riqbal-k/optimal hedge ratio Regression.ipynb

## optimal hedge ratio Regression.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "274457b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "setwd(\"C:/Users/mnf13/RM\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "cffd58c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "data<-read.csv(\"FTSESF.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "6fe1e05e",
   "metadata": {},
   "outputs": [],
   "source": [
    "###data<-read.csv(\"FTSESF.csv\", colClasses = c(\"Future\"=\"numeric\", \"Spot\" = \"numeric\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "ad502a54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Exchange.Date</th><th scope=col>Future</th><th scope=col>Spot</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>12-Oct-2020</td><td>5977.0     </td><td>6016.65    </td></tr>\n",
       "\t<tr><td>13-Oct-2020</td><td>5936.0     </td><td>6001.38    </td></tr>\n",
       "\t<tr><td>14-Oct-2020</td><td>5911.5     </td><td>5969.71    </td></tr>\n",
       "\t<tr><td>15-Oct-2020</td><td>5800.5     </td><td>5935.06    </td></tr>\n",
       "\t<tr><td>16-Oct-2020</td><td>5902.5     </td><td>5832.52    </td></tr>\n",
       "\t<tr><td>19-Oct-2020</td><td>5863.5     </td><td>5919.58    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " Exchange.Date & Future & Spot\\\\\n",
       "\\hline\n",
       "\t 12-Oct-2020 & 5977.0      & 6016.65    \\\\\n",
       "\t 13-Oct-2020 & 5936.0      & 6001.38    \\\\\n",
       "\t 14-Oct-2020 & 5911.5      & 5969.71    \\\\\n",
       "\t 15-Oct-2020 & 5800.5      & 5935.06    \\\\\n",
       "\t 16-Oct-2020 & 5902.5      & 5832.52    \\\\\n",
       "\t 19-Oct-2020 & 5863.5      & 5919.58    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| Exchange.Date | Future | Spot |\n",
       "|---|---|---|\n",
       "| 12-Oct-2020 | 5977.0      | 6016.65     |\n",
       "| 13-Oct-2020 | 5936.0      | 6001.38     |\n",
       "| 14-Oct-2020 | 5911.5      | 5969.71     |\n",
       "| 15-Oct-2020 | 5800.5      | 5935.06     |\n",
       "| 16-Oct-2020 | 5902.5      | 5832.52     |\n",
       "| 19-Oct-2020 | 5863.5      | 5919.58     |\n",
       "\n"
      ],
      "text/plain": [
       "  Exchange.Date Future Spot   \n",
       "1 12-Oct-2020   5977.0 6016.65\n",
       "2 13-Oct-2020   5936.0 6001.38\n",
       "3 14-Oct-2020   5911.5 5969.71\n",
       "4 15-Oct-2020   5800.5 5935.06\n",
