Quiz2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_hfi_returns():\n",
    "    \"\"\"\n",
    "    Load and format the EDHEC Hedge Fund Index Returns\n",
    "    \"\"\"\n",
    "    hfi = pd.read_csv(\"data/edhec-hedgefundindices.csv\",\n",
    "                      header=0, index_col=0, parse_dates=True)\n",
    "    hfi = hfi/100\n",
    "    hfi.index = hfi.index.to_period('M')\n",
    "    return hfi\n",
    "\n",
    "\n",
    "\n",
    "hfi = get_hfi_returns()\n",
    "hfi.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>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>2000-01</th>\n",
       "      <td>0.0227</td>\n",
       "      <td>0.0128</td>\n",
       "      <td>0.0088</td>\n",
       "      <td>0.0077</td>\n",
       "      <td>0.0075</td>\n",
       "      <td>0.0088</td>\n",
       "      <td>0.0041</td>\n",
       "      <td>0.0021</td>\n",
       "      <td>0.0075</td>\n",
       "      <td>0.0143</td>\n",
       "      <td>0.0173</td>\n",
       "      <td>0.0427</td>\n",
       "      <td>0.0169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02</th>\n",
       "      <td>0.0267</td>\n",
       "      <td>-0.0022</td>\n",
       "      <td>0.0421</td>\n",
       "      <td>0.0528</td>\n",
       "      <td>0.0253</td>\n",
       "      <td>0.0346</td>\n",
       "      <td>0.0097</td>\n",
       "      <td>0.0408</td>\n",
       "      <td>0.0699</td>\n",
       "      <td>0.0239</td>\n",
       "      <td>0.0185</td>\n",
       "      <td>-0.1340</td>\n",
       "      <td>0.0666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03</th>\n",
       "      <td>0.0243</td>\n",
       "      <td>-0.0138</td>\n",
       "      <td>0.0103</td>\n",
       "      <td>0.0318</td>\n",
       "      <td>0.0134</td>\n",
       "      <td>0.0069</td>\n",
       "      <td>-0.0061</td>\n",
       "      <td>-0.0104</td>\n",
       "      <td>0.0006</td>\n",
       "      <td>0.0131</td>\n",
       "      <td>0.0163</td>\n",
       "      <td>-0.0230</td>\n",
       "      <td>0.0039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04</th>\n",
       "      <td>0.0223</td>\n",
       "      <td>-0.0241</td>\n",
       "      <td>-0.0101</td>\n",
       "      <td>-0.0541</td>\n",
       "      <td>0.0168</td>\n",
       "      <td>-0.0059</td>\n",
       "      <td>-0.0006</td>\n",
       "      <td>-0.0304</td>\n",
       "      <td>-0.0201</td>\n",
       "      <td>0.0188</td>\n",
       "      <td>0.0092</td>\n",
       "      <td>0.1028</td>\n",
       "      <td>-0.0269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05</th>\n",
       "      <td>0.0149</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>-0.0132</td>\n",
       "      <td>-0.0433</td>\n",
       "      <td>0.0062</td>\n",
       "      <td>-0.0034</td>\n",
       "      <td>0.0107</td>\n",
       "      <td>-0.0070</td>\n",
       "      <td>-0.0097</td>\n",
       "      <td>0.0146</td>\n",
       "      <td>0.0080</td>\n",
       "      <td>0.0704</td>\n",
       "      <td>-0.0122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-07</th>\n",
       "      <td>0.0021</td>\n",
       "      <td>-0.0058</td>\n",
       "      <td>0.0093</td>\n",
       "      <td>0.0040</td>\n",
       "      <td>-0.0010</td>\n",
       "      <td>0.0055</td>\n",
       "      <td>0.0022</td>\n",
       "      <td>-0.0014</td>\n",
       "      <td>0.0067</td>\n",
       "      <td>-0.0021</td>\n",
       "      <td>0.0045</td>\n",
       "      <td>-0.0052</td>\n",
       "      <td>0.0018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-08</th>\n",
       "      <td>0.0024</td>\n",
       "      <td>0.0166</td>\n",
       "      <td>0.0002</td>\n",
       "      <td>-0.0277</td>\n",
       "      <td>0.0004</td>\n",
