PCA_3.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ts8FRZGidjNh"
      },
      "source": [
        "# PCA Statistical Arbitrage\n",
        "\n",
        "(Principal Component Analysis)\n",
        "\n",
        "(This notebook can be found on GitHub: https://github.com/rodler/quantinsti_statarb)\n",
        "\n",
        "### Dr Tom Starke \n",
        "\n",
        "*Homepage: www.aaaquants.com *\n",
        "\n",
        "*Email: tom@aaaquants.com *\n",
        "\n",
        "*Linkedin: Dr Tom Starke *\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FIRHmVfedpUL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "48e4ccf8-1974-4f2a-b10f-eb5dc5b7c65b"
      },
      "source": [
        "pip install yfinance"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: yfinance in /usr/local/lib/python3.9/dist-packages (0.2.13)\n",
            "Requirement already satisfied: cryptography>=3.3.2 in /usr/local/lib/python3.9/dist-packages (from yfinance) (39.0.2)\n",
            "Requirement already satisfied: beautifulsoup4>=4.11.1 in /usr/local/lib/python3.9/dist-packages (from yfinance) (4.11.2)\n",
            "Requirement already satisfied: numpy>=1.16.5 in /usr/local/lib/python3.9/dist-packages (from yfinance) (1.22.4)\n",
            "Requirement already satisfied: html5lib>=1.1 in /usr/local/lib/python3.9/dist-packages (from yfinance) (1.1)\n",
            "Requirement already satisfied: lxml>=4.9.1 in /usr/local/lib/python3.9/dist-packages (from yfinance) (4.9.2)\n",
            "Requirement already satisfied: pandas>=1.3.0 in /usr/local/lib/python3.9/dist-packages (from yfinance) (1.4.4)\n",
            "Requirement already satisfied: frozendict>=2.3.4 in /usr/local/lib/python3.9/dist-packages (from yfinance) (2.3.6)\n",
            "Requirement already satisfied: appdirs>=1.4.4 in /usr/local/lib/python3.9/dist-packages (from yfinance) (1.4.4)\n",
            "Requirement already satisfied: multitasking>=0.0.7 in /usr/local/lib/python3.9/dist-packages (from yfinance) (0.0.11)\n",
            "Requirement already satisfied: requests>=2.26 in /usr/local/lib/python3.9/dist-packages (from yfinance) (2.27.1)\n",
            "Requirement already satisfied: pytz>=2022.5 in /usr/local/lib/python3.9/dist-packages (from yfinance) (2022.7.1)\n",
            "Requirement already satisfied: soupsieve>1.2 in /usr/local/lib/python3.9/dist-packages (from beautifulsoup4>=4.11.1->yfinance) (2.4)\n",
            "Requirement already satisfied: cffi>=1.12 in /usr/local/lib/python3.9/dist-packages (from cryptography>=3.3.2->yfinance) (1.15.1)\n",
            "Requirement already satisfied: webencodings in /usr/local/lib/python3.9/dist-packages (from html5lib>=1.1->yfinance) (0.5.1)\n",
            "Requirement already satisfied: six>=1.9 in /usr/local/lib/python3.9/dist-packages (from html5lib>=1.1->yfinance) (1.16.0)\n",
            "Requirement already satisfied: python-dateutil>=2.8.1 in /usr/local/lib/python3.9/dist-packages (from pandas>=1.3.0->yfinance) (2.8.2)\n",
            "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.9/dist-packages (from requests>=2.26->yfinance) (3.4)\n",
            "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /usr/local/lib/python3.9/dist-packages (from requests>=2.26->yfinance) (1.26.15)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.9/dist-packages (from requests>=2.26->yfinance) (2022.12.7)\n",
            "Requirement already satisfied: charset-normalizer~=2.0.0 in /usr/local/lib/python3.9/dist-packages (from requests>=2.26->yfinance) (2.0.12)\n",
            "Requirement already satisfied: pycparser in /usr/local/lib/python3.9/dist-packages (from cffi>=1.12->cryptography>=3.3.2->yfinance) (2.21)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pip install quantstats"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "skX9jk8WLwsa",
        "outputId": "05171d2c-af27-4441-fe00-71a3f55b4f89"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting quantstats\n",
            "  Downloading QuantStats-0.0.59-py2.py3-none-any.whl (41 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m41.3/41.3 KB\u001b[0m \u001b[31m713.5 kB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: python-dateutil>=2.0 in /usr/local/lib/python3.9/dist-packages (from quantstats) (2.8.2)\n",
            "Requirement already satisfied: scipy>=1.2.0 in /usr/local/lib/python3.9/dist-packages (from quantstats) (1.10.1)\n",
            "Requirement already satisfied: pandas>=0.24.0 in /usr/local/lib/python3.9/dist-packages (from quantstats) (1.4.4)\n",
            "Requirement already satisfied: yfinance>=0.1.70 in /usr/local/lib/python3.9/dist-packages (from quantstats) (0.2.13)\n",
            "Requirement already satisfied: matplotlib>=3.0.0 in /usr/local/lib/python3.9/dist-packages (from quantstats) (3.7.1)\n",
            "Requirement already satisfied: tabulate>=0.8.0 in /usr/local/lib/python3.9/dist-packages (from quantstats) (0.8.10)\n",
            "Requirement already satisfied: seaborn>=0.9.0 in /usr/local/lib/python3.9/dist-packages (from quantstats) (0.12.2)\n",
            "Requirement already satisfied: numpy>=1.16.5 in /usr/local/lib/python3.9/dist-packages (from quantstats) (1.22.4)\n",
            "Requirement already satisfied: importlib-resources>=3.2.0 in /usr/local/lib/python3.9/dist-packages (from matplotlib>=3.0.0->quantstats) (5.12.0)\n",
            "Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.9/dist-packages (from matplotlib>=3.0.0->quantstats) (4.39.2)\n",
            "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.9/dist-packages (from matplotlib>=3.0.0->quantstats) (23.0)\n",
            "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.9/dist-packages (from matplotlib>=3.0.0->quantstats) (3.0.9)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.9/dist-packages (from matplotlib>=3.0.0->quantstats) (0.11.0)\n",
            "Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.9/dist-packages (from matplotlib>=3.0.0->quantstats) (8.4.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.9/dist-packages (from matplotlib>=3.0.0->quantstats) (1.4.4)\n",
            "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.9/dist-packages (from matplotlib>=3.0.0->quantstats) (1.0.7)\n",
            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.9/dist-packages (from pandas>=0.24.0->quantstats) (2022.7.1)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.9/dist-packages (from python-dateutil>=2.0->quantstats) (1.16.0)\n",
            "Requirement already satisfied: lxml>=4.9.1 in /usr/local/lib/python3.9/dist-packages (from yfinance>=0.1.70->quantstats) (4.9.2)\n",
            "Requirement already satisfied: frozendict>=2.3.4 in /usr/local/lib/python3.9/dist-packages (from yfinance>=0.1.70->quantstats) (2.3.6)\n",
            "Requirement already satisfied: cryptography>=3.3.2 in /usr/local/lib/python3.9/dist-packages (from yfinance>=0.1.70->quantstats) (39.0.2)\n",
            "Requirement already satisfied: multitasking>=0.0.7 in /usr/local/lib/python3.9/dist-packages (from yfinance>=0.1.70->quantstats) (0.0.11)\n",
            "Requirement already satisfied: beautifulsoup4>=4.11.1 in /usr/local/lib/python3.9/dist-packages (from yfinance>=0.1.70->quantstats) (4.11.2)\n",
            "Requirement already satisfied: requests>=2.26 in /usr/local/lib/python3.9/dist-packages (from yfinance>=0.1.70->quantstats) (2.27.1)\n",
            "Requirement already satisfied: html5lib>=1.1 in /usr/local/lib/python3.9/dist-packages (from yfinance>=0.1.70->quantstats) (1.1)\n",
            "Requirement already satisfied: appdirs>=1.4.4 in /usr/local/lib/python3.9/dist-packages (from yfinance>=0.1.70->quantstats) (1.4.4)\n",
            "Requirement already satisfied: soupsieve>1.2 in /usr/local/lib/python3.9/dist-packages (from beautifulsoup4>=4.11.1->yfinance>=0.1.70->quantstats) (2.4)\n",
            "Requirement already satisfied: cffi>=1.12 in /usr/local/lib/python3.9/dist-packages (from cryptography>=3.3.2->yfinance>=0.1.70->quantstats) (1.15.1)\n",
            "Requirement already satisfied: webencodings in /usr/local/lib/python3.9/dist-packages (from html5lib>=1.1->yfinance>=0.1.70->quantstats) (0.5.1)\n",
            "Requirement already satisfied: zipp>=3.1.0 in /usr/local/lib/python3.9/dist-packages (from importlib-resources>=3.2.0->matplotlib>=3.0.0->quantstats) (3.15.0)\n",
            "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /usr/local/lib/python3.9/dist-packages (from requests>=2.26->yfinance>=0.1.70->quantstats) (1.26.15)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.9/dist-packages (from requests>=2.26->yfinance>=0.1.70->quantstats) (2022.12.7)\n",
            "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.9/dist-packages (from requests>=2.26->yfinance>=0.1.70->quantstats) (3.4)\n",
            "Requirement already satisfied: charset-normalizer~=2.0.0 in /usr/local/lib/python3.9/dist-packages (from requests>=2.26->yfinance>=0.1.70->quantstats) (2.0.12)\n",
            "Requirement already satisfied: pycparser in /usr/local/lib/python3.9/dist-packages (from cffi>=1.12->cryptography>=3.3.2->yfinance>=0.1.70->quantstats) (2.21)\n",
            "Installing collected packages: quantstats\n",
            "Successfully installed quantstats-0.0.59\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g_eQkPSCdZNd"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy import stats as stats\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.decomposition import PCA\n",
        "import scipy\n",
        "import statsmodels.api as sm\n",
        "import pandas as pd\n",
        "from statsmodels.tsa.stattools import coint, grangercausalitytests\n",
        "import matplotlib\n",
        "from itertools import groupby, count\n",
        "import pickle\n",
        "import yfinance as yf\n",
        "from dateutil.parser import parse\n",
        "import datetime\n",
        "from scipy.optimize import brentq \n",
        "import traceback\n",
        "from google.colab import files\n",
        "import quantstats as qs\n",
        "%matplotlib inline"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ppwmuIwKeL06"
      },
      "source": [
        "## Build PCA from Scratch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uP1D9gXzdsps",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0ba6c309-f4e4-48b7-afbc-0267a36146ff"
      },
      "source": [
        "stocks = yf.download('SPY,QQQ',start='2005-1-1').Close"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  2 of 2 completed\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "stocks"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 455
        },
        "id": "V6XvwyLsIjHp",
        "outputId": "5522b586-4bbe-4521-c45c-6b80154e28dc"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                   QQQ         SPY\n",
              "Date                              \n",
              "2005-01-03   39.500000  120.300003\n",
              "2005-01-04   38.779999  118.830002\n",
              "2005-01-05   38.540001  118.010002\n",
              "2005-01-06   38.349998  118.610001\n",
              "2005-01-07   38.549999  118.440002\n",
              "...                ...         ...\n",
              "2023-03-20  305.970001  393.739990\n",
              "2023-03-21  310.339996  398.910004\n",
              "2023-03-22  306.119995  392.109985\n",
              "2023-03-23  309.750000  393.170013\n",
              "2023-03-24  310.890015  395.750000\n",
              "\n",
              "[4588 rows x 2 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-6cef9b35-7306-436b-97b9-cd932bc568ac\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>QQQ</th>\n",
              "      <th>SPY</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>2005-01-03</th>\n",
              "      <td>39.500000</td>\n",
              "      <td>120.300003</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2005-01-04</th>\n",
              "      <td>38.779999</td>\n",
              "      <td>118.830002</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2005-01-05</th>\n",
              "      <td>38.540001</td>\n",
              "      <td>118.010002</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2005-01-06</th>\n",
              "      <td>38.349998</td>\n",
              "      <td>118.610001</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2005-01-07</th>\n",
              "      <td>38.549999</td>\n",
              "      <td>118.440002</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-20</th>\n",
              "      <td>305.970001</td>\n",
              "      <td>393.739990</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-21</th>\n",
              "      <td>310.339996</td>\n",
              "      <td>398.910004</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-22</th>\n",
              "      <td>306.119995</td>\n",
              "      <td>392.109985</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-23</th>\n",
              "      <td>309.750000</td>\n",
              "      <td>393.170013</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-24</th>\n",
              "      <td>310.890015</td>\n",
              "      <td>395.750000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>4588 rows × 2 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6cef9b35-7306-436b-97b9-cd932bc568ac')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-6cef9b35-7306-436b-97b9-cd932bc568ac button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-6cef9b35-7306-436b-97b9-cd932bc568ac');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "stocks.plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        },
        "id": "UcUw0Y9lI7LZ",
        "outputId": "db00e965-aef0-4f01-a434-5611685d76a0"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Date'>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "stocks.pct_change().add(1).cumprod().add(-1).plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "a3oIb1yoJjeG",
        "outputId": "d7a20bf6-6500-43ce-c4ab-1b6b60b74335"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Date'>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5rC46RBBd8_T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "4fbeb5da-02b4-4551-abe4-c135362d129d"
      },
      "source": [
        "stocks.pct_change().add(1).cumprod().add(-1).plot()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Date'>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rDX-kQwme86V"
      },
      "source": [
        "Fist PCA step: De-Meaning of series\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qe48cma_ezyk"
      },
      "source": [
        "stocks_dem = stocks.pct_change().dropna()-stocks.pct_change().mean()"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "stocks_dem.add(1).cumprod().plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "CgwdyrbOKxVk",
