lab_107_efficient_frontier_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Efficient Frontier - Part I\n",
    "\n",
    "This week, we are going to learn how to compute the efficient frontier when we have a set of expected returns, volatilities (or variances) and correlations (or covariances). It's a fair question as to how we can get these numbers for the future, but for now, we'll assume that historic returns are a reasonable estimate. In future sections, we'll learn how to improve on it.\n",
    "\n",
    "Let's start by importing a new dataset. This is the Ken French dataset of the returns of 30 different industry portfolios. \n",
    "\n",
    "This datafile has a number of minor problems that we'll sort through as we go:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\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')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Food ', 'Beer ', 'Smoke', 'Games', 'Books', 'Hshld', 'Clths', 'Hlth ',\n",
       "       'Chems', 'Txtls', 'Cnstr', 'Steel', 'FabPr', 'ElcEq', 'Autos', 'Carry',\n",
       "       'Mines', 'Coal ', 'Oil  ', 'Util ', 'Telcm', 'Servs', 'BusEq', 'Paper',\n",
       "       'Trans', 'Whlsl', 'Rtail', 'Meals', 'Fin  ', 'Other'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the column names have embedded spaces. We can strip out the leading and trailing spaces in the Series by using the `.str.strip` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ind.columns = ind.columns.str.strip()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1110, 30)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks good, so let's add the following code to our module for future use:\n",
    "\n",
    "```python\n",
    "def get_ind_returns():\n",
    "    \"\"\"\n",
    "    Load and format the Ken French 30 Industry Portfolios 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",
    "```\n",
    "\n",
    "and then test it by loading the module as usual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1110, 30)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n",
    "\n",
    "import edhec_risk_kit_107 as erk\n",
    "ind = erk.get_ind_returns()\n",
    "ind.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1be36208>"
      ]
     },
     "execution_count": 7,
     "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.drawdown(ind[\"Food\"])[\"Drawdown\"].plot.line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Food     0.061207\n",
       "Beer     0.033881\n",
       "Smoke    0.080292\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "erk.var_gaussian(ind[[\"Food\", \"Beer\", \"Smoke\"]], modified=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x118c92d30>"
      ]
     },
     "execution_count": 9,
     "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.var_gaussian(ind).sort_values().plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use this as an opportunity to write functions for annualized returns, volatility and sharpe ratios. Add the following to the `edhec_risk_kit.py` file:\n",
    "\n",
    "```python\n",
    "def annualize_rets(r, periods_per_year):\n",
    "    \"\"\"\n",
    "    Annualizes a set of returns\n",
    "    We should infer the periods per year\n",
    "    but that is currently left as an exercise\n",
    "    to the reader :-)\n",
    "    \"\"\"\n",
    "    compounded_growth = (1+r).prod()\n",
    "    n_periods = r.shape[0]\n",
    "    return compounded_growth**(periods_per_year/n_periods)-1\n",
    "\n",
    "def annualize_vol(r, periods_per_year):\n",
    "    \"\"\"\n",
    "    Annualizes the vol of a set of returns\n",
    "    We should infer the periods per year\n",
    "    but that is currently left as an exercise\n",
    "    to the reader :-)\n",
    "    \"\"\"\n",
    "    return r.std()*(periods_per_year**0.5)\n",
    "\n",
    "def sharpe_ratio(r, riskfree_rate, periods_per_year):\n",
    "    \"\"\"\n",
    "    Computes the annualized sharpe ratio of a set of returns\n",
    "    \"\"\"\n",
    "    # convert the annual riskfree rate to per period\n",
    "    rf_per_period = (1+riskfree_rate)**(1/periods_per_year)-1\n",
    "    excess_ret = r - rf_per_period\n",
    "    ann_ex_ret = annualize_rets(excess_ret, periods_per_year)\n",
    "    ann_vol = annualize_vol(r, periods_per_year)\n",
    "    return ann_ex_ret/ann_vol\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Coal     0.084275\n",
       "Steel    0.126052\n",
       "Whlsl    0.143494\n",
       "Other    0.160862\n",
       "Mines    0.177109\n",
       "Books    0.192686\n",
       "Games    0.194420\n",
       "Txtls    0.194906\n",
       "Trans    0.214624\n",
       "Autos    0.227548\n",
       "Cnstr    0.229351\n",
       "FabPr    0.265297\n",
       "Servs    0.267263\n",
       "Fin      0.282243\n",
       "Carry    0.285916\n",
       "ElcEq    0.293063\n",
       "Clths    0.293105\n",
       "Util     0.306945\n",
       "Hshld    0.307349\n",
       "Oil      0.330358\n",
       "Meals    0.332717\n",
       "BusEq    0.342974\n",
       "Chems    0.344903\n",
       "Beer     0.351780\n",
       "Rtail    0.364325\n",
       "Paper    0.364722\n",
       "Telcm    0.383294\n",
