Multi_Factor_Analysis3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dbf91ead-9da7-4860-bb32-d4ac4c7ac742",
   "metadata": {},
   "source": [
    "# Fama French 3-Factor Modeling of NYSE stocks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7834fa58-dd16-4231-a152-b893affa28e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78a93b72-f8c9-426e-ad1f-a6ac363b2817",
   "metadata": {},
   "source": [
    "### Extracting and Preparing Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0843e918-0359-48a8-a8eb-75c4b61bdebf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: yfinance in d:\\users\\sujay\\lib\\site-packages (0.2.48)\n",
      "Requirement already satisfied: pandas>=1.3.0 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (2.1.4)\n",
      "Requirement already satisfied: numpy>=1.16.5 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (1.26.4)\n",
      "Requirement already satisfied: requests>=2.31 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (2.32.3)\n",
      "Requirement already satisfied: multitasking>=0.0.7 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (0.0.11)\n",
      "Requirement already satisfied: lxml>=4.9.1 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (4.9.3)\n",
      "Requirement already satisfied: platformdirs>=2.0.0 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (3.10.0)\n",
      "Requirement already satisfied: pytz>=2022.5 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (2023.3.post1)\n",
      "Requirement already satisfied: frozendict>=2.3.4 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (2.4.2)\n",
      "Requirement already satisfied: peewee>=3.16.2 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (3.17.7)\n",
      "Requirement already satisfied: beautifulsoup4>=4.11.1 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (4.12.2)\n",
      "Requirement already satisfied: html5lib>=1.1 in d:\\users\\sujay\\lib\\site-packages (from yfinance) (1.1)\n",
      "Requirement already satisfied: soupsieve>1.2 in d:\\users\\sujay\\lib\\site-packages (from beautifulsoup4>=4.11.1->yfinance) (2.5)\n",
      "Requirement already satisfied: six>=1.9 in d:\\users\\sujay\\lib\\site-packages (from html5lib>=1.1->yfinance) (1.16.0)\n",
      "Requirement already satisfied: webencodings in d:\\users\\sujay\\lib\\site-packages (from html5lib>=1.1->yfinance) (0.5.1)\n",
      "Requirement already satisfied: python-dateutil>=2.8.2 in d:\\users\\sujay\\lib\\site-packages (from pandas>=1.3.0->yfinance) (2.8.2)\n",
      "Requirement already satisfied: tzdata>=2022.1 in d:\\users\\sujay\\lib\\site-packages (from pandas>=1.3.0->yfinance) (2023.3)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in d:\\users\\sujay\\lib\\site-packages (from requests>=2.31->yfinance) (2.0.4)\n",
      "Requirement already satisfied: idna<4,>=2.5 in d:\\users\\sujay\\lib\\site-packages (from requests>=2.31->yfinance) (3.4)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in d:\\users\\sujay\\lib\\site-packages (from requests>=2.31->yfinance) (2.0.7)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in d:\\users\\sujay\\lib\\site-packages (from requests>=2.31->yfinance) (2024.12.14)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install yfinance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "24235b5b-e6ec-46e7-9dcf-91636c9ce9dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import yfinance as yf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc18c770-c213-4e89-b1c7-5d572b05a672",
   "metadata": {},
   "source": [
    "**Enter dates range:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ef07d9b0-21a5-4430-9ba1-89726c1d5734",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34\n"
     ]
    }
   ],
   "source": [
    "# Define the start and end dates (yyyy-mm-dd)\n",
    "start_date = pd.to_datetime(\"2022-01-01\")\n",
    "end_date = pd.to_datetime(\"2024-11-06\")\n",
    "\n",
    "# Calculate the difference in months\n",
    "months_diff = (end_date.year - start_date.year) * 12 + end_date.month - start_date.month\n",
    "\n",
    "print(months_diff)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b85b00a7-7285-4220-bf2f-9513014f3334",
   "metadata": {},
   "source": [
    "**Enter stock tickers:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9b201ffe-a3d3-4a3c-ab60-e970fa6e2f4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  10 of 10 completed"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ticker                            AMD        AMZN         CVX         DIS  \\\n",
      "Date                                                                        \n",
      "2022-01-03 00:00:00+00:00  150.240005  170.404495  119.260002  156.759995   \n",
      "2022-01-04 00:00:00+00:00  144.419998  167.522003  121.430000  155.729996   \n",
      "2022-01-05 00:00:00+00:00  136.149994  164.356995  122.220001  155.190002   \n",
      "2022-01-06 00:00:00+00:00  136.229996  163.253998  123.260002  156.899994   \n",
      "2022-01-07 00:00:00+00:00  132.000000  162.554001  125.029999  157.830002   \n",
      "\n",
      "Ticker                           GOOG         JPM        MSFT       PLTR  \\\n",
      "Date                                                                       \n",
      "2022-01-03 00:00:00+00:00  145.074493  161.699997  334.750000  18.530001   \n",
      "2022-01-04 00:00:00+00:00  144.416504  167.830002  329.010010  18.170000   \n",
      "2022-01-05 00:00:00+00:00  137.653503  163.779999  316.380005  16.959999   \n",
      "2022-01-06 00:00:00+00:00  137.550995  165.520004  313.880005  16.740000   \n",
      "2022-01-07 00:00:00+00:00  137.004501  167.160004  314.040009  16.559999   \n",
      "\n",
      "Ticker                           TSLA       UBER  \n",
      "Date                                              \n",
      "2022-01-03 00:00:00+00:00  399.926666  43.950001  \n",
      "2022-01-04 00:00:00+00:00  383.196655  44.419998  \n",
      "2022-01-05 00:00:00+00:00  362.706665  43.240002  \n",
      "2022-01-06 00:00:00+00:00  354.899994  42.029999  \n",
      "2022-01-07 00:00:00+00:00  342.320007  41.509998  \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# List of tickers for NSE stocks (append '.NS' to each NSE ticker)\n",
    "tickers = [\"JPM\", \"CVX\", \"PLTR\", \"AMD\", \"TSLA\", \"AMZN\", \"UBER\", \"GOOG\", \"MSFT\", \"DIS\"]  # Add more tickers as needed\n",
    "\n",
    "# Download historical data for 1 or 2 years\n",
    "data = yf.download(tickers, start=start_date, end=end_date)\n",
    "\n",
    "# Extract only the closing prices\n",
    "closing_prices = data['Close']\n",
    "\n",
    "# Display the combined DataFrame\n",
    "print(closing_prices.head())\n",
    "\n",
    "# Optionally, save to a CSV file if you want\n",
    "closing_prices.to_csv(\"nse_closing_prices.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b8aef829-d6c8-4333-b7ee-476dba28064f",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
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       "      <th>AMD</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>CVX</th>\n",
       "      <th>DIS</th>\n",
       "      <th>GOOG</th>\n",
       "      <th>JPM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>PLTR</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>UBER</th>\n",
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       "      <th>0</th>\n",
       "      <td>2022-01-03 00:00:00+00:00</td>\n",
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       "      <th>1</th>\n",
       "      <td>2022-01-04 00:00:00+00:00</td>\n",
       "      <td>144.419998</td>\n",
       "      <td>167.522003</td>\n",
       "      <td>121.430000</td>\n",
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       "      <td>144.416504</td>\n",
       "      <td>167.830002</td>\n",
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       "      <td>18.170000</td>\n",
       "      <td>383.196655</td>\n",
       "      <td>44.419998</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2022-01-05 00:00:00+00:00</td>\n",
       "      <td>136.149994</td>\n",
       "      <td>164.356995</td>\n",
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       "      <td>362.706665</td>\n",
       "      <td>43.240002</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2022-01-06 00:00:00+00:00</td>\n",
       "      <td>136.229996</td>\n",
       "      <td>163.253998</td>\n",
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       "      <td>16.740000</td>\n",
       "      <td>354.899994</td>\n",
       "      <td>42.029999</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2022-01-07 00:00:00+00:00</td>\n",
       "      <td>132.000000</td>\n",
       "      <td>162.554001</td>\n",
       "      <td>125.029999</td>\n",
       "      <td>157.830002</td>\n",
       "      <td>137.004501</td>\n",
       "      <td>167.160004</td>\n",
       "      <td>314.040009</td>\n",
       "      <td>16.559999</td>\n",
       "      <td>342.320007</td>\n",
       "      <td>41.509998</td>\n",
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      "text/plain": [
       "                        Date         AMD        AMZN         CVX         DIS  \\\n",
       "0  2022-01-03 00:00:00+00:00  150.240005  170.404495  119.260002  156.759995   \n",
       "1  2022-01-04 00:00:00+00:00  144.419998  167.522003  121.430000  155.729996   \n",
       "2  2022-01-05 00:00:00+00:00  136.149994  164.356995  122.220001  155.190002   \n",
       "3  2022-01-06 00:00:00+00:00  136.229996  163.253998  123.260002  156.899994   \n",
       "4  2022-01-07 00:00:00+00:00  132.000000  162.554001  125.029999  157.830002   \n",
       "\n",
       "         GOOG         JPM        MSFT       PLTR        TSLA       UBER  \n",
       "0  145.074493  161.699997  334.750000  18.530001  399.926666  43.950001  \n",