       "      <td>0.0011</td>\n",
       "      <td>0.0017</td>\n",
       "      <td>-0.0007</td>\n",
       "      <td>0.0035</td>\n",
       "      <td>0.0050</td>\n",
       "      <td>-0.0002</td>\n",
       "      <td>-0.0214</td>\n",
       "      <td>0.0015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09</th>\n",
       "      <td>0.0034</td>\n",
       "      <td>-0.0054</td>\n",
       "      <td>0.0050</td>\n",
       "      <td>-0.0110</td>\n",
       "      <td>-0.0016</td>\n",
       "      <td>0.0032</td>\n",
       "      <td>0.0036</td>\n",
       "      <td>0.0006</td>\n",
       "      <td>-0.0023</td>\n",
       "      <td>0.0028</td>\n",
       "      <td>0.0018</td>\n",
       "      <td>0.0036</td>\n",
       "      <td>-0.0022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-10</th>\n",
       "      <td>-0.0073</td>\n",
       "      <td>-0.0314</td>\n",
       "      <td>-0.0158</td>\n",
       "      <td>-0.0315</td>\n",
       "      <td>-0.0129</td>\n",
       "      <td>-0.0257</td>\n",
       "      <td>-0.0023</td>\n",
       "      <td>-0.0096</td>\n",
       "      <td>-0.0402</td>\n",
       "      <td>-0.0080</td>\n",
       "      <td>-0.0109</td>\n",
       "      <td>0.0237</td>\n",
       "      <td>-0.0269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-11</th>\n",
       "      <td>-0.0068</td>\n",
       "      <td>-0.0053</td>\n",
       "      <td>-0.0193</td>\n",
       "      <td>0.0120</td>\n",
       "      <td>-0.0211</td>\n",
       "      <td>-0.0034</td>\n",
       "      <td>-0.0067</td>\n",
       "      <td>-0.0087</td>\n",
       "      <td>-0.0044</td>\n",
       "      <td>0.0119</td>\n",
       "      <td>-0.0063</td>\n",
       "      <td>-0.0021</td>\n",
       "      <td>-0.0071</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>227 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Convertible Arbitrage  CTA Global  Distressed Securities  \\\n",
       "date                                                                \n",
       "2000-01                 0.0227      0.0128                 0.0088   \n",
       "2000-02                 0.0267     -0.0022                 0.0421   \n",
       "2000-03                 0.0243     -0.0138                 0.0103   \n",
       "2000-04                 0.0223     -0.0241                -0.0101   \n",
       "2000-05                 0.0149      0.0114                -0.0132   \n",
       "...                        ...         ...                    ...   \n",
       "2018-07                 0.0021     -0.0058                 0.0093   \n",
       "2018-08                 0.0024      0.0166                 0.0002   \n",
       "2018-09                 0.0034     -0.0054                 0.0050   \n",
       "2018-10                -0.0073     -0.0314                -0.0158   \n",
       "2018-11                -0.0068     -0.0053                -0.0193   \n",
       "\n",
       "         Emerging Markets  Equity Market Neutral  Event Driven  \\\n",
       "date                                                             \n",
       "2000-01            0.0077                 0.0075        0.0088   \n",
       "2000-02            0.0528                 0.0253        0.0346   \n",
       "2000-03            0.0318                 0.0134        0.0069   \n",
       "2000-04           -0.0541                 0.0168       -0.0059   \n",
       "2000-05           -0.0433                 0.0062       -0.0034   \n",
       "...                   ...                    ...           ...   \n",
       "2018-07            0.0040                -0.0010        0.0055   \n",
       "2018-08           -0.0277                 0.0004        0.0011   \n",
       "2018-09           -0.0110                -0.0016        0.0032   \n",
