Probabilities.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Probabilities of Events in Stocks with Risks and and Return"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "For machine learning and deep learning, probability is important to learn and understand. "
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Library\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import math\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "import fix_yahoo_finance as yf\n",
        "yf.pdr_override()"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "stock_name = 'AAPL'\n",
        "start = '2018-01-01' \n",
        "end = '2019-01-01'\n",
        "df = yf.download(stock_name, start, end)\n",
        "df = df.reset_index()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  1 of 1 downloaded\n"
          ]
        }
      ],
      "execution_count": 2,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df.head()"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 3,
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
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              "    }\n",
              "\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Date</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",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2018-01-02</td>\n",
              "      <td>170.160004</td>\n",
              "      <td>172.300003</td>\n",
              "      <td>169.259995</td>\n",
              "      <td>172.259995</td>\n",
              "      <td>168.987320</td>\n",
              "      <td>25555900</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2018-01-03</td>\n",
              "      <td>172.529999</td>\n",
              "      <td>174.550003</td>\n",
              "      <td>171.960007</td>\n",
              "      <td>172.229996</td>\n",
              "      <td>168.957886</td>\n",
              "      <td>29517900</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2018-01-04</td>\n",
              "      <td>172.539993</td>\n",
              "      <td>173.470001</td>\n",
              "      <td>172.080002</td>\n",
              "      <td>173.029999</td>\n",
              "      <td>169.742706</td>\n",
              "      <td>22434600</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2018-01-05</td>\n",
              "      <td>173.440002</td>\n",
              "      <td>175.369995</td>\n",
              "      <td>173.050003</td>\n",
              "      <td>175.000000</td>\n",
              "      <td>171.675278</td>\n",
              "      <td>23660000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2018-01-08</td>\n",
              "      <td>174.350006</td>\n",
              "      <td>175.610001</td>\n",
              "      <td>173.929993</td>\n",
              "      <td>174.350006</td>\n",
              "      <td>171.037628</td>\n",
              "      <td>20567800</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Date        Open        High         Low       Close   Adj Close  \\\n",
              "0 2018-01-02  170.160004  172.300003  169.259995  172.259995  168.987320   \n",
              "1 2018-01-03  172.529999  174.550003  171.960007  172.229996  168.957886   \n",
              "2 2018-01-04  172.539993  173.470001  172.080002  173.029999  169.742706   \n",
              "3 2018-01-05  173.440002  175.369995  173.050003  175.000000  171.675278   \n",
              "4 2018-01-08  174.350006  175.610001  173.929993  174.350006  171.037628   \n",
              "\n",
              "     Volume  \n",
              "0  25555900  \n",
              "1  29517900  \n",
              "2  22434600  \n",
              "3  23660000  \n",
              "4  20567800  "
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 3,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "rets = df['Adj Close'].pct_change().dropna()\n",
        "rets.head()"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 4,
          "data": {
            "text/plain": [
              "1   -0.000174\n",
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              "Name: Adj Close, dtype: float64"
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          "metadata": {}
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      "execution_count": 4,
      "metadata": {
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        "inputHidden": false
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      "cell_type": "code",
      "source": [
        "Positive = [x for x in rets if x >= 0]\n",
        "Positive "
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          "output_type": "execute_result",
          "execution_count": 5,
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      "source": [
        "len(Positive)"
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      "outputs": [
