t2jZcJLcFDIHMs5suhsSxSyQQWzpMLyr4Lu7Gl\nfxwDI1O+EAZjk3kkDKeRqMWj0meap1f1YeWG3fjYiQL9avz0DU7itYf5Hf27O+W7EHezkC84XlTz\nved1ecKLNvfZ0q6VfMqSnq9WoeAi1aHbUTIhze/twJZ+KahlUgmr+VLHKQOkQOS6rm8sTwaCjIaR\nTCQ8p+Zgn2ttgXnr0BOaRRdLqR/3Ld2C+XM68KqXLcD67aNS2Ivw+ws3X6o+quAz6A+JYXfpKIWJ\ncHzCYZ9xinB4PIt9O+wHNoDazJea3u6MJ1zozfJAyEEbG56jv6Epm9/bgVy+dEimpzNcf1LJfKkF\nau3or9FlFoqOpzE6YK85nlBmIyiUdmZSSCVLYz5XcHzrizYh688OWtSLDTtG8cQLO8sEX3PTFsTU\nfOk1S8/Hg5awKkFlxN7zu9DbnfE0ZXo9a0VNWfxwx21OKinDP2zYUb5bKRScSCk/SJ8aTLuGpzxJ\nPSjY2ASj8am8oSkzhTL/4O7IpHzmyyD+yPnKJOK6eHHDbmsePqA0eeoXqSOTkqasglMWhyeuRmLn\n4KQXZsEzX3akvB2tfrFSyYTnz6Prfsh+c8vK68ikypyxC0WnrH92G0Lj7tEpFB0XixZ0I51OYmQi\nj/XbR8omjELR8XbRgEyOu5T6LBOLFN5HJ/Led2Z/eJNCYDGSjv4JnyO4KTCHmYnm93RgYqog+y2j\nhYGApmyq3HxZKDq47M8r4QL40Akvx97zusrSq5RrytLIpFM+YWBoLIf5vR3oUv2+17wudHWk0Dc4\n4avr6ETeN2Zt5iHbmI8y0V10ywo8tGwbhsdznlCm/68X8GSiZLrYHXOzkC86Xjl7z+/yQrBoQSJo\nVjTrmUknPeHN3KyZpvgFaoMxNlkwFjN/f2hHf0D2Sy7v+ISSYP7CMLSjP1C+YNt8yqLC/ug4T5/9\n4Os8U3nRsc8XXnm+kBiGUJaMd/rSFzzW58Nl+pHJvtGfaW2QuTAPhZjjNF6sw0rmy+Bcm05ibk/G\na5sO+9A/VHqXKqUPmrCYL+fP6UB3ZxqTOZl/Ncq0V1lTZpgvDU2ZmadVu3kcsLcUXMP6Kzjf6fK8\nMV/wmy/7Az5lrzl4AQDgxQ27Q+u5pW/MF9IH8K9j2bw8ma+FbqumLOBTlkklcfC+vegfmpJpptS4\nCzsoMJOwUBaTVCqBfMHBd65cUpZHK190fLZ6E9MBWk/qO5RafWBkynshRydzmJjKl4I0WibHyWzB\nm2iGzBQfBb0TUk7w6WQpaGaFQad330upHz+5bhmuuGOV3adM3UPHKdPmSxfl2rbdo9mKJzAnswUM\nj+dw0KJedHWkvMm3W4XEkHVXmrJksizdiE0oy6ST6LCYKIImWvMl1sLgPgu6ZdDPgoPv/nYJtu4a\n98oE5IQR3CVu3TVe9llSnZjrN04/mhoaLRjsZUzAgD8huQ09LoKasrk9GUxkC+jpSpe0D0UHhaLj\nxeLJ+oQ7ef3jK3Zg485RvO0NB+CIV+6Dved1Ymwy75vUy4Sy7gzSqo8AuUgOjWWxoLfT66d0Kol9\nF3ajb3DSZ5oam8z7nH3tkcdtmjL7OAqGR+hXmgmtcQ06+gPRmrKXLSqlsCoUHM/McdCiOUbbZH+W\nTJIWTZkySQbb48WKSiYwTwk0k9mC99vgONIxzOR9nDIz/JQ6zdYRsVgDJfMlUHpPtbCXTmvh0hAe\nQ100SnG85vd2+ATGaE2ZITxph+5MyjvEUPPpS9Uf+pnk8kWvD+d2++cKINqfMF8oelr3rs40Eon4\n5st9F3ajI5PyhDg9xrWW3HGjneaB0nvW05n2Nvfze+UBE9ctT70UxHRlsZ0C1e9hKpnwrVP6MNjj\nL+zA8nUDAKT5UpZp38Do+UHPLVqwMxPfm+bLvsFJFB0Ha7dKn+ijXrUPgNKaZWrH8spl5Qe/W4pL\nbnvBd1+/T1kRu4YnvbFj22wFha10OoGDFklz7Nb+cW8sz1pNmRDiMCHE+4UQKSHEy5tdqVbEHDxB\noaxQcD2zU5CM4QOkfVu0RmJgeMoTPCazRZx+/mJc8v/Ze/M4OY76/vvTx5y7s6dmd3UfllSSbMuW\nLRnfF9jGYI4Adghg7iSE25BfIE8gQI6HBEL4QUwgHHmCgZAQIOEGh8MG2zLGxja2ZZcsWZItWcdK\n2nt3dnaO54/u6qnq6Z5j5+rZ+b5fL7+8mqOnqqu66lvf8zvWZPQ6fY5PpwvZxqUHUbwmNDnhUMGn\nzL0guBNhioVa+D/tfuyY50JZyN9VOO2GfKJlMtlik6YbodYeHogrUW0x29EfKKRyMAwNibi60K5M\ndhWFUIdt86Ubt3AhC2XC1DnUF1PujXBQjUcLzrDuU+hMKqPkAwOseSJMogL5JCu0Zu7+5HLWBuo3\njxzzpccGOJPKIB4JKSaEfL7QduU69vefsBMpXmc7rQ/02BnWJcFlbj6j+OF0u3zKpucWkM3l0dcd\ncQTpkKljqD+OdCanLJZTs2nl9C0W5ccPjeEvvnAvjo/Nes47P9cAWas3OjHnCHniZC42c9129AdK\nm9Xfc9O5+OgfXej8ZkEo63b6ZrrMl4rQJWvKTF15DZA1ZRr6ulSHbqCwmYo5LXzTAGvs3XN4dj6D\nTDaPmMcYy+haIfWFmL+ifV6aMr9UCFlb0Bffd4QyH/OlEC4yHubLaFh29C+j7XOZL2dTGRw/Petc\nS7g1zKcLWeoHeiJFlylVneFbdz6Fb/xin9Vu2y/VT1M2v5BV9oJkX8zygbU1mQWhzJqfs6mMZxF4\nGSfK3Cy4nfR2hR3zolsrKgc7ufFOiaFGXwo2rup13heHmeWD1uHEV1MmAiLsNVu0saApyzrlp9Yv\nTyCdyWHPwTHsPTyOjSt7sXFVr9P+WMTEhhWFGpgL2RyePj6FVDqLg8emFLcc1acs4/iTAdZe6N4v\n3al6QoaOVfbB65nRaSmgK1fk/tNqygpljLHfB/A9AJ8GMAhgN2PsNY1uWNCQH8RjUvqKXM5yjJU1\nHLJ2TD7JyklQAethPOpyrn5g7yjSC1nPE+uoK0v7/mcnkJMyUYsHJCw93O4TYiTkFsqsxV4IcVa7\n/DUWivmyxCm9nF+ZuIcjA3FFQImGDUcoE75Spq47/lKFfhjYvmHQOf0A1qImL1RiHNx+ZXKI/DO2\nOTHZF1U2vmdtTZk4TWYyxUIZgCJztihcL4+VEMTyUhoDeUMXztWyqcmN2Nzc+9/8guWkG4+ajmO4\nGFMvPxSxCe47Mo6uqOmYKwYdocxq62xqAaPjcxjujzlzvytqRV9mc5Zzt1i4+7rDkolPc/J6yc+J\n23wphKhv37kfR0/N4ss/esIzPYKfie6wFCQi53UaHZ9TnNV1TXOeu1JzMhyyNHziN585MY1kXxSx\niOmMiRBuDElYctopBBZJUyZem5xN40vf32N/V0eiq7AOiDk6L2mRxG8Zkt+VODz12JuhOPSU8jUC\n7JQYIVVTFnYEaDWthdUn7/udhyzUSZquXM5zrfLK2K9GXwrBtrTEklMc/fP45/95BH/++Xtx1C4P\nJ9aFeUlTtjLZXaRZ9/ORAoAHnxx1/g6ZuuMr60V6IackAB7ujztrTmo+6wTVnJpI2W4M1jNSiXtL\nOKQrQpkQuGddQlnI1HHdBavxkkuL9SOe0ZciyMRlvty0qrfos8t6ozB0zXlWZ1MLSoCBu86w0JSJ\nvWD3Y8fxMzsv3HmbkwCA//rFPuTzwPks6WjSAWBkIOYcBgFrjRUatWwuj6el51poykKmjlQ66zzz\nYVNHLp9X6pBa7VYPMSFTxyo7cOHIiRk17UgFCcabSSWasvcBuBjAJOf8BIAdAP58sT/IGNMZY59j\njO1mjN3BGNvoev8PGWP3M8buZYwFJgLU7YT4iwePYDZVsE3LvkDCmdIKeS98ryuqCmWAdxHWh/ad\n9Dx9jrrs7H972wN4eN/JIifVsKk7JpvxGXUxckcgiYVafui9MjqLSexEX0oaARlxn9ymoum5Bc/I\nqOH+mJODDLA2mSKfMkMrEmgB4F03noMPv3GX8+9wSHc2HKAgULnNl7IGR6TlGOqPKwECQhMjUj1k\nsjlPk5s7HNvQNZyaTOE3T5wAYC1eEzOWhlPOVyTfb3GSNnRNcYaXEfffbRaenE0jD+HvJepjWu30\n0qJkc3lMTM9jdDyFM1b2OmYIsTiKfj/AR5HJ5rGTDTlz23L0t80U2Zyz0fV1RxzBJWToGLLv2VEp\nFYjbfClO3CttofqJp8e9A0x8hAS5KoA72eZMKuM8P5peSAhaqs6iuPemoWF0fA7TcwtYPWSZyB0h\nxtGUqRGVQEErZko+ZULg+M5dB7DfNo8ZuqaY18Rnxf0IS2Zg4Xf10a884DyT/fY4ic0+VkYo8/Ip\nC7vMsbJ2rJQpUkTohVz+bl6HuEIeM9l8KQ50he+Xz1NW+DuXB/YctPzahLlNHCbmF3JSYmsDW9f1\nK9dxa8pyucIBST3YWUJZqShLeY2xzJfW/Tw5MeeIkNmcZdoXwvOy3pj7UkVYqYys8XRryuTnIJXO\n4vev3oTLz1muagAB9QAAIABJREFUfD8WMcv4lKnmS69KFaaho7c77By4vvGL/fjrL9+PB7gluBZM\nxN5CmcyOTZZQdnh0BhqA820hTWjjhvvjjhYbsO7ZXjv1EwAclNZWcZAe6o8hlc7i7keOwjR07No6\nBKD42Xb7UocMHSuWWdaVZ05MKYcBv1JxraISoSzLOXfuDuf8KIDKww2LeSmAKOf8IgDvB/AJ8QZj\nbATAOwFcAuA6AB9ljBXroluA4TL7feUnHHc/etSJkJM1NOI0ouuaE3oLFIQmAM5py52GAAD+8+f7\n8NC+4gSsbqEMsIQKoX4Vm3AoZPjmm3GrvE9OpPDDew8pWiKvckkLLvNlOKQrWh2xOApfry/+YI8j\nmH33rgN456d+ha/czp3Pq+ZLSVMWMR0T5Kzk6C9r8mR0TdVKykKnEDRmUxncft/TOGlnqpZPzc+c\nmHYWIq9rC9+v79x1QFHpD/YUZ98GCqHWTx+fxqpkN7autTaHsel5JUFwOpPDzx44jBNjs/jFg0fs\n3/PsIgBLUP7+PQeLTvDiRBuPmM4cFZuvlxYlk8vjSXvh27iycFIWBaKF2fXXdj6k52wbRjRsOCWg\n5NB3kZm7tzvsRPjJJ2FZC+zWlB08NoVfPvysI5QAqqldbHSiv/fuOYZHD1gb8ZOHx/GtO59yPvuM\nXThbaOhGx+cck5zI6A+UDkAR2q2QqTsatTX2yVoWlICCpuy3e0/i8YMi152kKTML5s1TEyn88qFn\nnd85Mjqjlg1zzJdqAs2QoTuHktn5DB6zf0fMx+/efRBAeU2Z7CQuTHSO+dKV0f++x48r5bvciGhc\nt/nSy6QunsNHnjqN3+0/qfTRbb6cT2fxvbsPYGImjXw+j188eATHT8/irt8ddRKDalpxQMJZ6wec\nuTa/kFX8XTcsL5jFAOCu3x3F7/Zb84c/PYb3fW433vbJX+I7dx1QnPenZhds82XhEPSL3x52Dhjp\nhayyhg71x5x/u9fnkxMpR3he1htFKTRY80sc3Hu6w47AM5vyDuqIRUxl/ZMDDo6fnsUPdh/ExPQ8\n/vPnVg1Td1Jj09Dxf/5gB95943blur1dEZyaTOEXvz3srANf/9leTM6knXqW4sAr2hiRgssEQgsP\nAJecvdxJASReHx6IO2ZQwROHxpy59bX/3Yuf3v8MZlMZnBifQ09XGL1dYWRzeRwfm8OuLUPOwWls\nch4/e+AwTtqacrcvtWnqiIQMDPfHcdBVp1nc3x/sPhgIAa30E23xGGPs7QBCjLFzAbwVwEM1/Oal\nAH4MAJzzexljO6X3LgBwN+d8HsA8Y2wfgO0AfuN3sf7+OMwSmYC9SCaLncTLEfPQch09PYc7bFXt\ngD3hhvpjWD2cwOh4CiODcWUh2bp+EA/a2e63rhvAg3tHi3w4Lj1nBe56+NkivzWgoOHZsLIXT9lq\n3mgsjKjtozLYGwdwGj3dESwf6UUkbBT5lIn0AID1EE/NLuCbd+xXIn/cJlUA6O6OIplMYGpuAV1R\nEyPDvVi9vBewN5wLzhzBj3YfxIsu24BPf+MhzM1n8dBTp3H9xevxP3YurCePTGLvs1PI5fM4MZZC\n2NTBzkhi77OTuOuRowCAzesHMW+fYubsRbavN4bNGywH0TM3DBaNn7gfy0d6sWXdAO548AjOOmMQ\nO7cMY+8z47iPj+LXjx3DTx84jE+8+wrllJRKZ7FiWReGh3pwxY5VuPPBwn3v74mg3z7hPuiqUvCC\nSzbgKz96XHlN1zUn0GCgJ4J/ft/VuO2Hj+O+x09AMw1kUFhA9z4zjt/uHVW+v3K4B8lkAiuT3UX1\nIcV8cGeVn7b97gb64xge6oFp6EjbC+9AbwxWhTS1jZP2grWdDTn3MmWv1elcHl2JKJ54ehybVvdh\n26YhnLGqD30Tcxga6kHCnmuJnhiy9oawenmvs7H39kSxcd0gADUYJbWgJjv96f1Wfzav6VPaF4uY\nSKUzWDOcwL7DE4jHI0gmE/j8d38OAPjeJ16CT3/7EeU7wkx69sYkjv/maWSgIWEL5InuKNauVrUm\nAJT6lJoGjAz3QNMsU58wdzN7rm2GBk0D1q3qQzKZwKAt3B04Oon/vGM//vj34njs4BgS8TBWLu9F\nT8L67a7uKL5/z0Fkc3lcvXM1fn7/M7hq52psszUIu7YNo8fe3MReuXo4gVw+jxXLe3HO5iR2P3YM\nQEEg2rp+EA/vO+mYsRPdEavItI8JZvWKPow8O2X/hvWlVcMJHD01izNW9+O+x0/AMAwkemL43Hce\n87yGQAgqy0d60G9rMeLxMLoTxVogoZ2cm8/g//7X7/C9T7wEOXv6r1je69QcNUMmfvbQs/jvXx3A\n06MzeNlVG/GVn3BEwmoVgng0VBRR95oXbMMeW1A3wyZmbE3cyLJu7DpzBP/+0yfx4ss34N5Hj+HE\n6Vl84ft78K8fuAbfvecQTk+l0NsVwXfuOuD4pQHAReesxG+fPInx6XkkkwnsfuQovnL7XgwNxPG5\n912N2fkMlie7nTm35YwkHjtkCbKzC1ZbhwfiOH56FvO5PGBY68GuM5fjd/tP4aKzl+M3e4r9dsNh\nA0NDPdi6YRBPPD2GMzcNOevFPXuOY8vaAeXz4rkd6Ik4/msDPVGcGJvD4GA3brn1LkxMp3Hg2LQz\nN85YO4CeeBhf+N4evPyqjUgmE0gmE8jn87j1249izbD1781r+3Hg6CS+cvte50ByenIe3/zlU9h7\neALnbkritTecifueOIGNa/qdtvzLnz8PYVPHzR/+MTat7sfQUA+uuWANfvnQEbz5987GoL2WXrh9\nBX6w+xB2nbUcfd0RJVfi7HwG57EhPLr/JNKZHP79p0/izoefxamJFNjaASdIBgBe9txNGLUtLvuP\nTeEn9x7CxNx63Hz91iINe39fHMlkAmuX9yhuFQDw3XsOYQdL4lt3PoU9h8bxsXdchlZSiVD2NgAf\nADAH4F8B/BzAe2v4zR4AE9K/s4wxk3Oe8XhvCkCx4VtirExFezfJZAKjo8UZgMuRkZwB3/WK7fjU\nN3+HUfu3w6aOa89fiZdftt6KSMwDJy5dj8GeCP7mtgec712xfQRHT07jjgeP4OwNllDm5g+u3oj7\nHz/umKB+/+qN2H7GIP7iC792TBiXb1+Ol1++AR//+oMYPTWDhK2ZS9japIihYXR0CmFTd4SyC7cN\n4/+8dhf+9FNW+rn+RAR93WFHvV4ubPvkqRk8degUjozO4Mz1AxgdncLF24bw1R9ZaRV2bl6GGy5c\ng1jExDtedjb+6duPYPT0DJ4+XBAKpmfS+LvbLPna0DWsHUng9KlpXLx1CBtHEohFTOTSGeTte33I\nNvnouRymJuZw67svRzRsFI3f+1+1w8oLdnIaOzcvw2duuRyxiIlf77FOeWKcTk6k8Pi+4nsej5oY\nHZ3Czddswgufsxp/9rndACx/lXmPk9NfvfECrEh24Rs/3eucTN/1iu3YsrYff3vb/QCsk+TJk9PQ\nbPPMs8cmFf8+t+P2OWcM4sYr1mN0dAofev1O5PN5/PE/FKcKFOP1Z3+wAx/7+oPONXOZLEZHpxAy\nNczaY57P5Zz6iV2xELJZy/9szI4Mm59LO/dyetJ6bXp6HrsfOoJcLo/Nq3oxOjqFN71gC/L5vPXZ\nvOjPBE6PW/c1nVpwBK70fAaT9vVT0ml1bDLl6bQ/7tJerU524R2v2I4H+Cj2HZ7AqbEZHD9e8GkZ\nHZ3CrD1X/+jF2/D57+4pCIRxa/6fODmNGVsoyCxkMDE249wHAHjTC7di06pevP9f7gVgnfJP2iW/\nFDcF+56GAXz6XZchHrHmybRkmp+Ymsf/993HkM3l8Mcv3obTp2ewYI/tfY88izsfPIx1Iwm86rkb\n8bJL1yMWMTAzlcJn33sFTEPDN+/YDwDOmL3mmk2IRUycOjWNXZuXYeK5m/D1nz2JUXsj6YuH8Im3\nX4pbv/U77H92EmMTc7hs+wrc/ptnlPt401Ubcfk5KzAxPovrLlyLvQdP43/vtz6zbrgbr712MzLZ\nPL5+O8exk9N44in/0mgRu8LG5EwapqHj5MlpzNhuEROTKTzzrCWUyMJhyFV268SJSZy2NUmpmXln\nXZqemce0fa3DJ6axz9YIul0F1o0k8JhdMeSs9QO48MxhDCXCeMrWSu5/egzPnLDm8nBvFFomi8/c\ncjkiIQOvvm4LPvONB/HLh4/iG7c/gROnZ9HXHcFFZ47gh/cewuRMGv2JCP76Tc9BPGpCh+Uf9v07\n9+EBfsIZ54cet4SpFQNx8EP2uraQQS5rtfXAkXGnrcdPz+LAM+PQ7PnUGzVw67svQzRiYhdLYja1\ngFjExD99yzpgiHXtyu3Lccm2YaRm5rFpeQLb1vXjN3uO4+ioWhVEPLcbVvQ4QpnQOh85Ou5YSJ61\n5/XN127GYDwEII/P3FK8jt767sug69a+cePlGzA5lcLux44rWkR+yLr/z79gNaI68Kl3Xuo8E4J5\nAJ98+6Uw7D3oxis24CUXr0MunXE+t7I/hlvffbkTiPSZWy7Hl3/8BO573LrXYVPDm2/YhpMTKTx6\n4JRjsu7rCuMJ+74vH4xjMB7CUdun92nb7+34yRnsO3gKblL2Wifbu3ZsWoZcLo+H9590xvDxg6cX\nJR9USynFUFmhjHM+A8uHbNF+ZC4mAcgt0m2BzOu9BAB/fXoTkRdrYaoTTp3X7FqNoX7VPr9yWZfy\nvZ645Y9z87UMN11pudHd9mMON8KxWHbK7etWLbhd0RCStjp8JpVxTtErl3Xhg6/b6fgKhE3d2cSj\nYcPKdu9ExvQogoGh68hk/R0eM9kc9h+xJr4we0VCBj71rsuw95lxrBtJOP5Qw/bvp9JZJeRY/jub\ny2PtiDXUmqY53wEKkT3iRCPMm17RhIAaUaprhVxfwozs5S831BdzIo6EX4OuaxjojULTLF+Wvu6w\nZ4mk3u6w7UBe8OHoioUQCRmO2lyYmWRnXXmBc/vu7Nwy5PgquSNkvYjbpU1E32S/J6E9Mw3NrjBg\naQOfHZ1GNlcIDJH9QIQZbUHKR7XFNr3K7RFm91Q6i/l0wYdnZbILZ20YwPaNg86cl4WwqbkFz+z8\nKZcPjGGbcORcX+6UK1m7+sFAQjUJCRPs3HzG6Vs0ZFVqiEdN51nolnzjANUvS+6rbI6R/UENSeCY\nnc9gYsZKC7JtnaXNEAEBj9sbyPOfswa63QaBO6JTzCPT1J32aJrmRBIKrWMkbKC3K4w/feUO/Ncd\n+3DhthEM9kaLhDLDKPyepmnYtKrXEcoMTUNXNOQEl4xPp3FqQjW9yUJszBbKZuYWnHkmlsNcrmAq\nSsTCmJsXlTnUZ3Uhk8OMnU9PThsi+xGauuabouCMFT2OUHY+S+Lisyx/KuHzOTo+h73PTCAaNpxM\n9OI+xqMh3HTVJtz3+Anc9bujmJxNY8WyLsVloStqOvcrHLJS/chpGTau6sXBY9ZmvXYkgXe+Yjtm\n5haUlCPCfHnGih78es9xjE7MSXVTw050vEgL8aRkKhZmaF3XHNOvrmm4+rxV2HNwTPHPlNmypt8R\nZiJOkuDCcyZ8q+T11csPUfaT03UNl21fgd2PHXe+e/z0rJN7TQRRePlIA6rfsjzWMvKzYO150vMY\nNrFzi+UrZuiaI5QN9cewrDeK791zEK+9jil9Ea4y03MLjkVJpOYBCgKrHKQRCRk4Y2UvHt5/SvHl\nzefzvr69zcBXKGOM5QDP6hkagDznvDqbYYG7AbwIwDcYYxcCkG0R9wH4W8ZYFEAEwFYAjy7yd+qK\nvGEKf5fpORFZ438rhM2/X9pAxKTtjoWsTOdQb7S1YYgcXdZDKgQF63um84DPphYc4SoWMbBe8qWQ\n2yUeDOHIvW4koWTEL1VQF7CEMuE/tVGK2umOhZwoG4F4UNxCmZu1HrnGxDWBguDiNtlVigi4kKPu\nTtjandXD3QWhTLq+rlnpN8TpedeWIWfRE4gNtSsawilb0yPU/MJfTfizxSW/EL8we0B1Nhb8/tUb\n8YPdhxQTtJgHuq45yXvlNpl2NBJgCThiXFcs68bx01baibQjlBVHqmazefCnLb8O2edMEJVqc87b\npW4iYSva9z03nQug4BsmC8NC89GfiCjjMe1KnSL7dgGWA707UCOXswQNeYHtipqOcJ1KZxEJqZGG\nsWjIEcrCIUM5ZMnXkQXV7nixnyFQnFtpcmZB8RkSfRBz3+8wIX9WjJM7oEisFSL3k2hrJGzgNdcy\n53N//aYLsOfQGL7+U8t/SHdtKrIAIvwedU2znbrnlWSngDWfZp11xcT4dBrZXME/TVxDzsOV6Ao5\nz5Q7oGh2PoOZ1IKzkctpRcQGqOuabzJPeS7KB2AhlD11dBLHTs/irPUDih+vIB41sXywCwePTSKf\ntwQLOUJTFjC8CmNHQobjeL5uJKHkSRR9FRqrdct7oMHyzxQHaq81TBZW/HwD3YXfu2MhvObazc77\nTDL/i8/Ka7kYm1J7lBfrl/dA16xyYVvW9Cn+sF7+t7UiP3dRKUJ03fLCfU72RXHB1mFcuWOl424j\nUnwIQWxmbsHxdZWFMnFQiroERvG7ch7A8em04s7TbHyP5JxznXNuePyn1yCQAcB/A0gxxu4B8EkA\ntzDG3sMYezHn/Bis1Bu/gmUm/QvOeWW1URqMOB1HpAg/EU0XKZEaQmwoXoMsFvJlfdb/hQZODp82\ndM06ZUsPbVcshGjEEtRm5jOOUBZ1nU7lxcV0tXHNcKJsUkO5LZlsDvuOTEDTUORE68ap3zifcSoW\ndHlsTOtGvIUydw4vv82xHEI4lPt5wBZE5bpuCZeDqgiz709EwNb04xNvu8R5T0NhAemSvifmhBCc\nhaYsLoe1+ySk1KA6xQquu2AN3vv75yqvic1W1zRlIRPjJDvOixQZALAi2WXXb805RdTlQA2xQaQW\nrBxB65YnPPMgyZoyocFyf87RlHloxgZ7VO2W26dSCIeFBKz5onJPuZxdJ1R6JrrjYeffc+mMkn4B\nUDe9cEhXNm75uZHvn9eclfsnmF/IKpGuwnQnRyv64aTE8BHKoiHruuIueY0JYEWxyvfWLZj0Stp2\n+Tf6uiMYn553kp0KZKHK6/6IeWhpymyhTIoqdad2mZvPYGYu4wTsyGWWnPQlJYSykYG4Mx4ioMP6\nTUtDvc8OXvFK8yDoT0Sc57MnHlYsELLg7BVJmMnmcOjYFEw7ik9GjIlwJUjEQuhLRDA6nnL2CK/o\ncXkc/KJo3eP9/lefhwu2Djv/liMoxZilpedF9LdckuGi3w0bWD1srZFuwc+9z9QD+Z7LWtY1Q4U9\nYqgvDtPQlb1UPNdirZmSNWVSbWExbxUtnlnIBShr4/1qjDaLsneXMdYH4MMArgaQAfBDAH/LOS8O\nBawAznkOwFtcLz8hvf8FAF9YzLUbSd4+qUTChjPB5ZxdfogSRP0eCQ2X9UZx8NgUhvrjeOcrznFO\nbqpZyZo08ahpFc6OGFg+GHcEtdlUximR4T5thULFm+7yQatw9PrliZK5ewDgA6/diRNjs/j89/Yg\nk83j9KR18isXhh+RNm4hMK5MditRnaahFS1uzvdDhlPYGli8pkzOySN47OAYTEN3wrIBFEUA9XaF\ncHi0EGEkL9hhu3A5oG7a7kWv39GU2Q7PqQw0n3VRZAX3wnD55ggFiK6rQpmcvFUgp2NZsazLMUmJ\n++ollIlkl15Z0QFVKBPzPxr2Fsq8NIMDPRHgiOelre8aIieYEOyyjnAjsEpSQckNmIiHVNOqEMrs\n1xTToWm4NsTiw0ssYviakd2R2ID67IlriLnvl2QZKGwWcloUGbfGyS+5MKBqx9zKIlkrpCtCWRgH\njuZx6JjqR+MVTQ4U5pccfSm0DPJz6u7z5Ewa8wtZRzhRC5LbY65rmJn3PijquoYdm5PY+8y4UiNS\n0zQk+6JO3rpt6wc8vw+oB+OerrBqvlQOWIXxFf6xmWwOh0ensXqou2hehF3jHQ4ZGOyNYv+RCcQi\nVu5Er+dbvo7fmurOb+YWGDVNw9/98YWApuFOO4rby+rhJ8yX4spzV+Dex447ZnkARfnf6oWiKZNN\njNLfyf7igBL3Gq9qygoCq1gLo4r1SCscRqU1xp0QvNlUIvJ+FZbQ9GpYT88bAHzR/nfHIJ+83Q9Y\nqQkvHF/dfmFAwQcmHjEdHzTAtbHqhc0SALauHXBMqV12RJJYFKOuCSpr8MTp/f2vPg/TcwtIxMNl\nSyH1dYcxYTvhZrI5LGRznhnz3eiaZXJNpTOOCWTlsi5HKPu9yzdguD/mu+kBlqB0enIeGqDksqkG\nv4Uu2RdVNnT3KVZEY4nFP2ynAMjm8spYe2nKBGLxKmjKFnw357U+GkOg2L/MEgjz0DV1njipFDz8\nxABgRbIbhqEjncl4+pQVToxq+Ro3jvkynXE+W6Qps7/rnNJDuiPADZZJDeAu/r2QzRf5lOVE8Xbp\nRJ2IhZwTdmo+g/loIVQfgFK3tBJNWalUE16FkxVNi2O+VDPoe+HWYLs1XG6B1/1v9bvS3y7zpTxG\nilBmz/F9R1TtgLwZypoLMR9l86XwW5I13O4+C/OoMBPqmgZD1+woxJxzTWGmlX3aAGvev/76LZ59\nG+ixhDLT0BX3DTdFQpkkYHT7mC97nVyHWWRz+aIDHFAsOEdCBpK9Uew7PIHDozO+6TDkZ8zPxO1e\nV7zmkhA+ZPOlaWhKhGe15ksAuOLclbji3JXI5/POIbmnAaZLoLSA+paXnImDx6acxMkykZDq2pPO\n5BxfZFmjKtZe+VATMgo5BcUac83O1UX535pNJULZOs65nMT13YyxQPh5NZN5SSsmTIpC7V5JtuY+\njxOGSCjonoTyoiA2AOFMy1YXVMnxqImxk/OST5nrOvKpwH6YE/Gws3i+/WXb8aUf7FGyo8tYyW8L\n5suFhVyRqc+PaNhAal7WlBWEzueet6qknw1gCUqnJ+fRFQt5+ohU2gYvhvpiavkgV582ruzFQ/tO\nYrXt5yU7istCqeyH4l4sxWYn+5TFo4V2iUXgxZesw5U7Vvr2wXT13Skf5DJfRsIe5ktp0V++rAum\nMF9mCpnZBZq9SYp2uYUFgVsbFTL1ovEp8mfqCjubstt8CVgbpDD9iEOI+P1MJlcUqSqKt4ds80Mm\nm7c0ZRHvIARAFbJCbk2Zh09ZpISJxlMo8wgWkMsS+eEWuouEKbdQVoH/KlAs3Mm4zZdyW53flX4n\n6qEpU8yXdmCJvGm6NcfCCb5LydGm2TVaC9cUSV69kti6741A+CiuHury/QwA9HfLQlkI0bDpRJbK\neRDl8UrEQ9A0KRBDLx5Ltw9aJKwryWK9TJdAZZoy94Gn1EE2LAllhqEGbrkruVSDpmno6Qrj5ETK\ncx+rB6qmTL0XF2wdVky27rbFwqbiu3x4dBrhkK6kOjEd9yNXEIKj5bTu1XmblzXEPFsNlYzUY4wx\nJ3EHY2w7gCcb16RgImvKrHxGsj9P+VNIj8dkljVlMl7mS+FztE3KVN0VNS1H41nVCdirXV4P89qR\nBG656VzpMxrkJc2QS8ZkLE1ZKVOMTDRsFmnKRJvLCWRA4dS9WNMlYAVneAnMO7cMKQ+n21R31Xmr\n8JlbrlDGzClhpWjKihfy1z6fYdeWIed07CSAnM842iJZmDtz/YCnFtXpg2vcRBmcSsyXhq7hfa/a\ngdc+nyERDyvmSytZpbqBmYYuacpKC2Vz6SzmF3KeWmJN05TNUfZn8uqrbAYu1pSp0Zc5u9aiEDrE\nApqIhxVfRrf5MqZEPvpryoQwUEr77Wm+lMbULdD6aR3d7+lacUUHWQhzC+JuNF29lh+ygrzPR/Oh\nCGXh4nmuS+ZL4bMpC1zudgqfNWWsdR2ZbB5ZyafMr0ZlqXPZiy5eBwC48cqN/h+CqinrtdeXPo9I\nwrDr4GXouhOo4nYnAFSBRxSSF37CQLGPrMCog/lSaUdY0pS5bthiNGUyQqvY29UYB/iQci+qa6v7\n3k3NLqA/EVUOBoXDlnrAcOq/5kXVg8ULr/WiEpFwC4A7GWMcQBYAA3CaMXYAVhTmhkY2MCi4HYfD\noYK2oxInSq+IlS1r+nDB1iE8Z5t6CggrG6v195++cgdOjM06ZWmAwkZwaiJlly7xf4D9nI3lBSVs\nGshoOcfnyLAj/ADL4Xohkyu5KMjEwgZOT6YcLUd/TxTJvmhR6hA/hEbOb0GrlFjYRHrBWujf++rz\n0R3SsXYkgRNSfjsvk4QbIUgKjRSgLuRiE7zy3JW48tyC5kuUbZlNZZzNrStm4pRtLSrn6+HeBMR+\nqmmaMqYF86UqiLM1/WBr+p1riZQYoZBeJACYRiElgd98kc2X8+mMb/sNQ0MuY+cPk81EHloDecMQ\nG5VcOUCOjMpkc475ErAW8Om5BSRi1uYp0smkXc9rTHH0NxShRdYEic23lJmwnKbMfe9KHWSUdC4e\n1w2ZuqOVj0j+jF7IffLzXwTUEjT9PgcCxXxZwqcsl7cc/WMRU+lLyNTxvlftwKMHTuMHuw8VIp2l\n8TcNDdlcDjk7q6ymFUfjOv0p0e/zWRL/8qdXlD0wus2XgDU3j4/Nqa4IpiogmIbmzCevTVuev2K+\niUoegP/BUjFf+gllrj6VChpxUmKks0VpgrzmbDWI+9Uo82UpTVk5vIS4/u6w5/6n1qjWPQ5Q7SGU\nvbjhrWgDCou8NWjyg+s2Mcg8b+cq/PyBI1gxWOzUHg2beMtLzip6PeRhvuxPRIoiOMWpc3w67emA\nGXFt0F7IC4q1URcyd5uG5ggFQoNSqVAWtTNyT0uFk//i5p0ltQYy3Y5QtnhNGWD5EEzMpGHoGq7Y\nsdJJEiqbp/zMCzJi0Yz4mC9LEYta6vVuew7Jv1dOKHOfeAWWpqzYIVa+v+4xN3QdWSFce8wH09Ad\nLYqvpkwyEabSWV8tnyxgyHPTazxl30fR/rikYZSdcDPZHHJ2njKgsIALwToaMTGnRIbaPmJynjHX\nPZUFNr8kQ45NAAAgAElEQVSIUplyPmXuOV5qI5Xf87quZvtnzs1nSgqKgKpN8tKUCd8buQarPH5r\nhrvxtF2yStbQxbyiL4VQZmvKumOmMubhkAG2ph+apuEHuw8V+ZQBsE1sOWSz1jVnUhnPHEyi7X5o\nmlaRBr/PSyiz++8XtCPM+sJ9xet5lOeKWE9l86WfKVk2hfoJZaZRcJUxXGX7itthXWN+IafMwUi4\n+ABWLeIZbob5slZNGWAFNoU8sg/4acrcn2sllQhlR2HVoVRqlXDOb2tIiwKK++StPIglFoRXPW8z\nXvW8zb7ve6GkxCghxMgbjXdCQGmzM30WBqPgxB42ddV8qRcmrRNZVKmmLKLmCItFjCJNXinEJlu7\npsx28HRpGeRNpxJzasxDKOv2qcfpJh6x/NHEHIq7tDal8DKVAdYGLI+FUxDcw/Tt/Fu3Fnd3UWWB\nItD5zJeCpsw2X/oICqauQcT2VqMpE8KgGP+pmTRSkqN0JmvVWjRD6slXzJOoHWDi1JJ0HP0L97zI\nRCj1QeReKyUAeR0svKIvBaUOMkYZTZloSyVCmfx8eQllF24bxu7HjitpFJYvi+Pis0awkw3h9t88\n7byu+pR5mC8dnzJLmFq5rEsRCp2ACfu+C59B2eQv/AGF+bJUVZF6JPOM2DWB5+azjmZsZCAODaqv\no/vZMAwds6m087ebsDQu8n3bfsYgfrf/VFF1gsJ1y6fEEK4yqXS2rMAgtPjCp8xpX5VlCL0QAq1X\nFoF6UJumrPjz29YNqJoyIZQVRV8WWwtaTSW9/xGsVEqHpNfyADpKKBsZ7MKpyXmM2L5dqk9ZfaVr\n1S/I/9ry6c7rdFGJ+RIoJIoMhwwIrzIN1ibhdoSsRlMGWEn9IqHqBDJA8imrMLDAD/HAuh90OV1I\nKf8bQcF86R19We67J8bmMJ/JWYXcPcwdfvgtEkU+ZeFinzK3U3JB65n1FERl7ZiXQzNQGNfZ1AIy\nWW+fMtE+QcIWyjR4axfDrggqwJr33bEQJmfTSp4yt/lSCAxCAxcLm5iYTiO9kFUCVUpFU8qaILGB\nltJ+e81lr+hLQamFXi5H5GdiEve4nFAmmyy9BLzXX78VF505gjOltBGGruPNN2wDAPzcruMLuKMv\ni4Vmcf25tBXN2x0LKc+RmIfu+66aL3XMpxec+pbuItJK3+q0V65f3oPpuQWnrddfuAbnblqmZLx3\nr3GmoTkaPK+xlDW98vPwxhduxX/+7Em85NL1nm2Rx7vUwVC4ypRaw+XfFnO/8P3a96erdqxEPGJi\n21r/lCO1UE+fMsByDZIFUzFvo65I4qIDVJuYL5dxzs9peEsCzptv2IZ7HzuGq89bBUA9fdTqROnG\nK/rSC9kR3et04Y408SMStoUyU3eclpx8Ufbvl/M1ciPaMz234OtMXIohO5xZPtUvBrGRuR/0SgQx\nGZFvbDHmy3gkZDlEzy4gbBqeUZN++LVT1zRlQXF8ygz1JCgjhIlUOuM5JopQ5iN8h03LxC0csn19\nyuRNwdTRFTWtAACP+Rw2dYRNA/OuouWJuJWFP+X2KctL5cu6wtBQMMNFw9Z1UumsIsTES4yV7FOW\nWihvvvTLGC9w+1aV0vLI97mUpqxcm4Dy0ZchU8dZGwb922IUC/nW7/s7+k85GrCQ0k/xOfeGqZgv\nhaO/nbrBT6MEAGoI0uJ5x8vPhhzYGQ2bRWk03JGf8lz2EsjVQ1bh/Z54GH/4ojN92yLfr1K5H8U1\nyx2InZQYLp+yeuxPiXgYz9u5uubr+GH6CLaV4HXv4nYZMYFXmSVP82WbCGU/Z4w9D8DP7cSvHUlv\nVxjXXbDG+bfyINZBPSxTygQlI6eZKFfPrJTq2wleMA1nwRK/W5QIs8IHRt7oyiWb9WLb2n78xWvP\nx/qR0tUDyuGnKQOswtTV+IUBbqGsQvOl4/s3j17JAVVEapVC07SinEOAqinTtYIaXs095q2xyWTz\nngu8Ikz4LE6anR9MFDz2097IG5muaTifJQGfjdXSHloloeT6oD3xMI6emnVSLoi2Z3OF2nQvvXQ9\nLtg65AhlYrwnZtLK/I+VGCt5buxkQ7jn0WNK6plKiHuY+IDyh5hKSu1EHRN86fmmJo+tXoiR1xrF\np6yEo/+kqCcaDSl50oQ5PeoqEdflcvTP5HKeherd1EtTVonvmbsShfyMemrKZFeWMtpMP0ppcp26\ntpUKZQtZZfzrYb5sNPJzUq2pWszPDSus0lBX7lgBQKyLOvL5QrR2UUqMKrTazaKSXeUQgNsB5Blj\nQO21L5cEsko4VGfzpRp9WUIokxLOxjwWg3CFm4OTTiFUqJsoNGRi0s4tUlMGVOaz5UbTNJyxwr9k\nSqUI05Q7sS4AXHJ25UkCvRz9wyEDO7cMYe1wcd1Kr+9atQMNZ5Gs9ETozjkEWAuOGF/ZkdcsMXfk\nf3ttTmqQgP+8i4YNx1fQz8yn+DfpGl5//Vbf64XNQpWMBSkbuTB7yiWA3I7+Az1Rp86oaBtgaWhl\nLWupOSgLHa97PsNVO1Ziw4rSh4EbrzoDA4moU7RaSYnh0pSVQv5sufQUXnNYRtaOVektUNSWspoy\n+6dm7RJL0YjhMl9a37d8oqxcYD1dYSXQwzSswJO0RwZ6N82sD+0WyuRnwcunTLfN5JkKk2t7Uerg\nWtCClx5UOU+ZrO2rJUdZs6jULcYLscb3xMN45yu2K++FQ7pS9F5+RryFstbfq0p2yz+ClUD26bKf\n7CDEJhK2Q9briV9W9uLPeS+czvseZZa8KESUGo5/RyEKzzZfpqqPvhQsRlNWL8RGFqsxIaCXTxkA\nvPWlxdGzft8FLP8TZ+5UuIDLTvMCXS+MhXwSLjV3VOff4nFUfDBKjHPUx7FZbZ+/r9Q7Xn42Hnnq\nNO7bc9zxZRRzeV7RlFkbuCgqDBQc/f2EDtkpXS0VVJmmLGQaOMOjELub65+zFgBw20+ewNx81lOb\n5P7bC3nD94tkFX0qt+GXi74shxxZ6FtmyeVTJrRchq4pedLkfguz5AVbh5R2mXaKFnfFBi/q4ehf\nKZecPYL7Hj+Ol12+AUB5TRlgraGlfCzLUUrgFutzOUd/8VymF3KK6a7e7jWNoCahzH4+/KxFGc1b\nExsyNIRcAU3tIpQdBXCq0Q1pN8REb8SEV8yOZfLL9CciGJuax3SqOL+PmhLD/zpC5R4O6cjlrL/d\nyfRErqiKoy9lTVkLhbLCA1vbOK0dTqCvO4z1JUoi+eFOTCmE5Wo0ZW50KU+ZfB2/jP6AW1NWfE3Z\n6bzUqVwWYirxKXP7N+3YlMSOTUk8vO+kLZQVkvzKmjLhMymf+h1H/zL+V1bbKtMUe2mZKyUWMW0f\nN+/7Xm6zkdvllcsQkB39y5gvK0we64c8z8omj7Wvn5FyGso99XIuv3DbiPp7UgLactSYZqsqEvEw\n/vL1u5x/G4aqXfEiHDIwk8os2nxZaryqNV+m0hnlni51oUzsL177TDRsIO1za01TV6OffXxem00l\nu+UpAI8yxu4G4MQsc87f2LBWtQFCO1HvyEtAnaDlJkmyL4axqXnFxCNQcpCV0nw4PmW647skhDJD\nt1xsxcFrMZoyr2oGzSJWoT9OOVYs68I/vv3SRX23p0vNdO4lTJXCLVxpUHMzKab0Ej5l5YQyeYEq\n5csYVUxb5YUyPxO8c7AxDVy3aw2+8P09uHR7waTc45EOxR196UYWsORcdKJA/EYPLVipIt/l2LEx\nqZR4ASrzzXM+K42Dr6ZMOPqXzVNW2tG/HH7CpCjcnMnmnL4Zbk2ZoVZJkPt901Ub8fSJKaxfrh5o\n/KwAcq1UQTM1ZW7MCuayV6qkSohHzKIyYm4coazMXBJm1PmFnFP5A1CjQ5ciQsvopW18/QvPxPjE\nbNHrgPWcisS62VzeNw1Qs6lkNfqB/R8hEa5S21HVtSv0KQOAP3juJvzDfzyIm64qLjFSTUoM6/MG\nwkIos59pTdMQkhbJSpPryapk9wm5mTimnxq0IbUiC6VyQftKfT3cc0Bsfl65d0oFiShZ7T19yiqb\nL/K99DuFV6K1cczmIR0XnTWC8zYnFcHDK0fdQiaHPPyfC1WLV+hDLGLi0++6zFNjWqn214tXX1uc\ng9A5yKA6n7LymrLSc7jSMkuVtMWt6RTmOXf0pfC/cpeIkgOCnv+cQoCU3+/JxCOFKhxBwCu1gpvF\n7geffMelgG/KXNjXtK5dyYE4EtKRXsiq5ssWrn2VUksqijNW9GL98gTO9ogsvuScFRgdnSr5m6ap\nI5vO+qYBaja+QhljbIRzfgzAL5rYnrZBPuXXGzWjf+mJsnYkgX969+We7ymRJiUeaNl8mbGza+ck\n9XdMWiQr3cDkBcR9Qm4mA3bSwwGPQtjNQtb4hEy94AtW4WLp3gjE5udcx8986Zo7chJXr+CUUtUA\nZCrSlBnltTZR1zPk1gTJGkaBEAL8NCfyadm9QfpVbqi3Fkaz05VUUpZM8SnzqSso+lReUya1YRH7\ni9+YGbrmmOfcQpnQrBu6Wu+0kk3Wz6UiFjExPq0KZfX2260GQ3H0r6+mrBJBq1JNGWDNkSJH/zaI\nvlzWF8Orr9nsqckuR09XGB983a7yH3Qh7lDI0DGP8sl5m0UpTdkXAdwA4E5Y7ZdnYx7Ahga2K/BE\nnA2x/gMZLqHtqOo6FTv6FzbHBdPa9OSTVjxSSIFQqfly/fIEdm0ZwtXnrWyp6WHz6j785et3YlWy\ndIRkI5GFoXCo4OhfsU9ZkabM+n85TZl705M1dl7CdSV5ygA1rYGvT5mmbupeyIcBL2Rhdt1IAgeP\nTTmZ+v2uuXJZYZzLCb0ffsMu53r1xjQsoazcQq9EXya8hTKn5FistBtArSkxZCHeLaC5K0a4r28Y\nmiIIVrIu+h04vSJlW7iEKPfFT5tSrfa7GoRQVZmmzKoFKydibsQe1Qiee/6qpv6eUDw46YQCkA4D\nKCGUcc5vsP+/vnnNaR8a6eivZvRf/ESp1nwZNnWkPR58NQdTZf0NmQb+pILIxEajaRrW1ZjrrFbk\ngudy8tjFOvqLDVGMqVpOS/f9XsKlsXNTqfnyinNX4qf3Hy76bb82+2nKImWeIeFjlYiHcPm5K3Dw\nx9zJY+Z3zbUjBaGs3P1dM9w4DW7I0DCH8toN+fn2ql8LABdsHUYkZGD7Gf6JX4HaHf0VTamrZJNb\nW+NlUtcrEMT9fk9GJGqWaeXBTu6Lf/RlIwO/bDNbJZqykIFTkyll/NrB0b+ZvO33zsZvnjiO1UPW\nWuH4SQYg8hIo41PGGLsBwB7O+VOMsZcCeBOA3wL4G855cbhfB9FIn7J6CWVq8lj/68gLSshDcyAn\n3qwlSqZTMZQFUncE28U6+usVmy/V7ynmy7J5yvzHeeWyLtx8HcN37z7gq4HUXT5JXsiHAc/3wwb+\n/i0XoScexv38BIBCDVo/ocPQLfPwQianFDJvNiGXZsmPSrK6R0IGLtg6XPY3a3f09xakRf1FoDij\nv8DQVKGsEiHK16dsEXkNG4lqvqyvT1klFHx+KxPK0gs5IKS+RhQ4nyXtZNYWzrMaEKHMtxWMsT8F\n8CEAUcbYdgBfA/AdAIMAPt6c5gWXRkZfyptsLSfEiJPAsbRvmlw30evB98tWTlRP2DQKIdwVbj7u\nsavc0V/9XlXmyzKq/Kt2rMQn336pr6+eO6O/F5VoF5J9MUTCBe2iI5SVEDpENn5RCqoViHvZzOdF\n1ZRV/30/R3+gsN6ZfkKZoVVtYvRzzWhlCh0vlHQn5aIvG+BUX2lKDPn35ejVWgJZOgEx74OQowwo\nIZQBuBnAFZzzPQBeBeC7nPMvAngHgOua0bgg00hH/3o9RMKZu9wJYNMqK3pl48pezw1UEcoCMnHb\nFU0D1gx34w9v2FZxLbliTZn1f5H/rMtHk+n+XkIxo5YTymob50pSYqwe7kY0bCDZF6vgerZQVsZ8\nCViFoHdsWoZXXHlGNU2uK6ajKSu/PrzphVvxjpedXfNvKslja0yJ4RaYIi7zpXud0PXqczwtJU3Z\nYh39K8GtpSz5WY/PkPmyNHLZuyBQavbnOeciwcdVAP4ZADjnotxSRyOH89ebep2uRe2vchvsqmS3\nE73yu/3FeYKVVApt4jQaNMKmjnQmh1Q6C03TcNFZlacJKYq+tDe/NcPdeOtLz8KWtf3Oe6ESglU5\nR37FfFnjHKzEfHnluStx2fblZSOMATiZt4UGoNT+39cdwTtevt3/A03A0ZRVINxWU+6rFFqNjv6G\nS1P2j2+/xMm27yUYiPxO1t/VVzbx9ykLllBWiQb57A2DOHh0siEBRULQq+Sg5PXc0ppdmqBpykrN\n/gxjrA9AN4AdsOpfgjG2FkDrnDUCwrLeGAxdU+rr1Yt6at8iIb0qB0YvrYZ8ciVN2eKIhg1HKKuW\nIqdqe/PTNA07twwp75XSlMl4zTF5ntQ6zpVoyqz3Kvsd0bZ0pnT0ZVAItdh8qdWqKdN1JZlt2CMC\nUFeEskVoynRvAa9U8fhWoDr6e4/nmesHcOb6gYb8fqyKXIvu51bXNQxVoInuZETUZTtoyv4OwEP2\nZ77IOT/KGLsJwP8L4COL+THGWAzAVwEMAZgC8DrO+ajH5zYC+B/OeevD93wY7I3aySjrv4DUs8B5\nJGxUdYL1Wlhj5FNWM7GIicnZBUeoqAa/6EsvVE2G/1h5CTWlSjRVSyU+ZdUgfHnKOfoHBSfMvplC\nmRz9WMfksQCwbV0/njkxjWRvYYN3BxbU4lO2ZjiBA0cnAbQ20bMXlR4wGsWWNf149TWbsWvrUNnP\nypqyszYM4C/ffBGmJ4urvRAFgqYp820F5/ybAC4G8ALO+Vvtl6cBvJlz/pVF/t6fAHiEc34ZgNsA\nfMD9AcbYzQD+A8CyRf5G02hUoe16bjg3XbURN3pk+/f/7eLXFpMSg1B5+8u3Y8OKHrz88ur9nNzO\nxaWUS44jdpk6bqKWqUwlNf4qRRYI61FPznQc/cv7lAWBgk9ZMzVl8t+LMF/65CkDgAvPHMGH3rBL\ncWR3J5itNihJnmPC4hAy9Yb46dZCPX0tF0PI1PHc81d5lh0r+qwsWGtaw/aopYR4VtsheSw4588C\neFb69w9r/L1LAXzM/vtHAD7o8ZkxAFcA2F/JBfv74zCrfIiTydZlmK+WWtv6Qtf3y12vp6dwEhaf\nXT5cqB22fKTHs/xNu9CqsU8mE/jU1sWVm+py5a8KmYZvP7rswvSmoRV9Rv53PB4per+/r2CKXz7S\nU5MALrc5uSyBZH9tJpTJeUtDlrcFgXg8XPVYNnPsu+xEr329sab9bl7KGJpc1u3U+wQq6/vg6Izz\n9/BQT9kNXdamDvZ3oa+veO0oRXd3oX09duLccMjA4EBX0WdrvYe1fD8hJfVNLusO9P7RK4153F6n\ng9zeZlCu/91xa3y7FrGmNIKGidGMsTcBuMX18nEAE/bfUwCKaipwzr9vf7+i3xkb8y426kcymfCt\nhRVE6tnWSvo+MzNf9NvpVCG1wMT4LFLSZ9qJdht7QTajFmfO5/O+/cg4BaI15TOi7x96/S785DdP\nY/u6vqJrzM0WxnXs9ExN6VjSkiZufHwGyNTmhjo1lQIAzNhpLtLpTFVj2eyxz9njMJ9aaOrvarDK\nrZwem0Fm3hLQK+37zLQ8/tOYLiOUy7NjamoOOWmMK/m9Q8+OA7A0QQv2fDENDbPTqaLP1nIPax37\ndKqQknNycg6jASlc7cWClJtvwTb1t+OaVy8qGfus7VKSzWSbdq9KCX8NE8o4518C8CX5NcbYtwGI\n1iQAjDfq99udj73lopZkGPZ09CefspZy5bkrAAB3PHgEQGnztiiG7edPtnYkgT960Zme7xV8K6o3\nRRW1o8ZEpm6EVkb45AXdp6xVCSmF832tGf0rCcBwR9iKclB+lQncaLZYx1b3KdGqQXORUAqSt4nZ\nHAh+MExQMFv0rPrRbIPz3QBeAOA+ANcD+FWTf79tWNaiiJnzNifxv795BjdcvM55TTZjBH0zXIqs\nGU7g5VdscISyUgKTpmkImfqiHPVDdXR4VWon1sXRX/UpC/qG04rksYCYG4sTyoTwoaEyQVr1KbOi\nNf/y9TuxrLeytesll66HYWi44aK1+MG9hwBY5stS1UdageLoH5CN249QiWANwhuxVgZlbJstlH0W\nwJcZY3cBSMNKSgvG2McAfJNzfl+T20O4iEVMfPiNFyivBS2ZYyeiRrqV/qwllFW/wBhOaHjti5Pb\nCbxWxGl2vk2iL1uREgOw50a2/BzxorA5VXZvvWpdVlNnNh41cZMdhCSE7lAFeRWbjRKVGpC0CX6Y\nrpQlRHlCRgdryuxktDd6vP5nHq8tziuaqDtUO631VFNsuqcrvKi0AvXU7hgu01atFMyX7RJ92fyU\nGEBhbizKfKl7l1Dyo55j7KQQCXmXemslSp6yxUi7TYQ0ZdVTKEgejPtFKhCiLLX6FxG146WV8OOW\nG8+pqSB1PRZzQ6/v5lAwX4ralzVfsqE4tXFbJZQtJiWG0JRVeHPrqQ1VfMok38ZMNl/qa01BTR4b\n7LVQNv2SUFYZne5TRrQp1+5aHbgTbCch75PlsrUv1h+xnglPKymzVA1mUZmlYG84F589gkwuhw0r\nigLMG4q414tz9K9OKK+nUCb8ecKm7mySkZCBTLb1xWNanaesGkKGdx45wh/nEBCQ/Y2EMqIiXvnc\nTa1uQkej+JQ1SCCpZ2ZrswpzayXomhWrl7NzcQV9wxnuj+PGKytP2lwvxG1ZzC2v1oxTjfa2/G8X\nDgSJWAjX7lqNWMTEd+46UNN164G4H5oW/HkXIk1Z1Yi5F5TI2mCIhgRBlETTCmVsGrV21FMoE5tX\nvTYGTdMo3L8CNLvc0WJcDgrmy+o1ZbX7lAl/RgOapuGVz92EczcGo6iLMOdWatZtJapPWfDbGwSC\nltE/GK0gCKIsYrNs1Gnd0VbUwW+mEW0165xmYymia9qi742pV2e+rGdNSPH9UAAF70JUcjDaUwqK\nvqwekYczKCWpgtEKgiDKoteQg6oSzDr6VjRCKDNEvoc6X3cpYeila56WwqzW0V82X9aoXfWK/A1M\nNJxev1QxjSaIQm3Q2bFpGd7ykjMDo5kloYwg2gS94ZqyeiaPLRRGrxfyhkOaMm9q0pTV4Ohf63gI\ngTCsCGXBEIKMgKVMKIVJKTGqJmQauGDrcKub4RCMWU8QRFlqyUFVCZGQDg1YVI4zN6KN9dwYFPMl\nbTieaDVoynTbH60V5ksvTVlQHK9F34KeowwgTdlSgDRlBNEmiM22UUqieDSEt/7eWViV7K75Wo0w\nX8o1EUko80bXagsE6YqGKq7gIf9OrVqkwd4oNABJKZ1LUIQKo8pKB61EdvSnZ6Q9IaGMINqERpsv\nAeB8NlSX61QbyVcJasFs2nC8uOTs5ZieW1j092+56Rx0VSqU6fUTAFYlu/Gpd12m/HZQzJdCQ9YO\nPmUUodz+kFBGEG2CWGPbwZ+qEaZW2TTTBregJbzgwrU1fX/98sprVzo50VCfce6OhZR/B0WoMAKW\nx6oUVGap/Qm+6E8QBIDGp8SoJ2Ijq6cbDm04wcLJRdcgs15QUlAYTj+Dv12GKCVG2xP8WUYQBIBC\nQtB2WGsLAmT9lhiToi8DRaMPCUFJfmpKtTiDjhp8EYz7R1QHjRpBtAnOJtgGAolRZSLSSiAn5mBR\n76oNftdvNUaD+1lPtDqWviJaAwllBNEmONGXbbDY1lIY2w/KUxYsCkLZ0t5G6pm/r5kERaglqqO9\nZhlBdDCNEHQaRSO0C+RTFiycYI4lPhbiMBAKSG3ESqFnpD2h6EuCaBPaaRMs+BvV75qyT1k7aAuX\nOo02XwLAJ99+iZKfrhXEIiZuvnYz1o5UHpkaBEgoa09IKCOINqGgKWtxQyqgETnVSFMWLJrha9Xb\nHWnYtavhqvNWtboJVdMOyW6JYtpLH0sQHUyjyyzVE2fDrmNbKfoyWLST5rYToXFpT0goI4g2oa3y\nlDVYU9YO92Cp0wzzJbF46nkgIpoHCWUE0Sa0U0Z/kWiznsKTqimr22WJRdJOqSI6ETq4tCcklBFE\nm1BIidHihlRA433K2uAmLHHIfEkQ9aepjv6MsRiArwIYAjAF4HWc81HXZz4O4FK7bZ/nnH+hmW0k\niKDSTuYiswE+ZUrtS5LJWk47zcdOJJdvdQuIxdDspe1PADzCOb8MwG0APiC/yRi7CsBGzvlFsASz\n9zHG+pvcRoIIJO3k6N8QTZlJ0ZdBQigrSWsZTHJ5ksrakWanxLgUwMfsv38E4IOu93cDeMj+Ow/A\nALBQ6oL9/XGYVeaxSSYTVX1+KdHJfQfau//RaAgA0N0dXVQ/mtn3RE8MIVNHcqCrbr/b3xd3/h4c\n6K76uu089rXSiL4nuqMAgEjEDPy9DXr7GkFPIgagM/su0279b5hQxhh7E4BbXC8fBzBh/z0FoFd+\nk3OeApBijIUAfBmW+XK61O+Mjc1W1a5kMoHR0amqvrNU6OS+A+3f/8xCFgAwN5euuh+t6PuH37AL\nfd2Ruv1uai7t/D0xMYvRcOUamnYf+1poVN/FeOSyuUDf204d+7Fxa2/sxL4Lgjr2pQTFhgllnPMv\nAfiS/Bpj7NsARGsSAMbd37PNld8EcAfn/KONah9BtBuFguQtbkiFLB/squv1TCkZZjuYcJc65FMW\nTN75iu2488Ej2LaOPH/akWabL+8G8AIA9wG4HsCv5DftQICfAfgE5/xrTW4bQQQarY3ylDUC8ikL\nFo3wGyRq59yNy3DuxmWtbgaxSJotlH0WwJcZY3cBSAN4FQAwxj4GSzt2CYANAP6QMfaH9nfewDk/\n0OR2EkTgKGjKOnMTlFNiUO3L1iPmIQnIBFE/miqUcc5nAdzo8fqf2X/eB+CTzWwTQbQL7ZQ8thHI\nyWMpW3nrIfMlQdQfimUmiDah05N1UpmlYNFOZb8Iol0goYwg2gS9zRz9643sU0aCQOspmC9pGyGI\nekCV/koAACAASURBVEFPE0G0CYUyS50pkJgG1b4MEmS+JIj6Q0IZQbQJeqc7+lP0ZaAg8yVB1B8S\nygiiTWinMkuNQNaUaR16D4KEY740aCwIol6QUEYQbUJBM9HihrQI0pQFC8d8SQIyQdSNDl3eCaL9\n6HRNGUVfBgtKHksQ9YeEMoJoEzp9E5T73an3IEiQ+ZIg6g8JZQTRJgizZadqymToHrQeg6IvCaLu\nkFBGEG2CEETIyZ0IAnRIIIj6Q0IZQbQJeoc7+hPBIhIyrP+HjRa3hCCWDs0uSE4QxCLpdEd/Ilhs\nXNWL11+/BTs2LWt1UwhiyUBCGUG0CZtX92HtcAKrh7pb3RSCgKHruPycFa1uBkEsKUgoI4g2YfPq\nPnzoDbta3YyWcv1z1mB8Ot3qZhAEQTQEEsoIgmgbbrxqY6ubQBAE0TDIZZggCIIgCCIAkFBGEARB\nEAQRAEgoIwiCIAiCCAAklBEEQRAEQQQAEsoIgiAIgiACAAllBEEQBEEQAYCEMoIgCIIgiADQ1Dxl\njLEYgK8CGAIwBeB1nPNR12f+FsDzAOQBvJNzfl8z20gQBEEQBNEKmq0p+xMAj3DOLwNwG4APyG8y\nxnYAuND+75UAvtDk9hEEQRAEQbSEZmf0vxTAx+y/fwTgg/KbnPMHGWPXcc7zjLG1AI6Xu2B/fxym\naVTViGQyUdXnlxKd3Hegs/vfyX0HOrv/ndx3oLP738l9B9qv/w0TyhhjbwJwi+vl4wAm7L+nAPS6\nv8c5z9gmzHcCeEe53xkbm62qXclkAqOjU1V9Z6nQyX0HOrv/ndx3oLP738l9Bzq7/53cdyC4/S8l\nKGr5fL5pDWGMfRvA33HO72OM9QK4m3N+ls9nEwDuBfBizvn+pjWSIAiCIAiiBTTbp+xuAC+w/74e\nwK/kNxljVzPGPmP/MwVgAUCuec0jCIIgCIJoDc3WlMUBfBnAcgBpAK/inB9jjH0MwDcBPADgVgDb\nARgAvsQ5J2d/giAIgiCWPE0VygiCIAiCIAhvKHksQRAEQRBEACChjCAIgiAIIgCQUEYQBEEQBBEA\nmp08tqEwxp4D4O8551cyxs4D8DkA8wAeAvAuANcCeL/9cQ1WMtuzOOeP299/FYB3cM4vanrja2Sx\nfQcQc3+Wc952Ea/l+s85zzHG/hFWv3MA3ss5v1v6/uUAvsY5X92C5tfEYvvOGFsPK/BGA3AIwB9x\nzqtL/BcAKuz/pwBcAmAawPs457+Wvr9kn3u/vvt9tjW9qB7GWAjAvwJYByAC4G8A7AHwb7BK9D0K\n4G12/z8E4IUAMgDeLZfua9exr7X/7Tz+1fTd/vxGAP/jTr8V1DV/yWjKGGN/BuCLAKL2S5+HNQEv\ng5Ww9lWc8x9zzq/knF8J4PuwFjMhkJ0L4E2wNqi2osa+F3226R2okUr6zxg7B8DFAJ4D4GYAn5a+\nvxrAewGEmtnuelBj3z8O4HP2Z+8A8J4mNr0uVNj/GwAwABcAeAWAz0jfX9LPfYm+t/tz/xoAp+z2\nXw8rav8fAXzAfk0D8BJb+LgC1tx/JZbI2KP2/rfz+FfUdwBgjN0M4D8ALJMvEOQ1f8kIZQD2A3iZ\n9O9VnPN77L/vhqUlAAAwxlbB2pw+Yv97EMDfAXh3c5padxbd91KfbSMq6f8RALOwTlY9sHLggTEW\nhXVifGvTWltfFt13ANtglTuTP9tuVNL/bQB+wjnPcc5PAsgyxkY65Ln37LvPZ9uJ/4Japi8D4HwA\nd9r//hGA58Hq1+2c8zzn/GkAJmMsuQTGvqb+o73Hv9K+A8AYLKHUIehr/pIRyjjn30JhswGApxhj\nYjBeBKBLeu89AD7JOZ9njBkAvgSrJFTw6jFUwGL7XsFn24IK+5+BZbp7AsBPAfyD/f6tAP6Bc36k\nSc2tKzX2/SEAL7b/fjGW7tg/BOD5jLEQY2wDgDPt1zvhuffre1s/95zzac75lF355ZsAPgBA45yL\nHE+ijF8PCqX9xOsDaP+xr6X/vWjj8a+i7+Ccf59zPuO6RKDX/CUjlHnwBgB/zhj7AYATAE4CAGNM\nB3ADLJUmYEnYmwB81n5tG2Ps/za/uXWl0r77frbN8erTawEcA3AGgPUAPswYWwngMgAfYozdAWCA\nMfYf3pdsG6rp+3sBvJgx9mNYQtuSHHvO+e0Afgng57AOJQ8AGEQHPPc+fT/l9dnWNHnx2CaoXwD4\nCuf836FWf0kAGAcwaf8tv96LJTD2NfR/HG0+/hX23et7KxDwNX8pC2UvBPBGzvkLYS3A/2u/fhaA\nJzjncwDAOb+Pc36m7Wv1SgB7OOftqtIWVNT3Mp9tZ7z6NAZgmnOehXWSmgfQzTlnkq/dac75K1vV\n6DpRcd8BXAPgI5zz58Na1Jbk2DPGNgM4Yfub/D2AXKc89z59H/f6bKsavRgYY8MAbocVuPCv9ssP\nMsautP8WZfzuBnAdY0xnjK0BoC+Fsa+x/yfRxuNfRd+L4Jw/G/Q1f0lFX7p4EsAPGWOzAH7BOf+h\n/ToD8FTrmtUUqum732fbmaI+2WbqSxhj98Aq4fU1zjlvaSsbQ8V9Z4z1AfhXxtg8gMcAvK11za4b\nXv2PwjLhvQlWTd2l0E8vqul7uz/3/w+AfgAfZIwJ/6J3Afg0YywM4HEA3+ScZxljvwKwG5YSYqmM\nfa39b+fxr6jvrWpcrVCZJYIgCIIgiACwlM2XBEEQBEEQbQMJZQRBEARBEAGAhDKCIAiCIIgAQEIZ\nQRAEQRBEACChjCAIgiAIIgCQUEYQBEEQBBEASCgjCIIgCIIIACSUEQRBEARBBAASygiCIAiCIAIA\nCWUEQRAEQRABgIQygiAIgiCIAEBCGUEQBEEQRAAgoYwgCIIgCCIAkFBGEARBEAQRAEgoIwiCIAiC\nCAAklBEEQRAEQQQAEsoIgiAIgiACAAllBEEQBEEQAYCEMoIgCIIgiABAQhlBEARBEEQAIKGMIAiC\nIAgiAJBQRhAEQRAEEQBIKCMIgiAIgggAJJQRBEEQBEEEALPVDaiV0dGpfDWf7++PY2xstlHNCTSd\n3Hegs/vfyX0HOrv/ndx3oLP738l9B4Lb/2Qyofm913GaMtM0Wt2EltHJfQc6u/+d3Hegs/vfyX0H\nOrv/ndx3oD3733FCGUEQBEEQRBAhoYwgCIIgCCIAkFBGEARBEAQRAEgoIwiCIAiCCAAklBEEQRAE\nQQQAEsoIgiAIgiACAAllBEEQBEEQAYCEMoIgCIIgiABAQhlBEARBEEQAIKGMIAiCIAgiAJBQRhAE\nQRAEEQBIKCMIgiAIgggAZjN/jDGmA/hnAOcAmAfwZs75Pun9twF4PYA8gL/inH+/me0jCIIggsWB\no5PI54ENK3pa3RSCaDjN1pS9FECUc34RgPcD+IR4gzG2DMBbAVwM4LkAPssY05rcPoIgCCJA/PWX\n78ff3HZ/q5tBEE2hqZoyAJcC+DEAcM7vZYztFG9wzk8yxs7hnGcYY+sAjHPO8+Uu2N8fh2kaVTUi\nmUxU1+olRCf3Hejs/ndy34HO7v9S6HstfVgK/V8sndx3oP3632yhrAfAhPTvLGPM5JxnAMAWyN4O\n4CMAPl3JBcfGZqtqQDKZwOjoVFXfWSp0ct+Bzu5/J/cd6Oz+L5W+L7YPS6X/i6GT+w4Et/+lBMVm\nmy8nAcit0YVAJuCc3wpgOYDLGWNXNbNxBEEQBEEQraLZmrK7AbwIwDcYYxcCeES8wRhjAD4K4OUA\nFmAFAuSa3D6CIAiCIIiW0Gyh7L8BXMMYuweABuANjLH3ANjHOf8uY+xhALthRV/+iHN+Z5PbRxAE\nQRAE0RKaKpRxznMA3uJ6+Qnp/Y/A8icjCIIgCILoKCh5LEEQBEEQRAAgoYwgCIIgCCIAkFBGEARB\nEAQRAEgoIwiCIAiCCAAklBEEQRCBJ58vW+CFINoeEsoIgiCIwJMjoYzoAEgoIwiCIAJPjlKJEx0A\nCWUEQSxJMtkc/u1Hj+PA0clWN6UlZLI5jE/Pt7oZdYM0ZUQnQEIZQRBLksOj0/jlw0dx72PHW92U\nlvDRrz6A99x6NyZn0q1uSl3I5UgoI5Y+JJQRBLEkyWatTTzboXavA0enAAAnx+da3JL6QI7+RCdA\nQhlBEEsSYe7qdA3LUun/EukGQZSEhDKCIJYkQhjJdPhu3s6+WLJ2bKkIlwRRChLKCIJYkohNvNM3\n83buvyxPtrNwSRCVQkIZQQSEufkMFjKd6f/UCIQskm1joaQetHP/c6QpIzoMEsoIIiD81b/9Bp/9\nn0db3YwlgxBG2lkoqQftrGEiTRnRaZitbgBBEBanJlOIhIxWN2PJQI7+Frls+/Zf8Slr324QRMWQ\npowgAkI2l+94rU49EcJYNtvZJuGFNu6/rBzL07NBdAAklBFEAMjl88jnrSzsRH1whLION3u1s5+i\n4lPW4eNIdAYklBFEAMiR/1PdEZt4to3Nd/Ug08ZCmeJTRs8G0QGQUEYQAYCEsvpDKTEsvMyXuXwe\njx8aQ3oh24IWVU4e5FNGdBYklBFEABDCGJkv6wdFX1p4zal9hyfw8a8/iLseOdqCFlWO4lNG5kui\nAyChjCACQJ5MbXXHMV92uFDm5VM2k1qw/59pdnOqIk8+ZUSH0dSUGIwxHcA/AzgHwDyAN3PO90nv\n3wLglfY/f8g5/0gz20cQrYK0OvWnYBLubO2jl6asXUy7qk9Z69pBEM2i2ZqylwKIcs4vAvB+AJ8Q\nbzDGNgB4NYCLAVwE4FrG2PYmt48gWkKOzJd1R8gbQRc8Go2XpizbJgIracqITqPZyWMvBfBjAOCc\n38sY2ym99wyA53POswDAGAsBSJW7YH9/HKZZXcLNZDJR1eeXEp3cdyC4/ddC1qOYzeWxbFk3NE2r\n+28Ete+NIh4PW3/Y97LT+i/IZHNFfe96ZgIAEImEAn1f9HBhi+rpiS26rUHuY6Pp5L4D7df/Zgtl\nPQAmpH9nGWMm5zzDOV8AcJIxpgH4OIAHOed7y11wbGy2qgYkkwmMjk5V9Z2lQif3HQh2/0+Ozzl/\nHz8xCUOvrxI7yH1vFJOT1plORBh2Wv8FC5lcUd/Hx611c3pmPtD35fRk4Vw+NjaD0dFw1dfoxLkv\n6OS+A8HtfylBsdnmy0kAcmt0zrnjacoYiwL4mv2Ztza5bQRRM4uNEJMTnJKzf33ItonfVKPxylPm\nmC8DPtcoTxnRaTRbKLsbwAsAgDF2IYBHxBu2huw7AB7mnP+xMGMSRLvwtdv34uNff3BR35U3nEzA\nN8p2IU/RlwB88pS1SbUDqn1JdBrNNl/+N4BrGGP3ANAAvIEx9h4A+wAYAK4AEGGMXW9//s8557ub\n3EaCWBRPHhnHsyerM6cLZMEh6M7X7QJFtFqU0pQFXfskt44c/YlOoKlCGec8B+AtrpefkP6ONrE5\nBFFXrILiixOocopQRptPPSiUWepsIdcr+rIRFSS+d89BbF7VC7amv27XVDRl9FwQHQAljyWIOpHN\nWkXFF3Oizyrmy84WIuqFk4urwzUsXvOp3j5lJyfm8N+/fAp//++LM9/7ofiUdfg4Ep0BCWVE25DP\n53Hrtx/BD+891OqmeCK0ZIs50ZOmrP5QQXIL7zxl9lytk6Dj9Rv1IKdoyhryEwQRKEgoI9qGXD6P\n3+4dxTfv2N/qpnhSiw+T4lPW4UJEvSCfMotSGf3rdW8aZVqk2pdEp0FCGdE2BF1YqcV5Okfmy7qT\nt29jNpfvuA1d1jC5tViTM/8/e98dZ8dVnv1MuX3vNu1qV71r3LuxjekYAglJ+EICBD5CEkpIgSSE\nJCR86SEfgTj0ZvKZhITExNg4LhhMsWy5yEW2JEuWr+pKK2m1vdx+75Tvj5lz5pwzZ+aW3ZXX9r6/\nn39e7d47c+bMKc953ud93xrjvlyYsbZY3buc0X/ZXmq2DMoW0WzbQbm6tAv+LnWzbBvf+mEOR0/P\nLnnGg4DGtpgyZ9l9udDG9uNS7NLduXEcH5lblGuHgfynD43jD774EA6emA58rlmr1Ezs3HeGJuUF\nFg8wLecpW7aXmi2DskW0f/3Bc/jzm3YtLybzsJGJEnY8fRoP7z+75MHKQjFlS/05Xyhmcwl5lx77\neNNdB/DfPz2yKNd2QpiyqXwVADAx62bKbydP2e7cOL75/eew9+gkc792Wxpt7DtcJsqW7aVgy6Bs\nEW1ipozZYm3ZHTUPMz11b920uI11KbqjiHh6/pqy5fGyENYs0H3m2CS+fd+hczqmbNtB3bRRYdim\n0+MFHDntVqG759Eh/M4/P9A2084+L5s8lowtwnK1Iwmo1NzvVpi2nQvX4rL7ctleCrYMyhbRzHm4\ns5bNNdKHpuVw/VhbpGiv+Zjvvmy9bZy7aXm8LIjZTbqEH9x7Bj956hTmirVz0SyvPe4YYQ9s//qD\n5/Cl290iJ7c9cAyVmoWTo+3V7WOHIJs8ljBj1Xr7kcKEeePcw+dA6L/scVi2l4Itg7JFNLLgLoOy\n9o2c7E3T5sBKZYlp9RzHWTj35RIPaHihWLPsIwEti13eynEcPLr/LKbzVf+wwQCmStUKMGPJeHv5\nvcOE/mSc0bWprZx6QUC5WGucvSz0X7aXmC2DskW05ZD8+RsBYnXL5jZW4kJZKtYsKxNmy2WWFt6c\nCPflvqMT2HN4gvvbYssMRiZL+Mbdz+JHTwxL72naTqAN7QKRMKG/CPjbOQDImLLFcrnzyWMX5RYv\nCbNsG88OTS1LaV4AtgzKmrC6aWNkstjy9+hpdHkitG2UKbNsbgMp15YWU8a2rR1QtsyULbyxLJC4\nGf3njw/jP398iPvbYm9Y5CBRqpr0XnXmXdu27VaEaHMsHDk1i6GzbjQnpykzwxmtdlhdX1IQfd2F\n0Ogtl1laGPvRE6fwT7fswe0PHnu+m7JsDWwZlDVhN911AJ/4xmM4cbY1fccLpejvUjaLcfNYnPty\naTFl89XXcGWWlpmyBTE74p3U6hYFKyZlrRZ3nlIgZtrcuCZGxkChUg98pxn7h//Yjb/91ycB8GCG\nvYbIvDU6QNz18HH83b89yX1PJssQdZB/+29P4F/vfQ7zteUySwtjJIBk/7HJBp9ctufblkFZE7Y7\nNw4AGJ0utfQ9a4lpyio1ExMz5ee7GS0Z675kwcqSY8rmmdKCT9+wNMbLC92iEvKygSPWOWLKLMqO\n+WNZxjZNz1UDv2v5XmFMmei+bHAA+N7O4zg+ModSxZ9vPrMod186joPh0QKGxwpttZ01LiXGEllH\nX4imqQqApbMXLVu4LYOyFqwjFWvp80st+vIbd+zH//mXx1CtLy2WKcroRmY63Iay1DRl8wZly3nK\nFtzYbhT71LRsRtd1bjRllJEzbXrPumlTVouMgcm5CtfOdixUU9am+1LOlMmvazsOHMm92jE+o/+8\nL/eStWVQ9sKx9kJ7XqLWKnu+1IT+U3MV1EwblZqFREx7vpvTlLEbJu++XGJMGesiWs5TtiQsoM3S\nFPpv03KgqeRn3o25WOa7L/2cewS86JpCDx1THChrvU1fvG0fnvaCGNz7ucBPUZQAM9bs2sSDPMIw\nytld01ycde+F7r50HAdfv/MAzt/Qg1dftuac3lsloGyZhV/ytsyUNTCewWhtsySL8FLRlNVNkjDy\nhbPps24etv9fzEzZcp6yhTE+IpZ3r1kMyLcYBivMHMfBfU8MY3SqhNliLVBPshmzGHbMkjBZJDCB\nZN0X2x1l7LOygMy/jlzf2uxY5aJEaQCTXAcpc822a2zzlso62q5VahYePziGJ58bO+f3JkzZCx3Y\nvhRsGZQ1sLmSn1Cy1c2WsjxLRLi91NypzRjdyJZ69OUCCv3bOc06joNb7z+CfUeDG/JL1cKAMnGv\nkfdkSTRSop2dKuGWnxzG93edwB9+8SH89Tcfl35ud24MX/uf/dIxYLKaMg7k8IBpqg33ZaODVljO\nxGbHKgfAJEmSrQZMWrv2YipILou4PVemebTwC2ntf6naMihrYFOs6DZiMu0/PhlIm0EWraVywiNM\n2QspVw2bPHYxoy8f3HsGN99zsO0wfovT7bSR0T+E1WnWpvNV3PvYSXzu1n0tf/fFamGpJYh7zXbc\ntA0ykCEaYWYJYBqZDAb92I6DL39vPx4/OIbx2WBADasjY9tD835ZQU1Zs8CmkZsz7EDW7CZdlzBl\nZoj7ks7ZBTiMvpgy+p8r7aLMNIW4L30W82+++QR++tSpc96WZYu2ZVDWwNhTa9gCZlo2vvDdffgO\nU1zYzdPjfW+J+PFlSR+XupG21gVN2UIzZY/uP4uHnhlpe8Gcr/tyvkxZO+60F7uFSQ9YsGA7DqP1\nisj6732mFHEYyJ2Y9u8neYd+HVc+kti0XM0XAeYzjPuyWVd2o3FLNuN23ZdSEBnClNUl7s127cUk\n9K8zgOhcmyq4L2fyVZwYzeO5kzPnvC3LFm3LoKyBTTeh76h70VSlajBsHEBbpUwWw8QT+QvB6Knc\ndBY1o3/NYxHrZptM2Tzdl/PVlC0FUFapmfjkt57E7ty518zIjI8YlP9s2w7t7yiAQvRmRSaHmGhP\nMFoh2ftgXfF8e/gDBwv8mt3AGzFl9Xm6L/mqABKmjAOZCyeTYC9xLgvGL4adq3JeMiN9R8YgqR0c\npaNctufHlkFZA0vE/SjFMDBTt4IDfL7Mx2KYuYBuhXNlVG/jOFwR8oWOvqzV53eKXVimrPU2LIXA\nh9GpMo6emcOB41PPd1MAhCeP5V3NDprJU0Z0QMVyOCgrlKOTvloMIycyT2z7KgwL3GjtmJgpc9Gc\nYWbN033JPk9dci2Z+3IhAopejJqy5wMIiZpCcmggkpZlWzq2DMoa2CsvWYX//cbtACLcl2SAS3QX\nwNLRQrwQmTK2z9n8aovFlLUNyuZZnHm+ecoq9cUPfDg0PIMfPHYy9O9k/NeWyOlbllsL4OepC8qI\n1ie838ncYZOoiiayX4G/MxuiyCyx75zFHlHjsVQx8eff2IVb7z/akF0l7RfXouaZsmjQJRX6L0ie\nMubnpTGs2rb683goFt+JD8pe4J36IrSGecoMw7gcwJ8D6AVAE/3kcrnXtXozwzBUAF8BcCmAKoD3\n53K5I8Jn+gE8AuDiXC5XCV7l3JqiKMim4wDCFxkZUxZG7S+WOY6DvUcnsXVNV2iSWx+Uzb89O/ee\nwWMHR/EHv3IpdG3xsD27KVUZIFZeaFBWly9SddNCTG+c020h3ZftgOZzUXbqU99+CgDwiktWSccY\nGf+1JZKcOIy9NAWWyqG/b6wpi3ozLOtQl4GyEKZMdF+GPYNohXINpuVgplBteJgIdV96wQ6Kosi+\nFmg7ey3Tlq9xLCvTzLWjzGF6/AXPlD2PLkMRCFK5xgso6OulYs3spt8C8ACAvwPwN8x/7dhbASRz\nudx1AD4O4Eb2j4Zh/AyA+wAMtHn9RTGaDTlkAMuYsjAR7GLZ6YkivvDdfbjvieHQzyyk0P+b9z6H\nZ4emMTm7uLiZi7hkgFh1sTRlzDt85tgkfuefH8RRr25clC2k+7Kdk/S5dF+GzYMlx5QxzeBYHeZn\nFkA2A8qijAX0pkSbyLIVNQHAhQH5ZlyqNQHksUbwkEycT6yZ8SpjAfk+lbOE811rXozRl89HSgwR\nCNYWmCmzbPsFr/lbKtZMRv9SLpf70gLd7xUAfgAAuVxul2EYVwl/twHcAGB3sxfs6UlDb4LJYK2/\nP9vS53vH3VQXyVRc+t3ZirvA2rZ/7bpPKiKTSaC/PzvvU2OUjXqpOxxFCX0+slhmOpIt9wFr7OTr\n6k7P61qNLBb3h6jKMHI10+bu++zxSRw4Nolfft22yD4OaytZnLLZFP3M3LNjsGwHZctp+IwdY346\nlHRaPk6iLJHwnzMW01v+fiwxTn+WfffoqRk88PRpvPfnLqCHjHYt25VGf2868PvUWa/WYcQYPJem\nMM9p2f47nC77LshMNkV/TiRioe1OpoKFnMXPOsy4S3tznjX2HevMuM5kEujuCfYnAMQj2jTrsaOK\nqqCjMyn9TCqho1QxaXs0LbhW9q7oaFjhI53xxzSZ/oqq0t/FmGfLdPht6enJIJlov3BMdiRPf04k\nw/uikTXzvbppYd+RCVy6rX9R2P+0t4+wY/FcWH9/FhqzR/b1dSB1Zg6AG0gx37Y4joNf+NiduMJY\nib/54HXzutZi2FJYi1qxZmbLDw3D+DCAHwKgtEgulwsXl4RbJwCWdrAMw9BzuZzpXfNHAGAYRtMX\nnG6xSHh/fxbj4/nGH2SsUHAfezZfkX53bML9XbVu0b+PjfvFeKdnyrjjp4fw3R1H8Xfvv6blGprN\n2PhEIbKNjuNQ4DE1XWy5D1ibKfgRqaNjeSQXUZlYYO41PefnfqrUTO4Z/vRLDwEANq7MYONgp/Ra\nYe/eZKLhxiby6Eq6C9jUjDu2pqZLDftratoHZbNz8ncQZQUmSXGxVG35+xNT/v1l3/2Dzz4AAFjX\nl8ZlW/taurZoo2NzUK0gM0f6oFiuzWt8LZTVGRbMsmzaJjJXAODs2Bz9OWzuAP5YYE38bJmJzJyU\nzLE5JpJ7Ysq/3uRUER1x+STKR7Rp3FtjiqU6Jibkxb/juooSgIlJtz2VajBQYXR0DqkGwImdA0Tb\nWan6c5Cdp1PMWDw7NodMsv31bpbJ91YstTeuml3zb3vgKO559ATe+spN+IXrN7V8n0Y26eWxrJtW\noD3f33UCh4Zn8Pu/fMmCHtzJsxfL/voycnYWk947EtfRdox4LZ7KjS2Jec9aO/v9ubAooNjMdvoe\nAB+FC8oe8P7b0WZb5gCwrVEJIFvKpqleNuRG7suQ6EvbcXDszBxmizWMTQeTSi6ENQpxnq97jbXT\nE/6iu9iaBNbdwrosxYg1YrKkno2MdzsFXVvNUPzzL7M0P5dPs+7LhdCzhPVHnWrKFjbqrl0LC54w\nOfelPDhHtNbdlzKhv/+7MhM9HOm+jBgLddMfn2FBCgmPkSPuUtnYama8yTP2y8dsPcSt2Y6xMjij\nBQAAIABJREFUOrLFdl8eHnZzdh0cmm7wyfaM6hKdoBt575EJ7Ds6ifIiaUPZ91Ct2wvqviwtsTrE\nL3Rrhin7cC6Xu3uB7vcwgJ8H8N+GYVwL4JkFuu6iGtWUNRL6W37hXzFaiSyKiyWCJtev1Cx89r/3\n4ortfVzRW27DmCeQOj3OgLJFFnWz/Vjx7pVK6ChXTVTrVuCEPzrVOihj30ldsmG3Dspa798wIXqz\nxoKyKDe52qbrkhN6S/rDtn0mdr6asplCFX998+N45w3bcO0Fg21fh6+SECb0Z9m0YL/XTQt3PHS8\nqc0yLPrav77/OzbthWk6gbUlldBQrkanuiD3E8s2sZb03JJRetJmwI609mVoSozoKNRWjNOUNQnU\n66aNmN46fU++02j8kgNDq4wWNz5MB1rc/xu5Z6FSRzrZvru3mXvX6hbqLaxtMqvWLeryLi+DsgW1\nZkbuPy7g/b4HoGIYxiMAPgvgDw3D+KhhGL+wgPdYcNO0BqDMDC74otiVbPC1RcoLQybZyFQJzxyb\nxL/9IMf93VzA0+tpxjW72KJuLiWGBzwy3qLFApHujrjXNr7UVTPGPgP7LltJk8H26fyjL9sR+jO5\nrSLu3y4oY0/D4jvPnZzG+z99P3Y9Owqg/dxHpmXjqUPjGB4rYK5Ux9DI/NwOYeyYFcKUyVjfux4Z\nwr27TmLH06cb3q/OjSNZ9KU8aEUWfZn0GK7oNB2e0L9uRTBlHiiLyLLflNDfJCyP40cRNoi+bPba\nUcYypk4T1xqbLuF3P/sgHtk/0vK9SJR1o/H75e/tx2dv3QsAeGT/CL5+54GmmF0uWEI4uJHxEpUH\nbz7Gjvlq3WKSZbe+1pweL+B3//lB7Hr2LIBlULbQ1gwkP2oYxs0AHgNAfW+5XO5brd4sl8vZAD4k\n/Po5yec2tnrtxTSdui/DmDJ+gY3pasCdtZCuHZn5dLR8QeEXhPktlBNMxOVi57kxOXbBfba0x46x\nDFc6GcNMoYbhcbm2JsrCIvCqLbkv57cRzdf9WRFcu2FCZb1NUMa524T++OHjbsTvIc/90+4Y/+Hj\nJ3HbA8fQ3+0KxefLsoS5vuqSdwzIwfBEC9HFHCiLSIkBgGPeZO7LpAemolhXsu64JcjknyNsBjm0\nydimZphdsmaQYu5AVJ6yRYq+FNpu2w5mizX0ZBP0d6PTZZiWjVNtHM7iMXfONJrvx0fm6Gd2HRjF\n/uNTeNcN22jqpDDjUiaJ0ZDeOCwsEigzOfelxTGntuNAbYH1G50uw3YcnPWkIgtd8u6lbs0wZZNw\n85NdC+C13n+vWcQ2LTnz3ZdhmrLggs8uWDYTAr9oTBmhv0MmdRhT0I5x7r7FZsokLp+0hCkjbRqf\nLrecLqMWwnC0kuV/QcsstfF+qjU5sBSt3S2STZoqvnPxfu2O8aGznhB/piK9T6vG96ncvca+exnb\n1MpYqje4FntfdiOTM2Va6HXE+9Xr4e7LAFPWgvtSlnyXXevC3Jd8n/LteubYJD7733tRiihXxRqf\np4z/2z2PDuFjX3mYK4VH1oF2UuY0676sMaCGvMdmDiJirjfTsukhutZg/W5kp8YL9FDU6N7VmoVG\n+scoIwcZ8v/F0sG9VK0hU5bL5X7jXDRkKVtD96UVHOAiM0Xdly2wCKWKCQdOU9FLvmaNAYPMCWgh\nT68su7DQINNxHMwU/NOv3H0ZC7SDLDIOXE3SgCRlQ5iFMWUtCf0t+WbVrC00UxZ6nzZd1zxTxr/z\nQMLdut1W+hcxVcd8g0hCC5K3kKcsKoDCth2/0LPt6sJ0zdWTSjP6swcMtr6lGeW+DO8DNj9iGHgL\naMpkWrcwUCY5KIiF1GXXqHHsI3/tb37/IGYKNfzPQ0P41Ru2Se/LWlSesvHZChwHmMpX6HpB1r9K\nG+wNGa+N5nu1bsGy3MS45D1Wm9DWigEQH/3SwyiU67j546/zmbJSe6Ds337wHEanyvjC779S+ndu\nzJs2fxC1bMQbpERhjQJfr6+X3ZcLa81k9D8OyQE7l8ttXpQWLUHzk8eGacqCbgt2E+CZsuY3mt/7\n3IMAgJs/3rh4gmwhKVVMmn5jIYX+PChbWKbsezuP4+5HhvB/fu0qbF7dKRf6e0xZGDhsZoFkTVyg\n6O/rLWjK5h19OV9QxjMvYdZudYlWmDIH7qEkprcKynjifr6RopzQP8R9z4OyYL9HBeZYtg1V5Zmo\nVEJHvlSXFyQPqW9Zt5wAWPLdlxFMGUlGajZmysj8kLsv5feQBUdw9X1DNFJiGSvWBnvTmCnUsPvQ\nWFOgjHNBC20nh7RaLTj320mm7AeqRL9zVjdMmLJm1hyRKWNZsUaejkZWKJsolOuhrkjOfVmz+OoT\nLTNlhGBwr8GuDexBZdnas2bcl6+B77Z8I4CvArh5Edu05IymxAhzX0oi08QyS76mbJGiLyUM3GzR\nz02zkCkxOHH0AoOyux8ZAuDqNgC+z8l9idC/yrkvg9qzZo3bmJnnqUoqNYSZCMJbNYtGdLUHmptl\nytqJ7ASCKRxYk/VPO2J/wkj715gvU+b/zAEM1kXN/Hz09Cxu/v5B7r6ViPkqlmsCQKOBGzJlgrs5\nqClzrxMZfcn0cdiYJ+CunehLGVPGeQVYHSXrvoxIM0L6Z2quivGZxumBopgy8szsO6rNA5Q1w4xX\na8z6ULep666Zdd00g/1JfibvpdCkW1c0cv+wdoha2UZBKVEWdF+yQUDLrsz5WjPuyxPCrz5jGMaT\nAP5+cZq09Kxx9KU/qE+NFxDXVUn0ZetMGbFmXEGyjXGuWMOavkygja1szDv3nUFfZxLnb+ylv5O5\nDRfChsd8kb6uEbdrsK1E6E/aYdm8+2ehmbKW3ZdtAB8SWRaPafN2X0a931aZsoefGUFMV7noy2B9\n0OA1q3UbaXmS+VATgxDmy+jymic5mGDHSqlq4qF9Izh/fQ+uu8hNxRGlTeJyczUDypjPsxuZadoU\nlBOLx1SoQmod0dh+D3MhEaE/AaKtRF/KNGNh41zWF7Jrs+P0xNk8+rtTiDIu+lJoZpWwVAvMlDkO\nQhknFnTU6hZlPKtNyFLElBjifYHG0ZemZeNLtz+D6y9ehavPW8m1BXD7IhkPbusmB5qtUB1tM+YD\nQM99WeMjs5PR8Q7L1sCacV++ivmnAuBCANEz6UVmjdyX7AJ8053PYv1AB153xVr6O8ty6CRohylr\nxhUkyxeWZ7LE8yCxOeZHVRR88/tucCxxoTqOq49TFHfxWsiT0b6jE/RnstDKNre0oCkTWcJqzYJp\n2Tg0PIPzN/Q0BLThmrIg6xlm3AbWRuJT8v1kXKORcq0Yx5R5z/D0oXFM5at4/ZX8WGzFvvPTI0gl\nNFx3oZ8vTDxYyBb1dpgy0e0xX8DvOA50TQ0I6c0QVocY6yaL0stYgjsK8A8MdUnty6hoRfG96Jrq\n6dP874xOlfAX/+8x/PZbL8Ll2/q5Tb4RKCPvTMaKNaMpq0uYMrbgeFg9UZHpY0HwSBM5BaOiLysC\nYwP4z9nqwYz9LuBq/mT5wtjr5kt12r6mmLKQqF/2u43cl+MzZew7Ool4TONBmdf2St1Cl+R7fEoM\nW8qUVWsWbMdpWN0hiil7Poqtv9isGfclW4T8r+C6M9+7iG1acua7LxszZQAwna8GFmAKytoYtM2I\nVmXXZd2XreQpK5Tr+MCndwRynbnXcUOos0SrtoApPvKMyJWADFmfpwX3pfjslZqFx54dxT/dsgcH\nhqYa3jfMHdtKLh8++rL1PrFtBwrcTb3VEHNTSB5K2vvF25/Bt390iGMbWmHhHMdBqWKiXLVa0pQB\n7Y1zUVM2X6G/ZfuHmTDWTHaoIEDGsm3uuWXXJ2Y2w5SFptQJui9jugpN41PrDI8VYFoOzd/WFFMm\nui8lB4Yw96Wsz8TnIp/hdHosKy9cm2W1zk42TlvhNKEp45gy4tJsQ+jPHiSKIW5E9l7s+tqUpoxl\nxJjrsyw0AWV108KewxOB/GfkPmz0qs2U0AtjdtmxV66a0oTZH/vKw/jdzz7Y8DlYVu72B48id9KP\n+lzMvJVPHxrHJ7/15IIEFpC1bSlaM6Dsw7lc7rXef6/L5XJvR3P5zV40RtyXYsI/YuImVa6agqbM\nd1+2kwG/GSpeBhzmOFDWvHvt5Ki76D+490zgb2RRyHigbCEnIbuQklOwTFOTEYT+pE/jXkh7tW5h\ncs5NqzA1Vw18XzR2Y2bdCq2lxAh32TRjluMKZN1qBa2NEXFDIJUliLHXa6VttboN23FQrprcxhHM\nsSRjylofFwImk7JNzRrZwGNevjZRZE1M1nbC2BXKZmQKEVPiskslSCqLaE0Z//tgRn8ZU0beAdmU\n+I22SU2ZNFWHvF2ylCIisCTtZq/LuS+tIKjo7ohD15SmSqKx3SImj5UzZR4oayNNAzsWwjZs9jPs\n+trMOsiOO5YRY+cWcV9+465n8YXb9uExLyEzMQK6iuwhqYGe1vZykZF1s1wzubbQxLUVkt4juu9I\nH5wYzePuR05wufyivnt2qoRv33eo7eTSe45M4OiZOZyZaC0Hne0Eo6G//aND+L3PPdhWBZjFtlBw\nZRjG9QA0AP9iGMb74LouyXe+BmD74jdvaVjD6EvhhZuWw4lP63WL0tzVtpiyxoNYduKfC2PKGjA5\nUSVKyKTLpmIYQXtuqjArMQspeWZZott0IsZ9hiyI2XQMk3NVVOsW3biaOVXJsrq7bto2NWVtRl9q\nqoJUXPPyF7lJiHfuPYOd+0bwJ++6PDQhrPiMpmlzp/gCU4y4lRx1ZLOwvCSdxNj+sG1H2sftuOnF\nfpsPU0YABRnLfMUEXl8jGpkreeaZZSZzX6ao+zLY9qjobfHZY5oCXVP53GbCmGbnXiP3Jfms1H0Z\n4m5nf+/nKROYMssGYhq3pnClq4S1plKzkE3HkEnFMDJVail1itj0qlTo77svW03Lwq6hYYJ7FgDO\nFv0DXzN50VhAy2rHyhxT5v78ZG4cAOjhUrw/y5RVG0Sek3fXkYqhWDFRrpockBPH6th0GWtXdoQ+\nRxQrGDVnd+49g588dQoXbe7FpVv7uPt/464DeM3la3ABo10WjYDGqOAb1u57/CTWrOrCd+57Dvly\nHZ/9vVfQv/30KbdCx8GT0y2lTzoXFsV4vQHAqwGsAvC3zO9NAF9fzEYtNWtU+1LmR2f1XGVJktNW\nrJkJLzupzYVspKbloFIzMTFTkU6+sM0fCDJlCyn0ZxcnwprJNjKSEsMPnnD/35GOY3KuikqtRVAm\nCQ83LZuyJI3AwZ7DE3jm2CT9d1vRl14oeTLhn2ZjehzfvNfV9J0YzWPLaplaxD/Va6riVo+wbC6y\njSz05D7NGnuCn2I2B7a/SlU5m9QOgyq+6/noU8g70PUgcyXmbBKNjIG5UiNQFmSH0pFC/zCmTOa+\n1KCpirSIeYmCMuZvIe66eEyDorifdRxHmhJDvLftuFoxKVMmPAM5NHGBNg2Ysv54Eis6kzg9XuRy\nEsosrCqD4zhy9yUN/nG86iot5N9qQnBf40AZy5SFr9HFSh1/9vVdHDvGzkmWlRMjI0XRPjmIliom\ndufGsaIrQdMeAfK9gry7bDqO0ekyytWg0J+959mpUvugLELOMlNwQex0gfdePH14HE/m3P+i0j+R\nd9IMC+o4Dm756RHud7OFKro6+LG2kPKbhbJQUJbL5f4aAAzDeE8ul/v3c9aiJWiKongbXoj7UrIA\nF0JOQs2CGHYBakYfIRtceaYNIlN2z6MncO+uk/j0b1+H3k4+TC6q8C85iXYskPvStGxUahY6UjFU\nmH5ihf4kqAAAZZMA/8RE2tTplTmp1nwNVKkpUBbcsNloqkbg4Au37eP+PS+mzNvUK1WTPg8AxJnN\nRWQAyAmyMxPHdL6KumljbJoFZXLGtJGx43aSLa3FXCNMe9NOqSWxbfNhytjACUCseBDNlFFQ1ogp\nk7gv4zEXTMnLLIUzZSLY0TUFmqaixrwD4qIkG3MzmjJNVRDTNa8UU2PtGAB89jt7MDpdxu/90sVM\n2wlTJrgvJVGZ9ZCUGKRofSKmYXCFy06cnSxGgrIwoX+t7h+awkTz5ZrVEihj2x0Gyth7zTWpKRuZ\nLAUE/GH7A8CzY+L65TNlJr56x35sX9eFd7/RiGwHy5SR+7FspmnZXBvONnDpRc3tqP2AgNhpQVLS\nrEaMrDXtaqwPnpjGtUzAkvu5pZfCoxlN2T2GYXzDMIyfGobRaxjGzYZh9Cx6y5aYaarSVPJYYgVO\ntM6EDDfJlLEAsF33ZZEDZfypd8yrX8aWKKH3jtCckUkvS0rbjn39fw7gI5/fibliDaWqSZkGVuhP\nNlbAfQ8k+7Qv9PdcqmkSlWm26L4MRl/KhLDNWjspMQhTlvJOxqJGiGCw3MlpvO8f70fu5DT9G3Fl\ndGXitL0sU8YGULQCGPn8Q3ZAn+TeW96/ddN1H335e8/g3l1iVh25iaBlPkwZ0dQRYBsWiSxlyry/\ni64j0biEqd51YprqRnw2iL4E3LGsIIwpczVl7HcCTBn3N/kaoSoK4rqKmhm8h98u/vcHhqYxMVvB\nDx8/GWh7QOgvSZZd49yXDIPmzalETEM2FfeeJXptCxP6sy4snimzpb9vxth2h7nIwkBZrRY+VmXg\nPkzoD4Cb22VhfpFncuD2x2yxxq1Vsr2CvLNkQkNMVz1Qxo9ddq430llFMmXedafzwTx0swUPlAlM\nWbMHOHL4bCaoQgaqnz0xHfjdYtWino81A8puAvAEgBUACgBGAPzHYjZqKZqmKeHuS8mmnedOQvJF\nI8q4TPbMRBPdCsREcJRK6JwYVMybRk5qMrdH1MZNFoBUQoemKqiZFk6O5vGpbz+F2UJjUb1ouw+5\n2onxmTIqNQuZlI6YrlIga1o2BWqA+x4o+0GF/r6mzP29TRf7ZkTzsujLqPp9rInRUUA00xhmJBM2\nEYqLp0Gycd758BAA4LsPHKV/I++526PmTdOm9SMB/lTekvtS2BAIo9FMXqWaacNxgN25cTz+3FhT\n91sMpiweU5GIa8gX5ayxVFNmElDmjueuDnniJY4d8oqDEzAVFn2ZYA4YuqZC93IainNa11ToqirN\nbUaF/k0wZaqqIB5Tpbo1YuJ4JXKNRw/4InNSPUB8Lpn7MixPGVnHEnGNyf0Y/Y755LH+z1VmfrBr\nqghQ9h+bxJlxP/9hmNm20zBVingvLvoygnGRucE5ob83z8hB9yADHkpVfn6JgCRfqnPPLGXKiCtf\nVZGKayjXBPelZXPAsDFTFgXK3L/90Zcfxp9+7VHub9R9KRABzbJV1H3ZBNguSg6LB4f8fvXrnL4w\nmbJNuVzuJgB2Lper5XK5TwBY2+hLLzZTlXBQ1ogpY4FPs8L4sJIsO/eN4Hc++wCn8ZG1obczgWKl\nThdcsSB5IcI/H7VQkkUpHnNPXXXTxp7DEzg0PMMtJs0Ye59ixY3wSyV0JOMaKjULtu3AccDpADTV\nZSI0VfHzlFGhv+++XFCmLIKxkW2+7da+1FSFakjE0zNhZcjCLdOkdHpMmWk5gqaMAWUtsHhi3xHQ\nx4Gy0Cg1i449di7cev8R3HjL09LvBECZaUtBbzNGXoGqKOhIxjDnibJrdUuoBCFxXxKmzHPZrl7h\nJmAWNeOc0J8wZboLtOTuS5u63gHXRalrKuqmEwhokTJlNUHoH5L3jDXCLMtAGXkc8fcJSR1E0g5y\nz3hM5X7fTEFyMl+TcY3qVhuNx1CmjEuDwQA05t7T+So+d+s+3HzXgch7AMHkv2GbNacpK9SkvxdN\nFjAic1/2eoeeI6dn6d9EJlEEXcVKnfudlCnznk3XSHR3NFPWCJRFMVUi8+yn+LDpWjEjgLJmvC1s\nwttm3Jeyw+LkXIW2J95k8fnnw5oBZaZhGF3w6l8ahrENwNJ7kkU2TVNDI9ekoKzMui/ZkO3gZydn\nKwGwJjthAsDQyBxqdRunhNOfeN2ebAKO4074g0NT2O1F8wDuyakQceqQLZTkJF+jLgiVgjJyEhwe\nK+Bzt+7FSBP5hwDg7JQPHGaLVVRrFlJxHYmYC8oIaEsndMowkFN8Iqb57ksmItR9Jj+Fg0xT5jgO\nbnvgKJ7wGBzSdwr8TacqAWoykzGfpK9OnM3jroePNwUsSAZxypQJizF5JxSUMadv4grp9hidumlx\nkWHsWAwTm8vYPRGUZdMxVy/FjLUw3VWdcZex97/3sZM4MDTdNJhttyQYubemKuhIxTDnAcMP3fgA\n9h71gzJk0dDk+SbnKkgndMqUpYWkmrI8ZTFdRUxTA8/nOG7ai64Mc8DQVMQ8Vi3gvvQOHqZX+Bpg\nmbLmo4IVxQ0aYN8HvUdMDoxk0ZiUEfM+m4zxtTl5pizEfenNV6K7AxprHNlxyabE4IBIiKbs7GQR\ntuM0lfaABgulvOjZUKaMD3Lx7xvlvgwCBFn0JdH2sml8yoJms1oTxxUww4BDudDf/Y6mqUgmdBTL\n9cD7Yud6sWJGun7FNe8jb7sEv/7m87xr2dxhe3Ta7Xt2nZgSQBnp06iof/bwR/asiZkyPn/r3gBB\n4X5ezuCTqjFEAlNr0cV9LqwZUPZXAHYA2GAYxh0AHgLwF4vZqKVoJLJNZrKFhZ284sl8tlDFV+7Y\nj6m5CmYKVfzZTY/inkd53Y14QqasAzltFPjNkF0IVUVBt7f4F8p1fOaWPRg6m+euXWzRfWkKYCUe\n01ytSt2mmqWd+0aw7+gknmzSXTU86reJMDsuU6ajUrOoO0FTFXR5LBhxeyTiGqp1CweGprBz3wgA\nIJlwXZ9cSgwJk1Oqmrjn0RP46h37AbgLsqYqiMc1pkZpkAWRmTz1gfu7ex87ge/tPI7T441BKmHK\nUkz0pchuAn7Ua7Fi4t5dJ5Av1ShT5mvKeFdMIUJTVqqY+OJt+/DBT+/AjqdP838TQFlHKuayQCwb\nUZC7+Kp1i96rWrcCTEJUKgrWmtUsmpbNHQYIAFEUBR3pGGp1S8qahgn9HcfBxGwZK7qSNMhisDeN\ny7f1YetaNwpWlqfM15QJ2ivvs5kUf8Ag7stAnjIveSz7XcKakJQpzfSNFuG+JDncREAuO5SJtS/J\nM5BxJqtRy34PkDNlspQ3rIUJ/cN0ZOz7HPWCXURmRmakLxsFMIWxROT30/kq7nzoOPfcMvclCzLI\n/GUDHhS46ziZg7bj4N5dJ3BmIuiKZUFJtR6+nsc0FemEzrn2AffZxbk+UwzvM3HObFqVpdrNumlz\nGlYScMRer1w1ObaLzMt4FCiTkByPHRzF3qOT2HNkIvj5EAafgjLvXs0Egp1rawjKcrncD+Cmx/g1\nuIXILwHw/UVu15KzKFDWiti9ZtrYfWgcTz43hieeG8PkXAWm5QQS4rH3unfXSbz/H++HadlU1M0u\nNKIeIh5T6eJSLAcHHRsSLWXKIkCZz5Rp3gncoiJqwoiIJ6EwY2tdksmbSmhIxjVaKglw9TXENUfq\n0aWTOvKlOm68ZQ+l+2O6ikRMQ7Hs0/OySSdG/1RqluuO1VTaj7xL02UrpvNVfODT92Mnk1RXtqkT\npoEATVYw7jgO9h2dDCzuvqaMCP35hK3knbBsza07juKb33+Ongo7PSDulu3xx2Q+wn1572Mn8PTh\nCdiOg0PDM9zfxL7LJGOeaNxvO9GJDPS40XTEJVYTXI+Fcl3YoOWaK9Ga1ZX9+MlT+D/feIwyyOQd\nEKYMkI9LGYlpeu79Wt1GX1eSbl7xmIYPv+0SXG245W1kecpct6NKNVjESL/rmopubyxT96UElBFw\nB/jvngWVboLqxn2jqgriuhZgMEhb2esTk2lWg/PfK5huu+85LE+fJdHGJhimrFHePLYlbLNC3Zcc\nKHNZmtlitaF2jab6SRJQ1th9Kfv9A3tO446HjmP/Mb+SSL5BahXyXllQlk3H0JGOUSD+9KFx3Lrj\nKA4MBSUi7PoSJfRn9biA/6x1yy+svsqLig0DsrIDRCqhU9a1ZlocK0ZYylmBRDgzUcJNdx3An920\nC08fdkFVXOI2J8YyX+QZSfJhWbCa6L7cMJgFAJzy9hydgLIlmNU/FJQZhpEyDOO3DMP4lVwuN5HL\n5e7J5XJ3ArgCwL6w771YTSx5wloraQbqpk0n0eRshTI57OkCkC+MhXKdgqyZkBxkgDu4Mx4NL6ul\nxp7cZP552UJJNkw2giruaWfmhLY3k0UfAE4xDNLoNMuUabAdh04+TVMoKCO/W9OXCSxACQ+UzRT4\nU5noPpzK8yBpYraCFZ0Jzx3rXlMU7pqWjacOjcOyHXzz3udwy08O4+CJ6cCJWlMV+u6I2J49yf70\nqdP43K178Z2fHOa+5yePdd/bDx8fxn/92P9MWDqFmUKVLiy++5JfOIscKPPbWyjX8ePdpyhomRDc\nACKz1JGKUZc1vb+3IPZ3u66Xns4EbRfbhnypzmtwJJuedNxFHHhOTxSpC/rEaB4O/GoUxNWlqkCH\nt/nI3BwyY+fois4k1VgREOOL1CVMma4G+gjw3caaqlCNpKIo7kFA4lrUPU0Z4PcLmzKmXDObOgwS\noT9biocYBWVMv4flMjMtB6fGCvj+rpNQAKzuS9Pf244TWvlAFn2ZjOs+U9aKpixE0kEAvmXb3PUI\nIHAcuQuRNdI3mQbl42SHCVXx9a1k7WE1neL6KFqJui99UNbVkXD1Xx4YiTqcsOut1H1JNWUqd6gj\n5epYTRnRT4qeGGIiKHVTrqiUeaqbNgfKxrx+IEERK3vcstkP7DmNXQdGMTpVontflPuS1dBWBVAm\n22/E5L9r+zPQNZUSAWQshTFqz6dFMWX/BuA3AfydYRi/YxjGSsMw7gFwC4D/PCetW0Kmq67oVqYP\nqpt2QAQcZWOelmpitkInZF4ATzJav1gx6YmBPcmIG1xcV303lwSUsaCF1S75iVMjTso0H5O7+bju\nS34CN7v5nZ0q0sk8JoAywAeUmuozZeT5ycmHtVjMZdlYoGTZwc2IZUzypTqqNQv93SlmXTMXAAAg\nAElEQVTomkIZBVEjUjcdGt0JAPc9MYwfPHYy0Pcx3QXv5aopZQ73ekXXj56Z477nJ4/1n50tsUJO\n+uL468rEUayY0DWFLrJuLUwGEIVEX/7Xjw+hWrPwlus2oLczEXhv4ikyk9IR03gR+0yh5mZo94DP\nQE8amqpgdKrMMRv5co1zYUQluWQtCnj8xb88hq/esR+Fcp1ugmQcWRSUqfSA0jQos2xMeIDadV+6\nY5QACZlInbRT132dGPuuTJYp88BzqWJ6BdOdIIul+e5L03ITobLjWhRrh5mqKDRXl3iIIW5ZrtpB\naNoMGw89M4Jy1cR7fsbAmv4O7/PBYuqssQdWcgCMxxjA2Ur0pRMEeIA7ltwKHD7wBfzoWYBf82RG\n+rYjGe2+FEGJqijIpmP03uTgMT7LgLIG+e58pszPF9nVEUc6odP9IRUPz/POuy8joi81Pzk1AGRI\nomMGlK3ywHZYf4mgNJ3U3cMFA8pmOabMA2Xe9batcV3/+xhdJzEyDmWsLs+UuQfts1PuoX46L9GU\nCR6iREzDmv4MTk8UYdm+679cjQbMz4dFgbKrAVwP4FUAfgPAYwCGAWzN5XL/cA7atqRMUxUUKybe\n94/3B9w8dcsJiIBlRnAbiW7hQJkAbGSsQZkFZcykERfnREyji4usXAi70JGF8sTZPH7rn3bg/qdO\nSRdKKoBnXBAEgIgs35RkkgSuZ9qYmK1gw2AWuqbQRSHFiPrJs2qagk4PEJG2bxgIgrK4rnIpB4iJ\njA97siInuZU9KeiaiplCDR/49A5KiROwLXMxnZkoBMAbcXOz9eBY9wK59woxYa/HlIWNI3JvkcXo\nzMRRqtSRTsaoRkhc1FhNGVmg9x2dxKMHRrF5dSded+VarOhMYjpf5TZROVOmcSzCdKGK7o4EdfEl\nYhr6u1MYmy5xm30hwJTJ2NjwcRdllapJQRn5P+knVfGjcptlcE3TD6RZ05ehbhXKlBGRelieMolb\nkMxnXVOo2L9QrkPXlVBNmc6I4cV3Ua649QsbHQaJpgwIgjLaziYK1puWQ9/ZtnXdFFTJ6nayxv6N\nzJVkXOcAZ5SFM2VufyjwaxsSwEQOcKyJ7jPRyHcJgA9zU4qgp68r6cotvN8TQEIidy3blnorWCMu\nyu6OOH2fXZk40kkdpuWgblqRVUJY8BnlvtQ1lcojALcCCgAMjxfonrSKMmXyuSL2C7keAf41JvAL\nAMam3VJaRFd70eYVAPh0IsTqlltr9y9vfhxf/x8+YlZ0X84Wa9TlKpMliEJ/XVOxbmUHTMvG2aky\n7ZMXmqZsJpfLmblcbgzAOgB/lMvlPpTLMWF8LyEjLgsAnFsJcBdksRwGMbZkEWEyyASYnCtz7su/\n/9aT+MnuUwDki2O+7A9EdtKQxZJs6PFYNFPGGpnEez2x5L/fdyhEU8a7L+MxLVQDUK7KRdWsjc2U\n4TiueDrLZK5PxTXal+S0o2sqFbETWy8DZTFNGs4vTjz2ZDXuMSsru1McfT404jJZhAEyTTuwIE/O\nVQOnYOK+nGDcF1OzLChzf+4WhPGUKQsZR2QREV9NTFdRrJjIJHW6yRKmjGzGLJAj4GCfx9i9/bVb\noWsqVnQl3UiuPO/6JQCE9EWMSfdQrrpRWj3ZBGVddF3Fyp4UihWTO2i47ktmzNaJC6KIb37/IEqV\nuhyUhTAW7MI/U6jRgwFxGduUKVN8pizisPCJ91zJRZARN8e6lR10nBMgIquFK2rKxLazEXDsu495\nsgiRbYppCl1zTDtYX7RUdcvxNDoMKoqfbJkAGdL+uB5k/MI2fze4wPLbpvrfla0XNN2GhCnjNGUN\nmDL20gSgOY7jJ7FmchOSSFpxbgHRwvVdB87in27ZQ9uma0rTQv+VPSkkYhplzAnYIOOw0MB1CbBC\nd42uN90dCfpuSxW+gDjpW1kEqzyjv8/SkuhuANi8uhMAcPT0HGWuGrkvyfUJGKN7DmHK6hYFwH1d\nSRQrJobHCnjm2CQGetO4dOsKei1dU7nDtWnaGJksYXSqhGeOTXFjsSi4L9li9tP5asCDIO57MV3F\nOo/dHR7L0z4pV6MB7/NhUaCMbeloLpe7fbEbs5SNLEIAcJqJgHG8Uxp7AmFPr4mY/z2i3fGFuxbH\nqBw7M4dv/+gQbFu+0E0wCUFni7WA+JaAvriu0XuJblGRSSILwooun7mRRl8JSVUJUxZmjVxFRO/h\ngjLfLSh3XyqB029HKoY1/Rm6UQLuwpAU8kC5z8gvVKww9LQXYNHfneL6nLwX0jbTsqXh0yeYqFbA\nBQGWzecJk51kxR62bQeawgtxWSPvxBHGRc20UaqYSCd1+j7IPWQbNnnGI6dmEdNVbFrlLsyEuSOs\nnmnZmJyrYkVXkm4CrKbMcRx6MOjuiPtskqZS0T+b7yhfrvOh+96YveUnR7Bz3wi+/aPDkW5z0diI\n1mEmPcyYwJRxQv8IpmygN42XX+SWYKlbNk6OFtCZiaOrI0HnMGEixahIQNCUaT44Jv8nBZDZoBXy\nb7Y/yNoR09lcXr4Qm2yqxUodjgNu3ZGZ5gn9AX9cELAuLdYe5r5kZABu23xQJWP1aXSmVFOmtacp\nc4DbHzyGj3x+Jw3W6aJaU5POz/UD2cA6F8WUsTUSXX2UFppPslqzOWCzsieFeExDteayPOSQNjlX\nhuNl3AcavyeAD9DqzMTpd0qCqzoR17BlTSdedv7KwDUaCf3ZdmxbG6ylO9ibhgL/cMbWGAXYknYx\n7rnIWHp4/1mq87zS6AcA3LHzOGqmjauMfiTjOlZ42rmB3hTVogLuvDvqBW1V6xYXTU2YL0Vx3zUJ\njCN1XUU2UtSKxTymDABOjRU5kLvU2LIoUBY3DGOdYRgbAGjez+vJf+3e0DAM1TCMrxmG8ahhGDsM\nw9gq/P0DhmE8aRjGLsMw3tLufRbaWMbAtBycGi94tDmJivMnKvH/KwrPlLGFY4mxEYjEcienpQsd\nu9E7DvDBz+zA4VMzvkjVO2XFYxoyHkATF6OkwCTJ6ujJqGXiqvHdl2o0KGsQgcmCMrbGY5IBZWQi\n6poi7buPveMy/N8PXkf/LTJlvZ5GI8p9Sfq/vyfFbfRnJn2wBrj9IzuFHh/htWGaqmK2WKMlPUjg\ngS2wHWx/E6G0qipQVbk/imxuovuyUHITBGeSMTrWKChLBvuM6N2GxwvYNJil71AEZc8cm0S5auKy\nrX1Uh5LxQBngzgGycLPuy5iuUDEve5otlOs8u0trqLrXfurwuDSHWhhTxubpY+fQXLGGSs30NWWK\nQkv6RI1JTVVo2aPZYg2TcxWs9xZxygISTZkkcpBsfKz7kqwNP3z8JO57Ypjeh2WGKShjZAHu7xXo\n3kHwv35ymDKDZEyTzT8jecesudGX/D3I85D/W02AMsAfV7qmcGyh7DsEFIVFX/ruz9Y0ZXc/MoRi\nxcSTXiUQEjThMmU+i3Peum7uOrI1jdhGRp8aj2mIxdRwTZlpcR6ClT1pJLxAitlCjTtwFysmPRT3\ndSWl12ONPUx3dyToIbtU5Zmyat3CJ95zFd7x+m3c91MJPTJPGUmJQWz9yqC3IRHXkE3H6Fy965Eh\nfPjzD9IAGrIGkjHsEwH+XkAOvVd6UcokZcVV3r9X9bls3GAP7yWpmzYOn/KlQcdH/AMv2cdWdCZR\nqVl47KCrt73Yc4eKEZii+zKmq7TI+vBYgQsgKoXkNHu+LAqUdQB4AG6OsgyAB71/k9+1a28FkMzl\nctcB+DiAG8kfDMMYBPARuFq2nwHwfw3DCK9Wew6NdV8CwF/+v8fx8L4RmsWeFVCS04Omqtz3Mgyw\nIKkdhiUlQG578FggRQaAQC0xADg07IMyOkGYE5dY+kg8QRbKdRwcmuK0AuzEIOYzZXyeMmLkfiSk\n+t5dJ+gC8fShcfzZTbvwPw8dp58nLMqAwJSlvTxlgE9Za6rK9R2xro4Ex/DFdJVbMMnfylUTh4Zn\nUPEiMdkJPDyWh6ooAY0X2Qz6u1yAsffoBMe4kcXt+FkRlCmo1izsOzqJVEKDsb4blu2emEmIvtuP\nNo6cnkWpYuLIKfd0GAbI3L6o48DxqYD7kiSJTSd1ytBUo5gyy8axM3NwHGDrWn/jIn1FWD0SZHDt\nhQNIJzQo3vX8KCuLMl/dHQkkdMKUaRjoJaDMH8P5Uo3bGCfnKsidnKbvtVqzOFcPmR9kbJ8czWNs\nmkRbVXAnM5ZIvjtyeh+fqcDx1lzWfTkdwd7qmgJFcfOGEXBOTtYBTZk3p09NFKmbmsvo7/29brks\n5g8e82tITs1VuAMGAXCsLIBch5zg9x+bohsbSTD64yddkEfmfJSRaz7ubWQEQIvat1PjBa7wvGjk\nUMG6aE3blgYlEXB5dqpED2AUeMY1n2203LJx+49NUnbq2Jk5FCt1HB+ZwwQjmOeSx9YsrO3vwBpv\ng6/WLMqUJWIatgmgbMfTp+n8G58p48u3P4NPfuvJQE7FWt3y8i/6c/3