Week1 Download yield curve dataset.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "HW1\n",
    "1.Download ‘Daily Treasury Yield Curve Rates’ from the site: https://www.treasury.gov/resource-center/data-chart-center/Pages/index.aspx\n",
    "a.Explain (briefly) how these CMT rates are constructed (the website has the info)\n",
    "\n",
    "2.Build a Jupyter Notebook to do the following:\n",
    "a.Download the dataset into pandas dataframe\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1 Mo</th>\n",
       "      <th>3 Mo</th>\n",
       "      <th>6 Mo</th>\n",
       "      <th>1 Yr</th>\n",
       "      <th>2 Yr</th>\n",
       "      <th>3 Yr</th>\n",
       "      <th>5 Yr</th>\n",
       "      <th>7 Yr</th>\n",
       "      <th>10 Yr</th>\n",
       "      <th>20 Yr</th>\n",
       "      <th>30 Yr</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-02</th>\n",
       "      <td>NaN</td>\n",
       "      <td>7.83</td>\n",
       "      <td>7.89</td>\n",
       "      <td>7.81</td>\n",
       "      <td>7.87</td>\n",
       "      <td>7.90</td>\n",
       "      <td>7.87</td>\n",
       "      <td>7.98</td>\n",
       "      <td>7.94</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>NaN</td>\n",
       "      <td>7.89</td>\n",
       "      <td>7.94</td>\n",
       "      <td>7.85</td>\n",
       "      <td>7.94</td>\n",
       "      <td>7.96</td>\n",
       "      <td>7.92</td>\n",
       "      <td>8.04</td>\n",
       "      <td>7.99</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>NaN</td>\n",
       "      <td>7.84</td>\n",
       "      <td>7.90</td>\n",
       "      <td>7.82</td>\n",
       "      <td>7.92</td>\n",
       "      <td>7.93</td>\n",
       "      <td>7.91</td>\n",
       "      <td>8.02</td>\n",
       "      <td>7.98</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>NaN</td>\n",
       "      <td>7.79</td>\n",
       "      <td>7.85</td>\n",
       "      <td>7.79</td>\n",
       "      <td>7.90</td>\n",
       "      <td>7.94</td>\n",
       "      <td>7.92</td>\n",
       "      <td>8.03</td>\n",
       "      <td>7.99</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-08</th>\n",
       "      <td>NaN</td>\n",
       "      <td>7.79</td>\n",
       "      <td>7.88</td>\n",
       "      <td>7.81</td>\n",
       "      <td>7.90</td>\n",
       "      <td>7.95</td>\n",
       "      <td>7.92</td>\n",
       "      <td>8.05</td>\n",
       "      <td>8.02</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            1 Mo  3 Mo  6 Mo  1 Yr  2 Yr  3 Yr  5 Yr  7 Yr  10 Yr  20 Yr  \\\n",
       "Date                                                                       \n",
       "1990-01-02   NaN  7.83  7.89  7.81  7.87  7.90  7.87  7.98   7.94    NaN   \n",
       "1990-01-03   NaN  7.89  7.94  7.85  7.94  7.96  7.92  8.04   7.99    NaN   \n",
       "1990-01-04   NaN  7.84  7.90  7.82  7.92  7.93  7.91  8.02   7.98    NaN   \n",
       "1990-01-05   NaN  7.79  7.85  7.79  7.90  7.94  7.92  8.03   7.99    NaN   \n",
       "1990-01-08   NaN  7.79  7.88  7.81  7.90  7.95  7.92  8.05   8.02    NaN   \n",
       "\n",
       "            30 Yr  \n",
       "Date               \n",
       "1990-01-02   8.00  \n",
       "1990-01-03   8.04  \n",
       "1990-01-04   8.04  \n",
       "1990-01-05   8.06  \n",
       "1990-01-08   8.09  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "df = pd.read_excel('D:\\\\fall 2017\\\\Fixed Income Trading Edit\\\\Python\\\\HW1.xlsx')\n",