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              "128"
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    {
      "cell_type": "code",
      "source": [
        "Negative = [x for x in rets if x <= 0]\n",
        "Negative"
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      "cell_type": "code",
      "source": [
        "len(Negative)"
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      "outputs": [
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          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
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              "122"
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      "execution_count": 8,
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    {
      "cell_type": "code",
      "source": [
        "Neutral = [ x if x in Negative else 0 for x in range(1,128)]\n",
        "Neutral"
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              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0,\n",
              " 0]"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 9,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Each needs same lengths\n",
        "Positive = Positive[:100] \n",
        "Negative = Negative[:100]\n",
        "Neutral = Neutral[:100]"
      ],
      "outputs": [],
      "execution_count": 10,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Markov_Models = pd.DataFrame({'Bear': Negative,'Bull': Positive, 'Neutral':Neutral})\n",
        "Markov_Models"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 11,
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Bear</th>\n",
              "      <th>Bull</th>\n",
              "      <th>Neutral</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.000174</td>\n",
              "      <td>0.004645</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.003714</td>\n",
              "      <td>0.011385</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.000115</td>\n",
              "      <td>0.005680</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.000229</td>\n",
              "      <td>0.010326</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.005082</td>\n",
              "      <td>0.016516</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>-0.004463</td>\n",
              "      <td>0.000893</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>-0.008181</td>\n",
              "      <td>0.000226</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>-0.015929</td>\n",
              "      <td>0.002338</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>-0.017851</td>\n",
              "      <td>0.002755</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>-0.020698</td>\n",
              "      <td>0.002090</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>-0.005894</td>\n",
              "      <td>0.041792</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>-0.043390</td>\n",
              "      <td>0.012231</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>-0.024984</td>\n",
              "      <td>0.040279</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>-0.021407</td>\n",
              "      <td>0.010018</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>-0.027516</td>\n",
              "      <td>0.018437</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>-0.003237</td>\n",
              "      <td>0.033578</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>-0.003364</td>\n",
              "      <td>0.008359</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>-0.004539</td>\n",
              "      <td>0.017391</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>-0.003241</td>\n",
              "      <td>0.019772</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>-0.001514</td>\n",
              "      <td>0.006914</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>-0.017516</td>\n",
              "      <td>0.003462</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>-0.000848</td>\n",
              "      <td>0.010912</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>-0.009283</td>\n",
              "      <td>0.017181</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>-0.009630</td>\n",
              "      <td>0.009668</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>-0.008501</td>\n",
              "      <td>0.001177</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>-0.003526</td>\n",
              "      <td>0.047472</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>-0.015279</td>\n",
              "      <td>0.007809</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>-0.000342</td>\n",
              "      <td>0.010259</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>-0.022655</td>\n",
              "      <td>0.019122</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>-0.014130</td>\n",
              "      <td>0.006934</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>70</th>\n",
              "      <td>-0.003131</td>\n",
              "      <td>0.009430</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>71</th>\n",
              "      <td>-0.016632</td>\n",
              "      <td>0.002001</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>72</th>\n",
              "      <td>-0.005603</td>\n",
              "      <td>0.058910</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>73</th>\n",
              "      <td>-0.009375</td>\n",
              "      <td>0.029231</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>74</th>\n",
              "      <td>-0.002979</td>\n",
              "      <td>0.002893</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75</th>\n",
              "      <td>-0.009743</td>\n",
              "      <td>0.005193</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>76</th>\n",
              "      <td>-0.001949</td>\n",
              "      <td>0.000676</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>77</th>\n",
              "      <td>-0.006525</td>\n",
              "      <td>0.007865</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>78</th>\n",
              "      <td>-0.016617</td>\n",
              "      <td>0.006457</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>79</th>\n",
              "      <td>-0.008068</td>\n",
              "      <td>0.004213</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>80</th>\n",
              "      <td>-0.013421</td>\n",
              "      <td>0.002336</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>81</th>\n",
              "      <td>-0.012419</td>\n",
              "      <td>0.014650</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>82</th>\n",
              "      <td>-0.011351</td>\n",
              "      <td>0.019970</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>83</th>\n",
              "      <td>-0.026626</td>\n",
              "      <td>0.000046</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>84</th>\n",
              "      <td>-0.010771</td>\n",
              "      <td>0.002046</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>85</th>\n",
              "      <td>-0.007966</td>\n",
              "      <td>0.003109</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>86</th>\n",
              "      <td>-0.017581</td>\n",
              "      <td>0.008235</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>87</th>\n",
              "      <td>-0.016229</td>\n",
              "      <td>0.008076</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>88</th>\n",
              "      <td>-0.002318</td>\n",
              "      <td>0.014929</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>89</th>\n",
              "      <td>-0.046326</td>\n",
              "      <td>0.009194</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>90</th>\n",
              "      <td>-0.008828</td>\n",
              "      <td>0.011554</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>91</th>\n",
              "      <td>-0.021386</td>\n",
              "      <td>0.003207</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92</th>\n",
              "      <td>-0.004321</td>\n",
              "      <td>0.025283</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>93</th>\n",
              "      <td>-0.023374</td>\n",
              "      <td>0.024155</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>94</th>\n",
              "      <td>-0.034302</td>\n",
              "      <td>0.001652</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>95</th>\n",
              "      <td>-0.015924</td>\n",
              "      <td>0.000596</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>-0.018770</td>\n",
              "      <td>0.007602</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>97</th>\n",
              "      <td>-0.066331</td>\n",
              "      <td>0.014380</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>98</th>\n",
              "      <td>-0.028388</td>\n",
              "      <td>0.006341</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>99</th>\n",
              "      <td>-0.003489</td>\n",
              "      <td>0.020552</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>100 rows × 3 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "        Bear      Bull  Neutral\n",
              "0  -0.000174  0.004645        0\n",
              "1  -0.003714  0.011385        0\n",
              "2  -0.000115  0.005680        0\n",
              "3  -0.000229  0.010326        0\n",
              "4  -0.005082  0.016516        0\n",
              "5  -0.004463  0.000893        0\n",
              "6  -0.008181  0.000226        0\n",
              "7  -0.015929  0.002338        0\n",