       "1  144.416504  167.830002  329.010010  18.170000  383.196655  44.419998  \n",
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       "3  137.550995  165.520004  313.880005  16.740000  354.899994  42.029999  \n",
       "4  137.004501  167.160004  314.040009  16.559999  342.320007  41.509998  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(r\"nse_closing_prices.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d1a5f0d2-99e1-414d-8458-6c8f76e6a9d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.set_index('Date', inplace =True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0203e59d-f785-4818-8c95-2d5d19c43141",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(715, 10)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94da3c63-3aed-4dea-9f1a-d76fb627faae",
   "metadata": {},
   "source": [
    "#### Calculating daily returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3f55a84f-45cb-4c8c-a69c-e1c3809f05f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2a5b94cd-52f6-4d71-8b30-55270b7e10c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "returns = df.pct_change()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7aa503f4-e8c2-4f4f-8b59-5b056dd368b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "returns.dropna(inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "77343d37-0d96-41e6-9dfc-272f1b4801ab",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AMD</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>CVX</th>\n",
       "      <th>DIS</th>\n",
       "      <th>GOOG</th>\n",
       "      <th>JPM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>PLTR</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>UBER</th>\n",
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       "    <tr>\n",
       "      <th>Date</th>\n",
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       "      <th>2022-01-04 00:00:00+00:00</th>\n",
       "      <td>-0.038738</td>\n",
       "      <td>-0.016916</td>\n",
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       "      <td>-0.006571</td>\n",
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       "      <td>0.037910</td>\n",
       "      <td>-0.017147</td>\n",
       "      <td>-0.019428</td>\n",
       "      <td>-0.041833</td>\n",
       "      <td>0.010694</td>\n",
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       "    <tr>\n",
       "      <th>2022-01-05 00:00:00+00:00</th>\n",
       "      <td>-0.057264</td>\n",
       "      <td>-0.018893</td>\n",
       "      <td>0.006506</td>\n",
       "      <td>-0.003467</td>\n",
       "      <td>-0.046830</td>\n",
       "      <td>-0.024132</td>\n",
       "      <td>-0.038388</td>\n",
       "      <td>-0.066593</td>\n",
       "      <td>-0.053471</td>\n",
       "      <td>-0.026565</td>\n",
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       "    <tr>\n",
       "      <th>2022-01-06 00:00:00+00:00</th>\n",
       "      <td>0.000588</td>\n",
       "      <td>-0.006711</td>\n",
       "      <td>0.008509</td>\n",
       "      <td>0.011019</td>\n",
       "      <td>-0.000745</td>\n",
       "      <td>0.010624</td>\n",
       "      <td>-0.007902</td>\n",
       "      <td>-0.012972</td>\n",
       "      <td>-0.021523</td>\n",
       "      <td>-0.027983</td>\n",
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       "    <tr>\n",
       "      <th>2022-01-07 00:00:00+00:00</th>\n",
       "      <td>-0.031050</td>\n",
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       "      <td>0.014360</td>\n",
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       "      <td>-0.003973</td>\n",
       "      <td>0.009908</td>\n",
       "      <td>0.000510</td>\n",
       "      <td>-0.010753</td>\n",
       "      <td>-0.035447</td>\n",
       "      <td>-0.012372</td>\n",
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       "    <tr>\n",
       "      <th>2022-01-10 00:00:00+00:00</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.006570</td>\n",
       "      <td>0.000640</td>\n",
       "      <td>-0.007793</td>\n",
       "      <td>0.011456</td>\n",
       "      <td>0.000957</td>\n",
       "      <td>0.000732</td>\n",
       "      <td>-0.003623</td>\n",
       "      <td>0.030342</td>\n",
       "      <td>0.026259</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "                                AMD      AMZN       CVX       DIS      GOOG  \\\n",
       "Date                                                                          \n",
       "2022-01-04 00:00:00+00:00 -0.038738 -0.016916  0.018196 -0.006571 -0.004536   \n",
       "2022-01-05 00:00:00+00:00 -0.057264 -0.018893  0.006506 -0.003467 -0.046830   \n",
       "2022-01-06 00:00:00+00:00  0.000588 -0.006711  0.008509  0.011019 -0.000745   \n",
       "2022-01-07 00:00:00+00:00 -0.031050 -0.004288  0.014360  0.005927 -0.003973   \n",
       "2022-01-10 00:00:00+00:00  0.000000 -0.006570  0.000640 -0.007793  0.011456   \n",
       "\n",
       "                                JPM      MSFT      PLTR      TSLA      UBER  \n",
       "Date                                                                         \n",
       "2022-01-04 00:00:00+00:00  0.037910 -0.017147 -0.019428 -0.041833  0.010694  \n",
       "2022-01-05 00:00:00+00:00 -0.024132 -0.038388 -0.066593 -0.053471 -0.026565  \n",
       "2022-01-06 00:00:00+00:00  0.010624 -0.007902 -0.012972 -0.021523 -0.027983  \n",
       "2022-01-07 00:00:00+00:00  0.009908  0.000510 -0.010753 -0.035447 -0.012372  \n",
       "2022-01-10 00:00:00+00:00  0.000957  0.000732 -0.003623  0.030342  0.026259  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b36fb94e-cdd9-48ac-9536-d8ceff198b7c",
   "metadata": {},
   "source": [
    "### Constructing portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b03525b-e169-4778-83d0-7d55204da818",
   "metadata": {},
   "source": [
    "__Equal weighted portfolio__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c8bf1e23-02ee-4df6-96f5-50ce826d0599",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#weights = [0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1]\n",
    "# Count the total number of stocks\n",
    "num_stocks = len(df.columns)\n",
    "num_stocks\n",
    "\n",
    "\n",
    "# Create an array of equal weights\n",
    "equal_weights = np.repeat(1/num_stocks, num_stocks)\n",
    "equal_weights\n",
    "\n",
    "weights = equal_weights\n",
    "weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "32d923cf-7deb-4dc6-840b-dde0dda0174b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create portfolio returns column\n",
    "returns['Portfolio']= returns.dot(weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "efffbd71-55f9-46a9-8b46-4d08f126e036",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AMD</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>CVX</th>\n",
       "      <th>DIS</th>\n",
       "      <th>GOOG</th>\n",
       "      <th>JPM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>PLTR</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>UBER</th>\n",
       "      <th>Portfolio</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",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>2022-01-04 00:00:00+00:00</th>\n",
       "      <td>-0.038738</td>\n",
       "      <td>-0.016916</td>\n",
       "      <td>0.018196</td>\n",
       "      <td>-0.006571</td>\n",
       "      <td>-0.004536</td>\n",
       "      <td>0.037910</td>\n",
       "      <td>-0.017147</td>\n",
       "      <td>-0.019428</td>\n",
       "      <td>-0.041833</td>\n",
       "      <td>0.010694</td>\n",
       "      <td>-0.007837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-05 00:00:00+00:00</th>\n",
       "      <td>-0.057264</td>\n",
       "      <td>-0.018893</td>\n",
       "      <td>0.006506</td>\n",
       "      <td>-0.003467</td>\n",
       "      <td>-0.046830</td>\n",
       "      <td>-0.024132</td>\n",
       "      <td>-0.038388</td>\n",
       "      <td>-0.066593</td>\n",
       "      <td>-0.053471</td>\n",
       "      <td>-0.026565</td>\n",
       "      <td>-0.032910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-06 00:00:00+00:00</th>\n",
       "      <td>0.000588</td>\n",
       "      <td>-0.006711</td>\n",
       "      <td>0.008509</td>\n",
       "      <td>0.011019</td>\n",
       "      <td>-0.000745</td>\n",
       "      <td>0.010624</td>\n",
       "      <td>-0.007902</td>\n",
       "      <td>-0.012972</td>\n",
       "      <td>-0.021523</td>\n",
       "      <td>-0.027983</td>\n",
       "      <td>-0.004710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-07 00:00:00+00:00</th>\n",
       "      <td>-0.031050</td>\n",
       "      <td>-0.004288</td>\n",
       "      <td>0.014360</td>\n",
       "      <td>0.005927</td>\n",
       "      <td>-0.003973</td>\n",
       "      <td>0.009908</td>\n",
       "      <td>0.000510</td>\n",
       "      <td>-0.010753</td>\n",
       "      <td>-0.035447</td>\n",
       "      <td>-0.012372</td>\n",
       "      <td>-0.006718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-10 00:00:00+00:00</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.006570</td>\n",
       "      <td>0.000640</td>\n",
       "      <td>-0.007793</td>\n",
       "      <td>0.011456</td>\n",
       "      <td>0.000957</td>\n",
       "      <td>0.000732</td>\n",
       "      <td>-0.003623</td>\n",
       "      <td>0.030342</td>\n",
       "      <td>0.026259</td>\n",
       "      <td>0.005240</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                AMD      AMZN       CVX       DIS      GOOG  \\\n",
       "Date                                                                          \n",
       "2022-01-04 00:00:00+00:00 -0.038738 -0.016916  0.018196 -0.006571 -0.004536   \n",
       "2022-01-05 00:00:00+00:00 -0.057264 -0.018893  0.006506 -0.003467 -0.046830   \n",