        "outputId": "8382bd77-ceab-40b0-ff06-2956905dcfaa"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Date'>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEHCAYAAABLKzaMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAAsTAAALEwEAmpwYAABq5ElEQVR4nO2dd3wU1fbAv1vSewhJaKETQUBEbFieWBB7wa7Prlefz/J79t67Pn32a+/6nuUpWLBiRcEC+FCJ0gk9CembbP39MVtmdmeTTbKbbML9fj75ZOfOnZmzszNn7pxz7jkWn8+HQqFQKPom1p4WQKFQKBSJQyl5hUKh6MMoJa9QKBR9GKXkFQqFog+jlLxCoVD0Yew9LUAYacDOwAbA08OyKBQKRW/BBgwAfgBa9SuSTcnvDHzd00IoFApFL2Uv4Bt9Q7KZazb0tAC1tbU9LYKSQUcyyJEMMkByyJEMMkByyJGkMkTo0GRT8j1uovF6vT0tgpJBRzLIkQwyQHLIkQwyQHLIkaQyROjQZFPyCoVCoYgjSskrFApFH0YpeYVCoejDKCWvUCgUfRil5LsRn6/nHTUKhWLbQin5bqJ2/ixW3nEsXqejp0VRKBTbEErJdxM1n76g/Z/7Citun4nX1drOFgqFQtF1lJLvBpzV64Kf63/8EIDmP37oKXEUCsU2hFLy3YBz8+qINmtGdg9IolAotjWUku8GNr99f0Rb/Q8fALDx33ew4vaZ3S2SQqHYRlBKPsFEq6GbNXYqAM3LfgLA01zfbTIpFIptB6XkE0zL6iUx9fM6WxIsiUKh2BZRSj7B1C/8xHxFWMy8Tyl5hUKRAJSSTwCNv33Littn0rxiMU2/fWvax+f10vDL3OBy8/Kfu0s8hUKxDRFT0RAhxN+BM4AJwKtSytPb6HsscDdQAnwLnCGlXBetf1/B53HT8L8vyNlhXzb/958ANC75irQBI2ndsJz0oeONphufly2zHw8u1nz+Evm7H9m9QisUig7R4nQDkJ6abPWWohPrSH49cCvwTFudhBBjgWeBc4EioAJ4tSsCdhSfz8eG126JbiZJEHUL3qPq/cepev+JUKPFgrtxKwClx19j6O9LglzUCoWiYxx3zfucfP2HPS1Gh4hJyUsp35ZSvgNUt9P1FOBDKeWnUkoHcB2wmxBiZNfEjB2f24ljxWKqPnii/c5xpObzlwBoWPxZqNHrIb1sHPaCUqwpaaSWjgiucm5e1a3yKRSKruPzgdPduwZo8X7nGA8sCCxIKeuEEKv87ctj3UltbW2nq644l4VmktbU1HR4e4fD0eHtvFHCH50uN15HPT57GjU1NVgGbgcbVwDQsPATsFgNDtjAcTsjQ7xJBhmSRY5kkCFZ5EgGGXpKju9+3Rz8XFNTkxTnIiCD1WolPz/ftE+8lXw2UBfWVgvkdGQn0YSNhRWfPBn8XFhY2OHta2pqOrzd+g8eNG1PTUulsWIJKf0GUVhYiO/A03FNmU7lk5cAkDlqMs1//hjsX5CXi8Vm75QM8SYZZEgWOZJBhmSRIxlk6Ck5fv7jz+DntVUeCrPsPX4uYjkP8Y6uaQRyw9rygIY4HycCzRZ/W6IPE4GnuZ6W1b+arnPXVQHg8ueusVht2PP6B9frFTxA4+/zEiSlQqHoKj5CExuvk/P415u/9aA0sRNvJb8E2CGwIITIBYb72xPKyjuOwbFiYZt9Wjet0kIb/bNMI9ZvXIF7fQUAPq8Hn7f9uuLrX7o+oi2laDC27ALziVDW6Ke8ccnXNFXMb/eYCoWi+3GF2eIr1vSOWeqxhlDa/X1tgE0IkQ54pJSusK4vA/OFEPsC36FF5HwvpYzZHh9PfD4fFosluLzlvccALV/MiGvfiui/7pnLASge/xZrHjoHbClkj51K3fxZDDrrPtJKh0ds46qqNCzbc4soPf5aNrxyU7CtZOblwc8WS3Ql71j+M47lP5N//lOxfUGFQpFwtja0kJeVRk1975ywGOtI/jrAAVyFFkHjAJ4CEEI0CiH2ApBS/g6cBTyNFokzFjgpzjLHjM9jfAY5N4aeNa1+ByiEcrwHt/N68DTV4amvom7+LABctRvbPV5q6QjKLpSk5BeD7uFizdC5JNoYySsUiuTi64XrOPWmj/hqYSWOVndPi9MpYhrJSylvAm6Ksi47bPkN4I2uCtZRlttGMtJjfGHwuV1gT9U+hyUKW/fM5Qw89TbSh4yldt7bhnUr7zwuYv/W1IyItvCkYqXHXR387N4aeijYc0KOEbORfOlJN7Dx1Vsi2hUKRc/y2Y9rAPi5YjPNjnDDRe+gzwwrn6naKaKttXIpAK6a9ay6+8SI9S3r/oy97qqJfd7b0hT8nDFyskGZ60kpHNDmrtsy4SgUip5jaKkWR1KUn8HY4f16WJrO0We0S5MvPfi5/6EXAJrt3dvazNrHL4ww3YAW9aJX1G1hNkO19vtZwc9FM84x3c6WHUOIVZiS97bGJpNCoUgsazZpgYEfz18dNW14stNnlPzuE0KjZVt2QfBz9WcvGjvaQhaqhkWf4mmOMbrTRMk3/6lNvCo55krNDm+Cz9u2HS97wl+whNnpHXNfiE0mhUKRMDweLz/+vgmAukYnLU4P2RkpPSxVx+kzSj4z3Y5s2JcXvIdhTcsMtjeE5bDJnbS/Ydnb0hjT/vV1WgN4HNoDIqt8l6jbRZsNG6D/oRdEjOQ9NetjkkmhUCSG9VsaOfKK2YY2R4ubLKXke44TDijnN9dgynaYYohsCceabqytWvut5nRN6V8W0Tdru92x5xYBUP/De5E783TO297/8AuDny1WW6S8tt6T4U6h6ItsrG6OaHM43WRn9j4l32e0SUmhNnrPSLMbRvLh2HONzpOAycXTYMxBMfCMu0kbMBKLxcKK22fidbbgdTux+qN1Gpd+F5NcxUf9I6Ittd/gsBajkrcoJa9Q9CjrqyLf8DdUNTGgX1YPSNM1+sxI3mKxYLHAax9XcM+s6Onrs8p3NW0PjK5/d2m2/dSiwYaJVD5XK1u/fB3Qomo2v3Vfm/JkT9xX+z9uDzNhtWOUDA/KblzfZ34WhaJXIv/7P9P2DdW9LyiiT2mTgPN7/q8bKTn2KsO6gaffyaCz78eWlcfgcx6I2DZr9BQurjkV2bA/wy5/BWtqekQfjz83/JpHzmtXluLDLjCdVWvGT39UGRvacdYqFIrEESgMEo0hJdmMtG+kwNoYdMwmM31Kyev5fq1xOX3QGNJKhgGQWlxG0cHnh1baUlheWQuAD4upggfwOh3a/9aQvc7sgdEegXBMi9UGwFPv/2lc73J2eJ8KhSI+bNnqiLouJzOVkrxULsr9mJvy32bL1kjbfbLRZ5X8S3MqIto8Xh8P/XshlZsbSBs4Ktg+r2kYlzzwZXC5ucV8ZlvL6l9xbl5taEstjnTYtkdgclTebocD4PClGjv4lb9Coeh+whORBci0tHBz3n/YsyA0erf2gjQlyS9hJ/ESGWHz5md/8MmCNVx43xcG56Y77DS0Os2zT3pbm6l8KuRI7XfAGZ2SzZaRzYhr3wra6/UTuWxZ+Z3ap0Kh6BgVq2uY9XVk7sRPFqw26Q0HpC/B1lrP8D9fC7bZrNEj+ZKFPhvG4fWFFHfhfqcB8MXPWsZIt8eLp6k2uL6f1ehJ93hjm9mWt8uhXZQyEltWHm5na9z3q1AojFz3xDxanB7237mMzPRQaGQgUg/g/ov3prHZxY1PfUe+NdLpau0FSn6bGMmvyN2ZtZsaqNwcUuaByBaAXKvRBherko8Hp940J7Ix1nw6CoWi07T439jrm5zI//7CI28sAiDFHjKXFuSkM7hYm1uTbol0yC790bw2RTLRZ5V8gy+UNfKmZ+bzt3s+Dy7vucNAbOmheNdwc80XPxu9toFcOIlga0P4qN0XChNSKBQJx+X28t43K/no+9Vsrmnmibd/AeCpa/anKD8di6MWgA2evIhtM5qSf3Z6n1XyAANOuZlBZ9+PL8w+/81i4w/j8hmtVi9/uNSwnLPDvhH7Lj76sjhJacTnQyl5hSLB1DeFIticrpAPbs73qxg+UMs8WVKYSdX7j9Hw/IWMsG+ivy0yz9X2I/tHtCUbfUrJn3rwWIaUhNIWpJdtT7W1KList7X97Z7Pgp9Xu0N9YiV77O6dlNKcZxv+AkBKQamhlqRCoYg/tz7zffCz0xUyj9ptVlau1/JNWSwWGhZrFoAhthompobFZQO+XjBxMdbyf/nAk8BBQD1wu5TyMZN+KcBtwMlADjALOF9KGVsWsC5y7H5jOHa/Mbz+SQWvzFmKx+szjNr1oZFrNzXiKUrF5nXyvmOS6f6+XrSOrIwUJpebZ5iMJ4tdQ2k8/gmyFr+Ar6Ean9uFxd778mQoFL2Bpau3Bj83OEKj+uaWkN1dn6HWbjGPuHNZkv8ejfUx9AjaA2EgcAhwsxBimkm/K4C/AJOBIUAR8FAc5OwQqX7HidPlCUbUADS1GB0n/9vtFl4pvQJflNNwz0s/cuOTseWoiQc+LzT5c+JUPntFtx1XodiWadCZbtZuCin25uU/Bz8fnvkzZvhcyV8tql0lL4TIAo4FrpNSNkgpFwHPAmeadD8SeEhKuVlKWQ/cBZwohIisnZdAUlO0r/X0u0s4ZOqwYLvX62NAUcjh+tx7v7Hgt41YLTBpjNG29v63K4Ofv13cPc4Vj84Wry8fqFAo4kuOLptkQ3NIyQcmQqXiYssss/Gp0b/ndfcBJQ+MASxSyt90bYuA8SZ9LRjPggVI9++j26iu06qqf7JgjcHBAlCYG5myIDc7jQkjjXb5gIcd4Kelm8gcFSovGJip2hk2Vjdx94s/4HR58IaFauorz2SNm9rpYygUirbRz2rV64jl62oBOHOkeZJDe16Yo9WT/ClIYrHJZ6PZ4fXUotncw3kfuFgI8TnQAgSyhEXP/WtCbW0tXpNKTLGSmRratmqr0SM+bmgOv66oNrSNGZxDS0v0fBX1jc2kHnUeqQeAe8tqKBxETU1N1P5tccdzC1m5oZHJo/MMowmAuroGCixW8HlpWr6I6urqYIZKn6sV9/o/SBk6oVPH7SgOh6PT37GvyZEMMiSLHMkgQ1flqK5rCcbIA8xfovfbaSbdsVu/Mt3WUjoS6jZjyS3GV7+ZISvfZdMvI7APLAcsEVXeEk3gPFitVvLz8037xKLkG4HcsLY8wKxu3p3+dfP9y/cBBwKVJn2jEk3YWJk4BpijTVf++AejqWXYoH7AKkNbZkY6RYXhXzHE/N+quO4sf63WwhhqtrbByg2aD9pDKmnpxmdfekYmxcdcxeY37sDXVEtGzSoyR2tvECvvPQWf08Hg8x4mtd/ALskQCzU1NRR28bv2FTmSQYZkkSMZZIhVDrfHy1FXzEYcNYFD9xwRbF9aadQJazYZZ7IWWqPHiZRMO5GG/CLyph7Nmge0tCZNsx8ALKQWD2XwOfd38Jt0jVjOQyyPnT8AnxBirK5tErAkvKOUskVKeYmUskxKWebfthKInuA9ATQ6QnYyqwXSUkMz2PKy0yL6Wyxw4K5DOe/oiVH3qbfbdYV+eZq5KC3Vht2mnf6zDt8egDtf+IFLXwr5AjzNdQB43U58/gyYajasQhEbTX498OpHxnkvqSltJwDMsrQEPw88/U7DOmtKOv32Px17Zvig0Idz86pOy5pI2h3JSymbhBBvArcKIc4AhqM5XY8P7yuEGIj24FgHTAD+CdwopexWzTRpTCjksSA3HbfHG0w6ZrNamH3/ERx26bvBPvN/3YjNZuWQPYYbbPF6NtU0k5OZarquI/TLS6e6rgWPx4vDn7danzejweHWvBiAq3YzAI4Vi0M7aKO0oUKhCOH2aGonMJgK8OearWbdg9gsIXVlsYapyF6QdTKcWBOUXQA8BWxAs8/fJKWcK4QoA34Dxkkp16A9AF4GSoCNwD+llM/GX+y2sVktzJw2irfmLsPR6iY7MxXQRuKBhEIDi7JYX6W9punV5kkHjODVT1ZE7NPjie9zyuP14fDb/7J0Sl6fc6f2mzew5/Untf8QvSBxlUOh6Ku4PVogg90eUsyNDhevfhyZhhzggtxPaPKkMtgesvVbbMZRf4TS7wXEJLGUshYtjDK8fQ2aYzaw/C2aou9x/jJ5MG/NXUZzi5t+eaEIzoBj5Z+X/IUTrvsAgLTU0GmYtmMpC/+s5fdVRqdOtBzTHeWPNbWAdgEu8xcqycoIHT88RbJj5WKcm1YFl7e89yiDzrw7LrIoFH0Zs5H8C+//Ztp3pH0TY+wbIjSiLywApLsdq/Gg90kcI/oUoJlpoV+uqlazbQdi6QGyMkIj6dQUG1edtnOwfcRALSmRxxM91cC6LY2ccN0HpsV/o9Hc4uKdLzXncLpOPq8vrKi31Ub9jx8El1s3LIv5GArFtozbHank53y3yrTvRbkfmbb7PG4G/PWWUIOt7XGxLwnzTvW+d48Yseps1xU6G9y+UzTTh/6H7xcWO5+fncYhewznoKnDaHK4uPKRb/C28eN9Mn81TQ4Xn/+wllaXh/Ej+rHr+AFtyvfZD2uCn/OyQs7g8GRqqqi3QtE5Am/fKTbze2jncSX88Fv0Gq2ZY3YmrXQYnubQ4M1ib8cv5/OCJbkqu/VZDRKezP+Ov+3ByTO2C3rWLbqHgN5mF9j2vKMnMrQ0N/iwaEvJz/leqyTT3OrmnS+Xc9tzCyL6VKyuMTh7120JhW3pfanesJ+k8X9fRD2uQqGIjtOt+a/sdvNghe2H92tz+9Jjr8JiSzGYaCztBD74vMnnM+u7Sj7sx5gwsogTDig37Ztij34aAg+L8NmpekoKtHj32V9HOmwBahtaueyhr9s9BpiXLVQoFB0nMJK3mdjRxw4r5JA9NfdhCpHFQPTYsjSTbeaYXdo9ZuvmyEyVPU3fVfI6xXnpyTu10RMOmRrdVxwcybeh5DPSI61eh1/2Ll8vXMfG6ib+alb9SYdFp9gjzDUKhaJTBM01disr19cZ7OWXnbIT6f6AiwxL+3NgRlz7FqXHXtluP8eq/3VS2sTRZ5W8fiCfm9W2HW2HMdET/wdH8m2Ya9wm4ZU+H7zy0dJgbuq20A80oil5S1omGcMnYkmNzL2jUCgicfnNNas31nPR/V/w9txQ0II+h1Wm1ajkrdmFlMzsXBbY2rkvdWq7RNJnHa/6KupZJiNtgOm7DmVoqVkKnhAhc030PtFqwnq9vjZNQR3C7cLjaMTnbMHn9WCxJpdzR6FINgLFQOoaNSW+4Dcts+vZR4w3BF6Ej+QHnfcwKWl9ZzDVZ5W83iafmxWZygDgwuMmxbAf7X80c01dYyvL1taarttQ3RThGzA/Rvt9fB43zo2azb9lzW9kDOueRGUKRW8lfG7Lbyu1uS/hM9czw5S8PSX5C4F0hD5rrtHnqMnL7nw6gkAMfXV9i+n6U26Mbm+fNLq/qSlHz4nTy8NTVEfBR/oQLX1Q3fzZsWygUGzTBMw14W/T4cuBkXzerodjTc+OOWz5gfoZcZAy8fRZJW+1WrhV7M6x+4025IbpKAHbXZMjsjhAdV0oPfHuEyLj4m02CxuqtVDJ0UPyAbhVGGvDHrf/GIPjtS0CMboeh1kCUIVCoccZKAASlpAsVafkU3Dz1+xvAMjb5RCGXfpCu2GSAVa5i3H6jPu2FZV1ReSE0GeVPGiJyk49eFyX9mGxWLBZLXhMjPL6AsAVqyOTHlksFp5+V0vWee9FezP7/iOYNKaYS07Y0dAn/Jp6yHcyQy8xpvwpPf4aLP7Zdq0blnf6+ygU2wpb/W/f4T65FH950LofPuC+wldDKzrh51rnKQh+3uzJgbTsNnr3DH1ayccLm83KL39WRUxZ1pti+hdEVjj88ffQbDq9I3iUf1QPms0/U3cR7jyuhHpfVjA2N0DmqJ3IHD1FW0jCCRcKRbIRSDkebjINDNiqP37G0G6xdfyN3+kL3bsen01NhuqtOF0eKtZs5eP5qw3tNXUhO312RuwXiF7hWywWUuw2Zt9/BLPvP8KQRydAwT4nAZCz4wFA18oPKhTbCoH04q1Oo+IdOsC8QJAto2Oj8Knjiw2GVjdWLXY6yeiz0TWJIDzm/To5L/i5rDSX846eSE5mKumpNs6/53M2VDWF7wKITLmgx0JkkiN7tvZKaLFYsKSkJ+WFpFAkG60uTbk3tRhntBYXZOKsXm+2SYcQR5Tz0yOhcfIQew3ejTW46jaTklfcxpbdixrJd4DmFqPzda9JgwC48ezdOPXgsZT2yyIrIwWbzRpRv1VPWyGTZk4fn8et75CUme4UimTC6/Xx3f82RF1f+cSFcTnOHOtfItq2zHo4LvuOF0rJd4Amh3FEEAjRmjK2JKL6jD5fxt+PnWS6v2ITOz5EDtT1St7ndFC/4L1YRVYotkk+jJJSGKBl3R9xO447syiizTAoSwJiMtcIIfKBJ4GD0CpD3S6lfCxK35uBs4Ac4HfgEinl93GRtodpdBgnTXy/ZGPUvvponKJ889lzZqN2iyXSXJM2cFRHxFQotnkCdSPM8Lkjc9UMPvfBTh0nM90OEYdKrvxTsY7kH0F7IAwEDgFuFkJMC+8khDgOOBeYBhQArwP/FUIk17fuJM06296WrdEvIghVgAIYOSjftI+Z0SUrPYXmVg8+n49hl73E4PMeJn3QmOD6tAGjsKZndURshULh55ITdjQt4WfPi56/qi1M57gkmbZrV8kLIbLQSv9dJ6VskFIuAp5FK+YdznDgaynln/7i3c8BpUDkO00v4tj9RgOwakM9D/17IQDf/S92x01+jnlaBTMy0u20OD24PV6saZmk9htoWG/P748tuyDK1gqFAqKnD7daLTRVzI9s70Liv1tqj+KeukN0LSEt3/jr16y4fSZep/mM+e4glpH8GMAipdQXR1wEjDfp+zowSgixnRDCDpwD/Cil3NJlSXsQ/YSqTxZoFZ3++0Xny/D1y8tgYFEW5x89MWLdvz/R7IULTCrWfLWwkhXrG8DrofqzF1lx+8xOy6BQ9FV8Ph+vRSnW3W/Ri9TNnxW3Y1ksUO3NYZ2nn64tpOSrPtYmNXqa6+J2zI4Si00+G80Or6cWzeYezkbga+A3wAtUA/t3VKja2lq8baV9TCAOh4Oampo2+9TU1NDc6jYsR2OviSWm6+8Uk9vc9v6Xf2TsVXsGl9/6YhWzvl3LqVmNlGRuoe57rcrUllV/YMuN/4tSLOehO0gGOZJBhmSRIxlkaE+OmvrWqNtlb/zZfJtOfCeHw4HbHZnupGXDcrYs/xVbwQC8Lk2W2upqbN74Jz4LnAer1Up+fr5pn1iUfCMQPnsgDzBLoHIjsBswFNgAnAjMEUKMlVK2n1jdTzRhu4OamhoKCwvb7FNYWBi0z8ur96OwMPokij13LGt3f2b4/McJMOtbrbLUTmmrQDe3o+GVqxlx7Vsd3n97xHIeuoNkkCMZZEgWOZJBhvbkuPf1b4Kf7XjwYI1apyFzzC70m34GKXkd/041NTUU5GUB2ii9hjwKqQO3k4bXb2DEtW9Rb7PjdbWSm5VBWgLOWyy/Ryzmmj8AnxBirK5tErDEpO9E4D9SyrVSSreU8iUgzd/eJxlYZK7gH79yX/5x0mSmThxour49Ykk/rFB0N+71f7DpnQeSeq7GkuXVANjwcH/hKxye8RMAGZbIEX764PIuTVz6+zE7BD//ZhkT2cGfD8fnjv52kWjaHclLKZuEEG8CtwohzkBzrp4JHG/SfT5wjBDiFWAzcAKQhfag6DP8+xNze5+ewcU5DC5uuyBJWwwflGfavqB1BLukmdeSVSgSTeOHj4DTgffAs7FldP76jgdeZwsWe0rUAjqpFu1te7e0P3nXMYW7Cv4dXDfglFvwOVvIGDmpSzJk63LT/2KfyJ6uHwzrA7K5tm4iffB2XTpWZ4k1hPICNAvCBmAOcJOUcq4QokwI0SiECOTXvAf4EfgZzW5/BXCclHJzfMXuWV6eszRh+370ci0yddpOQ4JtdY2hUUB4gQOFoltxaqHDnuaeTXftqd3IqntPZuPrt0XtY/EHKZuZajKGbk/m6J3iW2HNJDQzEGmzZdZD8TtOB4lpMpSUshYtjDK8fQ2aYzaw3Apc6P9TdIICf/56/WSqtZtCN5TH5Lns8/lizoGtUMSFHp7V6V6rBfs5Vv4StY81ipIf8NdbEiJTk8t4HJ/Ph6ex553UKq1BkmEL1pQN2TzT00LP4mWukohtfK3NiRdModDh8/ackm9dvwzHN68BkDVuj4j1wwdqcSJjU7S5LNnWVgqsjaEOCYrcq6wy3ofOjSsTcpyOopR8jNx49m4RbefPjL8/OZCh0uMJKXm9wl/qinTk1v/8cdzlUCjaoifzs2x47dbgZ7PZ34F03QGbPMBN+W/rtumewh7Ozau65TjtoZR8jEwZW8Kg/toFlZGm2fEOnjo87scJJDbzeM2V/GZvpEO2YclXcZdDoQjH3airfhZDcQxnVSWONb/GXQ5bdr5OjshReYs/f7zDZ17bObVkWNxlMsOSopvpbrHidbadCiVRKCXfAY7dTwuRSk+1M2l053JdtEfAXKNX8k0tkRMu9Li2rEmILAqFHq/O2erauhFXbeSs7AAb/3MnlfJiNrx0Q9zlcFVVBj+bVWJqdWoj+PIBkakKMkbs2G3+K2taZmjB52Xrl693y3Ej5OiRo/ZSAqaUrQ2tWG2JuVACx9A7W296qk8k8VT0cjyO0HzGLbMfYe2jf8NrktERoPnPH4OfHav+FzcZWjetMjaYKXmXl312GszBUzT/lVVX8cmeE/+8T4fuYf5GH27S8pnMju0OlJLvAPqyfZuqE+vs/HrROv5YYywOPn5kvyi9FYrE49wc+cbojSGUsiaOI9h1T19qWA5PK+Bye9hc04zVYsHrD0jQh0mmJSBW/dyjJvDOPYdFtIcreYP5phtRSr4D6Mv2ra9qbKNnfKjcbDxGUb6xyEjB3ickXAaFIoDXEXnNe8Miu3weV0TivPQhiZsEtHRllWH5jue1yUhfLVxH7TzN2eppCiUHs1jjr/IsFgs2W+R+qz95LrxjRJ/m5Qup++H9uMukRyn5DtDYHBo1dMes7kDlqQDjhhlzVORM2i/xQig6TeuG5ay4fSZVc57CXV+Ns3odK26fSUtl+zOmkxFXTWR67XBnYv3Pn0T2SeDEqYYG4/F//D3gJ4hyg1q6T+V5GqrDju0Pj3Y7gw+eja/fRvXHz5r6FuKFUvIdoLvnG7ndXipWhyZT7L/LUAC+ainHsd0MTrn7u+4VSNEh1j17BQD1P82h6kNJ5RMXAbD+hWt6UqxOUbfgPRp//Tqi3evQFHjr+mWsvPdkaj5/Kbgud8pB2PP64w5Xdp2k6uNnACjY5yRqJ2pvsdYoynxEeq1peyJG8nq+aimPui7g8N383wdY/eCZ+HyhyCCzh2O8UEq+k6SlxnE6dBSee/83LntIu7EGFmUFCyG81bwrjy4fGVFzVtEzOFb/is/twudxU/fjh7SsjUx7Ee589Hnc+NyuNmdsJgs+nzfS9ODH41fyDYs/x+dsMZTWS+k3GFtOP/DFZ/JR/Q8fAGCxpbClcCIrXf3JzzSftD8orcl8JwkcyRcXZvKBY0fWpEdT9JqSb/5jAQA+XSGR6o+eSphcMaU1UGiUlYQyLv/n9kPa6BkfWp2hVzi31zhi0UffKHqOlnV/suHlyDDBIec/YmywWLDnFeOu09I4rbwrlN9v4Ol3Gko8JhvuraFQydSxe+H8PTSi9zTX4/N68IWNqDNH7UTuTgfS9Ns3+DoxwzQ8VYfexGVNSWPlukZGYMFu9Rm2CWC3WQ0puUMbJ07Jp9gsOHypVGeNoKylfZNcd1WLUiP5DjB2eMgmrnfCJpJs/+w9t1u7UTLTzZ/LyVYhflvAVbOe9c9fZbquZe3vhmWfqzWo4MNZ//zVeFt7ZqJMLOjtxem7HGlY17ruT1beeRwNYbOuS4+/RlPSFmuHHFhep4MVt89k5R3HGEION7/7YPBzzqR9eX9eJV6sBiXv0BXyyUVzElvCyvqZ1mSNE5ecoBUCKimKkp3TYsVdH3IU6x2uiZyFq5R8B8nKSOGk6dHtbvFgxq6Dgp8bHdqFHnDCThlbwoCiLDLSjMo+UIFG0X00/vpt1HVb3nu0Q/taKy/uqjgJo9E/o7rfgWdHOKaafp8X0b9wv9O05FweLz6vG2c7k/WqPn6WFbfPxOdxs+X9x4Pt+slW7trQA9Ji0wY+HixYCb0lOFrd3FfwMgemL2ZvjyZXycwrDMdKZB780n7ajPjPflpnaG/2+mfeWmDNwyLYXvfdO8HPWWN3T5hcSsl3kNdvO5gTD0xsXuhpO5ZGtLn8I3mr1WJIcxAkTnZPRey0VMYv5bSnoZrN7zwYt/3FixW3z6T2W63yWNqAkUEF2xb27ALuf+VnZl71Hq2VFXgdDWx5//GoCrbeP6JtWPw5Tb+FHpze1mYafpmLzxMa0ZccdzUAU8cX4/VZseiue7fHS4rFy8GZi4NtEREuCbxPAs+/8KyX99X7TbttmK0aFn6SsLQHSsknIRYTU1BAyVuATTXNeMNvmCSu1NNXaF72E5veujc469K5ScsyOOis+4IVgPSkFg/t0P7Nold6kuY/fzIspw8aw5qa9s2C3/2wlC8XVhpSczQs+hS3SRqE5mU/6fp8ZlhX++3bbJn9CKvu/SsAqaUjyBo9hYZmJ/OWbGb71HXkt27AXa8p8kVLI/ffXXZvIBgrn24xTtDa6tVG+LXz3iZr7NSo29fMfTUhcikl30sI3DBzf9LyduidskCnnFuK9tn87r+offwc3PXVbP36DZqWfs+6py+l8dev8TTVkTlmZ9JKhwdnVab0DxV7aW+G44CTb4poa02S9LQAG/9zR0TbDc8sbHe7d383t3s3LJ5rCBsE2Pjv0DHCE4cF3pQCI/m0gaMAuO5xo4nI6X/obt5SG3HM9LJx7cobL+z+VCd7pBkL4Xl1I/vmFYuibq9G8tsQgVF7h1Aj+YQQsEevefhcWtf/GWwPmFYsds3eGggdzN/18GAfpy6RVoBBZ95D2UVPM/yqf5MxbAJlFxlD59Y9c1nELNJ4U7/oM6o+fNLQFnD8Niz+HHfdFm0E7A83LJ55GYPPeaDd/fY/9AI220pZ7TFP3lf77Zs0/vJFcDk8l4t+Zipozmo9BVOPBqCqzqgMA7ntR5RmEo4925irxpoambQsXqT4R/LeCOeutmyxp7ZZ+8HbXB91XVeIKYRSCJEPPAkcBNQDt0spHzPp9wRwiq4pBXBKKXu2GGQvw8zmfuWpU9reSNnk44q7YStrHjq73X6t6/40LGeN2yPodDW7oa3pWYYkWfacwog+LZUVZI7csaMix0zV+9qtm7f7EaTkl9BUMZ9Nb95j2jd7/N5kb9e+U9CSkctJLzYA09vsp3+A1Xz5mmFd85/G+qi+sORntqx8AOqbjO0ev3J84s2fuTk/1D7orHsj/ACppSPalK8rBJMLugsZYtcmMd5eewQAK1z9GZ3lwuP/TrbsAjyNxtxUzct+wudxY7HFN7I91pH8I2gPhIHAIcDNQohp4Z2klOdJKbMDf8BrwBtxk3YbYUhxFkf+ZaShbc8dtIibQE77AA78IxOl5ONKLAoeCIZFWlK1vEL6GzRr7FQGnXE3OZNDis+WmUt7JHK0qWfto38DYMv7EeO1INGm269yFxn3lTk2pmMGTFg+r4e679817VN0yPnm29qjOH39Hs+UsMB4r9OBPTuffgeeQ9lFTzHi2rciRvbxJBDX/12rNufBU1AWrP/gxoanqTbUN0pt2USkN2hXyQshstDqu14npWyQUi4CngXOjGG7mcALcZBzm8JisXD6odsHl+265EdjyowX6Z9WbWTSuFSlOOgJyi5+GoBBZ95Nv+lnYbHayBi+A6CFF6YNHEX/gwTDr3mDYZe+aMwx7scapvgDcx7qFrwX96pf4SaRFbfPNE08FqBg7+Mj2i6vOZGH6g8MLhcdcj73/znadPvnG/cyLAcegivvPM60f0r/MtI7mCnS4jcr2S1GBZnavwyAvCkzTN+YEkVADqc3pMgLC4xx8Pp4+cL9Tg21b90Yf3li6DMGsEgpf9O1LaK99zJNwW8BOly2qLa2Fm8PORIdDgc1NT1bfNfhMNoc/3rgyKBM/XKMP1mRZzNYoP7PhXhH7xlXGXr6PPSUHM7lP0Vdl3v6P6l//h8A5J//FPVOH9TUgCUDRu5GTU0NLlfInBAhe3PkfIasQy6h4Y1bsJdNwL3mf9TX1eGoqaHWn0qgNbsEW9GQuJwL98ZlMfe15pfSaMnQvh+hGHMnxhG1a8D2eFlguo8/XcZw4KZmB66w72BJz8bXoj1ovCnp1DWapySoqalhfVWkCayxsZE/lqyOGMnXOVzgSNy1E+33CMixpip0H+c4NkTdj2f4zsCLANS3uLB24DcOyGC1WsnPzzftE4uSz0azw+upBdqzs58GvCil7LBHMJqw3UFNTQ2Fhd331I9FhsL8nODyKYcU8OYXq4LrvD7AAil2e1zlTobz0FNyrHj8CWODPRX8ttSiQUODN0M0uVpT03ADRQcJcmORvbCQvHMewOtqYf3zV5OTlUl6Tha1/tUNb9zC8Kv/0+YxY6VxgxOzcbs1IztiRF8mHsBqD5XQW7/FuP6arcfxjwPyGVEygKkTBzDvl5AiS02x8Z87DuGkK980bJOdk0N2YWHwuwEMPPkm1j1zGQAWRz0Fhf0wS9pRWFjIrHmRyjIrI51f1zRFjOQTfd1EuzZdaCP4Kk/oDc3jckW1mxQW9SfwflVUNiouMuiJxSbfCIQbEvPA9HcAQAhRBuxD4PGk6BL6eGNbWAy9J/DCo6JrOo3P68HdUIPP46ZBF/0B0P+wv2Mv7lwtX09KJh9+tyqmWZapxWVBs4PP6zFUVgJo3bCiUzIE9lf73Tt4Xa00LzcPgbRl5TPg5JsYdNa9FPzlRIpmnGtQ8AAbwwrlNPnSqS/QbPFut/E7Wi3atWqxRo4j3Q1Gh2Na6XDs+cW6FpMQTL8N+6252pvI+BH5oVU5RbQ4PYaRvD2/xPR7dgcr3MW80LgX/20OBUu0+NqYRGZyjuJJLEr+D8AnhNB7ViYBS9rY5q/At1LKzl+ZiiBuj9F09X8nTg5+Dq5RjtcO4ardHCxMvfXL11jz0DlUf/IcW2Y/HOyTOXoKOROn4Q2bNWnLLiR38oFEI+Ag/GLheh57c3Ewx7nL7eGwS9/l9U+iJK8KOON83sjIiz/md+j76dn6zZvUfP4Sq+45icb/fQHAoLPvN/TJ2/UwMoZNIK10BAV7HkPuTpHf77slkaNol8fLEZe9y4LfjLbkQ/wl8cITpfq8Hmo+D4390gZrKUKKDj4P0GzSlrCHC0DeLsaEgPtNHhj8vHxTK43NTgptoTeNqE7absHCz87huHSGkkKb0QSVWb5rqLffYZsxYoeESNOukpdSNgFvArcKIXKEEBPRnK7PtrHZqcDzcZFQgdtjHCXtO2UIL988g2P3G43PFxj1qJF8R1j76Pms+dfZ+Nwuauf9F9BixANkjduDkqM1E0LmvmcYth168VMUHXRu1H0HlNSmLdpL+HPvae6sc+/4FIBX5iylpdXN1nrjbMxAxIXP68Wea4w1r53333bfCHxeD5VP/R/rw7JiBmL99aSVDAvKOfyaN8idtH+b+wYYPjAyMqihyUl4xO8eEwdy2iHaJKSImHGvN1hGMLV0RHBCmD7axJaZQ+5OMwAYdvkrDD7vIQr31ZyT/fK0yKNJo0MmiiZHC40OF5mWkC8klvQLPUnWaG2UX3zEJQAM/b/nI/LsxItYQygvQNMiG4A5wE1SyrlCiDIhRKPfPAOAEGJ3YDAqdDJueDyRo/S87DSy0nUXsjLXxIx+1qVesevjsu25RcHRoK1/x9ITBLYLmA8CaaGHlITcWLc+O59Tb/4oqLhfmbOUh97w51zxemhcGpn4y7lkbhvfycfKO4/DuXkNLat/NcwkzZlojHZOKRoMwND/e46h/3ghaCZqC0ermyf/G1mQ+6UPf49oG1CUFRydjh3Wj2prqDZxw+LPSS3VRvkBk9AXP63l3tnGpF5FM85hxLVvYU1NJ7XfoOD+nC4PB+xShtVq4akG7Xu5XS5+XVFNmi6dQM+O5NumYO8TyJ44jUFn30/2eC36yJaZk7DQ2ZiMQVLKWrQwyvD2NWiOWX3bd0BWeF9F59l+hHkBb6vVQmvA1pfgijd9CZ8zFOFSNedJ0z71P35Iv0BoW4wKw+fzUbm5kYIRk2j85QsWbgrdXv/+pAKX7mH9yzIthO7wy2bx8GXTeP2TCvpb6zk6X5v63vTrNxH7d29cHvXYjpWLDcv6nDDhWSAHnalNfIpVqdQ2tPLXm+bE1Bfg8L1DE45+X1XDLRzCvwo1E03L2t/Bn4Y5fZAWdnn/qz+ThgsKMQ0xDfDhvJU0NLvol6fNSWj0afJb8dHc4iYrM/S7JvNIPnviX7BYLKSFpXFIFKpoSBLz2BX7srG6iZGD803X26wWZjsmMzZ1PVlj9+he4Xoxrq2RtuWUwgG4akLt+lF9LCNdgMsf/pqK1VvJy07l2UufZvXNITPJy3OWUlZqHpB24X3aCN3jN200/mI+Yrf1Gxz87HW1suqekyjc71ScG1fSsu6PiP6u2s3YMnIMmR2HXfYy1nZy6ujx+XwxKfixwwq55MQdWb62joKcyIdH6jG34nzz+qjbt5LCxuEHMXnvPbn35R9ZsryaF240+gUee0uropWbpZmZvH5TZSAT5Z7poXOQO2VGuzJ3J26fFbtFkzORE7LMUMO/JGZISQ47j4tMOxzAatUq0QCGKjrJhNfpMCRlSmQ+71hp3RgZDxA+SajoYOOsy9Ljr6Hs72GhlWFUrNacpXWNTt79YYthXf+CjHZzEnlNbseCvUKTkSwZoYdEoMRgzWcv0vjr18EMjwP+emuwz9pHzzekQx5x7VtY0zLalCGc31fFFrM9aUx/BhZls9eOg8w7FAwhfdiEiGZ95NjqfntiKRnNVwvXUVPfYkhf8NvKkPM7cB4DD8Wff9/A9PRQGcUR175FdhvZHhPJ+TMnmrb/6go9oLv7LUMp+V7MpprmoGMrWbNQbn7nQTa+diuuus24ajez8o5jaPrjh/Y3TCCextqItvCkYLbsfMNy5qidsOeZJ95qbHZywb2fG9pe/MBoq96y1cGGqih1RwMy+CIf1PlTjwp+1tcE3fjaLab7SCkwDgo2vn4bQFiIohGfz0dDs9N03cr1sSXNau/Zff7dn4Mlcir/h/NCWTdLi7KCkUiAQaYrHwmZr9LTtP0EHoqbqho5JHNRTHImmoN2H8aUsZHhm5YeDIxQSr4Xk55qDymGJA2hDMR7N1csoHWDZlPe9MZdPSaPx9EYUVTbLGSPDpRTfOWjpazZ2PWau+GRKPa9zmBjbUjR+Zzag6j+p+jmE2u6uTssouasjo/nr+ak6z9k1teRNv8n3jYWGj9mH3MndNSwUB0uX0jdDDztdnw+H1LnzPX54K4XQgMAp8s8j8v0XTUZAtd+Vnpov9aMns2FaLFYTJX8j63midHm/rSWZ2f/mlCZlJLvxaTYraEqNEmq5ANUf/IcTUmQX2f9C9fQsto4xcPndpI5Zpd2t/164Tre+dKYFmBrfQvvfWOeA37U4LwOyRZurnnqg+Wce+en2PP8o3B/vvGqOU+FbxrEYk+lcN+/RrZHSYgF8M3i9QDM+W4Vi//YQl1jyIE5cZQxEdlhe5TRWXz6ST8+H3O+X21Yv3qD8a0hYJYJN/HZgyl9/UU6bKH1bTluu4vw+s8pdiuLXUOpzh9Ldlik0z9f/Zn/fhF7qolOyZPQvSsSitVqSWpzTXhGPb0DcOMbd3e3OGz95k1c1aFQvX4HhOLf0/2Tcuz5JWRPnEbGiEmGbef+tJZ7Xv6RZ2b9alA6TS3GnOjDBoRiydNSOxbX4Akz17T4c8RcuHI61sy8NnORB7BYLOTvfiTDrwmlE0jp37ZiDtjddxjdn+vkPE65cQ4ffb+a5hZXMAro0pMmc/ffo+dGuuSEGFIj65S8JSWdJcuqDKvf/iLyAfriB7/xwbxVgFbUfvb9RwTXB2zye/hCs4Ojvcl0J/r0D3abhXsv1MIkK7c/neLD/m66zZLlVabt8UBF1/RiUrtxJO/z+XAs+5mMkZPaHBXqCTeL6Gn+YwErbp9J/8MuJGfiPnGSMjpeVytbw/KX60v25e12BGmDRpNRtr2hywvv/8abnxtzxv/3i2UcPU0L/3O0Gs06B+xaxlPvaG8K4SkoAA7YpYzdJwxga0Mru40fQGqKlWOv1mqcho/kXT57sL3Vko7N3WqoHjT0H8+z+p+nm35fi8WCJSUNn6sVVxuFtD1eX7DK2JatoX0/8sYiHnljUXB5n520ilfREqRFC/M1fB9rGoEznlY6HB/Vbfa/7Tlj0rPUFON1t0N5KWyCIt1M145EDiWKb39ZH/z8xFX7k5etmQM//3EtR+1jnpvmejmPt+8+LCEBFGok34uZvtvQ0Eg+wUp+/fNXs/E/d7D1y9dj3mbja7e220efRiCRuLca63+ml40L3lA5O07HYrFEKHggQsFDaAbrqg31/ONB42zS0n6hkWRRfgblYamhj9lvNDuPK2X6rkPJzUolXTfaD7fJu3U2bKfHB14fLZUh27ctI4cBp9xC/8MvNP3Og8WDpu16Pvp+VfDz/F87n+Y2K8M8YuS8o0IRNV8t1n6DwJvFyvV1pttE4/ozdzUsT98tMqeQJcXEv9KDlBRmkmLXHk6rNkR3Yrs9Pg6/bFZEQZR4oJR8LyYtxRZKa5Dg0MRA6bvaeW/H1L8jxQ9a18dmk5z1xvv8NH9x1PVtHbPy2csNy9aMnNApizJ4uuvFtqOAFlZsjmjbbmgh5UM1xd6/IIObzjVWVcrNjK6EwpW8R3d7bm104XK5In7njKHbkzlyJ9P9WVPbt08//tYv7fYJZ2hpDsfuF8off+lJk8mJ8r122X5A8HPAvBKIE6/cHD2PvRk5WcZjVNWbKESTCJ7uxuUyDrgCb3RDo8yT0NMYJcqpKygl34uxWEI2eZLMJl/9aahWTJUnu42e5pOTwmn4/XvG//EsBZ+ahw6666tZeedxEVkkAZqWzo+IlkkfXI49VzMxpBQOjNjG6/Xx7eL1Ee0BmltcfLUoZN8/63DtLSA7I4UBRdpoPtVuIzsjhctODinhbBNleMahWp4Xu92ooHw6pe/FyqbqpuDvXHz0pcF10crFdTQmPhoXHTfJsPzI5fty6sHjuOzkneiXl85eOw4235Bg0SYg9NAKzM7deZwWhXLc/mMM21zxV/NSlxlpxu9pFnKaNdr8gdedhCcUBBg5OI/iQu2hu6Gqic9+MDehhTtt44FS8r2c7jDXdGbf9T+8H/w8t0VTYracQgaefqchAx9EFnQ2Y8vb97a5PpC1cetX/45Yt+mtUP3SgafdDhYrWeW7kjl6CqUn3RCR4RAibe1gvAG/XrSeZWtrAXjttoM58i+jmH3/EVitFjz+hHKpKdrtNXXiQPadMoSnrjFPAhaY8DZ2mNGurY+tLrNXU+JYwcb/aDlp9A+maCYKi9VG/h7HMPD0O03XxzIxrbysgAN2NQ+b/MvkwTx/w4GmvoegDLpV+odWbUMrP/y2CZvVwl8PMpYONEuEBpCTaTQJmT3cctrIDtpdHOEv3Tl5u9DcBLvVitsfLXTFw1/z4OsLTXNS9c+Pz4NZj1LyvRxfN0TXNC75ukP9PS2hST+X1Pw1mEu7tWAkx/7zd5rcYTdnB/PurLh9ZsTkpYDCctdtZvPsUEy4t9VYZSttUDkjrnmDlIJSLBYLmcN3ME1b8MXPlRFt+gLrFgsU5KQxfGAu2WH26MBILmCLTbFb+b8TJxvs9XqGlOTwwCV/4YxDt2d28460DNQiVZp9sdmX23KEF+5zIumDjCPlrQ0t/Pj7JmobIqtUhRMtFUOsBJy6AENsIUdrIFWCJyyF5YhBecHzpmfYgNwIp6TVZvzdMkfvnBQzv/vlamkdCnJCTmCbzYLH6+OH3zZS6w9RbXEazYtjhxVis8VfJavoml5OQMl7PfEtAOz4/i3W16xl4Cm3sGXWQx3advX9oZqVPiykWbRR8eYGTfl9++sW9tSnN2nnARWuqAFa1v9J5vBQ/u3aeW8FPzf+MjcYqhbwJQSIRQnc/PT3hpmXk8f04+c/jJEgbo+XhmYn+04ZErF9YCSflhL7DTtqSD6rN9TzacsEUjIHUp82ihpv9FFd+ASujOE7kBXjVP5Tb/rIsHz8AWPYf+cyzvGnQn7pphl4vF5Wb2hg+5HtR820RUlhyC/Q7Ise+TJz2ijemrsMl9tj+mZg5rS0JmlSvoAzPT879H2tVgu/LKsKhqQCtDiNb4uxppDoKMl5lhQxE1DynjgqeZ/PS+vCObSs/jVYVBrAmq7Z1qM5ON0NNay895Tg8pMN+wJg96fc9flzdugTSUH75ppV950S0RaQBfz5caKkSqhf9Gmb+zZDr+AfuXwawwdE+hQef+sX3B4fGemR46TAc8RsRNoWAXPQhwvW8+0GTcEHXvnnOsYZ+qb2M/oRBpx0A7k7tp8TfmN1ZGqF8rKCYGZHgPycNPrlZTB5u2LSUrrmyNSPTNsyDu3knyW6fksTZs9hM1t1xKSjfpG+lZ5gjx0Gcv7MiZw8I1SQfMnyyHDRlz9cGtGWCJSS7wN4fJa4mmv0tT7ddaEIEq+/2HJThXmVotZ1f+DTxXEHkjL97BzOenc+Ty/TIi1afUbF6PNGTyEQzR9QsTI0Iqr99i3TPi3r/gxOwBp8zj8ZeOptUY8TDQswclDIZFFcYBxdV26KjBAJzMjsqBPNZovsf+IB2iQtfdWjzDE7d2i/en5aGhkRlJuVSoo98aogMCBZSij0caR/VnAg6sjj9WEzGaGPHpIf0WYNexoU7nNSvETtElarhYOnDm/3If9pFOdr3OXplqMoEorN4sO9tfMxzgG8rQ5qv58VTGoF4KzWIkzeJjRK9EXJ66Iv1LDZFkqU1eDL4O76w6nxasry5cbQzEmPz0JjTfRJMa2LPjJtTydkTw5UdtLTsnYp65+/KricWjyU9CFjI/q1R1lpLtsPD8W6XxgWaRJe9g5CytrMsdYWZsqtfGgB/zhpsmEUnFoUaSKKFbNRckmh5iuYff8Rhhml8eKNO42O7Z8atYf9iEF53PU37VpISw0pxPycNC46bhJH7D2SmdO0yUP6CKUANt2DaW3KsKhRRts6MZ0VIUQ+8CRwEFAP3C6lfCxK36HAv4B9ATcwW0p5WlykVUTF+ef3Xdq+ecUiaua+ijOsMIWnXhsxL63NhHytLVp+9dbWUIzvwkbzjI0Av7hCSqrJl8baP9YwKEpQhM/EHg/gqdJGQeGmo3kto5ma/ifrX7w22JYzeXpUWfR4vT6+XBhyuO4+IRTjfcgew9ll+1LSUoy3zEXHRU7nD4zkw8s2tkf4yBQ0H8K0nYbw4nuhPDiWLszqXLm+HqvVwiOXTeNv92iZM/NzEjtLNGCjDp+WcM+FewXNQeFmoUBEj9fr44i9R1KQG5mjXv9b+GLM+b8tEuuZeQTtgTAQOAS4WQgxLbyTECIF+AT4zt+3FE3hKxLEOUeMj8t+Nr52a4SCBy3+HLTReJAozsvlK0Oj2myLNtKeff8RpKeGv7Za+NSxPT+2DseLldyM6GON1oUfAvBi457cVXcYrzVpk4vcHi+umvWsvOsEAFp8KTzesB9bvZERLBlDxkW0mTH3p7X889WfAa1O6eWnhOK1zzt6IpPLiynpZ5xgtJvuQRAg08ROHwvh5pqpE0P7rraFEoW1FU2zakM9S6M48DZUNTHnu1V4vT6GlOTw1l2H8u/bD+6UrJ3DX+SDgGM69D3SIq4RDavVYqrgAbYbqptNnASToDrL/jt3PulbLLR7NQohstBK/+0opWwAFgkhnkUr5h1ewuY0YIuUUp996ud4CauIRH9zrH3iQoacF980Ae76Kiy2FGwZIeUZiEnX43U7KVz8cnB5fOpafi3VXtP/78TJ3PmC0TE626G9ft+Q9xZWnd3dXV+FNSMHa0oaXlfIJPOzczg+LGzw5HNc5vd4W5tZ98K1wZw9Gz15LHUN0hU2D9HeyNfr9bF5a3Mw7h20/CNXnRZp+y7UKZwH/+8vppEgp8wYS4rdxl8mR58kZEb4vvbRbb/UMooj/LdbNMe3y+0JVpkCOGjqMM4/emIwomhLrTHsNDXFFpEPJpG0NcO4M3JYdOcr2Ufye0wcaMhpAzCofzbrtjSyw+iihNrnYxlyjAEsUsrfdG2LALN34N2BFUKI9/yfK4BL/XVfFQlA/4rvqo4+QzMa7rotrHnkvIh2W/FwPJtX0rhEy83S0OwGv37zuiKnXtcveN+wnGd1cNcFmr21rRvYixUbISW/5mFBaslwBp99nyEW3oeFo/YZxacL1tDiS8FavwFvcyisLrCPCvdAqvPG0q9OV7TDZNJPQ7OTzDQ7NpuVd75cznPvGXN6n3pw+/b7aGUZszJSOPOwyDw47RGu5PX5YCy2FBZl7MGkxm/xuVp47aOlvPpxBc9dP50i/wQafVQQwIfzVvHhvFXMuu9wLBYLX/ykmaJiSSaWCHxhI3k99k7Fh4fO19CW9vPZ9yThs2D75aWzzp+tstXl5Zh9R7Pr9tGrwHWFWJR8NpodXk8tYDZLYgiaLf4o/9/JwHtCiFFSysjhXxRqa2vx9tA0fYfDETXTXjLK4HAYR2cdld25wpgLxlYykqwDzqF5+ULYbJ4n3eF04gs7TkuTMcpklmsPTvX3qa/XCmqMGpzLmQeP4ponQy93Xiy4nU6D3M5NK6neuB5PjaaU5rZoCvfIPQaw/+QiNj/zGoVbjDnhZzdPDn62eo0hmQ0N9bSGyXva7V+TYrfy1BVTIxQ8QLrdG5TJ7PcoykuL+3USPsu2uamRmprAA9JLq1e7XZvra3n1K02pXffEN9xxrvZWdO/LP2HG+o1byEiz88kCbbR41iEjOy17Z++Pvx21HR/N3sTU9D9Z5tKUmdl++uenx7R/h8OBy2U8X91933bkXLS0GgdG+gfdluo6Dttde2vr6HcIyGC1WsnPzzftE4uSbwTC5xnnAWalcJqB76SUs/3LzwshrgSmAu+b9DclmrDdQU1NDYWFhT12/I7KkJ1tVK4dld3ROAD9YyItv4gaSxGffP47B0WZi5ORnkFB2HFWLHgHgMfq96fCrcUrX+Lvk5ahla3rX5DFhPIhZKX/QlOLdoN6fVbweINy1/r3l+VuYOMczbdf683i+rN2pbCwkHyvD7ctMtbbXTSKNy6exrFXv09m/SqwgC0rD09THfkDh5Guk7fVX3HI5fayaIV5Sb6srKygTOG/x/M3TCcjzU5menxrdYZPjiksyKewULM7p9jtLE8ZzZ6Ff1C859HwlWb+mrxdaVC20n5ZrN0UeVs6fWmcd/sXAOwwuojRwyL9CLHS2fvjoD0LefebtVy8JTRRLnw/D182jYKcNPKy23cE19TUkJObi/7X6+77tiPnYrthRSxeFlLgqSl28EeIZWZmdlr2WGSI5R3pD8AnhNC/v04Clpj0/YW25zwo4sznP67t0vbOzUZbYHPFfC7911d83xrKMviuf5S8wa1FeGz9/EU2vHYr3lYHjUu/MxTBDih4PYGp7QFH2zTdLFEPFlMb85b3HsXr0BTWvJbRjPebGKLFno8f1T+4/0Bx8/ypRzPwtNtJHzTa0Le6LhSx87NJJkmN6Jdxv7yMuCt4MA+hDLBqQz3zVzoZcv4j/Fqliyrx+YKhmuEPiQAX3f9F8PPebSQTSzTrtoRU8p1/2yNi/bABuTEp+ACWaOlDk5ATp5cbltcb6v0mVmW2O5KXUjYJId4EbhVCnAEMR3O6Hm/S/UXgMiHEDOBj4CSgCJgXP5EVeqpqzUMMY6W10tyWGcg3A7DUNYixwwp5ePWB3FHwHwAcKxaFZqKaxCcLXR7xgf6sjLv4E3HlZoVuZJ/FGnSeumpDCldfwclJSpszL79tGU1xUU7QwfibcxBT0//EYk8lffB2Ef31sw+/WrguYj3AgH5tZ85MBOE2eW+UBGI3PBlycS3+s4ojr5jNfjsPMRT9iEZ+B5RovAk4GiE+fgFLkqY1MKOtnDSjw2oOxJtYz9IFaI+bDcAc4CYp5VwhRJkQolEIUQYgpVwGnIAWNlkHXAgc1hF7vKJjdCWhkaepjsZfI5OPjRqch8sXUqq13kxOPXhs9NwjJpOjDt0zVLh4u2GFvHjjgey14yAAKjeHTAoWi410dwMta5cy5+vo07zb+p7/ad7dkJs86OAzK9ANLKusjbqvSWP68/iV+zJ2ePeb7MLfUrzeSCUfnsM+YJ757IfQG920nbTR+hNX7RexfW5WbEnPEsFu47WH/ISRRXFJJNZ7xvHRKS7MZMLIovY7doGYAnqllLVoYZTh7WvQHLP6tlnArHgIp2gfswk0seKsMjf1bKhqwkNIyTf7UikuyDSkijVjkbOMa8/YhR1GR06E0sc6GybfWK3kOzey/sVr+ax+OtubZ5k1sN42iIEebQT+QP0MgGBseFqqjfcdkzhor1Fkj4s0CQA4XZHmoX/ffjALftvE3pMGJSSnd2fQ508fP7IfS5ZXG0bxo4fk86cu7BO0maF7TRrEhcdNMq0yNLB/97+hBAg8qJsc7aeW7uvk56RR29CakNTC4fSe9x2FKWUlnU8Fu+X9xyPaFrSOCDpFQ1giqvKY8XLjngwoyooo7hBOhq7kXSmhkelFuR9H9J3jmBjRdt+WfYKfV7m1BF5n+yeFDSnOpsmXTv5+ZxjSLATY2tBiGPUGyExPYZ/Jg3tcwV9+yk48evk0bjx7N4YPDM1yzUyL/C5mynJ0WT5Wq4UUuy2ikPjbdx/WoyN5u//cruhg2b9oJEFW4Q6x16RBwc+BNM/d8XsoJd/LOXqaeWHg9vA4GiLy3cx1jOPt5l2Cyw/Uz+D3/tp0iFgSWLmwGyYLRUPveLXTdqjsNy3lQQUelN3/ltHsDd0gI/wKcVmlpkD+74Ev8Xp9yP/+wjtfLuP9b1dy2KXvGtLs9vcnGyvM7fnizwH23nEwZaW5TPFnZQyQnRmp5I3OO40snUM43I/RHUnI2qI+zqXtkiF3fEfQV7wK+Km++1/7VdG6isro08ux2aztqElzAtkZA1y99fgIm/sqdzFPL7OSlWGLebJKtFqfekoLM9vtE8CN1fSV9uXGPajzhvYTGIEfs+9o3vz8T1ZtqOeIy6NbDVPsVs48bHvufvFH+ufHLk9PEa6gbzl3d4PpJoB+ApVdlybhmWsPSJxwMVLXGP/6pb2Nl26agc1m4el3l5g+pBOBGsn3csKtC7GW6rNmGM080Zyqbo/XYBaY1zLatN9Cp3mJODM64iz2+Mz7/uAcyR/uULx3QAnuuUNsOcVL+2UGJ8IW5rX/9tHThFdxKsrPYMcxkb4P/cPYYrHw7HXTeeuuQ4P1RXuSRL5J5My4IGH7jif5OWnkZKaS2Y5JM54oJd/LiYjIaGmO0tOIc0soPv53p1ExThrTnyP2NE+atMRlHme92NmxJEtXnDLFtObpZo/x4ePGxi5h073107/vOH8P/nrQ2GDu7mipBsIpyEkPOmC7WhijOwhPkzCkJIfLdAnUotG/IKNb89O0RSKtK2nDIn03yUxgYNG5dA4dQyn5Xk54dI3P6WDNI+ex8T/mxZsD1H7zZvDzE40hZTtsQC63iqnsP8V8VmSN1zw6w+uzcvM5u8cqNnvtOMi05qkzrKCIF0vEjXDtGSG/wYRRRRy3v7GGaSw5QLYbVojTHajFmvy3wcD+2ZSXaaFHgeik3KxUZt9/BC/dNKMnRYuZRE5e6kqUWU9w9D6j+MdJk3nrrkMTfqzkv7oVbRI+kvd5PbjrttD8548xbb+hzJjIPXCz6Pd71D6ac/dvMyeywVPA4w2R8deF6R5DdfrOMtgemlJxY+1MdiqPjCG2WCwcsfdIbj7X/KESXhz6mtNDD4VhAzRFmZFmZ8p2JaTYrYaY/mRm1GBN9um7Gk1jvUy/cVFY4ZV40JsmRoFmspy205BuieZSjtdeTvgIZu1jbdsm3fXVWNMytSpJVhsri/ZCy1yh4fNPsdbPvgxU5zlo6nAee+sX1rgjFW//1K7NvDWj1ptFTX2r6brwiBs94dkY01Jt3HDWrtTUt7ChqolVG+qx2yz0L8jg7bsPi6vMiSRQIDzcntvTYZ+xksiHUW+LtOlOlJLv5dg7YGrwNNez5uFzAUgpHsZmZzr/XhhWVNs/CNY/PMKLYLjNnKGpiXHsrdwQWUO1o3i9Pnb2p1RodLhoanEzY7dhXd5vdxNIrBZeYKM3+BT0JCJTi7WXjeS7E3Vmejkdcdy467YEPzuamli5qSVqX32VovCCxG7dbNirtx7Pdy2jWJHb+eLS4Wz0hCYBjR4cwxTYMGbsPgwgGFGiD8HMzkjhgmN2IL0boxsSTW/wKUBotO2LkpOnS/vuJW8zPUHfudK3UWK9wVs3rWLds1cElx1NzbT6Qsr0nCPG89S7SxhaqinVth4eXp0DrdmXxuvNU6GiqqOim1Lvy+KfdQeTZtHCNq84qePlDQNZGY/ddzQTRxX16FT+eBJ4uwpPVxBQnoOLk/t7JtKiYk3yylA9iVLyvZwUu5XnGvfmjOyv2uzX+IuxUmOarwWn7uc/ZM8RtLo8HLLH8GDb7PuPiNjPqQeP5cUPfudzxzj+pyvI3Vleb9qNE7JCRci9WGglhVZ/FszOjFJn7D6MTxasYcrYkmDVpL5A4Fy43JFzIR6/ct8ezTAZCydOL6e2odUwvT9e2HrJ20xPoJR8L8dmtbDS1X5US+Ov3xiWUy0eQ7iizWrh2P3GhG8WwfRdh/LiB7/zrsMYox0exhgr37WO4bvWMQy1beEfeR9GlIbrjENtTFmB6QOqt3PCfsPZY1IZk8ZE/t6Dizufw6i76JeXwXVn7pqYnauRfFTUmenlWCwWg/kkGracyPzdrb6OP+PzstM4dM/hEe1DupAoDWCrV4uZ1ydpePvuxMcQ9yYsFoupglco2kIp+T5ALEo+d8fI2aVOv0nkmes6ltfEbNSuz5PSGTz+S1Gv5MMdvgpFNCxqJB8VdWb6ANHyvG/99q1QH5PCHq1+a11xQcfCH/Vl6gKTi9oqXdcWB/kjYQKmozXeYu6/eG/+78TJbWylUIShgmuiEtP7uhAiH3gSOAioB26XUj5m0u904BlAPzPmSCnlp10V1OVyUVlZSUtL9LC/eOD1etm0aVP7HZNEBpvNxk7l+fi2WLGEJSfb+sWrZI3emdTiMnzuyAyA240s5e/Hd3xKvH7UvmpDPQBbtsaWMyecE6aX8+F3q3Bh5566QxkyaiSHlBUwJsEl0RR9g5TCAbhqNqC0fHRiNco+4u87EBgJfCKE+F1KOdek7w9Syt3iJWCAyspKcnJyGDZsWEJnt7ndbuz2nvVHxyqDz+fD5XKxb7OXlnWHkbHo3Yg+LZVLSS0uw+uKnDmamZnRocLJAcxmWNY2ms9MbY/A7M1TDtqOKduV9JlwR0X3MOCUW2ldV4HFpM6wQqPdd2whRBZa6b/rpJQNUspFwLNoxby7jZaWFvr166emL+uwWCykpqaSV1iMtzCUBTJ354NDnaxWPI5Gar/WCnBfXHMqtV4trNDaSZt3YIblHjsM5MpTtSib3cabJzRrj/Q0O/+95zCO37+ckYPz260qpVDosecUkLVd3MeUfYpY7qgxgEVK+ZuubREwPUr/iUKIKqAGeAXNtBNpEO4ESsFHwWJlqy+bQE5HfQFri82OY+ViQ/dANaZUb+dG3xaLhddvO5iMNDtWq4U97+9a3HN3pFtVKLZVYlHy2Wh2eD21gFnM3FfA9sBq//9/A17g1o4IVVtbi9drtC97vV7c7rg8K9qku44Tbxn0zteWlpDybmpuoWXB64a+rzTtgcj5nOqsYdTU1Jjuz+FwRF0XoDX+Ock6Jce2IEOyyJEMMiSLHMkkg9VqJT8/37RPLEq+EQhPIJIHNIR3lFKu0C3+TwhxC3A1HVTyZsJu2rSpW2zlvckmH40UTysBNZ9hg+b6LYb1v7kGc3HNqZxfWExhYaHpPmpqaqKu606SQY5kkCFZ5EgGGZJFjt4iQyzvyX8APiHEWF3bJGBJDNsmIuGcoh1Si0Lmk+qPn4nar7NhjwqFovfQ7nBRStkkhHgTuFUIcQYwHM3penx4XyHEQcDPUspNQojtgOuBN8P79VVmz57Nyy+/TGVlJdnZ2UybNo2///3vZGdrESMrVqzg4Ycf5ueff8bn8zFu3DguuOACJkyYENyH0+nkiSee4KOPPqK2tpbi4mKOPvpoTjnllJh9ErbsUPhh3q6HUfd9ZNQNQIpd+TgUir5OrEO5C9BG5RuAOcBNUsq5QogyIUSjECIQ2rEf8IsQogn4AHgbuD3eQicjL7/8Mg8//DAXX3wxX375Jc899xzr16/nggsuwO12U1lZyVlnncWoUaOYNWsWH374Ifvssw8XXHABS5aEXoquvPJKfvzxR/71r3/x5Zdfcsstt/D222/zwAMPxCyL3vHaUlkR/PxdyyhDv8z0lC58Y4VC0RuIyfArpaxFC6MMb1+D5pgNLF8GXBYv4dri8x/X8MmCNe137CA+ny84Yj5glzL2ndJ+gerGxkaklNxwww1MnToVgIEDB3LXXXdx+OGHM2fOHObPn8+ECRO44IJQ5aYTTjiBlStX8vDDDyOlZMGCBcyfP5833niDQYM0k8uECRO49dZbOfPMMznuuOMYPNi8kLYefcxwa+XS4Of/NBtDzbKUklco+jzKKBsHfvnlF5xOJ9OmTTO0Z2Zmsscee/D999+zYMEC9t8/Mn/MAQccwKJFi2htbWX+/PmMHz+ekpISQ5/x48dTXFzMDz/8EJM86YPMM0J6/T93IP1uRrqKSVco+jq99i7fd0pso+yO0pnIltraWvLz8023KyoqYunSpdTW1lJUFFkbtaioCI/HQ319PbW1tfTrF5ktMtBv69atpuvCsWXlMeLat1j9r7PxNEZuM3XCAGZ9vYKSwsSU7FMoFMlDr1XyyUR+fj61tbWmD4iqqioKCgrIz8+nqiqyelJVVRUWi4X8/Hzy8/NZu3at6TEC++kIetu8njMP255j9htNTqb5eoVC0XdQ5po4MHHiRFJSUpg715jKp7m5mXnz5jFlyhR22WUXPv00Mk/bJ598Etx+l112YcmSJRHJyQJtO+20U4fksqSYK3GbzUpBTnqH9qVQKHonSsnHgezsbM455xzuvfde5s2bh9vtZv369Vx11VUUFhYyY8YMzjnnHH755RceffRR6urqaGpq4vXXX+e9997j/PPPB2DXXXdl55135uqrr2b58uV4PB7+97//cf3113PYYYdRVmZunsrOMDpQP12whq8XrsNqMpKfMrYkok2hUPRdlLkmTpx22mnk5eXx4IMPUllZidPpZMqUKTz66KOkp6dTVlbG008/zSOPPMLhhx+Ow+EgKyuL++67jylTQqX07rnnHh5//HEuuugiqqqq8Hg8nHjiiVx00UVRj12QY8wk+a9/L9T+Fy4Ptj3T8BcArjl9l3h+bYVCkeQoJR9HjjzySI488kgAZs2ahZTSkINm1KhRPPjgg4CWpuGMM85gyxZjyoG0tDT+/ve/c8kllwBw4403smLFCtpEN6epPpimzEilpx8XHLNDpwpjKxSK3otS8gni8MMPx2azsXjxYkpLSyPWl5SU8NBDD/HFF1/Q3NxMZqZ5pMv111/Pyy+/zNKlSw0zY/UEdPxddYdR508jHI4XCzP8VZgUCsW2g1LyCeSQQw5pc/2oUaMYNWpUm33sdjunn356O0fS1PwGT/Tom1qv+QhfoVD0bdS7ex9ApdlXKBTRUEq+D9Be4rJKt6qXqlBsqygl3weIpuNfadTy6FhVxmeFYptFKfk+gM2ksDaAG60Wq9WilLxCsa2ilHwfwGKx0C83cgarx6f9vBZ8bD/CPCeOQqHo2ygl30ewmozmA3Vfcy0OLjlhx+4WSaFQJAEqhDJOLF68mIcffphly5YBMGTIEIQQjBgxgsMPP5yMDC1+PTc3l+nTp3PWWWdx0kkncf7553PQQQcF9/P888/z8ccf8+KLL3a51uzYlEoAMqwurCoER6HYJlFKPg40NjZyySWXcOmllzJjxgy8Xi+//vqrIerl008/JS0tjeXLl3P++eczePBgrrvuOq655hp23XVXCgsLWb16Nc899xxPPPFEhxW8/ljTdhrM3J8qgyN5gJwslXFSodgWiUmTCCHygSeBg4B64HYp5WPtbPM8cBowVkq5tK2+vZ01a9bgdrs59NBDg2077qiZR9avX2/oO3LkSHbccUeWLVvGzJkz2Xfffbnnnnu48847ue222zj55JMZPXp0l+QJZJjc5MkPtmWkqee5QrEtEuud/4i/70BgJPCJEOJ3KeVcs85CiH3QCn4njIZfvqBh8edx36++/F/ODvuSM3GfdrcpKysjNTWV66+/ngMPPJDx48eTn59v2nfZsmUsXLgwWAbw4osv5vjjj+eKK66gqamJM888s8vfYfzIfrz9xTKWuAZzND/g8SlTjUKxrdKu41UIkYVW3/U6KWWDlHIR8Cxgqo2EEKnAw8Df4ihnUpOdnc2zzz5Lamoqd911F9OnT+f888+nsrIy2OfAAw9k2rRpXH755cycOZPDDz8cgKysLK666irmzp3L9ddf32U7PMCg4myev2F6MDrepkIoFYptllg0yhjAIqX8Tde2CJgepf9VwBwp5a9CiE4JVVtbi9frNbR5vV5DRseMcXuSMW7PTu2/LbxeL1Zr6NmnP2ZbDBo0iKuvvhqADRs2cNddd3H99ddz8803A/D++++TlhZKCezxeIKfA3niy8rKcLvdEd81VrkDOB2NpFtT8WUVAlDvy6KmpqZD+3M4HB3eJhEkgxzJIEOyyJEMMiSLHMkkg9VqjWo9iEXJZ6PZ4fXUAjnhHYUQo4G/Al2K1zMTdtOmTXEZ5bZHZ2q8hjNkyBBOOOEErr322uC+7HZ71P2G9+mMDPoH07AhWtbLEw8cx8PvTCd3wGBuLizs0P5qamoo7OA2iSAZ5EgGGZJFjmSQIVnk6C0yxBIn3wjkhrXlAQ0mfR8HrpZSNsYkYR9h1apVvPjii2zcuBGfz0dNTQ3vvPNO1NTA3cWm6iaWuUv5eW3H3goUCkXfIRYl/wfgE0KM1bVNApaY9N0PeEQIsVEIsdHf9rUQ4tSuiZncZGZm8vvvv3PmmWey9957c9JJJ5GZmRk01fQUW7Y6evT4CoWi52nXJiClbBJCvAncKoQ4Ay1q5kzgeJPuA8KWNwBHAT91VdBkpri4mDvvvDPq