       "2018-10           -0.0315                -0.0129       -0.0257   \n",
       "2018-11            0.0120                -0.0211       -0.0034   \n",
       "\n",
       "         Fixed Income Arbitrage  Global Macro  Long/Short Equity  \\\n",
       "date                                                               \n",
       "2000-01                  0.0041        0.0021             0.0075   \n",
       "2000-02                  0.0097        0.0408             0.0699   \n",
       "2000-03                 -0.0061       -0.0104             0.0006   \n",
       "2000-04                 -0.0006       -0.0304            -0.0201   \n",
       "2000-05                  0.0107       -0.0070            -0.0097   \n",
       "...                         ...           ...                ...   \n",
       "2018-07                  0.0022       -0.0014             0.0067   \n",
       "2018-08                  0.0017       -0.0007             0.0035   \n",
       "2018-09                  0.0036        0.0006            -0.0023   \n",
       "2018-10                 -0.0023       -0.0096            -0.0402   \n",
       "2018-11                 -0.0067       -0.0087            -0.0044   \n",
       "\n",
       "         Merger Arbitrage  Relative Value  Short Selling  Funds Of Funds  \n",
       "date                                                                      \n",
       "2000-01            0.0143          0.0173         0.0427          0.0169  \n",
       "2000-02            0.0239          0.0185        -0.1340          0.0666  \n",
       "2000-03            0.0131          0.0163        -0.0230          0.0039  \n",
       "2000-04            0.0188          0.0092         0.1028         -0.0269  \n",
       "2000-05            0.0146          0.0080         0.0704         -0.0122  \n",
       "...                   ...             ...            ...             ...  \n",
       "2018-07           -0.0021          0.0045        -0.0052          0.0018  \n",
       "2018-08            0.0050         -0.0002        -0.0214          0.0015  \n",
       "2018-09            0.0028          0.0018         0.0036         -0.0022  \n",
       "2018-10           -0.0080         -0.0109         0.0237         -0.0269  \n",
       "2018-11            0.0119         -0.0063        -0.0021         -0.0071  \n",
       "\n",
       "[227 rows x 13 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hfi2000 = hfi[\"2000\":]\n",
    "hfi2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.143017693928047\n",
      "4.966909110627918\n"
     ]
    }
   ],
   "source": [
    "def skewness(r):\n",
    "    \"\"\"\n",
    "    Alternative to scipy.stats.skew()\n",
    "    Computes the skewness of the supplied Series or DataFrame\n",
    "    Returns a float or a Series\n",
    "    \"\"\"\n",
    "    demeaned_r = r - r.mean()\n",
    "    # use the population standard deviation, so set dof=0\n",
    "    sigma_r = r.std(ddof=0)\n",
    "    exp = (demeaned_r**3).mean()\n",
    "    return exp/sigma_r**3\n",
    "\n",
    "def kurtosis(r):\n",
    "    \"\"\"\n",
    "    Alternative to scipy.stats.kurtosis()\n",
    "    Computes the kurtosis of the supplied Series or DataFrame\n",
    "    Returns a float or a Series\n",
    "    \"\"\"\n",
    "    demeaned_r = r - r.mean()\n",
    "    # use the population standard deviation, so set dof=0\n",
    "    sigma_r = r.std(ddof=0)\n",
    "    exp = (demeaned_r**4).mean()\n",
    "    return exp/sigma_r**4\n",
    "\n",
    "\n",
    "from scipy.stats import norm\n",
    "def var_gaussian(r, level=5, modified=False):\n",
    "    \"\"\"\n",
    "    Returns the Parametric Gauusian VaR of a Series or DataFrame\n",
    "    If \"modified\" is True, then the modified VaR is returned,\n",
