downside-risk-measures.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "# Calculating downside risk measures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "_cell_guid": "79c7e3d0-c299-4dcb-8224-4455121ee9b0",
    "_uuid": "d629ff2d2480ee46fbb7e2d37f6b5fab8052498a"
   },
   "outputs": [],
   "source": [
    "# Import libraries \n",
    "import pandas as pd \n",
    "import numpy as np \n",
    "\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(263, 13)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the data\n",
    "hfi_data = pd.read_csv('../input/python/edhec-hedgefundindices.csv',\n",
    "                           header=0, index_col=0, parse_dates=True)\n",
    "hfi_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Convertible Arbitrage</th>\n",
       "      <th>CTA Global</th>\n",
       "      <th>Distressed Securities</th>\n",
       "      <th>Emerging Markets</th>\n",
       "      <th>Equity Market Neutral</th>\n",
       "      <th>Event Driven</th>\n",
       "      <th>Fixed Income Arbitrage</th>\n",
       "      <th>Global Macro</th>\n",
       "      <th>Long/Short Equity</th>\n",
       "      <th>Merger Arbitrage</th>\n",
       "      <th>Relative Value</th>\n",
       "      <th>Short Selling</th>\n",
       "      <th>Funds Of Funds</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>1997-01-31</th>\n",
       "      <td>1.19</td>\n",
       "      <td>3.93</td>\n",
       "      <td>1.78</td>\n",
       "      <td>7.91</td>\n",
       "      <td>1.89</td>\n",
       "      <td>2.13</td>\n",
       "      <td>1.91</td>\n",
       "      <td>5.73</td>\n",
       "      <td>2.81</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1.80</td>\n",
       "      <td>-1.66</td>\n",
       "      <td>3.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-02-28</th>\n",
       "      <td>1.23</td>\n",
       "      <td>2.98</td>\n",
       "      <td>1.22</td>\n",
       "      <td>5.25</td>\n",
       "      <td>1.01</td>\n",
       "      <td>0.84</td>\n",
       "      <td>1.22</td>\n",
       "      <td>1.75</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.34</td>\n",
       "      <td>1.18</td>\n",
       "      <td>4.26</td>\n",
       "      <td>1.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-03-31</th>\n",
       "      <td>0.78</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>-1.20</td>\n",
       "      <td>0.16</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>1.09</td>\n",
       "      <td>-1.19</td>\n",
       "      <td>-0.84</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.10</td>\n",
       "      <td>7.78</td>\n",
       "      <td>-0.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-04-30</th>\n",
       "      <td>0.86</td>\n",
       "      <td>-1.70</td>\n",
       "      <td>0.30</td>\n",
       "      <td>1.19</td>\n",
       "      <td>1.19</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.30</td>\n",
       "      <td>1.72</td>\n",
       "      <td>0.84</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>1.22</td>\n",
       "      <td>-1.29</td>\n",
       "      <td>0.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-05-31</th>\n",
       "      <td>1.56</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>2.33</td>\n",
       "      <td>3.15</td>\n",
       "      <td>1.89</td>\n",
       "      <td>3.46</td>\n",
       "      <td>1.18</td>\n",
       "      <td>1.08</td>\n",
       "      <td>3.94</td>\n",
       "      <td>1.97</td>\n",
       "      <td>1.73</td>\n",
       "      <td>-7.37</td>\n",
       "      <td>2.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Convertible Arbitrage  CTA Global  Distressed Securities  \\\n",
       "date                                                                   \n",
       "1997-01-31                   1.19        3.93                   1.78   \n",
       "1997-02-28                   1.23        2.98                   1.22   \n",
       "1997-03-31                   0.78       -0.21                  -0.12   \n",
       "1997-04-30                   0.86       -1.70                   0.30   \n",
       "1997-05-31                   1.56       -0.15                   2.33   \n",
       "\n",
       "            Emerging Markets  Equity Market Neutral  Event Driven  \\\n",
       "date                                                                \n",
       "1997-01-31              7.91                   1.89          2.13   \n",
       "1997-02-28              5.25                   1.01          0.84   \n",
       "1997-03-31             -1.20                   0.16         -0.23   \n",
       "1997-04-30              1.19                   1.19         -0.05   \n",
       "1997-05-31              3.15                   1.89          3.46   \n",
       "\n",
       "            Fixed Income Arbitrage  Global Macro  Long/Short Equity  \\\n",
       "date                                                                  \n",
       "1997-01-31                    1.91          5.73               2.81   \n",
       "1997-02-28                    1.22          1.75              -0.06   \n",
       "1997-03-31                    1.09         -1.19              -0.84   \n",
       "1997-04-30                    1.30          1.72               0.84   \n",
       "1997-05-31                    1.18          1.08               3.94   \n",
       "\n",
       "            Merger Arbitrage  Relative Value  Short Selling  Funds Of Funds  \n",
       "date                                                                         \n",
       "1997-01-31              1.50            1.80          -1.66            3.17  \n",
       "1997-02-28              0.34            1.18           4.26            1.06  \n",
       "1997-03-31              0.60            0.10           7.78           -0.77  \n",
       "1997-04-30             -0.01            1.22          -1.29            0.09  \n",
       "1997-05-31              1.97            1.73          -7.37            2.75  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hfi_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "## Preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Convertible Arbitrage</th>\n",
       "      <th>CTA Global</th>\n",
       "      <th>Distressed Securities</th>\n",
       "      <th>Emerging Markets</th>\n",
       "      <th>Equity Market Neutral</th>\n",
       "      <th>Event Driven</th>\n",