       "2022-01-06 00:00:00+00:00  0.000588 -0.006711  0.008509  0.011019 -0.000745   \n",
       "2022-01-07 00:00:00+00:00 -0.031050 -0.004288  0.014360  0.005927 -0.003973   \n",
       "2022-01-10 00:00:00+00:00  0.000000 -0.006570  0.000640 -0.007793  0.011456   \n",
       "\n",
       "                                JPM      MSFT      PLTR      TSLA      UBER  \\\n",
       "Date                                                                          \n",
       "2022-01-04 00:00:00+00:00  0.037910 -0.017147 -0.019428 -0.041833  0.010694   \n",
       "2022-01-05 00:00:00+00:00 -0.024132 -0.038388 -0.066593 -0.053471 -0.026565   \n",
       "2022-01-06 00:00:00+00:00  0.010624 -0.007902 -0.012972 -0.021523 -0.027983   \n",
       "2022-01-07 00:00:00+00:00  0.009908  0.000510 -0.010753 -0.035447 -0.012372   \n",
       "2022-01-10 00:00:00+00:00  0.000957  0.000732 -0.003623  0.030342  0.026259   \n",
       "\n",
       "                           Portfolio  \n",
       "Date                                  \n",
       "2022-01-04 00:00:00+00:00  -0.007837  \n",
       "2022-01-05 00:00:00+00:00  -0.032910  \n",
       "2022-01-06 00:00:00+00:00  -0.004710  \n",
       "2022-01-07 00:00:00+00:00  -0.006718  \n",
       "2022-01-10 00:00:00+00:00   0.005240  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2a68d4d8-d912-48df-82fe-8cc03213b711",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
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       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Portfolio</th>\n",
       "      <td>714.0</td>\n",
       "      <td>0.000607</td>\n",
       "      <td>0.017998</td>\n",
       "      <td>-0.073726</td>\n",
       "      <td>-0.009293</td>\n",
       "      <td>0.000419</td>\n",
       "      <td>0.011122</td>\n",
       "      <td>0.078218</td>\n",
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      "text/plain": [
       "           count      mean       std       min       25%       50%       75%  \\\n",
       "Portfolio  714.0  0.000607  0.017998 -0.073726 -0.009293  0.000419  0.011122   \n",
       "\n",
       "                max  \n",
       "Portfolio  0.078218  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns['Portfolio'].describe().to_frame().T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c23af60d-8f01-451b-8314-1cab144dd034",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AMD</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>CVX</th>\n",
       "      <th>DIS</th>\n",
       "      <th>GOOG</th>\n",
       "      <th>JPM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>PLTR</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>UBER</th>\n",
       "      <th>Portfolio</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",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2024-10-30 00:00:00+00:00</th>\n",
       "      <td>0.989084</td>\n",
       "      <td>1.131015</td>\n",
       "      <td>1.241405</td>\n",
       "      <td>0.606532</td>\n",
       "      <td>1.214135</td>\n",
       "      <td>1.387817</td>\n",
       "      <td>1.292099</td>\n",
       "      <td>2.357798</td>\n",
       "      <td>0.643993</td>\n",
       "      <td>1.807281</td>\n",
       "      <td>1.368397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31 00:00:00+00:00</th>\n",
       "      <td>0.958932</td>\n",
       "      <td>1.093868</td>\n",
       "      <td>1.247862</td>\n",
       "      <td>0.613677</td>\n",
       "      <td>1.190354</td>\n",
       "      <td>1.372418</td>\n",
       "      <td>1.213891</td>\n",
       "      <td>2.242849</td>\n",
       "      <td>0.624740</td>\n",
       "      <td>1.639363</td>\n",
       "      <td>1.326097</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-01 00:00:00+00:00</th>\n",
       "      <td>0.944223</td>\n",
       "      <td>1.161530</td>\n",
       "      <td>1.283498</td>\n",
       "      <td>0.611189</td>\n",
       "      <td>1.190078</td>\n",
       "      <td>1.378726</td>\n",
       "      <td>1.225900</td>\n",
       "      <td>2.262277</td>\n",
       "      <td>0.622564</td>\n",
       "      <td>1.666667</td>\n",
       "      <td>1.340301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-04 00:00:00+00:00</th>\n",
       "      <td>0.936568</td>\n",
       "      <td>1.148913</td>\n",
       "      <td>1.291045</td>\n",
       "      <td>0.611062</td>\n",
       "      <td>1.176499</td>\n",
       "      <td>1.359184</td>\n",
       "      <td>1.220194</td>\n",
       "      <td>2.234754</td>\n",
       "      <td>0.607211</td>\n",
       "      <td>1.666667</td>\n",
       "      <td>1.329530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-05 00:00:00+00:00</th>\n",
       "      <td>0.942891</td>\n",
       "      <td>1.170744</td>\n",
       "      <td>1.286349</td>\n",
       "      <td>0.616420</td>\n",
       "      <td>1.181531</td>\n",
       "      <td>1.369759</td>\n",
       "      <td>1.229156</td>\n",
       "      <td>2.759309</td>\n",
       "      <td>0.628715</td>\n",
       "      <td>1.687144</td>\n",
       "      <td>1.373765</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                AMD      AMZN       CVX       DIS      GOOG  \\\n",
       "Date                                                                          \n",
       "2024-10-30 00:00:00+00:00  0.989084  1.131015  1.241405  0.606532  1.214135   \n",
       "2024-10-31 00:00:00+00:00  0.958932  1.093868  1.247862  0.613677  1.190354   \n",
       "2024-11-01 00:00:00+00:00  0.944223  1.161530  1.283498  0.611189  1.190078   \n",
       "2024-11-04 00:00:00+00:00  0.936568  1.148913  1.291045  0.611062  1.176499   \n",
       "2024-11-05 00:00:00+00:00  0.942891  1.170744  1.286349  0.616420  1.181531   \n",
       "\n",
       "                                JPM      MSFT      PLTR      TSLA      UBER  \\\n",
       "Date                                                                          \n",
       "2024-10-30 00:00:00+00:00  1.387817  1.292099  2.357798  0.643993  1.807281   \n",
       "2024-10-31 00:00:00+00:00  1.372418  1.213891  2.242849  0.624740  1.639363   \n",
       "2024-11-01 00:00:00+00:00  1.378726  1.225900  2.262277  0.622564  1.666667   \n",
       "2024-11-04 00:00:00+00:00  1.359184  1.220194  2.234754  0.607211  1.666667   \n",
       "2024-11-05 00:00:00+00:00  1.369759  1.229156  2.759309  0.628715  1.687144   \n",
       "\n",
       "                           Portfolio  \n",
       "Date                                  \n",
       "2024-10-30 00:00:00+00:00   1.368397  \n",
       "2024-10-31 00:00:00+00:00   1.326097  \n",
       "2024-11-01 00:00:00+00:00   1.340301  \n",
       "2024-11-04 00:00:00+00:00   1.329530  \n",
       "2024-11-05 00:00:00+00:00   1.373765  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate cumulative returns (growth factor)\n",
    "daily_cum_ret=(1+returns).cumprod()\n",
    "daily_cum_ret.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43ea4d81-2c1c-4b7e-a989-0106c5cef621",
   "metadata": {},
   "source": [
    "Assuming risk free rate to be 5% for the duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4b6e5505-f982-4d5c-867a-e20b5384a110",
   "metadata": {},
   "outputs": [],
   "source": [
    "returns['RF'] = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c3f4c134-05b3-4e1e-a0ee-7f1c64ed6115",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate excess portfolio returns\n",
    "returns['Portfolio_Excess'] = returns['Portfolio'] - returns['RF']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3de303a5-b252-4fb7-8f8a-953c4c9b3fba",
   "metadata": {},
   "outputs": [
    {
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       "      <th>DIS</th>\n",
       "      <th>GOOG</th>\n",
       "      <th>JPM</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>PLTR</th>\n",
       "      <th>TSLA</th>\n",
       "      <th>UBER</th>\n",
       "      <th>Portfolio</th>\n",
       "      <th>RF</th>\n",
       "      <th>Portfolio_Excess</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2024-10-30 00:00:00+00:00</th>\n",
       "      <td>-0.106165</td>\n",
       "      <td>0.009956</td>\n",
       "      <td>-0.003165</td>\n",
       "      <td>-0.010923</td>\n",
       "      <td>0.029216</td>\n",
       "      <td>0.006774</td>\n",
       "      <td>0.001343</td>\n",
       "      <td>-0.027599</td>\n",
       "      <td>-0.007591</td>\n",
       "      <td>0.002777</td>\n",
       "      <td>-0.010538</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.060538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31 00:00:00+00:00</th>\n",
       "      <td>-0.030485</td>\n",
       "      <td>-0.032844</td>\n",
       "      <td>0.005201</td>\n",
       "      <td>0.011780</td>\n",
       "      <td>-0.019587</td>\n",
       "      <td>-0.011096</td>\n",
       "      <td>-0.060528</td>\n",
       "      <td>-0.048753</td>\n",
       "      <td>-0.029897</td>\n",
       "      <td>-0.092912</td>\n",
       "      <td>-0.030912</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.080912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-01 00:00:00+00:00</th>\n",
       "      <td>-0.015340</td>\n",
       "      <td>0.061856</td>\n",
       "      <td>0.028558</td>\n",
       "      <td>-0.004054</td>\n",
       "      <td>-0.000232</td>\n",
       "      <td>0.004596</td>\n",
       "      <td>0.009893</td>\n",
       "      <td>0.008662</td>\n",
       "      <td>-0.003482</td>\n",
       "      <td>0.016655</td>\n",
       "      <td>0.010711</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.039289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-04 00:00:00+00:00</th>\n",
       "      <td>-0.008107</td>\n",
       "      <td>-0.010862</td>\n",
       "      <td>0.005880</td>\n",
       "      <td>-0.000209</td>\n",
       "      <td>-0.011410</td>\n",