    "    using the Cornish-Fisher modification\n",
    "    \"\"\"\n",
    "    # compute the Z score assuming it was Gaussian\n",
    "    z = norm.ppf(level/100)\n",
    "    if modified:\n",
    "        # modify the Z score based on observed skewness and kurtosis\n",
    "        s = skewness(r)\n",
    "        k = kurtosis(r)\n",
    "        z = (z +\n",
    "                (z**2 - 1)*s/6 +\n",
    "                (z**3 -3*z)*(k-3)/24 -\n",
    "                (2*z**3 - 5*z)*(s**2)/36\n",
    "            )\n",
    "\n",
    "    return -(r.mean() + z*r.std(ddof=0))\n",
    "# What was the Monthly Parametric Gaussian VaR at the 1% level \n",
    "# (as a +ve number) of the Distressed Securities strategy?\n",
    "print(var_gaussian(hfi2000[\"Distressed Securities\"],1, False)*100)\n",
    "print(var_gaussian(hfi2000[\"Distressed Securities\"],1, True)*100)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.2642"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def var_historic(r, level=5):\n",
    "    \"\"\"\n",
    "    Returns the historic Value at Risk at a specified level\n",
    "    i.e. returns the number such that \"level\" percent of the returns\n",
    "    fall below that number, and the (100-level) percent are above\n",
    "    \"\"\"\n",
    "    if isinstance(r, pd.DataFrame):\n",
    "        return r.aggregate(var_historic, level=level)\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\") \n",
    "#  What was the Monthly Historic VaR at the 1% level \n",
    "# (as a +ve number) of the Distressed Securities strategy?    \n",
    "var_historic(hfi2000[\"Distressed Securities\"],1)*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>Food</th>\n",
       "      <th>Beer</th>\n",
       "      <th>Smoke</th>\n",
       "      <th>Games</th>\n",
       "      <th>Books</th>\n",
       "      <th>Hshld</th>\n",
       "      <th>Clths</th>\n",
       "      <th>Hlth</th>\n",
       "      <th>Chems</th>\n",
       "      <th>Txtls</th>\n",
       "      <th>...</th>\n",
       "      <th>Telcm</th>\n",
       "      <th>Servs</th>\n",
       "      <th>BusEq</th>\n",
       "      <th>Paper</th>\n",
       "      <th>Trans</th>\n",
       "      <th>Whlsl</th>\n",
       "      <th>Rtail</th>\n",
       "      <th>Meals</th>\n",
       "      <th>Fin</th>\n",
       "      <th>Other</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1926-07</th>\n",
       "      <td>0.0056</td>\n",
       "      <td>-0.0519</td>\n",
       "      <td>0.0129</td>\n",
       "      <td>0.0293</td>\n",
       "      <td>0.1097</td>\n",
       "      <td>-0.0048</td>\n",
       "      <td>0.0808</td>\n",
       "      <td>0.0177</td>\n",
       "      <td>0.0814</td>\n",
       "      <td>0.0039</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0083</td>\n",
       "      <td>0.0922</td>\n",
       "      <td>0.0206</td>\n",
       "      <td>0.0770</td>\n",
       "      <td>0.0193</td>\n",
       "      <td>-0.2379</td>\n",
       "      <td>0.0007</td>\n",
       "      <td>0.0187</td>\n",
       "      <td>0.0037</td>\n",
       "      <td>0.0520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-08</th>\n",
       "      <td>0.0259</td>\n",
       "      <td>0.2703</td>\n",
       "      <td>0.0650</td>\n",
       "      <td>0.0055</td>\n",
       "      <td>0.1001</td>\n",
       "      <td>-0.0358</td>\n",
       "      <td>-0.0251</td>\n",
       "      <td>0.0425</td>\n",
       "      <td>0.0550</td>\n",
       "      <td>0.0814</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0217</td>\n",
       "      <td>0.0202</td>\n",
       "      <td>0.0439</td>\n",
       "      <td>-0.0238</td>\n",
       "      <td>0.0488</td>\n",
       "      <td>0.0539</td>\n",
       "      <td>-0.0075</td>\n",
       "      <td>-0.0013</td>\n",
