Week 2 - Quadprog to draw Efficient Frontier .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QuadProg to draw Efficient Frontier "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n",
    "import edhec_risk_kit as erk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ind = erk.get_ind_returns()\n",
    "er = erk.annualized_return(ind[\"1996\":\"2000\"], 12)\n",
    "cov = ind['1996':'2000'].cov()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def portfolio_return(weights, returns):\n",
    "    \"\"\"\n",
    "    Weights -> Returns\n",
    "    \"\"\"\n",
    "    return weights.T @ returns\n",
    "\n",
    "def porfolio_vol(weights, covmat):\n",
    "    \"\"\"\n",
    "    Weight -> Vol\n",
    "    \"\"\"\n",
    "    return (weights.T @ covmat @ weights)**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "assets = [\"Food\", \"Beer\", \"Smoke\", \"Coal\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Food     0.116799\n",
       "Beer     0.141126\n",
       "Smoke    0.107830\n",
       "Coal     0.414689\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "er[assets]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>Coal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Food</th>\n",
       "      <td>0.002609</td>\n",
       "      <td>0.002379</td>\n",
       "      <td>0.002061</td>\n",
       "      <td>0.000027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beer</th>\n",
       "      <td>0.002379</td>\n",
       "      <td>0.005264</td>\n",
       "      <td>0.001359</td>\n",
       "      <td>0.001728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Smoke</th>\n",
       "      <td>0.002061</td>\n",
       "      <td>0.001359</td>\n",
       "      <td>0.008349</td>\n",
       "      <td>-0.000733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Coal</th>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.001728</td>\n",
       "      <td>-0.000733</td>\n",
       "      <td>0.018641</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Food      Beer     Smoke      Coal\n",
       "Food   0.002609  0.002379  0.002061  0.000027\n",
       "Beer   0.002379  0.005264  0.001359  0.001728\n",
       "Smoke  0.002061  0.001359  0.008349 -0.000733\n",
       "Coal   0.000027  0.001728 -0.000733  0.018641"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov.loc[assets, assets]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.25, 0.25, 0.25, 0.25])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "weights = np.repeat(1/4, 4)\n",
    "weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19511097196038385"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "erk.portfolio_return(weights, er[assets])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.055059195776437045"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "erk.porfolio_vol(weights, cov.loc[assets, assets])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2-Asset Frontier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = [\"Games\", \"Fin\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_points = 20\n",