       "Hlth     0.437783\n",
       "Smoke    0.446361\n",
       "Food     0.454770\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "erk.sharpe_ratio(ind, 0.03, 12).sort_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1c66a0f0>"
      ]
     },
     "execution_count": 11,
     "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.sharpe_ratio(ind, 0.03, 12).sort_values().plot.bar(title=\"Industry Sharpe Ratios 1926-2018\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1c60b6d8>"
      ]
     },
     "execution_count": 12,
     "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.sharpe_ratio(ind[\"2000\":], 0.03, 12).sort_values().plot.bar(title='Industry Sharpe Ratios since 2000')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expected Returns and the Covariance Matrix\n",
    "\n",
    "Generating the efficient frontier requires a set of expected returns and a covariance matrix. For now, let's assume that we can estiamte these simply by looking back in time and naively assuming they will hold in the future. Clearly, they will not, but we will have plenty of time to dig into that in future lectures. For the moment, assume that our naive method of estimating these parameters will suffice.\n",
    "\n",
    "We can generate an estimate of expected returns using the `annualize_rets()` function, that returns a vector of expected returns. For instance, let's generate the set of expected returns based on historic returns from the 5 year period from 1996 through 2000:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "er = erk.annualize_rets(ind[\"1995\":\"2000\"], 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1c66a3c8>"
      ]
     },
     "execution_count": 14,
     "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": [
    "er.sort_values().plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's generate the covariance matrix. Fortunately, this is easy enough to do using the `.cov` method:"
   ]
  },
  {
   "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>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>Food</th>\n",
       "      <td>0.002287</td>\n",
       "      <td>0.002077</td>\n",
       "      <td>0.001757</td>\n",
       "      <td>0.000701</td>\n",
       "      <td>0.000886</td>\n",
       "      <td>0.001208</td>\n",
       "      <td>0.001474</td>\n",
       "      <td>0.001105</td>\n",
       "      <td>0.001253</td>\n",
       "      <td>0.001021</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000610</td>\n",
       "      <td>0.000211</td>\n",
       "      <td>-0.000280</td>\n",
       "      <td>0.001205</td>\n",
       "      <td>0.001312</td>\n",
       "      <td>0.000633</td>\n",
       "      <td>0.001165</td>\n",
       "      <td>0.001085</td>\n",
       "      <td>0.001839</td>\n",
       "      <td>0.000898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beer</th>\n",
       "      <td>0.002077</td>\n",
       "      <td>0.004599</td>\n",
       "      <td>0.001143</td>\n",
       "      <td>0.001147</td>\n",
       "      <td>0.000765</td>\n",
       "      <td>0.002447</td>\n",
       "      <td>0.001415</td>\n",
       "      <td>0.001689</td>\n",
       "      <td>0.001292</td>\n",
       "      <td>0.001721</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000978</td>\n",
       "      <td>0.000400</td>\n",
       "      <td>0.000028</td>\n",
       "      <td>0.001455</td>\n",
       "      <td>0.001974</td>\n",
       "      <td>0.000609</td>\n",
       "      <td>0.001442</td>\n",
       "      <td>0.001634</td>\n",
       "      <td>0.002236</td>\n",
       "      <td>0.001196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Smoke</th>\n",
       "      <td>0.001757</td>\n",
       "      <td>0.001143</td>\n",
       "      <td>0.007130</td>\n",
       "      <td>0.000296</td>\n",
       "      <td>-0.000099</td>\n",
       "      <td>0.000981</td>\n",
       "      <td>0.000761</td>\n",
       "      <td>0.000877</td>\n",
       "      <td>0.000687</td>\n",
       "      <td>0.000555</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000057</td>\n",
       "      <td>-0.000266</td>\n",
       "      <td>-0.000300</td>\n",
       "      <td>0.001061</td>\n",
       "      <td>0.000241</td>\n",
       "      <td>0.001363</td>\n",
       "      <td>0.000069</td>\n",
       "      <td>0.000590</td>\n",
       "      <td>0.001117</td>\n",
       "      <td>0.001418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Games</th>\n",
       "      <td>0.000701</td>\n",
       "      <td>0.001147</td>\n",
       "      <td>0.000296</td>\n",
       "      <td>0.003271</td>\n",
       "      <td>0.001485</td>\n",
       "      <td>0.001018</td>\n",
       "      <td>0.001814</td>\n",
       "      <td>0.001219</td>\n",
       "      <td>0.001547</td>\n",
       "      <td>0.001291</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001615</td>\n",
       "      <td>0.002399</td>\n",
       "      <td>0.002935</td>\n",
       "      <td>0.001615</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.001681</td>\n",
       "      <td>0.001649</td>\n",
       "      <td>0.001383</td>\n",
       "      <td>0.002080</td>\n",