       "      <td>-0.014174</td>\n",
       "      <td>-0.004654</td>\n",
       "      <td>-0.012166</td>\n",
       "      <td>-0.024661</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.008036</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.058036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-05 00:00:00+00:00</th>\n",
       "      <td>0.006751</td>\n",
       "      <td>0.019001</td>\n",
       "      <td>-0.003637</td>\n",
       "      <td>0.008769</td>\n",
       "      <td>0.004277</td>\n",
       "      <td>0.007781</td>\n",
       "      <td>0.007345</td>\n",
       "      <td>0.234726</td>\n",
       "      <td>0.035414</td>\n",
       "      <td>0.012287</td>\n",
       "      <td>0.033271</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.016729</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                AMD      AMZN       CVX       DIS      GOOG  \\\n",
       "Date                                                                          \n",
       "2024-10-30 00:00:00+00:00 -0.106165  0.009956 -0.003165 -0.010923  0.029216   \n",
       "2024-10-31 00:00:00+00:00 -0.030485 -0.032844  0.005201  0.011780 -0.019587   \n",
       "2024-11-01 00:00:00+00:00 -0.015340  0.061856  0.028558 -0.004054 -0.000232   \n",
       "2024-11-04 00:00:00+00:00 -0.008107 -0.010862  0.005880 -0.000209 -0.011410   \n",
       "2024-11-05 00:00:00+00:00  0.006751  0.019001 -0.003637  0.008769  0.004277   \n",
       "\n",
       "                                JPM      MSFT      PLTR      TSLA      UBER  \\\n",
       "Date                                                                          \n",
       "2024-10-30 00:00:00+00:00  0.006774  0.001343 -0.027599 -0.007591  0.002777   \n",
       "2024-10-31 00:00:00+00:00 -0.011096 -0.060528 -0.048753 -0.029897 -0.092912   \n",
       "2024-11-01 00:00:00+00:00  0.004596  0.009893  0.008662 -0.003482  0.016655   \n",
       "2024-11-04 00:00:00+00:00 -0.014174 -0.004654 -0.012166 -0.024661  0.000000   \n",
       "2024-11-05 00:00:00+00:00  0.007781  0.007345  0.234726  0.035414  0.012287   \n",
       "\n",
       "                           Portfolio    RF  Portfolio_Excess  \n",
       "Date                                                          \n",
       "2024-10-30 00:00:00+00:00  -0.010538  0.05         -0.060538  \n",
       "2024-10-31 00:00:00+00:00  -0.030912  0.05         -0.080912  \n",
       "2024-11-01 00:00:00+00:00   0.010711  0.05         -0.039289  \n",
       "2024-11-04 00:00:00+00:00  -0.008036  0.05         -0.058036  \n",
       "2024-11-05 00:00:00+00:00   0.033271  0.05         -0.016729  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "90e663b8-a492-4eee-97fb-14cefb032df4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1160ee95-fe2a-4764-8474-474d6e2420d2",
   "metadata": {},
   "source": [
    "### Benchmark data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "090599c3-1e90-4083-9ea2-fad63d2c8c16",
   "metadata": {},
   "source": [
    "get S&P500 data for benchmark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "b4d08e48-7076-4e74-8f49-46b9098f8e34",
   "metadata": {},
   "outputs": [],
   "source": [
    "sp500_ticker = \"^GSPC\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "a6d5bf27-e74e-42aa-9f0b-212a92ce3c75",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    }
   ],
   "source": [
    "sp500_data = yf.download(sp500_ticker, start=start_date, end=end_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3979edeb-151f-43f7-acad-dd4edfa53325",
   "metadata": {},
   "outputs": [],
   "source": [
    "sp500_closing_prices = sp500_data['Close']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "67d447bc-6a8f-454c-81ff-fb429a625233",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ticker                           ^GSPC\n",
      "Date                                  \n",
      "2024-10-30 00:00:00+00:00  5813.669922\n",
      "2024-10-31 00:00:00+00:00  5705.450195\n",
      "2024-11-01 00:00:00+00:00  5728.799805\n",
      "2024-11-04 00:00:00+00:00  5712.689941\n",
      "2024-11-05 00:00:00+00:00  5782.759766\n"
     ]
    }
   ],
   "source": [
    "# Display the closing prices for S&P500\n",
    "print(sp500_closing_prices.tail())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "82993ca2-6dc6-4018-ba5e-41e0fa007782",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate daily returns\n",
    "sp500_returns = sp500_closing_prices.pct_change().dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "fbf67ab0-2534-4875-9ed6-9cc0a5126a46",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ticker                        ^GSPC\n",
      "Date                               \n",
      "2024-10-30 00:00:00+00:00 -0.003300\n",
      "2024-10-31 00:00:00+00:00 -0.018615\n",
      "2024-11-01 00:00:00+00:00  0.004093\n",
      "2024-11-04 00:00:00+00:00 -0.002812\n",
      "2024-11-05 00:00:00+00:00  0.012266\n"
     ]
    }
   ],
   "source": [
    "# Display Nifty 50 returns\n",
    "print(sp500_returns.tail())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "356cc268-5845-49f0-b1b5-ea2b995a5def",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Ticker</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2024-10-30 00:00:00+00:00</th>\n",
       "      <td>1.212050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31 00:00:00+00:00</th>\n",
       "      <td>1.189488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-01 00:00:00+00:00</th>\n",
       "      <td>1.194356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-04 00:00:00+00:00</th>\n",
       "      <td>1.190997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-05 00:00:00+00:00</th>\n",
       "      <td>1.205606</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Ticker                        ^GSPC\n",
       "Date                               \n",
       "2024-10-30 00:00:00+00:00  1.212050\n",
       "2024-10-31 00:00:00+00:00  1.189488\n",
       "2024-11-01 00:00:00+00:00  1.194356\n",
       "2024-11-04 00:00:00+00:00  1.190997\n",
       "2024-11-05 00:00:00+00:00  1.205606"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate cumulative returns (growth factor)\n",
    "sp500_cum_ret=(1+sp500_returns).cumprod()\n",
    "sp500_cum_ret.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "94ce93b0-6196-4ace-8934-95f71309d2eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "sp500_returns['RF'] = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "99eaf159-1bb0-4642-82b8-12702b52b1ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "sp500_returns['Market_Excess'] = sp500_returns['^GSPC'] - sp500_returns['RF']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "b820a3e6-9eef-4034-a29f-7b2d2782d796",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Ticker</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>RF</th>\n",
       "      <th>Market_Excess</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2024-10-30 00:00:00+00:00</th>\n",
       "      <td>-0.003300</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.053300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31 00:00:00+00:00</th>\n",
       "      <td>-0.018615</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.068615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-01 00:00:00+00:00</th>\n",
       "      <td>0.004093</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.045907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-04 00:00:00+00:00</th>\n",
       "      <td>-0.002812</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.052812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-05 00:00:00+00:00</th>\n",
       "      <td>0.012266</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.037734</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Ticker                        ^GSPC    RF  Market_Excess\n",
       "Date                                                    \n",
       "2024-10-30 00:00:00+00:00 -0.003300  0.05      -0.053300\n",
       "2024-10-31 00:00:00+00:00 -0.018615  0.05      -0.068615\n",
       "2024-11-01 00:00:00+00:00  0.004093  0.05      -0.045907\n",
       "2024-11-04 00:00:00+00:00 -0.002812  0.05      -0.052812\n",
       "2024-11-05 00:00:00+00:00  0.012266  0.05      -0.037734"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp500_returns.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8aa6727-de58-489c-9ede-23ca7900700b",
   "metadata": {},
   "source": [
    "### Combining the required dataframes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "9a9ee1db-ee56-40da-b0d7-40e9fd7f117b",
   "metadata": {},
   "outputs": [],
   "source": [
    "FamaFrenchData = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "f017cf3f-e045-4eec-bb75-eee41f37265c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(714, 13)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "bf74d82e-bb95-42a7-9347-a1efd499b3d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(714, 3)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp500_returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "8073b1ee-f465-4eb6-8cf1-57a3612ee676",
   "metadata": {},
   "outputs": [],
   "source": [
    "Market_Excess = sp500_returns['Market_Excess'].reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "21d269fe-2208-40fb-91a1-fe180e0f6e2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Market_Excess</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2022-01-04 00:00:00+00:00</td>\n",
       "      <td>-0.050630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2022-01-05 00:00:00+00:00</td>\n",
       "      <td>-0.069393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2022-01-06 00:00:00+00:00</td>\n",
       "      <td>-0.050964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2022-01-07 00:00:00+00:00</td>\n",
       "      <td>-0.054050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2022-01-10 00:00:00+00:00</td>\n",