       "5 16-Oct-2020   5902.5 5832.52\n",
       "6 19-Oct-2020   5863.5 5919.58"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "70ddfbc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t504 obs. of  3 variables:\n",
      " $ Exchange.Date: Factor w/ 504 levels \"\",\"01-Apr-2021\",..: 197 212 229 247 266 315 329 346 365 384 ...\n",
      " $ Future       : num  5977 5936 5912 5800 5902 ...\n",
      " $ Spot         : num  6017 6001 5970 5935 5833 ...\n"
     ]
    }
   ],
   "source": [
    "str(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8caf0f2",
   "metadata": {},
   "source": [
    "Change variable names "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "1159f1d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "names(data)<-c(\"dates\",\"future\",\"spot\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "51443afb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>dates</th><th scope=col>future</th><th scope=col>spot</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>12-Oct-2020</td><td>5977.0     </td><td>6016.65    </td></tr>\n",
       "\t<tr><td>13-Oct-2020</td><td>5936.0     </td><td>6001.38    </td></tr>\n",
       "\t<tr><td>14-Oct-2020</td><td>5911.5     </td><td>5969.71    </td></tr>\n",
       "\t<tr><td>15-Oct-2020</td><td>5800.5     </td><td>5935.06    </td></tr>\n",
       "\t<tr><td>16-Oct-2020</td><td>5902.5     </td><td>5832.52    </td></tr>\n",
       "\t<tr><td>19-Oct-2020</td><td>5863.5     </td><td>5919.58    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " dates & future & spot\\\\\n",
       "\\hline\n",
       "\t 12-Oct-2020 & 5977.0      & 6016.65    \\\\\n",
       "\t 13-Oct-2020 & 5936.0      & 6001.38    \\\\\n",
       "\t 14-Oct-2020 & 5911.5      & 5969.71    \\\\\n",
       "\t 15-Oct-2020 & 5800.5      & 5935.06    \\\\\n",
       "\t 16-Oct-2020 & 5902.5      & 5832.52    \\\\\n",
       "\t 19-Oct-2020 & 5863.5      & 5919.58    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| dates | future | spot |\n",
       "|---|---|---|\n",
       "| 12-Oct-2020 | 5977.0      | 6016.65     |\n",
       "| 13-Oct-2020 | 5936.0      | 6001.38     |\n",
       "| 14-Oct-2020 | 5911.5      | 5969.71     |\n",
       "| 15-Oct-2020 | 5800.5      | 5935.06     |\n",
       "| 16-Oct-2020 | 5902.5      | 5832.52     |\n",
       "| 19-Oct-2020 | 5863.5      | 5919.58     |\n",
       "\n"
      ],
      "text/plain": [
       "  dates       future spot   \n",