    "df.set_index('Date', inplace=True)\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b.Remove ‘1M’ column and use the date from 1/1/1996 – 11/20/2016 (we will leave the last year out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>3 Mo</th>\n",
       "      <th>6 Mo</th>\n",
       "      <th>1 Yr</th>\n",
       "      <th>2 Yr</th>\n",
       "      <th>3 Yr</th>\n",
       "      <th>5 Yr</th>\n",
       "      <th>7 Yr</th>\n",
       "      <th>10 Yr</th>\n",
       "      <th>20 Yr</th>\n",
       "      <th>30 Yr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1996-01-02</th>\n",
       "      <td>5.20</td>\n",
       "      <td>5.25</td>\n",
       "      <td>5.17</td>\n",
       "      <td>5.18</td>\n",
       "      <td>5.26</td>\n",
       "      <td>5.39</td>\n",
       "      <td>5.51</td>\n",
       "      <td>5.60</td>\n",
       "      <td>6.03</td>\n",
       "      <td>5.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-01-03</th>\n",
       "      <td>5.20</td>\n",
       "      <td>5.22</td>\n",
       "      <td>5.16</td>\n",
       "      <td>5.17</td>\n",
       "      <td>5.21</td>\n",
       "      <td>5.36</td>\n",
       "      <td>5.49</td>\n",
       "      <td>5.58</td>\n",
       "      <td>6.01</td>\n",
       "      <td>5.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-01-04</th>\n",
       "      <td>5.19</td>\n",
       "      <td>5.23</td>\n",
       "      <td>5.19</td>\n",
       "      <td>5.17</td>\n",
       "      <td>5.26</td>\n",
       "      <td>5.39</td>\n",
       "      <td>5.55</td>\n",
       "      <td>5.65</td>\n",
       "      <td>6.08</td>\n",
       "      <td>6.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-01-05</th>\n",
       "      <td>5.19</td>\n",
       "      <td>5.22</td>\n",
       "      <td>5.19</td>\n",
       "      <td>5.20</td>\n",
       "      <td>5.29</td>\n",
       "      <td>5.42</td>\n",
       "      <td>5.59</td>\n",
       "      <td>5.69</td>\n",
       "      <td>6.11</td>\n",
       "      <td>6.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-01-08</th>\n",
       "      <td>5.18</td>\n",
       "      <td>5.22</td>\n",
       "      <td>5.19</td>\n",
       "      <td>5.20</td>\n",
       "      <td>5.27</td>\n",
       "      <td>5.41</td>\n",
       "      <td>5.56</td>\n",
       "      <td>5.68</td>\n",
       "      <td>6.10</td>\n",
       "      <td>6.04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            3 Mo  6 Mo  1 Yr  2 Yr  3 Yr  5 Yr  7 Yr  10 Yr  20 Yr  30 Yr\n",
       "Date                                                                     \n",
       "1996-01-02  5.20  5.25  5.17  5.18  5.26  5.39  5.51   5.60   6.03   5.97\n",
       "1996-01-03  5.20  5.22  5.16  5.17  5.21  5.36  5.49   5.58   6.01   5.96\n",
       "1996-01-04  5.19  5.23  5.19  5.17  5.26  5.39  5.55   5.65   6.08   6.03\n",
       "1996-01-05  5.19  5.22  5.19  5.20  5.29  5.42  5.59   5.69   6.11   6.05\n",
       "1996-01-08  5.18  5.22  5.19  5.20  5.27  5.41  5.56   5.68   6.10   6.04"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df['1996-01-01':'2016-11-20']\n",
    "del df['1 Mo']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>3 Mo</th>\n",
       "      <th>6 Mo</th>\n",
       "      <th>1 Yr</th>\n",
       "      <th>2 Yr</th>\n",
       "      <th>3 Yr</th>\n",
       "      <th>5 Yr</th>\n",
       "      <th>7 Yr</th>\n",
       "      <th>10 Yr</th>\n",
       "      <th>20 Yr</th>\n",
       "      <th>30 Yr</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",
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       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-11-14</th>\n",
       "      <td>0.55</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.77</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.27</td>\n",
       "      <td>1.66</td>\n",
       "      <td>2.01</td>\n",
       "      <td>2.23</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-11-15</th>\n",
       "      <td>0.51</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.78</td>\n",
       "      <td>1.02</td>\n",
       "      <td>1.28</td>\n",
       "      <td>1.68</td>\n",
       "      <td>2.03</td>\n",
       "      <td>2.23</td>\n",
       "      <td>2.64</td>\n",
       "      <td>2.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-11-16</th>\n",
       "      <td>0.47</td>\n",
       "      <td>0.62</td>\n",
       "      <td>0.76</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.28</td>\n",
       "      <td>1.68</td>\n",
       "      <td>2.03</td>\n",
       "      <td>2.22</td>\n",
       "      <td>2.61</td>\n",
       "      <td>2.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-11-17</th>\n",
       "      <td>0.44</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.77</td>\n",
       "      <td>1.04</td>\n",
       "      <td>1.31</td>\n",
       "      <td>1.73</td>\n",
       "      <td>2.08</td>\n",
       "      <td>2.29</td>\n",
       "      <td>2.69</td>\n",
       "      <td>3.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-11-18</th>\n",
       "      <td>0.44</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.77</td>\n",
       "      <td>1.07</td>\n",
       "      <td>1.36</td>\n",
       "      <td>1.80</td>\n",
       "      <td>2.14</td>\n",
       "      <td>2.34</td>\n",
       "      <td>2.70</td>\n",
       "      <td>3.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "            3 Mo  6 Mo  1 Yr  2 Yr  3 Yr  5 Yr  7 Yr  10 Yr  20 Yr  30 Yr\n",
       "Date                                                                     \n",
       "2016-11-14  0.55  0.65  0.77  1.00  1.27  1.66  2.01   2.23   2.65   2.99\n",
       "2016-11-15  0.51  0.61  0.78  1.02  1.28  1.68  2.03   2.23   2.64   2.97\n",
       "2016-11-16  0.47  0.62  0.76  1.00  1.28  1.68  2.03   2.22   2.61   2.92\n",
       "2016-11-17  0.44  0.61  0.77  1.04  1.31  1.73  2.08   2.29   2.69   3.01\n",
       "2016-11-18  0.44  0.60  0.77  1.07  1.36  1.80  2.14   2.34   2.70   3.01"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c.Construct series of daily differences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            3 Mo  6 Mo  1 Yr  2 Yr  3 Yr  5 Yr  7 Yr  10 Yr  20 Yr  30 Yr  \\\n",
      "Date                                                                        \n",
      "1996-01-02  5.20  5.25  5.17  5.18  5.26  5.39  5.51   5.60   6.03   5.97   \n",
      "1996-01-03  5.20  5.22  5.16  5.17  5.21  5.36  5.49   5.58   6.01   5.96   \n",
      "1996-01-04  5.19  5.23  5.19  5.17  5.26  5.39  5.55   5.65   6.08   6.03   \n",
      "1996-01-05  5.19  5.22  5.19  5.20  5.29  5.42  5.59   5.69   6.11   6.05   \n",
      "1996-01-08  5.18  5.22  5.19  5.20  5.27  5.41  5.56   5.68   6.10   6.04   \n",
      "\n",
      "            3 Mo_dR  6 Mo_dR  1 Yr_dR  2 Yr_dR  3 Yr_dR  5 Yr_dR  7 Yr_dR  \\\n",