       "      <td>-0.051441</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       Date  Market_Excess\n",
       "0 2022-01-04 00:00:00+00:00      -0.050630\n",
       "1 2022-01-05 00:00:00+00:00      -0.069393\n",
       "2 2022-01-06 00:00:00+00:00      -0.050964\n",
       "3 2022-01-07 00:00:00+00:00      -0.054050\n",
       "4 2022-01-10 00:00:00+00:00      -0.051441"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Market_Excess.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "8eea1bb1-6ff0-450a-9db3-fb3469344dca",
   "metadata": {},
   "outputs": [],
   "source": [
    "Portfolio_Excess = returns[\"Portfolio_Excess\"].reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "fc59921c-fb62-44a1-b143-c34901a8d789",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Portfolio_Excess</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2022-01-04 00:00:00+00:00</td>\n",
       "      <td>-0.057837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2022-01-05 00:00:00+00:00</td>\n",
       "      <td>-0.082910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2022-01-06 00:00:00+00:00</td>\n",
       "      <td>-0.054710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2022-01-07 00:00:00+00:00</td>\n",
       "      <td>-0.056718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2022-01-10 00:00:00+00:00</td>\n",
       "      <td>-0.044760</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        Date  Portfolio_Excess\n",
       "0  2022-01-04 00:00:00+00:00         -0.057837\n",
       "1  2022-01-05 00:00:00+00:00         -0.082910\n",
       "2  2022-01-06 00:00:00+00:00         -0.054710\n",
       "3  2022-01-07 00:00:00+00:00         -0.056718\n",
       "4  2022-01-10 00:00:00+00:00         -0.044760"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Portfolio_Excess.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "7c79bf20-ca3f-45e3-8375-8d54b391107d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert 'Date' column in both dataframes to datetime64 (make sure they're both in the same format)\n",
    "Portfolio_Excess['Date'] = pd.to_datetime(Portfolio_Excess['Date'], errors='coerce')  # Coerce invalid formats to NaT\n",
    "Market_Excess['Date'] = pd.to_datetime(Market_Excess['Date'], errors='coerce')  # Same here\n",
    "\n",
    "# Now merge on 'Date' (after converting to datetime)\n",
    "FamaFrenchData = pd.merge(Portfolio_Excess, Market_Excess, on='Date', how='inner')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "9e3ab338-2c02-4b8a-8ebf-914649353bcd",
   "metadata": {},
   "outputs": [],
   "source": [
    "nat_count = FamaFrenchData['Date'].isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "477615ff-c54b-46bf-8641-bcde1c873f6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nat_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "65ef1a0b-61ed-4c8f-96be-cfcb79ec5a28",
   "metadata": {},
   "outputs": [],
   "source": [
    "FamaFrenchData.set_index('Date', inplace = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "303eb791-dc4b-4159-9216-7324904e7ca9",
   "metadata": {},
   "source": [
    "**Fama French Data:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "b046a6a1-2aea-479b-a984-7fccd08b932f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Portfolio_Excess</th>\n",
       "      <th>Market_Excess</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>2024-10-30 00:00:00+00:00</th>\n",
       "      <td>-0.060538</td>\n",
       "      <td>-0.053300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31 00:00:00+00:00</th>\n",
       "      <td>-0.080912</td>\n",
       "      <td>-0.068615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-01 00:00:00+00:00</th>\n",
       "      <td>-0.039289</td>\n",
       "      <td>-0.045907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-04 00:00:00+00:00</th>\n",
       "      <td>-0.058036</td>\n",
       "      <td>-0.052812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-05 00:00:00+00:00</th>\n",
       "      <td>-0.016729</td>\n",
       "      <td>-0.037734</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Portfolio_Excess  Market_Excess\n",
       "Date                                                      \n",
       "2024-10-30 00:00:00+00:00         -0.060538      -0.053300\n",
       "2024-10-31 00:00:00+00:00         -0.080912      -0.068615\n",
       "2024-11-01 00:00:00+00:00         -0.039289      -0.045907\n",
       "2024-11-04 00:00:00+00:00         -0.058036      -0.052812\n",
       "2024-11-05 00:00:00+00:00         -0.016729      -0.037734"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FamaFrenchData.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "153944cc-362f-4ed5-97ad-1ee97e12ad1f",
   "metadata": {},
   "source": [
    "### Calculating Beta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a0cce2d-a59b-45f5-a1a5-61778e63bcd5",
   "metadata": {},
   "source": [
    "**with Covariance and variance of benchmark**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "628bb961-810a-4d42-ba53-a7e2bc6f5c61",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the co-variance matrix between Portfolio_Excess and Market_Excess\n",
    "covariance_matrix = FamaFrenchData[['Portfolio_Excess', 'Market_Excess']].cov()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "4079e057-cf87-4a04-b482-d42a9c29216d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Portfolio_Excess</th>\n",
       "      <th>Market_Excess</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Portfolio_Excess</th>\n",
       "      <td>0.000324</td>\n",
       "      <td>0.000179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Market_Excess</th>\n",
       "      <td>0.000179</td>\n",
       "      <td>0.000124</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Portfolio_Excess  Market_Excess\n",
       "Portfolio_Excess          0.000324       0.000179\n",
       "Market_Excess             0.000179       0.000124"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "covariance_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "fc67e0a4-cad8-407c-b120-56ae514a72c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00017850929377744525\n"
     ]
    }
   ],
   "source": [
    "# Extract the co-variance co-efficient\n",
    "covariance_coefficient = covariance_matrix.iloc[0, 1]\n",
    "print(covariance_coefficient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "a59f9402-e6bb-44f9-8add-858bb3ef2657",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00012416761304298387\n"
     ]
    }
   ],
   "source": [
    "# Calculate the benchmark variance\n",
    "benchmark_variance = FamaFrenchData['Market_Excess'].var()\n",
    "print(benchmark_variance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "576599b8-2535-4166-b60a-4310c462fdea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4376477843352726\n"
     ]
    }
   ],
   "source": [
    "# Calculating the portfolio market beta\n",
    "portfolio_beta = covariance_coefficient/benchmark_variance\n",
    "print(portfolio_beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ed5eae7-7778-4d39-a8d4-0f3c3613ab15",
   "metadata": {},
   "source": [
    "#### Calculating beta with CAPM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a865caaa-f365-4cd2-806d-c9d5d2d94427",
   "metadata": {},
   "source": [
    "<img src=\"screenshots/capm.JPG\" alt=\"Image Description\" width=\"50%\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "dc2ba46e-d3bd-418f-99e7-6133a12c6143",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7919854577210157\n",
      "1.4376477843352697\n"
     ]
    }
   ],
   "source": [
    "# Import statsmodels.formula.api\n",
    "import statsmodels.formula.api as smf \n",
    "\n",
    "# Define the regression formula\n",
    "CAPM_model = smf.ols(formula='Portfolio_Excess ~ Market_Excess', data=FamaFrenchData)\n",
    "\n",
    "# Print adjusted r-squared of the fitted regression\n",
    "CAPM_fit = CAPM_model.fit()\n",
    "print(CAPM_fit.rsquared_adj)\n",
    "\n",
    "# Extract the beta\n",
    "regression_beta = CAPM_fit.params['Market_Excess']\n",
    "print(regression_beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efc96761-e356-4fc9-8d6d-61d350fa9394",
   "metadata": {},
   "source": [
    "### Alpha and multi-factor models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff327b0c-2a3d-499b-a5fe-9c9fa7872fbf",
   "metadata": {},
   "source": [
    "##### The Fama French 3-factor model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad81de68-5891-442f-8c8d-6868b9d87cb7",
   "metadata": {},
   "source": [
    "#### Data Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "2991bb3a-84a9-4d0d-b955-ba34695aa36b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Require SMB and HML\n",
    "small = \"VB\"\n",
    "big = \"^DJI\"\n",
    "value = \"IWD\"\n",
    "growth = \"IWF\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "bb26a1c5-2f1c-4344-a300-0f4a39ae4204",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    }
   ],
   "source": [
    "# Download data\n",
    "def download_data(symbol, start_date, end_date):\n",
    "    data2 = yf.download(symbol, start=start_date, end=end_date)\n",
    "    # Convert index to datetime\n",
    "    data2.index = pd.to_datetime(data2.index)\n",
    "    return data2['Adj Close']\n",
    "    \n",
    "\n",
    "# Fetch adjusted close prices for each\n",
    "small_data = download_data(small, start_date, end_date)\n",
    "big_data = download_data(big, start_date, end_date)\n",
    "value_data = download_data(value, start_date, end_date)\n",
    "growth_data = download_data(growth, start_date, end_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "9ded7a45-f147-4904-aed7-b69aed488e95",
   "metadata": {},
   "outputs": [],
   "source": [
    "# changing column names for convenience\n",
    "small_data.columns = ['small']\n",