    "weights = [np.array([w, 1-w]) for w in np.linspace(0, 1, n_points)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0., 1.]),\n",
       " array([0.05263158, 0.94736842]),\n",
       " array([0.10526316, 0.89473684]),\n",
       " array([0.15789474, 0.84210526]),\n",
       " array([0.21052632, 0.78947368]),\n",
       " array([0.26315789, 0.73684211]),\n",
       " array([0.31578947, 0.68421053]),\n",
       " array([0.36842105, 0.63157895]),\n",
       " array([0.42105263, 0.57894737]),\n",
       " array([0.47368421, 0.52631579]),\n",
       " array([0.52631579, 0.47368421]),\n",
       " array([0.57894737, 0.42105263]),\n",
       " array([0.63157895, 0.36842105]),\n",
       " array([0.68421053, 0.31578947]),\n",
       " array([0.73684211, 0.26315789]),\n",
       " array([0.78947368, 0.21052632]),\n",
       " array([0.84210526, 0.15789474]),\n",
       " array([0.89473684, 0.10526316]),\n",
       " array([0.94736842, 0.05263158]),\n",
       " array([1., 0.])]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "rets = [erk.portfolio_return(w, er[l]) for w in weights]\n",
    "vols = [erk.porfolio_vol(w, cov.loc[l,l]) for w in weights]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "ef = pd.DataFrame({\"R\": rets, \"Vol\": vols})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f052e0a2278>"
      ]
     },
     "execution_count": 34,
     "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": [
    "ef.plot.scatter(x=\"Vol\", y=\"R\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f052eca9da0>"
      ]
     },
     "execution_count": 41,
     "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": [
    "erk.plot_ef2(n_points, er[l], cov.loc[l,l])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# N-Asset Efficient Frontier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "def plot_ef(n_points, er, cov, style=\".-\"):\n",
    "    \"\"\"\n",
    "    Plots the 2-asset efficient frontier\n",
    "    \"\"\"\n",
    "    weights = minimize_vol(target_return)\n",
    "    rets = [portfolio_return(w, er) for w in weights]\n",
    "    vols = [porfolio_vol(w, cov) for w in weights]\n",
    "    ef = pd.DataFrame({\n",
    "        \"Returns\": rets,\n",
    "        \"Volatility\": vols\n",
    "    })\n",
    "    return ef.plot.line(x=\"Volatility\", y=\"Returns\", style=style)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Games', 'Fin']"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f052dff7748>"
      ]
     },
     "execution_count": 47,
     "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": [