      "Date                                                                        \n",
      "1996-01-02      NaN      NaN      NaN      NaN      NaN      NaN      NaN   \n",
      "1996-01-03     0.00    -0.03    -0.01    -0.01    -0.05    -0.03    -0.02   \n",
      "1996-01-04    -0.01     0.01     0.03     0.00     0.05     0.03     0.06   \n",
      "1996-01-05     0.00    -0.01     0.00     0.03     0.03     0.03     0.04   \n",
      "1996-01-08    -0.01     0.00     0.00     0.00    -0.02    -0.01    -0.03   \n",
      "\n",
      "            10 Yr_dR  20 Yr_dR  30 Yr_dR  \n",
      "Date                                      \n",
      "1996-01-02       NaN       NaN       NaN  \n",
      "1996-01-03     -0.02     -0.02     -0.01  \n",
      "1996-01-04      0.07      0.07      0.07  \n",
      "1996-01-05      0.04      0.03      0.02  \n",
      "1996-01-08     -0.01     -0.01     -0.01  \n"
     ]
    }
   ],
   "source": [
    "# calculate daily returns for different rate levels\n",
    "cols = list(df.columns)\n",
    "for col in cols:\n",
    "    df[col+'_dR'] = df[col].diff() #add cols\n",
    "print(df.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#df.diff(axis=0)\n",
    "#Take difference over rows (0) or columns (1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d.Compute correlations and volatilities among the series (using level data)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlations of level data:\n",
      "            3 Mo      6 Mo      1 Yr      2 Yr      3 Yr      5 Yr      7 Yr  \\\n",
      "3 Mo   1.000000  0.998661  0.995022  0.982424  0.969463  0.939976  0.913463   \n",
      "6 Mo   0.998661  1.000000  0.997935  0.986755  0.974125  0.944606  0.917551   \n",
      "1 Yr   0.995022  0.997935  1.000000  0.994271  0.984721  0.959111  0.934114   \n",
      "2 Yr   0.982424  0.986755  0.994271  1.000000  0.997182  0.980729  0.961411   \n",
      "3 Yr   0.969463  0.974125  0.984721  0.997182  1.000000  0.991992  0.977669   \n",
      "5 Yr   0.939976  0.944606  0.959111  0.980729  0.991992  1.000000  0.995774   \n",
      "7 Yr   0.913463  0.917551  0.934114  0.961411  0.977669  0.995774  1.000000   \n",
      "10 Yr  0.881846  0.885966  0.904464  0.934932  0.955020  0.982770  0.994175   \n",
      "20 Yr  0.818543  0.821451  0.842255  0.878593  0.904401  0.945193  0.968500   \n",
      "30 Yr  0.859671  0.861925  0.876887  0.902888  0.919767  0.949261  0.968016   \n",
      "\n",
      "          10 Yr     20 Yr     30 Yr  \n",
      "3 Mo   0.881846  0.818543  0.859671  \n",
      "6 Mo   0.885966  0.821451  0.861925  \n",
      "1 Yr   0.904464  0.842255  0.876887  \n",
      "2 Yr   0.934932  0.878593  0.902888  \n",
      "3 Yr   0.955020  0.904401  0.919767  \n",
      "5 Yr   0.982770  0.945193  0.949261  \n",
      "7 Yr   0.994175  0.968500  0.968016  \n",
      "10 Yr  1.000000  0.987124  0.985607  \n",
      "20 Yr  0.987124  1.000000  0.995188  \n",
      "30 Yr  0.985607  0.995188  1.000000   \n",
      "\n",
      "correlations of daily difference data:\n",
      "            3 Mo_dR   6 Mo_dR   1 Yr_dR   2 Yr_dR   3 Yr_dR   5 Yr_dR  \\\n",
      "3 Mo_dR   1.000000  0.755014  0.582606  0.368780  0.333814  0.281852   \n",
      "6 Mo_dR   0.755014  1.000000  0.815619  0.591769  0.549108  0.481813   \n",
      "1 Yr_dR   0.582606  0.815619  1.000000  0.823267  0.778006  0.704141   \n",
      "2 Yr_dR   0.368780  0.591769  0.823267  1.000000  0.953321  0.893134   \n",