       "      <td>0.002088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Books</th>\n",
       "      <td>0.000886</td>\n",
       "      <td>0.000765</td>\n",
       "      <td>-0.000099</td>\n",
       "      <td>0.001485</td>\n",
       "      <td>0.002302</td>\n",
       "      <td>0.000876</td>\n",
       "      <td>0.002037</td>\n",
       "      <td>0.000657</td>\n",
       "      <td>0.001559</td>\n",
       "      <td>0.001362</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001627</td>\n",
       "      <td>0.001996</td>\n",
       "      <td>0.001624</td>\n",
       "      <td>0.001481</td>\n",
       "      <td>0.001576</td>\n",
       "      <td>0.001205</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>0.001026</td>\n",
       "      <td>0.001979</td>\n",
       "      <td>0.001283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hshld</th>\n",
       "      <td>0.001208</td>\n",
       "      <td>0.002447</td>\n",
       "      <td>0.000981</td>\n",
       "      <td>0.001018</td>\n",
       "      <td>0.000876</td>\n",
       "      <td>0.002849</td>\n",
       "      <td>0.001046</td>\n",
       "      <td>0.001253</td>\n",
       "      <td>0.001226</td>\n",
       "      <td>0.001172</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000889</td>\n",
       "      <td>0.001111</td>\n",
       "      <td>0.000906</td>\n",
       "      <td>0.001594</td>\n",
       "      <td>0.001366</td>\n",
       "      <td>0.000578</td>\n",
       "      <td>0.001157</td>\n",
       "      <td>0.001076</td>\n",
       "      <td>0.001652</td>\n",
       "      <td>0.001322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Clths</th>\n",
       "      <td>0.001474</td>\n",
       "      <td>0.001415</td>\n",
       "      <td>0.000761</td>\n",
       "      <td>0.001814</td>\n",
       "      <td>0.002037</td>\n",
       "      <td>0.001046</td>\n",
       "      <td>0.004896</td>\n",
       "      <td>0.000759</td>\n",
       "      <td>0.002547</td>\n",
       "      <td>0.002105</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.001401</td>\n",
       "      <td>0.000746</td>\n",
       "      <td>0.002683</td>\n",
       "      <td>0.002466</td>\n",
       "      <td>0.001654</td>\n",
       "      <td>0.002607</td>\n",
       "      <td>0.002229</td>\n",
       "      <td>0.002699</td>\n",
       "      <td>0.001974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hlth</th>\n",
       "      <td>0.001105</td>\n",
       "      <td>0.001689</td>\n",
       "      <td>0.000877</td>\n",
       "      <td>0.001219</td>\n",
       "      <td>0.000657</td>\n",
       "      <td>0.001253</td>\n",
       "      <td>0.000759</td>\n",
       "      <td>0.002252</td>\n",
       "      <td>0.000444</td>\n",
       "      <td>0.000538</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001093</td>\n",
       "      <td>0.001390</td>\n",
       "      <td>0.001264</td>\n",
       "      <td>0.000552</td>\n",
       "      <td>0.000880</td>\n",
       "      <td>0.000907</td>\n",
       "      <td>0.000770</td>\n",
       "      <td>0.000900</td>\n",
       "      <td>0.001412</td>\n",
       "      <td>0.001099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Chems</th>\n",
       "      <td>0.001253</td>\n",
       "      <td>0.001292</td>\n",
       "      <td>0.000687</td>\n",
       "      <td>0.001547</td>\n",
       "      <td>0.001559</td>\n",
       "      <td>0.001226</td>\n",
       "      <td>0.002547</td>\n",
       "      <td>0.000444</td>\n",
       "      <td>0.002944</td>\n",
       "      <td>0.001705</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000860</td>\n",
       "      <td>0.001072</td>\n",
       "      <td>0.000935</td>\n",
       "      <td>0.002581</td>\n",
       "      <td>0.001966</td>\n",
       "      <td>0.001257</td>\n",
       "      <td>0.001661</td>\n",
       "      <td>0.001425</td>\n",
       "      <td>0.002143</td>\n",
       "      <td>0.001832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Txtls</th>\n",
       "      <td>0.001021</td>\n",
       "      <td>0.001721</td>\n",
       "      <td>0.000555</td>\n",
       "      <td>0.001291</td>\n",
       "      <td>0.001362</td>\n",
       "      <td>0.001172</td>\n",
       "      <td>0.002105</td>\n",
       "      <td>0.000538</td>\n",
       "      <td>0.001705</td>\n",
       "      <td>0.002882</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000790</td>\n",
       "      <td>0.000582</td>\n",
       "      <td>0.000685</td>\n",
       "      <td>0.001869</td>\n",
       "      <td>0.001760</td>\n",
       "      <td>0.001426</td>\n",
       "      <td>0.001696</td>\n",
       "      <td>0.001126</td>\n",
       "      <td>0.001789</td>\n",
       "      <td>0.001668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cnstr</th>\n",
       "      <td>0.001282</td>\n",
       "      <td>0.001945</td>\n",
       "      <td>0.001181</td>\n",
       "      <td>0.001723</td>\n",
       "      <td>0.001531</td>\n",
       "      <td>0.001770</td>\n",
       "      <td>0.002486</td>\n",
       "      <td>0.001217</td>\n",
       "      <td>0.001829</td>\n",
       "      <td>0.001648</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001488</td>\n",