       "1 12-Oct-2020 5977.0 6016.65\n",
       "2 13-Oct-2020 5936.0 6001.38\n",
       "3 14-Oct-2020 5911.5 5969.71\n",
       "4 15-Oct-2020 5800.5 5935.06\n",
       "5 16-Oct-2020 5902.5 5832.52\n",
       "6 19-Oct-2020 5863.5 5919.58"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98713478",
   "metadata": {},
   "source": [
    "summary statistics of future and spot prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "98e910e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     future          spot     \n",
       " Min.   :5540   Min.   :5577  \n",
       " 1st Qu.:6844   1st Qu.:6881  \n",
       " Median :7096   Median :7125  \n",
       " Mean   :7029   Mean   :7055  \n",
       " 3rd Qu.:7320   3rd Qu.:7343  \n",
       " Max.   :7620   Max.   :7672  \n",
       " NA's   :2      NA's   :1     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(data[,-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17b55a84",
   "metadata": {},
   "source": [
    "Calculate log returns for both spot and future prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "251f8cc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "data['rspot']=c(NA,100*diff(log(data$spot)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "09e17bf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "data['rfuture']=c(NA,100*diff(log(data$spot)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "fb4a3c51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gEiuWB3kTqVEWl3EMkF/aFeP+GJSOYo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\nAARAJAABEAlAgP9xqWhqgGOrqwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Monthly closing price of FTSE Spot Price\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$spot, type=\"l\", col=\"blue\", lwd=2, \n",
    "     ylab=\"Spot Price\", main=\"Monthly closing price of FTSE Spot Price\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "409600f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hbYkk1+/zEhwQqpgw3R5NWfl9/SI+EREnZmZUj3GYe/88eZorzBg3aEhL1ZGVI4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\n0QAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Monthly closing price of FTSE Future Price\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$future, type=\"l\", col=\"blue\", lwd=2, \n",
    "     ylab=\"Spot Price\", main=\"Monthly closing price of FTSE Future Price\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "19ad04ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9SuuzT781UEtNvM6LqhgEEqDs76O3op\nAvptM0chg5SZ5JrbqfstMZmPIqDeRnMUMkiJybvp3CQ+ioByGz2uK4MGabDePq/ELa1hODY2\nnMFBi4RwttoclaHPkW53O8U50i5tbziDI2T399H5c3QovBQBvTZ7emSFvY6U2etISXrmOtLu\nbDtHjGxAEBuPEUFCENvt9m4xRAj+bT5GDBFCANtvjxgiBP92ECMuyMI/giQ2Sz0fQ4T2aA/H\ndSUtEjzbR4wYIgTPdpIjhgjBJ5uePeSIIULwaC/HdSUjG+BPn6DNx0hTkPbzx2snhod1W9+k\nDBGCHzvp9m4xRAheDJuj7W9QhgjBCxue3cSIC7LwwzZI5X5yxBAheND2MzQN0x7QIkFcl6O9\nNEclQ4QgbleXjzoMEYKw7pBuTzliiBCENfHZTS9DQ8/IhsBFwIu+n25fOSJIkORcgCVIHmap\n50u+HNAtLwJx7WtU0EDQ60gm/djFsLwIRDUcphq7NmEFDVLV6z0pSjvbCBux5xwFHtlQpMac\nbv6KQEzNsKB9dXu3Qg8RyqsO8PSSf26Y9rcdNmCHwxkc4cfa5Vnytenf4YZYvX3nKM6g1fyS\nHgjSprSDvfeao2ijv/0UgUj2OSzIRZCwWHcT335zxMgGLNeMCdrdaAYXQcJC/aCgPW84goRl\n+oF1Zs/bjSBhEWes944P7AgSFhncNbHrrUaQsED3dIZ9N0clQcIC+71p4hVBwlz9lSPzy0XC\nbSJImGnXd028IEiYyXSNETEiSJiraZDIUY0gYQ6O654QJMzRHdORoxpBwu+4a+IFQcKvnG5v\nctQiSPhRd/PR7kczuAgSfmQ3ju34Zjv1CBJ+44xRpUHqEST8og8Qx3UDBAk/6B4WxDZ6QpDw\ng+4ePg7rnhAkTNcc09Ht/YogYbomPsToFUHCRM1gbzsZuSoKESRM4j6YgQbpFUHCJO1BHedH\n4wgSpmi3CDF6gyBhCvP0E08IEqYgSF8QJHxFd913BAlf9A+BpLvuPYKEz3i09yQECZ+1x3Rs\nk48IEj5qmyGao88IEj4iSNMQJLzH8LrJCBLeYXjdDwgS3mh66RheNwlBwqjmeVslw+umIUgY\nVZ8b8XCGqQgSxrTNEA+vm4gg4VX/HFUuxE5EkPDKdGdInB9NRJDwrBulSjfDdAQJTwZfNhG7\nMqtBkDDQfwsf7dEvCBIGOK6bZ2mQLoeyvB/M4U+qQq9FICAzELs2K7IwSLdqZSfVOhdNElsw\nDo7rZlsYpKO5lrk5lFdzFKtSSZBi4bvKZ1sYpGpt5yaTHh3MNoyCGM0nEKTU3AjSBnBct8Ti\nQ7v8ZpKSQ7v1I0aLLO9sMOZcbYWbWJVKghRBf3rEddg5Fnd/J9UZUnm4CtVnpAj4N+z1ZvX/\njguyKLkMuxxBAt3eAggSaI8ELA3S+eDj7xhbMyC6vSUsDNLZzwkqmzOc7qCOHC2xMEiJuYhV\n5U0R8Ku+n5zTo4UERjZ4wAYNpnviFjlaZGGQUlOIVeVNEfCqfY4qOVpmYZDuyVH2TqTXIuBV\n85ggYrTQ4kM7OhtWrB8QRI4WIkj75X4XH2t8IS7I7pdp/k+MBCztbMjEavKuCHhinn5iCbq/\nd6pvhljZEhYG6UD39yq5TyNmZUtYGKQipft7herehe77JrAcvXb706TITROWIkj70185or9O\nDN3fu2O6wQysZzkEaXdMkyCaI0kEaWe6u2EJkijOkfaljhHDGcQRpD3pb4RleJ0wmUO7v2O6\nvCqfi8By3WEdMRIndI5UmNPiqnwpAku1l4/qu8shSqqzgUM7/doLsPR7eyAUpEv1JH05bGd5\n3akRT2fwQayz4SxWpZIgeUC3t19CQTrIPpWLLS2u7fI2jK7zgguyu0B/nW8EaQf6MyNy5IvU\nHbIJnQ16dUMZiJE3QkG60/2tVnvfUTM6CF4sCNLNuA6Ra4VxhuO6IJa0SAc3R6J3nLO9xTQX\nYOn29oynCG1b/2hvDuu8otdu2/iyiUAWB+mWVhsovQvVZ6wIzNWlhxj5tjRIx6ZPKBFNEhtd\ngtNPR4x8WxikizkW1Ua6cBuFOk5PHe2RdwuDlJiiO5/97u+c2mP1NPvSx8dmX47vmghKoNdu\napAKt7v8KF0rDDXxobMukIVBOjQtUj7hgmxmkmtup+63xHz8Ggu2/UJ9Px3NURgy50i3Kd9u\nnpi8m84/3wjItl/Ivfsodl32YWmvXTrpUK2eb/qVXDb+Ml0/A0d2oYhcRzLpdcJ8tEihdMd0\n9DMEE3Bkw+Mc6VZfbeIcya/2mI4chRNyiNDRHeT68QvK2PxLtMOBiFFAUkHKpzwh8i+zp1RJ\neuY6kjduPwPrMZglQfp7NDFHe96Tp9zYp8PgHjFWYzgLgvRXb6y8vFftjOjXm7MHzNQPCyJH\nYS0I0rEKT2aO1Z2y6aTvZGaIkGeDmyZYiSEtCFI7rjgxaf7h7R2GCPlm2q9XJkbBCQRp6l3m\nDBHyq2+HiFF4AkGaOh8XZL3qxjIwLCiGgEFiiJBXg9uPYldmf2iRNqIfXseBXQyLgvTbNQuG\nCPlDt3dsAYPEECF/TPs9E8QokpBj7Rgi5Ek3KojmKJqgQdJUxHb0xwTkKB49QWKQ2EzdKmPF\nRRQ+SJeDMenNaxF70vfWEaSYAgap3spNj8PnMa7sD5PVX1FOSx5b6CBlJivK8p59flgKO8RU\ndYz6m/kQSeggVU+UfCg+P76LXWKq9nsmyFFkoYPUbm6GCEnoBgQRo9hCB+nUBokhQosNRgWx\nyuIKGqT0fLmZ6sldRcYQoaWcHm9iFF/QIHV/Oo1JGCK0ULsmiZEKIa8j5fnlkqa2yyH7fGs6\ne8Y3zWEdrZEWekY2BC5i5ZpjOoKkBUFaJdNeiOUmPiVCBqnIqq6688GY45dnhbNzfGHKvs8u\ndl1QCRike/LY6EVS9zjwFKFFmmM6cqRGwCCdqqffnczp/sjUie7v+eq7+BjtrUrQ7u+i+V81\nRIgLsjM5D9wiR3qEH2vn/CJexB6Y5v80R6oEPbTLy/JcP0qo+HySxC7yThcfVpEuAYOUmyTL\nyzR5JOl2MB9v7WMvGdc+4qRkFWkTsvv7lvT3kp/9FLFx3WVYVpE2YS/IXk/2Qfrp+e6tiC3r\nRtexhtRhZMN69MNU6a9ThyCtRTdMlf46jQjSWpjmP9aOSgRpJdoRqhzW6USQVqE5PWJYkFoE\naQXaG/i4kU8vgrQC3cOCiJFaBEk956HEnB+pRZC0658TRHOkGEHSru3yNqwVzQiScu3gOpoj\n3QiSbjyUeCUIkmY8vW41CJJe7tfwESTlCJJezR18PCxoDQiSWm16iNEaECSl3G8cYHXoR5CU\nar+Kj9OjdSBIOjVNEd/ashYESaVuSBAnSCtBkBRyLx/tfFWsBkHSx30ocey6YCKCpE93+Yh+\nhvUgSOp0DyUmRitCkNTpgxS3HvgFQdLFtF9+tOeVsEYESZO2m4HrsKtDkDRpB9fR7706BEmR\n9mMTo/UhSIqYp59YD4KkhdMM7fHjrx1B0sHtX9jfp98AgqRD181Ad906ESQV6GZYO4KkAmdH\na0eQVCBIa0eQdKCbYeUIkg50M6wcQdKCboZVI0iRkZ9tIEhRcUS3FQQpKvoYtoIgxUSv92YQ\npJgI0mYQpJgI0mYQpKg4R9oKghQVvXZbQZAi4zrSNhAkQABBAgQQJEAAQQIEECRAAEECBBAk\nQABBAgQQJEAAQQIEECRAAEECBBAkQABBCoRR3ttGkILgvqOtI0hBcCfs1hGkEHg2w+YRpBAI\n0uYRpBAI0uYRpCA4R9o6ghQEvXZbR5AC4TrSthEkQABBAgQQJEAAQQIEECRAAEECBBAkQABB\nAgQQJEAAQQIEECRAAEECBBAkQABBAgQQJEAAQQIEECRAAEECBBAkQABBAgQQJEAAQQIEECRA\nAEECBAQN0t85NZU0+/NVBBBFwCAVB9M7eikCiCRgkDKTXHM7db8lJvNRBBBJwCAlJu+mc5P4\nKAKIJGCQBk+R//xIeYKElaFFAgSEPUe63e0U50jYmpDd30en1+5QeCkCiCPsdaTMXkdK0jPX\nkbAtjGwABBAkQABDhAABDBECBDBEaAa+oRzPuCD7M5siooQBhgj9zDj/B2q0SL8yTz+BkiFC\nv+pPj/TWEREwROgXVYraKGmtI6JgiNAvbL3qIGmtIuJgZMMPmqaobpci1wW66AmScfkpYqnu\n9EhrBRENQ4R+QD8D3mGI0C/oZsAbDBH6BYMa8AYXZH/D6RFGMURoCuKDL2iRvuOADl8xROg7\nuhjwFUOEvqLTG98xROgrgoTv9IxsCFzEdAQJ3xGk7zhHwlchg1RkVVfd+WDM8eqpCC/otcNX\nAYN0Tx47Y5GscYgQ15HwRcAgnUxaPP53uj8ydVpD9zfxwWRBRzYUzf8eR3n6L8hyQIcfhB4i\nlBjnF/EiJNHFgB8EPbTLy/JcjxMqPp8kKdh96fTGLwIGKTdJlpdp8kjS7WBuPooQw8OC8JuQ\n3d+3pB8idPZThAweFoRfhb0gez3Zu2TT891bERJ4WBB+xciGkdKbDjseFoTJCNJL2VWC+igB\nUxCk56IfKWrbpHi1wNoQpJGiTfMfMBVBeiq5Gc+g9ymVUIkgPZXcdHoTI/yEIA3KNe0RHTnC\nTwiSU2p/IZYGCb8hSF2ZTYw4P8IMBKkrsx3JQIzwO4LUFWkGP4FfEKSuSIKE+QhSX6QzVhX4\nDUHqyzScIGEuglQ6A72JEWYiSP1TTogRZiNIDGWAAILEwxkggCARJAggSAQJAggS50gQsOcg\nNb10DPfGcvsNkpMf+r2x1I6DFKwk7MBug0QfAyQRJP9FYQcIkv+isAO7DRLnSJC04yDR6w05\n+w0Svd4QtOcgAWIIEiBgb0HicA5e7CtIdDDAk70FyXhcOnZsT0HqH87gZfHYs90FqSRI8GBH\nQWr7GXiWKuTtJkj9l5TT2QB5+wlSSZDgz16C1PbWcR0JXuwqSIYgwZM9BYkYwZu9BInbj+DV\nfoJEPwM82k2QOK6DTzsKEuAPQQIEECRAAEECBGw6SHQvIJQNB4kOb4Sz5SDJLQr4YrtB4pnE\nCIggAQIIEiBgu0HiHAkBbTlI9NohmA0HietICGfTQQJCIUiAAIIECCBIgACCBAggSIAAggQI\nIEiAAIIECCBIgACCBAjYRpAYVIfIthAkhnkjuk0EacY8gKgNBIlbYREfQQIEECRAwAaCxDkS\n4ttEkOi1Q2xbCBLXkRDdNoIEREaQAAEECRBAkAABBAkQQJAAAQQJEECQAAEECRBAkAABBAkQ\nsLYgMaoOKq0rSDZGRAn6rClIbYwIEtRZV5CafyNJ0GZFQWqbIpok6BM0SH/n1FTS7G9GEQQJ\negUMUnEwvePvRbTHdHQ2QJ+AQcpMcs3t1P2WmOz3IkxZ9zYQJKgTMEiJybvp3CS/F0GMoFbA\nIA0i8DkPH68jAfqsqUUC1Ap7jnS726mZ50iAWiG7v49Or92h8FIEEEfY60iZvY6UpOc515EA\nvVY0sgHQiyABAlY0RAjQa0VDhAC91jRECFCLC7KAgHUNEQKUokUCBDBECBDAECFAAEOEAAGM\nbAAE6AmScfkpAvAlfJAuB2PSm9cigNCCX0dqehw+dtoNWydgBWYEYlaMmiBlJivK8p6Zi59C\nvNNaMa31omLiFbBBSozt9y7MwU8h3mmtmNZ6UTHxCtggtU3gt6Yw+qd8R2vFtNaLiolXwGbn\n1Abp4xAhBZ/yHa0V01ovKiZeAWPS8+Vmro/JIvvS2xD/U76jtWJa60XFxCvgdG8Yk3wcIqTg\nU76jtWJa60XF5CuQ55dLmtouh+xLjuJ/yne0VkxrvahY3ApE/5TvaK2Y1npRsbgViP4p39Fa\nMa31omK+KjBliJCCT/mO1opprRcVE6/AD0OEFHzKd7RWTGu9qJh4BRgi5JPWelEx8Qr8NEQI\n2LogQ4SArQsyRAjYuiBDhICtCzJECNi6IEOEgK2jmwAQQJAAAQQJEECQAAEECRBAkAABBAkQ\nQJAAAQQJEECQAAHiQXKeQu4+kDxLTDuUyJkMKj8Zc7p/qE2kivX1UrXCBg+U17TCzGCcp5Y1\nJh2kvP9ozmRzT/rhaTKomy3Xjq8dr02kivX10rXC2t01eVub+BVTtMbkg5SOTP6ZJC/zxPwN\nJsNKHuUWaXXHx3htYlWsr5eyFWbd3q8lBRVTtMakg3Qx55HJzFRPGrpWLziTQV3tTVNF9Z10\nrHAAAASqSURBVHdsvDaRKubUS9cKs4okfVsbBRVTtMbkg3QZmUxNdQ5g/344k0GdTP65NpEq\n5tRL1wpr6lG8rY2CiilaY9JBSs3t9DjRe5psTgerH85kUAdTnhNzKt7WJlLFnHrpWmGV3Hyo\njYKKKVpj8kGyjsPJ2J/SFpi2p86q9gunXrpWWFm2f/d1rTC3YorWmHRhpnqMQ2GfdDeYbP4x\nZpCqk/pTdeCsar8Y1EvTCiurv/snt2wdK2xYMTVrzE9hzpPu7GTsT2kLrM5F7u9rEy1IXb1q\nWlZY2Z61K1thbsVqKtaYp8KcD1FNJmZsMigzWoX4FXvd6jrqVWmK1rXC3Io1NFQsTJDqfpR7\n36VyD97Xk/Zrd7w2kSqWjgYpfr1Kp99L1QorXzvkNKwx6SDVTzG2H8KZPNum+FZ1tTiTQdXl\n3qsT0/HaRKqYUy9dK8zpXFa1wtyKKVpj0kGyD4ss7DGsMxn7snNpz0KK6qT+quxCvVMvXSus\n+sveXOJStcLciilaY9JBKhLbIZkNJ8tD103pTgZ1Hq1C/Ir19VK2wh4FF92UohXmVEzRGhM/\nRyqyxBwuY5P1hTN3MqzbcaQKCio2rJeiFdaft+laYU8V07HGYlxNAzaHIAECCBIggCABAggS\nIIAgAQIIEiCAIAECCBIggCABAggSIIAgAQIIEiCAIAECCBIggCABAggSIIAgAQIIEiCAIAEC\nCBIggCABAggSIIAgAQIIEiCAIAECCBIggCABAggSIIAgAQIIEiCAIAECCNJ6se0UYWPo9Pzd\n9rfnN9xP1bfSFc8vj3mZF/IIkk5PQTo8b6fcfk2qSSYs6mVeeMBK1ukpSM8NVHk0WWGKo5nw\nTakv88IDVrJO34JUvWDKYkqTRJBCYCWrkyWPdsbu