    "big_data.columns = ['big']\n",
    "value_data.columns = ['value']\n",
    "growth_data.columns = ['growth']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "1d42d78b-a463-42d2-9579-2f8a6bcefaa5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime64[ns, UTC]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "small_data.index.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "a7204a70-f1b2-4d7d-a51e-12f36ee57398",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>big</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2022-01-03 00:00:00+00:00</th>\n",
       "      <td>36585.058594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-04 00:00:00+00:00</th>\n",
       "      <td>36799.648438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-05 00:00:00+00:00</th>\n",
       "      <td>36407.109375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-06 00:00:00+00:00</th>\n",
       "      <td>36236.468750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-07 00:00:00+00:00</th>\n",
       "      <td>36231.660156</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                    big\n",
       "Date                                   \n",
       "2022-01-03 00:00:00+00:00  36585.058594\n",
       "2022-01-04 00:00:00+00:00  36799.648438\n",
       "2022-01-05 00:00:00+00:00  36407.109375\n",
       "2022-01-06 00:00:00+00:00  36236.468750\n",
       "2022-01-07 00:00:00+00:00  36231.660156"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "big_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "999b65e5-ca87-49e6-b23f-e81452c9bf56",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate daily returns\n",
    "small_returns = small_data.pct_change().dropna()\n",
    "big_returns = big_data.pct_change().dropna()\n",
    "value_returns = value_data.pct_change().dropna()\n",
    "growth_returns = growth_data.pct_change().dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "78df9130-34a5-4dfe-b73d-f37268fe3a3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>small</th>\n",
       "      <th>big</th>\n",
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       "      <th>growth</th>\n",
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       "    <tr>\n",
       "      <th>Date</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2022-01-04 00:00:00+00:00</th>\n",
       "      <td>0.002242</td>\n",
       "      <td>0.005866</td>\n",
       "      <td>0.008782</td>\n",
       "      <td>-0.010365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-05 00:00:00+00:00</th>\n",
       "      <td>-0.028074</td>\n",
       "      <td>-0.010667</td>\n",
       "      <td>-0.008765</td>\n",
       "      <td>-0.031912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-06 00:00:00+00:00</th>\n",
       "      <td>0.004829</td>\n",
       "      <td>-0.004687</td>\n",
       "      <td>0.001958</td>\n",
       "      <td>-0.002781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-07 00:00:00+00:00</th>\n",
       "      <td>-0.007681</td>\n",
       "      <td>-0.000133</td>\n",
       "      <td>0.002488</td>\n",
       "      <td>-0.011019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-10 00:00:00+00:00</th>\n",
       "      <td>-0.003802</td>\n",
       "      <td>-0.004493</td>\n",
       "      <td>-0.001536</td>\n",
       "      <td>-0.000584</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              small       big     value    growth\n",
       "Date                                                             \n",
       "2022-01-04 00:00:00+00:00  0.002242  0.005866  0.008782 -0.010365\n",
       "2022-01-05 00:00:00+00:00 -0.028074 -0.010667 -0.008765 -0.031912\n",
       "2022-01-06 00:00:00+00:00  0.004829 -0.004687  0.001958 -0.002781\n",
       "2022-01-07 00:00:00+00:00 -0.007681 -0.000133  0.002488 -0.011019\n",
       "2022-01-10 00:00:00+00:00 -0.003802 -0.004493 -0.001536 -0.000584"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined_returns = pd.concat([small_returns, big_returns, value_returns, growth_returns], axis = 1) # axis = 1 to join along columns \n",
    "combined_returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "f3b05759-59c6-4b6a-8e6a-760d7bcd8e8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "combined_returns['SMB'] = combined_returns['small'] - combined_returns['big'] \n",
    "combined_returns['HML'] = combined_returns['value'] - combined_returns['growth'] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "b3e09320-bcca-43a9-994c-9b1686b827ad",
   "metadata": {},
   "outputs": [
    {
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       "      <th>HML</th>\n",
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       "    <tr>\n",
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       "  <tbody>\n",
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       "      <th>2022-01-04 00:00:00+00:00</th>\n",
       "      <td>0.002242</td>\n",
       "      <td>0.005866</td>\n",
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       "      <td>-0.003623</td>\n",
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       "    <tr>\n",
       "      <th>2022-01-05 00:00:00+00:00</th>\n",
       "      <td>-0.028074</td>\n",
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       "      <td>0.023147</td>\n",
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       "      <th>2022-01-06 00:00:00+00:00</th>\n",
       "      <td>0.004829</td>\n",
       "      <td>-0.004687</td>\n",
       "      <td>0.001958</td>\n",
       "      <td>-0.002781</td>\n",
       "      <td>0.009516</td>\n",
       "      <td>0.004739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-07 00:00:00+00:00</th>\n",
       "      <td>-0.007681</td>\n",
       "      <td>-0.000133</td>\n",
       "      <td>0.002488</td>\n",
       "      <td>-0.011019</td>\n",
       "      <td>-0.007548</td>\n",
       "      <td>0.013506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-10 00:00:00+00:00</th>\n",
       "      <td>-0.003802</td>\n",
       "      <td>-0.004493</td>\n",
       "      <td>-0.001536</td>\n",
       "      <td>-0.000584</td>\n",
       "      <td>0.000691</td>\n",
       "      <td>-0.000952</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              small       big     value    growth       SMB  \\\n",
       "Date                                                                          \n",
       "2022-01-04 00:00:00+00:00  0.002242  0.005866  0.008782 -0.010365 -0.003623   \n",
       "2022-01-05 00:00:00+00:00 -0.028074 -0.010667 -0.008765 -0.031912 -0.017407   \n",
       "2022-01-06 00:00:00+00:00  0.004829 -0.004687  0.001958 -0.002781  0.009516   \n",
       "2022-01-07 00:00:00+00:00 -0.007681 -0.000133  0.002488 -0.011019 -0.007548   \n",
       "2022-01-10 00:00:00+00:00 -0.003802 -0.004493 -0.001536 -0.000584  0.000691   \n",
       "\n",
       "                                HML  \n",
       "Date                                 \n",
       "2022-01-04 00:00:00+00:00  0.019147  \n",
       "2022-01-05 00:00:00+00:00  0.023147  \n",
       "2022-01-06 00:00:00+00:00  0.004739  \n",
       "2022-01-07 00:00:00+00:00  0.013506  \n",
       "2022-01-10 00:00:00+00:00 -0.000952  "
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined_returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "9f41fde8-f579-4c30-ac4c-655f28ed41ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "ff = combined_returns[['SMB', 'HML']]\n",
    "ff.to_csv(\"fama_factors.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "19214040-4862-4d9e-af4d-332df37a28ad",
   "metadata": {},
   "outputs": [
    {
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       "      <th>Date</th>\n",
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       "      <td>0.009516</td>\n",
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      ],
      "text/plain": [
       "                                SMB       HML\n",
       "Date                                         \n",
       "2022-01-04 00:00:00+00:00 -0.003623  0.019147\n",
       "2022-01-05 00:00:00+00:00 -0.017407  0.023147\n",
       "2022-01-06 00:00:00+00:00  0.009516  0.004739\n",
       "2022-01-07 00:00:00+00:00 -0.007548  0.013506\n",
       "2022-01-10 00:00:00+00:00  0.000691 -0.000952"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ff.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fa33175-3db2-4149-bb4f-66b149767f97",
   "metadata": {},
   "source": [
    "##### Fama French Data Final:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "997d37e5-9695-4905-98be-db7c74381305",
   "metadata": {},
   "outputs": [],
   "source": [
    "FamaFrenchData_final = pd.merge(FamaFrenchData, ff, on='Date', how='inner')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "3845767b-3829-4b80-a682-4c0cfadb385a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Portfolio_Excess</th>\n",
       "      <th>Market_Excess</th>\n",
       "      <th>SMB</th>\n",
       "      <th>HML</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2024-10-30 00:00:00+00:00</th>\n",
       "      <td>-0.060538</td>\n",
       "      <td>-0.053300</td>\n",
       "      <td>0.002543</td>\n",
       "      <td>0.003310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31 00:00:00+00:00</th>\n",
       "      <td>-0.080912</td>\n",
       "      <td>-0.068615</td>\n",
       "      <td>-0.005334</td>\n",
       "      <td>0.021311</td>\n",
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       "    <tr>\n",
       "      <th>2024-11-01 00:00:00+00:00</th>\n",
       "      <td>-0.039289</td>\n",
       "      <td>-0.045907</td>\n",
       "      <td>-0.004367</td>\n",
       "      <td>-0.007248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-04 00:00:00+00:00</th>\n",
       "      <td>-0.058036</td>\n",
       "      <td>-0.052812</td>\n",
       "      <td>0.008792</td>\n",