      "3 Yr_dR   0.333814  0.549108  0.778006  0.953321  1.000000  0.946606   \n",
      "5 Yr_dR   0.281852  0.481813  0.704141  0.893134  0.946606  1.000000   \n",
      "7 Yr_dR   0.241211  0.427409  0.642890  0.833235  0.898593  0.968334   \n",
      "10 Yr_dR  0.215992  0.394929  0.601083  0.783938  0.854731  0.938828   \n",
      "20 Yr_dR  0.167423  0.325457  0.514503  0.682268  0.758118  0.860455   \n",
      "30 Yr_dR  0.153730  0.290892  0.456692  0.620182  0.702064  0.814514   \n",
      "\n",
      "           7 Yr_dR  10 Yr_dR  20 Yr_dR  30 Yr_dR  \n",
      "3 Mo_dR   0.241211  0.215992  0.167423  0.153730  \n",
      "6 Mo_dR   0.427409  0.394929  0.325457  0.290892  \n",
      "1 Yr_dR   0.642890  0.601083  0.514503  0.456692  \n",
      "2 Yr_dR   0.833235  0.783938  0.682268  0.620182  \n",
      "3 Yr_dR   0.898593  0.854731  0.758118  0.702064  \n",
      "5 Yr_dR   0.968334  0.938828  0.860455  0.814514  \n",
      "7 Yr_dR   1.000000  0.972818  0.918814  0.881975  \n",
      "10 Yr_dR  0.972818  1.000000  0.952314  0.926211  \n",
      "20 Yr_dR  0.918814  0.952314  1.000000  0.977506  \n",
      "30 Yr_dR  0.881975  0.926211  0.977506  1.000000  \n"
     ]
    }
   ],
   "source": [
    "ColNum1 = len(df.columns)\n",
    "ColNum2 = int(ColNum1/2)\n",
    "mycorr=df.corr()\n",
    "corr1 = mycorr.iloc[:ColNum2,:ColNum2]\n",
    "corr2 = mycorr.iloc[ColNum2:ColNum1,ColNum2:ColNum1]\n",
    "print('correlations of level data:\\n', corr1, '\\n\\ncorrelations of daily difference data:\\n', corr2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "e.Compute correlations and volatilities among the series (using daily differences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "volatilities of level data:\n",
      " 3 Mo     2.206642\n",
      "6 Mo     2.234710\n",
      "1 Yr     2.207733\n",
      "2 Yr     2.156923\n",
      "3 Yr     2.047274\n",
      "5 Yr     1.822660\n",
      "7 Yr     1.670006\n",
      "10 Yr    1.479687\n",
      "20 Yr    1.389998\n",
      "30 Yr    1.319702\n",
      "dtype: float64 \n",
      "\n",
      "volatilities of daily difference data:\n",
      " 3 Mo_dR     0.051101\n",
      "6 Mo_dR     0.041219\n",
      "1 Yr_dR     0.042234\n",
      "2 Yr_dR     0.054750\n",
      "3 Yr_dR     0.058659\n",
      "5 Yr_dR     0.062308\n",
      "7 Yr_dR     0.062737\n",
      "10 Yr_dR    0.059707\n",
      "20 Yr_dR    0.055883\n",
      "30 Yr_dR    0.054588\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "mystd=df.std()\n",
    "sd1 = mystd.iloc[:ColNum2]\n",
    "sd2 = mystd.iloc[ColNum2:ColNum1]\n",
    "print('volatilities of level data:\\n', sd1, '\\n\\nvolatilities of daily difference data:\\n', sd2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "f.Plot the volatility curves computed in 2d & 2e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XT5zHw++u1O6kInVAJSAha2SPNGbedx43D2rHK19s4TvjP+WTNdqdVCSYVAIS0hLjonnk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\nTCUgIhLG/j/xjB3h0s7cawAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3895fd2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sd1.plot()\n",
    "plt.title('volatilities for level data')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TFWmrlTHtnX0KmID4ZOt+yk5U24mTxhjAiosJkKzcQhJiozh7UFevoxhjgoAV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c38b4a3da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sd2.plot()\n",
    "plt.title('volatilities for daily difference')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}