       "      <td>0.002169</td>\n",
       "      <td>0.001968</td>\n",
       "      <td>0.001922</td>\n",
       "      <td>0.002030</td>\n",
       "      <td>0.001453</td>\n",
       "      <td>0.001852</td>\n",
       "      <td>0.001810</td>\n",
       "      <td>0.002331</td>\n",
       "      <td>0.001573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Steel</th>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000131</td>\n",
       "      <td>0.000167</td>\n",
       "      <td>0.002670</td>\n",
       "      <td>0.001797</td>\n",
       "      <td>0.001050</td>\n",
       "      <td>0.001702</td>\n",
       "      <td>0.000836</td>\n",
       "      <td>0.002327</td>\n",
       "      <td>0.001321</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001987</td>\n",
       "      <td>0.003934</td>\n",
       "      <td>0.005049</td>\n",
       "      <td>0.002306</td>\n",
       "      <td>0.001528</td>\n",
       "      <td>0.002210</td>\n",
       "      <td>0.001423</td>\n",
       "      <td>0.000553</td>\n",
       "      <td>0.001851</td>\n",
       "      <td>0.003370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FabPr</th>\n",
       "      <td>0.000613</td>\n",
       "      <td>0.000666</td>\n",
       "      <td>0.000668</td>\n",
       "      <td>0.002498</td>\n",
       "      <td>0.001704</td>\n",
       "      <td>0.001125</td>\n",
       "      <td>0.002430</td>\n",
       "      <td>0.000768</td>\n",
       "      <td>0.002273</td>\n",
       "      <td>0.001576</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001428</td>\n",
       "      <td>0.002647</td>\n",
       "      <td>0.003732</td>\n",
       "      <td>0.002367</td>\n",
       "      <td>0.001949</td>\n",
       "      <td>0.002082</td>\n",
       "      <td>0.001669</td>\n",
       "      <td>0.001507</td>\n",
       "      <td>0.001985</td>\n",
       "      <td>0.002458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ElcEq</th>\n",
       "      <td>0.001146</td>\n",
       "      <td>0.001107</td>\n",
       "      <td>-0.000013</td>\n",
       "      <td>0.001980</td>\n",
       "      <td>0.002084</td>\n",
       "      <td>0.001426</td>\n",
       "      <td>0.002239</td>\n",
       "      <td>0.001108</td>\n",
       "      <td>0.001560</td>\n",
       "      <td>0.001102</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002058</td>\n",
       "      <td>0.003312</td>\n",
       "      <td>0.002968</td>\n",
       "      <td>0.001540</td>\n",
       "      <td>0.001623</td>\n",
       "      <td>0.001080</td>\n",
       "      <td>0.002326</td>\n",
       "      <td>0.001300</td>\n",
       "      <td>0.002323</td>\n",
       "      <td>0.001556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Autos</th>\n",
       "      <td>0.000547</td>\n",
       "      <td>0.001296</td>\n",
       "      <td>0.000223</td>\n",
       "      <td>0.001994</td>\n",
       "      <td>0.001550</td>\n",
       "      <td>0.001466</td>\n",
       "      <td>0.002521</td>\n",
       "      <td>0.000851</td>\n",
       "      <td>0.001882</td>\n",
       "      <td>0.001811</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001544</td>\n",
       "      <td>0.001800</td>\n",
       "      <td>0.002273</td>\n",
       "      <td>0.001957</td>\n",
       "      <td>0.001963</td>\n",
       "      <td>0.001543</td>\n",
       "      <td>0.001792</td>\n",
       "      <td>0.001624</td>\n",
       "      <td>0.002226</td>\n",
       "      <td>0.002055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Carry</th>\n",
       "      <td>0.001419</td>\n",
       "      <td>0.001804</td>\n",
       "      <td>0.001485</td>\n",
       "      <td>0.001644</td>\n",
       "      <td>0.001301</td>\n",
       "      <td>0.001704</td>\n",
       "      <td>0.002873</td>\n",
       "      <td>0.000755</td>\n",
       "      <td>0.002374</td>\n",
       "      <td>0.001842</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000845</td>\n",
       "      <td>0.001082</td>\n",
       "      <td>0.001261</td>\n",
       "      <td>0.002619</td>\n",
       "      <td>0.002232</td>\n",
       "      <td>0.001461</td>\n",
       "      <td>0.001702</td>\n",
       "      <td>0.001868</td>\n",
       "      <td>0.002368</td>\n",
       "      <td>0.002159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mines</th>\n",
       "      <td>0.000829</td>\n",
       "      <td>0.000272</td>\n",
       "      <td>0.001311</td>\n",
       "      <td>0.001600</td>\n",
       "      <td>0.001281</td>\n",
       "      <td>0.000598</td>\n",
       "      <td>0.002467</td>\n",
       "      <td>0.001103</td>\n",
       "      <td>0.002345</td>\n",
       "      <td>0.001274</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001456</td>\n",
       "      <td>0.002260</td>\n",
       "      <td>0.002199</td>\n",
       "      <td>0.002562</td>\n",
       "      <td>0.001623</td>\n",
       "      <td>0.001991</td>\n",
       "      <td>0.001537</td>\n",
       "      <td>0.001218</td>\n",
       "      <td>0.001757</td>\n",
       "      <td>0.002606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Coal</th>\n",