              "8  -0.017851  0.002755        0\n",
              "9  -0.020698  0.002090        0\n",
              "10 -0.005894  0.041792        0\n",
              "11 -0.043390  0.012231        0\n",
              "12 -0.024984  0.040279        0\n",
              "13 -0.021407  0.010018        0\n",
              "14 -0.027516  0.018437        0\n",
              "15 -0.003237  0.033578        0\n",
              "16 -0.003364  0.008359        0\n",
              "17 -0.004539  0.017391        0\n",
              "18 -0.003241  0.019772        0\n",
              "19 -0.001514  0.006914        0\n",
              "20 -0.017516  0.003462        0\n",
              "21 -0.000848  0.010912        0\n",
              "22 -0.009283  0.017181        0\n",
              "23 -0.009630  0.009668        0\n",
              "24 -0.008501  0.001177        0\n",
              "25 -0.003526  0.047472        0\n",
              "26 -0.015279  0.007809        0\n",
              "27 -0.000342  0.010259        0\n",
              "28 -0.022655  0.019122        0\n",
              "29 -0.014130  0.006934        0\n",
              "..       ...       ...      ...\n",
              "70 -0.003131  0.009430        0\n",
              "71 -0.016632  0.002001        0\n",
              "72 -0.005603  0.058910        0\n",
              "73 -0.009375  0.029231        0\n",
              "74 -0.002979  0.002893        0\n",
              "75 -0.009743  0.005193        0\n",
              "76 -0.001949  0.000676        0\n",
              "77 -0.006525  0.007865        0\n",
              "78 -0.016617  0.006457        0\n",
              "79 -0.008068  0.004213        0\n",
              "80 -0.013421  0.002336        0\n",
              "81 -0.012419  0.014650        0\n",
              "82 -0.011351  0.019970        0\n",
              "83 -0.026626  0.000046        0\n",
              "84 -0.010771  0.002046        0\n",
              "85 -0.007966  0.003109        0\n",
              "86 -0.017581  0.008235        0\n",
              "87 -0.016229  0.008076        0\n",
              "88 -0.002318  0.014929        0\n",
              "89 -0.046326  0.009194        0\n",
              "90 -0.008828  0.011554        0\n",
              "91 -0.021386  0.003207        0\n",
              "92 -0.004321  0.025283        0\n",
              "93 -0.023374  0.024155        0\n",
              "94 -0.034302  0.001652        0\n",
              "95 -0.015924  0.000596        0\n",
              "96 -0.018770  0.007602        0\n",
              "97 -0.066331  0.014380        0\n",
              "98 -0.028388  0.006341        0\n",
              "99 -0.003489  0.020552        0\n",
              "\n[100 rows x 3 columns]"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.hist(Negative, 50, normed=True)\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<matplotlib.figure.Figure at 0x23aeac05a58>"
            ],
            "image/png": [
              "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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 12,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.hist(Positive, 50, normed=True)\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<matplotlib.figure.Figure at 0x23aeaffadd8>"
            ],
            "image/png": [
              "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEACAYAAABbMHZzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAFARJREFUeJzt3W+MZXV9x/H3l11F/rksNuykYhmSprDa1oEmikHjtBhFTIAHDanaxpXGNlHRaNOwtA/ok8bSpHVtbB8YDbvaWgX6R1LbigQujSaIBhAiiDRkV0R3rPKnNRoC8u2De3YZlrk7s+fPnHN+9/1Kbvaec++55/vdM/OdO59z597ITCRJ8+W4vguQJG0+h78kzSGHvyTNIYe/JM0hh78kzSGHvyTNoXWHf0R8KiJWIuLeVeu2R8TNEfFgRHwpIratuu3qiHgoIh6IiDd3Vbgkqb6NPPO/DnjLEet2A7dk5tnArcDVABHxSuByYCfwVuDvIiLaK1eS1IZ1h39mfgV4/IjVlwL7quv7gMuq65cAn8vMZzJzP/AQ8Jp2SpUktaVu5n96Zq4AZOZB4PRq/cuBR1bd79FqnSRpQNo64et7REjSiGytud1KROzIzJWIWAB+WK1/FHjFqvudUa17gYjwB4Yk1ZCZjc+lbvSZf1SXQ24CdlXX3wV8YdX634mIF0fEWcAvA3fOetDMLPZyzTXX9F6D/dnfPPZXcm+Z7T1nXveZf0R8FlgGXhYR3wWuAf4CuCEirgAOMH2FD5l5f0RcD9wPPA28N9usdkT279/fdwmdsr9xK7m/kntr07rDPzPfMeOmN824/0eAjzQpSpLULf/CtyO7du3qu4RO2d+4ldxfyb21KfpKZSJiXhMhSaotIshNPOGrYzSZTPouoVP2N24l91dyb21y+EvSHDL2kaQRMfaRJNXm8O9I6bmj/Y1byf2V3FubHP6SNIfM/CVpRMz8JUm1OfxnWFhYJCLWvCwsLK67fem5o/2NW8n9ldxbm+q+pXPxVlYOMOtjClZW/GRKSeNm5j/D9KOHZ9UXrb61qiRtlJm/JKk2h39HSs8d7W/cSu6v5N7a5PCXpDlk5j+Dmb+kITLzlyTV5vDvSOm5o/2NW8n9ldxbmxz+kjSHzPxnMPOXNERm/pKk2hz+HSk9d7S/cSu5v5J7a5PDX5LmkJn/DGb+kobIzF+SVJvDvyOl5472N24l91dyb21y+EvSHDLzn8HMX9IQmflLkmpz+Hek9NzR/sat5P5K7q1NDn9JmkNm/jOY+UsaIjN/SVJtDv+OlJ472t+4ldxfyb21yeEvSXOoUeYfER8Cfh94FrgPeDdwEvB54ExgP3B5Zj65xrZm/pJ0jHrP/CPiF4ErgfMy89eBrcDbgd3ALZl5NnArcHXTIiVJ7Woa+2wBToqIrcAJwKPApcC+6vZ9wGUN9zFKpeeO9jduJfdXcm9tqj38M/P7wF8B32U69J/MzFuAHZm5Ut3nIHB6G4VKktqzte6GEXEq02f5ZwJPAjdExDt5YVA+MxzftWsXi4uLAJx66qksLS2xvLwMPPfTu6/lqQmwvOo6h5c3sv1kMhlMP138/9jfeJdL7m95eXlQ9TRdnkwm7N27F+DwvGxD7RO+EfHbwFsy8z3V8u8B5wO/BSxn5kpELAC3ZebONbb3hK8kHaPeT/gyjXvOj4iXxHRSXgjcD9wE7Kru8y7gC40qHKlDP7lLZX/jVnJ/JffWptqxT2beGRE3AncDT1f/fgI4Bbg+Iq4ADgCXt1GoJKk9vrfPDMY+koZoCLGPJGmkHP4dKT13tL9xK7m/kntrk8NfkubQIDP/hYVFVlYOrHnbccedyLPP/vQF63fsOJODB/e3WR9m/pKGpq3Mf5DDf73Bu/Zt7Q5kh7+kIfKE78CVnjva37iV3F/JvbXJ4S9Jc8jYZ9ZejH0kDZCxjySpNod/R0rPHe1v3Erur+Te2uTwl6Q5ZOY/ay9m/pIGyMxfklSbw78jpeeO9jduJfdXcm9tcvhL0hwy85+1FzN/SQNk5i9Jqs3h35HSc0f7G7eS+yu5tzY5/CVpDpn5z9qLmb+kATLzlyTVtrXPne/bt6/P3XdqMpmwvLzcdxmdsb9xK7m/kntrU6/D/73v/SIRJzxv3TPPPLxp+z/ax0VKUsl6zfxhBTj9iFv+EXgHm5H51zu3UG9fktQGM39JUm0O/46U/lpj+xu3kvsrubc2OfwlaQ6Z+Zv5SxoRM39JUm0O/46Unjva37iV3F/JvbXJ4S9Jc8jM38xf0oiY+UuSanP4d6T03NH+xq3k/krurU0Of0maQ40y/4jYBnwS+FXgWeAK4DvA54Ezgf3A5Zn55BrbmvlL0jEaSub/MeDfM3Mn8Grg28Bu4JbMPBu4Fbi64T4kSS2rPfwj4qXAGzLzOoDMfKZ6hn8pcOiN+vcBlzWucoRKzx3tb9xK7q/k3trU5Jn/WcCPIuK6iLgrIj4REScCOzJzBSAzD/LCXEeS1LPamX9E/AZwB/C6zPxGRHwU+D/g/Zl52qr7/TgzX7bG9mb+knSM2sr8m3yS1/eARzLzG9XyPzHN+1ciYkdmrkTEAvDD2Q9xJbCzun4qsLTqtkn17/IRy7Nuf/7Htx361W+95aM93nTdkfs/tsd32WWXXW6yPJlM2Lt3LwCLi4u0pemrfW4H3pOZ34mIa4ATq5sey8xrI+IqYHtm7l5j26Kf+U8K/xxR+xu3kvsruTcYxjN/gA8A/xARLwIeBt4NbAGuj4grgAPA5Q33IUlqme/tY+YvaUSG8jp/SdIIOfw7cuiETansb9xK7q/k3trk8JekOWTmb+YvaUTM/CVJtTn8O1J67mh/41ZyfyX31iaHvyTNITN/M39JI2LmL0mqzeHfkdJzR/sbt5L7K7m3Njn8JWkOmfmb+UsaETN/SVJtDv+OlJ472t+4ldxfyb21yeEvSXPIzN/MX9KImPkP0MLCIhGx5mVhYbHv8iTpMId/i1ZWDjD9bSGB21Zdz+q2cpSeq9rfeJXcW5sc/pI0h8z8W8z813s8zxNIasrMX5JUm8O/M5O+C+hU6bmq/Y1Xyb21yeEvSXPIzN/MX9KImPlLkmpz+Hdm0ncBnSo9V7W/8Sq5tzY5/CVpDpn5m/lLGhEzf0lSbQ7/zkz6LqBTpeeq9jdeJffWJoe/JM0hM38zf0kjYuYvSarN4d+ZSd8FdKr0XNX+xqvk3trk8JekOWTmXyvzfwnw1IzbzPwldWcwmX9EHBcRd0XETdXy9oi4OSIejIgvRcS2pvsYnqdY/RGNz10kaRzaiH0+CNy/ank3cEtmng3cClzdwj5GaNJ3AZ0qPVe1v/Equbc2NRr+EXEGcDHwyVWrLwX2Vdf3AZc12YckqX2NMv+IuAH4c2Ab8EeZeUlEPJ6Z21fd57HMPG2NbUec+c+uwcxfUpd6z/wj4m3ASmbew3TqzeLEk6SB2dpg2wuASyLiYuAE4JSI+AxwMCJ2ZOZKRCwAP5z9EFcCO6vrpwJLq26bVP8uH7E86/Zp1re8vHz4OrDu8tEeb7ruyP2vt3zIHqb9NKtvqMt79uxhaWlpMPXYn/0dWl79vT2EetroZ+/evQAsLi7SllZe6hkRb+S52OcvgR9n5rURcRWwPTN3r7FN4bHPhOf/ICkr9pms+kFWIvsbr5J7g/Ziny6G/2nA9cArgAPA5Zn5xBrbFD78m9cnSUdqa/g3iX0Oy8zbgdur648Bb2rjcSVJ3fDtHToz6buATq3OVUtkf+NVcm9tcvhL0hzyvX3M/CWNSO+v85ckjZfDvzOTvgvoVOm5qv2NV8m9tcnhL0lzyMzfzF/SiJj5S5Jqc/h3ZtJ3AZ0qPVe1v/Equbc2FTT8jyci1rxs2XLSmuuHUN/CwuIxP9LCwuLMXofweJKGr6jMf3O2ab+Gts9V9P14krpj5i9Jqs3h35lJ3wV0qvRc1f7Gq+Te2uTwl6Q5ZOZv5m/mL42Imb8kqTaHf2cmfRfQqdJzVfsbr5J7a5PDX5LmkJm/mb+ZvzQiZv6SpNoc/p2Z9F1Ap0rPVe1vvErurU0Of0maQ2b+Zv5m/tKImPlLkmpz+Hdm0ncBnSo9V7W/8Sq5tzY5/CVpDpn5m/mb+UsjYuYvSarN4d+ZSeNHmPXxipv7eGt//ORppy3UrmMMSs+NS+6v5N7atLXvAjTbysoBZsdLm/V4T625zeOPb/ZnIEtqk5n/gDP/2Vl8vYy+7uO1da5CUnNm/pKk2hz+nZn0XYAaKD03Lrm/kntrk8NfkuaQmb+Z/7qPZ+YvDYeZvySpttrDPyLOiIhbI+JbEXFfRHygWr89Im6OiAcj4ksRsa29csdk0ncBaqD03Ljk/krurU1Nnvk/A3w4M18FvA54X0ScA+wGbsnMs4FbgaublylJalNrmX9E/Cvw8eryxsxciYgFYJKZ56xxfzP/ar2Zv6SNGlTmHxGLwBJwB7AjM1cAMvMgL5zukqSeNX57h4g4GbgR+GBm/mT6jP55jvL08EpgZ3X9VKY/Pw6ZVP8uH7E86/ZD6468/3rLXT3eHqb9rPd41VKVUy4vLz9veXZ9R99/24+31v/PZDJ5weOXsrxnzx6WlpYGU4/9bXx59df6EOppo5+9e/cCsLi4SFsaxT4RsRX4N+A/MvNj1boHgOVVsc9tmblzjW0Lj30mPH/wG/uMyeofbCUqub+Se4P2Yp+mw//TwI8y88Or1l0LPJaZ10bEVcD2zNy9xraFD/+Nb+Pwl7RRbQ3/2rFPRFwAvBO4LyLuZjoh/gS4Frg+Iq4ADgCXNy1SktSu2id8M/OrmbklM5cy89zMPC8z/zMzH8vMN2Xm2Zn55sx8os2Cx2PSdwFqoPTXipfcX8m9tcm/8JWkOeR7+5j5r/t4Zv7ScPSe+astxzf6aEZJqsPYpzOTDd7v0MckrnVRX0rPjUvur+Te2uTwl6Q5ZOY/gMy/7W3M/KVyDeq9fSRJ4+Lw78yk7wLUQOm5ccn9ldxbmxz+kjSHzPzN/GvXYOYvbT4zf0lSbQ7/zkz6LkANlJ4bl9xfyb21yeEvSXPIzN/Mv3YNZv7S5jPzlyTV5vDvzKTvAtRA6blxyf2V3FubHP6SNIfM/M38a9dg5i9tPjN/SVJtDv/OTPouQA2UnhuX3F/JvbXJ4S9Jc8jh35nlnvY7/VjItS6btZ+FhcU1t1hYWJy5zZYtJx3zbbP2czRHq2H14y0vL9f6X9nIvurU3eb+I4ILL3xbq//fbfa60WM0SxvHbrM07bUJT/gWeMJ3CDWs9XU1+4Rz/RqO9et3vRra/H442gn2zfi+28z/7zZ73cxj1Lc6vXrCd/AmfRegBsyNx8tjtzEOf0maQ8Y+A49Pxlq3sY+xz3rbzGLsc/hWYx9JUrsc/p2Z9F2AGjA3Hi+P3cY4/CVpDpn5Dzw7H2vdZv5m/uttM4uZ/+FbzfwlSe1y+Hdm0ncBasDceLw8dhvj8JekOWTmP/DsfKx1m/mb+a+3zSxm/odvNfOXJLWrs+EfERdFxLcj4jsRcVVX+xmuSd8FqAFz4/Hy2G1MJ8M/Io4DPg68BXgV8PaIOKeLfQ3XPX0XoAbuucfjN1Yeu43p6pn/a4CHMvNAZj4NfA64tKN9DdQTfRegBp54wuM3Vh67jelq+L8ceGTV8veqdZKkAdja585POeV3iTj+eeuefvpRfvazngpq1f6+C1AD+/fv77sE1eSx25hOXuoZEecDf5aZF1XLu4HMzGtX3aec12tJ0iZq46WeXQ3/LcCDwIXAD4A7gbdn5gOt70ySdMw6iX0y8+cR8X7gZqbnFT7l4Jek4ejtL3wlSf3p6nX+6/6BV0T8TUQ8FBH3RMTSsWzbtxr9nbtq/aciYiUi7t28ijeu7rGLiDMi4taI+FZE3BcRH9jcyjemQX/HR8TXIuLuqr9rNrfyjWnyvVfddlxE3BURN21Oxcem4ffe/oj4ZnUM79y8qjeu4ezcFhE3RMQD1ffha4+6s8xs9cL0B8p/A2cCL2L6107nHHGftwJfrK6/Frhjo9v2fWnSX7X8emAJuLfvXlo+dgvAUnX9ZKbnfEo7didW/24B7gBe03dPbfZXrfsQ8PfATX3308HxexjY3ncfHfa3F3h3dX0r8NKj7a+LZ/4b+QOvS4FPA2Tm14BtEbFjg9v2rUl/ZOZXgMc3sd5jUbu3zDyYmfdU638CPMDw/raj6bH7aXWf45l+cw0tM23UX0ScAVwMfHLzSj4mjfpj+o51Q34/s9r9RcRLgTdk5nXVbc9k5v8ebWdd/Eds5A+8Zt1nDH8cVqe/R9e4zxC10ltELDL97eZrrVfYTKP+qkjkbuAg8OXM/HqHtdbR9Ph9FPhjhvdD7ZCm/SXw5Yj4ekS8p7Mq62vS31nAjyLiuiq2+0REnHC0nQ3lp2Dj16xqGCLiZOBG4IPVbwDFyMxnM/Nc4AzgtRHxyr5raktEvA1YqX57C8r8nrwgM89j+tvN+yLi9X0X1KKtwHnA31Y9/hTYfbQNuhj+jwK/tGr5jGrdkfd5xRr32ci2fWvS39A16i0itjId/J/JzC90WGddrRy76tfp24CLOqixiSb9XQBcEhEPM/1Qjd+MiE93WGsdjY5fZv6g+vd/gH9hGrMMSZP+vgc8kpnfqNbfyPSHwWwdnLTYwnMnLV7M9KTFziPuczHPnbQ4n+dOGq67bd+XJv2tun0RuK/vXtrujWkW+dd999HR1+YvANuq6ycA/wVc3HdPbX9tVuvfyDBP+DY5ficCJ1fXTwK+Cry5757aPH7A7cCvVNevAa496v46auIipq/2eAjYXa37Q+APVt3n41Wj3wTOO9q2Q7s07O+zwPeBp4DvUp2dH8qlRm/nVusuAH5efcHeDdwFXNR3P20dO+DXqp7uAe4F/rTvXtr+2lx1+yCHf8Pjd9aqr837Cp0trwa+XvX5z1RPVmZd/CMvSZpDQznhK0naRA5/SZpDDn9JmkMOf0maQw5/SZpDDn9JmkMOf0maQw5/SZpD/w/x2yX/wAmUDwAAAABJRU5ErkJggg==\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 