Risk Adjusted Return.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Risk Adjusted Return Computation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the Sample price file for the blue and orange asset prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "prices=pd.read_csv(\"sample_prices.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>BLUE</th>\n",
       "      <th>ORANGE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.7000</td>\n",
       "      <td>10.6600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.9055</td>\n",
       "      <td>11.0828</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     BLUE   ORANGE\n",
       "0  8.7000  10.6600\n",
       "1  8.9055  11.0828"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computing returns on prices data frame using pct_change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "returns=prices.pct_change()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>BLUE</th>\n",
       "      <th>ORANGE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.023621</td>\n",
       "      <td>0.039662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.021807</td>\n",
       "      <td>-0.033638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.031763</td>\n",
       "      <td>0.082232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.034477</td>\n",
       "      <td>0.044544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.037786</td>\n",
       "      <td>-0.026381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.011452</td>\n",
       "      <td>-0.049187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.032676</td>\n",
       "      <td>0.117008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.012581</td>\n",
       "      <td>0.067353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.029581</td>\n",
       "      <td>0.078249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.006151</td>\n",
       "      <td>-0.168261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.012162</td>\n",
       "      <td>0.024041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.021149</td>\n",
       "      <td>-0.055623</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        BLUE    ORANGE\n",
       "0        NaN       NaN\n",
       "1   0.023621  0.039662\n",
       "2  -0.021807 -0.033638\n",
       "3  -0.031763  0.082232\n",
       "4   0.034477  0.044544\n",
       "5   0.037786 -0.026381\n",
       "6  -0.011452 -0.049187\n",
       "7   0.032676  0.117008\n",
       "8  -0.012581  0.067353\n",
       "9   0.029581  0.078249\n",
       "10  0.006151 -0.168261\n",
       "11  0.012162  0.024041\n",
       "12  0.021149 -0.055623"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "returns=returns.dropna()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This take care of the row 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>BLUE</th>\n",
       "      <th>ORANGE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.023621</td>\n",
       "      <td>0.039662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.021807</td>\n",
       "      <td>-0.033638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.031763</td>\n",
       "      <td>0.082232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.034477</td>\n",
       "      <td>0.044544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.037786</td>\n",
       "      <td>-0.026381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.011452</td>\n",
       "      <td>-0.049187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.032676</td>\n",
       "      <td>0.117008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.012581</td>\n",
       "      <td>0.067353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.029581</td>\n",
       "      <td>0.078249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.006151</td>\n",
       "      <td>-0.168261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.012162</td>\n",
       "      <td>0.024041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.021149</td>\n",
       "      <td>-0.055623</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        BLUE    ORANGE\n",
       "1   0.023621  0.039662\n",
       "2  -0.021807 -0.033638\n",
       "3  -0.031763  0.082232\n",
       "4   0.034477  0.044544\n",
       "5   0.037786 -0.026381\n",
       "6  -0.011452 -0.049187\n",
       "7   0.032676  0.117008\n",
       "8  -0.012581  0.067353\n",
       "9   0.029581  0.078249\n",
       "10  0.006151 -0.168261\n",
       "11  0.012162  0.024041\n",
       "12  0.021149 -0.055623"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.023977\n",
       "ORANGE    0.079601\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "deviations from mean "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computing Standard deviation by ourselves and checking against the formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "deviation=returns-returns.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "sqrdeviation=deviation**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "variance=sqrdeviation.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.022957\n",
       "ORANGE    0.076212\n",
       "dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Stddev=variance**0.5\n",
    "Stddev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### The Difference in system computed measure and the one above is because we took the mean for n observations when we should have taken (n-1). Next we will compute using (n-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### We need to know what is the number of observations and will use the shape funtion for it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 2)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.023977\n",
       "ORANGE    0.079601\n",
       "dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numofobsv=returns.shape[0]\n",
    "variance=sqrdeviation.sum()/(numofobsv-1)\n",
    "StdDev=variance**0.5\n",
    "StdDev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### The above now matches with the System computed values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.023977\n",