       "      <th>Fixed Income Arbitrage</th>\n",
       "      <th>Global Macro</th>\n",
       "      <th>Long/Short Equity</th>\n",
       "      <th>Merger Arbitrage</th>\n",
       "      <th>Relative Value</th>\n",
       "      <th>Short Selling</th>\n",
       "      <th>Funds Of Funds</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>1997-01</th>\n",
       "      <td>0.0119</td>\n",
       "      <td>0.0393</td>\n",
       "      <td>0.0178</td>\n",
       "      <td>0.0791</td>\n",
       "      <td>0.0189</td>\n",
       "      <td>0.0213</td>\n",
       "      <td>0.0191</td>\n",
       "      <td>0.0573</td>\n",
       "      <td>0.0281</td>\n",
       "      <td>0.0150</td>\n",
       "      <td>0.0180</td>\n",
       "      <td>-0.0166</td>\n",
       "      <td>0.0317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-02</th>\n",
       "      <td>0.0123</td>\n",
       "      <td>0.0298</td>\n",
       "      <td>0.0122</td>\n",
       "      <td>0.0525</td>\n",
       "      <td>0.0101</td>\n",
       "      <td>0.0084</td>\n",
       "      <td>0.0122</td>\n",
       "      <td>0.0175</td>\n",
       "      <td>-0.0006</td>\n",
       "      <td>0.0034</td>\n",
       "      <td>0.0118</td>\n",
       "      <td>0.0426</td>\n",
       "      <td>0.0106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-03</th>\n",
       "      <td>0.0078</td>\n",
       "      <td>-0.0021</td>\n",
       "      <td>-0.0012</td>\n",
       "      <td>-0.0120</td>\n",
       "      <td>0.0016</td>\n",
       "      <td>-0.0023</td>\n",
       "      <td>0.0109</td>\n",
       "      <td>-0.0119</td>\n",
       "      <td>-0.0084</td>\n",
       "      <td>0.0060</td>\n",
       "      <td>0.0010</td>\n",
       "      <td>0.0778</td>\n",
       "      <td>-0.0077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-04</th>\n",
       "      <td>0.0086</td>\n",
       "      <td>-0.0170</td>\n",
       "      <td>0.0030</td>\n",
       "      <td>0.0119</td>\n",
       "      <td>0.0119</td>\n",
       "      <td>-0.0005</td>\n",
       "      <td>0.0130</td>\n",
       "      <td>0.0172</td>\n",
       "      <td>0.0084</td>\n",
       "      <td>-0.0001</td>\n",
       "      <td>0.0122</td>\n",
       "      <td>-0.0129</td>\n",
       "      <td>0.0009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-05</th>\n",
       "      <td>0.0156</td>\n",
       "      <td>-0.0015</td>\n",
       "      <td>0.0233</td>\n",
       "      <td>0.0315</td>\n",
       "      <td>0.0189</td>\n",
       "      <td>0.0346</td>\n",
       "      <td>0.0118</td>\n",
       "      <td>0.0108</td>\n",
       "      <td>0.0394</td>\n",
       "      <td>0.0197</td>\n",
       "      <td>0.0173</td>\n",
       "      <td>-0.0737</td>\n",
       "      <td>0.0275</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Convertible Arbitrage  CTA Global  Distressed Securities  \\\n",
       "date                                                                \n",
       "1997-01                 0.0119      0.0393                 0.0178   \n",
       "1997-02                 0.0123      0.0298                 0.0122   \n",
       "1997-03                 0.0078     -0.0021                -0.0012   \n",
       "1997-04                 0.0086     -0.0170                 0.0030   \n",
       "1997-05                 0.0156     -0.0015                 0.0233   \n",
       "\n",
       "         Emerging Markets  Equity Market Neutral  Event Driven  \\\n",
       "date                                                             \n",
       "1997-01            0.0791                 0.0189        0.0213   \n",
       "1997-02            0.0525                 0.0101        0.0084   \n",
       "1997-03           -0.0120                 0.0016       -0.0023   \n",
       "1997-04            0.0119                 0.0119       -0.0005   \n",
       "1997-05            0.0315                 0.0189        0.0346   \n",
       "\n",
       "         Fixed Income Arbitrage  Global Macro  Long/Short Equity  \\\n",
       "date                                                               \n",
       "1997-01                  0.0191        0.0573             0.0281   \n",
       "1997-02                  0.0122        0.0175            -0.0006   \n",
       "1997-03                  0.0109       -0.0119            -0.0084   \n",
       "1997-04                  0.0130        0.0172             0.0084   \n",
       "1997-05                  0.0118        0.0108             0.0394   \n",
       "\n",
       "         Merger Arbitrage  Relative Value  Short Selling  Funds Of Funds  \n",
       "date                                                                      \n",
       "1997-01            0.0150          0.0180        -0.0166          0.0317  \n",
       "1997-02            0.0034          0.0118         0.0426          0.0106  \n",
       "1997-03            0.0060          0.0010         0.0778         -0.0077  \n",
       "1997-04           -0.0001          0.0122        -0.0129          0.0009  \n",
       "1997-05            0.0197          0.0173        -0.0737          0.0275  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert to percentages \n",
    "hfi_data = hfi_data/100\n",
    "hfi_data.index = hfi_data.index.to_period('M')\n",
    "hfi_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "## Semideviation\n",
    "\n",
    "Formula \n",
    "\n",
    "$$\\sigma_{semi} = \\sqrt{\\frac{1}{N}\\sum_{x_{t} \\leq \\bar{x}} (x_{t} - \\bar{x})^{2}}$$ \n",
    "\n",
    "<p style=\"text-align:center;\"> N = number of entries which fall below the mean.</p> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Short Selling             0.047655\n",
       "Emerging Markets          0.032476\n",
       "CTA Global                0.023290\n",
       "Long/Short Equity         0.019897\n",
       "Distressed Securities     0.017009\n",
       "Event Driven              0.016712\n",
       "Convertible Arbitrage     0.016536\n",
       "Funds Of Funds            0.015536\n",
       "Global Macro              0.014694\n",
       "Fixed Income Arbitrage    0.011517\n",
       "Relative Value            0.011462\n",
       "Merger Arbitrage          0.009600\n",
       "Equity Market Neutral     0.008115\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the standard deviation \n",
    "std = hfi_data.std(ddof=0)\n",