+h9//LHN7QcOHNhun86QrsImFYptnli1wAXAU2hKux64SUo5VwhRBvwGjJNSrpFSbtRv5He8Vkkp1ZCymxg2IGRZ22fyYD6ev7oHpVEoFD1NTEpeSlmLFkYZ3r4GzTEbbTsVoN2NPHPdAWRnpASXy0ojfOMKhWIbQ73P9yGKC4x1YrN0Cl+hUGybqCyUfRi7Tft5C3PT2umpUCj6Kr1qJK9POaAI4fNFn9F61wV7UtovM+p6hULRt+k1St5ms+FyuUhNVdkUw3E4HKSkmJtmVLEQhWLbpteYa/Lz89m0aVNEuoNtGZ/PR3NzM+vWraO4uLinxVEoFElIrxnJFxUVUVlZSUVFRUKPE567pifoiAwpKSmUlJSQmxs+KVmhUCh6kZK3Wq3BRF6JpLfko1AoFIpY6DXmGoVCoVB0HKXkFQqFog+jlLxCoVD0YZJNydt6WoCedroqGYwkgxzJIAMkhxzJIAMkhxxJKkOEDrW0NZGmB9gT+LqnhVAoFIpeyl7AN/qGZFPyacDOaNkuPe30VSgUCoWGDS3V+w9Aq35Fsil5hUKhUMSRnjcqKRQKhSJhKCWvUCgUfRil5BUKhaIPo5S8QqFQ9GGUklcoFIo+jFLyCoVC0YdRSl6hUCj6MErJKxQKRR9GKXmFQqHow2wzSl4Isb8Q4nIhxKAelmN7IcRwIYTdv9ztv4H/+Pm65W6vji6EKBFCpHf3cU3k2FMIsYf/c48U0RFCHCCEuFsIMbYnjq+TY5IQYoIQIse/vE1em/7j9vj1Ga9rs8+nNRBC5AIvAn8BbgDelFJu6AE5BgAvACOBzcBPwHVSytpulKEEeB0tx8VW4FXgBSllvRDCIqVM+MUghBgCSCAXcAH3AJ9JKZ2JPraJLBOBRcAKKeUof1u3nAf/sbKA54AD0K7Nd6WUa7rj2GFylAAvAeXAaqABOF1KuaUbr4sevzb9ciTF9RnPa3NbGMkfhJawp1BK+XAPKfhMtJt5hZRyJHA/MBA4pptFuRNYLaXcDvgPMB14sLsOLoQ4Evgc+BM4yv9fALt0lwxheID3gCYhxK3+tu68J3bDn1jKf232hIK3Aw8Da6SUQ4FLASdwIUB3KVd6+NqEpLs+43Zt9lklr3vNOwT4XUrpE0KcIYS4RwhxqBBioL9fd5yDEUAe8JR/+W0gEwje1Il8LRVCWPyv4MOAD/3NDwF3A8cIIfb1n59En4sy4Ekp5cVSyi3AxcD2QFaCjxuNoUA2cBVwlhBisJTSI4TorroGRwHVUsoWIcTZQogn/dfoSOg2U0UJUIqmUJBS/gBUA38EOiT42rT637aH0bPXJmjXQ7Jcn3G7NvuUkhdCjPX/pfovjEwgFVgjhHgS+Id/+Wo00wlSSm8C5UjzNzUBg4DxfpkmA2OASUKIA/xyxHXE5DcFIIRI8e87Fe2G3uo/nkdK+Q3aq+mD/ra4ngudDIHz8CLwir8tXUrpAKqA/Hgetw05wu2aW9HMZj+hvRoHRkxxV/JRZGhCuzYfA/4OrAdOBmZBYkbR+uvC3+T2/x8vhCgVQkwGZgAThBB/TYQcfrv7IP++vUA63Xxt6uXQKc6X6ObrU38u/MsBnRy3a7NPKHkhRJYQ4h3gC+Bp4G0hxDgpZTOwBbgOSJNSTpBSXgIcCwwTQpzp3z4uIxUTOd4SQmwvpVwJXA7siJbv+RvgZWAIcJ8Q4pR4ySGEyBdCvAksBpBSuoQQdillNfAzcGXYsZ4EfEKIg7p67DZkaPXbE2ullOv9bS1CiFKgH/BlvI7djhzusC4jge2klJvRfp+DhBDfor2iJ0wG3Y1cj2ayGwDsIqW8SUq5P5AhhAj/neItR+C62ARcj1bL4WPge+AJtPvmLiHExf7tu6wrhBD9hBD/BeYAbwghHhJCDPGf/8V0w7VpJgfwgBBioJSypruuzyjnYqDuYRa3a7NPKHngeMAupSxBOwmbgVlCiAzgZqAA2NF/Yi1oRUnmAjtAXEcqZnK8I4TIk1L+G7gPWA5MkVLegHZRf4tmf+yyHEJz7r6IZgrKCygKQr/zDcDeQogZumM1+OXM7MqxY5DBbAQyCdgkpdwYj2PHIkfYSLoWzQYLcBLaiLLcv13CZAACMtyLNoLdHc1HE+AVYA+Iz7XZ3nUhpfzSL8tSYD8p5W1SyvvQBirH+B/QXRpJC82R+D5Qh2YCeRDt4XaBv8u1JPjajFEOPZNIwPUZowy1xOna7CtKfje0E4aUcomU8kw0x8X1UsoqNA/5IGCclNLnv4gGEFYmK4FyXOFfvxMwTUq5xN+nGW00/1Wcju9Ei1C4EO2CuVkIkSmldPpHbSvRzsXjAbuv/wLOB+J1IUeTITiC1Y0Kdwfm+9tOE0J8JoTYrRvkCCjZUuB6IcQitNKTF6KZL45PsAxOIUSaP2LjerRrZG/ddsPx28i7QY7AbzEZLQJtrW67kcDsOA2C+gP/Bc6QUrqllP8B1gFegG66NtuSwwJB/1Wir882ZfATt2uzR+KCu4IQYjwwHs2ZuthvT6sGGoQQuVLKen/XS4FnhRCPSSnvFEJMBf4lhJiP9oS2oNm7ukOO54QQj0sp3xVCNAshXgA+A85Gc+p0qq5tuAxADfC2lLIFWC6EuBDtlfeUwDZSymv9dteXhRDfo11AzWiRBImWweKXITAqHAtsFkJ8AmwHXCil/L4b5AgwD8189h8p5TP+/djpnnMRUG5PCyG2By4XQsxAc9KnA7d3RoZOyGEFvFLKL4QQm9FMF18CR6Mp2Lu7KMNSKeUitDfWpX5fWYqU0uX/njmBbeJ9bXZGDv8DLfBQi8v12ZlzQRyvzV4TJ+9/ut4PnIPmhT8QuAUt/OtINGV6rv8kBrb5CfhUSnml0OJwt0czjWySUj7QzXJ8LKW8WgixK9oNNBH4QkrZ4Zsoigw3Aa9JKTcIIWx+T/wUtJHIjlLKX/yjx1b/uZiEFl5a6X817y4ZrFJKr9/euR7NwfRPKWWnlFpn5fBvmw54/DdZp+nCuUj1j6Yz0ZTIPoBTSvlIN8sRuC7God0fU4EfpJT3xkmGm/0yrNf9/jY0c8Q9Usr3dbIVo/muOn1tdkUO3fYlaGbdTl+fXZEhXtcm9C5zTSmaYtpZSnkscCbahXCJ397tAk4QQhTptvkACHjPN0spP5dSXtVZBd9FOYb4TSbzpZRXAod2RsG3I8PZoEUn+O2oP6JFET3jb28VWtTAJinlR1LKSzp7E3VBBq/fVLARLURtWGcVfFfkCCA1B2RXo2k6ey6c/t+jWUr5s5Tyn51V8F2Uo1UIkSGl/E1K+SBwQmcUfBsyzADO8h8r8BaXgxYi+ItOtlQp5eY4XJudlgO0aDCpOaS7en12Wgb8Cl7EweGd1EpeaBEBgRtwZzRv8+/+p/6bwDvAXkKIXdCcmAcAx+tsrqOBb6UWktXpV5Y4yhGM7pBSeuIswyxgshDicH+fgH3vAmCEEOIxIYTHL1+niKMMVwFIbQJQQw/KcaVfjg79FomQobPEUY6A36jD4YqdkAFgHNAopVwrhDhcCLEGTQl2mjjKEXgodvj6jKMM4Q+CTpOU5hohxGjgUTSHlAf4P7QR8sdoppAv/P0Gor2O1kspLxNCnA+cjvaKlY3mXD1aanbJXilHB2W4ES0i4QapOXURmr33C7RwvduklM/1RhmSRY5kkCFZ5OikDDdKKZuEEDehmYbq0KLcrpRSvtRRGZJFjmSQIRpJp+SFEGehKcxX0FIBPIZmG/snWliiRUp5rq7/34DDgEPRRilD0CIVcqWUD/dmOTopw8FoHvhmtIiiCuBpKeXFvVWGZJEjGWRIFjm6KEMrWrTPQcD9Ugsn7hTJIEcyyNAWyWiuGQ7cIjXbeQVwKnAE2qj4M6BMCHGSrv9XwF5Af6mFI62UUr7QFQWfRHJ0RoZ9gByphYpWAsVdUShJIkOyyJEMMiSLHJ2VIc9vtnwWGBIHpZYMciSDDFFJRiX/BJqNG6FNh28EVqJNiJiLNiPvRqFNKAAt9vx9tPDFviZHl2WQUjb1ARmSRY5kkCFZ5OiSDFLKD6SUNV2UIVnkSAYZopJ05poAwp9WUwixA9pr0GSpRSPkAf9CO1EtaBM2zpFSvtVX5VAyJJccySBDssiRDDIkixzJIIMpPp8vqf/OPffcS84999y3TdrLzj333KO2JTmUDMklRzLIkCxyJIMMySJHMsig/0vaGa/+kCMPsCtaEh+EEOfhL/4hpfwTXareviyHkiG55EgGGZJFjmSQIVnkSAYZzEhacw0Ep/G+j5YF7iC0iJVzpJSfbGtyKBmSS45kkCFZ5EgGGZJFjmSQIZykHcn7GYs2sWgiWnhRV2bA9XY5lAzJJUcyyJAsciSDDMkiRzLIYCDZlXwFcBnwmNSSK23LcigZkkuOZJAhWeRIBhmSRY5kkMFAUptrFAqFQtE1kjFOXqFQKBRxQil5hUKh6MMoJa9QKBR9GKXkFQqFog+jlLxCoVD0YZSSVygUij5MssfJKxRxp7y8/Au0OqataAW1a9Fqnj5WUVHxRYz7uAnYp6KiYp9EyKhQxAs1kldsq9xRUVGRU1FRkQfsBvwIfFReXv73HpZLoYgraiSv2OapqKjYANxTXl6eAdxdXl7+Elo5tqvR0sK2AJ8CF1dUVFSVl5efDFwD2MrLyxv9u9mroqJiYXl5+a7A3cAEtLziLwI3V1RUuFEoegA1klcoQryGVuhhd7QanKcBhWh5wEeg5QSnoqLiFeAO4OuKiops/9/C8vLycrSHwaNACVr5x8PoYrFuhaIrqJG8QhFirf9/YUVFxau69sry8vJ70CoAtcUFwDsVFRVv+JdXl5eX3wnc7v9TKLodpeQVihBD/P+ry8vLpwE3omUVzEB7681qZ/vRwLTy8vLDdG1W1BuzogdRSl6hCHEC0IxWk3MdcB1wSEVFRVN5eflRwNu6vl6T7TcCL1ZUVJybcEkVihhRSl6xzVNeXl4KnITmTL0U8ADpQK1fwY8ArgrbbCMwtLy8PK2ioqLV3/YY8El5eflHwGz/foYDoyoqKuZ0w1dRKCJQr5GKbZVrysvLG8vLyxuABWjO1oMqKioeraioaAQEcIs/euYV/5+efwPLgA3l5eW15eXlkyoqKn4ADvRvuw6oBt4EhnbPV1IoIlH55BUKhaIPo0byCoVC0YdRSl6hUCj6MErJKxQKRR9GKXmFQqHowyglr1AoFH0YpeQVCoWiD6OUvEKhUPRhlJJXKBSKPoxS8gqFQtGH+X/iNj/FZx5YpQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D1rtCB2WfmyU"
      },
      "source": [
        "Calculate the covariance matrix of the array"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cxvHoZ7kfZ4T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "outputId": "9fd8628b-b3ea-404f-d496-fda5cb19b685"
      },
      "source": [
        "S = stocks_dem.cov()\n",
        "S"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "          QQQ       SPY\n",
              "QQQ  0.000191  0.000156\n",
              "SPY  0.000156  0.000153"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-48f692d4-f01c-451b-ac73-f356aa6c839b\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>QQQ</th>\n",
              "      <th>SPY</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>QQQ</th>\n",
              "      <td>0.000191</td>\n",
              "      <td>0.000156</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>SPY</th>\n",
              "      <td>0.000156</td>\n",
              "      <td>0.000153</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-48f692d4-f01c-451b-ac73-f356aa6c839b')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-48f692d4-f01c-451b-ac73-f356aa6c839b button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-48f692d4-f01c-451b-ac73-f356aa6c839b');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1KWln54jf243"
      },
      "source": [
        "Calculate the eigenvalues and eigenvectors of the covariance matrix"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2Nden9m5fvFw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7b54a5f8-1d62-4217-f79b-090aedd3b598"
      },
      "source": [
        "EIG = np.linalg.eig(S)\n",
        "EIG[1]"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.74856963, -0.66305619],\n",
              "       [ 0.66305619,  0.74856963]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VR9I4ZNmgMll"
      },
      "source": [
        "Eigenvalues:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J2kyv36SgBys",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cede420a-fb5c-40fe-e8cf-6948ef5ff8f0"
      },
      "source": [
        "print(EIG[0])"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[3.29325761e-04 1.40413575e-05]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bn15azRKgQEH"
      },
      "source": [
        "Eigenvectors:\n",
        "\n",
        "Each eigenvector is one column of this matrix\n",
        "\n",
        "We can see that the vectors are orthogonal to each other. This is also true for eigenvectors of higher dimensionality."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mdczQowFgGzc"
      },
      "source": [
        "evect = EIG[1]"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dp8qGt5Wg3CV"
      },
      "source": [
        "Plotting the eigenvectors:\n",
        "\n",
        "First, we create some x-values from the array R containing our time series."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4WMkFuQogTnc"
      },
      "source": [
        "xx = np.linspace(np.nanmin(stocks_dem.SPY),np.nanmax(stocks_dem.SPY),200)"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "dx1 = evect[0,0]\n",
        "dy1 = evect[1,0]\n",
        "slope1 = dy1 / dx1\n",
        "\n",
        "dx2 = evect[0,1]\n",
        "dy2 = evect[1,1]\n",
        "slope2 = dy2 / dx2"
      ],
      "metadata": {
        "id": "kJCDvKg8jM3x"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "yy1 = slope1 * xx\n",
        "yy2 = slope2 * xx"
      ],
      "metadata": {
        "id": "AHLEmmdjjqlE"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uKEn0vo-hjSO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "outputId": "a4574fe2-2a11-43f8-c304-abf744d0eddd"
      },
      "source": [
        "# Plot de-meaned x - y correlation\n",
        "plt.plot(stocks_dem.SPY,stocks_dem.QQQ,'.',alpha=0.5)\n",
        "\n",
        "# Plot the first principal component\n",
        "plt.plot(xx,yy1,label='first component')\n",
        "\n",
        "# Plot the second principal component\n",
        "plt.plot(xx,yy2,label='second component')\n",
        "\n",
        "plt.legend()\n",
        "\n",
        "plt.xlabel('Values of R0')\n",
        "\n",
        "plt.ylabel('Values of R1')\n",
        "\n",
        "plt.grid()\n",
        "\n",
        "plt.axis('equal');"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZwAAAEPCAYAAAB2s3LUAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAAsTAAALEwEAmpwYAABU8ElEQVR4nO3dd3wUdfrA8c+2JJveCzVKGZqICKJ0BCmKpz8rcoqi4qjA2U49xI6onF1RHPUQu9j7ISIKWECQQ1FgEKSnh03Z7CbZ9vtjkxggCUlIdlOe9+uVF7sz35l9dkny5NsNPp8PIYQQorkZgx2AEEKI9kESjhBCiICQhCOEECIgJOEIIYQICEk4QgghAsIc7ABasFBgMJAJeIIcixBCtAYmIA1YD5QdflISTu0GA2uCHYQQQrRCI4DvDj8oTWq1ywx2AEII0UrV+PtTEk7tpBlNCCEap8bfn5JwhBBCBIQkHCGEEAEhCUcIIURASMIRQggREJJwhBBCBIQkHCGEEAEhCUcI0e75PC5yP3uOzLfuD3YobZokHCFEu+Ytc5C19EGKf/ka6/EDgh1OmyZL24hm4/P5MBgMwQ5DiFq5i/LJWjqf8rz9JJ09i6j+Y4IdUpsmNRzRbOau+Ddv/fpxsMMQokbluXs58ModuAqySb34Dkk2ASA1HNFseiV248Oty4gOjeQsZWywwxGiinPP72S/twCDyUKHy+YRmno8uTYnOTYHyXHhJMVZgx1imyQJRzSbS088j1zHQV7d9D7x4bGc1vnkYIckBPYt35PzydNYYlNInXInlthkcm1O3lq+DY/Xh8lo4JLxvSTpNANpUhPNxmg0MnvIFfRMPJ6Fa5ewNfePYIck2rmCdZ+S8+HjhHXoQYfL52OJTQYgx+bA4/WREh+Ox+sjx+YIcqRtkyQc0axCzCHcPvw6kiMS+feaRewvlF0fROD5fF7yvnqZgyuWENHrVFKn3o3JGlV1PjkuHJPRQPZBByajgeS48CBG23YZfD5fsGNoqdKBXcEOoq3IKcnnzhX/xmw088C4W4m3xgY7JNFOeN3l5H7yNCVbfyR68JkkjLsCg9F0RDnpw2lSxwG7Dz8oCad26UjCaVK7bPu4Z+VjpEQmcd/pNxNukR9q0bw8TjvZ7y2gdO8W4sdeTsyQs2WofmDUmHCkSU0EzHFxnbll2DXsL8zgse9fwO1xBzsk0Ya5C3PJeHUupQe2k3zuTcSe+jdJNkEmCUcE1ImpfVAHX8rm7G08v/51pIYtjkWuzcnvf+aTa3MecrwsezcHlszBU3yQtEvuIrLv8CBFKKqTYdEi4EYfdxoHnQW8vfkT4sNjmdr/3GCHJFqh2oYyO3b9QvZ7j2AMDafDtPmEJHcJdqiigiQcERT/13sieQ4bH239ksTwOMZ3HxXskEQrU30oc/ZBBzk2B2H7fyL3s2cJSexI6sV3Yo5OCHaYohpJOCIoDAYDVw28GJuzgP9sXEqcNZbBHU8MdliiFTlkKLMBYnatIHftO4R17UfqBbdhDIsIdojiMDJKrXbpyCi1ZlfqLuP+b55kb+EB7h59Iz0Tjw92SKIVybU5ycm3E/3bu7h+/5qIvsNJnjwLg9kS7NDau9YxLFpV1VjgBWASUATM1zTtuRrK9QMeAwYB8ZqmGQ47HwI8A1wMuIBFmqbd3YBQ0pGEExBFpcXc+fUjlJQ7mDfuVjpEpQQ7JNFKeF1l5Hz0BI7t64k57Vzix/wdg0HGQrUArWZY9EL8TX0dgLOA+1RVrWkZVxfwDnBlLfe5G+gPdAcGA1NVVZ3e9OGKYxUdFsUdo2ZjMBh4cNUzFJQWBTsk0Qp4HEVkvnEvju0bSBh/FQmnXybJpoVrUf87qqpGABcCd2qaVqxp2iZgMTUkFU3TdE3T/gP8XsvtpgPzNE3L0zRtN/7aUG3JSQRZamQS/xoxk8LSYh5e/SylrtJghyRaMJcti4xX7qA8ezcp5/+TmMFnBjskUQ8tKuEAPQGDpmlbqh3bBPRryE1UVY3DX0P65VjuIwKre0I6Nw69ml0F+3jix//g8XqCHZJogcoydpDxyh14nMWkTb2HiF6nBjskUU8tLeFE4u+3qa4AiDqy6FHvA1B4jPcRAXZyhxOYcfJU/pf5Gy9ueFMmhopDOHZsJOP1ezCYQ+kwbT5hnXsFOyTRAC1tWLQdiD7sWAxQ3Ij7UHGvyseNuY8IgnHdhpPvsPH+li9ICI/jwn6Tgx2SaAGKNq0g7wuNkOSupE6ZizkyLtghiQZqaTWc7YBPVdXe1Y4NAH5ryE00TbMBGUD1iR0Nvo8Inov6TWZ0+mm8+/vnrPzzh2CHI4LI5/NxcPVS8j5fhPW4/nS4bJ4km1aqJQ6LfgMIxd/pfxywArhY07RvDitnqCh3PP6BA1YATdNKK87PB0YD5wARwFfAQ5qmvVzPUNKRYdFB5fZ6WLDmOTZnb+P2EddxUpp0wbU3Po+bvP++QPEvXxPZfwxJZ16LwdTSGmZEDVrNsOiZgA/IBJYB92qa9o2qql1UVbWrqlq5MFJXwMlfo9ScFV+V7sNfo9kJ/AwsbUCyES2A2Wji5qEz6Brbkcd/eImdB/cEOyQRQN5yJ1nvPkzxL18TO/wCkibPlGTTyrW4Gk4Lko7UcFqEAmchc79+hHJ3OQ+Mu5WUyKRghySamdteQNbSBynP3kXixBlEDxwf7JBEw7SaGo4Qh4i1xnDHyFl4fF4eXLWQojL70S8SrVZ5fgYZr8zBlb+flAtvl2TThkjCEa1Cx+hUbht+HXlOG/9es4gyd3mwQxLNoHS/TsYrd+AtLyXt7/cR0WNQsEMSTUgSjmg1eiV144ZTr+SP/F08vXYxXq832CGJJlSi/0TmG/diDIug4+UPEtaxR7BDEk1MEo5oVU7pNIDpAy9i/YFfWPy/pTIxtBWpbXdOgKKfl5H9/iOEJHel4+UPYolPC0KEornJkA/R6kzsMZo8h41Pti0nMTyec3tPCHZI4ihq253T5/Nh+/YNCn74kPDuJ5P8fzdjDAkLdriimUjCEa3S1P7nkO84yJu/fkSCNY4R6acEOyRRh5p250yMNpP72XPYf1tN1EnjSZx4NQajKdihimYkCUe0SkaDketPmUZBaRHPrX+VWGs0J6TIulot1SG7cxoNJEVA1tIHce76lbhRlxA77HwMBsPRbyRaNZmHU7t0ZB5Oi+cod3L3ysfILcnnvtNvIT2uU7BDErXItTn9NZuQMlz/fZTyvP0knXUdUf1r2u5KtHIyD0e0PeEhVuaMnEm4xcpDaxaSV3Iw2CGJWiTFWekR5aD0w/sot2VTNnIWpZ1la4H2RBKOaPUSwuOYM3ImZe5yHly9EHt5SbBDatXqGk12LJx7fyfj1bl43S5Wp17Ksr2RvLV8W5O/jmi5JOGINqFLbEduHX4tWfZcHvlOo9zjCnZIrVLlaLJP1uzkufc3oe+2Ncl97Vt/IPPN+zFFxOIcezs2Swop8eF4vD5ybI4meQ3R8knCEW1G3+SezBwyja25f/Dsulfw+mRiaEPl2ByUlLrIynewL9vO0hX6MddACn/6jJwPHic0rTsdLp9PUucuhwwgSI4Lb6LoRUsno9REmzKsy2AOOgp57Zf3SbDGMu2kC4IdUquSHBdOuctDidNFRJgZi9lEjs1BUpz1kHKVAwCS48KPOFfJ5/NycMUrFP70GeHKEJLPuQGjJZQkK1wyvtdRrxdtjyQc0eZMVsaS5zjIZ9u/JiE8jrOUscEOqdVIirMyZVwvlq7QsZhNRFjNR9RAapvEWZ3XXU7uJ89QsvUHogefScK4Kw6ZY5MUZ5VE0w5JwhFtjsFg4PIBF3DQWcCrm94nPjyW0zqfHOywWg0lPY7rzj+x1hpITZM4q5fxOO1kv7eA0r1biB87jZghf5M5NgKQPhzRRhmNRmafOh0l8XieWbuELTl/BDukViUpzkrf4xNqrIUcPomzeg3IXZhLxqtzKd2/neRzbyT21HMk2YgqMvGzdunIxM9Wz15Wwl1fP0pBaSHzxt5KpxhZFLIp1NSHU5a9m6y35+NzlZJywW1Y008IcpQiiGqc+CkJp3bpSMJpE3JK8rlzxb8xG808MO5W4q2xwQ6pzXHu+pWs9/6NMdRK2pQ7CUnuGuyQRHDJSgOifUqOSOCOkbOwl5fw0KqFOFwy0bAmtU34PNpE0OLfVpP59nzMMUl0vOJhSTaiVlLDqV06UsNpU37N2spDqxfSJ7kHc0bMwmySMTOVaht5Vv24y+1lWP8O9OwSV7W1wIGV71C+9h1MHXrT6ZI5mMIigv1WRMsgNRzRvvVP7c21gy9jc7bOovWvyeZt1VQfeVZ99n/l8UirhR37bCxft4e3lm8jJ7+E/Z88T/nad9gf0Yd3jWexVi+UZWpEneRPPNGujDruVPKdNt7e/AkJ4XFM7X9usENqEWobeVZ5fH9OMRigU0okDruDws8ex7R/E3/EnMreTuPZvjWH4rLd/Lwtu8Z5OUKAJBzRDv1f74nkOWx8tPVLEsPjGN99VLBDCrqkOGuNs/8rj2/fa+P7Xw5QXlzIsOx3MZUeIHT4NPSsLuTnOMAHnZKjsDtdNa5MIARIwhHtkMFg4KqBF2NzFvCfjUuJs8YyuOOJwQ4rYGpblqbycWVzWvWkkxRnpXuMi+JPFmB0HST5/FuI7HUal9ic/mT0awZ2p0vWRhN1anGDBlRVjQVeACYBRcB8TdOeq6XsLGAOEA18AczQNK2o4ty3wKmAu6J4tqZp3RoQSjoyaKBNK3OXc/83T7C78AD3jL6RnonHBzukZlfXsjQ1nQN/AkpwZVH238fweTykXjSHsM69jrivrI0mqmk1gwYW4q95dQDOAu5TVfWILQFVVT0DuKeiTEfAAjxzWLEbNU2LrPhqSLIR7UCoOYTbR1xPgjWWBWueI6M4O9ghNbuqQQDhFjLzS/h6/Z6qjv7DBw5s32vjreXb2PTN1xS9Pw+v0UKHy+cfkWyg7pUJhKjUohKOqqoRwIXAnZqmFWuatglYDFxZQ/ErgJc1TdtUUauZC1ysqqrU50W9RYdFcceo2RgMBh5c9QwFpUXBDqnZ5NqcFBSXYS8pZ+3mTHbuL+Crn/by8qe/kWtzHjFwAKBjwf84Netd7JZ4HGNvIyRRtvAWjdeiEg7QEzBomral2rFNQL8ayvYDfql8omna1oqHPaqVeUBV1XxVVX9QVfX0pg5WtA2pkUn8a8RMCkuLeXj1s5S6SoMdUpOrbC77aUsWpS4PEVYLCTFWQi0msg862L7XVjVAYPyQrkw5Q6Fr1kpOyvucXGs6P3aaRnKHDsF+G6KVa2kJJxJ/v011BUBULWULDztWWK3s7fjbETsAGvCpqqo9EKIG3RPSuWno1ewq2McTP76E2+sJdkhNqnpzWWS4hajwEMpdHvIKneQXOfnih13ou/1Jp0/XGAw/LKF8w4eYlRFE/e2fXDTxRGkuE8espY1Ss+MfAFBdDFBcz7LRlWU1TVtX7fgrqqpeAkwGnmiaUEVbM7DDCcw4eSovbHiDlza8iTr40la70vHhnfjVm8siwiycN6oH/9uew/qtWZSWuck+6ODtFdu47m+98Kx8FufO/xE77ALiRk1ptZ+BaHlaWsLZDvhUVe1drYlsAPBbDWV/A04E3gRQVbUXYABqW4e+ZQ3HEy3SuG7DyXfYeH/LFySEx3Fhv8nBDqlONY0Oq20kWuU8G7PRiNvr5bi0aH7elo2j1E10ZChRxlKK3p+H0baPxEkq0QPHB/ndibamRSUcTdNKVFV9D5inqup0/E1iVwIX11B8CfCGqqpv4B++/ACwVNM0R8XQ6iHAKvzDoi8GRgI3NfubEK3eRf0mk++08e7vn5MQHsfpxw8Ldkg1OmSdM5eHYSd2pGeXODZsyWZPZhFd06Ipcbr5ev1eOqdE0bNLHMlx4by1fBsHi0rZk1lEYqw/SXWxlnBG7gcYcWCddCP7YnqRbHNKM5poUi0q4VSYCbwIZOLvz7lX07RvVFXtAmwB+miatlfTtK9UVZ0HLOOveTizK+5hwZ+AegEeYBtwrqZp2wL7VkRrZDAYuGbQ37E5C3lhw5vEhsUwsENN41aCq/oQ5/Vb8ikpdbFyw17+PFBAkcPFzgOFhIYY0ffmE2Ix0Tkpih5d4sjKLyEjr4RiRzkhFhODEu2cUfQRFrMJ61lzeecXFx7vnlq3jxaisVrcxM8WJB2Z+NmuOV2l3PvN42QUZXPv6TfTLT64y+4f3nxWWcPJLywlM8/O4D6pbNt9kMz8EhylLjxe/3VhISbCrWa8Hh/J8eHsySzCB3i9PgZHZnCB6Rss0fF0+vvdbC8IYfm6PVXbR48f0pW+xycE9X2LVqlpJ34qimJUFGXasUQkREtmtYQxZ8RMosOieHj1s2Tbc4MWS2VyqVytObeiuatyGHP3znHYnS5io0LBB16vv0MToLTcQ0FxOc4yN9ERIURY/aPUTo/cwUWmFRgTOtHlyoexxKfVuX20EMfqWIZFW4CXmyoQIVqiWGsMc0fOwuPz8uCqhRSV2YMSR23bB1RKT40mOiKEQb1TmHhaV0ymQ0fJmA3g8/koKinHYjIwOWwjZ5m+h44ncPyV8zFFxAAcksSkOU00tTr7cBRF6VLH6bAmjkWIFqlDdCq3j7iO+799igVrnuPu0TcSag4JaAzJceG4XB70PTYiwswkx4WTa3Py8qe/oe+1UWgvw+P1YTYZSIi20jU1muyDThylLnyA0WQkLMRE3y7RdP1zBceVbuHPiAH0P/smjCGH/ihXLtYpRFM7Wg1nN/5+jJq+pANetBtKYjduOPVKduTv5qm1i/F6vQGPoczlwe4op9hRzoatWXy9fi+24jJ8Ph/lbi9uj4/Sci8H8krYnVmE2+3F5wOfD1xuD13izZy0/22OK93Cvg7j2Jx8JrmFZQF/H6L9OtootYPAZfhHhx0urJbjQrRJp3QawPSBF7F441IW/28pVw1s/kmRlQMF9mYWsy+7GJPJyJ6sInbsLyA0xITXC44yF4eP/fF4wVNttYRoHPzN/jmR2PjIPYpi9wDiwo3SRyMC6mgJZxOQqOv6nsNPKIoSyl/9kkK0CxN7jCbPYeOTbctJDI/n3N4Tmu21qs+zySvw9+GUuV2UV9RcylxeXO6j17RSjQVcG72CcF85r5SNY0t5Gmk2B1POkD4aEVhHSzgPAiW1nCsHjtg2QIi2bmr/czjosPHmrx8Rb41lZPqQJn+NXJuTdb9nUlLqomtqNKXlbuJdXvbn2MEH5fVINADdzNlcHfkNbkw875zEnvJ4AA4WlfFnRgFKelyTxy5EbepMOLqur6zjnA//TH4h2hWjwch1p1yGrbSQRT+9SmxYNP1TezfZ/SsHA9iKy8jKt1NkLyc81EyvrvF4vZBbUIKtuPyo9xlg2c1lkd+R743kQ/PZGBLjMWYV4/V6cbk9fLfpAIN6p9arliMbrImmcCzzcCIVRbmvKYMRorWwmCzcOuxaOkan8dj3L7Dbtr/J7r19r40dBwootJdhd7optJfyZ2YhG/Vs9uUU1SvZjArdwuWRq9nrTuBZxyRyPRGceVo6XVKiiIwIISU+gsiIkCOGV9ekpjlAQjTGUROOoijDFUW5WVGUsyqeGxVFmQ38CVzU3AEK0VKFh1iZM3Im4RYrD61ZSF7Jwaa7uQ9cHv/sTaPBwMGCUvZm23GW1b1tggEf54av57yIDWx2deGlsgmkpKVgMhopd3u57rwT6dEplk4pkUSEWeo1aOBoc4CEqK86E46iKFfjbzabA3yiKMrtwJfAjcCtQN/mDlCIliwhPI45I2dS5i5n/upnsJfX1uVZfz27xNE5JQqL2QT42JNtpz49NmY8TItYzZiwrawq7cXrzpFYw8MptJdjMhro0SkOJT2O688fwN9GdKv3xE5ZfUA0lTrXUlMUZTNwv67r7yqKMhV4Bf/qArN0XT96vb51S0fWUhP19HvOduaveoYeCccxd9RsQkyWRt8r1+bkqaUb+WOvDcdRajSVrIYyro78lu6WbD52DGRlaV+O7xDDxNPS8Xh9VcnmWGKSPhzRAI1aS62zruvvVjxeWvHvTe0g2QjRIH2TezJzyDS25v7Bs+tewetr2MTQXJuT3//MJ9fmZMPWrAYlmzijnRuilpFuzuVV+3BWlvYjPMxCYow/McRFhREfc2wLgyTFWel7fIIkG3FMjjYsuioh6bruURSlWNf1Y28zEKINGtZlMAcdhbz2y/vEW2O5/KQL6nVdrs3Jy5/9TomzHLPJyIHc4nonmw6mg6hRXxOKm0XF49jhTiU8zMSgXikUlpTx3so/cHu9dO8Yy7XnyTbRIriOlnBCFUW5u9rzsMOeo+v6/U0flhCt02RlLPmOg3y+/WsSwuOYrIw96jXb99rQd+djNBmxO1yUlrvq9Vo9zZlcFfUtpT4LTxVPJNMTR0SYie6d4rA7y9mTVUx5uQeDAXYeKGD7XpskHBFUR0s4P3Lo5M51hz33AZJwhKhgMBiYNuAC8p0FvLrpPeKtsQztcnKd1xzILcZmL8dgAJfLW6+90E8O+ZOpET+Q64nmeftYCrwRAMTHhGMyGemUHMmfGYW4PV5CLCZMxmNZGF6IpnG0iZ+jAxSHEG2G0Whk9qnTKfy2iIXrlhAbFk2f5B41ls21Oflmw756LVHj52Nc2G+cHf4//nCl8B/7GJw+/8rVMREW0hLCCbWYsDtd9OwcR1GJv5kuLiqUnl1kVQERXLLjZ+3SkVFq4hjYy0q4a+WjFDgLuX/sP+kc0+GIMu+s0Hntv/VbeN2Al/PD1zMiTOfnsnTeKBmGBxMAcVGhXDJeYVDvVICqEWXVH0tzmgigGkepScKpXTqScMQxyi3JZ+6Kf2Mympg/9jbiw2PRd9v4Y7+NELORd1ZsJ7seM/ctuJkWuYb+Ifv42tmXT50D8VVbOzfUYuSqs09g0rD0Znw3QtSbJJwGSkcSjmgCu237uHvlYySExTM65iI+/XYvLo+XAns5Xu/Rf/4iDKXMiPyGruZcPnAMZk3Zkeu2mU0G+hyXwI1TBkpNRrQEDZuHoyhK42euCSGqpMd15uoTryDDnsV7f75NgcOJ1+urV7JJMBZzQ/QyOpnzWWIfVWOyAUiOs2IxmVj3e6asdSZarLqGruRXPlAU5f0AxCJEm5Rrc1KUFU3n8uGUhWbj6/grBfaj77TZyZTPTdH/JdJQyrPF4/nF1fWIMkYDdE2JIi0hisx8O5t35MsCm6LFqmuUmktRlHBd1x3AGYEKSIi2pHKl5YOFZeRkxGOI64UpdRvm8lDc+5Var+ttOcD0yFXYvaE8XzyBHG/MEWUirWamT+7LSUoK637PZPMOE13Tosg+6CDH5pCmNdHi1JVwvgK2KoqyE7AqilLj3ji6rp/eLJEJ0Qbk2ByUON3Yip243F6ce7tiNpZg6bALX7kVT06XI64ZEvIHF0esJcMTxwvFp1Pkq3mxzKH9OzL+1HT/NX3T+PNAoSywKVq0uhLOZcAFQDdgGAHabE1V1VjgBWASUATM1zTtuVrKzsK/knU08AUwQ9O0oobeR4imcvgil8lx4did5eQXlmI0GgADrt29MVhKsXTdgq88FG9BSsXVPiaG/cqk8F/Y6krj5eLRlFFzV6oBKCguJdfmJCnOSlKclUvG95Ih0KJFqzXh6LruAt4CUBSlq67rgdpsbWFFXB3wJ7uvVFXdqmnaN9ULqap6BnAP/ua+P4ElwDPA5Q25jxBNpbL5zOP1YTIauGR8L8Dfz+IodeP1+SpWETBSvnMAob1+IqT7L5RvGwz2GC4MX8vQsB2sK+vG2yWn4a2ji/WEbglEhocc0nRWmXiEaKmOtrQNALquzwBQFCUZ6ALs1XU9p6mDUVU1ArgQOEnTtGJgk6qqi4ErgcMTxRXAy5qmbaq4di7wP1VVr8P/B2B97yNEk6i+UVn2QQfb99rYl11MzkEHHq+XQwaleU2UbT+Z0D5rCemxkXP3+DiNDL50nsAXzgFQbY5NdUYjmI1GSl0eXC4PyXHhsnWAaDXqlXAURYkBXgXOrjjkUxTlM+ByXdcLmjCenoBB07Qt1Y5tAsbXULYf/mY0ADRN26qqKkAP/KPv6nsfIRqt+i/76huVudxeVq7fy86MAmxFZdQ4AtodgmV7P0L6rGN1Vy87tw9ivbNPra9lMIDSOY6cAgcul5e8Aiff/LyX3ZnFWMzGqlqVJB3RUtV3Rb/HACtwQsW//YFQ4NEmjicSf39LdQVAVC1lCw87VlhRtiH3EaJRKpvQlq/bw1vL/cvTXDK+F+OHdOWEbgnkFjgpKnHVnGyAJGMRN4V+y7SMQgqMZn5NLwCju9bXiwyzVDTXGSlzediVWcTHq3ei7zlIpNUi2z+LFq++CWcicImu67/rul6m6/rvwKX4O+Sbkh3/AIDqYoDiepaNrijbkPsI0SjVm9Aqf9lXDhTYsDWb/TnFtS7K2dWUy43R/yXM4OKD3HGU7jgJQ3gxId03gaHmazxeL0P6ppGaEEFpuRuzyUi41UK528u23Qdxub0yOk20aPVNOBbg8JlkzorjTWk74FNVtfp06gHAbzWU/Q04sfKJqqq98Dd8/9HA+wjRKMlx4bjcXvQ9h/6y377Xxu7MItyemqs2/Sz7mBW9HKcvhCeKJrHXk4i3MBnX7j6YYvOwpP8ONWxSYDIa6ZgcybRJfeiUHEV4qAmvx4fZCCEhJpBlqkQLV68+HGAN8IyiKP/Qdb1EUZQI4Cngu6YMRtO0ElVV3wPmqao6Hf96PFcCF9dQfAnwhqqqb+Bf8+wBYKmmaQ6ABtxHiEYrK3djKyrDUermYGEpSXFWiuzlFDvKa9zXZliozgXhP7HPE88Lxadj9/3V3+LJ7YwrpBRLx534ysNwH/hrSwOz0YDZbGRfdhE9u8Rx45SBFYMSitiVWUTX1GiZ8ClavPrWcG4EBgM2RVEyAFvF8xuaIaaZ+P+8ywSWAfdqmvaNqqpdVFW1q6raBUDTtK+AeRVlMgEvMPto92mGeEU7VVmTybY52HmggGfe2cjytbv5ePUOnEdsEe1jsnUjF0WsY4urIwuLxh+SbCq5D3THndsRS8edmBL3YzZUXu3DUepC32Or6i8admIHxg7uSkSYRSZ8ilah3qtFK4piBE4BOgP7gPW6rtdv4/XWKR1ZLVrU4ftfMnj+w18ptvtHoZlMBixm4xHJxoSHKRE/ckron3xf2oP3HEPqnGODwUtoj40YY/Ix7hmMrzAZi8VfflDvFHw+GD+kK32PTwCOnGwqRAtQ42rR9W1SQ9d1L7C24kuIdq9nlzhS48OxO8rB48Pn81F2WLIJpZyrolahWDL53DGA5aUnUNscmyo+I5aMwRjC1+Lu8jOhe4cTUh6HwWjEWeohwmo+pCYjEz5Fa1HvhCOEONLpgzpTXFJORn4JnsMGl0UbHKhRX5NmKuAN+1B+Ku9e7/t6yo3EZQ+jIHUlvvSfOP/4q+iW1AG31ys1GdFq1bcPRwhRTeUcnG17bISFmrGGmLGY/qq5pBgLuCn6vySainnBfnqDko3RAB6fj6ICA+H7T8NohC9z3iEtzULf4xMk2YhWSxKOEI2wfa+N/MJSIsMthIeZ8Xi9uCqGQXczZ3Nj9DJMBi/PFE1gm6tjg+6dFGclNT6CEIuRDjFpzBx0NXlOGwvWPEeZu7w53o4QASEJR4gG0nfb+OKHXezPLmLt5gz2ZhVT5vK3pw2w7Ob6qK8o9oXxZNEk9nsSGnRvkwHKXV6S46x06xjLtEl9GHJcH2449Up25O/mqbWL8XprnhgqREtXr4SjKMpMRVEGVDweoCjKbkVRdiiKMrBZoxOihcm1OVm6Qif7oAOz2QQYKCl1ATAqdAuXR65mrzuBJ4smctAb2aB7G4CUhAiO7xDLyb1TuO78E1HS4wA4pdMApg+8iA0HfmHxxqXUd3SpEC1JfQcN3AK8W/H4AeB9/MvHPAaMaYa4hGiRcmwOfD7/iLT8wlIAPB4v54ZvYEzYVn4p78Jr9uG4GjgeJzTESEK0lfS0GCKsZob0Tavqq6kc9nxy4hDyetn4ZNtyEiPiObf3hCZ/f0I0p/r+VCToup6jKIoZGA5cBJQD2c0WmRAtkL2knN2ZRTjL3bg9XkIMXqZFrGFg6B5WlfbiQ8cgfA1sqTYZIcoawpWT+xIZEXLIKLTD99i5+IzxHHQW8OavHxFvjWVk+pDmeJtCNIv6/mQ4FEWJA04Dtum67sDfAtDUa6kJ0WLl2px8uW4PLo+X0jI3Ib4yrg7/ioGhe/jYMZAPHIMbnGzAv+3A5OHHMeSEtKrJnL//mV9Vs6m+QGheQSnXD76MfskKi356lV+ztjb12xSi2dT3p+NDYAXwEvBOxbH+wJ7mCEqIliTX5uT3P/PZsDWLopIyHKUuorFzQ9Qy0s25vGofzsrSfhx1QmcNYqNCiLCG4HL7ql6r+pYHZqOxao+dyqVrzCYz/xym0jE6jce+f4Hdtn1N/I6FaB71bVK7Af/WzeXA6xXHovH35wgRdM21vEtlAihxutl5oABnmYskXz5q9NeE4mZR8Th2uFMbfN+wECNerw9nqRuj0cAf+2xH1GiyDzpwe71cMr7XEe8tPMTKnJEzuXPFIzy0+lkeGHcrSRENGxEnRKDVey21digdWUutVTi8n6OuXS8bmph+/zOfT1b/SZnLza6MQtI5wMWmryj1WXi+eCyZnrgGx2syQkp8OP27JfFnRgFd02LweH2MH9KV5Ljwer8XgH2FGdz19aPEWWOYN/afRIZENDgeIZpB49dSq1i483b8S/wn67oeoyjKBKCLrusvNmWUQjTU4bWC2pbor29iqp6UzEYjuzMLcbk99CjfxkXW78n1RPO8fSwF3sb9cjeZjJS7vGTkl5ASH1EVT2USrKlGU5vOMR24bfi1PLDqGR757nnmjvoHISbpWhUtU32b1O4FJgNzgRcqju0EHgIk4YigSo4LP6KfoyaHJ6bte23k2ByYjcaqNcqAQ5LSyb1SSE+LokfBjww0ruEPVwr/sY/B6QtpVKwWs4FQi4kQi4kQs5FhJ3YkNir0kOTS0MU4+yT3ZNaQy3nyx/+wcN0SbjztKowGmdMtWp76JpzLgJG6ru9TFOX5imN/4m92EiKo6lsrqJ6YXC4PKzfsxVHqJtfmoFNKFAYD9O6aQH5hKZ1SIrE7XODzcnLhCrqXbOR/5em8Zh+GB1OD4osIM4MPOqVEEhZqZm9WMS63h4y8EhJjrFWTO4/F0C6DyHcU8Nov7/OqNZYrTrrwmO8pRFOrb8KJAvYfdswEuJs2HCEapz61guqJaW9mMR+u+gMfUGAvwwd4vT527i/EYjaSmW+nZ1oEnbe8itu+kXWcyDuOE2noBlAhFiNms5EOCRGcM8q/gOfqTfuxhppxlrlxN+EyNZOVseQ7DvLF9pUkhsczWRnbZPcWoinUN+FsBv4P+KDasbOB/zV5REI0o8rEVFBcBgawGP1NT2UuD+GhZgweHz06x+F1FjLZ8QGuA7tZbRnJJ3nH4fE2bICN0QBmoxGzyUhUeAg9u/hrMj9vy8bj9RERZmnSHToNBgPTTrqAg85CXt30HvHWWIZ2ObnJ7i/EsapvwvkX8JWiKOcAYRXNahcBsraGaJUSY6wkxYbj9fqIjwmjvNyDx+ej0F5OuKuA0UXvYPEU8UXIRL7JS8Hr9VKfdGM2GXB7fBgNEBFmIS0pgl7p8dgdLnJsDvoen9CgQQENZTQYmXXqFRR8W8jCdUuIDYuiT3LPJn0NIRqrXj2Luq6vAwYDBcC3QAgwXtf19c0WmRDNxL9iwG4iwy2EhZo4e9jxJMZaibSG0De6mAn5rxFOKV/GXMA6e0e8Xh/1mT2QGBNKr67xDOqdTNfUaM4d3Y2uqdHYHa5DBjMkxVmbdV+bEJOF24ZfR0pkIo989zz7CjOa5XWEaCiZh1O7dGQeTpv0+5/5LF+3h5T4cPZkFZEYYyWv0Ili2k+f3UspNVj5OPRvlIUnU2gvJzOvGFctnTehIQbAiMVooFvnWKLDQ7BYTFXDroFmq80cTW5JPneueASj0cj8sbcRHx4b0NcX7VqN83DqlXAURRlZ2zld11cfU1gtVzqScNqkqtUDSl3sziiiQ2IECbkbmOhbRaYnjiVlZ1DgsRJqMZGeGkNGfjEHC8uOaFIzGCAyzEJ8dChREaHERYdxzohuLWob6N22fdyz8nGSIxK47/RbCA8JfkyiXWj8xE/8zWiHq/z5a9gYUSGCrHK02rrfM8ELQ1lPZ9+37PR1ZHHxSJyEAF68JiP5RQ7MJuORyQYICzFhMhuJigjhhO6JVUvRVC7A2VzL7TREelxnbhl2DQ+tXshjP2jMGTELs6lhWycI0VTq9Z2n6/ohfT2KonTAP+nzg5qvEKLlOTwBnNI7mbANr9O55Bc2eXvwqXckHosXXB4MBv9CnMUOF263F4vZiNvtBQNEh4cQGxlKVGQIJqMBnw/2ZBYTYTVX9dM0ZLmd5tY/tTfXDr6MZ396hefWv8asIZfLxFARFI36U0fX9QxFUf4B/AR83LQhCdH0Dk8AU8ak4/zyGY4v+YV1pkF8Vtofa5iZEK+H+KgwzCYDxU4XzjI3Lo9/rozJaAAD+PARGx3KsP4d2LwjD4/PR7nLzXlDulcllfoutxMoo447lXynjbc3f0JieBxT+58btFhE+3UsdWsfkNZUgQCoqhoCPANcDLiARZqm3V1H+QuBBUAK8D0wXdO0AxXnlgBT8a9wXSlB07SypoxZtA7VE0BBTg5F78/DYNvLz7ET+K6kG+UuJ87yMiKsFjomRTJ+SFde++9WikvKMZuNmDAQFmrCWebB44X9OXYK7WVYLCY6VQw++GO/jfiYMJLirPVebieQ/q/3RPIdNj7a+iUJ1jgm9BgV7JBEO1PfxTunHXYoAv8v8x+aOJ678e+z0x2IBFaoqrpL07SXDy+oqmpvYDH+CanfA/8G3gSq/xQ9rmnav5o4RtFCNKSPpDIB2LP2MSLrbYw4cI+cyfqNJpxlpcREWigt99K9Ywxur4892UX4DIDBgNHgTzaRYSGUlDoqfmh8lDjduFwe9mQVsTujCHwG/jxQWNV81pzzbRrDYDBw1cAp2JyFLN64lDhrDKd0GhDssEQ7Ut+G3PsO+7oO+AP/6tFNaTowT9O0PE3TdgOP1fEalwL/1TRthaZpTuBO4FRVVbs1cUyiBTp8o7Jcm/Oo15ya4uD07NcIN7nJGzKbj/6MJMJqwevzERcdhtEAuzIL2Z9dxGff7cLuKCfE7N8ALTLMwqDeKaSnRdMhKRKzyUSOzQkGA8elRZOeFkPXtCg8Xh85NgfQ/PNtGsNoNHLDaVfRPb4rT61djJ63M9ghiXakvhM/jzvsq7+u61fqut5kM8pUVY0DOgC/VDu8CehXyyX9qpfVNK0Q/zC86uWvUVX1oKqqG1VVvaipYhXBd/jWy5W/5OGvHTork1CuzcnKDz8h9oencfgsfBk3lc+3w44DBXRMjiQ9LRqX20dkRChut4+4aCsGg38UWmiIfxCmvdTFD79lEB0RQp/jEkiKtZIYG4bFbKRzSjQRVnOLaj6rS6g5hNtHXE+CNZYFaxaRUZQV7JBEO9GShqpEVvxbWO1YAf6FQ2srX3jYserlnwZ6AMn4az+LVVWtdT6RaF1q6yOpqeaT/9MXDMp8l1JrCp/HXEK2J5pOyVHgg/3ZdlxuL8WOctxuD8XOcjLy7DjL3CTG+Pti0hLDiQoPJTTEjKPUzZ8HCsgvcrJ+SxYut5eeXeK4ZHwvxg/pGtTRaA0RHRbFHaNmYzIYeXD1Qgqch/8oCdH0au3DURTlGzj68lG6rp9enxdSVXUZta+9tgc4qeJxNGCveBwDFNdyjb2ibHVV5TVN21jt+Beqqr4OnA+01Ymq7UptfSSHjA7LL+Hgt28QsuW/ZId3Z33y/2Hymonw+bA7XXTvHMew/h0oKinjw1U7cLu9mAwG0pIiiLKGMKh3Cj06xfHxmp3s2GerGhIdGW4hvUMM+7PtDOvf4ZB9bFqT1Mgkbh9xPfd98wQPr3mOe8fcRJglLNhhiTasrkED3zblC2maNvFoZVRVzQBOBCqb6gYAv9VS/LeKspXXRuOf3VpbeVnDp42paUuCyppPTn4xJ+d9jqV4M1EDxhF56mVEF5ZV1YSqJ6pcm5MNW7LZvr8Ao9FAQVEZKbHhDOmbRlKclekxfdm+1wb4F/38ct1u7A4XCTFhVStAt1bdE9K5aejV/Pu753n8hxe5bcT1mI0yl1s0j1oTjq7r9wUykApLgDtVVV2PfyTczfgnmNbkdWCdqqqnAz8C84C1mqbtBFBV9QJgGeAAxuEfZHBOs0Yvgi4pzsqU0V0o/PQJTMVbiRs5hdjhF2AwGEhOiDykXPXHpw/ugtvrJSHGSn6hk2Endqx1B874mLAWNfrsWA3scAIzTr4EbcMbvLjhTa4dfGnVxFchmlJL6sMB/wi43/BvX/0zsLT6kGhVVe2qqo4A0DRtK3AV8BKQD/TGP1S70g3AAfz9Oo8AMzRNWxmA9yCCyF18kPJPHsSUo5M0eSZxIy6s1y/Pnl3iSIix4vH6SIix1llzaYmjz47V2G7DuaDvmXyz6wfe/f3zYIcj2qj6Lt6ZADyJv6aQXP2crutttf6djize2aqU5+4j6+0HcDuKKRt+LYl9BjcoKbSEtc+CyefzsWj9a3y760fUQX9nbLfhwQ5JtF41Lt5Z3xrOU8Dx+OffOPB3vq/HX4sQIuice7eQ8epcPC4Xq1MvZdneyHrPz6nUFmsuDWEwGLhm0N8ZkNqHF39+i40ZtXWHCtE49U04Y4ELdV3/CPBU/DsVuKSZ4hKi3uxbfyTrzfsxRcTgHHc7tpDUGufnHM3h83faI7PRxM1DZ9A1tiNP/PAiOw/uCXZIog2pb8KxVpvkWaooSpiu638CJzRTXELUS+FPn5HzwWOEpB1Ph2kPktS5S6PWMGvMygVtVZgljDkjZhIdFsXDq58l254b7JBEG1HfhLNTUZS+FY+3AjMq1lezNU9YQtTN5/OSv2IJ+V+9TLhyCmlT78EUHlU1P6ehkzDrWrmgPYq1xjB35Cw8Pi8PrlpIUWlt0+GEqL/6JpyHgI4Vj+8HHsQ/OuzeZohJiDr53C5yPnqSwnWfEj1oEinn3YLRElp1vjF9MS1xdedg6xCdyu0jriPPaWPBmucoc5cf/SIh6lDnKDVFUb4GFgEf6rruqXbcAoToul7S/CEGTToySq3FycnMo/CzxzDlbCf+9MuIOfWcJpsz0t5HqdXmp/2beOz7Fzi5wwncMuwaTDIxVBxdo0ap7QJeBvYpijJPUZQuALquu9p4shEtUPbe/WS8fieGnB1sTDkXV68JTTpBsb2PUqvNKZ0GMH3gRWzI+JWXN75DfaZSCFGTOhOOrutX41/BeT7wN/x9OZ8qijIpEMEJUaksezf29+7B6ipiW88r2BfRt933swTSxB6jOafXeJbvXM1HW78MdjiilTpqH46u68W6rj+r6/qJ+Dc3Owi8ryjKLkVR5jR7hKLdc+7eTMZrd2E0Gvih0zT+cKdJP0sQXNL/HIZ3PYW3Nn/M6t3rgh2OaIXqtdLA4RRF6Qd8BBwnKw2Ipla9L8V6YAM5ny7EkpBG2pQ7sXkipJ8liNweNw+uXsjW3D+YM3IW/VN7Bzsk0TLV2IfToISjKMoEQAUmA1uARbqua00UYEuTjiScgKucD+PxeOlZtJbe+SsJ69KXlAtvxxQWEezwBOAod3LPysfIKcnnvtNvJj2uc7BDEi1P4xKOoihJ+BfJnIG/P+dd/Inmx6aPsUVJRxJOwP3+Zz7L1+5iiH0lqbnrcHcZRI9L/onBbAl2aKKag44C5q74N16flwfG3UpSREKwQxItS8NHqSmK8g6wD3/CWQR00nV9WjtINiJIkqLMnJLzAam569gZeyqxZ/3jkGQjy8+0DPHhsdwxahZlnnIeXL0Qe5kMWhVHd7R5OB/ir80sD1xILUY6UsMJKI+jmKx3HqLswHbKB15EwqlnH9JPU9Xc5vVhMhpazXbObdmWnO08sOoZeiSkM3fUPwgxSU1UAI2p4ei6/n/tNNmIAHMVZJPxyh2UZ/1J8nm30GvSRUckE1l+puXpk9yTWUMuZ2vuDhauXYLX5w12SKIFa2kbsIl2qCxzJxlL7sDjKCJ16t1E9j6txnKy/EzLNLTLIKYNOJ+1+zfy6qb3gx2OaMFq3WJaiEBw7NhI9gePYbJGknbpfYQkdqq1bOXCnDIsuuWZrIwjz2Hji+0rSQyPY7IyLtghiRZIEo4ImqJNX5P3xfOEJHUhdcpczFHxR70mKc4qiaaFmjbgfA46Cnh10/vEW2MZ2mVQsEMSLYwkHBFwPp+PgjXvYluzFOtxJ5Jy/j8xhkrzWGtnNBiZdeoVFK4qYuG6V4gNi6ZPcs9ghyVaEOnDEQHl83rI++J5bGuW4k4/DdP4myTZtCEhJgu3DruWlMhEHvnuefYVZhz9ItFuNGppm3YiHRkW3aS85U6yP3gc586N/BE3jC2xo3C5vQw7sSM9u8RJU1kbkluSz50rHsFoMDJ/3G3Eh8cGOyQRWI3ankCIJuG2F5D5+j04/9xE+aC/syVuNJERIew4UMDydbvb/bbObU1SRAJzRs7E4XLy4OqFOMrl/1ZIwhEBUJ6f4Z9jk7uPlAtuI+GUSZiMBvZn28EHnZKjZF5NG5Qe15lbhl3DgaJMHv1ew+1xBzskEWSScESzKj2wnYxX7sBb7iTt0vuI6Dm4anjz+CFd6d45DrvTJfNq2qj+qb257pRp/Jaj89z612RiaDvXYkapqaoaAjwDXAy4gEWapt1dS9k0QAMGA6nAcZqm7T6szAPAtfjf41vAPzRNczXbGxBHKNm+npwPH8cUFU/alLlY4jtUnasc3tyzS5zMq2njRqYPId9h463NH5NgjeXvJ/5fsEMSQdKSajh3A/2B7vgTyVRVVafXUtYLLAPOq+mkqqpXA1OAQRX3GwDc2cTxiqPI/2oxIUld6Hj5g4ckm+pkW+f24dzeEzij2wg+3racZX98G+xwRJC0mBoOMB2YoWlaHpCnqupjwJXAy4cX1DQtG3hOVdXa4p8OPF5Z61FV9X7gBeCe5ghc1KzDtAcxhUdikAUd2z2DwcBVA6dgcxby8sZ3iLfGckqnAcEOSwRYi6jhqKoah3+vnV+qHd4E9GvkLfvVcK9OqqrGNPJ+ohHMUXGSbEQVo9HIDaddRfeEdJ5auxg9b2ewQxIB1iISDhBZ8W9htWMFQNQx3O/we3EM9xNCNIFQcwi3j7ieRGscC9YsIqMoK9ghiQAKSJOaqqrLgAm1nN4DnFTxOBqwVzyOAYob+ZL2intVqqzZNPZ+QogmEh0ayZxRs7hrxSPMX72Q+WNvJdYqjQ/tQUASjqZpE49WRlXVDOBEoHItjAHAb418yd8q7vVDtXvt1zStsNYrhBABkxqZxO0jrue+b57goTXPcu+Ym7FawoIdlmhmLWnQwBLgTlVV1wMRwM3AQ7UVVlU1DDBVPA2teF6maZqv4l63qqr6BVAC3AUsbr7QhRAN1T0hnZuGzuDf3y3iiR9e5LYR12M2mo5+oWi1WkofDsB9+GsmO4GfgaWaplWNUFNV1a6q6ohq5Z381fy2reJ514rnLwHvVtxnJ7AZeKBZoxdCNNjADv2YcfIlbMrawgsb3kDWdmzbZPHO2qVTy+KdLpeL/fv3U1paGtiIRLtlMpmIjY0lMTERo7El/Z3YNN757VPe+/0LLuh7Jhf1OzvY4YhjV+PinS2pSa3V2L9/P1FRUaSnp2MwGIIdjmjjfD4fLpeL7Oxs9u/fT5cuXYIdUpO7sO9k8h0FvPf7F8Rb4xjXbXiwQxLNoO39qRQApaWlJCQkSLIRAWEwGAgJCaFjx46UlJQEO5xmYTAYmDFoKgNS+/DSz2+xMWNzsEMSzUASTiNJshGB1hab0qozG03cPHQGXWM78sQPL7Ejf3ewQxJNrG1/BwshWpUwSxhzRswkOiyKh9c8S5Y9N9ghiSYkCaeNyc/P55prrmHUqFEsWLCAxYsXc++99wY7LCHqLdYaw9yRs/D5fDy46hmKSmW+dlshgwbamA8//JCIiAi+/fbbY272u+aaaxg/fjwXXHBBo653ub24PV7MJiMWc9v72+bTTz/l/fffZ8mSJcEOpc3pEJ3qnxj67ZMsWPMcd4+5iVBzSLDDEseo7f0WaOcyMzM5/vjj65Vs3O7m24HR5fZysKiUInsZB4tKcbll4y3RMD0Tj+eGU69kx8E9PPXjf/B4PcEOSRwjSThtyF133cVnn33GG2+8wYgRI1izZg2apjFnzhwAMjIyGDRoEB999BFnn302V1xxBWVlZdx1112MHTuW0aNHc9lll5GXl8ezzz7Lpk2bePzxxxkxYgTz5s2r8TV//fVXrrrqKkaPHs3EiRN5++23AXCWlvGS9iyX//0C/n7ROcybdz92u/2QOD7++GPOOussRo8ezdtvv42u60ydOpVRo0Yxb968qkmAn376KZdffjmPPvooo0aN4rzzzuP777+visFut3Pfffcxfvx4zjzzTJ588klcLv9eexs2bGDChAm8/fbbTJgwgXHjxrF48V+LTni9XpYsWcK5557L2LFjufXWW7HZbIfE+fnnn/O3v/2NMWPGsGDBAnw+H7t27eKhhx5iy5YtjBgxghEjRuDxyC/EpnZKpwFMH3gRGzJ+ZfHGpTIxtJWTJrVjVPzrtxT/srLZXyfqxNOJ6j+6zjLz5s3DZDKRkJDA7NmzAdiyZcsR5davX8/SpUsxGo189tln2O12Pv/8cywWC3/88QdhYWHMnDmTX375pc4mtaysLGbPns1tt93GhAkTcDqd7Nu3D4A3XnuF3zb/whNPa4Raw3jykfk89thj3HPPX1sSbd68mQ8++IBff/2VWbNmMXToUJ5++mkA/v73v/P9998zfLh/Psa2bdsYO3YsX3/9NatWreJf//oXH3/8MfHx8Tz66KPYbDY++OADSktLufnmm3n55Ze55pprACgoKCA7O5tPP/2UnTt3Mn36dEaNGkW3bt1YunQpK1eu5Pnnnyc+Pp7HH3+c+fPn8+ijj1bFuW7dOpYuXcrBgweZNm0aw4YNY/jw4cyZM0ea1AJgYo/R5DtsfLxtOQnhcZzXZ1KwQxKNJDWcduiaa64hPDycsLAwzGYzhYWF7N27F5PJRK9evYiMjDz6TYBly5YxcOBAzjrrLMxmM1FRUfTp0weAL79cxoyrrya9awc6pyXyj3/MZtmyZXi9fzWtXXXVVYSGhjJ48GBiYmIYO3YsiYmJJCYmMnDgQLZt21ZVNjo6mksvvRSz2czYsWPp0aMHq1atwuPx8OWXXzJr1iwiIyNJTExkxowZfPHFF1XXGgwGrr/+ekJCQujduzc9e/ZE13UA3n//fa677jpSU1MJCQlBVVVWrVpFWVlZ1fXXXnstVquVjh07MmjQoEPiEoFxSf9zGN71FN7e/Amrdq0NdjiikaSGc4yi+o8+as2jpUlJSal6fNZZZ5GTk8Odd95JYWEhEydOZObMmYSEHL2DNisri06dOtV4Ljc3l06dOmAN9X+LdejQAZfLVdVcBRAfH1/1ODQ09IjnTqez6nlSUtIh81BSU1PJzc2loKAAl8tFWlpa1bm0tDRyc/8aThsTE4PF8tdGcGFhYTgcDsDf5/Wvf/3rkD4vi8VCbm5u1eslJCRUnbNarYfEJQLDaDBy/eDLKCwt5Pn1rxFnjaF/au9ghyUaSGo47VD1X65ms5kZM2bwzjvv8Morr7B27Vo++uijI8rVJCUlhf3799d4LikpiczMzKrnGRkZWCwW4uLiGhVzXl7eIbWjrKwskpKSiI2NxWKxHPJamZmZJCUl1eu+KSkpPP7443z77bdVXz/88EOtibQ6mfwbWGaTmVuGqnSKTuOx719gt21fsEMSDSQJp53bsGEDO3bswOPxYLVaMZlMVX/Zx8fHc+DAgVqvnTRpEj///DPLli3D7XZTXFzM1q1bq8795z//IS8vD7vdzrPPPsuECRMaPVu+sLCQN998E7fbzTfffMP27dsZOXIkJpOJ8ePH89xzz2G328nLy+PFF19k0qT6tfOff/75LFq0qOp9FhQU8M0339Tr2vj4eHJzcykvL2/UexINFx5iZc7IWYSHWHlw9UJyS/KDHZJoAEk47VxeXh633XYbo0eP5sILL+SEE07g3HPPBeCSSy5h1apVjBkzhvnz5x9xbWpqKk899RRLly5l7NixXHTRRWze7F8Da/r06QwYMIBLL72U8847j5iYGP75z382Os5evXqRlZXF2LFjefrpp3n44YermrpuvfVWYmJiOO+887j00ksZMGAA06dPr9d9L7nkEkaPHs3s2bMZNWoUl19+Ob/++mu9rh08eDA9evRg4sSJjB49WkapBUh8eCx3jJyFy+PiwdULsZe1zfXl2iLZnqB26dSyPcHWrVvp3VvajwNFJlj+Rb73/rIlZzsPrHqGHgnpzB31D0JMlqNfJAKlxu0JpIYjhGiV+iT3ZNaQy9mau4OFa5fg9cnk4pZOEo4QotUa2mUQ0wacz9r9G3n1f+/JxNAWToZFixbv7LPP5uyzZRdIUbPJyjjyHDa+2L6SxIh4Jivjgh2SqIUkHCFEqzdtwPkcdBbw6qb3ibfGMrTLoGCHJGogCUcI0eoZDUZmDbmCwtIiFq57hZiwaPom9wx2WOIw0ocjhGgTQkwWbh12LSmRiTzy3fPsLah9DpkIDkk4Qog2IzI0grkjZxNqCuGh1c9y0FEQ7JBENZJwhBBtSmJEPHNGzsThcvLg6oU4ymXtu5ZCEo4IqEGDBrF79+5ghyHauPS4ztwy7BoOFGXy6Pcabk/zbTYo6q/FDBpQVTUEeAa4GHABizRNu7uWsmmABgwGUoHjNE3bXe38vcBcoKzaZQM1TdveLMEL0QQGDRrEe++9R3p6erBDaRP6p/bmulOmsXDdEp776VVmnXoFRoP8jR1MLSbhAHcD/YHuQCSwQlXVXZqmvVxDWS+wDHgI+KGW+72vadqUZolUCNEqjEwfQr7DxlubPyY+PI5LT/y/YIfUrrWkdD8dmKdpWl5FbeUx4MqaCmqalq1p2nPA+gDG1yosWbKEM888s2or5rVr/ZtV1bWVMtS+VbTL5eLJJ5/kzDPPZPz48dx3331HbBVd0xbMla+5cOFCzjjjDM4880w++eSTOmMvKipi3rx5TJo0idGjR3PttddWnfvuu++YMmUKo0aN4oorruC3336rOnfNNdfw7LPPcuWVVzJ8+HBuuOEGCgoKuPfeexk1ahRTp05lz549VeUHDRrEW2+9xTnnnMPYsWN57LHHDll489NPP+W8885jzJgxXH/99Ydce/bZZ/P6669z6aWXMmrUKGbPnk1BQUHV+c2bN3PllVcyZswYpkyZUvX5V8a5aNEiVFVl5MiRTJ8+vWp7hxkzZgBw6aWXMmLECD777LM6PytRf+f2nsD4biP5ZNtylv3xbbDDaddaRA1HVdU4oAPwS7XDm4AHj+G2k1RVPQhk4m+eW3gM96rVql1r+WZXbZWspjPmuKGMOu7UOsvs3r2bd999l1deeaVqPxq32992XddWynVtFb148WI2btzIq6++SlhYGHPnzj1iq+jatmD++OOPWbFiBS+//DLx8fHcf//9dcZ/zz33YLFYeOutt4iMjGTTpk0A7N27l3/9618sWLCAIUOG8Pnnn3PDDTfw4YcfEh0dDcDy5ct55plniI+P56qrruKKK67g1ltv5c4772T+/Pk899xzLFiwoOq1Vq5cySuvvEJZWRkzZ86kU6dOXHzxxWzYsIEnnniCp59+GkVRWLJkCTfddBPvvPMOZrP/x+WLL77g8ccfJyYmhtmzZ/PKK69www03kJOTww033MB9993H0KFD2bhxI7fddhvvvvsuiYmJAHz++ec8+eSTpKenc9ddd7Fw4UIefvhhXnzxRQYNGsTrr78uTWpNzGAwcOXAiznoLODlje8Qb43llE4Dgh1Wu9RSajiVexoXVjtWAEQ18n7vAL2BJGAGMFdV1csaHV0rYTKZKC8vZ+fOnbjdbtLS0ujcuTNQ91bKdW0V/d///perrrqKxMREIiMjmT37yK2ia9uC+csvv2TKlCl06tSJ8PDwQ2osh8vLy2PNmjXccccdxMbGYjabGTTIP1t8+fLlnHbaaQwbNgyz2cw555xDhw4d+O6776quP+uss+jSpQuRkZEMGzaMlJSUqvLjxo2r2lK60rRp04iNjSUlJYWpU6fy5ZdfVr3fyZMn069fPywWC1deeSV2u/2QGtUll1xCamoqVquV8ePHV937iy++4NRTT2XEiBGYTCYGDx5M//79WbVqVdW1Z599Nt27d8dsNnPWWWfJdtUBYjQaueG0q+iekM5Taxej5+0MdkjtUkBqOKqqLgMm1HJ6D3BSxeNowF7xOAYobszraZq2pdrTH1RVfQq4AHitMfery6jjTj1qzSNQOnfuzC233MJLL73EnDlzOOWUU7jppptITU2tcyvlo20VXX375pq2iq5tC+bc3FxSU1OrzlW/z+GysrKIjIwkNja2xhiq36fyXjk5OVXPG7JdNRy6zXZaWhp5eXlVr9W9e/eqcyaTiZSUlENe6/D3W7lddVZWFt9++y2jR4+uOu92u6uS9+HXhoWFyXbVARRqDuH2Eddz14pHWLBmEQ+M/ScdolOPfqFoMgFJOJqmTTxaGVVVM4ATgYyKQwOA32q9oGHazRKyEydOZOLEidjtdhYsWMATTzzBggULSElJYe7cuZx88slHXJOSklLrpmOVTXM9e/qXCam+VXRWVladsSQlJR1Spq7yqamp2O12CgoKjkg6SUlJR9RQMjMzD/nF3lDZ2dlV7ykrK6uqyevwrbG9Xi/Z2dkkJycf9Z4pKSlMmDDhkOZG0bJEh0Zyx6hZ3LniEeavXsj8sbcSa40JdljtRktpUgNYAtypqmqiqqpdgZuBxbUVVlU1DAiteBqqqmqYqqqGinPnqKoap6qqQVXVU4B/AB82b/jBt3v3btavX095eTmhoaGEhoZWbelc11bKzbVV9BlnnMHSpUs5cOAADoeD559/vtayiYmJDBs2jIcffpiCggLcbjcbNmyous+PP/7Ijz/+iNvt5rPPPuPAgQMMHz680Z/Va6+9RmFhITk5Obz55puMHz++6v1+/vnnbNmyBZfLxeLFi4mIiKBfv35HveekSZP4/vvv+e677/B4PJSXl7Nx48ZDElhdEhISqgYRiOaTEpnE7SOup6i0mIfWPIvTVRrskNqNFjFooMJ9QCKwk7/m4VQNiVZV1Q5M0jRtTcWh6m0RlQ3hlbvMTcGfrEKB/cACTdOWNGfwLYHL5WLhwoXs2rULk8nECSecwB133AH4+x18Ph+zZ88mPz+f2NhYTj/9dMaMGVO1VfTTTz/NQw89RHh4ONOnT6d3795Mnz6dkpISLr30UrxeL0OHDq33VtHnnnsuBw4c4PLLLyckJIRrr72Wr776qtby999/P0888QQXXXQRLpeL3r17M2jQILp27cqDDz7Ik08+SVZWFl27duXJJ5+sGjDQGGPGjGHatGkUFxczadIkLrjgAsA/gm327NnceeedHDx4kF69evHEE09UDRioS2pqKo8//jhPP/00d999N0ajkT59+nDbbbfVK6YZM2Ywb948ysrKuPXWWznrrLMa/f5E3bonpHPT0Bn8+7tFPP7Di9w+4nrMRlOww2rzZIvp2qUjW0y3Sa15gqV87zWtlX9+z/PrX2d0+mlcd8plh/RximNS4xbTLamGI4QQAXX68cPIc9h47/fPSYyI46J+stFfc5KEI4Ro1y7sexb5Dhvv/f4FCdY4xnZrfN+gqJskHNHuVA5GEAL8E0NnDJpKYWkRy3esloTTjCThCCHaPbPRxO0jrqfMXXb0wqLRWtKw6FZFBluIQKu+uoNoegaDgTBLWLDDaNMk4TRCWFgY+fn5knREQPh8PsrLyzlw4AARERHBDkeIRpMmtUbo1KkT+/fvJzc3N9ihiHbCbDYTExNTtSKCEK2RJJxGsFgsHHfcccEOQwghWhVpUhNCCBEQknCEEEIEhCQcIYQQASEJp3aykp8QQjROjb8/JeHUrvbdwoQQQtSlxt+fslp07UKBwUAm4AlyLEII0RqY8Ceb9cARyzZIwhFCCBEQ0qQmhBAiICThCCGECAhJOEIIIQJCEo4QQoiAkIQjhBAiICThCCGECAhJOEIIIQJCEo4QQoiAkP1wmomqqiHAM8DFgAtYpGna3bWUPQuYA/QDSoEvgJs1TSsITLTNr4GfRxqg4V/pIRU4TtO03QEKtVmoqhoLvABMAoqA+ZqmPVdL2Vn4vx+i8X8vzNA0rShAoQZEfT8PVVX7AY8Bg4B4TdMMgYwzUBrweVwO/APoARQDS4F/aZpWHrhoG09qOM3nbqA/0B3/L86pqqpOr6VsDPAA0AHoBSQDTwYgxkBqyOfhBZYB5wUotkBYiP8PvA7AWcB9qqqOObyQqqpnAPdUlOkIWPAn6ramXp8H/j9O3gGuDGBswVDfzyMcuBFIwp+ERwB3BCjGYyY1nOYzHf9fpnlAnqqqj+H/oXn58IKapr1Z7alDVdUX8P9V15Y05PPIBp5TVbVNfH+qqhoBXAicpGlaMbBJVdXF+N//N4cVvwJ4WdO0TRXXzgX+p6rqdZqmOQIXdfNpyOehaZoO6Kqqdg98pIHRwM9jUbWnmaqqvgacHbBgj5HUcJqBqqpx+P9S+aXa4U34m8zqYyTwexOHFTRN8Hm0dj0Bg6ZpW6od20TN778f1T4nTdO2Vjzs0WzRBV5DPo/24Fg+j1b1u6JN/AXZAkVW/FtY7VgBEHW0C1VVPR24GhjW9GEFTaM/jzYiEn+7fHUF1Pz+Izn0c6LieVv6rBryebQHjfo8VFWdBgwHBjRLVM1AEk4jqKq6DJhQy+k9wEkVj6MBe8XjGPydfHXddwj+TsCLNE1rNX+1NNfn0YbY8b/36mp7/zWVja6lbGvVkM+jPWjw56Gq6t+AR4HxmqZlNWNsTUoSTiNomjbxaGVUVc0ATgQyKg4NAH6ro/xJwKf4+zmWN0GYAdMcn0cbsx3wqarau1oT2QBqfv+/4f+c3gRQVbUXYAD+CECcgdKQz6M9aNDnoarqRGAxMLmyr6+1kP1wmomqqvOB0cA5QATwFfCQpmlHdJJXDP38GrhB07S3AxlnoDTk86goH4Z/Myc7/pF7e4AyTdNa5Tesqqpv4N/UbzpwHLACuFjTtG8OK3cG8AYwDtiFf1BFiaZplwc24ubVgM/DUFHuePx9FVYATdNKAxpwM2vA53E68C5wnqZpqwIe6DGSGk7zuQ9IBHby17yTql+uqqragUmapq0BbsE/zPElVVVfqiyjaVokbUdDPg8AZ7Vrt1X8exywu/lDbRYzgRfx7yBbBNyrado3qqp2AbYAfTRN26tp2leqqs7DPyy8ch7O7GAF3Yzq9XkAXfEn3kqV3xdtbT5OfT+Pu/A3t32uqmrltXs0TesbhJgbTGo4QgghAkKGRQshhAgISThCCCECQhKOEEKIgJCEI4QQIiAk4QghhAgISThCCCECQubhCNEMFEW5Fxit6/roIIdSI0VRQoBXgfFACJCg63pZcKMSbZ0kHCEOoyjKR4BL1/ULazj3EtBN1/Wa9ippTS7Av0BsV13Xa1yzS1GUb4GhQDn+PYr2AU/quv7iYeVuBG7GP7H3f8D1uq7/ghCHkSY1IY60CDhHUZSU6gcVRYkGpgDPByWqpnU8sLO2ZFPNg7quRwKx+FeL0BRFGVl5UlGUKfg317sIiAeWA8sURWmvKz+LOkgNR4gjLQf2AlcBD1Y7fhn+td0+UBTlQvzbQHfDvy34CuAGXdfzarqhoii7gXt1XV9S7ZgPGKPr+rcVz4cAC4ATKl7nVeA+XdfdFU1gT+LfBTUCyAce03W9xt1AFUXpXFF+BOAG/gv8U9d1W0UtbRpgUhTFDnyl6/r/1fWB6LruBd5RFOU54BRgdcWpa4EXdV1fW/G68yqO/V9F/EJUkRqOEIfRdd0HaMAMRVGq/4yowGJd1134l46/HP9f9SfjrzE81djXVBRFwZ+0ngVS8G+sdTZwe0WRy4HTgH66rkcBpwLf13IvE/B5RYzd8K8+3QV4peL9XY0/ka7RdT3yaMmm4p5mRVGmAgmAXu3UicCGyicViWkjrWiPFhE4UsMRomYvA/Pw7/PzX0VRhgJ9gb8B6Lq+rFrZ/Yqi/Jtja2qbCXyk6/q7Fc/3KIryEDC/4qsc/0ZdfRRF+VHX9Sygtn1QTgH6AMMrmsyKFUW5CdisKEpqxbX19a+KPppI/Atm3qHr+qfVzkfj3yysugKO3N9FCKnhCFGTiqaxd/HXaqj4d5mu67sBFEUZoyjKt4qiZCuKUgS8BiQfw0v2AC5UFKWg8gv/6sGpFedfx1/regTIUxTlC0VRTqr5VnQG8nRdr76L5I6Kf7s0MK6HdV2PBeLwJ+FxiqJU/0O1CP/qxdXFcuQOlkJIwhGiDouAyYqinIC/U3wRVA0p/hT4CDhe1/Vo/P07dSnG3/dCxT06HHY+C3hV1/XYal/RFR326Lru0XX9UV3XhwAd8W/Z8FEtr7UPSDys475bxb97jxJnjSpqSjPxbxExs9qpX4BB1d6XEf8Or5sa8zqibZMmNSFqoev6D4qi/I7/F3sO/r1pwD9vJQwo0HW9RFGU44F/HeV2G4CpiqK8XvH84cPOPwd8pSjKl/iTmQf/L/fuuq4vUxTldPy1hl/xD1KwV5SpyXpgK/CUoij/qIj1ceDzBjanHULX9TJFUe4HHlEU5eWKGtTzwLOKonyAP/nchr/p7cPGvo5ou6SGI0TdFuEfEPBiRYc4uq7b8Tex3V8xyuuNiq+63AmUAPvxJ59DfiHrur4ef3+RChzAPwrtPfwbkIG/uW4JcBDIBUbhr3UdQdd1NzAZfzPYLmAz/q29p9XvLdfptYoYbq14rbeBB4D38ffdTAIm1mO4tWiHZAM2IYQQASE1HCGEEAEhCUcIIURASMIRQggREJJwhBBCBIQkHCGEEAEhCUcIIURASMIRQggREJJwhBBCBIQkHCGEEAHx/1rRpvVsIOSeAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Difference between OLS and PCA:\n",
        "\n",
        "OLS minimizies squared residuals parallel to the axis while PCA minimizes residuals orthogonal to eigenvectors.\n",
        "\n"
      ],
      "metadata": {
        "id": "61FGcPD-ktqv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "KmYvtmhFm81u"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "OLS does not give exactly the inverse slope if x and y axis are swapped while PCA does give the reverse slope exactly."
      ],
      "metadata": {
        "id": "utkAypE59NRj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "s1 = np.polyfit(stocks_dem.SPY,stocks_dem.QQQ,1)[0]\n",
        "s2 = np.polyfit(stocks_dem.QQQ,stocks_dem.SPY,1)[0]\n",
        "print(s1,1/s2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y2pKybyDlFoy",
        "outputId": "f9f42783-d212-4a6c-c47d-c1a9dc7f275e"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.025124354762666 1.2186958050000145\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Downloading some more instruments for further use."
      ],
      "metadata": {
        "id": "Y9w703Ue9xe0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "stk = yf.download('GOOG,AMZN,NFLX,BAC,JPM,WFC',start='2010-1-1').Close\n",
        "pair = yf.download('RB=F,CL=F',start='2010-1-1').Close"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9a5Ud69wt3SG",
        "outputId": "9a4526c3-ab3d-4657-926c-b3d7ca6bd2d5"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  6 of 6 completed\n",
            "[*********************100%***********************]  2 of 2 completed\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here we build a PCA funtion that returns eigenvectors in order of their \"significance\" based on the size of the eigenvalues."
      ],
      "metadata": {
        "id": "bpGD1ENV93g2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def pca(stk):\n",
        "  x = stk.pct_change().dropna()\n",
        "  p = np.linalg.eig((x-x.mean()).cov())\n",
        "  evals = p[0]\n",
        "  evec = p[1]\n",
        "\n",
        "  # Sorting the eigenvalues and eigenvectors\n",
        "  return np.sort(evals/sum(evals))[::-1],evec[:,np.argsort(evals)[::-1]]\n",
        "\n",
        "evals,evec = pca(stk)"
      ],
      "metadata": {
        "id": "3xbzRwovvg7H"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "\"Explained variance\" tells us how many principal components we need to explain x% of the variance in the data set."
      ],
      "metadata": {
        "id": "S_pMmDzl-O5L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"Explained Variance\"\"\"\n",
        "\n",
        "plt.plot(np.cumsum(evals),'-o')\n",
        "plt.xlabel('component')\n",
        "plt.ylabel('explained variance')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 305
        },
        "id": "XZUrleNWvyNq",
        "outputId": "bcb489ca-f2e3-4fcf-bf7a-5b33e020f3bc"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'explained variance')"
            ]
          },
          "metadata": {},
          "execution_count": 22
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can use PCA to find \"hidden\" factors or clustering in the data.\n",
        "\n",
        "Here we can see that by plotting the first two prinicpal components of the returns for different products we can clearly distinguish between technology stocks (blue), banking stocks (green) and oil-based commodities (red)."
      ],
      "metadata": {
        "id": "ZXlSXTgm-hBC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"Factor Analysis\"\"\"\n",
        "r = []\n",
        "\n",
        "lkbk = 50\n",
        "r.append(pair['CL=F'].pct_change().iloc[-lkbk:].values)\n",
        "r.append(pair['RB=F'].pct_change().iloc[-lkbk:].values)\n",
        "\n",
        "r.append(stk['GOOG'].pct_change().iloc[-lkbk:].values)\n",
        "r.append(stk['AMZN'].pct_change().iloc[-lkbk:].values)\n",
        "r.append(stk['NFLX'].pct_change().iloc[-lkbk:].values)\n",
        "\n",
        "r.append(stk['JPM'].pct_change().iloc[-lkbk:].values)\n",
        "r.append(stk['WFC'].pct_change().iloc[-lkbk:].values)\n",
        "r.append(stk['BAC'].pct_change().iloc[-lkbk:].values)\n",
        "\n",
        "R = np.array(r)\n",
        "\n",
        "evs = np.linalg.eig(np.cov(R-np.mean(R)))\n",
        "\n",
        "c=['r']*2 + ['b']*3 + ['g']*3\n",
        "for j,i in enumerate(evs[1]):\n",
        "  plt.plot(i[0],i[1],'o',c=c[j],ms=10)\n",
        "\n",
        "for i in np.linspace(-np.pi,np.pi,1000):\n",
        "  plt.plot(np.cos(i),np.sin(i),'k.',ms=0.3)\n",
        "\n",
        "\n",
        "plt.axis('equal');\n",
        "plt.xlabel('first component')\n",
        "plt.ylabel('second component');"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "outputId": "a590882d-884b-4fc2-c251-1996c9c89177",
        "id": "BobRKr3GYm5S"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Cointegration\n",
        "\n",
        "### Short recap: cointegration versus correlation\n",
        "\n",
        "- Cointegrated price series do not necessarily have to be correlated and vice-versa \n",
        "\n",
        "- Drunk and her dog: https://www.researchgate.net/publication/254330798_A_Drunk_and_Her_Dog_An_Illustration_of_Cointegration_and_Error_Correction\n",
        "\n",
        "- Same behaviour in the markets and causality relationships change. For more information please refer to Engle-Granger causality (https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=2ahUKEwjcvKPcsqDeAhXTbCsKHTmNAe8QFjAAegQIBxAB&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FGranger_causality&usg=AOvVaw1mYq3HhcjsVNJ9zJ6zgqdV)"
      ],
      "metadata": {
        "id": "HA9nDKet_mYi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Adjusting for volatility, the RBOB gasoline vs Crude Oil pair seem to be highly cointegrated."
      ],
      "metadata": {
        "id": "MatDbc1C_zCO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "((pair-pair.mean())/pair.std()).plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "_li6PPkX3lCb",
        "outputId": "59db085f-1463-437c-f8ea-dfa0344d48f7"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Date'>"
            ]
          },
          "metadata": {},
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's run the Granger cointegration test. The first component gives us the t-statisic, the second component is the p-value of the t-statistic and the the third component are the critical values of the t-statistic for the 99%, 95% and 90% confidence level."
      ],
      "metadata": {
        "id": "0hA1D2YLAEFj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "spread = ((pair-pair.mean())/pair.std()).dropna()\n",
        "spread.diff(axis=1)['RB=F'].plot()\n",
        "print(coint(spread['RB=F'],spread['CL=F']))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "JrOyY6ZnEWHz",
        "outputId": "004ea148-f8d0-44a9-c52f-66242b62b9ec"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(-4.983193824244974, 0.0001767626566562605, array([-3.89973386, -3.33796658, -3.04572464]))\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The Engel-Granger causality test tells us the direction of causality in our data. There are for directions of causality, here explained with the drunk and dog analogy:\n",
        "- Drunk owns dog but no leash, leads dog\n",
        "- Big dog on leash lead drunk\n",
        "- Small dog on leash (drunk and dog may lead)\n",
        "- Dog not owned by drunk (no-one leads)\n",
        "\n",
        "Here we can clearly see that price of Crude strongly leads the price of RBOB gasoline."