omVnKxFTrFnfwI0wZuS5r\nk7MVOqbF9UVmMWbd7srE6fwtV0wORJC1KZPUwa4YnekYqnU36KFUMfHs0BTqpoVdXrkscQ9LxDW8\n83Vb8b9euYn7fXdHAqPTZRw5NYsfPn4SpuXg5u8fhGnZdAxlBaZMJmXZtMoHfedv6MH6AXc+ERfp\nQG+aW9cdB5xe+/6nT+Po6Vk4joOxmTJSCR0rOpPu2nlqFhdt6oXhveepfBVHTs/SMSoK/XXN7due\nbAInx/LcQaLk7QsHhqYautPPhYXO6Fwut3GR7vkKAD/w7rHLMIyrmL+9DMDDuVyuCqBqGMYRuHnR\nngi7WE9PGroent9EZv39wRNCI0tJTqRnpsv45r3PAQCyTCmgvp4UJucq6MzEqAASANYPdlLf/Za1\nXTg8PBM42fR2JnDszByOCdF5ADDlAazOTJyelFPpOFKecLi3OwWcmEZnRwJrVncjpqvICzSuy564\ni0dcVzExW8FnbtmDzWt8KntIcMkBQKYjif7+LCo1GzFdxarBLvT3ZujfL9y8Ao8dOIvrL12D7/70\nMJ47OYMnj0zijdesx9fuPIC6aePJ3Bhef80GAMDEXBWqAlywrR/7hqZpnb1N63tQIbnCvP93dSax\nbaN7IkoltND3t3qwC2sHO4G9Z6BrKq48fwAHT0zj2eEZ7Nh9Cpdv78cfv+cqjvGaKdSwsieFVYNd\nWNPfgdMMSO7MxNHrsT63PXCMY0tffcVa3PvoUEDoH/MWp45UDF/509fh9vuPYN/RSTiaiprtf//0\neBH/8O+7sbovQzetns5U6LPd/uAxAMBGz91ILO8tPiu60xgY6HQz7nsn4+7OJMCUbAEAVVMx4YGp\ny84boPfb4hXQrtRtdPdksPfoJFb3ZXDVRauxcscxaJqKgYFOdHhjLduVhgk3F9P61V10kctmEzA2\n9QEApll3pVDK5bs7jrpt2NZPf8culH3dSYxNl5HOJNDfn8VvfuqnAIC7bvxFfP2uZzn3BGE1L92+\nEjv3nIYJBR3eJpjtSGLjul4A0SVVBge6vPQRfgLh87f0ob8/iw0Vd7wM9HWgvz+LXi+i7KF9Ixif\nreBj774Sx0bmENNVrF7VjWyHe+/OzhTu3z2MYsXEqr4MRiaK2LKuB+dtcfunO5tAh+d+Iy3r9ZiA\n1YNd2LKuG48eOAvAF4NvXtuNZ45N0jQLvV0pqOpMqC5mcKATnRl3zXnu5Az9zvhMBYPe5qjHNXT3\npGkfhxnJvbZ6sAtHR90+T6UT6OxMBT7bkYpjbLqM4yNz+LObduGuG3/RzU8CYPVgJ133YnEdjx+a\nwE13PIM3v3wj3nTtRvz9t57E1nXdOD2W5w5CYsmhd73pPJp3KpaMoeZ1QV9vGhdv6cN3dxzFRVtW\n4PjpWRQrJj536z587eOvx5fv2E9r7n7ljv1Y2Zum11y/phvp/WcxOVtBf38Wz52Ywie/tRuXbe/H\n33zgOpSrFvq6UzTK97zNfdh71J0HZW8OZVIxFMt1VB1A8cDnxdv6sefIBAZ609IKAzFdxcDKTqxb\n1Yl9xyZhbO5D0VtbjozkucMn4O9hWWYv6O1KYXS6jJ7eDP7pq4/g4NAUfmZomhIHawa6aHT3Zdv6\n0d+fxbt/7kJYtoPv7TxOr7t2MIuTYwV86j+f8oChhZOjBdz56Ans3DeClT0pvPW12/D04QmsWZml\nbfnU774C6aSOj9y4A6mEhsGBLpy/sRcHh6bwobddipUrO2lf3PfEMC7c2odsOo67HxmizzU+U6Hf\nOT4yh0/++25cc+EgJmbKWDeYRSeTy+0XX7OVpok5NVHC7TuO4O03bMc7btge8Gr0dLtr66Y1XXhK\nAOJP5CZQrNm48ZY9eMPL1uMj77g88H7OpTU+Zi28dQJgdwrLMAw9l8uZkr/lAQQd34xNTzcuocFa\nf38W4+NB0NHILGZBf8vLN+DuR05ghNnAX3HhAG64fA0yKR22AxwensH6gSy+4mWNB4DXX74aTxx0\nc7MY67pxeDjISP3Vr1+NP/nqo3RQ3XDVWlywoRdfuG0fRjz27Gev3YC6aeG2B45hfLKIDo/9SnuA\nQHEcjI/nEddVWnftvPXd+L13XI7P/PuTANxTVm9nkrp+hhgQKHMZTU4Vcer0DIZG5rBplduHL79g\nALfd7+oxXnXxIF518SDO29CDcrmGex49gTNjczg+PE2vly/V8ZEbdwBwT7Or+jKYmS7hVRcNojul\nI5uOI+Y4sL0T84kRdygoto1ysYpP/NqV6M0mA+/vxt+9HqVKHZOTBVx/wUqs7klim7d5AcDhk+6i\n9PShcRw8EoxTySRjGB/P42PvvAxDI3P4/HfdNHxdmTjqkgSu7/u583HF9n786PGT1DXwq6/fhgs3\n9dIqAb2dCZiVOlTvWHvm7BzHFBEGgDCinZk4fumVmzA+nsenP3QdTNvBn9+0K9DWkx5gfusrN+GO\nncfp+7UtC+PjeeiaSk/1KqNci8c02LaNcsXEpDdn7LpJ+7JQcBmSuUIFTzxzGtWahfM39GBiooDf\neLPh1tMcz9Oq0GdGZjE57ba9VqlTIGjWTeTn3GcrMTqP6dmKNCeeWJJr06pO/NKrN+PUWAHf+ekR\nTE4VMTbmj83x8TxlvN7y8o24+5EhunH3ZNyD09mxPD2Bm3UT+dkSFMVnGH7h+o3Yvq6birvjMRWT\nk15SSQZ4q7aN8fE8OhMq/uidl2HL6k6Mj+dRYAIGxqZK+PwtT2G2UMO7btiGmekiTO85Dxwew/d2\nHEFvZwJ/+d6rcOJsHusHOlAr1/DXv3E1ujsSuM0rLF/w3uO7btgGTVUwNVXEdeevxNFh98Ay7r2z\nVT1J/OHbL8UXb9vnJp0eL+Aqox+PH+Q3mtdesQbXX7QKhbkyfvb6TXjgqVPU1X7+um685doN6OtK\n4u6Hj2N0oojcsWBWdGIKXA3kXLEKRQGmpoookvEyV8YpMk/hayVFZcP4eB5T3pivFKvUHVsoVrEn\n5x7InnpuDKu9Q9ARYW1ctSJN3eE92QSu2N6P7auymPDGz7GTU/TvfR1xdCY0/MV7r0J/dwq2quKf\nv70bJ8cKuPuBIzg1mkdnOoZrLxzEfU8MY2yqhExSx2+/9SJsG+yAqriM2LOHx/DjJ93Aqz2HxrH/\n0ChqdQsru1I46rHbmm3D8ebEsWF3ndm0Kov9x6Zw7OQ0XcdXdiXw8XdfgVUr0nhgzxnMFmvo707h\nFi9fYTKuYXw8jzdeuQaXbe6FUzdx/tpODPamcefOY7hoc2+gPwHX9UoO+gmv00+PzOLgkAsUn/EY\n1usvGsSaniRUVcHH330FNgzy++A/fPBaqKqC8fE83vbKzTg6PIPR6TKn1dqTc8fYr/2MgXW9Kfzx\nOy/DhsFOep2VWfeA8ckPXAPNu9YH3nI+pvNVZOMq/dz567rwR++8DMaaTqiKgj//31fizoePY/9x\nt83ZlI6ff/lGnJ0q4cxkEY95B5OeTByj3vvOJHVsWpnBfm+NP+L1/cmRWRweCqbbqJTr7p7IzO/t\n67pRqpi499EhDHsejx89fhK/+rqtge8vtEURQ82UWVpomwPAtkj1AJnsb1kAQeTyPBhL/V653fWN\nkwiPN1+zHsb6HmwYzKKvK4WV3Slcf/EqrFvZQdmVVEJHV0cCf/e+l+Hj774Cr79SXtO9g9HtAK77\nbMsa94RBNCo92QT1zxcrJmUgNg5m8Z43bscbr14HwN2IyUmiryuFDcwJdeNglhN9hgnMiZmWjaGz\nc7Adh5aZ6ckm8Lfvexl+7roN2LauG+dv7IWiKLjm/AEAroaETXjJRipW6xaNvEkndVx74SAu3OQu\nPKSGJXFxkgirLau7uKzXxHqyCZo3KZXQccHGXsRY0T9DIpATbifjMmVdBqQN5LpnJaD/go29SCV0\n6hYDgPUDHVjNJLQl2h9WrBtV5PwXX7GJPltfdwqDzOmdNRJvctGmFVzSSuo+1FUKfmKan9RxdV/G\nS4Bsc3UaiVGdlO1QRuW89a5roK/Lbw9xLVdqln/vuIZVK9LIJHVsGMjSMc8+Y75U4xJAEjPFPG+a\nggs39nLZxgPVDxwHigKcv553UfV5ruZKze/ruK5CUXiB8/qBLNUKss8EyDWgiuK2iXyO/UypamJ8\npoLOTBw3XOXOO9Kvu3PjMC0Hb7luIxIxDdvXddNrrB/IojMTD7gvV3QmafBFKqHj0q0uq0Y0NYmY\nhos3r8Cnfus6bFqVxRuuXoufvXZDoF97swkaXZdK6HjD1f56E9NVXLipl7Ivs4VqpNuSSDOKFZM+\nG3Ev27ZD18EOZk4lBde56ZV2IxIDnQmGIIcdTVVCRddbGSb/Tdesx7vfsB2qqlCh+MRsBYdPzUBT\nFdp/m1Z1oiMVw5a13fjw2y6Bpir48e5TmCvV0JlJoLuDzaAfxwXe+kVqhf7p1x7Fjzw38ba1XdSD\nsHEwi1957Ra84ap13vO4z0Lcl1tXd3lt8kFNNhXD9nXdyKbjeMvLN+Ldb9hONYuAv05kkjHa/mRc\nxy++wnUtHj7FM97EDMZNS9Y71vtCcg1ec+EAlUdsX9cdiFIf7E1jpTcnerIJvON1vl6NrJUE9BId\n3/kbe6Xu81UrMljpBft0dyTo8xBTvflExtDWtV382Inr+F+v2ozffutFeJm3lwCu7pcEEb39tVuh\nKn60OtEJF8p1qnXlAmp0vzwf+1yvvmy126YI6ci5tucDlD0M4GcBwDCMawE8w/ztcQCvNAwj6RVB\nPx/A/uAlzr2RjUbX/ElIK85HlIcg3+v1NlxdU7F9XTc60zF6HdbYRHyACwbFgZ9O6vR35YpJgUAy\noeG1V6ylEyKm+1wJWfwJ0Nm4qpMDYrIamKzVLZuWM2IXyLX9HXjbq7dwGxW5bqVBagxZAljAX9zJ\nc7Fi0FaMTNhZSYbpdcyCyGl8NJUGSXR3xHHxJj+EmxhZ0DoYlzYZA0TjRTLbU7FuxYx0nxFtDGvn\nCaADcMcH4IIzdpywaRtoEk0mtH9VX8ZNgGw7VBcYY94ZGw2X85jF7euC9yeLWqVm0kSS8ZiGvq4U\nvvD7r8SVxkq6wLHi5HypjmrdCujcRKBGtEY0oMC0AxFlju0Wb2c3/kRMozoXDjB6/cLeN66rnCua\nnQdsn8qCS9w2+t91tXA17vqkL4mLlc3ULlpMCM7QhM2BtI2MYfLv3s4k/uK9V+PaCwaxfiCLD/78\nBXiNt8EAPmgixhZCV5m1LJuOYbpQ46LAxe+zmz1pLxmHtuOLqrnUNsJ7LlfdHItkbumCpozcM6zs\nzRZmzRno8QE1AeKnx4s4cbaAjauy0vV4RVcSa/oyOD1eRLlqoTMT49LssAcsWQ3GzkycRlpvGMzi\nzddswK/e4AKXhKAp2+wdoidmK3SPkI0lds0Mi84k/cUCrddevob+bKzv8dtNSx0xOQrJHtWixIcQ\nAew9CHgW0xMthMW4vvDbuonZI/q7U3jXG7bj93/5ErziklXeZz29qMdeF8t1mvpmJTNOyPVZMOrW\nl3XHMdu/YcXMz5U1dF8ahvGXwq8cuKKkg7lc7p427vk9AG8wDOMRuIz3bxiG8VEAR3K53J2GYXwB\nwE64gPETuVyuuTTci2wkJUYiptIB7g/4cGxL3FvdAsOjeOLykckSOlIxjibmQJnq5gRKePUgAXei\npujpte4nXhVyXLETURdEnusHsjT8GJDXAGTNshwqSGcXSJmRzbJS8+s36poSCH+XJYAFfKYs7N/N\nmphaA/Brn61d2UHryIkLZqeXJb+7I4FrLhxAf3cK//Afu+nfE3H3/bBgmY1KBHwQztayjCq+vFoC\nyj76jstw5NQsPv1fT9Pfkb1S9cC7LxDns80DPsAh1z9wdAKWxaQ2iLGgzANSdQtHTs1iTX9GCoZT\nZIOuW7TmIEkZQTZqGVNGnry3M4kS4/YXWTBdAGV1ywmAMtshOd388Z1Nx+i/yzULybjP4gFAKqlT\nYUScyZMFhIMyWXAJ+3zEihUTAwyzSQ5AVBivha8P5HkJsxcQY8dI4W+bex7Rrr1wEA6AHXvcuqxK\nAJT575Jtf3dHAuMz5QAoS8RVJg2HToNjyLORa9i2Q4E1O08TwoGzXDVRLJv0sMLm2CJjw03QLd8Q\n1w900HQs5NAJuKyOpio0EGLb2uBBgj5rNoGT3vx3050woExywGLNshwMnc1D8drCmn8g8yME0wkd\nE7MVyn7LQBn7rsPyzYkR7n/x3qu4w+yGQb8tZL3n6/b6FVhasWw6joEeV6N23vpumuZCU4MkwUIY\n+5wsc80+68ruFLoyccoeA/56RA5ALlPmvoeB7hTds8j1+ZRJfvqaCtNnQ2fzuHAj7y4+l9ZM724F\nsA3Af3n/fhtcN+MrDMN4dS6X+5NWbpjL5WwAHxJ+/Rzz928A+EYr1zwXRtYxN2mq+yLJqS6KKSMu\nO5nbra8rhZHJEtb2Z3D9xasoSGFBHjnVZpJuuLOmKhjoSUPXXKBWEpgy1tiJKBQu9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WETdpd5DJR2juVPHIgsrmhmAI6c93vcoOq3HbNedFXrco3DRDMSbS6y/biVuv3pP5nnlqyvza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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x26fe8c98358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#fig = plt.subplots(2,1, figsize=(10,8), sharey=True)\n",
    "fig = plt.figure(figsize=(10,8))\n",
    "ax1 = fig.add_subplot(211)\n",
    "ax2 = fig.add_subplot(212)\n",
    "fig.suptitle('Time plots of monthly returns of IBM stock from January 1976 to Jan 2015 \\n \\\n",
    "Upper panel is for simple returns, and lower panel is for log returns')\n",
    "\n",
    "y_min = df[['Simple Return', 'Log Return']].min().min()\n",
    "y_max = df[['Simple Return', 'Log Return']].max().max()\n",
    "ax1.set_ylim([y_min, y_max])\n",
    "ax1.plot(df['Simple Return']); \n",
    "ax1.axes.set_ylabel('Simple Return');\n",
    "\n",
    "ax2.set_ylim([y_min, y_max])\n",
    "ax2.plot(df['Log Return'])\n",
    "ax2.axes.set_ylabel('Log Return');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}