    "std.sort_values(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Emerging Markets          0.028039\n",
       "Short Selling             0.027283\n",
       "Convertible Arbitrage     0.019540\n",
       "Fixed Income Arbitrage    0.017763\n",
       "Event Driven              0.015429\n",
       "Distressed Securities     0.015185\n",
       "Long/Short Equity         0.014051\n",
       "CTA Global                0.012443\n",
       "Relative Value            0.012244\n",
       "Funds Of Funds            0.012122\n",
       "Equity Market Neutral     0.009566\n",
       "Merger Arbitrage          0.008875\n",
       "Global Macro              0.006579\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the standard deviation for returns which have negative values \n",
    "semi_std = hfi_data[hfi_data<0].std(ddof=0)\n",
    "semi_std.sort_values(ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "#### Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa66fd89d50>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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55pucfvrpPProo0ybNo3Jkydz11131R/boEGDeP7559lll124+uqryz4ex3GWxxV9mXTo0IGpU6cyduxYOnfuzIgRI7juuutKbjtu3DgGDBhA//79mTFjRgPFe8ABBwCwzTbbMHv2bAAef/xxjjjiCAD22Wcf1l577frtL7vssvqe7euvv84//vEPAOrq6vjGN74BwKRJkxg8eDCdO3embdu2jBgxouzjKrw9fPDBBzz11FMcdNBB9OvXj2OPPZa5c+cCwdxz661h+s9bbrmlZP3jx49n++23p0+fPjz66KPMmDGjSbmTJ0+ub/Mqq6zC4YcfzuOPhxRIbdu2Zd99913uPDmOs2JUrY1+ZVBXV8fgwYMZPHgwffr04frrr2fkyJENtnnttde45JJLmDx5MmuvvTYjR45s4ApYMP3U1dWxdOnS+vJSniQTJkzgkUce4emnn2aNNdZg8ODB9XW1a9eugV1+RT1RnnvuOXr27Mlnn31Gp06dmDZt2nLbDBs2jDPPPJP33nuPqVOnsvvuuzdY//HHH3P88cczZcoUNtxwQ84999xm3R+bisheddVV64+n+Dw5jtNyvEdfJrNmzarvTQNMmzaNjTfeGIA111yTRYsWAfD+++/Tvn17OnbsyNtvv80DDzzQbN277LILN954IwAPPPAA//nPfwBYuHAha6+9NmussQYzZ85k4sSJJffffvvtmTBhAvPnz2fJkiXcdtttZR3TY489xtixYznmmGNYa6216N69e/2+Zsbzzz8PhLeZ7bbbjlNOOYV99913uYHfglJfd911+eCDD+rt9sXnprjNjz32GO+++y6ffvopN998M7vuumtZ7XYcp2V4j75MPvjgA0466SQWLFjAKquswmabbVY/iDlq1CiGDh1Kly5dGD9+PP3796dXr15ssskm7LTTTs3WPWbMGA499FAGDBjArrvuykYbbQTAkCFDuOqqq9h6663ZYostGDRoUMn9u3TpwrnnnssOO+xAly5dGDBgAJ9++mnJbW+99VaeeOIJFi9eTPfu3bnjjjvqPW5uvPFGjjvuOC688EKWLFnCIYccQt++fYFgvjnooIOYMGHCcnV26tSJY445hj59+tCtWze23Xbb+nUjR45k9OjRrL766jz99NMN2nzRRRex2267YWbsvffeDB9ePHGZ4zgpqJqkZi+//PIKuQA6tYlfD06eVKN7ZVNJzdx04ziOU+O4onccx6lxXNE7juPUOK7oHcdxahxX9I7jODWOK3rHcZwaxxV9C2gsTXFr2HHHHUuWn3vuuWywwQb069ePHj16cMABB7QqvW856YGL0y3vvffeLFiwYIVlOo7z+aB6A6bO7Zi4voVNrm4qTXFraCof/Pe+9z1OPfVUIAQ67b777rzwwgt07ty5xXLKSQ9cnG75/vvvb7Ecx3E+f3iPvkwaS1M8depUdt11V7bZZhv22muv+kRggwcP5nvf+x677LILPXv2ZPLkyRxwwAH06NGDs88+u77eDh06lCV/xIgR7Lnnntx0000AJeW+/PLLbLfddvX7zJ49m6233rq+PYUgtFJplEulW85OgPKLX/yC3r1707t3by699NL6+nv27MkxxxxDr1692HPPPfnoo49W7AQ7jpMbrujLpFSa4iVLlnDSSSdx++23M3XqVL7zne9w1lln1e/Ttm1bHn/8cUaPHs3w4cO54oorePHFF7nuuuvq0w23hEJK4cbk9uzZk08++YRXX30VCG8BBx988HL1lEqjXCrdcoGpU6dy7bXXMmnSJCZOnMjVV1/Nc889B8A//vEPTjjhBGbMmEGnTp244447WnxcjuPkS/WabipMIU3x3/72N8aPH8+IESM4++yzefHFF9ljjz2AMNNTly5d6vcZNmwYAH369KFXr1716zbZZBNef/111llnnRa1oZCuYtasWY3KPfjggxk3bhxnnHEGt956a3164Szjxo1j7NixLF26lLlz5/LSSy/V9/xL8cQTT7D//vvTvn17IKRa/tvf/sawYcPo3r07/fr1AzylsON8XnFF3wKK0xRfccUV9OrVq0GyriwFM0+bNm3qfxeWi1PvnnXWWdx3X8ivUSpVMISUwgMHDsTMGpVbSD52wAEHIIkePXo0WN9cGuVSNJUPKXtcdXV1brpxnM8hbropk1Jpinv27Mm8efPqFe6SJUuanXCjMX784x8zbdq0RpX8HXfcwUMPPcShhx7KFlts0ajcTTfdlLq6Oi644IKSE4Q0lUa5sZTCu+yyC3fddReLFy/mww8/5E9/+hM777zzCh2n4ziVx3v0ZdJYmuJRo0Zx8skns3DhQpYuXcp3v/tdevXqlUTmL3/5S2644Yb6aQMfffTReo+b22+/vVG5I0aM4LTTTuO1115brs6+ffs2mka5ON1ygQEDBjBy5Mj6gd6jjz6a/v37u5nGcaoET1PsVCV+PTh54mmKHcdxnKrCFb3jOE6N44recRynxqkqRf95HE9wKo9fB47TMqpG0bdr14758+f7Tf4Fx8yYP38+7dq1W9lNcZyqoWrcK7t27cqcOXOYN2/eym6Ks5Jp164dXbt2XdnNcJyqoWoU/aqrrkr37t1XdjMcx3GqjrJMN5KGSJol6RVJZ5RYL0mXxfXTJQ0oWl8n6TlJ96ZquOM4jlMezSp6SXXAFcBQYCvgUElbFW02FOgRP6OAK4vWnwK83OrWOo7jOC2mnB79dsArZvaqmX0C3AIML9pmOPAHC0wEOknqAiCpK7AP0PzMF47jOE5yylH0GwCvZ5bnxLJyt7kU+AHwWVNCJI2SNEXSFB9wdRzHSUc5il4lyop9HEtuI2lf4B0zm9qcEDMba2YDzWzgikyV5ziO45SmHEU/B9gws9wVeLPMbXYChkmaTTD57C7phhVureM4jtNiylH0k4EekrpLagscAtxdtM3dwJHR+2YQsNDM5prZmWbW1cy6xf0eNbMjUh6A4ziO0zTN+tGb2VJJJwIPAnXANWY2Q9LouP4q4H5gb+AVYDHw7fya7DiO47SEsgKmzOx+gjLPll2V+W3ACc3UMQGY0OIWOo7jOK2ianLdOI7jOCuGK3rHcZwaxxW94zhOjeOK3nEcp8ZxRe84jlPjuKJ3HMepcVzRO47j1Diu6B3HcWocV/SO4zg1jit6x3GcGscVveM4To3jit5xHKfGcUXvOI5T47iidxzHqXFc0TuO49Q4rugdx3FqHFf0juM4NY4resdxnBrHFb3jOE6N44recRynxnFF7ziOU+O4onccx6lxXNE7juPUOK7oHcdxahxX9I7jODWOK3rHcZwaxxW94zhOjbPKym6Aky/dzriv0XWzL96ngi1xHGdl4T16x3GcGscVveM4To3jit5xHKfGcUXvOI5T47iidxzHqXFc0TuO49Q4ZSl6SUMkzZL0iqQzSqyXpMvi+umSBsTydpKekfS8pBmSzkt9AI7jOE7TNKvoJdUBVwBDga2AQyVtVbTZUKBH/IwCrozl/wV2N7O+QD9giKRBidruOI7jlEE5PfrtgFfM7FUz+wS4BRhetM1w4A8WmAh0ktQlLn8Qt1k1fixV4x3HcZzmKUfRbwC8nlmeE8vK2kZSnaRpwDvAw2Y2acWb6ziO47SUchS9SpQV98ob3cbMPjWzfkBXYDtJvUsKkUZJmiJpyrx588poluM4jlMO5Sj6OcCGmeWuwJst3cbMFgATgCGlhJjZWDMbaGYDO3fuXEazHMdxnHIoR9FPBnpI6i6pLXAIcHfRNncDR0bvm0HAQjObK6mzpE4AklYHvgbMTNh+x3EcpxmazV5pZkslnQg8CNQB15jZDEmj4/qrgPuBvYFXgMXAt+PuXYDro+dOG2Ccmd2b/jAcx3GcxigrTbGZ3U9Q5tmyqzK/DTihxH7Tgf6tbKPjOI7TCjwy1nEcp8ZxRe84jlPjuKJ3HMepcXwqwS8y53ZspHxhZdvhOE6ueI/ecRynxnFF7ziOU+O4onccx6lx3EbvOI7TEqpwbMt79I7jODWOK3rHcZwaxxW94zhOjeOK3nEcp8ZxRe84jlPjuKJ3HMepcVzRO47j1Diu6B3HcWocV/SO4zg1jit6x3GcGscVveM4To3jit5xHKfGcUXvOI5T47iidxzHqXFc0TuO49Q4rugdx3FqHJ94pATdzrivZPnsi/epcEscx3Faj/foHcdxahxX9I7jODWOK3rHcZwaxxW94zhOjeOK3nEcp8ZxRe84jlPjuKJ3HMepcVzRO47j1Diu6B3HcWocV/SO4zg1TlmKXtIQSbMkvSLpjBLrJemyuH66pAGxfENJ4yW9LGmGpFNSH4DjOI7TNM0qekl1wBXAUGAr4FBJWxVtNhToET+jgCtj+VLgf82sJzAIOKHEvo7jOE6OlNOj3w54xcxeNbNPgFuA4UXbDAf+YIGJQCdJXcxsrpk9C2Bmi4CXgQ0Stt9xHMdphnIU/QbA65nlOSyvrJvdRlI3oD8wqZQQSaMkTZE0Zd68eWU0y3EcxymHctIUq0SZtWQbSR2AO4Dvmtn7pYSY2VhgLMDAgQOL63ccZwXxtNtOOYp+DrBhZrkr8Ga520halaDkbzSzO1e8qU1wbscm1i3MRaTjOE61UI7pZjLQQ1J3SW2BQ4C7i7a5Gzgyet8MAhaa2VxJAn4PvGxmv0jacsdxHKcsmu3Rm9lSSScCDwJ1wDVmNkPS6Lj+KuB+YG/gFWAx8O24+07AN4EXJE2LZT80s/vTHobjOI7TGGVNJRgV8/1FZVdlfhtwQon9nqC0/d5xHMepEB4Z6ziOU+O4onccx6lxXNE7juPUOK7oHcdxapyyBmMdx4k0FrPh8RrO5xjv0TuO49Q4rugdx3FqHDfdrEQ8B4njOJXAe/SO4zg1TlX16BvtAbercEOclYa/BTlOy/EeveM4To3jit5xHKfGcUXvOI5T47iidxzHqXGqajDWcRrFZxlzqpBKORe4ov884mH2juMkxE03juM4NY736B1nJdHYazt4XICTFu/RO47j1Diu6B3HcWocN904zhcV91T6wuA9esdxnBrHFb3jOE6N44recRynxnFF7ziOU+O4onccx6lxXNE7juPUOO5e2RLcHc1xnCrEFb3jOLWBJwNsFFf0juM4nzcSWw/cRu84jlPjeI/ecUrQ6IQQ7SrcEGc5/L9pOd6jdxzHqXFc0TuO49Q4ZSl6SUMkzZL0iqQzSqyXpMvi+umSBmTWXSPpHUkvpmy44ziOUx7NKnpJdcAVwFBgK+BQSVsVbTYU6BE/o4ArM+uuA4akaKzjOI7Tcsrp0W8HvGJmr5rZJ8AtwPCibYYDf7DARKCTpC4AZvY48F7KRjuO4zjlU46i3wB4PbM8J5a1dBvHcRxnJVCOoleJMluBbZoWIo2SNEXSlHnz5rVkV8dxHKcJylH0c4ANM8tdgTdXYJsmMbOxZjbQzAZ27ty5Jbs6juM4TVBOwNRkoIek7sAbwCHAYUXb3A2cKOkWYHtgoZnNTdpSpzrxRHBfGBoNZLp4nwq3xCmm2R69mS0FTgQeBF4GxpnZDEmjJY2Om90PvAq8AlwNHF/YX9LNwNPAFpLmSDoq8TE4juM4TVBWCgQzu5+gzLNlV2V+G3BCI/se2poGOo7jOK3Dc904jpMvbr5b6XgKBMdxnBrHFb3jOE6N46YbJwmeOtZxPr94j95xHKfGcUXvOI5T47iidxzHqXFc0TuO49Q4rugdx3FqHFf0juM4NY67VzrO55HGokk9ktRZAbxH7ziOU+O4onccx6lxXNE7juPUOK7oHcdxahxX9I7jODWOK3rHcZwaxxW94zhOjeOK3nEcp8ZxRe84jlPjuKJ3HMepcVzRO47j1Diu6B3HcWocV/SO4zg1jit6x3GcGscVveM4To3jit5xHKfGcUXvOI5T47iidxzHqXFc0TuO49Q4rugdx3FqHFf0juM4NY4resdxnBrHFb3jOE6N44recRynxilL0UsaImmWpFcknVFivSRdFtdPlzSg3H0dx3GcfGlW0UuqA64AhgJbAYdK2qpos6FAj/gZBVzZgn0dx3GcHCmnR78d8IqZvWpmnwC3AMOLthkO/MECE4FOkrqUua/jOI6TIzKzpjeQDgSGmNnRcfmbwCwv7C8AACAASURBVPZmdmJmm3uBi83sibj8V+B0oFtz+2bqGEV4GwDYApjVguNYF3i3BduvKC7n8ynD5Xx+ZbicysnY2Mw6l1qxShk7q0RZ8dOhsW3K2TcUmo0FxpbRnuWQNMXMBq7Ivi4nXzm1dCy1JqeWjqXW5KSWUY6inwNsmFnuCrxZ5jZty9jXcRzHyZFybPSTgR6SuktqCxwC3F20zd3AkdH7ZhCw0Mzmlrmv4ziOkyPN9ujNbKmkE4EHgTrgGjObIWl0XH8VcD+wN/AKsBj4dlP75nAcK2TycTkVkVNLx1JrcmrpWGpNTlIZzQ7GOo7jONWNR8Y6juPUOK7oHcdxahxX9F9QJLWRtNbKbofjOPlTlTZ6SWsA/wtsZGbHSOoBbGFm9yaq/0tNrTez91LIycg7CPiLmS2SdDYwALjQzJ5NLOcmYDTwKTAV6Aj8wsx+nqDuAU2tz+FYdgLOBTYmOBUoiLFNEsvZnJDSYz0z6y1pa2CYmV2YUk6UNQzYJS4+Zmb3JK7/ROBGM/tPynpLyMn1/iyS9RWgh5ldK6kz0MHMXkss47ISxQuBKWb250Qy2gMfmdln8ZrbEnjAzJYkqb9KFf2tBEV1ZLz5VgeeNrN+iep/jSYCvnJQJtPNbOt40V4EXAL80My2Tyxnmpn1k3Q4sA0henmqmW2doO7xTaw2M9u9tTKK5M0Evke4Dj7NCJqfWM5jwGnAb82sfyx70cx6J5ZzESFlyI2x6FCCIjkzoYwLCS7OzwLXAA9aDgog7/szI2cMMJDwENlc0vrAbWa2U2I5YwmK97ZY9A1gBiFG6FUz+24CGVOBnYG1gYnAFGCxmR3e2roBMLOq+xBuAIDnMmXPr+x2teJ4novfFwGHFR9bQjkzgFUJF+yusWz6yj7+FTyWSRWSM7n4/wCm5SBnOtAms1yXx39D6LzsRcg79QrwE2DTxDIqcn8C0+LxZOXkcc4eBVbJLK8Sy+qAlxLJeDZ+nwT8oPj8tfZTTmTs55FPYi8hXLnSpsB/8xAkaW1CVs52hTIzezyxmDck/Rb4GvBTSauRz/jJb4HZwPPA45I2JryCJkVSb0K20uw5+0NiMeMl/Ry4k8x/b4lNRMC78foqXGsHAnMTyyjQCSiYBTvmIcDMTNJbwFvAUkIP8nZJD5vZDxKJqdT9+Uk8noKc9jnIANgAaM+ye6U9sL6ZfSop1XFJ0g7A4cBRsSydfk799KvEB9gDeAyYR3jVnQ0MzkHO0cALwH+A8cBHwKM5yFkDOIBgawToAuyZg5zuRcsqyEwoY0w8V28D1xIUyu05HMv4Ep88/ptNgEcIgYBvAE8A3XKQcwjwL+A64HrgNeCQxDJOJphUHgQOAlaN5W2AfyaUU6n781RC5+VV4BjgaeCkHOQcFf+Pa+P/82rUDe2BnyeSsSsha8DpmevuslTHUJU2egBJ6wCDCMpqopklzyYn6QVg21h/P0lbAueZ2YgcZFViUOlZMxtQVDbVzLZJKOMFoC/htbOvpPWA35nZ11PJWBnE3mIbM1uUQ91tgAOBvxGuNxFMU28llnM+8Hsz+1eJdT3N7OWEsnK/P6OcPYA9o5wHzezhnOQU0q4LeMbMqipnV1WabjIeHoVX6I0kdQT+ZWZLE4r62Mw+loSk1cxspqQtEtYPNBxUIvQaVgVuAJIMKsUHVC+go6QDMqvWImNeSUTBc2BpdN98h9A7SUp8gPyE8Ao9NE5os4OZ/T6xnO8XLUN4hZ9qZtNSyIjn60QzG0e+uaC6Fyt5SX80s28mVvKVuj+Jij0X5V5EG8IbyirAZpI2swQmXEn30EhGXwAzG9ZaGVClih74DcEFcTrhCds7/l5H0mgzeyiRnDmSOgF3AQ9L+g/5ZN/cH+hP8IbAzN6UtGbC+rcA9iXYgLM960WEV96UTInn7GqCmeAD4JnEMiC8Ql8LnBWX/w7cCiRV9IQH8ECg4Oq4DyFZ32hJt5nZzxLJeVjSqYRj+LBQaGldeXtlFxRmgEv2NpehIvenpEUsU5JtCR2kD80saXyIpJ8CIwjODJ/FYgNSjNVdEr8PAP6H0MGD4HU1O0H9gdT2rEp8CB4DvTLLWxFu+k3IwSMiY0MbBrTNoe5n4ndh5L09+XgP7JDz/yJgw8xyN2DrnGRVyhvmQYIZrbDcAfgLsDqJPC5iva+V+LyaqO4zCQ/1pcD78bMImA9clMM5q/j9GeXsB/wkh3pnAavl1e4o4/Fyylb0U62RsVtaJgummb0E9DezV1MLkjRA0snA1sAcC1MipmZc9LrpJOkYwuDf1TnImS/pr5JeBJC0dQzQSoKFq/OuzPJsM5ueqv4iPox24ILHxSBy8CACNgKy//kSwkw+H5HQk8TMupf4JDF5mdlFZrYmYeBwrfhZ08zWsYR++hkqdn9mMbO7gKTxGpFXCW8LedJZUv3/Lak7UHK2qBWhWk03syRdSeg5QHit+nt0S0wSSQYg6RyCd8Kdseja+LqeNCrSzC6Jg0rvE8ws51g+g0pXE4N/otzpMVo25fFMlLStmU1OWGcp/pdgz95U0pOEm+LAHOTcRDimQgTk14Gb4+DsS6mESDqBELW6IC6vDRxqZr9JUPeWZjYTuK1UBLOld0mt1P2ZHW9qQzCx5eFdshiYpjBFataV9+SEMr4HTJBUeBh2A45NVXlVet1EH93jga8QzAVPEOyCHwNrmNkHieS8TOiJfJyR+6yZ9UxRf6WRNNnMtpX0nC2L8pxmCSMWJb0EbE5wFfyQZakJWh19W0LWKoQHo4BZlihcvIScgYSBcQFPmNmUHGQs9z9k/6dW1j3WzEY1Er1slj5quVL357WZxaUEm/bVZvZOivozcr5VqtzMrk8sZzVCBC7ATDNL9sZYlYq+Ukh6gNCrKvSyOgE3mNm+iep/wsy+UjSoBMuUY+pBpQeAEwlh4gNi8M9RZjY0oYyNS5VbCZe+Vsp5njBweauZ/TNl3Y3I+zINA8D+nbj+6UDfaP4qDJRON7NeTe/p1AqSdiT05OstLZYo0LAqTTcKSZIuYvnoyyQ2TUmXExTvf4EZkh6Oy3sQeidJMLOvxO+UHjZNcQJh5potJb1BGPBLk0tjGRea2TezBZL+CHyzke1XlGEEk8A4SZ8RlP64HBTwMOD/gPUJrqIbATMp8mBJwIOEY7mKcK2NJgz6JkPSkaXKUymTjJxK3Z8lSWVSkTTOzA6OsSHLyUv5lhrvkU0JaR0KuZsM+OIqesII/hjgl8BuhKkLSyUgW1EKr+ZTgT9lyicklFFPwZe5ubIErG1mX8sG/0j6OsHMkoqKuPDFN4SfAT+LiuVHwE8J+UdScgEh8OcRM+svaTeC61tqTifYZI8jXMsPAb9LLGPbzO92wFcJLr2p01NU6v7Mm1Pid5I3+GYYCGxleZlYUrnvVPJDCFYBeCFT9recZLUl+AH3JoaM5yDj2aLlVUjoupeVA/TJLB9CouRgLO/Ct4gcXfiizG7ADwgP5GeA/81BRiFB1/PEpGNEd9hq/xDy6dydQ70Vuz9r5UNINNglr/qrtUf/cQwb/4dCju03gC+nFiJpMCHvyGyij7ikb1mipGaSzgR+CKwu6f1CMcGdL48JiA8kJLA6nDBQdiQhfLzVmNlFwEWSLrJ8XPYaIGkSyzJxHmT5ue4tkNSBEBxzo6R3CA+zpORt7miExYSEfamp1P3ZmfAmVHzOkgwulxg7q19F+jG0dYGXJD1DQ8+eJJGxVTkYK2lb4GVCpOcFhFD+n5vZxMRyphLSBs+Ky5sDN1vC3DCx3oooxyhrc4Kv++vAfhb8wVPWv0up8lQPx4ycgstgrkQz10cE973DCb3gGy193vsnWGbu+DrR3GFmYxLKyIbbtyEoyHFmdkYqGVFOpe7PhwhjM6cSxjS+Bcwzs9NTyqkEknYtVW5mjyWpv9oUfbT5Xmxmp1VA1nQrGnApVdaK+re0kD+n5OxMlsi/ucRg0pcJwUX/jXJSDiplZ0VqR0gENTVhL+sIM7tBRTloCpjZL1LIibLqCImyvpaqziZkTTWzbSS9YGZ9YtnfzGznhDKyymQpIffMnFT1RxmVvD8L56z+npT0mJmVVJorUH9FZ5rLk6oz3VjIAb2NJFn+T6kpkn4P/DEuH06wB6fi+8AogldHMUa6KL9KDCYBYEVZKiVtSBg0TUUh53junkrxWlssqaOZ5RF1myV3c0eq3mEzMip5fxbiJuZK2oeQh6prwvqn0sRMcyRM1qec8/ZUXY8eQNL/EWyLt9EwAdSdje60YnJWI7gkFgI/Hgd+YykDGcLNvYOZPZmqzibkTLfEU+CVIVdRbp+EddYBJ5vZL1PV2YSscQSvm4dpeK2ljIosZe7oCPwspbmjUjbnvO9PSaua2RJJ+xJSO28IXE4wEZ1nZnlmAK0IkvYDtjOzHyapr0oV/bUlis3MvlPxxiRA0tNmtkMF5NwInGmJfc2LZGR9nNsA/YDZZnZEYjnjzWy3lHU2IqdUVKRZ+hmzckchH/1bhDdUEd5Q17R0GTgLcnK9P+OA+J+Bm4Hxeb85xM7K4YQ0zxdI2gj4HzPLIytrVu5EMxuUoq6qM91EflfcA5aUbELgxgIkCqS0aUcekvQN4M6cL9ouhACwZ2jY00oysh/J+jgvJQxe5/G28pSkX7N8Wt/UeVs6mdmvsgWSTmls45YiqcneZ+L/Zi9rOOH8ldF7KamiJ+f7E+hJ8CD7EfAHSbcTrrNJCWVk+Q0hPfHuhLetRcAdNIxLaBXKOW9PtfboS82UtFxZK+ovGcZfwNKH8y8i2J6XEvKB5JUCIdeR/Yyc1YGNCt5KeaDK5W0pda0lyUET65pH8IC6GZhEkT045X8j6SngCkKyMSMEfp1gZjumkhHl5Hp/FtW7PiHx4CGEMY1bzOyspvdqsYxnLaQMyeaIet7M+iaUkWvenqrq0StMnrsjIaVn1utiLRJGRKZW5GXIq0gKhEoMxsVI20sIA0rdJfUDzk/cMyVvs42kQ4HDCMeQ7XWvSQgCS8X/EFJrFOTdR+idzmhyrxXjMOBX8WPAk7EsCZW6P7NYmKTn94R5nb9PmMs1qaIHlsRxoUIeos4sm4CkVUg6wMzuNLNvS1rbzP6Tot5iqkrRE5RHB0K7s8rxfRKmqJV0FPAlM/t5XH4jyhPwAzO7MpWsWH+lfM8HEQatehLOZR3pZ+Q5l+BSOQHAzKZJ6pawfhSmcxzFskx/LwNjzezvCcU8RZgKb10aekUtIsyWlAQz+5SQ0+YvcfD/UEK62vPN7PJUcqKs2cDwlHUWUZH7E0BSO0K8waGEzKJ/IURnp5pdLstlhFQoX5b0Y8KxpJrH4WyWpUH/K2FmrvTY5yD8t6UfwsQPedY/GVgns/xc/G5HwllfMvXfk/k8TPBxfzQHOVOAzYDnCEr+2ySekYeYUoGGMz8lmy0L2IGggM8jKK394u83gUF5Xhc5Xm+rEaaSuy1eez8CNkhY/7jM758WrXsoh+PZOOfzdRMhwdztBKXbrgL/0ZYED7wTgJ4J632u1O/Un6rq0Uu61My+C/xaUqlscqnMA22sYeTjbbH+j6P9OSmWv+95VtYrkuos9CSvjXbblLwo6TCgTiGs/2RC7zgV5xBSR0/IlN0l6VFCZGmSlMuqUAppSdcT8ig9QHANfDFFvUVk0xzsQUgbUCDZLEYVvD8fBI41s0WJ6iuJpDWAJWa2xEJgowF7E96IU02mvrqk/oQB2Hbxd/04jaUKmoxPkqpA0jZmNjXvQUVJr5jZZiXK2wCvWL75R3LxPY/1Pg58jZAV8S1Cz3ikpR1UWoNgI92TcME+CFxgcfKWBPX/3cw2b2TdLDPbIoWcSqGQYrngNZTLAyU7EFo8KJrYiaEi92eliPfLUWb2D0mbERLn3UhIHfGMJUhb0ohTQQGzVBHl1aTos0hqS3idMsLsQsnmcpX0G+A9Mzu7qPxCYF0zG51KVqy3Ur7nGxNeeVclTF3WkRAA9kpKOXmiGPbeyLq8PDsGEILmjDDD1HOpZeSJpJkEW3Yb4AbCAKzi5wbLYca0PO/PSqGG6SguIIzbnRCPbWrqjlieVKWiVwh3vgr4J+Fi7U54lXsgUf3tCb3ebQnpaQH6EmzcR1uiqdAy8rJBOUsJSj7XSNnURPewxi4mM7OjEsl5h2VzkTZYBRxsZuulkJORVzxv8H6EGbqSzhucJ830GrHEHkx535+VQg1z6DxJSMx2V1xO6l6ZN9Wq6GcC+xZ6opI2Be4zsy2b3rPFcjZh2UQaL1lOU9bFB8vH0W5eCPFfzcwWJ6q/SS8RSxAAFgO+itkI+C5QZ2ZJcpCokfk7C1j6eTxrat7gSlDB+3MNwiTxG5nZMXFMaAszuzdR/TcQTJxvAGcQImMXK0wp+lg1KfqqGozN8E6RueFVgkkiKRZynOeV5zzLXwm288KbwuoEN7FUgSyfEXrbNxE8e5KmJgYwszsKv+MD8ofALsDFwO8TykmqyMtgNsHbqjDGsBqhp+o0TkXuT8JMVlMJnlgAcwiOE0kUPXAMYZapbsCemY7XVoRYkVYjaScze1LSapYwh1YxVaXoM2HCMyTdD4wjKLCDCG5p1Uq7rDnIzD6IvZUkmFk/SVsS7LQ3AS/F74fMLNkkGpJ6EgZi+wM/B0anrL+SqELzBtcSK+H+3NTMRsTgNszso+jIkAQLczVcXKL8KdJ5kl1GmGrzafLyoafKFD0hQKLA20BhdH8esHblm5OMDyUNKLhSSdqGxL1uC5N0jAHGSBpBmCf0pwSF3Gok3UbIz3EJYaD3U2Ctwn1nVZS7O1KReYNLuG/WryKHNBg5U+n785NoSitErG5KZnamKmFJHN/aQNJlxSst1UTn1WajVwVT1BbJbQ/sT/Dh3idx3dsSBhjfjEVdgBFmliz3vaQNCPlA9ieEi48D/pRqYFnSbJYprMJ3oXdlqV1SC6+8zZW1UkYdcH1q76eVhaS/mtlXmytrpYxKppDek/AGuRXB1LkTwV14Qt6yUyFpXYLZ9qeEGJEGpDJVVp2ih+BFkNpToBE5bQkBEocBQwgZ6+40s3ua3HHFZK0KbEFQjjPNbEkzu7Sk7scIIenjCNGEDXrXVdjbrljiLEkPAl+vlHugpC/TcP7TVqeUjukC1gDGA4NZ9gBeC3gg9cBype7PKGsdwnwBAiaa2bs5yDjIzG5rrqyVMvqa2fPNb7mC9Vepov8xwQc8lxS1kgpJpvYi3By3ApebWbcU9ZeQtwYhIdPGOXkPzGb53jYsMw/kGgCWEi1LnPVdwvyqBdYC9k/tCSHptwTb6d00vNaSTVkY5Qwj5NRZnzBwuTHwspn1anLH8uo+hXC+1id4kBQU/fuEDIm/bq2MInm53p8ZOXcTsn7ebWYfNrd9K+TknS13KCFPz1aE+/MlQqqK+1PUD9Vnoy9Q8EY5P1OWcuq9Bwkz13zFzF4DkPSrpndpFbl6D+T1gFpJVCxxVuTN+GmTkZdH7+gCQs/0ETPrL2k3Qmej1ZjZrxRy9//QzC5IUWcz5H1/Fvg/YARwscIcC7cC91q6KOyhhDf6Yvv5WoR4lxQyjgGOBX7AsnGhgYRj6mpmY5PIqcYefSkkrWdmbyeqqz/Bnn0gwTXsFuAcM2syT30r5E0xs4HKMd91rSFpY6twOukotx3BlJPstT3WW7gGnif47X8m6Rkz2y6hjIrMZNaI7GT3Z4m66wgPkWOAIakGsCX1JUSpn09D+/kiwsxWrU4pLOklQofyvaLydQhR2EnMatXaowdAUkfgGwQbek9ggxT1Wghxfw44XWFmnEOBtpIeIAxgJnnKZqgF7wEAJP3RzL7ZXFkCVpM0luDjXH8dW+KJR6BekexJuA72JLhXJlX0wAJJHQhvkjfGCODUrqmVmskMyO/+LJKxOsHbZwTBxJYszsLMnpf0IsGHPq/4DZUaIzOz+Qk9RasvTTEhmGgEYc7I14EFhAGmNgllLJe6lfDqvhdwbQ7HtAfwGMEN7UZCkM7glX2uV/BYni1ariNEFaeW8zxwHCH3/TaFT2IZuxBC+V8nDMS/BayR03lrH8/VKsC3CFk/10ksYxEheG4JwdS1CHg/sYzc78+MrFvjvXIVoUefXEaU8xegbU51TwL6lijvS0iclkROVZluFCa33oXgSnUL8Cghm2T3xHKSTRXXApmV8B74UoniRZbAw0fSmYRo2NWBxSwb8PuEMClIqzP9FclrNLlZovrnAP8GrgTuMrNFkl5Lfa0VyfwfwoPLgMlm9lZesvKgUvdnRt4Q4GGLqUPyIs8BeUlfIXTuCuN0Rsix9S3gCDNLEpxXbaab3gQf8JcJLoifqkTe6wR0VMPJehtgZnc2tq4lKGSTXGBmCy28qi0mJM3aXNKvLb1L37PAhoRzKKATMDeaCY6xVvjtm9lFwEWSLkqt1BvhHknHE4KZ6s1cls5V9A7CfzEC+FTSn8lnEBYASUcT7MCPEv6byxVmmbomsZxhBGUMMMESeXZFKnJ/StrdzB4luIwOLzZxpLo/M5QakE+CmT0haTvChCYjCf/9DMIkOske9FXVowdQCOU/jHADvkNIhdon6UmR5hNePUsZyczMvpNIziSCS+CbCnOrPgJcBGxNmPDg6BRyMvKuIowxPBiX9yTEB4wDfmVm2yeQ0YY416qZXaAwiUoXM3umtXUXyXmtRLFZQldRBQ1S8H7Zm+BtcRRwv6XPYDoL2NHihDfxDe8pS5hfX9LFhN7ijbHoUEK63TMSyqjE/XmemY1Rwwm1CyS7P0vIXTPWn/S/rwRVp+izSBpIuFgPAuZYotns8wi8aURONg3qJcBnZvaDqCynWYKskkXyppjZwFJlkqaZWb8EMq4k2IF3N7OektYmjHls29q6VyYxoG0IcUDWzNZNXP9fgaGFt7gYrHe/mX0toYzpQD8z+ywu1xGmr0t6nWXk5XJ/ZurvbtH9uamyBHJ6A38ECqbPd4EjLZ8J3HOh2kw3DTCzKcAUSaey7HU0BQmHu8uWszshaAILrnV5yHtP0uksy+c+AvhPvOGTzGoPbG9mAyQ9B2Bm/4lKKymZILONzGxU6iCzYuI4xj0Ek1Gy6SQlfT/+fAOYlDERDSfMaJSaTiyLjO6YQ/315Hh/FriD5ROB3U4YmE/JWOD7ZjYeQNJg4GrSZZfNnapW9AUsvJaknKbsWyqdS2Vn4E1Ll5f+UUnjCFP6rU2wzyKpC2EQMzWHERKb3UV4yDwRy+qAgxPJWBIfHAVX0c6ke4hkKQxeFW621ClqG8VCVsNUFGy+/6Rh+uM/J5RR4CLgOYWJSERQvrmPp6S+P6N5qBfLj6WtRSZ9RELaF5Q8gJlNUMh9lQvxjb6Dmb2frM5qNt3khaR7CVGE04vKBwJjrGgy71bIEaFX3QUYZ2ZvxPL+wJcLtvRqQtLhNPRpPhA42/ILMKqpILO87cCxE7EtQdFPqjbPHgBJwwkD5cMInjAFFgG3WEgjnFLenwiODH+MRUcAA81sv4QybgJGE7K+TiW8bf3CzNJkl3VFvzySXjSz3o2sq59HstqQtDlwKjkGGUlaDegOfJWgTP4KvJ3QG6Yg56ko48loKtoUuNkSRpIWyWtv+eZTqYgdWCGL6cY0/P8fT1h/G+BAMxuXqs4mZO1gZk9XQM7awHmEeYMFPA6cawkiYzMyplmYN+JwgunpdMJAeZLxk6o03UhaD/gJsL6ZDZW0FbCDmaWayaip179k9tmVwG2E4JLfEXoOeXAnsJ+F/PeFHuTDpLebnksIZNkw+m/vRHBPS4qkHQnnqwOwkUJY/LFmdnxiUbnbgSX9lPC2NYNl5jQjKK4kxPGlEwmeXHnznKQTCGacbMbPpF43UaEnyQvfBKvGAf/9gF+b2ZKUrqlVqeiB6wg22rPi8t8JUXKpFP1kSceY2dXZQklHEV6rqpWlZnZlzjLuAm5TCLXfkPBqfWpqIWb2kKSpLAsyO8VyCDIjZMjci2gisBAWn8fAYiXswPsRBqzzTq/xcByALc5emTod9h+BmYT/53zgcIIPf1Iq8SYM/JYQ5fs88HiMsfli2+glTTazbYvss0ncA2Nd6xECcT5hmWIfSMicuH812jUBJJ1L8G3OK8ioIOcEgitiN0LvN6nNNMqoVIraSWa2fd5jARWyAz8AHJS3H3glYhyinOcsZPqcbmZbxx7xg4kVMAqJ5q4i6IL6N2FLODFQI3JXsURTcVZrj/7DGFBS8OwYBCxMVbmFLHs7KqSKLdjq77MQjZcMSS/QRLRlDv7N34rfp2XFAK2+ATNughB62BsC04BBkgZZ4vzt5JyiNsPr0Xxj0U30ZHLoNQLfIdiB72SZHfjbKSrWsvlvFwPTos9+9kGf1CxhOaaJKKKQumNBHON4i9C5SE1ub8JF900pktw31arov094ld5U0pNAZ3LIRR5fpcc3u+GKs2/8PiF+F3pzhxNuyqTkfAMWh4b/qZHyJJjZY8Bjapii9hqCi11KRgO/ImRenEPI43JCk3usADnbgbPz397d1IYpqGCMw9g4UPojwnF1oMR0fCuKluWGyjPdRuH+2ILgDVX4f75OwrGTqjTdQHitYdnUe7Ms4dR7lUbSk2a2U3Nlrah/dzN7VI3k77F0uXvqgIvN7LRmN04jrzhF7b1mdlIlZKdC0j00/VY3LAeZqxLeVN8ws3dyqP9WwkPlSDPrHf+np1OZVitFNEEZjadCSZlu4yHgG2a2KC6vCdxmZkNS1F9VPfrGFBUhCVgeyYwqRXtJX7GYqS6aClIOxO1KCMYq5f9vBHNBq7GQxCr31BFQr0y2J3jeXEFI0JU8MEtSd+Aklh+IS6WAL0lUT6Mo5Di63MxmKOSIf5pga/6SpFPN7ObEIjc1sxGSDoUQYBZjRpLQnLkjlZmwgiYogI1oGCT5CQnNUFWl6CmtqAokU1grgaOAa+JNaITxhmQuYmY2Jn4nsfk2w7Q4UHobDT0uUv83C1THUQAAER1JREFU1wKHWc4pagleRL8npD9I/iCJJqi82dnMRsff3wb+bmb7KaRFfoAwqJ2SvCfSycUcWIykbYHXC84Xko4kTKTyL4IffUonhj8Cz8RBeQP2B/6QqvKqNd3UIpLWIvwnyQaWi+ov1RNaSAjMmJZIRq4ZBSX9wMx+Fn8flI24lfQTM/thCjmZOidZgqyeTdQ/HOhqZlcU5BHGnAB+YGa3J5CR9Ri6j2ASuK54XSok7QGcTZjs+iFijIOZTUgpJ28kPQt8zczeiy61txDe7voBPc0s6bigpG0IQVkAj1uY6S5N3dWo6KPHzRjCSTFCzpbzLaZ4rTYqEABWkHMTwU30nli0DzCZkEr2toIC/TyjTGZRFWUZLV5OJO8woAdBYWUH4p5NVP+TwCFm9npcnkaI+G1PmM3sqwlkjCd4Kb1BcC7Y0szeiuNcL5rZlq2VUUJmJSbS2ZwwMcx6cSxga2CYmV2YqP56N1pJVwDzzOzcuJzMnTsjrw5Yj4Ymwn+nqLvaTDcFbiGMSH8jLh9OcK9LltK1wlxHvgFgBdYBBhT8qCWNIWT724UweNZqRa8wefZR5BetqEZ+l1pOQR/gmwTPnmw0aSpf7bYFJR95InZY5icMmDoWuIyQU+m7mTiQrwL3JZJRT2acZm783iiaJf+Vyi88cjXBVfi3AGY2PXZmkih6oC7jy/5VYFRmXVLdKekkQuf1bcL4iQjX2Rc3BQLwJTO7ILN8oaRkgSUrgXXNbJzCdHyY2VJJedieiwd8lgAbx8GyVDbUvKMVrZHfpZZTsD+wiaWf7avA2tkFMzsxs9iZNGwDHF78xmshaV4eifN+Q/CCmk5QWL3j73UkjTazhxLJWcPMnika5035ILmZ4ML7LvARYeJ2JG1GwridyCkEF9RcrBLVqujHSzqEZfk0DiSHnkkFyTUALMNNwESFnOcQBrdvjj3HlxLJ2MzMDpI03Myujz2slMqkr6T3CQpk9fibuJxHitrnCTnck7shRiapdLqNY0mXj35jQlqKVQlJ5h4gTDydl912NnCUxYRs0RR5GnABwWEilaJ/Nw70Fu6bA1n2FtFqzOzHMbisC2HynML5akOw1afkdfK554Eqs9FLWsQyv9b2LAtHrgM+MLPUwTIVIb7qXk7o+bxIDACzojTJrZQhoCvwZZZl4XvCwuQQyZD0jJltJ+lx4HhCtOIzKX2OK4mkCYTX58k0tNEnca+U9GWCZ89/CSkQIPTAVyMkh3s7hZwoa02CeXMIYRLylwnuqQ8mlrOc/VrLsjOmTFWyCSEZ3I6EuWpfI7y5/CtF