      ],
      "metadata": {
        "id": "VMG4m8yAAv8c"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X = pair['CL=F'].ffill()\n",
        "Y = pair['RB=F'].ffill()\n",
        "\n",
        "lags = 10\n",
        "\n",
        "# Calculating the EG-Test in one direction\n",
        "result = grangercausalitytests(np.array([X,Y]).T, lags, verbose=False)\n",
        "\n",
        "# Extracting results\n",
        "res_fwd = [(list(result.values())[lag][0]['ssr_ftest'][0]) for lag in range(lags)]\n",
        "\n",
        "# Calculating the EG-Test in reverse direction\n",
        "result = grangercausalitytests(np.array([Y,X]).T, lags, verbose=False)\n",
        "\n",
        "# Extracting results\n",
        "res_rev = [(list(result.values())[lag][0]['ssr_ftest'][0]) for lag in range(lags)]\n",
        "\n",
        "plt.bar(range(lags),res_fwd,label='CL -> RB')\n",
        "plt.bar(range(lags),res_rev,label='RB -> CL')\n",
        "plt.legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "0gqsPCzbJIbc",
        "outputId": "53f2ec60-400b-46e4-a76e-4d91dcb355e1"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f4abfbf1d90>"
            ]
          },
          "metadata": {},
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now we can backtest the Crude/RBOB spread. Futures have a dollar value associated with each tick. In this example, for simplicity, we assume the tick value is equal to the dollar value.\n",
        "\n",
        "***This is for demonstration purposes only, do not attempt to trade this!***"
      ],
      "metadata": {
        "id": "M5fnC_lLCDYZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "inpos = 0\n",
        "pnls = [0]\n",
        "unrlzd = []\n",
        "dt = []\n",
        "dates = [pair.index[1500]]\n",
        "th = .1\n",
        "comms = 0.0\n",
        "\n",
        "# Looping through each time step\n",
        "for i in range(1500,len(pair)):\n",
        "  if not inpos:\n",
        "    pos = pair.iloc[:i].std()\n",
        "    spread = ((pair-pair.iloc[:i].mean()).mul(1/pos)).diff(axis=1).values[:,1]\n",
        "\n",
        "  # Calculating the unrealized PnL based on position\n",
        "  unrlzd.append((spread[i]-spread[i-1])*inpos)\n",
        "  dt.append(pair.index[i])\n",
        "\n",
        "  # Short entry condition when spread exceeds threshold\n",
        "  if not inpos and spread[i]>th:\n",
        "    inpos=-1\n",
        "    entry = spread[i]\n",
        "\n",
        "  # Short exit conditions, spread goes below zero\n",
        "  elif inpos<0 and spread[i]<0:\n",
        "\n",
        "    # Adding trading costs\n",
        "    unrlzd[-1]-=comms\n",
        "    inpos = 0\n",
        "    pnls.append(entry-spread[i])\n",
        "    dates.append(pair.index[i])\n",
        "  \n",
        "  # Long entry condition when spread goes below threshold\n",
        "  elif not inpos and spread[i]<-th:\n",
        "    inpos=1\n",
        "    entry = spread[i]\n",
        "\n",
        "  # long exit conditions, spread exceeds zero  \n",
        "  elif inpos>0 and spread[i]>0:\n",
        "    unrlzd[-1]-=comms\n",
        "    inpos = 0\n",
        "    pnls.append(spread[i]-entry)\n",
        "    dates.append(pair.index[i])\n",
        "\n",
        "# Plotting the results\n",
        "plt.plot(dates,np.cumsum(pnls),'-o')\n",
        "plt.plot(dt,np.cumsum(unrlzd))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "u6DIz1Mi0zet",
        "outputId": "12df2c52-6790-4691-8a7a-7153f2c152e4"
      },
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f4ab7a71250>]"
            ]
          },
          "metadata": {},
          "execution_count": 98
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD+CAYAAAAas+94AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAAsTAAALEwEAmpwYAAAxXUlEQVR4nO3deXxU9b3/8deZLZnMZE9IQthBEJBFEBdQARWVitYN61Kp1urRSnt/ta3XurS2Vtvb2nvrUu2xdSlaW4tQ64ZrxbovCIqAILIkbFlIJstkktnO748zM5kswCSZNXyej4cPMmf9zJi8c/I93/P9KrquI4QQInOYUl2AEEKIvpHgFkKIDCPBLYQQGUaCWwghMowEtxBCZBhLgo+fBcwC9gKBBJ9LCCEGCzNQAXwEdHRfmejgngW8leBzCCHEYHUS8Hb3hYluKtkbj4O4XK54HCbhpM74kjrjS+qMryTV2WuGJjq449I8EgwG43GYhJM640vqjC+pM76SVGevGSo3J4UQIsNIcAshRIaR4BZCiAwjwS2EEBlGglsIITJMovtxCyHEoLF6TTXLVm2ivtFDUV4WVyyazLyZw5NehwS3EELEYPWaau5f/ikdvgBzsjZzmvI5v11+AUDSw1uaSoQQIgbLVm2iwxcgV/FwkeMDisxuRrKbZas2ARBsd+N695+07/oi4bXIFbcQQsSgvtFDFj5+Wbg8sqzc7OKLRg/+5v1U3XdNZPmYW1YktBYJbiGEOIhwu7YOlJibI8tbgtmMt+yluXBol9AG0PUgipK4Bg0JbiGEOIDodu0yk4trc18HYIV7FjOytjPJtodJ7Omxn+7zotiyE1aXtHELIcQBhNu1r3G+zs0Fz5Jnagdgb6CAVczrsu2Q839E4bxLAdD9voTWJcEthBAHUN/owYqfybbdXZZv85fxk6ULuixzTjwBsz0XAD2Q2OCWphIhhOjF6jXVKCaFiWajKeQz73CcSjt/bp1PUaGjSxv2iO//CQDFYgVA93sTWpsEtxBCdBNu2w4GdfKtbgD+7j4Bt55NltXMkoUTASg46SJa17+J2VkAgGIOBXfAn9D6JLiFEKKbcNu2FT/n5qwBwKPbMJkUli6exryZw2loaKDo5G9QeNLiyNV3sq64pY1bCCG6qW/0YCbAD/NewKIYEyYEMaEH9R5PSUY3mYSvuGue/i3BDk/C6pPgFkKIbpw5VqbaqqiwNAHwTvt4AEoK7QfdL3zF7W+qpfGdpxNWnwS3EEJEWb2mmrZ2P5XmxsiyFz3TsJiVSNv2gdjKx0S+9tVVJ6xGCW4hhIiybNUmsnUPC+yfR5a59WzsWZZDDiZlznZQMPt8ANq2rklYjTHdnFRVdQTwADAb8AMvAks1TWtNWGVCCJFE4Ufb6xo9FJuMftj/9kziWc9MdBRa22Lrm100/zLcWz7EV78LX8MerEVD415rrFfcfwQagUrgSGA0cFvcqxFCiBQId/+ra/RQad5PiakFgN2BInQU4NDt29GsRRUA7Hn8p/Evlti7A44G7tc0zQN4VFVdCZyekIqEECLJwt3/TAS5Mf+FyPJAKLSj+27HInyVHWhtPMSW/RNrcP8euFRV1TeBHOBC4KmEVCSEEElW32h03TvS2nXAKF1XKC20s2ThxD5NllA071KCXg+5R82Na51hsQb328DVQBNgBp4HHoz1JC6Xi2Aw2PfqQjweDw0NDf3eP1mkzviSOuNL6jyworws9jd3kGfq2vfakWPj7u8eA9CjpkPVaT5uMW1AWz/ei8lkoqCg4IDrDxncqqqagZeAPwNzAEfo63uApbEUcbACYtHQ0EBRUdGAjpEMUmd8SZ3xJXUe2BWLJnPPU2txKu1dls8/ZuQBa0nl5xnLzclCYBhGG3eHpmkNwCPAmQmtTAghkkjXYaSlvuuyBE6GMBCHrErTtHpgG3CtqqpWVVXzgSuAzxJcmxBCJMWyVZsIBoNMtXV9aOa1NbtSVNHBxfrr5DzgVKAW+ApQiLGZRAgh0tnqNdXUNXqYbtsBwH/aJ0TWNbYkdpS//orp5qSmaZ8BpyS4FiGESKpw/22AK5xvAdAQdEbWB3JLU1LXoaRnA44QQiRBuP/2cHNn23a7bo18fe6Zs1JR1iHJeNxCiMNO9OPtANflvhZZ1xzsfEJy3jEjkl5bLCS4hRCHleiZ28Mcps6JDzb4hqWirD6R4BZCDGqBoE69y8Pe+lb21rt59PmNdPgCzLJ9xTed73Cn6+sEdAWzoqO1nEKW1YhFxWJLceUHJsEthEhr4WaN+kYPJQd4/DwQCFLn8rCn3s3eejd7QiG9t97Nvv1t+ANdn9y24uebzncAOCn7C8yKzsueKdQ5j2DpwomMmbkCXdeT9h77SoJbCJG2ops1rPhZ4H2Nfzy9j/WbxpLtzAsFdSs1DW34A51Bm2UzU1HsYHhZLsdNLqeixMnQEgdDSx38+N63aGlqimx7cvZmAPZnD+eRWzvHzlMUJXlvtI8kuIUQaSvc6+MKx5scnbUTgOOyvqJtu42ft13G0BInoyryOWHKUIaWOKgI/VeUl33A4F3ytYk88vQHPZafeOZpCX0v8STBLYRIO9G9PiZY9kRCOyzH5OXvt5+COSunz8eeN3M4po5meKNzmad0EvOOGTnQspNG+nELIdLKu5/XRiY1AJjYbajVMNc7K/p9jtlHlUW+zp12KhOvuKXfx0oFCW4hRFp5+o0ddPgCmAmwyP4Jk2y7qA84e2zX9P6z6IHYphML03UdX+M+9IDxKHvp2UspXfRdTLbsuNSeLBLcQoi00d7hZ39zBwBXO99ggf1zcpV2NvoqqfZ3G0JVD1L34h/7dPzmNS9T/cD1tFdtBNK7y9/BSBu3ECLpunfxO+ekMexvaufVD6sAMBFkos1oIvlF0/l4dBulhXbuv7iU2n/+L8GONgBaP1uNv7GGoUt+GdN527YYNyXrnv+DcR57zyv5TCDBLYRIqugufnlKG74mNyueN8YKOWFiGUXOHCwbXgagJpCHR7dF5nzMGTucUT96nG13XhA5Xnv1pkOeU9d1Wte/iWd719Gozfa8OL6z5JHgFkIk1V9eMJ5cPM62lUud73ZduTf0b6gF47dNZ/c652PpoutxffAcvjrjCl33+1AsVg7Es20ddc/d12O5OSd3QO8lVSS4hRAJ0b055MwTRlHb0MaMjg9ptDk4LmsrXt3MCvexkX2+943puN1uPG89Sf6xi1h5yvm9Hjt32inkTjuFls/eoO65+/E11WErHnrAWvwtvc/7aLJLcAshBBDdHOKn2NQKTc289FINZgV+kr8ust0efwHve48AoLTQTt700/A3NFAx5+sxncdaXAmAt3bHAYM70NZMx67Nva4zWbP68K7ShwS3ECIu2r1+duxpZusuF4+FmkPmZG3hIkfPpxTDnnTPBoi0YfdVVsVYTNkOPF+txTlxdq/bVN1/Lbqvo8/HTmcS3EKIPtn15x/hrdmO7+w72NpiZ2u1i627XFTVtBAMdo4XYibARY4PcAdtrGjrbA657lgd98Z3qNUL2RUo6bUNO1aKyYy1uBJ/y/4DbtNbaJvzSiiaf1mfz5cuJLiFEAfl8wfYvqeZr3a5+LLaxaKa7QBYn7uNokAeHwUuYtywAo6bXM644QWMG1bAjff9h+FtRm+P3YEi1njHAEZzyJBzF9BUNoqhI4/i2crxA66vY/cWAAKeVswxdO9zHHk8ZRf8eMDnTSUJbiEOU+Gbh3pTLcX5NhYtPIE50yrZuddo7tgaCuqqfc2RkffGONwQ1SxcZm7mgbOt5B19Qpdj32p6CEIZ+njriUBnc4iiKBTM7v2m40C0bV1D7pS5h9xOMR+490mmkOAW4jAUvnnoCLj4WcE/jYUvPcXvV87iP+1GW3Ou3cKEYU5mzB0XuZLO2vIqDa93PVb9iw+SO20+isnc67ladPuAmkNiFfS09Fim6zqK2dr10Xhz5sde5r8DIcQh6bpOfVM7G6p2s6Wqkeff3kax3sjNBc922e6CnI848eyzGB6oxrv6YWyW0Qw76250vw/3lg+pfX0ZAAVzLiRr6DiaP3kFz1efsO+pu6i45DbjXEFjSrDsEZOp+ObPeTbB41pXXH4Hex+/jeZPXib/2EVd3nOwrRk94KP49Kvo2L2F1g1vyRW3ECJ1Wje+Q9DrwTn5pB7d2tweH19WN7K5qpEtO11sqW7E1WLcpLunaBkn5yn8pfXkXo9b9vrthGdg9NZsp+XTf1P/8p8jN/lyxs+iaN4lAGQNPYKqe67Cs20d2+68gLLFN1Gz4m4A7GOmJWUyAvuISQD49u9h250XUHH5HZis2ex+5MfkH290K7TkleBvrgNAsWR+7GX+OxDiMND5MEsb0wpbuKhyF449HwPQ+PYK/OfcyZZdTUZQVzWyq7aV8MxblaVOZowv5Xj36wxxKLAdzIrON51vA3Br42J+Wbi8xzlzZ5xOyyevRMb1ALAUllN24X93vnYWUH7Jbez72x0A1Cz/dWTdgZpOEiFnwnG0bTa6He59/DaKTrkcgKb3/wWAOScPs9MYpEr3eXs/SAaR4BYizUWP7XF81lYuUd6DqCGqA021PPXHh2kMOnBmW6gYdhRzjx7GESMKGT+8gByrTtW91xBsb+1yXJsSoNpfRItu52+tJ+A12zn1a/MZs/ERcqefRv4xZ5I1ZCT1L/0JgLwZZ1Cy8Joe9dlHTyNvxhk0f/Jyl+VKEtuSLc7CLq/bq7/o8tqUnYO1wBiD299Um7S6EkWCW4g0F56+6+SsTVzg+Ciy/HPvMLbnH8PZnme42PF+ZHm2rYryk29GsWXT8MZfqX3vmS7HK5x7CbqvA9e7K+kwO1CArxxTWbJwIifPHA6z745smzfzTPJmnom/1XXArnaKolA495IewR0ewS8pul3d6/6ufbdNWQ7MDmNAqWCHJ2llJYoEtxBpLjwTzOysLwF4rPUk1npHowDP/vzruN510vDGE5Ht26s3sePuy7scI2vYBLLmf5uSEeOMbXZvwfXuSuZceDGnH3n8IWuwOAsOut6ck0veMQtxb/6AQGhcEMekE2N9iwNmHzGZ5o9eiLwOdnvoxpTtgNZGACwFQ5JWV6JIcAuRZqIHZ8p1hAf616mwuHiz/UjWekcDUFJoB6Bg9nkUzD6PoK8D9xfvUf/yw+hRV7tF879JwezzaGjoHGgpu3I8I294DHMcB1kqOeM7lJzxHQLuJlBMSR15L2fCsV1edx+bRLFmkVUxlpKzrjvgo/GZRIJbiDQS3Z4N0Ow2bqRNy9oFgI7RS6O3sT1M1ixyp8zDOfkkAq0uqu67hiHn/gDn5N6vfOMZ2l2O68hPyHEP5lC9V8Lr86ZnzkzuByPBLUQaWbZqEwGflyWOd3CYOlCACda9kfWveY465MMsismMJa+YMbf0fzJdkd4kuIVIA+HmkbpGD9/PfZWx1lr2+gvwR00L65g0hyfPuziFVaY5kwVrcQW+uuquizN0erKDkeAWIsXCzSM+n49Ks4uxVqO72kOtp9AQdDLSXMeUvEauOef7Ka40vY360TIUk4mq+64l4HZRMPt87GOnYxsyKtWlxZ0EtxApEn2VbSbAuTlrmJtt9D9+3TOZhqBxpbjPVM6FC89Iar/oTBR+ejRnwrG0fPIKeTPPwJJXkuKqEkO+E4RIge43Ia/LfY0jrDXs8hfyavsU1nuN9utkDM402BSfdgV5Ry8YtKENEtxCpITxUI2fcZYaJll3c4S1BoDnPTPY5DOm4yottPPIraenssyMZLJmkVU+JtVlJFTMwa2q6gXAz4HRQD3wA03TViaqMCEGM7fLxXG26i6znC93HxsJ7f5O5SUODzEFt6qqpwC/By4B3gWKgcycHlmIFNv/2l/4VeGzPZa/3XEkIM0j4tBiveL+BfALTdPeDr2uC/0nhOijpg86Q7staOPR1rlYlABZVjNLF0+TwBaHdMjgVlXVDBwLPKeq6haMCYleBv6fpmlNCa5PiEGl+wBHOSYvW/wVlBbaWSpX2SJGsVxxlwFW4GLgFKAVeByj6eTKWE7icrkIBoP9LBE8Hk+XcRbSldQZX4OxzmBb12udhoCDW5ZMZfxw4zHxRL7fwfh5plIi6zSZTBQUFBxwfSzBHR6t5n5N03YBqKr6S+D5WIs4WAGxaGhooKioaEDHSAapM74GY51+m4nmqNePu0/kR+UlFBUl/pbRYPw8UymVdZoOtYGmaS6gGtATXo0Qh5HaMV9jm78Mpz3z50AUyRXrzck/A0tVVX0RcAM3Az1viwshDqHz+mdX4THADpw5Etyibw55xR1yF/A2sBH4CmgAfpCoooQY7ErOvIYmr5ksmxmrJXlzM4rBIaYrbk3T/MD3Q/8JIforqsGxtc1HrjSTiH6I9YpbCBEXoeRWFFo9Xpw5toNvLkQvJLiFSJGWNp+0b4t+keAWIpn0zrYSt8cnPUpEv0hwC5EKikJLm5dcaSoR/SDBLUSKtHp8OOSKW/SDBLcQKRAI6nR4A3LFLfpFgluIpDLauDu8xsw3cnNS9IcEtxDJFLo52R4K7ly7XHGLvpPgFiIFwnNNOuSKW/SDBLcQSaTT7Ypbglv0gwS3ECkQvuJ2SlOJ6AcJbiGSKfT8TXuHXHGL/pPgFiIFPN4AigI52RLcou8kuIVIqs7ugI5sKyaTkuJ6RCaS4BYiBdq9AenDLfpNgluIZIr04/bLkK6i3yS4hUiBDm9QRgYU/SbBLUQKeLx+GadE9JsEtxDJFPXIu1xxi/6S4BYiBeTmpBgICW4hksq44tZ1eWpS9J8EtxApoCNPTYr+k+AWIomippyUphLRbxLcQqSI9OMW/SXBLURSdV5yS68S0V8S3EIkU6itREeRftyi3yS4hUgBHbniFv0nwS1ECphNClk2c6rLEBlKgluIFMiyWVAUGdJV9I8EtxDJFGrjtmfJ1bboPwluIVIg2ybt26L/JLiFSCrjilvat8VASHALkQLZWZZUlyAymAS3EMkUev7GbpPgFv0nwS1EEvkDAQCyJbjFAPTpu0dV1RLgC2CrpmnHJ6YkIQYvT4cfgCxpKhED0Ncr7t8CGxNRiBCHg7Z2HwB2CW4xADEHt6qqc4EjgEcTV44Qg1tbu3HFLTcnxUDEFNyqqtqA+4HriR7eTAjRJ20e44pb2rjFQMT63XMT8JqmaZ+qqnp0X0/icrkIBoN93S3C4/HQ0NDQ7/2TReqMr8FYZ31jM/lAMNCR9Pc2GD/PVEpknSaTiYKCggOuP2Rwq6o6DrgCmN7fIg5WQCwaGhooKioa0DGSQeqMr0FZp8n4kSsuzE/6exuUn2cKpbLOWK64TwTKgS2qqgLYAbuqqvuAkZqmdSSwPiEGlTaPtHGLgYvlu+cp4KWo198AlgBnSWgL0TdtHUYbt9kkj1CI/jtkcGua5gE84deqqjYBPk3T9iWyMCEGI0+oO6AQA9Hnv9c0TXsMeCzulQgxyK1eU826zXXMc8K9y9dxwsIK5s0cnuqyRAaSv9eESILVa6q5f/mn+AJG76rmVi/3L/+U1WuqU1yZyEQS3EIkwbJVm+jwBRhpqQeMhyE6fAGWrdqU2sJERpLgFiIJ6huN20Rn2dcC0BrM7rJciL6Q4BYiCYoL7ACYFZ01HaPYGSgFoKTQnsqyRIaS4BYiCSqKcwCwEKAx6AAgy2pmycKJqSxLZCh5CkCIBFm9ppplqzZxq6IxyjMZKo7B0hHErWdTWmhnycKJ0qtE9IsEtxAJEOlF4vNBEZxm38BHrV6wwvU3XIGteGiqSxQZTJpKhEiAcC+SJc63IstmWb8EwFpUnqqyxCAhwS1EAoR7ixxt29ljnaLIj50YGPkOEiIBpLeISCQJbiESYMnCiZgUpcdyr1OaScTASXALkQBzplViMfdcXlA5MvnFiEFHgluIBFi/tR6vX0c3dXbcsuSXUnrWdSmsSgwW0h1QiDgK992ua/SgAL7sQmxtdQAUzbsMsz03tQWKQUGCW4g4Cffd7vAFAJhsrY6ENoBiy05VaWKQkeAW4gD0gA9d1zFZbL2v13Wa3V6+3NVM61etPPTMejp8Ac6yr+V0+/oe2ytm+XET8SHfSeKwFW7WqG/0UNLtEXR/cz1V96nGhmYrgbnXscs2hj11bvbUt7Kn3s3eulbc7f4uxxxjqek1tAGQ/tsiTiS4xWGpe7NGXaOHe/+xji92NlBhdjHl83s7Nw74cL36MP/bdAGKAqUFdoaWOJk7YxhDS53kZulMGFPObX98l3l+Y3ztfYF8ft10Dgvt6+jILmbx8L1kD5uQircqBiEJbnFYaWrtoGpfC9o/1+P3efm28y3yFA9BFJ71zMC69gOmZPec3KDY7Oa+bxQSfO1eyi78bxzjZ0XWNTQ0UFTkZMnCIxnxsgbAr5rOARRe9x/D0oXTqJTBpEQcSXCLjHKw5o1orR4fVfuaqdrXws7Qv1X7WnC1dkS2GW+pZZqtih3+EkaZ65lmrWJ+VGiP/MGjYDLj3vA29S89RPDVewCoWf5rxtyygqDfS6C5Ht2n0F79BTMsu6gP7augHLQ+IQZCgltkjN6aN55Z8RojXnqe/ePO4jP7saGAbqa+qT2yX7bNzIgyJ8dMLGNkRS4jyvO496m1nKt/DMADzQu4If9FZmZtj+xTcfkdmHPyAHBMmkP9Sw91qcX9xQfUrPgNAJZR02ja8Wlk3bBr/o9nS0ck5kMQAglukSECgSCPPr+BDl+AY2zbmGnbjkUJ4NeNG37FW19gVXMxlUPyOWpcCSPKchlZkceIfAVH8zbqVt5N2dE34pgwDoArFo6n8pVGPEErHVjx6hbKzU0A5M08E/uISZFzm+1OyhbfxP5XH6XghHOpX6VFQhvAHxXaZkc+NgltkWAS3CLtNLu97NjbxIat+6h17WT73iaq9rXg8xszpH/D8R42JdBjv4cWecmdOok9y27DUTwLZ/5c9jx2E22h9TVP/4Yxt6xADwaYlV9PDfAv5VQUYKjZFTlO4UkX9Ti2Y/wsHONnEWhrpn6VFlluGzISb+1OLAVlBNvdlC3+SRw/CSF6J8EtUsYfCLK7tpXte5vZsaeJHXub2b6nmYbmzmaOfKeN0RX5nDVnNK9/VEVLm4+AboKo4A7qCiZFx/Wfv2OyWAk019P88SqaP17V45wd+7ax++EfR17f+F8XYMktwrN9NHuf/DlDv3UXZkf+AWs25+RR/o2bQYfskZMw2ezUrPk3pVPnYLJmxemTEeLgJLhFXPV283CGeTOutW/QcPx17NzbzLaadnbsaaaqpgV/wLiKtpgVhpflMu2IEkZV5DNqaB6F9iCjR3SOpje2Mp/7l3+KWQnyumcSbXoWZ+espW3YLJy7PwSg4d+PH7S+6NAGMDsLAbCPnsqYW1bE9B5zxs3s8to6erqEtkgqCW4RN+GbhzmBJoab2zG3BHlu+TZG5L4KQN7K/2JM0MbK4LcYVZHP0RNKGVWRx6ih+VSWOrFaTOjBAK63V2BTRtNu79pWHO6dYVkVJICZTfbpzK+0MvHcKzBnL2XH75b0Wteo//4bO+6+HAJdH5bJPfp0lF6GXhUi3Ulwi7h56Jn1mP1ubiv4J2ZF73Ubh8nLr8a8z9DLbu91fdvWT2h86ykAlGwnxT/8S5f1J47LpkrR+fpEuPayRcCiyLqC2efjencl2SMmUXbhjZhsdnRfByaLjVE/eIyG1U/S+vl/KL/kNvxNteQccUxc3rcQySbBLeJi9ZpqWtp8DDO7MSs6qzxT2e4bQgATXt3Cry4dha+uiqYPn6d9x3r8zfux5BUD0L5rM+4tH9L03jNdjqm3txLwtERG1Gte+xr1Lz4IgCnb2aOGwnmXYB87nazyMZhsxgw04fFBTFl2Ss64ipIzrjI2HjouER+DEEkhgyeIuFi2ahMmgnwv7xUAvvANZbN/KFv95XjyhpM3/VSKF1yJrXwsAFX3XUPtM7/H39LAnr/c3CO0SxYa44Q0r3kZf6sLXQ+y/9VHI+uL5l/WowZFMWEfMTkS2kIMVhLcIi7qGz2Ms9SQrfgA2OUvjqxbsnBi5Ouy82+IfN264S2q7r26x7Eqr/wfco8+DVNBOY1v/o3qB66ndf1/0H1Gb5OKS3+GtagiUW9FiLQnwS36bfWaar79y1c454f/AgUKTW4AtvjK8WPM25WbY+3yyLelYAj2MdN6HGv0zcuxDRlF8YIryRo6zrh6nm30p9Z97bRtNZ5ytJWPxT56aqLfmhBpTdq4Rb9EP34+1rIPu+LjUue7AGgtpwKQZTVzzblTuuynKCYqLvkpAU8LrrefpunD5ylddD2KYmLY1b/rsq115BSGXf2/7PrTDbg3vYfZkU/FpT9NzhsUIo1JcIt+WbZqEx2+AA6lne+H2rXDApgpPcQAS2Z7LsULrqR4wZUHPY+1tHP/vFmLMNt73pQU4nAjwS36pNXjY+3mWuoaPQBMsu7usv6PLafy7O++HrfzKYoJ++hpeLZ/iq1URtkTAiS4RciBhksNtLupfulxPs05nqYN77Bq7xBaAzYUBXQdxlv3Ro7xTNtM6p3x72ZXftFPcG/+QPpdCxFyyOBWVTULeAA4DSgCtgG3aZr2bIJrE0nSfbjUwpZtjHhJY+WbxzHV8yEmdKZgPP145IiJ5J51A3v3u/nj02s5NmsbAP9qm8G7gSksjepBEi+KxYpz8olxP64QmSqWXiUWoBqYC+QDNwFPqqo6PpGFieQJt1ePsdSw0L6O6/OMkJ7u+QATXZ+ALGnaxPgyK6ccM5ybp1YDsLZjJOvts1i6eLpMGiBEEhzyilvTNDdwe9SiVaqqbgFmAVsSVJdIAn8gyCdR7dWL7GsZa63tso3JnotjwnG0rHstsqzqD9cy6kdPkLf93wB87TtXccGIyckrXIjDXJ/buFVVLQUmAhviX46Ip+7t1t9aMIbZEwv5ancL/1i9i7fW7abZ7Y20V1uVABu9lWitRne+0kI7j9xwOgD5x52NJbeIHXdfju5tZ/tdF0bOY5fQFiKp+hTcqqpagCeApzRNWxfrfi6Xi2Aw2MfSOnk8HhoaGvq9f7KkU53vfl7Loy98idcf5Ejrbs4PfoT1lQDVr7l5t+1o3vVP5ttln1E5tINtR3yDv7xShYkgAYzR8mwWE+efPKLz/ZhywN2O46z/wv3CPZHz5My/MmHvOZ0+z4OROuNL6gSTyURBQcEB18cc3KqqmoDwYMfX9KWIgxUQC2MW7aIBHSMZUlmnt7YKS14xbbqNffvd/O217Xj9QYaaG7ku9/Uu256ds5av52wj2NYEHpgz/jPyLppH1qpnCAQP0Qe76GSa8VL/woPYx86gfPaintvEifx/jy+pM75SWWdMwa2qqgI8DAwFFmqa5k1oVYcR95cfo3d4cB51Ukzb+/xB6hrb2Le/jZoGN/v2t9FUV8M5e/8AGF3y3mg3mi7GWfZFBn0K2+CtZLJttxHaIU3vPcOcpWdQrbgYOWUC5194+kFryJt+GtnDJ0ZG7RNCJFesV9wPYrRrL9A0re1QG4tOB+ofDRD0tlPzj18B4Jg0G8VkRtd19rz6BJ6dG6k++jpqGj3s2++mpsEI6/1NHvSojh4Ws4n5Bbsir8/NWcOJZ57G/a838D1rZ2i/0T6R+dmbeM56BsfM9eH9+DlKF13PvqfuBKD6/usA8NbujOl92YorB/S5CCH6L5Z+3CMBFegA9qqqGl51l6ZpdyWwtozXtX+0ziLfKpavqKHDdxLjRxRSv+NLwmPobf/VRXxqmoSn3c/xti2YgOJVN/Flxzg+tZ3AkCInU8eVUFZop7zEQVmRg/LiHApzs2lc/QRN73Wed5TrA24u3AytxutbGhfTqttZ5TuepYunkjXaQcWJ5wIw4nsPUXVfZ8tX+YU3JuOjEUIMQCzdAXcCMr9TP4T7R4+y1HGV8w3yTO1Mt1Xxg+VORlrquczxDqFB9ACYFtwIts7XTlMHp9k3cBobqFh0O7rPy75/3ErOhOMYctT1KFYL23/V2btj9M1Ps/2uC2n9bHXkMPfo38Stm7q0W0ffULHkFTPmlhUE2t0EPS1YCzvneBRCpCd55D2Bwv2j52RtJs/UOXP5/xU90WW74d97iOqoq97CuZdgHzUF9xfv0/SB8YDq3r/eHlnftvkDqnZ+TuW3f9PlOIqiYCksx9+4D4DSs5dyz9T5MdVqznZgznbE/uaEECkjwZ0Abe0+/vbK5shrM0FqA7k82zaT7+Sujix3HnUy+cedgzV01avrOp6tn2AfOx3FZCZ72AQcE2ez57GbIvs4jjwe9xfvE2x3U/3A9ZHlw675PwDKF/83ux76ASVnXk1ujKEthMgsEtxxEL4BWdfoIc9hIxAI4m73c0nldj6qz8WsBAnoJtb7RvCL1ou5YcJ2RowfR8Hs87scR1EUco6Y2WVZduURVFz6M5o/eRl/834K512KyZ5Ly9pXI9sMu/p/sZUaM6LbSkcw5pYViX/TQoiUkeAeoPANyJxAE5VmL7SDosBdRc+DB453QLVeRjAQbmeewdSZi/t0DvvoqV1mfdED/sjXudNOxTZkZNzejxAi/UlwD0DA3cTjz63jhzkrKTM3H3C74UoN1rJKHrn24P2jY1Uw+zxaP3sDQEbNE+IwJMEdoy79sQvszJ9SyJwNv+YWa+c2D7fMRUeh3NzEopy1Xfb37d9NvFjySjq/LpJeIEIcbiS4YxBuDvH6/FSYXRS7q5izYXWXbZ5sPYHPfEaTxXofrLMfy8O3LIgMxmQNtUHHg8maFfnaklt8kC2FEIORBHcMwv2xj7bt4ArnW5HlG/SxTLRU0+yz8IH3iMjyLKuZJQsnoigKld/+De3Vm8g/NjFjeigm86E3EkIMKrFMpHDYC/fHLjYZjyK6g8bjLY82Hs/o7/2RltN/RmmhHTCGQl26eFrksfasirEJC20hxOFJrrgPILqLH8DinPc5MduYN+Jm18WAEdJmRz5zj8tn7nHjMmZUMyFEZpPg7kW4TTvo6yBHCTDZuisS2vsC+UBnc4gQQiSbBHcvlq3aRE6giVsLn8GidJ0A4u6mRQcfr1oIIRJMgrsX9Y0exlhasShB3mw/kjbdRk0gn8+8I3nmd+elujwhxGFOgrsXzhwrdp8PgI87xlAVMPpNh29ACiFEKkmvkm5Wr6mmrd3PUHMjAPuDTgAsZkXatIUQaUGCu5tlL24iENSZZtuJO2jDrWcDYM+ySJu2ECItSHBHqdrXTJ3L6P5nRmd/sHNOxdY2X6rKEkKILqSNG2j3+nnq1S38c/VWFAV0HbIVL9X+znFASqR9WwiRJg7L4I4eMCrPYSOo67S0+Th11nDGDy/ksefWk2fy4AoaM8JIn20hRDo57II7/HANvnaKTR7wGBNqnnfiKM6dWwHAsC0bMe/RqQ3kSZ9tIUTaOeyCe9mLmzD5Pfy0YCU5Jm/nio1QvdH40hladOsvru8yEl86yR41hfYd61NdhhAiBQ6r4F67uRaXq4W7i/4OwJe+Mt7v6BzV74ZLZ6D7OvA17CX36AVpG9oAQy+7PdUlCCFS5LAI7rpGDw//az0Tt/+Vu4t2RZY/2HIaAYxhUUsL7eROmZuqEoUQImaDOrh9/iDPvLmVp17bwiTTTqbkdIb2f9onREJbbj4KITLJoA3utZtreWLl+3Q01jLjyMlcXunC93Hn+k+zZqK0Gd385OajECKTDLrgrmv08PCzn/POZ3u4q2g5jnwP2ZYdtH+8CYD8Yxfh2bmB//vOBSmuVAgh+mfQBHd0s4ge1PnWqSNwrDWegmyvNkJbsdkpXnBlKssUQogBy8jg7jLjeqGdk6dX8v7n+9hd18rxR5Vz1RmjUT78K+6ofSyF5VRe+euU1SyEEPGSccEdfoCmwxcAdIa7N5L74UtcZ6vF953fMfOIIrb/z8U99is88ULM9tyeBxRCiAyTccEdnnG91NTMj/OfJ0vxd65c+V22R21rHz2Nikt/mvQahRAikTIuuDtcDQw3uxlv3dc1tLsZ/t0/YMkvTWJlQgiRHBkX3D8rWIlFCRx0G/uY6VgLyw+6jRBCZKq0Dm7d7yPgaYm8rv/snR6hrbWcwgWOj/Cd9F2OP26itGMLIQa9tJ5Ioe7FB6m692r0gJ8OX4DtLyzrsv5p97HUOY+g7Wt3MGfesRLaQojDQlpfcXu2fQpAy99/RlNzLcXd1n/v2kXYR0xOfmFCCJFCMQW3qqoFwEPAQqAZuFPTtAcSWBcA9lFTaN3wFsHm2l7X24aMSnQJQgiRdmJtKrkfI+SHAmcBP1dVdX7CqsLor/3u5zU9ljunzqf80p+Sf/zXMWc7ElmCEEKkpUMGt6qqDmAxcKumaS2apq0DHgG+naiiwg/Z5PobcQW7zfWoB8kZPY3iU5ck6vRCCJHWYrniHg8omqZtjFq2DjgqIRVhPGTj93kZba0jV2nn3uYzuLf5DAByxs1M1GmFECIjxNLG7cRo147mAmLuwuFyuQgGgzEXVdfoQQn9TvnIO4av/GUA3NhwMQ+VT6ShoSHmYyWTx+NJ29qiSZ3xJXXGl9QJJpOJgoKCA66PJbhbgbxuy/KBll627dXBCuhNaaGdukYPNzZcgi802QFAXmE+RUVFfTpWMjU0NKR1fWFSZ3xJnfEldR5aLE0lWwBdVdXoKWKmA58npCJgycKJZFnNdGAlGCpRZqkRQgjDIYNb0zQ38DRwh6qquaqqTsW4MflIooqaN3M4SxdPo7TQjgIU52WxdPE0maVGCCGI/QGc64E/AXsx2rtv1zTtjYRVhRHe4aDOlD+dhBAiGWIKbk3TXBhdAoUQQqRYWo9VIoQQoicJbiGEyDAS3EIIkWESHdzmQ29yaCZTZvx+kTrjS+qML6kzvpJUZ68Zqui6nsiTngi8lcgTCCHEIHYS8Hb3hYkO7ixgFkY3woPPNyaEECLMDFQAHwEd3VcmOriFEELEWWY0JgkhhIiQ4BZCiAwjwS2EEBlGglsIITKMBLcQQmQYCW4hhMgwEtxCCJFhJLiFECLDxDqRQlyoqpoFPACcBhQB24DbNE17NrT+KODPwNTQuus0TXsrat3vgGOAIk3TlF6OPxf4LTAJY07MOzVNuz+d6lRVdQMwMmpRNrBK07Sz06zOQuAPwOmAAvwntP++NKuzHLgfmA/4gPs0TbszyTV+C/g+cATG991TwE2apnlD623AfcA3QjU+qGnaT/taYxLqvAj4fxhTE36oadq8/tSYhDrvBr4OlAN7gN9omvZwGtb5Q4xJaEow5u59CrhR0zRff2qNluwrbgtQDczFmHD4JuBJVVXHq6pqBZ4D/gkUAr8C/hUKEDC+4f+BMW1aD6qqTgCWA3eE9p8AvJ5udWqaNlnTNKemaU4gN3Se5elWJ3AnMAQYB4zAeOz2njSs83GgDhiKMTbONaqqLklyjTkYgVeK8QvmJODmqGP/FOMHfxzGEBCXqqp6ZT9qTHSdDcDvgV/3s7Zk1ekGzg4d95vAb1VVnZ+GdT4DHK1pWh4wBZgG/KCfdfYoOmlC81feHrVolaqqWzC+mUcCduC3mqYFgb+qqvp94HzgYU3TNgObVVUdd4DD3wb8SdO050KvfRjTrKVbndFOxvhtvCIN6xwNrAzNfoSqqn8D7kqnOlVVdQKnAt/SNK0D2Kqq6iPAVcCyJNb4YNR+e1VVfRwjWMKuBK7WNK0eqFdV9XcYv4ge7UuNia5T07TXAFRV/U5f60pynT+LWv+RqqqrgdlAn6dTTHCdX3U7XRDjl/eAJTW4u1NVtRSYCGzA+FN3fegDClsHHBXj4U4Atqmq+inGn1DvAN/TNG13mtUZ7VvAitA3z4DFuc4/AEtVVX0K8GJc2axKszqVqP+il01NcY0nh/YLNzkNBT7ttm+/fgkmqs5ES1SdoaaOY+njL+pk1amq6qXAHzH+ut4P/Dgedabs5qSqqhbgCeApTdPWAU6gqdtmLow3HIvhwBXAxcAooD50/HSrM3zcHOBC4LGB1hg6XrzrXIsxQlldaL+RdL0ySXmdmqa1YLS9/0xVVbuqqkdiXN3mpKrGUDPNiXQ2NzhD/0bv3+u+Ka4zYRJc5wPAFuDZdKxT07QnQ00l44EHMUZKHbCUBLeqqiaMtkmAa0L/tgJ53TbNx2j0j0Ub8BdN0zZpmubBaDqZq6qqI83qDDsfo03xzf7WF5agOpdj3IzJC/33EfD3NKzzmxht8Tsx2sL/AuxKRY2qqp4D3A2cGXUTtzX0b97B9k2DOhMikXWqqvo/wAzg/G5XxWlVJ4CmaV9iXI0/MJA6w5Ie3KqqKsDDGH8+nhe+Awt8DkwJfYBh00PLY/EZ0NsYtT16n6S4zrBvAcs0TRvQuLoJrHMq8JCmaa2hppwHgTNC50ubOjVNq9Y07VxN04ZomjYVsAHvJ7tGVVXPBB4BzgldrYXra8To+TDtQPumQ52JkMg6VVX9OUZ78unh+zDpWGc3FmDsQGqNPlCyPYjRhrRA07S2qOWrgXbgh6qq3otxRToe445u+MPNwvjBRFXVbABN09pD+/8ZuENV1WUYd4lvB97QNK2V/klUnaiqOgyj/ezaftaWjDo/AK5SVXUjxi/EazDa+/r7iyYhdYaaR/YAHuBM4DsYf7Ims8ZTgL9iXPn19kvjMeBWVVU/AhzADRg9FPorIXWqqmoGrBi5YAp91sGoIEuXOn8CXAacpGlaXT9rS0adVwPPaJpWp6rqJOAnwMtxqDfp/bhHAipG17K9qqqGV92ladpdoT85/gz8AuPP9HM1TWsIbTMS2B51OE/oXwVA07RlqqqOwLgpacVogrg83eoMuRx4r5e7zulU57cx+h7vCi37GOOHJd3qPA2ju50D2AhcpGnaF0mu8TaMP6FfiNpvp6Zpk0Nf/xyj99BXdPbj7nOPkiTUeTlde7p4MH6O5qVZnXdh3DD/Mmr9E5qm9flCKMF1ngzcGWqurcNofrytrzX2RmbAEUKIDCOPvAshRIaR4BZCiAwjwS2EEBlGglsIITKMBLcQQmQYCW4hhMgwEtxCCJFhJLiFECLDSHALIUSG+f+Yo9FtHaRu+QAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Index arbitrage\n",
        "\n",
        "We copy a list from the top S&P500 components from a website and extract the tickers:\n",
        "https://topforeignstocks.com/indices/components-of-the-sp-500-index/"
      ],
      "metadata": {
        "id": "7_8A4kW1EJ0Y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "q=\"\"\"Apple Inc.\tAAPL\tInformation Technology\n",
        "2\tMicrosoft Corporation\tMSFT\tInformation Technology\n",
        "3\tAmazon.com Inc.\tAMZN\tConsumer Discretionary\n",
        "4\tBerkshire Hathaway Inc. Class B\tBRK.B\tFinancials\n",
        "5\tAlphabet Inc. Class A\tGOOGL\tCommunication Services\n",
        "6\tUnitedHealth Group Incorporated\tUNH\tHealth Care\n",
        "7\tAlphabet Inc. Class C\tGOOG\tCommunication Services\n",
        "8\tJohnson & Johnson\tJNJ\tHealth Care\n",
        "9\tExxon Mobil Corporation\tXOM\tEnergy\n",
        "10\tJPMorgan Chase & Co.\tJPM\tFinancials\n",
        "11\tNVIDIA Corporation\tNVDA\tInformation Technology\n",
        "12\tProcter & Gamble Company\tPG\tConsumer Staples\n",
        "13\tVisa Inc. Class A\tV\tInformation Technology\n",
        "14\tHome Depot Inc.\tHD\tConsumer Discretionary\n",
        "15\tTesla Inc\tTSLA\tConsumer Discretionary\n",
        "16\tChevron Corporation\tCVX\tEnergy\n",
        "17\tMastercard Incorporated Class A\tMA\tInformation Technology\n",
        "18\tEli Lilly and Company\tLLY\tHealth Care\n",
        "19\tPfizer Inc.\tPFE\tHealth Care\n",
        "20\tAbbVie Inc.\tABBV\tHealth Care\n",
        "21\tMerck & Co. Inc.\tMRK\tHealth Care\n",
        "22\tMeta Platforms Inc. Class A\tMETA\tCommunication Services\n",
        "23\tPepsiCo Inc.\tPEP\tConsumer Staples\n",
        "24\tCoca-Cola Company\tKO\tConsumer Staples\n",
        "25\tBank of America Corp\tBAC\tFinancials\n",
        "26\tBroadcom Inc.\tAVGO\tInformation Technology\n",
        "27\tThermo Fisher Scientific Inc.\tTMO\tHealth Care\n",
        "28\tCostco Wholesale Corporation\tCOST\tConsumer Staples\n",
        "29\tWalmart Inc.\tWMT\tConsumer Staples\n",
        "30\tCisco Systems Inc.\tCSCO\tInformation Technology\n",
        "31\tMcDonald's Corporation\tMCD\tConsumer Discretionary\n",
        "32\tAbbott Laboratories\tABT\tHealth Care\n",
        "33\tDanaher Corporation\tDHR\tHealth Care\n",
        "34\tAccenture Plc Class A\tACN\tInformation Technology\n",
        "35\tNextEra Energy Inc.\tNEE\tUtilities\n",