       "      <td>0.000034</td>\n",
       "      <td>0.001261</td>\n",
       "      <td>-0.000544</td>\n",
       "      <td>0.001557</td>\n",
       "      <td>0.002051</td>\n",
       "      <td>0.001787</td>\n",
       "      <td>0.002433</td>\n",
       "      <td>0.001549</td>\n",
       "      <td>0.001910</td>\n",
       "      <td>0.000652</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000912</td>\n",
       "      <td>0.002373</td>\n",
       "      <td>0.002643</td>\n",
       "      <td>0.002099</td>\n",
       "      <td>0.001213</td>\n",
       "      <td>0.001793</td>\n",
       "      <td>0.000597</td>\n",
       "      <td>0.000382</td>\n",
       "      <td>0.002425</td>\n",
       "      <td>0.001443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oil</th>\n",
       "      <td>0.000933</td>\n",
       "      <td>0.000672</td>\n",
       "      <td>0.000849</td>\n",
       "      <td>0.000968</td>\n",
       "      <td>0.000868</td>\n",
       "      <td>0.000541</td>\n",
       "      <td>0.001646</td>\n",
       "      <td>0.000523</td>\n",
       "      <td>0.001843</td>\n",
       "      <td>0.001104</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000394</td>\n",
       "      <td>0.001002</td>\n",
       "      <td>0.000920</td>\n",
       "      <td>0.001570</td>\n",
       "      <td>0.001280</td>\n",
       "      <td>0.001423</td>\n",
       "      <td>0.000806</td>\n",
       "      <td>0.001091</td>\n",
       "      <td>0.001608</td>\n",
       "      <td>0.001688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Util</th>\n",
       "      <td>0.000858</td>\n",
       "      <td>0.000631</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.000023</td>\n",
       "      <td>0.000455</td>\n",
       "      <td>0.000350</td>\n",
       "      <td>0.000646</td>\n",
       "      <td>0.000543</td>\n",
       "      <td>0.000545</td>\n",
       "      <td>0.000777</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000136</td>\n",
       "      <td>-0.000596</td>\n",
       "      <td>-0.001000</td>\n",
       "      <td>0.000387</td>\n",
       "      <td>0.000468</td>\n",
       "      <td>0.000719</td>\n",
       "      <td>-0.000099</td>\n",
       "      <td>0.000315</td>\n",
       "      <td>0.000978</td>\n",
       "      <td>0.000840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Telcm</th>\n",
       "      <td>0.000610</td>\n",
       "      <td>0.000978</td>\n",
       "      <td>0.000057</td>\n",
       "      <td>0.001615</td>\n",
       "      <td>0.001627</td>\n",
       "      <td>0.000889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.001093</td>\n",
       "      <td>0.000860</td>\n",
       "      <td>0.000790</td>\n",
       "      <td>...</td>\n",
       "      <td>0.003065</td>\n",
       "      <td>0.002971</td>\n",
       "      <td>0.002708</td>\n",
       "      <td>0.001097</td>\n",
       "      <td>0.001366</td>\n",
       "      <td>0.001001</td>\n",
       "      <td>0.001718</td>\n",
       "      <td>0.001013</td>\n",
       "      <td>0.001560</td>\n",
       "      <td>0.001129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Servs</th>\n",
       "      <td>0.000211</td>\n",
       "      <td>0.000400</td>\n",
       "      <td>-0.000266</td>\n",
       "      <td>0.002399</td>\n",
       "      <td>0.001996</td>\n",
       "      <td>0.001111</td>\n",
       "      <td>0.001401</td>\n",
       "      <td>0.001390</td>\n",
       "      <td>0.001072</td>\n",
       "      <td>0.000582</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002971</td>\n",
       "      <td>0.006484</td>\n",
       "      <td>0.006079</td>\n",
       "      <td>0.001173</td>\n",
       "      <td>0.001299</td>\n",
       "      <td>0.001794</td>\n",
       "      <td>0.002447</td>\n",
       "      <td>0.000964</td>\n",
       "      <td>0.001630</td>\n",
       "      <td>0.002029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BusEq</th>\n",
       "      <td>-0.000280</td>\n",
       "      <td>0.000028</td>\n",
       "      <td>-0.000300</td>\n",
       "      <td>0.002935</td>\n",
       "      <td>0.001624</td>\n",
       "      <td>0.000906</td>\n",
       "      <td>0.000746</td>\n",
       "      <td>0.001264</td>\n",
       "      <td>0.000935</td>\n",
       "      <td>0.000685</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002708</td>\n",
       "      <td>0.006079</td>\n",
       "      <td>0.008346</td>\n",
       "      <td>0.001267</td>\n",
       "      <td>0.001225</td>\n",
       "      <td>0.002178</td>\n",
       "      <td>0.001756</td>\n",
       "      <td>0.000630</td>\n",
       "      <td>0.001395</td>\n",
       "      <td>0.002305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Paper</th>\n",
       "      <td>0.001205</td>\n",
       "      <td>0.001455</td>\n",
       "      <td>0.001061</td>\n",
       "      <td>0.001615</td>\n",
       "      <td>0.001481</td>\n",
       "      <td>0.001594</td>\n",
       "      <td>0.002683</td>\n",
       "      <td>0.000552</td>\n",
       "      <td>0.002581</td>\n",
       "      <td>0.001869</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001097</td>\n",