/ZVE0u8JcUH30fA6S+IqWlWKvpapRACYpKlmljqLZLGMowkz/2xNGHfoAJxjZlflKTcvJO1aqjy1W6Sk3QnjGgAzLHG6jUZkbgUMJUyNuFfCescB82k4k9m6hLGOJyzxtJLxjbQNwbwywsxubGaXzx1xvGw5zOy8JPVXk6KXtKWZzWwsKCeVJ0SlkXQQ8BczWyTpbIJ988LUxxM9B64zs8kp6611oldUQTk9k0c0aSVo5L5ZSOJB0uhDfzyZN0eC3f5jgl29VUnVohvyCYS0FH8GHonLpwLPm9nw1tRfi1Sboh9rIXdGqfwzZomz1lUKLcu+9xXCdG+XEGa4Suq/LeklwlvDbEIwkwjnrdUj+5WKVqw0kg4Gfg5MIJyvnYHTUvi3VxpJE2lkkBRIMkgaXQQftISTmpeQ8WeCqeZpgjfM2oTMsqekigepNFGnLaeMU+m0qhqMNbOCe9NQK8pSGN36qpXCWMM+wJVm9meFlMKpGZpDnQUuIWSrfIBgY6zUBOt5cxawbaEXrzAH7iMEt9RqYzY5D5JaSIOxWFLHvAL/CF5QfQAk/Y4wG9dGFvPEVCnZORvaEVzHk71lVZWiz/AUy8/+XqqsWnhD0m8JA2U/VZiOr01qIWb2r/jW0MPMro1Kq0Oi6gcAhxAeVlMJrml/zdGzo1K0KTLVzCeH/6ZCbGmZqQnN7CVJ/c3sVaVLRQPBRPOCpIdpmAYjVXbO+vGr+GB5rcqVfKnc9k9KSjYOVFWKXiE3xwYEt7r+LOs1rgWssdIa1noOJnhCXGJmCxSm30ueATIO+AwkmG+uBVYFbiCEqLeK+Mo8DThDISnbocDlkk43s9xT4+bIXyQ9yLJ8MCMIby3VyCxJV9JwkPTvsWORcvD/PvJ1dy642EJDN9uCKbLqvO+0LCUyhI7ENsD/JKu/mjpckr5FmBd0IMHdraDo3weutyrNXhl9geeY2X8V5grdGviDmS1ILGca0B941pblPpmewkafkdGZ8OA6iKA8fmRmE1PVvzJQyJpaPzG0mf2pmV0+l+Q9SFpC1kZmNitVnbWMGs7KtZTgKnq+xYy2ra6/mhQ9gMIs84dWowtVY0QFPJCQlvRBwuQDW5jZ3onlFHzcnzWzAdEt7elEg7HfJvQQ2xHs1+Oq1Tsli0Ka4rmFMaGowNYzs9krtWGfYyR9nTBm09b+v71zj5WrqsL47ysgaAAxYjCElBYRFUEURS0vxQjUNBDFSHhYUQnBGAOtDyJExYCgQQ01hMirKAVFXoIgFKghBREVKQRB8QUVkBBFI1AtAbGff+w9dDqMt/fO7Dnn7un6JZN7Hndmr3vn3jXnrMe37NmS3kxyWsW19WtH0sxSejYTUV2s0Ulz/Ni27SjMmlzedgiwyPZCUjdeaS7PuYCtJB1DSiqev57nTJbFJJtXkeQPLpB0bedRaI02uIJ15Yn/m49Vh6S9JC2T9AdJD3UeI1jqy6SGrCfhhbBek9ruNXFNZ0PSVaNapKoYfRdNTZlviv8oDWn4CGs19zcpvYjtbyhJyD5NitN/yfayQi+/X6HXmW5s3K1zY/s5pdmxNbIYWEjPkOsR8Lztp3oSvHWFDpqj+5c0su7xWh19Rwmxe3ZnkSHXLfEx0mzS02yvzOGCS0axkO1lSprnG0NKApX4gCzdKTqNeELSwZ2EspJ+fHHJ3YZ4ynYTieT7leSdN1KaF3scqSoueDETifQVo7oY/bjSRPIqC2WdQmoVX8PaKoVaPyBHTk6Ufw/YlvT7epQ0C/VPrRo2AJK+RtKF+iEj0NbvWudlpP6DA0i/s5uAU3t7XwJQUqntNC++FFjdOUXBCqIqHb2amzLfCE0lryT9kTTQpNYr0taQtDnp/6Xaeu1x6ygPJk+toZvvkOKMe+b9v5ASZFU6etYmr5ZDSl7l8E1pHmTtFcNIkLSL7ftHuUaT5BrzD5KHg3fizrZPadGsgbA90jzK+pLuUXXTHrU6+pFOmW+BppJXJwJ35Bh99617qY5FgHNysvK7wPdL9wK0wI/Ic3UpO+C6cZSmPJ1MmigGcCvpzrGUVMEcUmjrUuCXjI8MRvXU6uhHPWW+aZpKXp0L3ALcx7olg8WwvXf+GT4O3CXpTtLs01LVPU2zne25bRtRiAtJ8w4OzfvzSXfHhxR6/VcD+5O6oo8gdcde2i27ELRDrTH6A0jJnqqnzHfoSV5BSl59pXTyStIdtvdc/3cWWWsj4P2kWaWd9vSTautelnQecJbt+9q2ZVg0wUCQEay1Kcnhf51013BW6TWCyVOlowcamTLfBE3IunatdRrwMHAd64ZuivUfSHoTqVx0HrAMWGz7bknbkrpwty+1VhNkaecdSS3pHVXOItLOTSPp5ySJ5dvz/l4kfaU5BdfYlPTeH07Ka1wLXGj7sVJrBFOnSkefkz6XAtfa/vf6vn+6k3+e+SOUde2ss7LP4aLllUojBM8HrrT9TM+5+bYvLrVWE0jq+8HkOsfV7QYsAV6eD/0TOMqFRlZKuoikcb8U+ME4JeVrp1ZH/y6Srso80gDly4Af11qnqzR67Z2kK+BRyLo2hqQFthf1HDve9rfasmkQetQEX0TFXdidCU3Yfrrf+zXE665h7d9vt2OpVlVyXKjS0XfIYY/3AMcAc2v9Q8qqnL3Y9pJCr3+C7TPy9odsX9F17nTbJ5VYJ7/e3bZ37zl2T0ctsxby3U9nEH0vY9NkJukR2zPbtiMYLbVW3XQ6SQ8iXdnvDlzUrkVDsVXvFa+k4wu+/mHAGXn7RNYV5ZoLDO3oc6nrEcDsnnrqLUjDOqrC9oYiwhUlkBsAVTp6SZcB7wBuBM4GlmdVy1o5CugNbXy0z7FB0f/Z7rc/KHcAjwNbA9/sOr6KNJc0mJ7Ue0sfTJoqHT2p9vcI26NU4Bs5E1wFb0nZq+CJhJOK/KPn5OTDpKaZYBohaRX93+eOvkow5lQbo1caVzeLrg+rUjHtpsgVHbOBrwKf7zq1Cvh11qgvsc5Ewkmb2R5aElnS7blZqtepRCIuCFqmSkcv6WLgNaQZpZ2retdYpQKQJz09Y3uNpJ2A1wNLbZec4xlMgXGuugk2PGp19A8AO7tG4/sgaQWwD/AK4BfAXcBq20e2atgASOpbwdHEuLSS9FTdzCTVnAvYCnhkA0rWBmNArTH6+0m6Go+3bUghZHu1pKNJ7fZnSLqnbaMG5Pqu7c1IoanfA29sx5zB6DhySeeQGvNuyPvvA0bexRwEJanV0W8N/DYLZnW38tcqgypJc4AjgaPzsSrfG9u7du9L2p26Z/zuYfsTnR3bSyWd2qZBQTBVqnQmJP32cWIBqb79atu/kbQD0G9IRHVknZs92rZjCP4u6Quk0Y4GPkyFfQHBhk2VMXoASdsAHQdyp+2/tWlPkJD06a7dGaRmtlfaPrAlk4YiJ2U7Gu4GbiOpMUYyNqiGKh29pENJ8qfLSQmyfUiqfFe2addUkbTI9gJJ19GnzrnGUJSkk7t2nwf+DFxVqw5RB0mb2/5X23YEwSDU6ujvBfbvXMVLehXwE9u7tWvZ1JD0Vtsrskjbi7B9a9M2BeuS+zUuADa3PTMrQB5r+5MtmxYEk6bWGP2MnlDNP0hhgqqwvSJ/vTV/WGH7iXatGo4xnBt6JnAgSVcd2/dK2nfipwTB9KJWR3+jpJtImvSQhM2WtmjPQOQ5tycDnyKFoGZIep5UYlnd8OnMSlLp6yV5/3BS+OamtgwaFtuP9szzrVp6I9jwqNLR2/6cpEOAvUkO8jzbV7ds1iAsII1B3MP2SoBccfNtSQttn9mqdYPxFtvdV7zXSbqtpBRywzyawzfOQ8+PAx5o2aYgmBJVxegl7QhsY/tnPcf3BR6z/WA7lg1Gborav3cMYg7j3Fybhju80LU8z/ZDeX82cIPtN7Rr2WBI2pqkIvpe0kXFzcDxtqPEMqiG2q7oF9FfO311PndQs+YMzSb9Zt3afkLS0EJjLbEQWC7pobw/i7obpmb0SlFIeh1RSx9URG2Ofla/+Za275I0q3lzhua5Ac9NW2zfKOm1JGE2gN/Zfnai50xzfirpi7YvB5D0GVL38s7tmhUEk6e2SpXNJjhXo672bpKe7vNYBey63mdPIySd0LV7sO178+NZSae3ZtjwvBuYL+mKPPh8J+Dt7ZoUBFOjNkf/K0nH9B7MYmArWrBnKGxvZHvLPo8tSmjEN8xhXdsn9pyb26QhJbH9OGmS2RxSGGpJNE4FtVFb6GYBcLWkI1nr2N8GvAT4QGtWBdDMuMLGkbSMpJK6C7AdcGGuIvpsu5YFweSpytHb/iuwp6T9SP94ANfbvqVFs4LEyMcVtsTZtq/J20/mUsveO5YgmNZUVV4ZTF+aGFcYBMFghKMPgj7EDNxgnAhHHwR9kLS97YfbtiMISlBb1U0QNMULkhqSrmrTkCAYlnD0QdCf7kqhHVqzIggKEI4+CPozURVREFRFxOiDoA/rqSKKZGxQFeHogyAIxpwI3QRBEIw54eiDIAjGnHD0QRAEY044+iAIgjEnHH0QBMGYE44+CIJgzPkfidKFGvRs5IIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "comparison = pd.concat([std, semi_std], axis=1)\n",
    "comparison.columns = [\"Standard Deviation\", \"Semi-Deviation\"]\n",
    "comparison.plot.bar(title=\"Standard Deviation vs Semideviation\")"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "## Value at Risk (VaR) and Conditional VaR \n",
    "\n",
    "We will try three different methods to calculate the VaR\n",
    "\n",
    "* Historical VaR\n",
    "* Parametric VaR - Gaussian \n",
    "* Modified Cornish-Fisher VaR"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "### Historic VaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.01576, -0.03169, -0.01966, -0.04247, -0.00814, -0.02535,\n",
       "       -0.00787, -0.01499, -0.02598, -0.01047, -0.01174, -0.06783,\n",
       "       -0.02047])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(hfi_data, 5, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def var_historic(r, level=5):\n",
    "    '''\n",
    "    ARG\n",
    "        r: Dataframe with the returns\n",
    "        level: percentile level\n",
    "    Returns \n",
    "        percentile for each column\n",
    "    '''\n",
    "    # Check the type of data\n",
    "    if isinstance(r, pd.DataFrame):\n",
    "        return r.aggregate(var_historic, level=level)\n",
    "    \n",
    "    elif isinstance(r, pd.Series):\n",
    "        return -np.percentile(r, level)\n",
    "    else: \n",
    "        raise TypeError(\"Expected r to be a series or dataframe\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Convertible Arbitrage     0.01576\n",
       "CTA Global                0.03169\n",
       "Distressed Securities     0.01966\n",
       "Emerging Markets          0.04247\n",
       "Equity Market Neutral     0.00814\n",
       "Event Driven              0.02535\n",
       "Fixed Income Arbitrage    0.00787\n",
       "Global Macro              0.01499\n",