        "36\tVerizon Communications Inc.\tVZ\tCommunication Services\n",
        "37\tLinde plc\tLIN\tMaterials\n",
        "38\tWalt Disney Company\tDIS\tCommunication Services\n",
        "39\tWells Fargo & Company\tWFC\tFinancials\n",
        "40\tAdobe Incorporated\tADBE\tInformation Technology\n",
        "41\tPhilip Morris International Inc.\tPM\tConsumer Staples\n",
        "42\tBristol-Myers Squibb Company\tBMY\tHealth Care\n",
        "43\tComcast Corporation Class A\tCMCSA\tCommunication Services\"\"\"\n",
        "\n",
        "stk_list = []\n",
        "for  string in q.split():\n",
        "  if all(l.isupper() for l in string) and len(string)>2 and len(string)<5:\n",
        "    stk_list.append(string)"
      ],
      "metadata": {
        "id": "67uFgM1No0Jj"
      },
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now we can download the price data for those tickers"
      ],
      "metadata": {
        "id": "Q4k-7szcEb6V"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.shuffle(stk_list)\n",
        "tickers = \",\".join(stk_list)\n",
        "top40 = yf.download(tickers,start='2010-1-1').Close.dropna()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "40ca6f9e-abd5-46c5-85e5-5b395ff390a0",
        "id": "U1oInm3clJ_k"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  33 of 33 completed\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here we plot them:"
      ],
      "metadata": {
        "id": "NOrMXsZSEg1v"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "top40.pct_change().cumsum().plot(legend=False)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "b4XJ1XO_q3dZ",
        "outputId": "56180222-2b20-493e-dc47-c840baaee80a"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Date'>"
            ]
          },
          "metadata": {},
          "execution_count": 30
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we can create an eigen-porfolio using the first principal component as weights."
      ],
      "metadata": {
        "id": "pXPgBCs2EpAw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "top40\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 692
        },
        "id": "0hdp24M_cSey",
        "outputId": "465b80a0-a221-4dbc-f752-063a10da3ed6"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                  AAPL        ABBV        ABT         ACN        ADBE  \\\n",
              "Date                                                                    \n",
              "2013-01-02   19.608213   35.119999  32.049999   69.059998   38.340000   \n",
              "2013-01-03   19.360714   34.830002  33.270000   68.809998   37.750000   \n",
              "2013-01-04   18.821428   34.389999  33.070000   69.190002   38.130001   \n",
              "2013-01-07   18.710714   34.459999  33.340000   68.889999   37.939999   \n",
              "2013-01-08   18.761070   33.709999  33.349998   69.290001   38.139999   \n",
              "...                ...         ...        ...         ...         ...   \n",
              "2023-03-20  157.399994  156.119995  97.870003  252.550003  362.880005   \n",
              "2023-03-21  159.279999  156.770004  98.330002  257.619995  374.220001   \n",
              "2023-03-22  157.830002  153.669998  96.860001  253.270004  361.709991   \n",
              "2023-03-23  158.929993  155.300003  97.040001  271.660004  369.000000   \n",
              "2023-03-24  160.250000  158.020004  98.050003  272.000000  374.959991   \n",
              "\n",
              "                  AMZN        AVGO        BAC        BMY        COST  ...  \\\n",
              "Date                                                                  ...   \n",
              "2013-01-02   12.865500   32.540001  12.030000  32.709999  101.449997  ...   \n",
              "2013-01-03   12.924000   32.709999  11.960000  33.240002  102.489998  ...   \n",
              "2013-01-04   12.957500   32.500000  12.110000  33.349998  102.160004  ...   \n",
              "2013-01-07   13.423000   32.320000  12.090000  33.400002  101.370003  ...   \n",
              "2013-01-08   13.319000   32.099998  11.980000  33.490002  101.180000  ...   \n",
              "...                ...         ...        ...        ...         ...  ...   \n",
              "2023-03-20   97.709999  643.710022  27.750000  67.239998  489.290009  ...   \n",
              "2023-03-21  100.610001  636.750000  28.590000  67.510002  490.850006  ...   \n",
              "2023-03-22   98.699997  630.919983  27.639999  67.239998  487.519989  ...   \n",
              "2023-03-23   98.709999  639.229980  26.969999  66.980003  487.760010  ...   \n",
              "2023-03-24   98.129997  636.169983  27.139999  67.680000  495.269989  ...   \n",
              "\n",
              "                  NEE        NVDA         PEP        PFE         TMO  \\\n",
              "Date                                                                   \n",
              "2013-01-02  17.629999    3.180000   69.330002  24.582542   65.000000   \n",
              "2013-01-03  17.632500    3.182500   69.360001  24.525618   64.800003   \n",
              "2013-01-04  17.719999    3.287500   69.459999  24.629980   65.370003   \n",
              "2013-01-07  17.637501    3.192500   69.449997  24.648956   65.879997   \n",
              "2013-01-08  17.825001    3.122500   69.660004  24.686907   65.470001   \n",
              "...               ...         ...         ...        ...         ...   \n",
              "2023-03-20  75.970001  259.000000  177.589996  40.810001  550.570007   \n",
              "2023-03-21  75.360001  261.989990  178.009995  40.660000  556.700012   \n",
              "2023-03-22  74.129997  264.679993  176.509995  40.009998  554.320007   \n",
              "2023-03-23  73.809998  271.910004  175.649994  40.180000  555.190002   \n",
              "2023-03-24  75.690002  267.790009  179.089996  40.389999  558.260010   \n",
              "\n",
              "                  TSLA         UNH        WFC         WMT         XOM  \n",
              "Date                                                                   \n",
              "2013-01-02    2.357333   54.540001  35.049999   69.239998   88.709999  \n",
              "2013-01-03    2.318000   51.990002  34.759998   68.800003   88.550003  \n",
              "2013-01-04    2.293333   52.090000  34.939999   69.059998   88.959999  \n",
              "2013-01-07    2.289333   52.090000  34.770000   68.400002   87.930000  \n",
              "2013-01-08    2.245333   51.400002  34.709999   68.589996   88.480003  \n",
              "...                ...         ...        ...         ...         ...  \n",
              "2023-03-20  183.250000  476.959991  37.480000  140.899994  102.449997  \n",
              "2023-03-21  197.580002  480.100006  38.480000  140.419998  107.040001  \n",
              "2023-03-22  191.149994  475.519989  37.200001  139.520004  104.589996  \n",
              "2023-03-23  192.220001  469.910004  36.610001  140.649994  103.410004  \n",
              "2023-03-24  190.410004  475.989990  36.230000  141.800003  103.529999  \n",
              "\n",
              "[2575 rows x 33 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-f92c617d-bd48-413d-a52f-e48d496bc22e\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>AAPL</th>\n",
              "      <th>ABBV</th>\n",
              "      <th>ABT</th>\n",
              "      <th>ACN</th>\n",
              "      <th>ADBE</th>\n",
              "      <th>AMZN</th>\n",
              "      <th>AVGO</th>\n",
              "      <th>BAC</th>\n",
              "      <th>BMY</th>\n",
              "      <th>COST</th>\n",
              "      <th>...</th>\n",
              "      <th>NEE</th>\n",
              "      <th>NVDA</th>\n",
              "      <th>PEP</th>\n",
              "      <th>PFE</th>\n",
              "      <th>TMO</th>\n",
              "      <th>TSLA</th>\n",
              "      <th>UNH</th>\n",
              "      <th>WFC</th>\n",
              "      <th>WMT</th>\n",
              "      <th>XOM</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2013-01-02</th>\n",
              "      <td>19.608213</td>\n",
              "      <td>35.119999</td>\n",
              "      <td>32.049999</td>\n",
              "      <td>69.059998</td>\n",
              "      <td>38.340000</td>\n",
              "      <td>12.865500</td>\n",
              "      <td>32.540001</td>\n",
              "      <td>12.030000</td>\n",
              "      <td>32.709999</td>\n",
              "      <td>101.449997</td>\n",
              "      <td>...</td>\n",
              "      <td>17.629999</td>\n",
              "      <td>3.180000</td>\n",
              "      <td>69.330002</td>\n",
              "      <td>24.582542</td>\n",
              "      <td>65.000000</td>\n",
              "      <td>2.357333</td>\n",
              "      <td>54.540001</td>\n",
              "      <td>35.049999</td>\n",
              "      <td>69.239998</td>\n",
              "      <td>88.709999</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2013-01-03</th>\n",
              "      <td>19.360714</td>\n",
              "      <td>34.830002</td>\n",
              "      <td>33.270000</td>\n",
              "      <td>68.809998</td>\n",
              "      <td>37.750000</td>\n",
              "      <td>12.924000</td>\n",
              "      <td>32.709999</td>\n",
              "      <td>11.960000</td>\n",
              "      <td>33.240002</td>\n",
              "      <td>102.489998</td>\n",
              "      <td>...</td>\n",
              "      <td>17.632500</td>\n",
              "      <td>3.182500</td>\n",
              "      <td>69.360001</td>\n",
              "      <td>24.525618</td>\n",
              "      <td>64.800003</td>\n",
              "      <td>2.318000</td>\n",
              "      <td>51.990002</td>\n",
              "      <td>34.759998</td>\n",
              "      <td>68.800003</td>\n",
              "      <td>88.550003</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2013-01-04</th>\n",
              "      <td>18.821428</td>\n",
              "      <td>34.389999</td>\n",
              "      <td>33.070000</td>\n",
              "      <td>69.190002</td>\n",
              "      <td>38.130001</td>\n",
              "      <td>12.957500</td>\n",
              "      <td>32.500000</td>\n",
              "      <td>12.110000</td>\n",
              "      <td>33.349998</td>\n",
              "      <td>102.160004</td>\n",
              "      <td>...</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>3.287500</td>\n",
              "      <td>69.459999</td>\n",
              "      <td>24.629980</td>\n",
              "      <td>65.370003</td>\n",
              "      <td>2.293333</td>\n",
              "      <td>52.090000</td>\n",
              "      <td>34.939999</td>\n",
              "      <td>69.059998</td>\n",
              "      <td>88.959999</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2013-01-07</th>\n",
              "      <td>18.710714</td>\n",
              "      <td>34.459999</td>\n",
              "      <td>33.340000</td>\n",
              "      <td>68.889999</td>\n",
              "      <td>37.939999</td>\n",
              "      <td>13.423000</td>\n",
              "      <td>32.320000</td>\n",
              "      <td>12.090000</td>\n",
              "      <td>33.400002</td>\n",
              "      <td>101.370003</td>\n",
              "      <td>...</td>\n",
              "      <td>17.637501</td>\n",
              "      <td>3.192500</td>\n",
              "      <td>69.449997</td>\n",
              "      <td>24.648956</td>\n",
              "      <td>65.879997</td>\n",
              "      <td>2.289333</td>\n",
              "      <td>52.090000</td>\n",
              "      <td>34.770000</td>\n",
              "      <td>68.400002</td>\n",
              "      <td>87.930000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2013-01-08</th>\n",
              "      <td>18.761070</td>\n",
              "      <td>33.709999</td>\n",
              "      <td>33.349998</td>\n",
              "      <td>69.290001</td>\n",
              "      <td>38.139999</td>\n",
              "      <td>13.319000</td>\n",
              "      <td>32.099998</td>\n",
              "      <td>11.980000</td>\n",
              "      <td>33.490002</td>\n",
              "      <td>101.180000</td>\n",
              "      <td>...</td>\n",
              "      <td>17.825001</td>\n",
              "      <td>3.122500</td>\n",
              "      <td>69.660004</td>\n",
              "      <td>24.686907</td>\n",
              "      <td>65.470001</td>\n",
              "      <td>2.245333</td>\n",
              "      <td>51.400002</td>\n",
              "      <td>34.709999</td>\n",
              "      <td>68.589996</td>\n",
              "      <td>88.480003</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-20</th>\n",
              "      <td>157.399994</td>\n",
              "      <td>156.119995</td>\n",
              "      <td>97.870003</td>\n",
              "      <td>252.550003</td>\n",
              "      <td>362.880005</td>\n",
              "      <td>97.709999</td>\n",
              "      <td>643.710022</td>\n",
              "      <td>27.750000</td>\n",
              "      <td>67.239998</td>\n",
              "      <td>489.290009</td>\n",
              "      <td>...</td>\n",
              "      <td>75.970001</td>\n",
              "      <td>259.000000</td>\n",
              "      <td>177.589996</td>\n",
              "      <td>40.810001</td>\n",
              "      <td>550.570007</td>\n",
              "      <td>183.250000</td>\n",
              "      <td>476.959991</td>\n",
              "      <td>37.480000</td>\n",
              "      <td>140.899994</td>\n",
              "      <td>102.449997</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-21</th>\n",
              "      <td>159.279999</td>\n",
              "      <td>156.770004</td>\n",
              "      <td>98.330002</td>\n",
              "      <td>257.619995</td>\n",
              "      <td>374.220001</td>\n",
              "      <td>100.610001</td>\n",
              "      <td>636.750000</td>\n",
              "      <td>28.590000</td>\n",
              "      <td>67.510002</td>\n",
              "      <td>490.850006</td>\n",
              "      <td>...</td>\n",
              "      <td>75.360001</td>\n",
              "      <td>261.989990</td>\n",
              "      <td>178.009995</td>\n",
              "      <td>40.660000</td>\n",
              "      <td>556.700012</td>\n",
              "      <td>197.580002</td>\n",
              "      <td>480.100006</td>\n",
              "      <td>38.480000</td>\n",
              "      <td>140.419998</td>\n",
              "      <td>107.040001</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-22</th>\n",
              "      <td>157.830002</td>\n",
              "      <td>153.669998</td>\n",
              "      <td>96.860001</td>\n",
              "      <td>253.270004</td>\n",
              "      <td>361.709991</td>\n",
              "      <td>98.699997</td>\n",
              "      <td>630.919983</td>\n",
              "      <td>27.639999</td>\n",
              "      <td>67.239998</td>\n",
              "      <td>487.519989</td>\n",
              "      <td>...</td>\n",
              "      <td>74.129997</td>\n",
              "      <td>264.679993</td>\n",
              "      <td>176.509995</td>\n",
              "      <td>40.009998</td>\n",
              "      <td>554.320007</td>\n",
              "      <td>191.149994</td>\n",
              "      <td>475.519989</td>\n",
              "      <td>37.200001</td>\n",
              "      <td>139.520004</td>\n",
              "      <td>104.589996</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-23</th>\n",
              "      <td>158.929993</td>\n",
              "      <td>155.300003</td>\n",
              "      <td>97.040001</td>\n",
              "      <td>271.660004</td>\n",
              "      <td>369.000000</td>\n",
              "      <td>98.709999</td>\n",
              "      <td>639.229980</td>\n",
              "      <td>26.969999</td>\n",
              "      <td>66.980003</td>\n",
              "      <td>487.760010</td>\n",
              "      <td>...</td>\n",
              "      <td>73.809998</td>\n",
              "      <td>271.910004</td>\n",
              "      <td>175.649994</td>\n",
              "      <td>40.180000</td>\n",
              "      <td>555.190002</td>\n",
              "      <td>192.220001</td>\n",
              "      <td>469.910004</td>\n",
              "      <td>36.610001</td>\n",
              "      <td>140.649994</td>\n",
              "      <td>103.410004</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-24</th>\n",
              "      <td>160.250000</td>\n",
              "      <td>158.020004</td>\n",
              "      <td>98.050003</td>\n",
              "      <td>272.000000</td>\n",
              "      <td>374.959991</td>\n",
              "      <td>98.129997</td>\n",
              "      <td>636.169983</td>\n",
              "      <td>27.139999</td>\n",
              "      <td>67.680000</td>\n",
              "      <td>495.269989</td>\n",
              "      <td>...</td>\n",
              "      <td>75.690002</td>\n",
              "      <td>267.790009</td>\n",
              "      <td>179.089996</td>\n",
              "      <td>40.389999</td>\n",
              "      <td>558.260010</td>\n",
              "      <td>190.410004</td>\n",
              "      <td>475.989990</td>\n",
              "      <td>36.230000</td>\n",
              "      <td>141.800003</td>\n",
              "      <td>103.529999</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>2575 rows × 33 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-f92c617d-bd48-413d-a52f-e48d496bc22e')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-f92c617d-bd48-413d-a52f-e48d496bc22e button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-f92c617d-bd48-413d-a52f-e48d496bc22e');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "split = -800\n",
        "evals,evec = pca(top40.iloc[:split])\n",
        "eigportf = (top40.pct_change().mul(evec[:,0])).sum(axis=1).cumsum()\n",
        "index = stocks.loc[eigportf.index[0]:].SPY.pct_change().cumsum().ffill()\n",
        "\n",
        "plt.figure(figsize=[10,7])\n",
        "plt.bar(top40.columns,evec[:,0])\n",
        "plt.xticks(rotation=90);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 458
        },
        "id": "6JTpDiG9tNoC",
        "outputId": "f9473a4d-7568-4948-9e28-d2467037a296"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "index.mul(10).plot()\n",
        "eigportf.mul(1).plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "gi27pnAGRiEM",
        "outputId": "e8a4195b-cd3f-4555-972a-6a6eea8f1541"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Date'>"
            ]
          },
          "metadata": {},
          "execution_count": 33
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can see that there is a strong correlation between our eigenporfolio and the SPY ETF."
      ],
      "metadata": {
        "id": "zjj_f4yJGAp6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(eigportf,index,'.',alpha=0.5)\n",
        "m = np.polyfit(eigportf.iloc[1:split],index.iloc[1:split],1)\n",
        "xx = np.linspace(eigportf.min(),eigportf.max(),100)\n",
        "yy = np.polyval(m,xx)\n",
        "plt.plot(xx,yy,lw=3)\n",
        "plt.title(f'y = {m[0]:.2f}x + {m[1]:.2f}');"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "LISyZslEEyW7",
        "outputId": "003fbc79-944a-45e8-9497-25c81ed670b8"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The portfolio also looks strongly mean reverting."
      ],
      "metadata": {
        "id": "_MZT-yKpGrIN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "(eigportf*m[0]+m[1]-index).plot(figsize=[15,5])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 346
        },
        "id": "6hAEmP-XtTJ3",
        "outputId": "17a87f18-7b23-4fcf-8ff0-2081cf086f4e"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Date'>"
            ]
          },
          "metadata": {},
          "execution_count": 35
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x360 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can confirm that the pair is cointegrated at the 95% \n",
        "\n",
        "---\n",
        "\n",
        "confidence level."
      ],
      "metadata": {
        "id": "lrvLhm0tG25t"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "coint(eigportf.iloc[1:]*m[0]+m[1],index.iloc[1:])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Tsc5ShUY0ODj",
        "outputId": "c62f5a25-11ed-42f3-c9b8-8b86187ce7e6"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-3.540827908092854,\n",
              " 0.028943677033498167,\n",
              " array([-3.90070154, -3.33850573, -3.04609876]))"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "resid = eigportf*m[0]+m[1]-index"
      ],
      "metadata": {
        "id": "kbFe0g9qGPEp"
      },
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "inpos = 0\n",
        "pnls = []\n",
        "bw = .1\n",
        "unrlzd = []\n",
        "dates = []\n",
        "pdates = []\n",
        "for i,p in enumerate(resid):\n",
        "  if i>100:\n",
        "    unrlzd.append((p-resid.iloc[i-1])*inpos)\n",
        "    dates.append(resid.index[i])\n",
        "\n",
        "    #\"\"\"Long Side\"\"\"\n",
        "    if not inpos and p<resid.iloc[:i].std()*bw:\n",
        "      entry = p\n",
        "      inpos = 1\n",
        "    elif inpos==1 and p>0:\n",
        "      pnl = p-entry\n",
        "      pnls.append(pnl)\n",
        "      pdates.append(resid.index[i])\n",
        "      inpos = 0\n",
        "\n",
        "    #\"\"\"Short Side\"\"\"\n",
        "    elif not inpos and p>resid.iloc[:i].std()*bw:\n",
        "      entry = p\n",
        "      inpos = -1\n",
        "    elif inpos==-1 and p<0:\n",
        "      pnl = entry-p\n",
        "      pnls.append(pnl)\n",
        "      pdates.append(resid.index[i])\n",
        "      inpos = 0"
      ],
      "metadata": {
        "id": "bhCcW-LRT5wz"
      },
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(dates,np.cumsum(unrlzd),'-')\n",
        "plt.plot(pdates,np.cumsum(pnls),'-o')\n",
        "plt.xticks(rotation=45)\n",
        "xmin,xmax,ymin,ymax = plt.axis()\n",
        "plt.plot([resid.index[split]]*2,[ymin,ymax],'--',label='oos split')\n",
        "plt.legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "id": "c71Ep9RjVBPi",
        "outputId": "9b13bf16-b87c-46a9-d466-6ea93e53a06e"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f4ac6684df0>"
            ]
          },
          "metadata": {},
          "execution_count": 39
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "q3DtLOs7mmqV"
      },
      "execution_count": 39,
      "outputs": []
    }
  ]
}