       "ORANGE    0.079601\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Annualized volatility would be multiplying the above with the Square root of the period. This was monthly data so Multiply by Sqr(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.083060\n",
       "ORANGE    0.275747\n",
       "dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "StdDev*np.sqrt(12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real World Data Analysis. \n",
    "#### US stock Return data grouped on Market Capitalisation between 1926 to 2018"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will try to do the analysis on real set of data.\n",
    "A data set that provides us grouped returns on stocks based on market capitalisation\n",
    "If you see Hi 30 as a column that essentially means the returns on 30% of the sample which had the highest Market Capitalisation\n",
    "Similiarly lo 30 is the other end of the spectrum in market capitalisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "returns=pd.read_csv(\"Portfolios_Formed_on_ME_monthly_EW.csv\",header=0,index_col=0,parse_dates=True,na_values=-99.99)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The additional arguements after the read command on the file would lead to the first row to act as header,\n",
    "first column to act as index which is the date field and python would also try to parse the dates for timestamp\n",
    "Also there are values with -99.99 in the data which would be treated as na values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>&lt;= 0</th>\n",
       "      <th>Lo 30</th>\n",
       "      <th>Med 40</th>\n",
       "      <th>Hi 30</th>\n",
       "      <th>Lo 20</th>\n",
       "      <th>Qnt 2</th>\n",
       "      <th>Qnt 3</th>\n",
       "      <th>Qnt 4</th>\n",
       "      <th>Hi 20</th>\n",
       "      <th>Lo 10</th>\n",
       "      <th>Dec 2</th>\n",
       "      <th>Dec 3</th>\n",
       "      <th>Dec 4</th>\n",
       "      <th>Dec 5</th>\n",
       "      <th>Dec 6</th>\n",
       "      <th>Dec 7</th>\n",
       "      <th>Dec 8</th>\n",
       "      <th>Dec 9</th>\n",
       "      <th>Hi 10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>192607</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.43</td>\n",
       "      <td>1.52</td>\n",
       "      <td>2.68</td>\n",
       "      <td>-0.57</td>\n",
       "      <td>0.59</td>\n",
       "      <td>1.60</td>\n",
       "      <td>1.47</td>\n",
       "      <td>3.33</td>\n",
       "      <td>-1.45</td>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>1.33</td>\n",
       "      <td>1.24</td>\n",
       "      <td>1.98</td>\n",
       "      <td>1.55</td>\n",
       "      <td>1.38</td>\n",
       "      <td>3.38</td>\n",
       "      <td>3.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192608</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.90</td>\n",
       "      <td>3.04</td>\n",
       "      <td>2.09</td>\n",
       "      <td>3.84</td>\n",
       "      <td>3.59</td>\n",
       "      <td>3.71</td>\n",
       "      <td>1.61</td>\n",
       "      <td>2.33</td>\n",
       "      <td>5.12</td>\n",
       "      <td>2.59</td>\n",
       "      <td>4.03</td>\n",
       "      <td>3.15</td>\n",
       "      <td>2.72</td>\n",
       "      <td>4.72</td>\n",
       "      <td>1.60</td>\n",
       "      <td>1.63</td>\n",
       "      <td>0.98</td>\n",
       "      <td>3.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192609</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.08</td>\n",
       "      <td>-0.54</td>\n",
       "      <td>0.16</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>-1.40</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>0.93</td>\n",
       "      <td>-1.87</td>\n",
       "      <td>-2.27</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>0.07</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>-1.64</td>\n",
       "      <td>0.64</td>\n",
       "      <td>-0.86</td>\n",
       "      <td>0.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192610</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.32</td>\n",
       "      <td>-3.52</td>\n",
       "      <td>-3.06</td>\n",
       "      <td>-3.29</td>\n",
       "      <td>-4.10</td>\n",
       "      <td>-2.89</td>\n",
       "      <td>-3.36</td>\n",
       "      <td>-2.95</td>\n",
       "      <td>-4.84</td>\n",
       "      <td>-1.77</td>\n",
       "      <td>-3.36</td>\n",
       "      <td>-4.83</td>\n",
       "      <td>-2.98</td>\n",
       "      <td>-2.80</td>\n",
       "      <td>-3.45</td>\n",
       "      <td>-3.27</td>\n",
       "      <td>-3.47</td>\n",
       "      <td>-2.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192611</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.46</td>\n",
       "      <td>3.82</td>\n",
       "      <td>3.09</td>\n",
       "      <td>-0.55</td>\n",
       "      <td>2.18</td>\n",
       "      <td>3.41</td>\n",
       "      <td>3.39</td>\n",
       "      <td>3.16</td>\n",
       "      <td>-0.78</td>\n",
       "      <td>-0.32</td>\n",
       "      <td>-0.29</td>\n",
       "      <td>4.65</td>\n",
       "      <td>3.24</td>\n",
       "      <td>3.57</td>\n",
       "      <td>3.82</td>\n",
       "      <td>2.95</td>\n",
       "      <td>3.61</td>\n",
       "      <td>2.70</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        <= 0  Lo 30  Med 40  Hi 30  Lo 20  Qnt 2  Qnt 3  Qnt 4  Hi 20  Lo 10  \\\n",
       "192607   NaN  -0.43    1.52   2.68  -0.57   0.59   1.60   1.47   3.33  -1.45   \n",
       "192608   NaN   3.90    3.04   2.09   3.84   3.59   3.71   1.61   2.33   5.12   \n",
       "192609   NaN  -1.08   -0.54   0.16  -0.48  -1.40   0.00  -0.50  -0.09   0.93   \n",
       "192610   NaN  -3.32   -3.52  -3.06  -3.29  -4.10  -2.89  -3.36  -2.95  -4.84   \n",
       "192611   NaN  -0.46    3.82   3.09  -0.55   2.18   3.41   3.39   3.16  -0.78   \n",
       "\n",