       "      <td>0.001173</td>\n",
       "      <td>0.001267</td>\n",
       "      <td>0.003004</td>\n",
       "      <td>0.002107</td>\n",
       "      <td>0.001396</td>\n",
       "      <td>0.001644</td>\n",
       "      <td>0.001420</td>\n",
       "      <td>0.002150</td>\n",
       "      <td>0.001686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Trans</th>\n",
       "      <td>0.001312</td>\n",
       "      <td>0.001974</td>\n",
       "      <td>0.000241</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.001576</td>\n",
       "      <td>0.001366</td>\n",
       "      <td>0.002466</td>\n",
       "      <td>0.000880</td>\n",
       "      <td>0.001966</td>\n",
       "      <td>0.001760</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001366</td>\n",
       "      <td>0.001299</td>\n",
       "      <td>0.001225</td>\n",
       "      <td>0.002107</td>\n",
       "      <td>0.002633</td>\n",
       "      <td>0.001084</td>\n",
       "      <td>0.001831</td>\n",
       "      <td>0.001741</td>\n",
       "      <td>0.002270</td>\n",
       "      <td>0.001557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Whlsl</th>\n",
       "      <td>0.000633</td>\n",
       "      <td>0.000609</td>\n",
       "      <td>0.001363</td>\n",
       "      <td>0.001681</td>\n",
       "      <td>0.001205</td>\n",
       "      <td>0.000578</td>\n",
       "      <td>0.001654</td>\n",
       "      <td>0.000907</td>\n",
       "      <td>0.001257</td>\n",
       "      <td>0.001426</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001001</td>\n",
       "      <td>0.001794</td>\n",
       "      <td>0.002178</td>\n",
       "      <td>0.001396</td>\n",
       "      <td>0.001084</td>\n",
       "      <td>0.002341</td>\n",
       "      <td>0.001061</td>\n",
       "      <td>0.000848</td>\n",
       "      <td>0.001594</td>\n",
       "      <td>0.001896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rtail</th>\n",
       "      <td>0.001165</td>\n",
       "      <td>0.001442</td>\n",
       "      <td>0.000069</td>\n",
       "      <td>0.001649</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>0.001157</td>\n",
       "      <td>0.002607</td>\n",
       "      <td>0.000770</td>\n",
       "      <td>0.001661</td>\n",
       "      <td>0.001696</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001718</td>\n",
       "      <td>0.002447</td>\n",
       "      <td>0.001756</td>\n",
       "      <td>0.001644</td>\n",
       "      <td>0.001831</td>\n",
       "      <td>0.001061</td>\n",
       "      <td>0.003197</td>\n",
       "      <td>0.001890</td>\n",
       "      <td>0.002010</td>\n",
       "      <td>0.001314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Meals</th>\n",
       "      <td>0.001085</td>\n",
       "      <td>0.001634</td>\n",
       "      <td>0.000590</td>\n",
       "      <td>0.001383</td>\n",
       "      <td>0.001026</td>\n",
       "      <td>0.001076</td>\n",
       "      <td>0.002229</td>\n",
       "      <td>0.000900</td>\n",
       "      <td>0.001425</td>\n",
       "      <td>0.001126</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001013</td>\n",
       "      <td>0.000964</td>\n",
       "      <td>0.000630</td>\n",
       "      <td>0.001420</td>\n",
       "      <td>0.001741</td>\n",
       "      <td>0.000848</td>\n",
       "      <td>0.001890</td>\n",
       "      <td>0.002630</td>\n",
       "      <td>0.001765</td>\n",
       "      <td>0.001129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fin</th>\n",
       "      <td>0.001839</td>\n",
       "      <td>0.002236</td>\n",
       "      <td>0.001117</td>\n",
       "      <td>0.002080</td>\n",
       "      <td>0.001979</td>\n",
       "      <td>0.001652</td>\n",
       "      <td>0.002699</td>\n",
       "      <td>0.001412</td>\n",
       "      <td>0.002143</td>\n",
       "      <td>0.001789</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001560</td>\n",
       "      <td>0.001630</td>\n",
       "      <td>0.001395</td>\n",
       "      <td>0.002150</td>\n",
       "      <td>0.002270</td>\n",
       "      <td>0.001594</td>\n",
       "      <td>0.002010</td>\n",
       "      <td>0.001765</td>\n",
       "      <td>0.003459</td>\n",
       "      <td>0.001945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Other</th>\n",
       "      <td>0.000898</td>\n",
       "      <td>0.001196</td>\n",
       "      <td>0.001418</td>\n",
       "      <td>0.002088</td>\n",
       "      <td>0.001283</td>\n",
       "      <td>0.001322</td>\n",
       "      <td>0.001974</td>\n",
       "      <td>0.001099</td>\n",
       "      <td>0.001832</td>\n",
       "      <td>0.001668</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001129</td>\n",
       "      <td>0.002029</td>\n",
       "      <td>0.002305</td>\n",
       "      <td>0.001686</td>\n",
       "      <td>0.001557</td>\n",
       "      <td>0.001896</td>\n",
       "      <td>0.001314</td>\n",
       "      <td>0.001129</td>\n",
       "      <td>0.001945</td>\n",
       "      <td>0.003655</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>30 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Food      Beer     Smoke     Games     Books     Hshld     Clths  \\\n",