13,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.hist(rets, 100, normed=True)\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<matplotlib.figure.Figure at 0x23aeb0033c8>"
            ],
            "image/png": [
              "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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 14,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import binom\n",
        "n = 5 # number of stocks \n",
        "p = 0.7 # Selecting a stock above 5% returns is 0.70\n",
        "k = 2 # Picking stocks above 5% returns\n",
        "binomial = binom.pmf(k, n, p)\n",
        "binomial"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 15,
          "data": {
            "text/plain": [
              "0.1323"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 15,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Standard Normal Distribution\n",
        "from scipy.stats import norm\n",
        "norm.cdf(rets)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 16,
          "data": {
            "text/plain": [
              "array([ 0.49993051,  0.50185311,  0.50454198,  0.49851822,  0.49995423,\n",
              "        0.49990845,  0.50226605,  0.50411956,  0.49797255,  0.50658871,\n",
              "        0.50035638,  0.49821964,  0.49673624,  0.50009014,  0.49364565,\n",
              "        0.49287885,  0.50093258,  0.49174311,  0.49764858,  0.50109905,\n",
              "        0.50083397,  0.48269526,  0.49003376,  0.51666756,  0.49146046,\n",
              "        0.48902389,  0.50487954,  0.51606455,  0.50399645,  0.50735501,\n",
              "        0.51339332,  0.49870854,  0.49865808,  0.49818928,  0.50333475,\n",
              "        0.50693777,  0.50788744,  0.49870715,  0.49939613,  0.49301239,\n",
              "        0.50275841,  0.50138103,  0.49966157,  0.49629673,  0.50435333,\n",
              "        0.50685387,  0.5038568 ,  0.49615816,  0.49660847,  0.5004695 ,\n",
              "        0.49859317,  0.49390477,  0.49986342,  0.49096286,  0.49436325,\n",
              "        0.49076264,  0.51893146,  0.4897718 ,  0.49559214,  0.50311521,\n",
              "        0.49738448,  0.50409272,  0.50762827,  0.50276633,  0.48979674,\n",
              "        0.50395664,  0.50750682,  0.49813485,  0.50393287,  0.50135167,\n",
              "        0.50248867,  0.50549089,  0.49910468,  0.48869547,  0.483659  ,\n",
              "        0.4988445 ,  0.49444728,  0.50173833,  0.50138956,  0.49538439,\n",
              "        0.50722536,  0.50926904,  0.51761759,  0.50072297,  0.51564785,\n",
              "        0.50288628,  0.5019176 ,  0.50280899,  0.50570624,  0.49848273,\n",
              "        0.49906922,  0.49637428,  0.50372313,  0.49747726,  0.49854924,\n",
              "        0.50282645,  0.49900071,  0.50255781,  0.49955524,  0.50091175,\n",
              "        0.49856147,  0.4991507 ,  0.49865956,  0.50719415,  0.50333423,\n",
              "        0.50307788,  0.5013827 ,  0.49893059,  0.49637066,  0.49902193,\n",
              "        0.50219045,  0.49672186,  0.50020919,  0.49590192,  0.49978878,\n",
              "        0.49355342,  0.50174024,  0.49777535,  0.49883838,  0.49406748,\n",
              "        0.50494913,  0.49941598,  0.50290277,  0.49916128,  0.50446103,\n",
              "        0.49305223,  0.50321025,  0.50553   ,  0.50553917,  0.49951852,\n",
              "        0.49482346,  0.50668836,  0.50062653,  0.49912425,  0.50112843,\n",
              "        0.497812  ,  0.50310103,  0.49908518,  0.50035425,  0.50289404,\n",
              "        0.503762  ,  0.49875088,  0.49336525,  0.4977649 ,  0.50079824,\n",
              "        0.52348814,  0.51165974,  0.5011542 ,  0.50207152,  0.49626003,\n",
              "        0.50026967,  0.5031376 ,  0.49881171,  0.50257594,  0.50168078,\n",
              "        0.50093196,  0.50584429,  0.50796633,  0.49611298,  0.49922232,\n",
              "        0.50001854,  0.50081625,  0.50124037,  0.50328514,  0.50322166,\n",
              "        0.50595574,  0.50366771,  0.50460928,  0.50127938,  0.49739699,\n",
              "        0.49337093,  0.49678131,  0.49464607,  0.51008533,  0.49504566,\n",
              "        0.50963561,  0.49547162,  0.48937899,  0.50065915,  0.50023765,\n",