/bfU1N/ObQ/j3BfKxBTdtrsdjTne7NvK\nrPs678uh/r7vdl54xSrW5ljt+Gm175/r86CsC0P/wiMwh1uz7S71q5fqbfYdx24x1SRBCoJV\nrMzVJHmZJ/bQzVyr36tNVEfBeaE8PeJx+qumEpNXrx6qf6/nvfaLuXJoFwYrWZnUVOm49Xu/\nEyTnhbLMs6rlsr/fun+52XnTajH15JEghcFKVqbZ7esf99v5OAhS94J9z+1QHdA9ApXm+dO8\nr5PwipWsjBuk+jzHCVL/gn1PWVQHdOU5qa4o3QlSTKxkZZwEnMzhcrs7QXJesO/p3n3LDvU5\nUjcvQQqMlaxMfXLz1yXADZLzQt397VxHqmeoz69O/TlSSpDCYCUrc3N77f7KvD1HupeDF04m\nbUc2HOpeOqfX7vbUa3eP/Jn2gCBpk1ZnQacqLVl9RlQ1Mwc7rM55oUi6sXbX7kVj6otQ1WK6\n60jNvPCLIKlz7kY2POJ0/LOHZ38HG4b+hfKedaO/7ciG6qDuMVNaD2d4uCTNZDMvvCJI6/Wy\n7TgbiodVv14ESRFW/YYQpHhY9RtCkOJh1QMCCBIggCABAggSIIAgAQIIEiCAIAECCBIggCAB\nAggSIIAgAQIIEiCAIAECCBIggCABAggSIIAgAQIIEiCAIAECCBIggCABAggSIIAgAQIIEiCA\nIAECCBIggCABAv4Bxi6FbGh7jiIAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Scatter Plot: Spot Vs Future Returns\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$spot,data$spot, main=\"Scatter Plot: Spot Vs Future Returns\", ylab=\"Returns\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "19b43da0",
   "metadata": {},
   "outputs": [],
   "source": [
    "data2<-data[,-2:-3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "9227b8c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>dates</th><th scope=col>rspot</th><th scope=col>rfuture</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>2</th><td>13-Oct-2020</td><td>-0.2541183 </td><td>-0.2541183 </td></tr>\n",
       "\t<tr><th scope=row>3</th><td>14-Oct-2020</td><td>-0.5291093 </td><td>-0.5291093 </td></tr>\n",
       "\t<tr><th scope=row>4</th><td>15-Oct-2020</td><td>-0.5821212 </td><td>-0.5821212 </td></tr>\n",
       "\t<tr><th scope=row>5</th><td>16-Oct-2020</td><td>-1.7427984 </td><td>-1.7427984 </td></tr>\n",
       "\t<tr><th scope=row>6</th><td>19-Oct-2020</td><td> 1.4816346 </td><td> 1.4816346 </td></tr>\n",
       "\t<tr><th scope=row>7</th><td>20-Oct-2020</td><td>-0.5918235 </td><td>-0.5918235 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & dates & rspot & rfuture\\\\\n",
       "\\hline\n",
       "\t2 & 13-Oct-2020 & -0.2541183  & -0.2541183 \\\\\n",
       "\t3 & 14-Oct-2020 & -0.5291093  & -0.5291093 \\\\\n",
       "\t4 & 15-Oct-2020 & -0.5821212  & -0.5821212 \\\\\n",
       "\t5 & 16-Oct-2020 & -1.7427984  & -1.7427984 \\\\\n",
       "\t6 & 19-Oct-2020 &  1.4816346  &  1.4816346 \\\\\n",
       "\t7 & 20-Oct-2020 & -0.5918235  & -0.5918235 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | dates | rspot | rfuture |\n",