       "Food   0.002287  0.002077  0.001757  0.000701  0.000886  0.001208  0.001474   \n",
       "Beer   0.002077  0.004599  0.001143  0.001147  0.000765  0.002447  0.001415   \n",
       "Smoke  0.001757  0.001143  0.007130  0.000296 -0.000099  0.000981  0.000761   \n",
       "Games  0.000701  0.001147  0.000296  0.003271  0.001485  0.001018  0.001814   \n",
       "Books  0.000886  0.000765 -0.000099  0.001485  0.002302  0.000876  0.002037   \n",
       "Hshld  0.001208  0.002447  0.000981  0.001018  0.000876  0.002849  0.001046   \n",
       "Clths  0.001474  0.001415  0.000761  0.001814  0.002037  0.001046  0.004896   \n",
       "Hlth   0.001105  0.001689  0.000877  0.001219  0.000657  0.001253  0.000759   \n",
       "Chems  0.001253  0.001292  0.000687  0.001547  0.001559  0.001226  0.002547   \n",
       "Txtls  0.001021  0.001721  0.000555  0.001291  0.001362  0.001172  0.002105   \n",
       "Cnstr  0.001282  0.001945  0.001181  0.001723  0.001531  0.001770  0.002486   \n",
       "Steel  0.000027  0.000131  0.000167  0.002670  0.001797  0.001050  0.001702   \n",
       "FabPr  0.000613  0.000666  0.000668  0.002498  0.001704  0.001125  0.002430   \n",
       "ElcEq  0.001146  0.001107 -0.000013  0.001980  0.002084  0.001426  0.002239   \n",
       "Autos  0.000547  0.001296  0.000223  0.001994  0.001550  0.001466  0.002521   \n",
       "Carry  0.001419  0.001804  0.001485  0.001644  0.001301  0.001704  0.002873   \n",
       "Mines  0.000829  0.000272  0.001311  0.001600  0.001281  0.000598  0.002467   \n",
       "Coal   0.000034  0.001261 -0.000544  0.001557  0.002051  0.001787  0.002433   \n",
       "Oil    0.000933  0.000672  0.000849  0.000968  0.000868  0.000541  0.001646   \n",
       "Util   0.000858  0.000631  0.001118  0.000023  0.000455  0.000350  0.000646   \n",
       "Telcm  0.000610  0.000978  0.000057  0.001615  0.001627  0.000889  0.001263   \n",
       "Servs  0.000211  0.000400 -0.000266  0.002399  0.001996  0.001111  0.001401   \n",
       "BusEq -0.000280  0.000028 -0.000300  0.002935  0.001624  0.000906  0.000746   \n",
       "Paper  0.001205  0.001455  0.001061  0.001615  0.001481  0.001594  0.002683   \n",
       "Trans  0.001312  0.001974  0.000241  0.001438  0.001576  0.001366  0.002466   \n",
       "Whlsl  0.000633  0.000609  0.001363  0.001681  0.001205  0.000578  0.001654   \n",
       "Rtail  0.001165  0.001442  0.000069  0.001649  0.001995  0.001157  0.002607   \n",
       "Meals  0.001085  0.001634  0.000590  0.001383  0.001026  0.001076  0.002229   \n",
       "Fin    0.001839  0.002236  0.001117  0.002080  0.001979  0.001652  0.002699   \n",
       "Other  0.000898  0.001196  0.001418  0.002088  0.001283  0.001322  0.001974   \n",
       "\n",
       "           Hlth     Chems     Txtls  ...     Telcm     Servs     BusEq  \\\n",
       "Food   0.001105  0.001253  0.001021  ...  0.000610  0.000211 -0.000280   \n",
       "Beer   0.001689  0.001292  0.001721  ...  0.000978  0.000400  0.000028   \n",
       "Smoke  0.000877  0.000687  0.000555  ...  0.000057 -0.000266 -0.000300   \n",
       "Games  0.001219  0.001547  0.001291  ...  0.001615  0.002399  0.002935   \n",
       "Books  0.000657  0.001559  0.001362  ...  0.001627  0.001996  0.001624   \n",
       "Hshld  0.001253  0.001226  0.001172  ...  0.000889  0.001111  0.000906   \n",
       "Clths  0.000759  0.002547  0.002105  ...  0.001263  0.001401  0.000746   \n",
       "Hlth   0.002252  0.000444  0.000538  ...  0.001093  0.001390  0.001264   \n",
       "Chems  0.000444  0.002944  0.001705  ...  0.000860  0.001072  0.000935   \n",
       "Txtls  0.000538  0.001705  0.002882  ...  0.000790  0.000582  0.000685   \n",
       "Cnstr  0.001217  0.001829  0.001648  ...  0.001488  0.002169  0.001968   \n",
       "Steel  0.000836  0.002327  0.001321  ...  0.001987  0.003934  0.005049   \n",
       "FabPr  0.000768  0.002273  0.001576  ...  0.001428  0.002647  0.003732   \n",
       "ElcEq  0.001108  0.001560  0.001102  ...  0.002058  0.003312  0.002968   \n",
       "Autos  0.000851  0.001882  0.001811  ...  0.001544  0.001800  0.002273   \n",
       "Carry  0.000755  0.002374  0.001842  ...  0.000845  0.001082  0.001261   \n",
       "Mines  0.001103  0.002345  0.001274  ...  0.001456  0.002260  0.002199   \n",
       "Coal   0.001549  0.001910  0.000652  ...  0.000912  0.002373  0.002643   \n",
       "Oil    0.000523  0.001843  0.001104  ...  0.000394  0.001002  0.000920   \n",
       "Util   0.000543  0.000545  0.000777  ...  0.000136 -0.000596 -0.001000   \n",
       "Telcm  0.001093  0.000860  0.000790  ...  0.003065  0.002971  0.002708   \n",
       "Servs  0.001390  0.001072  0.000582  ...  0.002971  0.006484  0.006079   \n",
       "BusEq  0.001264  0.000935  0.000685  ...  0.002708  0.006079  0.008346   \n",
       "Paper  0.000552  0.002581  0.001869  ...  0.001097  0.001173  0.001267   \n",
       "Trans  0.000880  0.001966  0.001760  ...  0.001366  0.001299  0.001225   \n",
       "Whlsl  0.000907  0.001257  0.001426  ...  0.001001  0.001794  0.002178   \n",
       "Rtail  0.000770  0.001661  0.001696  ...  0.001718  0.002447  0.001756   \n",