       "      <td>0.002226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-05 00:00:00+00:00</th>\n",
       "      <td>-0.016729</td>\n",
       "      <td>-0.037734</td>\n",
       "      <td>0.006537</td>\n",
       "      <td>-0.003208</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Portfolio_Excess  Market_Excess       SMB       HML\n",
       "Date                                                                          \n",
       "2024-10-30 00:00:00+00:00         -0.060538      -0.053300  0.002543  0.003310\n",
       "2024-10-31 00:00:00+00:00         -0.080912      -0.068615 -0.005334  0.021311\n",
       "2024-11-01 00:00:00+00:00         -0.039289      -0.045907 -0.004367 -0.007248\n",
       "2024-11-04 00:00:00+00:00         -0.058036      -0.052812  0.008792  0.002226\n",
       "2024-11-05 00:00:00+00:00         -0.016729      -0.037734  0.006537 -0.003208"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FamaFrenchData_final.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9257ff69-6074-4b56-ba13-e96e39c15993",
   "metadata": {},
   "source": [
    "### MODEL VALIDATION 1: Checking Multicollinearity OF features or independent variables w/ Correlation matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "4769649e-4b18-402c-9651-f20ef8dd5e30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Portfolio_Excess</th>\n",
       "      <th>Market_Excess</th>\n",
       "      <th>SMB</th>\n",
       "      <th>HML</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Portfolio_Excess</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.890100</td>\n",
       "      <td>0.556204</td>\n",
       "      <td>-0.648375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Market_Excess</th>\n",
       "      <td>0.890100</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.474747</td>\n",
       "      <td>-0.555809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>0.556204</td>\n",
       "      <td>0.474747</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.190215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>-0.648375</td>\n",
       "      <td>-0.555809</td>\n",
       "      <td>-0.190215</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Portfolio_Excess  Market_Excess       SMB       HML\n",
       "Portfolio_Excess          1.000000       0.890100  0.556204 -0.648375\n",
       "Market_Excess             0.890100       1.000000  0.474747 -0.555809\n",
       "SMB                       0.556204       0.474747  1.000000 -0.190215\n",
       "HML                      -0.648375      -0.555809 -0.190215  1.000000"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FamaFrenchData_final.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55c17d9e-ddc4-41bf-99c5-061d563f69b9",
   "metadata": {},
   "source": [
    "**No Multicollinearity: It WON'T be difficult for the model to find which feature is actually contributing to predict the target** <br/>\n",
    "Features in the model are not highly correlated with each other, ensuring that each feature independently contributes to predicting the target variable **without REDUNDANCY**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ece9f633-e42e-4383-8d2a-a6c1576688d4",
   "metadata": {},
   "source": [
    "### MODEL VALIDATION 2: Checking Llinearity w/ Scatter plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "1244011e-2ea0-4526-a463-e941aaa06752",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'SMB vs Portfolio_Excess')"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "# Portfolio vs Treasury\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.scatter(FamaFrenchData_final['Portfolio_Excess'], FamaFrenchData_final['SMB'])\n",
    "plt.xlabel(\"Portfolio_Excess Returns\")\n",
    "plt.ylabel(\"SMB Returns\")\n",
    "plt.title(\"SMB vs Portfolio_Excess\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "d877075e-9d4a-45bc-bd13-5221e4db5919",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'HML vs Portfolio_Excess')"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "# Portfolio vs Treasury\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.scatter(FamaFrenchData_final['Portfolio_Excess'], FamaFrenchData_final['HML'])\n",
    "plt.xlabel(\"Portfolio_Excess Returns\")\n",
    "plt.ylabel(\"HML Returns\")\n",
    "plt.title(\"HML vs Portfolio_Excess\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "7821e265-02c6-430e-8139-0ae2b76d3962",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Market_Excess vs Portfolio_Excess')"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "# Portfolio vs Treasury\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.scatter(FamaFrenchData_final['Portfolio_Excess'], FamaFrenchData_final['Market_Excess'])\n",
    "plt.xlabel(\"Portfolio_Excess Returns\")\n",
    "plt.ylabel(\"Market_Excess Returns\")\n",
    "plt.title(\"Market_Excess vs Portfolio_Excess\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "640814b4-f29a-4cb9-a4f7-c2469d362a1d",
   "metadata": {},
   "source": [
    "**All the plots have a linear plot: This means that a change in the independent variables (Market_Excess, HML, SMB) results in a proportional change in the dependent variable**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6be9f4f-a749-47cb-a4a4-94cc12b608e8",
   "metadata": {},
   "source": [
    "### **The Fama French 3-factor model**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "b9cf4784-2102-41a7-a3f7-62be094aceb1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8551768756153967\n"
     ]
    }
   ],
   "source": [
    "# Import statsmodels.formula.api\n",
    "import statsmodels.formula.api as smf \n",
    "\n",
    "# Define the regression formula\n",
    "FamaFrench_model = smf.ols(formula='Portfolio_Excess ~ Market_Excess + SMB + HML', data=FamaFrenchData_final)\n",
    "\n",
    "# Fit the regression\n",
    "FamaFrench_fit = FamaFrench_model.fit()\n",
    "\n",
    "# Extract the adjusted r-squared\n",
    "regression_adj_rsq = FamaFrench_fit.rsquared_adj\n",
    "print(regression_adj_rsq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "5757cd73-948f-4715-a78c-d2a242c9b7d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The SMB coefficient is  0.4867636199045067  and is  significant\n"
     ]
    }
   ],
   "source": [
    "# Extract the p-value of the SMB factor\n",
    "smb_pval = FamaFrench_fit.pvalues['SMB']\n",
    "\n",
    "# If the p-value is significant, print significant\n",
    "if smb_pval < 0.05:\n",
    "    significant_msg = 'significant'\n",
    "else:\n",
    "    significant_msg = 'not significant'\n",
    "\n",
    "# Print the SMB coefficient\n",
    "smb_coeff = FamaFrench_fit.params['SMB']\n",
    "print(\"The SMB coefficient is \", smb_coeff, \" and is \", significant_msg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce1588a5-cfaa-40ad-abf6-bbdda958e066",
   "metadata": {},
   "source": [
    "Historically, since 1982, value stocks have outperformed growth stocks in the majority of cases, and the tide often shifts during times of crisis and during bubbles such as the dot-com bubble during the late 1990's and early 2000's."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "1027e809-79c0-456a-a9ee-52942200a2f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0036654220162840668\n",
      "0.0012921473017779572\n"
     ]
    }
   ],
   "source": [
    "# Calculate your portfolio alpha\n",
    "portfolio_alpha = FamaFrench_fit.params['Intercept']\n",
    "print(portfolio_alpha)\n",
    "\n",
    "# Annualize your portfolio alpha\n",
    "portfolio_alpha_annualized = ((1+portfolio_alpha)**(12/months_diff))-1\n",
    "print(portfolio_alpha_annualized)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1fe8ee9-2976-4c2a-aa3a-b8db7ae27e0c",
   "metadata": {},
   "source": [
    "### MODEL PERFORMANCE: Checking R squared and other metrics in OLS Regression Summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "75bb4ad6-2bd7-4a0f-8635-5658fa8b1edd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:       Portfolio_Excess   R-squared:                       0.856\n",
      "Model:                            OLS   Adj. R-squared:                  0.855\n",
      "Method:                 Least Squares   F-statistic:                     1404.\n",
      "Date:                Sun, 19 Jan 2025   Prob (F-statistic):          5.52e-298\n",
      "Time:                        11:02:21   Log-Likelihood:                 2547.2\n",
      "No. Observations:                 714   AIC:                            -5086.\n",
      "Df Residuals:                     710   BIC:                            -5068.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=================================================================================\n",
      "                    coef    std err          t      P>|t|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "Intercept         0.0037      0.002      2.341      0.020       0.001       0.007\n",
      "Market_Excess     1.0693      0.031     34.444      0.000       1.008       1.130\n",
      "SMB               0.4868      0.040     12.020      0.000       0.407       0.566\n",
      "HML              -0.4941      0.035    -14.113      0.000      -0.563      -0.425\n",
      "==============================================================================\n",
      "Omnibus:                       54.097   Durbin-Watson:                   1.943\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              152.458\n",
      "Skew:                           0.357   Prob(JB):                     7.84e-34\n",
      "Kurtosis:                       5.148   Cond. No.                         182.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(FamaFrench_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e31551d-161e-4ffa-9c64-c60ce9195031",
   "metadata": {},
   "source": [