    "erk.plot_ef2(20, er[l], cov.loc[l,l])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def minimize_vol(target_return, er, cov):\n",
    "    \"\"\"\n",
    "    Target return -> Weight vector\n",
    "    \"\"\"\n",
    "    n_assets = er.shape[0]\n",
    "    init_guess = np.repeat(1/n_assets, n_assets)\n",
    "    bounds = ((0.0, 1.0),)*n_assets\n",
    "    return_is_target = {\n",
    "        'type': 'eq',\n",
    "        'args': (er,),\n",
    "        'fun': lambda weights, er: target_return - erk.portfolio_return(weights, er)\n",
    "    }\n",
    "    weights_sum_to_1 = {\n",
    "        'type': 'eq',\n",
    "        'fun': lambda weights: np.sum(weights) - 1\n",
    "    }\n",
    "    results = minimize(erk.porfolio_vol,\n",
    "                        init_guess,\n",
    "                        args=(cov,), \n",
    "                        method=\"SLSQP\",\n",
    "                        constraints=(return_is_target, weights_sum_to_1),\n",
    "                        bounds=bounds)\n",
    "    return results.x\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "w15 = erk.minimize_vol(0.1455, er[l], cov.loc[l,l])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05609066849341863"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol15 = erk.porfolio_vol(w15, cov.loc[l,l])\n",
    "vol15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.50187865, 0.49812135])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimal_weights(n_points, er, cov):\n",
    "    \"\"\"\n",
    "    Generate a list of weights to run the optimizer on\n",
    "    \"\"\"\n",
    "    target_returns = np.linspace(er.min(), er.max(), n_points)\n",
    "    weights = [minimize_vol(target_return, er, cov) for target_return in target_returns]\n",
    "    return weights\n",
    "    \n",
    "def plot_ef(n_points, er, cov, style=\".-\"):\n",
    "    \"\"\"\n",
    "    Plots the 2-asset efficient frontier\n",
    "    \"\"\"\n",
    "    weights = optimal_weights(n_points, er, cov)\n",
    "    rets = [portfolio_return(w, er) for w in weights]\n",
    "    vols = [porfolio_vol(w, cov) for w in weights]\n",
    "    ef = pd.DataFrame({\n",
    "        \"Returns\": rets,\n",
    "        \"Volatility\": vols\n",
    "    })\n",
    "    return ef.plot.line(x=\"Volatility\", y=\"Returns\", style=style, title=\"Multi-asset Efficient Frontier\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = [\"Smoke\", \"Fin\", \"Games\", \"Coal\", ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f052dd1d940>"
      ]
     },
     "execution_count": 114,
     "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": [