       "      <td>0.0446</td>\n",
       "      <td>0.0676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-09</th>\n",
       "      <td>0.0116</td>\n",
       "      <td>0.0402</td>\n",
       "      <td>0.0126</td>\n",
       "      <td>0.0658</td>\n",
       "      <td>-0.0099</td>\n",
       "      <td>0.0073</td>\n",
       "      <td>-0.0051</td>\n",
       "      <td>0.0069</td>\n",
       "      <td>0.0533</td>\n",
       "      <td>0.0231</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0241</td>\n",
       "      <td>0.0225</td>\n",
       "      <td>0.0019</td>\n",
       "      <td>-0.0554</td>\n",
       "      <td>0.0005</td>\n",
       "      <td>-0.0787</td>\n",
       "      <td>0.0025</td>\n",
       "      <td>-0.0056</td>\n",
       "      <td>-0.0123</td>\n",
       "      <td>-0.0386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-10</th>\n",
       "      <td>-0.0306</td>\n",
       "      <td>-0.0331</td>\n",
       "      <td>0.0106</td>\n",
       "      <td>-0.0476</td>\n",
       "      <td>0.0947</td>\n",
       "      <td>-0.0468</td>\n",
       "      <td>0.0012</td>\n",
       "      <td>-0.0057</td>\n",
       "      <td>-0.0476</td>\n",
       "      <td>0.0100</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.0011</td>\n",
       "      <td>-0.0200</td>\n",
       "      <td>-0.0109</td>\n",
       "      <td>-0.0508</td>\n",
       "      <td>-0.0264</td>\n",
       "      <td>-0.1538</td>\n",
       "      <td>-0.0220</td>\n",
       "      <td>-0.0411</td>\n",
       "      <td>-0.0516</td>\n",
       "      <td>-0.0849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-11</th>\n",
       "      <td>0.0635</td>\n",
       "      <td>0.0729</td>\n",
       "      <td>0.0455</td>\n",
       "      <td>0.0166</td>\n",
       "      <td>-0.0580</td>\n",
       "      <td>-0.0054</td>\n",
       "      <td>0.0187</td>\n",
       "      <td>0.0542</td>\n",
       "      <td>0.0520</td>\n",
       "      <td>0.0311</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0163</td>\n",
       "      <td>0.0377</td>\n",
       "      <td>0.0364</td>\n",
       "      <td>0.0384</td>\n",
       "      <td>0.0160</td>\n",
       "      <td>0.0467</td>\n",
       "      <td>0.0652</td>\n",
       "      <td>0.0433</td>\n",
       "      <td>0.0224</td>\n",
       "      <td>0.0400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Food    Beer   Smoke   Games   Books   Hshld   Clths    Hlth  \\\n",
       "1926-07  0.0056 -0.0519  0.0129  0.0293  0.1097 -0.0048  0.0808  0.0177   \n",
       "1926-08  0.0259  0.2703  0.0650  0.0055  0.1001 -0.0358 -0.0251  0.0425   \n",
       "1926-09  0.0116  0.0402  0.0126  0.0658 -0.0099  0.0073 -0.0051  0.0069   \n",
       "1926-10 -0.0306 -0.0331  0.0106 -0.0476  0.0947 -0.0468  0.0012 -0.0057   \n",
       "1926-11  0.0635  0.0729  0.0455  0.0166 -0.0580 -0.0054  0.0187  0.0542   \n",
       "\n",
       "          Chems   Txtls  ...   Telcm   Servs   BusEq   Paper   Trans   Whlsl  \\\n",
       "1926-07  0.0814  0.0039  ...  0.0083  0.0922  0.0206  0.0770  0.0193 -0.2379   \n",
       "1926-08  0.0550  0.0814  ...  0.0217  0.0202  0.0439 -0.0238  0.0488  0.0539   \n",
       "1926-09  0.0533  0.0231  ...  0.0241  0.0225  0.0019 -0.0554  0.0005 -0.0787   \n",
       "1926-10 -0.0476  0.0100  ... -0.0011 -0.0200 -0.0109 -0.0508 -0.0264 -0.1538   \n",
       "1926-11  0.0520  0.0311  ...  0.0163  0.0377  0.0364  0.0384  0.0160  0.0467   \n",
       "\n",
       "          Rtail   Meals     Fin   Other  \n",
       "1926-07  0.0007  0.0187  0.0037  0.0520  \n",
       "1926-08 -0.0075 -0.0013  0.0446  0.0676  \n",
       "1926-09  0.0025 -0.0056 -0.0123 -0.0386  \n",
       "1926-10 -0.0220 -0.0411 -0.0516 -0.0849  \n",