       "Long/Short Equity         0.02598\n",
       "Merger Arbitrage          0.01047\n",
       "Relative Value            0.01174\n",
       "Short Selling             0.06783\n",
       "Funds Of Funds            0.02047\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_historic(hfi_data, level=5) "
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "#### Parametric VaR - Gaussian \n",
    "\n",
    "z-score = $ \\frac{x - \\mu}{\\sigma} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.6448536269514729"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the z score assuming the data is gaussian \n",
    "# Percent point function\n",
    "z = norm.ppf(0.05)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Convertible Arbitrage     0.021691\n",
       "CTA Global                0.034235\n",
       "Distressed Securities     0.021032\n",
       "Emerging Markets          0.047164\n",
       "Equity Market Neutral     0.008850\n",
       "Event Driven              0.021144\n",
       "Fixed Income Arbitrage    0.014579\n",
       "Global Macro              0.018766\n",
       "Long/Short Equity         0.026397\n",
       "Merger Arbitrage          0.010435\n",
       "Relative Value            0.013061\n",
       "Short Selling             0.080086\n",
       "Funds Of Funds            0.021292\n",
       "dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the gaussian VaR\n",
    "var_gauss = -(hfi_data.mean() + z*hfi_data.std(ddof=0))\n",
    "var_gauss"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "#### Cornish Fisher VaR (Non Gaussian)\n",
    "Adjustments made for Skewness and Kurtosis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make a skewness function \n",
    "def skewness(r):\n",
    "    '''\n",
    "        ARGS:\n",
    "            Series or Dataframe\n",
    "        \n",
    "        RETURNS: \n",
    "            Float or a series data with the calculated skewness\n",
    "    '''\n",
    "    \n",
    "    # Calculate the demeaned returns \n",
    "    demeaned_r = r - r.mean()\n",
    "    \n",
    "    # Use the population standard deviation, ddof=0\n",
    "    sigma_r = r.std(ddof=0)\n",
    "    \n",
    "    # Calculate the expectation of the demeaned returns raised to the third power\n",
    "    exp = (demeaned_r**3).mean()\n",
    "    \n",
    "    # Calcualte the skew\n",
    "    skew = exp/sigma_r**3\n",
    "    return skew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make a kurtosis function \n",
    "def kurtosis(r):\n",
    "    '''\n",
    "        ARGS:\n",
    "            Series or Dataframe\n",
    "        \n",
    "        RETURNS: \n",
    "            Float or a series data with the calculated kurtosis\n",
    "    '''\n",
    "    \n",
    "    # Calculate the demeaned returns \n",
    "    demeaned_r = r - r.mean()\n",
    "    \n",
    "    # Use the population standard deviation, ddof=0\n",
    "    sigma_r = r.std(ddof=0)\n",
    "    \n",
    "    # Calculate the expectation of the demeaned returns raised to the fourth power\n",
    "    exp = (demeaned_r**4).mean()\n",
    "    \n",
    "    # Calcualte the skew\n",
    "    kurt = exp/sigma_r**4\n",
    "    return kurt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update z \n",
    "k = kurtosis(hfi_data)\n",
    "s = skewness(hfi_data)\n",
    "z = norm.ppf(0.05)\n",
    "z = (z + (z**2 - 1)*s/6 + (z**3 - 3*z)*(k-3)/24 - (2 * z**3 - 5*z)*(s**2)/36)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Convertible Arbitrage     0.025166\n",
       "CTA Global                0.033094\n",
       "Distressed Securities     0.025102\n",
       "Emerging Markets          0.053011\n",
       "Equity Market Neutral     0.010734\n",
       "Event Driven              0.025516\n",
       "Fixed Income Arbitrage    0.017881\n",
       "Global Macro              0.013581\n",
       "Long/Short Equity         0.027935\n",
       "Merger Arbitrage          0.012612\n",
       "Relative Value            0.016157\n",
       "Short Selling             0.066157\n",
       "Funds Of Funds            0.021576\n",
       "dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mcf_var = -(hfi_data.mean() + z*hfi_data.std(ddof=0))\n",
    "mcf_var"
   ]
  },
  {
   "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>Skewness</th>\n",
       "      <th>Kurtosis</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Convertible Arbitrage</th>\n",
       "      <td>-2.639592</td>\n",
       "      <td>23.280834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CTA Global</th>\n",
       "      <td>0.173699</td>\n",
       "      <td>2.952960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Distressed Securities</th>\n",
       "      <td>-1.300842</td>\n",
       "      <td>7.889983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Emerging Markets</th>\n",
       "      <td>-1.167067</td>\n",
       "      <td>9.250788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Equity Market Neutral</th>\n",
       "      <td>-2.124435</td>\n",
       "      <td>17.218555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Event Driven</th>\n",
       "      <td>-1.409154</td>\n",
       "      <td>8.035828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fixed Income Arbitrage</th>\n",
       "      <td>-3.940320</td>\n",
       "      <td>29.842199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Global Macro</th>\n",
       "      <td>0.982922</td>\n",
       "      <td>5.741679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Long/Short Equity</th>\n",
       "      <td>-0.390227</td>\n",
       "      <td>4.523893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Merger Arbitrage</th>\n",
       "      <td>-1.320083</td>\n",
       "      <td>8.738950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Relative Value</th>\n",
       "      <td>-1.815470</td>\n",
       "      <td>12.121208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Short Selling</th>\n",
       "      <td>0.767975</td>\n",
       "      <td>6.117772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Funds Of Funds</th>\n",
       "      <td>-0.361783</td>\n",
       "      <td>7.070153</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        Skewness   Kurtosis\n",
       "Convertible Arbitrage  -2.639592  23.280834\n",
       "CTA Global              0.173699   2.952960\n",
       "Distressed Securities  -1.300842   7.889983\n",
