Time Series Modelling with Python 1.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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\nTUJBCCGEm4SCEEIIt/8HNeBU7V70/HUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25cd9b6ce10>"
      ]
     },
     "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": 42,
   "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": 43,
   "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": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert to percentage returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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": 44,
     "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": 45,
   "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": 46,
   "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": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.iloc[idx][0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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": 48,
   "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": 48,
     "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": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = [0.10, 0.20, 0.30, 0.20, 0.20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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": 51,
   "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": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = df2.iloc[:, 0:5]\n",
    "df3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(758, 5)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "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": 53,
     "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": 54,
   "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": 55,
   "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": 55,
     "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": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "JB Value is \t 1.0797 \n",
      "p-value is \t 0.5828\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": 58,
   "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": 59,
   "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": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.describe(df3.iloc[:, 1].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "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": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.stattools import jarque_bera"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "JB Value is \t 10.9208 \n",
      "p-value is \t 0.0043 \n",
      "skew is \t 0.0058 \n",
      "kurtosis is \t 3.0112\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": 63,
   "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": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df4 = np.log(df3.dropna() + 1)\n",
    "df4.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "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": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pcWIT23GCxuv1KjNzjIqKCrVgQY7tOACA41CAAYTMhx9OldQwP/x2vNGjx0qSPvqIaRAA\nEG4owABCoqioSDk589QitY3O6ny+7ThB16HDGerevadWr16lbdu22o4DADgKBRhASMybN0dlZYfV\nvU96g/3w2/HGjBknSZox40PLSQAAR6MAAwiJGTM+VFRUlLpdkmY7SsgMHjxUSUlNNHPmdJWXl9uO\nAwAIoAADCLotWzbriy/WqXfvPmrSrIXtOCETFxenESNG6cCB/Vq+fKntOACAAAowgKCbOdM/BSAz\nc4zlJKE3atSlkqTZs2dYTgIAqEIBBhBU5eXlysqaoaSkJhowYLDtOCF37rlddOaZHbV4ca4KCwtt\nxwEAiAIMIMiWL1+qAwcOaPjwkYqLi7MdJ+Q8Ho9GjsxUWVmZcnLm2o4DABAFGECQzZw5XZKUmTnW\nchJ7hg8fJY/Ho6wspkEAQDigAAMImoKCg1qyJFcdO3bSueca23GsadWqtbp166G1a9do584dtuMA\ngOtRgAEEzfz52SovL9eoUaNdc+zfkxk5crQkac6cWZaTAAAowACCJitrpjwejzIyRtqOYt2QIUMV\nFxenrKwZ8vl8tuMAgKtRgAEExY4d27Vu3Vr17NlbqaktbcexrnHjRA0aNETbt2/T+vWf244DAK7m\ntR0AQMM0e/ZMSdKIEZmWk4RGzprq5/a27nyJlD1bs2bNUNeuF4QgFQDgRNgDDKDe+Xw+zZ49U/Hx\n8Ro8eKjtOGGjk+mm5ORkzZs3W0eOHLEdBwBciwIMoN59/vln2rFjuwYNSlNCQoLtOGEjOjpaGRkj\nVVBQoGXLltiOAwCuRQEGUO+qjnc7cqQ7pj/UxogR/qNBcExgALCHAgygXpWXl2v+/GwlJ7dQjx69\nbccJO+ecc646duykpUsXqbCwwHYcAHAlCjCAevXxx8tVUFCgYcOGy+vlc7bHq1oa+ciRI5o3L9t2\nHABwJQowgHo1d+5sSVJ6+nDLScJXRsZIlkYGAIsowADqzeHDpcrNXaA2bdpymK9TaNmylXr06KV1\n69Zqx47ttuMAgOtQgAHUm6VLF6ukpFjp6SNcv/RxdaqOj5ydnWU5CQC4DwUYQL3Jzmb6Q00NHpym\n2NhYzZ07m6WRASDEKMAA6sWhQ0Vatmyxzjqro84+u7PtOGGvceNE9e07QFu2bNamTRttxwEAV6EA\nA6gXubkLVFZWxvSHWqjaU171wUEAQGhQgAHUi++P/jDCcpLI0a/fQDVqlMA0CAAIMQowgNOWn5+v\nlStXqEuX89S+fQfbcSJGfHy8Bg4crF27dmr9+s9txwEA16AAAzhtCxbMVUVFhYYNY+9vbWVk+MeM\naRAAEDoUYACnbe7cOfJ4PBo2LMN2lIjTq1cfJSU10bx52aqoqLAdBwBcgQIM4LTs3btHn366Whdd\n1E0tW7ayHSfixMTEKC1tmPbv36e1a9fYjgMArkABBnBa5s2bI5/Px7F/T8OwYRwNAgBCiQIM4LTM\nnTtH0dHRSktLtx0lYnXr1kPJyS20YME8lZeX244DAA0eBRhAnW3fvk1ffvmFevW6RM2aNbcdJ2JF\nR0dr6NAMHTx4UCtXrrAdBwAaPAowgDqresu+6i181N33i2JkWU4CAA0fBRhAnc2bN0exsbEaPDjN\ndpSId