       "1926-11  0.0652  0.0433  0.0224  0.0400  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_ind_returns():\n",
    "    \"\"\"\n",
    "    Load and format the Ken French 30 Industry Portfolios \n",
    "    Value Weighted Monthly Returns\n",
    "    \"\"\"\n",
    "    ind = pd.read_csv(\"data/ind30_m_vw_rets.csv\", header=0, index_col=0)/100\n",
    "    ind.index = pd.to_datetime(ind.index, format=\"%Y%m\").to_period('M')\n",
    "    ind.columns = ind.columns.str.strip()\n",
    "    return ind\n",
    "ind = get_ind_returns()\n",
    "ind.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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>Books</th>\n",
       "      <th>Steel</th>\n",
       "      <th>Oil</th>\n",
       "      <th>Mines</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-01</th>\n",
       "      <td>0.0513</td>\n",
       "      <td>0.0428</td>\n",
       "      <td>0.0788</td>\n",
       "      <td>0.0059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-02</th>\n",
       "      <td>-0.0654</td>\n",
       "      <td>-0.0268</td>\n",
       "      <td>0.0052</td>\n",
       "      <td>-0.0756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-03</th>\n",
       "      <td>0.0778</td>\n",
       "      <td>0.0210</td>\n",
       "      <td>0.0209</td>\n",
       "      <td>0.0091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-04</th>\n",
       "      <td>-0.0029</td>\n",
       "      <td>-0.0441</td>\n",
       "      <td>-0.0129</td>\n",
       "      <td>-0.1057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-05</th>\n",
       "      <td>0.0479</td>\n",
       "      <td>0.0384</td>\n",
       "      <td>0.0307</td>\n",
       "      <td>0.0022</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Books   Steel     Oil   Mines\n",
       "2013-01  0.0513  0.0428  0.0788  0.0059\n",
       "2013-02 -0.0654 -0.0268  0.0052 -0.0756\n",
       "2013-03  0.0778  0.0210  0.0209  0.0091\n",
       "2013-04 -0.0029 -0.0441 -0.0129 -0.1057\n",
       "2013-05  0.0479  0.0384  0.0307  0.0022"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = [\"Books\",\"Steel\",\"Oil\", \"Mines\"]\n",
    "ind5yr4as = ind[\"2013\":\"2017\"][l]\n",
    "ind5yr4as.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>Books</th>\n",
       "      <th>Steel</th>\n",
       "      <th>Oil</th>\n",
       "      <th>Mines</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Books</th>\n",
       "      <td>0.002720</td>\n",
       "      <td>0.001940</td>\n",
       "      <td>0.001637</td>\n",
       "      <td>0.001539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Steel</th>\n",
       "      <td>0.001940</td>\n",
       "      <td>0.004391</td>\n",
       "      <td>0.002122</td>\n",
       "      <td>0.003391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oil</th>\n",
       "      <td>0.001637</td>\n",
       "      <td>0.002122</td>\n",
       "      <td>0.002697</td>\n",
       "      <td>0.002179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mines</th>\n",
       "      <td>0.001539</td>\n",
       "      <td>0.003391</td>\n",
       "      <td>0.002179</td>\n",
       "      <td>0.005232</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Books     Steel       Oil     Mines\n",
       "Books  0.002720  0.001940  0.001637  0.001539\n",
       "Steel  0.001940  0.004391  0.002122  0.003391\n",
       "Oil    0.001637  0.002122  0.002697  0.002179\n",
       "Mines  0.001539  0.003391  0.002179  0.005232"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov = ind5yr4as.cov()\n",
    "cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Books    0.095312\n",
       "Steel    0.100716\n",
       "Oil      0.025275\n",
       "Mines    0.005136\n",