    "**The model explains 87% of the variance in the portfolio's excess returns, indicating a strong fit between the independent variables (Market_Excess, SMB, and HML) and the dependent variable.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33482c58-a5b1-42ba-8422-69f54e5a7caf",
   "metadata": {},
   "source": [
    "### Extract residuals / errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "b42abdb5-ce72-4da6-903d-63a174b8afd8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2022-01-04 00:00:00+00:00    0.003861\n",
       "2022-01-05 00:00:00+00:00    0.007538\n",
       "2022-01-06 00:00:00+00:00   -0.006169\n",
       "2022-01-07 00:00:00+00:00    0.007761\n",
       "2022-01-10 00:00:00+00:00    0.005775\n",
       "dtype: float64"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract residuals\n",
    "residuals = FamaFrench_fit.resid\n",
    "\n",
    "# Display residuals\n",
    "residuals.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "b90d787e-ade7-4335-b78b-5c5b36761289",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Residuals</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2022-01-04 00:00:00+00:00</th>\n",
       "      <td>0.003861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-05 00:00:00+00:00</th>\n",
       "      <td>0.007538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-06 00:00:00+00:00</th>\n",
       "      <td>-0.006169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-07 00:00:00+00:00</th>\n",
       "      <td>0.007761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-10 00:00:00+00:00</th>\n",
       "      <td>0.005775</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Residuals\n",
       "Date                                \n",
       "2022-01-04 00:00:00+00:00   0.003861\n",
       "2022-01-05 00:00:00+00:00   0.007538\n",
       "2022-01-06 00:00:00+00:00  -0.006169\n",
       "2022-01-07 00:00:00+00:00   0.007761\n",
       "2022-01-10 00:00:00+00:00   0.005775"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert residuals to a DataFrame\n",
    "residuals_df = pd.DataFrame({'Residuals': FamaFrench_fit.resid})\n",
    "\n",
    "residuals_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eda0f74c-8fd0-4689-8a35-f1139ff021ff",
   "metadata": {},
   "source": [
    "### MODEL VALIDATION 3: Checking Idependence of of residuals w/ Autocorrelation Function (ACF) and D-W test"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a94827d-feb4-4d7c-af59-a0da82b69aaa",
   "metadata": {},
   "source": [
    "#### Autocorrelation Function (ACF) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "aa3f1e8d-c0ae-45a5-a875-7d6239ad5bed",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "a0e2f6f3-2da1-4346-ab61-85957c778d98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(FamaFrench_fit.resid, lags=20)\n",
    "\n",
    "plt.title('ACF of Residuals')\n",
    "plt.xlabel('Lags')\n",
    "plt.ylabel('Autocorrelation')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3400a828-6472-46f0-98dc-8f71b40e4ad8",
   "metadata": {},
   "source": [
    "By default, alpha=0.05 (for 95% confidence level)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8dc82f4-4991-4186-b733-8beb7ccaba04",
   "metadata": {},
   "source": [
    "**In this analysis, most autocorrelations fall within the intervals, suggesting no significant autocorrelation in the residuals.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11471fc8-6c79-4148-85dc-0faf45674894",
   "metadata": {},
   "source": [
    "**This means the model has NOT missed something importatnt and capturing most of the information**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b2f6f99-1975-4d5a-a92b-ffed6eae3eac",
   "metadata": {},
   "source": [
    "#### Durbin Watson test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "f24c17b7-a3f2-4c81-99e4-d09ffd85a586",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Durbin-Watson statistic: 1.942803089276677\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.stattools import durbin_watson\n",
    "\n",
    "# Perform the Durbin-Watson test\n",
    "dw_stat = durbin_watson(FamaFrench_fit.resid)\n",
    "\n",
    "# Display the result\n",
    "print(f\"Durbin-Watson statistic: {dw_stat}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "860b7133-7d26-41d5-be4d-e75ee78e431e",
   "metadata": {},
   "source": [
    "Durbin-Watson statistic range: The value ranges from 0 to 4.\n",
    "- **~2**: **No autocorrelation.**\n",
    "- **<2**: Positive autocorrelation.\n",
    "- **>2**: Negative autocorrelation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d198c73-39f6-47bf-bfb9-61f7f4ed32eb",
   "metadata": {},
   "source": [
    "**The Durbin-Watson test statistic is [DW value], which is close to 2, indicating no significant autocorrelation in the residuals**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91902f9f-ea65-49d8-b884-8a711d491923",
   "metadata": {},
   "source": [
    "### MODEL VALIDATION 4: Checking Normality of residuals w/ histogram "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "7ec31e85-6aff-4b1b-bc35-4c7ca5cd85d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Plot histogram of residuals\n",
    "plt.hist(FamaFrench_fit.resid, bins=30, edgecolor='k', alpha=0.7)\n",
    "\n",
    "plt.title('Histogram of Residuals')\n",
    "plt.xlabel('Residuals')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "f6288530-0621-4617-b37f-2c02a999f21c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import skew, kurtosis\n",
    "# Calculate skewness and kurtosis of residuals\n",
    "residual_skewness = skew(residuals)\n",
    "residual_kurtosis = kurtosis(residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "7b10b2e9-d4e7-4509-b07c-09cda9cd0cde",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual Skewness: 0.3571078315868412\n",
      "Residual Kurtosis: 2.1481488167769234\n"
     ]
    }
   ],
   "source": [
    "print(f'Residual Skewness: {residual_skewness}')\n",
    "print(f'Residual Kurtosis: {residual_kurtosis}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4af50c5-be8b-4205-9c54-32f921368606",
   "metadata": {},
   "source": [
    "- The residuals are roughly symmetrical, with only a slight right skew.\n",
    "- The distribution of residuals is flatter than normal, meaning the model might not have as many outliers as a normal distribution would expect."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8748ab7-7869-4814-862a-25bcb348ce68",
   "metadata": {},
   "source": [
    "**Both skewness and kurtosis values are within a reasonable range, suggesting that the residuals do not exhibit extreme departures from normality, which is good for model assumptions.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28c854ea-109f-4fa1-8329-d1b908a5ff5c",
   "metadata": {},
   "source": [
    "Ideal value: Skew (0) and Kurtosis (3) Reasonable range: Skew (-1 to 1) and Kurtosis (2 to 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b4f954a-b432-49d5-b4a2-a2ede0de2c43",
   "metadata": {},
   "source": [
    "**The histogram of the residuals suggests that they follow a distribution similar to normal, indicating that the assumption of normality is reasonably met.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b94688a4-f232-48eb-a0a2-eea650798211",
   "metadata": {},
   "source": [
    "#### Shapiro-Wilk Test:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "c039bcad-d2a0-433e-a5a6-a95d41736848",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shapiro-Wilk Test Statistic: 0.9785720109939575, p-value: 1.01289296949858e-08\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import shapiro\n",
    "\n",
    "# Perform Shapiro-Wilk test\n",
    "stat, p_value = shapiro(FamaFrench_fit.resid)\n",
    "\n",
    "# Display the result\n",
    "print(f\"Shapiro-Wilk Test Statistic: {stat}, p-value: {p_value}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2533b861-14bc-495f-b9f3-d89d3137fdb3",
   "metadata": {},
   "source": [
    "**The Shapiro-Wilk test for normality returned a p-value of 0.0012. Since the p-value is less than 0.05, we reject the null hypothesis, suggesting that the residuals are not normally distributed.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff6da3c1-d5b1-4951-996b-525c97b7a9fb",
   "metadata": {},
   "source": [
    "Apply **transformations** (e.g., logarithmic, Box-Cox) to make the residuals more normal, preserving the linear framework of your model. <br/>\n",
    "Explore PCA, Consider **robust regression methods** for more reliable coefficient estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4f67669-373b-43f3-8c2a-d69a63d33e6c",
   "metadata": {},
   "source": [
    "### MODEL VALIDATION 5: Checking Homoscedasticity of Residuals w/ scatter plot of residuals and fitted values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "16685ffa-5b03-4c12-ac73-3648007fd409",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "residuals = FamaFrench_fit.resid\n",
    "fitted_values = FamaFrench_fit.fittedvalues\n",
    "\n",
    "plt.scatter(fitted_values, residuals)\n",
    "plt.axhline(y=0, color='r', linestyle='--')\n",
    "plt.xlabel(\"Fitted Values\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.title(\"Residual vs Fitted Values Plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60cfed28-0867-494c-835a-e1b259a23c47",
   "metadata": {},
   "source": [
    "**The residual plot shows a random scatter around the zero line without any discernible pattern, indicating that the variance of the residuals is constant. This suggests that the model satisfies the assumption of homoscedasticity**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80f286bc-4062-4863-9216-5c2fe40ae761",
   "metadata": {},
   "source": [
    "**Most of the Model assumptions are met**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0a185e7d-1acc-4f6a-82b5-3de9e9c477e0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}