/75F6p16zbKzV2ow4dLbccBgAaNAgygTjZu3KDNmzepb98Batw40XaciOc/jNxwFRcf0rJl\nS23HAYAGjQIMoE6+X/qY6Q/15ftFMZgGAQDBRAEGUGs+n09z585Wo0YJ6tdvoO04DUanTufojDPO\n0pIli1VcfMh2HABosCjAAGpt/frPtWvXTg0cOFjx8fG24zQYHo9H6enDVVZ2WIsWLbQdBwAaLO+p\nzjTGxEj6h6SzJMVJ+p2kLyS9IcknaZ2kexzHqQxqSgBhJTvbP/2h6i171J/09BF6/fVXNHfubI0Y\nkWk7DgA0SNXtAb5B0n7HcQZJypT0vKRnJD0eOM0jaVxwIwIIJxUVFZo/P1tNmjRRr159bMdpcM44\n40ydc47RihXLdPBgvu04ANAgVVeA35P066O+L5fUU9KCwPczJWUEIReAMPXpp6u1f/8+DRkyTDEx\nMbbjNEgZGSNUUVGhhQtzbEcBgAbplFMgHMcpkiRjTJKkSZIel/S04zi+wCaFkppWdyPNmyfI642u\ndbjU1KRaXwZ1x3iHVqSO9+LF8yVJV155eZ3uQ1KivTnDNm+7Sk3G7KqrLteLL/5NubnzdOutN4Yg\nVXBE6nM8kjHmocV4h1Z9jvcpC7AkGWM6SJoi6QXHcd42xvz3UWcnSar2Pbq8vOJaB0tNTdLevYW1\nvhzqhvEOrUgd7yNHjigrK0stWqTozDNNne5DYZGdRR6SEuOt3fbRajJmMTFJuvDCi7V8+XKtX79Z\nKSkpIUhWvyL1OR7JGPPQYrxDqzbjXZOifMopEMaYVpJmS/qF4zj/CJy82hiTFvg6U1JujdIAiHgr\nVy5XQUGBhg7NUHR07d/VQc0NGzZcPp9POTlzbUcBgAanuj3Av5LUXNKvjTFVc4EfkPQ/xphYSevl\nnxoBwAU4+sPpy1mzo0bbxaWer6ioKM2dm6Wrrro6yKkAwF2qmwP8gPyF93hDghMHQLgqLS3VokUL\n1aZNW5133vm24zR4iU2aqUePXlq5coV27tyhtm3b2Y4EAA0GC2EAqJGlSxeppKRY6ekj5PF4bMdx\nhWHD/MtMz5uXbTkJADQsFGAANVI1/SE9nekPoTJkyFB5vV7NnZtlOwoANCgUYADVKioq0vLlS9Sx\n49nq1Kmz7TiukZTURH369NfGjRu0Zcsm23EAoMGgAAOoVm5ujsrKyr57Sx6hk57uH/O5c+dYTgIA\nDQcFGEC15s5l+oMtAwYMVnx8vLKzZ8vn81V/AQBAtSjAAE4pPz9Pq1Z9rC5dzlP79h1sx3GdRo0a\nacCAwdqxY5scZ73tOADQIFCAAZzS/PlzVVFRoYyMkbajuFbVnveqDyICAE4PBRjAKWVnZ8nj8TD/\n16JLLumrxMQkzZ+frcrKSttxACDiUYABnNS33+7SZ599qm7deiglJdV2HNeKjY3VkCFDtXfvHq1d\nu8Z2HACIeBRgACdV9eE3pj/YVzUNouoxAQDUHQUYwEnNnTtbXq9XQ4YMtR3F9bp376nk5GTl5MxV\neXm57TgAENEowABOaMuWTdqw4Wtdckk/NWnS1HYc14uOjtbQoRk6ePCgVq5cYTsOAEQ0CjCAE6o6\n4sDw4Ux/CBffT4NgaWQAOB0UYAA/4PP5lJ2dpfj4ePXvP8h2HAScf/6Fat26jRYuXKDDh0ttxwGA\niEUBBvAD69d/oZ07d2jgwCFq1KiR7TgI8Hg8Sk8foZKSYi1dusR2HACIWBRgAD+Qne1/iz0jg6WP\nw016uv94zBwNAgDqjgIM4BgVFRWaN2+OmjRpot69+9qOg+N06nSOzjyzo5YuXaRDh4psxwGAiEQB\nBnCMNWtW6cCB/UpLS1dMTIztODiOx+NRRsYIlZWVKTd3ge04ABCRKMAAjjFnTtX0B47+EK6qjgZR\nNVUFAFA7FGAA3ykrK9PChfOVmtpSF13UzXYcnET79h3UtesFWrlyhfbt22c7DgBEHAowgO8sX75E\nRUVFGjZsuKKieHkIZ8OHj1JlZSXHBAaAOuA3HIDvVC1+wfSH8JeePkLR0dGaPXuW7SgAEHEowAAk\nScXFh7R4ca46dDhD555rbMdBNZo1a6Y+ffrr668dbd680XYcAIgoFGAAkqQFC+arrOywMjJGyuPx\n2I6DGhg5MlOSlJU103ISAIgsFGAAkqRZsz6SJI0cOdpyEtRU//4D1bhxY82ZM0uVlZW24wBAxKAA\nA9C33+7S6tWrdNFF3dS2bTvbcVBDcXHxSktL1969e7RmzSe24wBAxKAAA9Ds2f630EeNYu9vpKna\nY1/1GAIAqkcBBlzO5/MpK2uGYmPjlJaWYTsOaumii7qpVavWysmZp9LSUttxACAieG0HAGDXF1+s\n07ZtW5WePkKJiYnfnZ6zZofFVKipqKgoDR8+Sm+99YYWL1743SpxAICTYw8w4HJZWTMkSaNGXWo5\nCepqxAj/0SCYBgEANUMBBlysrKxMc+fOUXJyC/Xs2dt2HNTRWWd1lDFdtGLFMuXlHbAdBwDCHgUY\ncLElSxapsLBAw4ePktfLjKhINmLEaFVUVGju3Dm2owBA2KMAAy7G9IeGIz19eGBp5Bm2owBA2KMA\nAy6Vn5+nZcsW65xzzlWnTp1tx8FpSk5uoV69+ujLL9frm2+22I4DAGGNAgy4VHb2bFVUVGjkSPb+\nNhRVSyPzYTgAODUKMOBSWVkfKTo6WhkZHDaroRg4cIgSEhorK2uGKioqbMcBgLBFAQZcaPPmjXKc\nL9WnTz8lJ7ewHQf1JD4+XsOGZWjPnt365JOVtuMAQNjiY9+AC82a5f+gVNUyughPtVmMJK1bO0nS\n6NFjNX36B5ox40P17t0nWNEAIKKxBxhwmYqKCs2ZM0uJiUnq33+Q7TioZ+eff6HOOONM5ebmqLCw\nwHYcAAhLFGDAZVatWqF9+/Zq2LAMxcXF2Y6DeubxeDR69FiVlZUpO3u27TgAEJYowIDLfPTRNElS\nZuYYy0kQLCNGjFZ0dLRmzJhmOwoAhCUKMOAi+fl5ys1doI4dO6lr1wtsx0GQpKSkqE+f/nKcL7Vh\nw1e24wBA2KEAAy4ya9YMlZeXa8yYcfJ4PLbjIIhGj/bv4Z8xY7rlJAAQfijAgEv4fD5Nn/6BYmJi\nNGLEKNtxEGT9+g1Us2bNNXv2DB0+fNh2HAAIKxRgwCXWrVurrVu3aMiQoWratJntOAiymJgYZWZe\nqoKCAi1cON92HAAIKxRgwCWmT/9AknTppeMsJ0GojBlzuSTpww+nWk4CAOGFAgy4QFFRkebPz1bb\ntu3UvXtP23EQIh06nKEePXppzZpPtHXrN7bjAEDYoAADLpCdPUulpaUaPXqsoqL4sXeTsWPHS2Iv\nMAAcjd+EQAPn8/k0der7io6O1qWXXmY7DkJs8OA0NWvWXLNmTVdZWZntOAAQFijAQAO3bt1abdq0\nQYMHp6lFixTbcRBiVR+GO3jwoHJzc2zHAYCwQAEGGripUydLksaNu9JyEtgyZoz/g4/Tpk2xnAQA\nwgMFGGjA8vPzlJMzV2eccSYffnOxDh3OVI8evbR69Spt2bLJdhwAsI4CDDRgM2dO15EjR3TZZVew\n8pvLXXHFBEnS++9PspwEAOyjAAMNVGVlpaZNm6K4uDhlZl5qOw4s699/kFq2bKWsrBk6dKjIdhwA\nsIoCDDRQK1cu144d25WePkJJSU1sx4FlXq9X48ZdoZKSYs2aNcN2HACwigIMNFCTJr0rSbr8cj78\nBr8xY8YpJiZGU6ZMks/nsx0HAKyhAAMN0LZt32jZssW64IKL1KVLV9txECaaN0/W0KEZ2rp1iz75\n5GPbcQDAGgow0ABNnuzf+3vVVVdbToJwU/VhuKrnCAC4kbcmGxlj+kj6L8dx0owxnSW9IcknaZ2k\nexzHqQxeRAC1UVRUpJkzP1JqaksNHjzUdhyEmfPOO19dupynJUsWaefOHWrbtp3tSAAQctXuATbG\nPCLpVUnxgZOekfS44ziDJHkkjQtePAC1NWPGNJWUFGv8+Anyemv0Ny5cxOPxaMKEa1VZWalJkyba\njgMAVtRkCsRGSVcc9X1PSQsCX8+UlFHfoQDUTUVFhSZPfldxcXEaO5a/TXFiQ4dmKDW1pT76aJoK\nCwttxwGAkKt295DjOJONMWcddZLHcZyqjw8XSmpa3XU0b54grze61uFSU5NqfRnUHeMdWsEY77lz\n52rXrp2aMGGCOnfucFrXlZQYX/1GEaYh3qcqqzbsr/G2o/qdpZtuulF/+ctflJMzS7feemtQMvGa\nEnqMeWgx3qFVn+Ndl/dHj57vmyQpv7oL5OUV1/pGUlOTtHcveyZChfEOrWCN98svvyJJGjPmitO+\n/sKi0vqIFDaSEuMb3H2qq717CzVsWKZeeOEFvfnmP5WZOb7ep8vwmhJ6jHloMd6hVZvxrklRrstR\nIFYbY9ICX2dKyq3DdQCoZ599tlZr136qfv0GqGPHTrbjIMwlJTXR6NFjtWfPbuXkzLUdBwBCqi5/\n8j8k6RVjTKyk9ZJYWB4IA++88y9J0rXX3njK7XLW7AhFHESAq666Ru+//54mTvy30tNHyOPx2I4E\nACFRowLsOM4WSX0DX38laUjRjRzbAAAYFElEQVQQMwGopW++2aJFixaqa9cLdPHF3W3HQYRo1669\nBg1K08KF8/XJJyvVs2dv25EAICRYCANoACZO/Ld8Pp+uvfZG9uKhVq6//mZJ0ltvvWE3CACEEAUY\niHD79u1TVtYMtW/fQQMHDrYdBxHmvPO6qlevS7Rq1cf64ovPbccBgJCgAAMR7r333taRI0d0zTU3\nKDq69ocbBG644T8kSf/+9xsWUwBA6FCAgQiWn5+vqVMnKyUlVSNHjrYdBxGqe/ee6tr1AuXmLtDm\nzRttxwGAoKMAAxHs3XffVklJia677ibFxcXZjoMI5fF4vtsL/Pbb/7QbBgBCgAIMRKiCgoOaPPld\nJSe3YNljnLb+/QeqY8dOys6ere3bt9mOAwBBRQEGItS77/6fSkqKdd11NyouruEu8YvQiIqK0s03\n36qKigq9+eZrtuMAQFBRgIEIVFhYoMmTJ6p582RddtkVtuOggUhLS9fZZ3fWnDmz9M03W2zHAYCg\noQADEei9997RoUOHdM01Nyg+nr2/qB9RUVG69dbbVVlZqTfeeNV2HAAIGgowEGHy8g5o4sS3lZyc\nrHHj2PuL+jVoUJrOPbeL5s2bo02bOCIEgIaJAgxEmH/96w2VlBTrpptuU0JCgu04aGA8Ho9uu+0O\n+Xw+vf76K7bjAEBQUICBCLJr10598MFktWnTVmPHXm47Dhqovn0HqGvXC7RgwTx9+eUXtuMAQL2j\nAAMR5PXXX9GRI0d02213KSYmxnYcNFAej0d33nmPJOmFF/5HPp/PciIAqF8UYCBCbNq0UVlZM9Sp\nU2dlZIywHQcNXPfuPdW//0CtWfOJlixZZDsOANQrCjAQIV566Xn5fD7dccdPFBXFjy6C76677lVU\nVJRefPFvKi8vtx0HAOoNv0WBCLB8+VItXbpY3bv3VN++A2zHgUucddbZuvTScdq6dYs++mia7TgA\nUG8owECYKy8v19/+9ldFRUXp/vt/Jo/HYzsSXOTWW29Xo0aN9I9/vKxDh4psxwGAekEBBsLclCmT\ntHXrFo0de7k6dTrHdhy4TIsWKbruupuUl3dAb7zBEskAGgYKMBDG8vPz9frrrygxMUm33Xan7Thw\nqWuuuV5t2rTVpEnvaPNmFscAEPkowEAYe/XVF1VUVKhbbrldzZo1tx0HLhUXF68HHnhIFRUVevbZ\npzksGoCIRwEGwtRnn63VtGlTdNZZHTV+/FW248Dl+vcfpP79B2n16lWaN2+O7TgAcFoowEAYOnLk\niJ5++g+SpJ///FF5vV7LiQDp/vt/ptjYWD3//LN8IA5AROO3KhCG3nnnLW3evEljx47XRRd1q3b7\nnDU7QpAKbte2bTtdf/3Nev31V/TSS3/Xz372C9uRAKBO2AMMhJnt27fpzTdfU3Jysu666x7bcYBj\nXH/9zerY8WxNnTpZq1evsh0HAOqEAgyEkcrKSv35z39QWVmZ7rvvISUlNbEdCThGbGysfvGLXysq\nKkr/9V+/U0lJie1IAFBrFGAgjEyaNFGrV6/SgAGDNWxYhu04wAl17Xq+rr76Ou3cuUOvvfa/tuMA\nQK1RgIEwsWXLJr388t/VrFlzPfzwo6z4hrB26613qH37DnrvvXe0du0a23EAoFYowEAYKC8v1+9+\n91uVlZXp4YcfVXJyC9uRgFOKi4vXo48+IY/Ho6eeekKFhQW2IwFAjVGAgTDwxhuv6quvvlRm5hgN\nGpRmOw5QIxdeeLFuuulW7d79rZ5++k8skAEgYlCAAcs+/ni5/vWv19W6dRvdf//PbMcBauWmm27V\nhRderPnzszVjxoe24wBAjVCAAYv27t2jp556QtHR0frtb/+gxo0TbUcCasXr9erXv/5PJSYm6rnn\nntaWLZttRwKAarEQBmBJeXm5nnzyMeXn5+mBBx5S167n244EHKM2C6w8/PCv9Jvf/EqPP/6IXnrp\ndaWmJgUxGQCcHvYAA5a8/PILWrv2Uw0dmq4rrviR7TjAaRk6NENXX329tm79Rr/73W9VWVlpOxIA\nnBQFGLBg6tSpeuedt9Shwxl65JHHOOQZGoQ777xHPXv21uLFC/Xiiy/ajgMAJ0UBBkJszZpP9MQT\nTygpqYn+9Ke/MO8XDYbX69VvfvN7tW7dRs8//7wWLJhvOxIAnBAFGAih7du36fHHH5HP59NTT/1J\nHTqcaTsSUK+aNWum3//+z0pISNBTTz2hzz771HYkAPgBCjAQInl5B/SLX/xUBQUFeuKJJ9SjRy/b\nkYCgOOecc/Xss8+qoqJcv/zlQxwZAkDY4SgQQAgUFhbooYfu07ZtWzUwY7yS2veu1SfsgfoUiufe\noEGD9Mgjj+mPf/xPPfzwA3rxxdeUkpIa9NsFgJpgDzAQZMXFxXrkkQe1YcPX6j1gpIaPvdF2JCAk\nMjPH6Mc/vku7d3+rBx/8ifbt22c7EgBIogADQVVSUqJHH31In3++TsOHj9KlE+7giA9wlRtvvEXX\nXnujtm79Rg8++BPt308JBmAfBRgIksLCQj300H1avXqVBg0aokcffUJRUfzIwV08Ho/uuuteXXvt\nDdq6dYseeIA9wQDs47cxEAR5eQf04IN3a926tcrIGKEnn/yjvF6m3MOd/CX4Pl1zjb8E33PPj7Vt\n2ze2YwFwMQowUM+2b9+me++9Q19//ZUuu2y8HnvsScovXM/j8ejuu+/TLbfcrl27duonP7ldX3yx\nznYsAC5FAQbq0SefrNRdd92ibdu26rrrbtJDD/1S0dHRtmMBYcHj8eiWW27Xww//SoWFBXrggbu1\ncCGLZQAIPQowUE+mTZuihx66L3DUh8d011338oE34ATGjr1cf/jDn+XxePT447/QK6+8oIqKCtux\nALgIBRg4TcXFh/T73/9GTz/9RyUmJuqZZ57XmDHjbMcCwlr//oP04ouvqW3bdvrXv97QI488qIMH\n823HAuASTEwEToPjfKknn3xM27dvU5cuXfXb3/5ebdu2sx0LCLnjF9dISoxXYVHpCbdN6+b/GenU\n6Ry98sqbeuqp32jZssW65Zbr9ctfPq5LLukX9LwA3I09wEAdHDlyRK+//oruvvtWbd++Tddee4P+\n/vdXKL9ALSUlNdGf/vQX3XHHT5SXd0A///kDeuaZ/1ZJSYntaAAaMAowUEtffLFOP/7xjXr99VfU\nrFlz/fnPz+nuu+9XTEyM7WhARIqKitINN/yHXnrpDXXseLamTp2km2++RosX59qOBqCBYgpEiB3/\nNuHJVL1FiPCxd+8evfrq/2rWrI/k8/k0btwVuvPOe5WYmGg7GhBRTv46mKgb7v2j5s98R0vmTdOj\njz6k/v0H6b77fqp27dqHNCOAho0CDFSjqKhI7777tt555y2Vlpbq7LM768EHf65u3XrYjgY0ODEx\nsRpx2U3q1nuopr/3spYsydWKFUs1ZszluummW5WSkmI7IoAGgAIMnERBwUFNmjRRkyZNVFFRoZKT\nW+j++3+mzMyxHNsXCLKWbTrolvv+U5UH1uvVV1/U1KmTNHPmhxo37kpNmHCtWrVqZTsigAhGAUbE\nq+m0EqlmU0u2bNmkKVMma9asj1RSUqymTZvp9tvv1pVX/kgJCY1PJyqAWvB4PEpPH64hQ4ZqxowP\n9eabr+ndd9/W5MkTlZ4+QhMmXCNjzrMdE0AEogADkoqLi5Wbm6MZMz7U6tWrJEmpqS112213aOzY\n8WrUqJHlhIB7eb1eXXbZeI0adamys7P0zjtvafbsmZo9e6bOOcdozJhxysgYqaSkJNtRAUQICjBc\nq7i4WB9/vFwLFszTokULVFrqP2Zpjx69NH78BA0YMEheLz8iQLiIjY3V6NFjlZk5RsuXL9W0ae9r\n6dLF+utf/1vPP/9X9e7dR0OHZmjAgMF8OBXAKfHb3WVONl3gRAetD8aRKOp7ukJt+Hw+TZyxRJu+\nWqsNX67RJmetKirKJUnJqW3UN22wLu41WC1atpVPovwCYcrj8ahv3/7q27e/9u3bp1mzPtIH0z/S\nkiWLtGTJIkVFRatDR6NzuvZQ5y7d1LrdWYqK+n7ePkfZAcBveDRYRYX52rlto3Zu3aid2zZq2xZH\nhwoPfnd+q7ZnqcuFvdXlwkvUtkMneTwei2kB1EVKSopuuOFmtb8gQ/t279Dna5boy3Ufa+um9fpm\n4xfK/vAtxcUn6Iyzu+iMs89Tm3YddUH7WLVokcLPPOBiFGBENJ/Pp8KCPB3Yu0sH9n2rA/u+1Z5d\nW7Vz20YdzNt3zLZNmrbQxb2GqOO5F+rscy9Us+SWllIDCIaUVu00ZOQEDRk5QYeKCrTxyzXa9NVa\nfbPxC339xSf6+otPJElvvSQ1bdpMnTufo86dz1WnTp3Vtm07tWnTVi1apCgqijWigIauTgXYGBMl\n6QVJF0s6LOnHjuNsqM9gcLfKykoVFhaqsLBA+fn52r9/nw4c2Kf9+/cH/u3Tnj3faseO7SdcMjWx\nSXOde34vte3QSe3O6KS2HTopqWly0PLWZmoHgJqr689W48QmuqjXYF3Ua7AkqbAgT9u3fKVvd2zR\ntzs269sdW7Rq1cdaterjYy7n9caoaXKqmie3UrMWqUpMaq7EpKZqnNRMjZOaKjGxqRonNVVcfKNj\nplVI9qeNTRjepd5vH/bZnDrYkNV1D/DlkuIdx+lnjOkr6S+SxtVfrPpRVlam4uLio07xff+Vz3fM\ntkd/f+zXx19rTa/jxJfLP7D3mOv44bb+b3buPP7yJ8/4w+9Pfv17d397/JVKkooT4lR06PAx17G5\naekxm1VUVKiiojzwv/9fefnR3x973tHblJUdVmlpqb7auk/lR8p0pOyw/9+RMh054v+6tKRYpSWH\nVFpySIdLi39wH4/XqFEjtW3bTnGJKUpOaaPk1NZKTmmjlFbtlNSkOW9vAvhOUpPmOu+iPjrvoj7f\nnVZaUqzdO7doz66tytu/R3n7dyvvwB7l79+t/XtO8CJ8nNi4eMXFNVJcfIJi4xtpakozNW7cWAkJ\nCUpISFRcXJxiYrzyemMUExOrmBhv4P8Yeb1excbGyuuNUWxsjLzeGEVHRysqKkoej0dRUVGKiorS\n9m/2yePxn/b9/4GvozzHnL5jR5Ly8ooleXSil7+TvSae+PSTbVuzywfrtsKJ11uugweLgn47xYcK\narztwYPhc6jO2Ni4sD6CUl0L8EBJsyTJcZxlxphe9Repfhw+fFg/+tE45eUdsB0FNRQX10jxCY3V\ntHmq4hslqH3rFCUlJalp02Zq0SJFyckt1KJF1b8UJSYmyePxsPcVQJ3EN0rQmZ266sxOXX9w3uHS\nEuUf2KNDRQdVVHhQhwrzdajooA4V+v+VlhbrcGmJDh8uUUlJkQ7m7dXOrXbfCH3W6q0Dx4qOjtbf\n//6Kuna9wHaUE/JUt5ftRIwxr0qa7DjOzMD3WyWd7ThOeT3nAwAAAOpVXWf6F0g6+ojjUZRfAAAA\nRIK6FuDFkkZLUmAO8Gf1lggAAAAIorrOAZ4iabgxZon8s9dvqb9IAAAAQPDUaQ4wAAAAEKk42jcA\nAABchQIMAAAAVwn5UsjGmEaS3pLUUlKhpJsdx9l73Da/kXSppHJJDzqOs8IY846k1oFNzpK0zHGc\na4wx0yS1kHREUonjOJmhuSeR4TTGu4ekDyV9HdjsRcdxJp5o2xDdlYhwGuPdTdLfJFXIv7riTY7j\n7DbG/I+kAYHrkqRxjuMcDM29CW/VrUhpjLld0p3yj/PvHMeZboxJkfS2pEaSdkq6xXGc4hNtG9p7\nE/7qON5nSPqH/L9rPJLucBzHMcb8TNJtkqp+Nu50HMcJ3b2JDHUc82RJX0laF9hsiuM4z/Ecr14d\nx/tZSd0Cm7SWlO84Tl9eu6tXk1WFjTGpkpZIutBxnNKT/Y41xoyV9IT8j80/HMd5pbrbt7EH+G5J\nnzmOM0jSPyU9fvSZgeI1RFIfSddI+rskOY5zjeM4aZLGS8qX9NPARTpLGug4Thrl94TqNN6Sekh6\nJjCuaYHye7Jt8b26jvdzku4LPMffl/SLwOk9JI086nHgBfR7361IKemX8q9IKUkyxrSWdL/8v4BG\nSvqjMSZO/hfItwOPz2pJd55iWxyrLuP9lKTnA8/rP0j6Y+AiPeT/I6/qeU35PbG6jHkPSf931Ng+\nx3O8xmo93o7jPBh4fg+XdFDS7YGL8NpdvZOOtyQZY0ZKmi2p1VEn/+B3rDEmRtJfJY2Q//frHYHH\n65RsFODvVpGTNFNSxgnOn+04js9xnK2SvIG/AKo8KelvjuPsMsa0ktRM0ofGmEXGmDHBDh+B6jre\nPSVdaoxZaIx5zRiTdIpt8b26jvc1juOsCWzjlVQa+Ov4HEkvG2MWG2NuDUH+SHLMipSSjl6R8hJJ\nix3HORz4xbNB0kU68eNzsm1xrLqM90OSPgps45VUtb56T0mPBl63Hw1F+AhVlzHvKamHMWaBMeY9\nY0ybU2yLY9VlvKvcJ/9r+2e8dtfYqcZbkirlf40+cKLL6PvX8PMkbXAcJ89xnDJJiyQNqu7GgzoF\nwhhzm77fU1tlt/x/JUn+3ddNjzu/iaT9R31ftc1eY0xLSelHXWes/H8xPCcpWdJiY8wKx3H21Nud\niCD1PN4rJL3qOM4qY8xjkn4j/573Ez429XIHIkx9jnfV2z7GmP6S7pU0WFJj+adFPCMpWtJ8Y8xK\nx3HW1uf9iGBN9P1YS1KFMcYbWJTn+POqHoujTz/RaUefjmPVerwdx9knScYYI+lp+ff4SNI78r/7\nUSBpijFmDG/Jn1BdnuNfSlrlOE62MeZ6+V9Dpp5kWxyrLuMtY0ys/FMjLgmcx2t3zZxqvOU4zhxJ\n8r98nPAyp/UaHtQC7DjOa5JeO/o0Y8z7+n4VuST5S9XRjl9l7uhtrpL/7cuKwPffSvrfwGDtMcas\nlmQkubIA1/N4T3Ecp2rbKfL/MH9wkm1dqb6f38aYqyU