       "dtype: float64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def annualize_rets(r, periods_per_year=12):\n",
    "    \"\"\"\n",
    "    \"\"\"\n",
    "    compounded_growth = (1+r).prod()\n",
    "    n_periods = r.shape[0]\n",
    "    return compounded_growth**(periods_per_year/n_periods)-1\n",
    "ann_ret = annualize_rets(ind5yr3as)\n",
    "ann_ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def portfolio_return(weights, returns):\n",
    "    \"\"\"\n",
    "    Computes the return on a portfolio from constituent returns and weights\n",
    "    weights are a numpy array or Nx1 matrix and returns are a numpy array or Nx1 matrix\n",
    "    \"\"\"\n",
    "    return weights.T @ returns\n",
    "\n",
    "\n",
    "def portfolio_vol(weights, covmat):\n",
    "    \"\"\"\n",
    "    Computes the vol of a portfolio from a covariance matrix and constituent weights\n",
    "    weights are a numpy array or N x 1 maxtrix and covmat is an N x N matrix\n",
    "    \"\"\"\n",
    "    return (weights.T @ covmat @ weights)**0.5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00000000e+00 1.00000000e+02 2.48065457e-14 6.44449771e-14]\n",
      "1.0000000000000004\n",
      "Steel\n"
     ]
    }
   ],
   "source": [
    "# MSR\n",
    "from scipy.optimize import minimize\n",
    "def msr(riskfree_rate, er, cov):\n",
    "    \"\"\"\n",
    "    Returns the weights of the portfolio that gives you the maximum sharpe ratio\n",
    "    given the riskfree rate and expected returns and a covariance matrix\n",
    "    \"\"\"\n",
    "    n = er.shape[0]\n",
    "    # start with EW\n",
    "    init_guess = np.repeat(1/n, n)\n",
    "    bounds = ((0.0, 1.0),) * n # an N-tuple of 2-tuples!\n",
    "    # construct the constraints\n",
    "    weights_sum_to_1 = {'type': 'eq',\n",
    "                        'fun': lambda weights: np.sum(weights) - 1\n",
    "    }\n",
    "    def neg_sharpe(weights, riskfree_rate, er, cov):\n",
    "        \"\"\"\n",
    "        Returns the negative of the sharpe ratio\n",
    "        of the given portfolio\n",
    "        \"\"\"\n",
    "        r = portfolio_return(weights, er)\n",
    "        vol = portfolio_vol(weights, cov)\n",
    "        return -(r - riskfree_rate)/vol\n",
    "\n",
    "    weights = minimize(neg_sharpe, init_guess,\n",
    "                       args=(riskfree_rate, er, cov), method='SLSQP',\n",
    "                       options={'disp': False},\n",
    "                       constraints=(weights_sum_to_1,),\n",
    "                       bounds=bounds)\n",
    "    return weights.x\n",
    "# What is the weight of the largest component of the MSR portfolio?   \n",
    "msr_w = msr(0.1, ann_ret, cov)\n",
    "print(msr_w*100)\n",
    "print(msr_w.sum())\n",
    "print(l[msr_w.argmax(axis=0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.77024876e+01 6.50521303e-17 4.34112019e+01 8.88631054e+00]\n",
      "0.9999999999999999\n",
      "Books\n"
     ]
    }
   ],
   "source": [
    "# GMV\n",
    "def gmv(cov):\n",
    "    \"\"\"\n",
    "    Returns the weights of the Global Minimum Volatility portfolio\n",
    "    given a covariance matrix\n",
    "    \"\"\"\n",
    "    n = cov.shape[0]\n",
    "    return msr(0, np.repeat(1, n), cov)\n",
    "gmv_w = gmv(cov)\n",
    "print(gmv_w*100)\n",
    "print(gmv_w.sum())\n",
    "print(l[gmv_w.argmax(axis=0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21.983988181484186\n",
      "18.973734471589985\n"
     ]
    }
   ],
   "source": [
    "\n",
    "ind2018 = ind[\"2018\"][l]\n",
    "cov2018 = ind2018.cov()\n",
    "print(portfolio_vol(msr_w, cov2018)*(12**0.5)*100)\n",
    "print(portfolio_vol(gmv_w, cov2018)*(12**0.5)*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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