       "|---|---|---|---|\n",
       "| 2 | 13-Oct-2020 | -0.2541183  | -0.2541183  |\n",
       "| 3 | 14-Oct-2020 | -0.5291093  | -0.5291093  |\n",
       "| 4 | 15-Oct-2020 | -0.5821212  | -0.5821212  |\n",
       "| 5 | 16-Oct-2020 | -1.7427984  | -1.7427984  |\n",
       "| 6 | 19-Oct-2020 |  1.4816346  |  1.4816346  |\n",
       "| 7 | 20-Oct-2020 | -0.5918235  | -0.5918235  |\n",
       "\n"
      ],
      "text/plain": [
       "  dates       rspot      rfuture   \n",
       "2 13-Oct-2020 -0.2541183 -0.2541183\n",
       "3 14-Oct-2020 -0.5291093 -0.5291093\n",
       "4 15-Oct-2020 -0.5821212 -0.5821212\n",
       "5 16-Oct-2020 -1.7427984 -1.7427984\n",
       "6 19-Oct-2020  1.4816346  1.4816346\n",
       "7 20-Oct-2020 -0.5918235 -0.5918235"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(data2[-1,])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "a0bad326",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Br7EqlEpLgIRIqoWxz7mtnFI0Kk5SXK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\nCUABRAJQAJEAFEAkAAUQCUABRAJQ4D/2hLwAN7tg1QAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Monthly Returns on SBUX\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data2$rspot, type = \"l\", col = \"blue\", lwd = 2, ylab = \"Return\",\n",
    "               main = \"Monthly Returns on SBUX\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "2b7b5e98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Br7EqlCpLgIRIqoWxz7mtnFI0Kk5SXK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\nCUABRAJQAJEAFEAkAAUQCUABRAJQ4D+N49IqONsuRwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Monthly Returns on SBUX\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data2$rfuture, type = \"l\", col = \"red\", lwd = 2, ylab = \"Return\",\n",
    "               main = \"Monthly Returns on SBUX\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "748f16c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "log_lm = lm(rspot ~ rfuture, data = data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "6694756e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CAd5dJ3+vvf/r+e0m3XrL49N+eRFut/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\nkCDA/4sbah202drvAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$rspot,data$rfuture)\n",
    "abline(lm(rspot ~ rfuture, data = data), col=\"red\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1212defc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}