       "        Dec 2  Dec 3  Dec 4  Dec 5  Dec 6  Dec 7  Dec 8  Dec 9  Hi 10  \n",
       "192607   0.29  -0.15   1.33   1.24   1.98   1.55   1.38   3.38   3.29  \n",
       "192608   2.59   4.03   3.15   2.72   4.72   1.60   1.63   0.98   3.70  \n",
       "192609  -1.87  -2.27  -0.53   0.07  -0.07  -1.64   0.64  -0.86   0.67  \n",
       "192610  -1.77  -3.36  -4.83  -2.98  -2.80  -3.45  -3.27  -3.47  -2.43  \n",
       "192611  -0.32  -0.29   4.65   3.24   3.57   3.82   2.95   3.61   2.70  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here we are interested on the Lo 10 and Hi 10 columns for doing our analysis. \n",
    "So we will trim our data set to only show this two columns. \n",
    "Do also notice that the arguement na_values=-99.99 has cleaned the data set to show NA values in the first column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>Lo 10</th>\n",
       "      <th>Hi 10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>192607</th>\n",
       "      <td>-1.45</td>\n",
       "      <td>3.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192608</th>\n",
       "      <td>5.12</td>\n",
       "      <td>3.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192609</th>\n",
       "      <td>0.93</td>\n",
       "      <td>0.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192610</th>\n",
       "      <td>-4.84</td>\n",
       "      <td>-2.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192611</th>\n",
       "      <td>-0.78</td>\n",
       "      <td>2.70</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Lo 10  Hi 10\n",
       "192607  -1.45   3.29\n",
       "192608   5.12   3.70\n",
       "192609   0.93   0.67\n",
       "192610  -4.84  -2.43\n",
       "192611  -0.78   2.70"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "columns= [\"Lo 10\",\"Hi 10\"]\n",
    "returns= returns[columns]\n",
    "returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>Smallcap</th>\n",
       "      <th>Largecap</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>192607</th>\n",
       "      <td>-0.0145</td>\n",
       "      <td>0.0329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192608</th>\n",
       "      <td>0.0512</td>\n",
       "      <td>0.0370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192609</th>\n",
       "      <td>0.0093</td>\n",
       "      <td>0.0067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192610</th>\n",
       "      <td>-0.0484</td>\n",
       "      <td>-0.0243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192611</th>\n",
       "      <td>-0.0078</td>\n",
       "      <td>0.0270</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Smallcap  Largecap\n",
       "192607   -0.0145    0.0329\n",
       "192608    0.0512    0.0370\n",
       "192609    0.0093    0.0067\n",
       "192610   -0.0484   -0.0243\n",
       "192611   -0.0078    0.0270"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns=returns/100\n",
    "returns.columns=[\"Smallcap\",\"Largecap\"]\n",
    "returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x27af663f688>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "returns.index=pd.to_datetime(returns.index,format=\"%Y%m\")\n",
    "returns.plot.line()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: old versions of Python might have to use the command - %matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Volatility in the returns exhibited by the Small cap stocks in the period of time is much higher than the large cap stocks.\n",
    "This is evident from the plot but let us try to see if the calculation on the same also adds up to what we said"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Smallcap    0.106288\n",
       "Largecap    0.053900\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly above the Standard deviation of largecaps are considerably less than that of smallcaps.\n",
    "Lets try to bring out the Annualized Volatility by converting the above from monthly data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Smallcap    0.368193\n",
       "Largecap    0.186716\n",
       "dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Annualized_vol= returns.std()*np.sqrt(12)\n",
    "Annualized_vol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Annualizing returns - To do that we will compute returns per month"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Smallcap    0.012986\n",
       "Largecap    0.007423\n",
       "dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_mon= returns.shape[0]\n",
    "Ret_per_mon=(1+returns).prod()**(1/num_mon)-1\n",
    "Ret_per_mon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Smallcap    0.167463\n",
       "Largecap    0.092810\n",
       "dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annualized_ret=((Ret_per_mon+1)**12)-1\n",
    "annualized_ret"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Return Risk Ratio & Sharpe Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Smallcap    0.454825\n",
       "Largecap    0.497063\n",
       "dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annualized_ret/Annualized_vol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets introduce a risk free rate of 3%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Smallcap    0.373346\n",
       "Largecap    0.336392\n",
       "dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "riskfree_rate=0.03\n",
    "excess_return= annualized_ret-riskfree_rate\n",
    "Sharpe_ratio = excess_return/Annualized_vol\n",
    "Sharpe_ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Smallcaps show a better Return vs Risk performance over the period compared to large caps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have imported a real Data dump which was the US Equity market data between 1926 till 2018 consisting of many portfolios segregated on market capitalisation. We have then succesfully calculated the Return, Variance and Volatility of two portfolio series in it and then have gone on to compute the Annualized return to Risk ratio and finally the Sharpe ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}