              "        0.50303265,  0.49570298,  0.50573664,  0.50252965,  0.49682199,\n",
              "        0.50819834,  0.50140106,  0.50268621,  0.50354595,  0.50485443,\n",
              "        0.4929866 ,  0.49352591,  0.49907509,  0.50552656,  0.4815252 ,\n",
              "        0.4964782 ,  0.51424693,  0.49146895,  0.50879082,  0.49827604,\n",
              "        0.49067612,  0.50607571,  0.50243752,  0.50376066,  0.48631833,\n",
              "        0.50873527,  0.49364767,  0.49251225,  0.50199242,  0.51039786,\n",
              "        0.50612443,  0.47355728,  0.48867624,  0.50431413,  0.51209734,\n",
              "        0.49860809,  0.49230826,  0.4799121 ,  0.49601413,  0.48873244,\n",
              "        0.50984442,  0.50441848,  0.4841932 ,  0.48094661,  0.49954918,\n",
              "        0.48986843,  0.50539502,  0.49913185,  0.51533663,  0.49693532,\n",
              "        0.49784478,  0.51393712,  0.4824567 ,  0.49555208,  0.48577793,\n",
              "        0.50262817,  0.49771831,  0.50111194,  0.50436442,  0.48723696,\n",
              "        0.49628741,  0.50518315,  0.48755834,  0.4899339 ,  0.48448678,\n",
              "        0.48967892,  0.52807093,  0.49741094,  0.50020441,  0.50385582])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 16,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.hist(norm.cdf(rets), 50, normed=True)\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<matplotlib.figure.Figure at 0x23aeb251ba8>"
            ],
            "image/png": [
              "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEACAYAAABbMHZzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAFd9JREFUeJzt3X+MHHd5x/H3EzuYJEDsUOIrJPioqiaBqj0opVCKuJaIX1WTCKG0gFoOKlrKTwF/4KBK6T8VTSVaU9FWoqDYICiEUEFE+RHSeIsAhZQfkQ2BJC09A6E+CiFpI0oI8dM/dh2f7d3z3ezMzc533i9pdTuzOzvf52b2ub3PzO5GZiJJ6pfT2h6AJGnz2fwlqYds/pLUQzZ/Seohm78k9ZDNX5J66JTNPyLeHRErEXFg1bwdEXF9RNwWEZ+KiLNX3XZFRNwREV+PiGc3NXBJUnXreeV/NfCcE+btBm7IzAuAG4ErACLi8cDlwEXA84C/i4iob7iSpDqcsvln5meBH54w+1Jg3+j6PuCy0fVLgA9k5k8zcxm4A3hKPUOVJNWlauZ/bmauAGTmYeDc0fzHAN9edb87R/MkSTOkrgO+fkaEJHXI1orLrUTEzsxciYg54Huj+XcC56+633mjeSeJCP9gSFIFmTn1sdT1vvKP0eWo64Cl0fWXAh9dNf/3IuIhEfE44OeBmyc9aGYWe7nyyitbH4P1WV8f6yu5tsz6XjOf8pV/RLwfWAQeGRHfAq4E/gL4UES8HDjE8AwfMvPWiLgGuBW4H3hV1jnaDlleXm57CI2yvm4rub6Sa6vTKZt/Zr54wk0XT7j/W4G3TjMoSVKzfIdvQ5aWltoeQqOsr9tKrq/k2uoUbaUyEdHXREiSKosIchMP+GqDBoNB20NolPV1W8n1lVxbnWz+ktRDxj6S1CHGPpKkymz+DSk9d+x6fXNz80TESZe5uXmg+/WdSsn1lVxbnap+vIPUaSsrhxj3kVQrK34CufrBzF+9NPyaiXH7X9T6Fnqpbmb+kqTKbP4NKT13tL5uK7m+kmurk81fknrIzF+9ZOavrjLzlyRVZvNvSOm5o/V1W8n1lVxbnWz+ktRDZv7qJTN/dZWZvySpMpt/Q0rPHa2v20qur+Ta6mTzl6QeMvNXL5n5q6vM/CVJldn8G1J67mh93VZyfSXXViebvyT1kJm/esnMX11l5i9Jqszm35DSc0fr67aS6yu5tjrZ/CWph8z81Utm/uoqM39JUmU2/4aUnjtaX7eVXF/JtdXJ5i9JPWTmr14y81dXmflLkiqz+Tek9NzR+rqt5PpKrq1ONn9J6qGpMv+IeAPwh8AR4CDwMuAs4IPALmAZuDwz7xmzrJm/WmPmr65qPfOPiEcDrwWelJm/BGwFXgTsBm7IzAuAG4Erph2kJKle08Y+W4CzImIrcAZwJ3ApsG90+z7gsinX0Uml547W120l11dybXWq3Pwz87vA24BvMWz692TmDcDOzFwZ3ecwcG4dA5Uk1Wdr1QUjYjvDV/m7gHuAD0XESzg5SJ0YoC4tLTE/Pw/A9u3bWVhYYHFxETj217ur00fnzcp4rO/k8cMAWFx1/Xhdrq/07bfW9OLi4kyNZ9rpwWDA3r17AR7sl3WofMA3Il4IPCczXzGa/n3gqcBvAYuZuRIRc8D+zLxozPIe8FVrPOCrrmr9gC/DuOepEfHQGD6TngXcClwHLI3u81Lgo1ONsKOO/uUulfV1W8n1lVxbnSrHPpl5c0RcC3wFuH/0853Aw4FrIuLlwCHg8joGKkmqj5/to14y9lFXzULsI0nqKJt/Q0rPHa2v20qur+Ta6mTzl6QeMvNXL5n5q6vM/CVJldn8G1J67mh93VZyfSXXViebvyT1kJm/esnMX11l5i9Jqszm35DSc0fr67aS6yu5tjrZ/KV1mJubJyJOuszNzW/o/mstI20mM3/10kYz//ruP3kZaT3M/CVJldn8G1J67mh93VZyfSXXViebvyT1kJm/esnMX11l5i9Jqszm35DSc0fr67aS6yu5tjpV/g5fSQDbRhGP1C1m/uqlOjP/jc2fvA5pPcz8JUmV2fwbUnruaH3dVnJ9JddWJ5u/JPWQmb96ycxfXWXmL0mqzObfkNJzR+vrtpLrK7m2Onmev3Qcz9tXP5j5q5fqy/DN/LW5zPwlSZXZ/BtSeu5Yen0waHsAjSp5+5VcW51s/pLUQ2b+6iUzf3WVmb8kqTKbf0NKzx1Lr8/Mv7tKrq1ONn9J6qGpMv+IOBt4F/CLwBHg5cDtwAeBXcAycHlm3jNmWTN/NW5ubp6VlUMTbjXzV/fMSub/duDjmXkR8MvAN4DdwA2ZeQFwI3DFlOuQKhs2/hxzkfqtcvOPiEcAz8jMqwEy86ejV/iXAvtGd9sHXDb1KDuo9Nyx9PrM/Lur5NrqNM0r/8cB34+IqyPiyxHxzog4E9iZmSsAmXkYOLeOgUqS6lM584+IXwFuAp6WmV+MiL8G/hd4TWaes+p+P8jMR45Z3sxfjWvvfH4zfzWjrsx/mk/1/A7w7cz84mj6wwzz/pWI2JmZKxExB3xv0gMsLS0xPz8PwPbt21lYWGBxcRE49q+b005PM33M0enFE+YtnnB70/c/fnxt/36cnv3pwWDA3r17AR7sl3WY9myffwVekZm3R8SVwJmjm+7KzKsi4s3AjszcPWbZol/5DwaDBzdkibpSX/VX/gOOb+RlvfLvyvarouTaYDZe+QO8DnhfRJwOfBN4GbAFuCYiXg4cAi6fch2SpJr52T4qmpm/SjMr5/lLkjrI5t+Qkw84lqX0+jzPv7tKrq1ONn9J6iEzfxXNzF+lMfOXJFVm829I6blj6fWZ+XdXybXVyeYvST1k5q+imfmrNGb+kqTKbP4NKT13LL0+M//uKrm2Otn8JamHzPxVNDN/lcbMX5JUmc2/IaXnjqXXZ+bfXSXXViebvyT1kJm/OmVubp6VlUMnzd+5cxeHDy+fNN/MX6WpK/O3+atT1mrm4/Ynm79K4wHfGVd67lh6fWb+3VVybXWy+UtSDxn7qFOMfdR3xj6SpMps/g0pPXcsvT4z/+4qubY62fwlqYfM/NUpZv7qOzN/SVJlNv+GlJ47ll6fmX93lVxbnWz+ktRDZv7qFDN/9Z2ZvySpMpt/Q0rPHUuvz8y/u0qurU42f0nqITN/dYqZv/rOzF/qrG1ExEmXLVvOGjt/bm6+7QGrQDb/hpSeO5ZeX7OZ/30M/ys4/nLkyI/Gzh/3zWXTKnn7lVxbnWz+ktRDZv7qlFIy/40+ls8VHTUzmX9EnBYRX46I60bTOyLi+oi4LSI+FRFnT7sOSVK96oh9Xg/cump6N3BDZl4A3AhcUcM6Oqf03LH0+jzPv7tKrq1OUzX/iDgPeD7wrlWzLwX2ja7vAy6bZh2SpPpNlflHxIeAPwfOBt6UmZdExA8zc8eq+9yVmeeMWdbMXxtm5q++az3zj4jfBlYy8xaGe+0k7rXaBOPPnZc03tYpln06cElEPB84A3h4RLwXOBwROzNzJSLmgO9NeoClpSXm5+cB2L59OwsLCywuLgLHcruuTu/Zs6eoemalvmOOTi+Oft4H7F81ffT235xw/6PzTrz/UXuAhQ3cf72Pf6rp8Y9XyvbbjOnV+8osjKeOevbu3QvwYL+sQy2nekbEMzkW+/wl8IPMvCoi3gzsyMzdY5YpOvYZDAYPbsgStVXf5sU4A45v5GXFPiXvnyXXBvXFPk00/3OAa4DzgUPA5Zl595hlim7+asbsZfjdbP7qrplq/pVWbPNXBTZ/9V3rB3y1tpMz6rKUXp/n+XdXybXVyeYvST1k7KNOMfZR3xn7SJIqs/k3pPTcsfT6zPy7q+Ta6mTzl6QeMvNXp5j5q+/M/CVJldn8G1J67lh6fWb+3VVybXWy+UtSD5n5q1PM/NV3Zv6SpMps/g0pPXcsvT4z/+4qubY62fwlqYfM/NUpZv7qOzN/SVJlNv+GlJ47ll6fmX93lVxbnWz+ktRDZv7qFDN/9Z2Zv4owNzdPRJx0mZubb3toUtFs/g0pPXesq76VlUMMX+0efxnOb9Og5fU3q+T9s+Ta6mTzl6QeMvNXq9bK8MftH2b+6jszf0lSZTb/hpSeO5Zen5l/d5VcW51s/pLUQ2b+apWZ//rm+1zRUWb+Um9s870Qqp3NvyGl546l1zdbmf991P1eiJK3X8m11cnmL0k9ZOavVpn5Tzff51D/mPlLkiqz+Tek9Nyx9PpmK/OvX8nbr+Ta6mTzl6QeMvNXq8z8p5vvc6h/zPwlSZVVbv4RcV5E3BgRX4uIgxHxutH8HRFxfUTcFhGfioiz6xtud5SQO671RSsbrW/SY82uQdsDaFQJ++ckJddWp2le+f8UeGNmPgF4GvDqiLgQ2A3ckJkXADcCV0w/TLWhzi9amfRYktpRW+YfER8B3jG6PDMzVyJiDhhk5oVj7m/mP+M2msdXfSwz/+rzfQ71z0xl/hExDywANwE7M3MFIDMPA+fWsQ5JUn22TvsAEfEw4Frg9Zl5b0Sc+FJk4kuTpaUl5ufnAdi+fTsLCwssLi4Cx3K7rk7v2bOniHqOOTpdrb5jj7G46vrkxz/6GOsdT5XHX/v+exi+nqn78U81Penx1r5/X/fPcdOr95VZGE8d9ezduxfgwX5Zh6lin4jYCnwM+ERmvn007+vA4qrYZ39mXjRm2aJjn9WNq6vWilj279+/ofq6F/sMOL6RlxX7lLB/TlJybVBf7DNt838P8P3MfOOqeVcBd2XmVRHxZmBHZu4es2zRzb8EZv5NzK93HT6H+qf15h8RTwc+Axzk2KkbbwFuBq4BzgcOAZdn5t1jlrf5zzibfxPz612Hz6H+af2Ab2Z+LjO3ZOZCZj4xM5+UmZ/MzLsy8+LMvCAznz2u8fdB2ecaj/9ykXq/YGT8OjbPYBPXVVX1L3kpef8subY6TX3AV310H7Cf4zPxoZWVuhr00S8wOdEsvzFss43/HdW3DVQyP9tHE208YhneVmZcM5uxj3FQ/7Qe+0iSusvm35Dyc8dB2wNo2KDtATSq5P2z5NrqZPOXpB4y89dEZv5NzN+cdfvcKpeZvySpMpt/Q8rPHQdtD6Bhg7YHULu1vp+hJOU/9+ph85d64vjvVNj/4PUq38+g7jPz10Rm/k3M35x1b3Qb+FzsDjN/SVJlNv+GlJ87DtoeQMMGbQ+gYYO2B9CY8p979bD5S1IPmflrIjP/JuZvzrrN/Mtl5i9Jqszm35Au5Y6Tzv9e22DC/LY/h78ug7YHMIX1bIPBpo1ms99f0KXnXpv8PH+tOv/7RFWatp/D377Z2gaT9i+/d6BdZv6qMY+vskzf5s/imJrN/D3WUC8zf0lSZTb/hpSfOw7aHkDDBm0PoGGDtgfQmPKfe/Ww+UtSD5n5y8x/U+fP4pjM/LvEzF+SVJnNvyFVcsdJ50Nv2XLWhs6T3ujjVKyw4nJdMWh7AA0b1P6I1d4vUj8z//XxPP8ZMul86CNHxv/bPOk86Y0+jufgqw71vl9ETTPznyFVsvfZ+hydzVhH1+fP4pjqyd7r2n+1NjN/SVJlNv+GlJ87DtoeQMMGbQ+gYYO2B9CY8p979bD5S1IPmfnPEDP/PsyfxTGZ+XeJmb8kqbIimv+BAwd41KN2sWPHeSddXvnKN7UypvJzx0HbA2jYoO0BNGzQ9gAaU/5zrx5FnOd/xx138OMfP5577/2HE265ic9//m8aX//c3PzoHOfjnXbamRw58qN1z9+4bR39ohTNlvH7UZv770bXvXPnLg4fXp56RJOey115/I0oovnDcKeA806Ye+6mrHujb6qq781WbX5px+ImrKNNi20PoGGLq66P34/a2383vu7Vb3hcXFzc4DhWP87453JdXzwzS19sU0TsI0namMaaf0Q8NyK+ERG3R8Sbm1rP7Bq0PYCGDdoeQMMGbQ+gYYO2B9AYM//1aaT5R8RpwDuA5wBPAF4UERc2sa7ZdUvbA2iY9XVbufXdcku5tdWpqVf+TwHuyMxDmXk/8AHg0obWNaPubnsADbO+biu3vrvvLre2OjXV/B8DfHvV9HdG8yRJM6CIs31OP/10fvKTz/GIR/zOcfMfeOAHbNt2RkujWm5pvZtlue0BNGy57QE0bLntATRmeXm57SF0QiMf7xARTwX+LDOfO5reDWRmXrXqPr6vW5IqqOPjHZpq/luA24BnAf8F3Ay8KDO/XvvKJEkb1kjsk5kPRMRrgOsZHld4t41fkmZHa5/qKUlqT1Pn+a/rDV4R8asRcX9EvGA0/QsR8ZWI+PLo5z0R8bomxjiNqvWN5r0hIr4aEQci4n0R8ZDNGfX6TFnb6yPi4Ogyc9sNTl1fRDwzIu4e7YNfjog/Xe+ys2DK+t4dESsRcWBzR71+VeuLiPMi4saI+FqJ+2dEbIuIL4z65sGIuPKUK8vMWi8M/6D8O7ALOJ3hu0kunHC/fwE+Brxgwu3fBc6ve4xt1Qc8Gvgm8JDR9AeBP2i7pppqewJwANgGbGEY+f1c2zVttD7gmcB1VX83Xa1vdNtvAAvAgbZraWD7zQELo+sPY3hMsrTtd+bo5xbgJuApa62viVf+632D12uBa4HvTXici4H/yMxvT7i9LdPWtwU4KyK2Amcy/AM3K6ap7SLgC5l5X2Y+AHwGeMGYZdu03vrGnUnRhTcuTlMfmflZ4IcNjm9alevLzMOZecvo+r3A15m99x5Nu/2OftzpNobHc9fM9Jto/qd8g1dEPBq4LDP/nskfBfi7wD82ML5pVa4vM78LvA34FnAncHdm3tD4iNdvmm33VeAZEbEjIs4Eng+c3/B4N2q9bz58WkTcEhH/HBGP3+CybZqmvi6opb6ImGf4H84XmhjkFKaqLyJOi4ivAIeBT2fmv621srY+1XMPsDrPOu4PQEScDlwCfGgzB1WjsfVFxHaGf8l3MYyAHhYRL9784U1lbG2Z+Q3gKuDTwMeBrwAPbPropvcl4LGZucDw86k+0vJ46tbr+iLiYQz/a3396D+ArplYX2YeycwnMvxs+1871R/2Jpr/ncBjV02fN5q32pOBD0TEfwIvBP42Ii5ZdfvzgC9l5n83ML5pTVPfxcA3M/OuUTTyT8Cvb8KY12uqbZeZV2fmkzNzkeGHx9ze/JA35JT1Zea9R/99zsxPAKdHxDnrWXYGTFNfF0xV3yhqvRZ4b2Z+dHOGvCG1bL/M/B9gP/DcNdfWwEGLLRw7aPEQhgctLlrj/ldzwgFfhnHPS5s8uNJGfQwzvYPAQxm+Yt4LvLrtmuradsCjRj8fC9wKPKLtmjZaH7Bz1fWnAMtVfjddq2/VvHngYNu1NFEf8B7gr9quo4n6gJ8Bzh5dP4PhMbfnr7W+2t/klRPe4BURfzy8Od954iKrJ0Z58cXAH9U9tjpMU19m3hwR1zKMRO4f/Tzx/q2ZdtsBHx69CrkfeFUOX4HMjHXW98KI+BOGNfwfw2NPE5dtpZAJpqkPICLez/Arvh4ZEd8CrszMqze7jkmmqS8ing68BDg4ysUTeEtmfrKNWsaZcvv9LLAvhh+nfxrwwcz8+Frr801ektRDfo2jJPWQzV+SesjmL0k9ZPOXpB6y+UtSD9n8JamHbP6S1EM2f0nqof8HOiL+N9ZZst0AAAAASUVORK5CYII=\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    }
  ],
  "metadata": {
    "kernel_info": {
      "name": "python3"
    },
    "language_info": {
      "name": "python",
      "file_extension": ".py",
      "version": "3.5.5",
      "pygments_lexer": "ipython3",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "nbconvert_exporter": "python"
    },
    "kernelspec": {
      "name": "python3",
      "language": "python",
      "display_name": "Python 3"
    },
    "nteract": {
      "version": "0.12.2"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 4
}