9JunSwJymaEnPOY5THDh/nvxzpXgR9TvV\nipQnG+eq00tOcNrx2+JYdRlvGWOGyj/P78bA/F+PpGer3hI2xnwkqbskCvAP1WXMl0sqDpw2RdJ/\nyv9WMc/x6tXpOS7/XsiFR01zKBav3TVRl1WFj77Mab2G25gC8d0qcpIyJeWe4PyRxpiowAcooqr2\nIsj/JJt51LYZkt6VJGNMoqQLJK0PVvAIVdfxzjLGVP01my5p1Sm2xffqNN7GmBvk3/Ob5jjOpsC2\n50paZIyJDsxxGijpk+DfhYhxqhUpV0gaZIyJN8Y0lf8tsnU68eNzsm1xrFqPd6D8PidplOM4KwPb\nNgmclxgow8Pkf33BD9XlOf6qpCsD21S9dvMcr5m6jLf0w27Ca3fN1GVV4RO9hq+XdI4xJjmwN36w\npKXVXVHIjwIh6UVJbxpjFkkqk3SdJBlj/lvSJMf/ifhc+cNHSbrnqMsaSVXlQI7jzDTGjDTGLJN/\nrsivKGQ/UNfxvlvS88aYMvn3tN/hOE7BKR4b+NV6vAN7ev9H0lZJ7wfe7lngOM5vjDH/lrRM/qOc\n/NNxnM9Dfo/C1w9WpDT+owtscBxnmvF/CjtX/nF+LPAJ4t/J//jcLmmfpOscxzl0om2t3KPwVpfx\nflb+qWpvBp7XjuM4dxpjfiVpvvyf/J7rOM4MG3coAtRlzH8p6R/GmJ9IOiT/J+u/5TleI7Ue78Dl\njPx72SVJjuOs57W7Rk453ie5zA9+xzqOcyRwuSz5H5t/OI6zo7obZyU4AAAAuAoLYQAAAMBVKMAA\nAABwFQowAAAAXIUCDAAAAFehAAMAAMBVbBwGDQBczxjjcxzHY4xJk38RiA3yHwooVv4Ffp4LbJcj\n/0IRLR3HOXzU5ddIynccJy3E0QEg4rEHGADsW+k4TjfHcS6WfznVnxtjuh51foGkEVXfBJYWbhvi\njADQYFCAASC8NJJUoWPXtp8s/1LwVa6WNCmUoQCgIaEAA4B9vYwxa4wxayVtkZQjaedR58+UlBZY\nVlWSxsg/bQIAUAcUYACwr2oKxEWSWks6V9Ivjzr/sPxLsGYYYy6Qf0n44tDHBICGgQIMAGHEcZwC\nSRMlDTjurPfknwbxo8D5AIA6ogADQBgxxkRLSpP0yXFnzZI0VFKm/FMiAAB1RAEGAPuq5gCvlvSp\n/NMb/uvoDQKHQFss6UvHcUotZASABsPj8/lsZwAAAABChj3AAAAAcBUKMAAAAFyFAgwAAABXoQAD\nAADAVSjAAAAAcBUKMAAAAFyFAgwAAABXoQADAADAVf4fJSbJaP0WojgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25cdab662e8>"
      ]
     },
     "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": 304,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2Ad8Cq4E1pmmuAN4DGhiG8Q0wivxlFiIiAePz+Zg9eyYA/foNxBboPYGLyb5n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25cdba571d0>"
      ]
     },
     "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": 230,
   "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": 231,
   "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": 301,
   "metadata": {},
   "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": 303,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VO/3xkDtnWX9hLUNlCUWm0ul0DKv2LqtCVnA56tID1zp16oqjoyP79u3l7NmH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\nKXEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25cdb3c7c18>"
      ]
     },
     "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": [
    "***"
   ]
  }
 ],
 "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
}