    "plot_ef(30, er[k], cov.loc[k,k], )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f052dc8e860>"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k59vyZQxJ6MWRGk9Tr73sqDOPfUCfWC7ITGF6RpI7FNN1g725056M7WwtnYy1K0z5x64wZczJVJU9Fcd5YfUeFn9QeNJ0xwF9YpmWkcj04UmdPt2xI3ToydjOEB0dbVdNMsb4ZV/VCVYWlPNJgXMCtXGtmEYC3HlBOg9eObpLB3tbdImgN8aYUymtrmVlYTkrC8pYWfDZsr0JvaKZPjyJuy7KoG/PaO57ZUPTdMfZ4wZ2m5AHC3pjTBdTeayOVbvKm3rtOw8dBSC+RxTZGYncMn0Y5w1P4uyzTl4EbHBCr5CZ7tjZLOiNMSGtuqae1bsqmoJ964EjqELP6EimpCdy7eRUpmckMXZQH6IiT32JjVCa7tjZLOiNMSHlRF0DuUUVfFLg9No3lhymwavEREUwOS2Bey8byXnDkxif2s+54IY5LQt6Y0xQ5RSW8eqn+2hQpajsOJ/uraS+QYmKECYM6ce3Lx7O9Iwkzh2aQGx0ZLDL7ZIs6I0xnarBq2zed5iP88v5z6b9rC8+3LRveEocX5+RzvSMJKYMSySuh0VUINi7aIzpUI1XUfokv4yP851VHg+fcFZ4TO4d09QuUuCac1O5+wsjglVq2LKgN8YE3MEjNXzsBvsnBWXsP+x82XFwv55cPuYsZmQmM314EnsrTpx0kaBpGUlBrjw8WdAbY9rt8Il6cgrL+SS/jI/yyygoPQZ8Npd9wYhkzh+ezNCkk7992j8+tsMuEmQ+Y0FvjGmzmvoG8ooq3V57GRtLDuN1pzxOTU/k+ilDOG94MmMG9jnlBa0bdedpj53Fgt4Yc1oNXmVjyeGmYM8tqqTO4yUqQpg4pB8LLsnk/OFJTEpLsCmPIciC3hjzOarKv9bv45/r93HkRD3bDlRTXeNcpH7UgHhumTaU80ckMTU9id42Mybk2d+QMQaA8qO1fJRfxkc7y3h326GmC24IcOno/syZOJjzhieR3LtHcAs1bWZBb0w3VVPfQO7uSj7ML+XDHWVs2X8EgL49ozmrTw8qjtWhQITApLQE5kwYFNyCzRmzoDemm/B6lW0Hqvkov5QPd5axelcFtR4v0ZHCuWkJ/ODykVyQmcK4wX1Zt7fKpj2GEQt6Y8LYgcM1fLizlI/ck6iNl8nL7N+bm7KHckFmMlPTP/8N1MlDE2zaYxixoDcmjByr9bBqVzkf7nTG2huX8E3uHcOMEcnMyExhxohkBvQ9/SUnbdpj+LCgN6YLcq5/Ws7U9ESiIyP4aKczHLN2j7MgWI+oCKamJ/KVrFRmjEhh1ID4085nN+HLgt6YLmb55gMseH4t9Q0nX+957KA+fH1GOheMSCFrmK30aD7jV9CLyGzgMSASeEpVFzbbfxdwN9AAHAXmq+oWERkGbAW2u01zVPWuwJRuTPdQU9/A6l0VvL+jlPd3lJLvDsc0unr8QH42Z6xNezSndNqgF5FIYBEwEygG1ojIMlXd4tPseVV93G0/B/gNMNvdV6CqEwNbtjHhS1XZVXasKdhzCsupqfcSExVBdnoiM0Yk8cLqvXganBkxt5+fbiFvWuVPj34qkK+qhQAishSYCzQFvaoe8WkfB5z8mdIY06qjtR5WFpTz/o5DvL+jlL0VJwDISI7jhilpXHR2CtPSk+gZ4wzHfHHCYJsRY/zmT9APBvb63C8Gsps3EpG7ge8BMcAlPrvSReRT4AjwY1X9sIVj5wPzAdLS0vwu3piuSlXZur+a93eU8sGOUnKLKqhvUHrFRHLe8GTmXzicizJTSEvq1eLxNiPGtEXATsaq6iJgkYjMA34M3ArsB9JUtVxEJgOvisjYZp8AUNXFwGKArKws+zRgwlLV8To+3FnWFO6HqmsBGD2wD3fMyOCikSlMHmqLgpnA8yfoS4AhPvdT3W2nshT4I4Cq1gK17u08ESkARgK5Z1StMV2A79THqAhpGmtfv7cKrzpLDFyQmcxFI1O4cGQKZ/U5/Zx2Y9rDn6BfA2SKSDpOwN8AzPNtICKZqrrTvXsVsNPdngJUqGqDiGQAmUBhoIo3JtSs2H6I+X/JPWnqowhMSO3Hf12SyUVnpzAhtR+RNqfddKLTBr2qekRkAbAcZ3rlM6q6WUQeBnJVdRmwQEQuA+qBSpxhG4ALgYdFpB7wAnepakVHvBBjgkFV2bL/CCu2HeLdbYdYu6fqpP1Xjx/Iz+eOIyEu5hSPYEzHE9XQGhLPysrS3Fwb2TGh63idh4/zy3l32yHe236o6Xqo41P7MmpAPK+u20eDO/VxyZ3T7KSp6RQikqeqWS3ts2/GGuOHvRXHedftta8sLKfO4yUuJpILMlO4d2Z/Lj47hf7xzlj79VPSbOqjCSkW9Ma0wNPgJa+osincGxcHS0+O4+bsoVwyqj9T0xNbnCFjUx9NqLGgN8ZVcayO93cc4p2th/hgRylHajxERQjZGc7Fri8Z1Z+MlN7BLtOYNrOgN92SMwWyjAF9enLgSA3vbjvEp3sq8aqzpO+ssQO4ZFR/ZmQmEx8bHexyjWkXC3rTrdR5vPw1Zze/eH0bDd7PJiKcM7gvCy7J5NJR/TlncF9b0teEFQt6E/aO1nr4YEcpyzcf4N1th6iu8TTtE+BbFw/nvtmjglegMR3Mgt6EpdLqWt7ZepA3txzko/wy6jxeEnpFM3vsAIb3783/vbWDencK5KWjzwp2ucZ0KAt6EzZ2lx3jzS0HeHPzQfL2VKIKqQk9uTl7KLPGnsXkoQlERTqzZKYMS7QpkKbbsKA3XZaqsqnkSFO4bz9YDcCYgX34zqWZXD5mAKMHxiPy+fF2mwJpuhMLetOl1Dd4Wb2rgjc3H+DNLQfZf7iGCIGp6Yn8z9VjmDnmLIYktry0rzHdlQW9CXmf5JfxYu5eKo7XsW5PFUdqPMRGR3BhZgrfv/xsLhnVn0RbS8aYU7KgNyHpeJ2Hd7Ye4q85Raza9dk6eBePTOHG7DQuzExputqSMaZ1FvQmZNTUN7Bi2yFe27Cfd7YdpKbeWU+mUaTAlPREZo0dEMQqjel6LOhNUNXUN/DBjlJe27Cft7ce5HhdA0lxMVw3OZWrxw8iMkK45elV1HucqZDTMpKCXbIxXY4Fvel0dR4vH+WX8tr6/by15SDVtR4SekUzd+Igrh4/iOz0xKZpkABL7pxmUyGNaQcLetMp6hu8fFJQzmvr97F88wGO1HjoExvF7HEDuHrCIM4bnkR0ZMvXSrWpkMa0jwW96TCeBi85hRX8e+M+/rPpAJXH64nvEcXMsWdx9fiBzBiRYhfCNqYTWNCbgMrdXcFLecVUHa8jr6iSsqN1xMVEctmYs7jqnIFcODKF2GibLWNMZ7KgNwGxu+wYv1+xk1fySmhcE/K84Un8fO5QvjCqv4W7MUFkQW/O2NFaD69v2M9LeXtZs7sSgaaQjxQ4f0QyV5wzMJglGmPwM+hFZDbwGBAJPKWqC5vtvwu4G2gAjgLzVXWLu+8B4A533z2qujxw5ZvO5vUqOYXlvJxXzBubDnCivoGMlDjum302mSnx/NfStTYV0pgQc9qgF5FIYBEwEygG1ojIssYgdz2vqo+77ecAvwFmi8gY4AZgLDAIeFtERqpqQ4Bfh+lgReXHeGVtCa/kFVNSdYL42Ci+fO5grpucyqQh/ZoWDrOpkMaEHn969FOBfFUtBBCRpcBcoCnoVfWIT/s4PvsEPxdYqqq1wC4RyXcfb2UAajcd7Gith9c37uflvGJW76pABGaMSOa+2Wcza+yAFsfdbSqkMaHHn6AfDOz1uV8MZDdvJCJ3A98DYoBLfI7NaXbs4BaOnQ/MB0hLS/OnbhNgzjVUy8lOT6S+Qd2hmf0cr2sgIzmOH846m2vOHczAvj2DXaoxpo0CdjJWVRcBi0RkHvBj4NY2HLsYWAyQlZWlp2luAiyvqJJ5T+ZQ5/ECzsex+B5RzJ3oDM2cm9avxTXdjTFdgz9BXwIM8bmf6m47laXAH8/wWNOJVJWVBeX8dNlmat2QB7h6/EAe/coEmxJpTJjwJ+jXAJkiko4T0jcA83wbiEimqu50714FNN5eBjwvIr/BORmbCawOROHmzB2t9fCPtcX8eWUR+YeOEh8bRVSE4FUlJiqC289Pt5A3JoycNuhV1SMiC4DlONMrn1HVzSLyMJCrqsuABSJyGVAPVOIO27jtXsQ5cesB7rYZN8FTUHqU51YW8UpeMdW1Hsan9uX/+8oErho/kM37jthsGWPClKiG1pB4VlaW5ubmBruMsNHgVVZsO8SfV+7mw51lREcKV48fxNemD2XiEBt7NyZciEieqma1tM++GRumKo/V8WLuXp7LKaK48gQD+sTyg8tHcv2UNFLiewS7PGNMJ7KgDxON0yP7x/cgd3clr64rodbjJTs9kQevHM3MMWedchlgY0x4s6APA2t2VzDvyRzqG5xhuJjICK7LSuVr04cyakCfIFdnjAk2C/ourKa+gb+vLeHXy7c1hbwAd12UwfcuPzu4xRljQoYFfRd0pKaeJTl7eObjXZRW1zI8JY5jtR68XiU6KoKLzu4f7BKNMSHEgr4LOXSkhmc+3s2SnCKqaz1ckJnMY9dPZPrwJNbuqbLpkcaYFlnQdwG7yo6x+INCXskrxuP1csU5A/nWRcMZN7hvUxtbTMwYcyoW9CFsY/FhHn+/gNc37SfaPcE6/4IMhiXHBbs0Y0wXYkEfQpwpkmX0io7inW2H+Ci/jPgeUdx10XBuP38Y/eNjg12iMaYLsqAPEXm7K7jxyRzq3Nkz/XpF88AVo5iXnUZ8bHSQqzPGdGUW9CEgd3cF3126rinkBbj9vGF886LhwS3MGBMWLOiDaNuBIzy6fDtvbz1Ev17RREUIqs4UyRmZKcEuzxgTJizog2BvxXF++/YO/vFpCb17RPHDWWdz+/nD2Lq/2qZIGmMCzoK+E5VW17JoRT5LVhURIcL8CzP41kXD6dcrBrApksaYjmFB3wmqa+p58sNdPPVhIbUeL1/NGsJ3Ls1kQF+bRWOM6XgW9B1oZUEZiz8oJHd3BdW1DVw1fiDfnzmSjJTewS7NGNONWNB3kCfeL2DhG9tQIELgkWvH85UpQ057nDHGBJoFfYAdOlLDQ//awr837m/aJsCho7XBK8oY063ZlSgCxOtVnl+1h0t/8z5vbT3IvOw0YqMjiBSIjopgWkZSsEs0xnRTfvXoRWQ28BjOxcGfUtWFzfZ/D7gT5wLgpcDXVbXI3dcAbHSb7lHVOQGqPWTkH6rmgb9vZM3uSqZnJPHLa84hPTmOa89NtemSxpigO23Qi0gksAiYCRQDa0Rkmapu8Wn2KZClqsdF5FvAr4Hr3X0nVHVigOsOCbWeBv74XgF/WFFAz5hIfn3deL4yObXpgts2XdIYEwr86dFPBfJVtRBARJYCc4GmoFfVFT7tc4CbA1lkKFq9q4IH/r6BgtJjzJ04iJ9cPYbk3nbRbWNM6PEn6AcDe33uFwPZrbS/A3jD536siOTiDOssVNVXmx8gIvOB+QBpaWl+lBQ8H+wo5dE3t7Oh+DCpCT350+1TuNiu6GSMCWEBnXUjIjcDWcBFPpuHqmqJiGQA74rIRlUt8D1OVRcDiwGysrI0kDUF0ku5e/nhyxsAiIwQfn3teM4bkRzkqowxpnX+zLopAXwngKe6204iIpcBPwLmqGrTXEJVLXH/LATeAya1o96g+ee6Eu7/+8bPNqjy6d6q4BVkjDF+8ifo1wCZIpIuIjHADcAy3wYiMgl4AifkD/lsTxCRHu7tZOB8fMb2u4IGr/KrN7bynaXrGNm/Nz2ibMqkMaZrOe3Qjap6RGQBsBxneuUzqrpZRB4GclV1GfAI0Bt4yZ1x0jiNcjTwhIh4cX6pLGw2WyekHT5Rzz0vfMr7O0q5eVoa/3P1WDaWHLYpk8aYLkVUQ2tIPCsrS3Nzc4NdBvmHqvnGX/IorjzOQ3PGMS87tE8SG2O6NxHJU9WslvbZEgjN5BVVsmRVEW9sPEBcj0ie/8Y0pgxLDHZZxhhzxizofeTtruD6xTl4vIoI/N8NEy3kjTFdnq1141JVfvXGNjxeZygrAsg/dDS4RRljTABYjx4n5Be+sY3cokoiIwTc67barBpjTDjo9kGvqjz65nae+KCQr00fytwJg8jZVWGzahftouwAABLxSURBVIwxYaPbB/3/vb2TRSsKuHFqGj/74lgiIoTJNi5vjAkj3XqM/vfv7uSxd3by1axUfvGlcURESLBLMsaYgOuWPfq8okp+985O3t9RyjWTBvOra8ZbyBtjwla3C/q8okquf2IlHq8SIXBjdppzAtYYY8JUtxu6eeajwqYplIKzrrwxxoSzbtWj/zi/jP9sPkCEOCFvUyiNMd1Btwn6rfuPcNdzeYxIiedHV41mY8lhm0JpjOkWukXQ76s6we3PriGuRxTP3j6FQf16cuHIlGCXZYwxnSLsx+gPn6jntmdXc6zWw5++7oS8McZ0J2Hdo88pLOOHL21g3+ETPPf1bEYN6BPskowxptOFbdDn7a5g3pOr8CpERwo9oiODXZIxxgRF2A7d/H5FPu4sSrxeJaewPLgFGWNMkIRlj35VYTnv7yi1aZTGGEMYBv3BIzXc/fynDEuK46G5Y9lQbNMojTHdW1gFfX2Dl7uXrOVYrYfnv5HNyLPiuSDTplEaY7o3v8boRWS2iGwXkXwRub+F/d8TkS0iskFE3hGRoT77bhWRne7PrYEsvrlfve5cPOR/rxvPyLPiO/KpjDGmyzhtj15EIoFFwEygGFgjIstUdYtPs0+BLFU9LiLfAn4NXC8iicBPgSxAgTz32MpAvoi8okqe/XgXr23Yz23nDWPOhEGBfHhjjOnS/OnRTwXyVbVQVeuApcBc3waqukJVj7t3c4BU9/Ys4C1VrXDD/S1gdmBKd+QVVTLvyRxe27AfEbhi3IBAPrwxxnR5/gT9YGCvz/1id9up3AG80ZZjRWS+iOSKSG5paakfJX1mZUEZtR4v4LyY3KKAflgwxpguL6Dz6EXkZpxhmkfacpyqLlbVLFXNSklp28nTsqO1AESITaM0xpiW+DPrpgQY4nM/1d12EhG5DPgRcJGq1voce3GzY987k0JbUlB6lBdW7yVraAJfGJXCtIxkm0ZpjDHN+BP0a4BMEUnHCe4bgHm+DURkEvAEMFtVD/nsWg78UkQa0/dy4IF2Vw00eJX7Xt5AbHQkf7jpXPr3iQ3EwxpjTNg5bdCrqkdEFuCEdiTwjKpuFpGHgVxVXYYzVNMbeElEAPao6hxVrRCRn+P8sgB4WFUDckmnZz/eRV5RJb+9foKFvDHGtEJUNdg1nCQrK0tzc3NbbfOv9SV892/rmTSkHy/dNR33l4sxxnRbIpKnqlkt7etyi5rl7a7gO0vX0eBVNpYcZu2eqmCXZIwxIa3LBf2SVXuaVqX0NHhtVUpjjDmNLrXWjafBy+rdFQg2ndIYY/zVpYL+5bxiiitPcN+skShiq1IaY4wfukzQn6hr4Ldv7+DctH586+IRdgLWGGP81GXG6J/5eBcHj9TywJWjLeSNMaYNukTQr9h2kMfe3smUYQlMGZYY7HKMMaZLCfmgzyuq5M6/5FHX4GVD8WHybNEyY4xpk5AP+o92ltLgzqe06ZTGGNN2IR/0HjfkbTqlMcacmZCfdfPBzjIG9Yvlpuw0W53SGGPOQEgH/YbiKtbvreKnXxzD7eenB7scY4zpkkJ26CavqJIH/76RHlERXDs59fQHGGOMaVFIBn3jdWA37TuCx6vsPHg02CUZY0yXFZJBn1NYTp17HVhVtZk2xhjTDiEZ9NMykmj88muMzbQxxph2CcmTseNT+xIbFcmI/r356ZyxNtPGGGPaISR79Ov2VnG8voG7Lh5uIW+MMe0UkkH//vZSIgTOH54c7FKMMabL8yvoRWS2iGwXkXwRub+F/ReKyFoR8YjIdc32NYjIOvdnmT/P98am/QzoG0t+qc22McaY9jpt0ItIJLAIuAIYA9woImOaNdsD3AY838JDnFDVie7PnNM9X3WNh4LSY+yvquGmp3JsETNjjGknf3r0U4F8VS1U1TpgKTDXt4Gq7lbVDYC3vQUdPlHnPCZQ77FFzIwxpr38CfrBwF6f+8XuNn/FikiuiOSIyJdaaiAi8902ubU1NQBE2iJmxhgTEJ0xvXKoqpaISAbwrohsVNUC3waquhhYDDBoxFjtFRPJ3V8YbouYGWNMAPgT9CXAEJ/7qe42v6hqiftnoYi8B0wCCk7VvtbjJfOseO7+Qqa/T2GMMaYV/gzdrAEyRSRdRGKAGwC/Zs+ISIKI9HBvJwPnA1taO6bW4yUjOc6fhzfGGOOH0wa9qnqABcByYCvwoqpuFpGHRWQOgIhMEZFi4CvAEyKy2T18NJArIuuBFcBCVW016OsbvJRW19psG2OMCRBR1WDXcJIeAzN10K3/R4/oCJbcOc3G6I0xxg8ikqeqWS3tC8lvxtrUSmOMCZyQDHq7PqwxxgROSK5eecOUNK6dnGrDNsYYEwAh2aO/dvJgC3ljjAmQkAx6abzqiDHGmHYLyaDfebA62CUYY0zYCMmg/8k/N9s8emOMCZCQDHpPg02tNMaYQAnJoI8QsamVxhgTICEX9ALMHjvAZt0YY0yAhFzQ94iKpMbT7uuXGGOMcYVc0MdERbC34niwyzDGmLARckEvAgWlR8nbXRHsUowxJiyEXNAfOVGPx6vMe2qVTbE0xpgACLmgb1w0uc6mWBpjTECEXNA3rn4QgU2xNMaYQAi5oM9I7s2oAfHE94zi3LR+wS7HGGO6vJAL+l4xkXx9RjpVx+vZbmveGGNMu4Vc0ANckJkMwMLXt9kJWWOMaaeQDPp9VTUI8N6OUm56KsfC3hhj2sGvoBeR2SKyXUTyReT+FvZfKCJrRcQjItc123eriOx0f2715/l8Z9vYtWONMaZ9Thv0IhIJLAKuAMYAN4rImGbN9gC3Ac83OzYR+CmQDUwFfioip13EZlpGEtFREY2PYbNvjDGmHfzp0U8F8lW1UFXrgKXAXN8GqrpbVTcAzRepmQW8paoVqloJvAXMPt0TTh6awAvfmMbAvrGc1aeHzb4xxph28CfoBwN7fe4Xu9v84dexIjJfRHJFJLe0tBRwwv57M0dSUlXDql22HIIxxpypkDgZq6qLVTVLVbNSUlKatl89fhB9YqNYsmpPEKszxpiuzZ+gLwGG+NxPdbf5oz3H0jMmkmsnp/L6xn08stymWhpjzJnwJ+jXAJkiki4iMcANwDI/H385cLmIJLgnYS93t/lt0pB+NHjhDysKbKqlMcacgdMGvap6gAU4Ab0VeFFVN4vIwyIyB0BEpohIMfAV4AkR2eweWwH8HOeXxRrgYXeb3/ZWnnDqwKZaGmPMmYjyp5Gqvg683mzb//jcXoMzLNPSsc8Az5xpgdMykoiJjKCuwWtTLY0x5gyExMnY1kwemsAL86eRkRJHTFQEI1J6B7skY4zpUkI+6MEJ+0XzzuVEfQN/fL8g2OUYY0yX0iWCHmD0wD58aeJgnv14FwcO1wS7HGOM6TK6TNAD3HvZSLyq/OSfm1i0It9m4BhjjB/8OhkbKtKSenHZ6LN4Y9MB3t5ykKhI4Y83T+ay0WcFuzRjjAlZXSroATJS4gB3umWDcuefc+kf34Nxg/s6P4P6cE5qXwb0iUUar0tojDHdWJcL+ktGncXTH+2i3uMlMiKCm6alcfh4PZv2Hea97YfwulcXT4qLYezgvpwzuA/jBjm/BFITelr4G2O6nS4X9JOHJrDkzmnkFJYzLSOJyUM/W/X4RF0DW/YfYfO+w2wsPsymfUd44v1CPG769+0ZzbjBfdyef1/OGdyXtMReRERY+BtjwpeoarBrOElWVpbm5uYG7PFq6hvYfqCaTfsOs6nkMJtKjrD9QDV1Dc6KyvE9ohgzqA/nNA79DO5LenIckRb+xpguRETyVDWrpX1drkffVrHRkUwY0o8JQz5b077O42XHwWqn5++G/3M5RdR6nPDvFRPJmIF9moL/nMF9GZ4SR1Rkl5qkZIwxQDfo0fvL0+Alv/Qom0qOuD3/w2zed4QT9Q0A9IiKYPTAxp5/H8YO6suxWg+5RZWfG0IyxpjO1lqP3oK+FQ1eZVeZE/4bfcL/aK3npHax0REsuXOahb0xJmi69dBNe0RGCCP6xzOifzxfmuRcGMvrVYoqjvObN7fz2ob9J62qaUFvjAlFNujcRhERQnpyHLedn06P6AgiBaKjImxVTWNMyLIe/RlqbZqnMcaEEgv6dpg8NMEC3hgT8mzoxhhjwpwFvTHGhDkLemOMCXMW9MYYE+Ys6I0xJsxZ0BtjTJgLuSUQRKQUKAp2HaeQDJQFu4gWhGpdYLWdqVCtLVTrAqttqKqmtLQj5II+lIlI7qnWkgimUK0LrLYzFaq1hWpdYLW1xoZujDEmzFnQG2NMmLOgb5vFwS7gFEK1LrDazlSo1haqdYHVdko2Rm+MMWHOevTGGBPmLOiNMSbMWdADIjJbRLaLSL6I3N/C/h4i8jd3/yoRGeazb7yIrBSRzSKyUURiQ6E2EblJRNb5/HhFZGKI1BYtIn9236+tIvJAIOtqZ20xIvKsW9t6Ebm4k+u6UETWiohHRK5rtu9WEdnp/twayLoCUNt/RKRKRF4LdF3tqU1EJvr8/9wgIteHUG1D3e3r3PruCnRtTVS1W/8AkUABkAHEAOuBMc3afBt43L19A/A393YUsAGY4N5PAiJDobZmbc4BCkLofZsHLHVv9wJ2A8NCpLa7gWfd2/2BPCCiE+saBowH/gJc57M9ESh0/0xwbyd08nvWYm3uvkuBLwKvBfLfWQDet5FApnt7ELAf6BcitcUAPdzbvd3/B4MC/f6pqvXogalAvqoWqmodsBSY26zNXODP7u2XgUtFRIDLgQ2quh5AVctVtSFEavN1o3tsILWnNgXiRCQK6AnUAUdCpLYxwLsAqnoIqAIC9UWX09alqrtVdQPgbXbsLOAtVa1Q1UrgLWB2gOpqb22o6jtAdQDrCUhtqrpDVXe6t/cBh4AWvz0ahNrqVLXWvduDDhxhsaCHwcBen/vF7rYW26iqBziM03sfCaiILHc/gt0XQrX5uh54IYRqexk4htO72gM8qqoVIVLbemCOiESJSDowGRjSiXV1xLGh8PjtEZDaRGQqTi+6IEB1QTtrE5EhIrLBfYz/dX8ZBZxdSrB9ooAZwBTgOPCOiOS5vZuQICLZwHFV3RTsWnxMBRpwPkonAB+KyNuqWhjcsgB4BhgN5OKsufQJTq2mCxORgcBzwK2q+rlPJMGiqnuB8SIyCHhVRF5W1YOBfh7r0UMJJ/fYUt1tLbZxhxv6AuU4v70/UNUyVT0OvA6cGyK1NbqBwPfm21vbPOA/qlrvDo98TOCGR9pVm6p6VPVeVZ2oqnOBfsCOTqyrI44Nhcdvj3bVJiJ9gH8DP1LVnFCqrZHbk98