       "Meals  0.000900  0.001425  0.001126  ...  0.001013  0.000964  0.000630   \n",
       "Fin    0.001412  0.002143  0.001789  ...  0.001560  0.001630  0.001395   \n",
       "Other  0.001099  0.001832  0.001668  ...  0.001129  0.002029  0.002305   \n",
       "\n",
       "          Paper     Trans     Whlsl     Rtail     Meals       Fin     Other  \n",
       "Food   0.001205  0.001312  0.000633  0.001165  0.001085  0.001839  0.000898  \n",
       "Beer   0.001455  0.001974  0.000609  0.001442  0.001634  0.002236  0.001196  \n",
       "Smoke  0.001061  0.000241  0.001363  0.000069  0.000590  0.001117  0.001418  \n",
       "Games  0.001615  0.001438  0.001681  0.001649  0.001383  0.002080  0.002088  \n",
       "Books  0.001481  0.001576  0.001205  0.001995  0.001026  0.001979  0.001283  \n",
       "Hshld  0.001594  0.001366  0.000578  0.001157  0.001076  0.001652  0.001322  \n",
       "Clths  0.002683  0.002466  0.001654  0.002607  0.002229  0.002699  0.001974  \n",
       "Hlth   0.000552  0.000880  0.000907  0.000770  0.000900  0.001412  0.001099  \n",
       "Chems  0.002581  0.001966  0.001257  0.001661  0.001425  0.002143  0.001832  \n",
       "Txtls  0.001869  0.001760  0.001426  0.001696  0.001126  0.001789  0.001668  \n",
       "Cnstr  0.001922  0.002030  0.001453  0.001852  0.001810  0.002331  0.001573  \n",
       "Steel  0.002306  0.001528  0.002210  0.001423  0.000553  0.001851  0.003370  \n",
       "FabPr  0.002367  0.001949  0.002082  0.001669  0.001507  0.001985  0.002458  \n",
       "ElcEq  0.001540  0.001623  0.001080  0.002326  0.001300  0.002323  0.001556  \n",
       "Autos  0.001957  0.001963  0.001543  0.001792  0.001624  0.002226  0.002055  \n",
       "Carry  0.002619  0.002232  0.001461  0.001702  0.001868  0.002368  0.002159  \n",
       "Mines  0.002562  0.001623  0.001991  0.001537  0.001218  0.001757  0.002606  \n",
       "Coal   0.002099  0.001213  0.001793  0.000597  0.000382  0.002425  0.001443  \n",
       "Oil    0.001570  0.001280  0.001423  0.000806  0.001091  0.001608  0.001688  \n",
       "Util   0.000387  0.000468  0.000719 -0.000099  0.000315  0.000978  0.000840  \n",
       "Telcm  0.001097  0.001366  0.001001  0.001718  0.001013  0.001560  0.001129  \n",
       "Servs  0.001173  0.001299  0.001794  0.002447  0.000964  0.001630  0.002029  \n",
       "BusEq  0.001267  0.001225  0.002178  0.001756  0.000630  0.001395  0.002305  \n",
       "Paper  0.003004  0.002107  0.001396  0.001644  0.001420  0.002150  0.001686  \n",
       "Trans  0.002107  0.002633  0.001084  0.001831  0.001741  0.002270  0.001557  \n",
       "Whlsl  0.001396  0.001084  0.002341  0.001061  0.000848  0.001594  0.001896  \n",
       "Rtail  0.001644  0.001831  0.001061  0.003197  0.001890  0.002010  0.001314  \n",
       "Meals  0.001420  0.001741  0.000848  0.001890  0.002630  0.001765  0.001129  \n",
       "Fin    0.002150  0.002270  0.001594  0.002010  0.001765  0.003459  0.001945  \n",
       "Other  0.001686  0.001557  0.001896  0.001314  0.001129  0.001945  0.003655  \n",
       "\n",
       "[30 rows x 30 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov = ind[\"1995\":\"2000\"].cov()\n",
    "cov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next lab session, we'll take the expected returns vector and the covariance matrix we've constructed and start to plot the efficient frontier!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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>0.002302</td>\n",
       "      <td>0.001797</td>\n",
       "      <td>0.000868</td>\n",
       "      <td>0.001281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Steel</th>\n",
       "      <td>0.001797</td>\n",
       "      <td>0.006351</td>\n",
       "      <td>0.001804</td>\n",
       "      <td>0.003757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oil</th>\n",
       "      <td>0.000868</td>\n",
       "      <td>0.001804</td>\n",
       "      <td>0.002771</td>\n",
       "      <td>0.002184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mines</th>\n",
       "      <td>0.001281</td>\n",
       "      <td>0.003757</td>\n",
       "      <td>0.002184</td>\n",
       "      <td>0.006775</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Books     Steel       Oil     Mines\n",
       "Books  0.002302  0.001797  0.000868  0.001281\n",
       "Steel  0.001797  0.006351  0.001804  0.003757\n",
       "Oil    0.000868  0.001804  0.002771  0.002184\n",
       "Mines  0.001281  0.003757  0.002184  0.006775"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov = ind[\"1995\":\"2000\"][[\"Books\",\"Steel\",\"Oil\", \"Mines\"]].cov()\n",
    "cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Food', 'Beer', 'Smoke', 'Games', 'Books', 'Hshld', 'Clths', 'Hlth',\n",
       "       'Chems', 'Txtls', 'Cnstr', 'Steel', 'FabPr', 'ElcEq', 'Autos', 'Carry',\n",
       "       'Mines', 'Coal', 'Oil', 'Util', 'Telcm', 'Servs', 'BusEq', 'Paper',\n",
       "       'Trans', 'Whlsl', 'Rtail', 'Meals', 'Fin', 'Other'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind.columns\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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