       "Emerging Markets       -1.167067   9.250788\n",
       "Equity Market Neutral  -2.124435  17.218555\n",
       "Event Driven           -1.409154   8.035828\n",
       "Fixed Income Arbitrage -3.940320  29.842199\n",
       "Global Macro            0.982922   5.741679\n",
       "Long/Short Equity      -0.390227   4.523893\n",
       "Merger Arbitrage       -1.320083   8.738950\n",
       "Relative Value         -1.815470  12.121208\n",
       "Short Selling           0.767975   6.117772\n",
       "Funds Of Funds         -0.361783   7.070153"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the skewness and kurtosis \n",
    "stats = pd.concat([s, k], axis=1)\n",
    "stats.columns = [\"Skewness\", \"Kurtosis\"]\n",
    "stats"
   ]
  },
  {
   "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>Gaussian</th>\n",
       "      <th>Cornish-Fisher</th>\n",
       "      <th>Historic</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Convertible Arbitrage</th>\n",
       "      <td>0.021691</td>\n",
       "      <td>0.025166</td>\n",
       "      <td>0.01576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CTA Global</th>\n",
       "      <td>0.034235</td>\n",
       "      <td>0.033094</td>\n",
       "      <td>0.03169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Distressed Securities</th>\n",
       "      <td>0.021032</td>\n",
       "      <td>0.025102</td>\n",
       "      <td>0.01966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Emerging Markets</th>\n",
       "      <td>0.047164</td>\n",
       "      <td>0.053011</td>\n",
       "      <td>0.04247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Equity Market Neutral</th>\n",
       "      <td>0.008850</td>\n",
       "      <td>0.010734</td>\n",
       "      <td>0.00814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Event Driven</th>\n",
       "      <td>0.021144</td>\n",
       "      <td>0.025516</td>\n",
       "      <td>0.02535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fixed Income Arbitrage</th>\n",
       "      <td>0.014579</td>\n",
       "      <td>0.017881</td>\n",
       "      <td>0.00787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Global Macro</th>\n",
       "      <td>0.018766</td>\n",
       "      <td>0.013581</td>\n",
       "      <td>0.01499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Long/Short Equity</th>\n",
       "      <td>0.026397</td>\n",
       "      <td>0.027935</td>\n",
       "      <td>0.02598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Merger Arbitrage</th>\n",
       "      <td>0.010435</td>\n",
       "      <td>0.012612</td>\n",
       "      <td>0.01047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Relative Value</th>\n",
       "      <td>0.013061</td>\n",
       "      <td>0.016157</td>\n",
       "      <td>0.01174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Short Selling</th>\n",
       "      <td>0.080086</td>\n",
       "      <td>0.066157</td>\n",
       "      <td>0.06783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Funds Of Funds</th>\n",
       "      <td>0.021292</td>\n",
       "      <td>0.021576</td>\n",
       "      <td>0.02047</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        Gaussian  Cornish-Fisher  Historic\n",
       "Convertible Arbitrage   0.021691        0.025166   0.01576\n",
       "CTA Global              0.034235        0.033094   0.03169\n",
       "Distressed Securities   0.021032        0.025102   0.01966\n",
       "Emerging Markets        0.047164        0.053011   0.04247\n",
       "Equity Market Neutral   0.008850        0.010734   0.00814\n",
       "Event Driven            0.021144        0.025516   0.02535\n",
       "Fixed Income Arbitrage  0.014579        0.017881   0.00787\n",
       "Global Macro            0.018766        0.013581   0.01499\n",
       "Long/Short Equity       0.026397        0.027935   0.02598\n",
       "Merger Arbitrage        0.010435        0.012612   0.01047\n",
       "Relative Value          0.013061        0.016157   0.01174\n",
       "Short Selling           0.080086        0.066157   0.06783\n",
       "Funds Of Funds          0.021292        0.021576   0.02047"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compare all three by plotting \n",
    "results = [var_gauss, mcf_var, var_historic(hfi_data, level=5)]\n",
    "comparison=pd.concat(results, axis=1)\n",
    "comparison.columns = [\"Gaussian\", \"Cornish-Fisher\", \"Historic\"]\n",
    "comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Value at Risk')"
      ]
     },
     "execution_count": 20,
     "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": [
    "\n",
    "# Plot the comparison DataFrame\n",
    "ax = comparison.plot.bar(title=\"Hedge Fund Indices: VaR\")\n",
    "ax.set_xlabel(\"Indices\")\n",
    "ax.set_ylabel(\"Value at Risk\")"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "source": [
    "### Conditional VaR or Beyond VaR\n",
    "\n",
    "$$ CVaR = -E(R| R \\leq VaR) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a cvar function \n",
    "def cvar_historic(r, level=5):\n",
    "    \"\"\"\n",
    "        Computes the conditional VaR of Series or DataFrame\n",
    "    \"\"\"\n",
    "    \n",
    "    if isinstance(r, pd.Series): \n",
    "        is_beyond = r <= -var_historic(r, level=5) \n",
    "        return -r[is_beyond].mean()\n",
    "    elif isinstance(r, pd.DataFrame):\n",
    "        return r.aggregate(cvar_historic, level=level)\n",
    "    else: \n",
    "        raise TypeError(\"Expected a dataframe or series\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Convertible Arbitrage     0.036550\n",
       "CTA Global                0.041264\n",
       "Distressed Securities     0.036429\n",
       "Emerging Markets          0.072364\n",
       "Equity Market Neutral     0.016879\n",
       "Event Driven              0.038336\n",
       "Fixed Income Arbitrage    0.028257\n",
       "Global Macro              0.020629\n",
       "Long/Short Equity         0.041943\n",
       "Merger Arbitrage          0.019143\n",
       "Relative Value            0.024650\n",
       "Short Selling             0.096821\n",
       "Funds Of Funds            0.033207\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cvar_historic(hfi_data, level=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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