EXBCguk5iQQ9rgEwRSReRGJxgXNaszTKgcZbDdcC76pxBWQ6cIyK93LC4CNgSIrUhIhHAVwn8+Hx7a9sDXOLWGAdMA7aFQm3u32WcW9tMwKOqgfo79aeuU1kOXC4iCSKSgHN+aHmA6mpvbR3tjGtz2/8D+IuqvhxitaWKSE/3dgLO6MD2DqjRZt24mXglTq+tAOe3PsDDwBz3dizwEpAPrAYyfI69GdiM89v41yFW28VATqi9bzgzDF5y37ctwA9DqLZhOP/ZtgJv4yz92pl1TcH5pHgM59PPZp9jv+7Wmw/cHoT3rLXaPgRKgRNum1mhUJv7/7MeWOfzMzFEapuJM2tvvfvn/ED/nTb+2BIIxhgT5mzoxhhjwpwFvTHGhDkLemOMCXMW9MYYE+Ys6I0xJsxZ0JuwJCIrRGRWs23fFZE/nqL9MBFp9dvDbpt5PvezROR37u3bROT37u27RORrPtsHtff1GNMeFvQmXL2A8+UVX+39lvAwnG/1AqCquap6T/NGqvq4qv7FvXsbzlIPxgSNBb0JVy8DV7nfVkSc9eYH4ayr84iIbBJnzfnPrU/u9tw/dBeqWysi57m7FgIXuOuH3ysiF7e0/rqI/ExEfuCuPZ4FLHGPuUpEXvVpN1NE/hHwV25MMxb0JiypsxrmauAKd9MNwIvANcBEYAJwGfCIu+CVr0PATFU9F2flz9+52+8HPlRnHZzf+lHDyziLo92kqhNx1kIaJSKNy+TejrOImjEdyoLehDPf4ZvGYZsZwAuq2qDOKoHv43xF3Vc08KSIbMRZJmFMIIpR52vozwE3i0g/YDrwRiAe25jW2DLFJpz9E/itiJwL9FLVPBG52Y/j7gUO4vT6I4CaANb0LPAv9zFfUmctfGM6lPXoTdhS1aPACpzhkcaTsB8C14tIpDuEciHOEI+vvsB+ddYtvwXncnHgXEEpvo1lnHSMOsvR7gN+jBP6xnQ4C3oT7l7A6Zk3Bv0/+GzFwHeB+1T1QLNj/gDcKiLrgVE4qw7iHtcgzkXD7/Xz+f8EPO6ejO3pblsC7FXVrWfygoxpK1u90phO5s63/1RVnw52LaZ7sKA3phOJSB7OJ4SZ+tmFoY3pUBb0xhgT5myM3hhjwpwFvTHGhDkLemOMCXMW9MYYE+Ys6I0xJsz9/2afwKglO3BMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "erk.plot_ef(30, er[k], cov.loc[k,k], )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f052dc62e48>"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "er.sort_values().plot.bar(figsize=(12,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = [\"Coal\", \"Fin\", \"Mines\", \"Food\", \"Oil\", \"Beer\", \"Food\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f052da14630>"
      ]
     },
     "execution_count": 122,
     "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": [
    "erk.plot_ef(30, er[k], cov.loc[k,k], )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Mines   -0.053554\n",
       "Txtls   -0.042721\n",
       "Other    0.043349\n",
       "Meals    0.067400\n",
       "Games    0.068212\n",
       "Trans    0.071099\n",
       "Chems    0.077456\n",
       "Clths    0.079160\n",
       "Autos    0.080954\n",
       "Cnstr    0.084076\n",
       "Paper    0.097163\n",
       "Smoke    0.107830\n",
       "FabPr    0.108280\n",
       "Steel    0.115809\n",
       "Food     0.116799\n",
       "Telcm    0.122771\n",
       "Whlsl    0.126431\n",
       "Hshld    0.134766\n",
       "Beer     0.141126\n",
       "Util     0.145903\n",
       "Oil      0.165377\n",
       "Carry    0.173904\n",
       "Servs    0.175264\n",
       "Books    0.187286\n",
       "Rtail    0.207247\n",
       "Fin      0.223371\n",
       "Hlth     0.246641\n",
       "BusEq    0.271952\n",
       "ElcEq    0.272420\n",
       "Coal     0.414689\n",
       "dtype: float64"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "er.sort_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}