pca_eigen_portfolios_m2_ex3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigen-portfolio construction using Principal Component Analysis (PCA)\n",
    "\n",
    "### PCA via sklearn.decomposition using S&P 500 Index stock data\n",
    "\n",
    "Welcome to your 2-nd assignment in Unsupervised Machine Learning in Finance.\n",
    "\n",
    "In this assignment we look in-depth at model-free factor analysis using PCA. By model-free we mean that we do not rely on any factors such as value or momentum to decompose portfolio returns, but instead using Principal Component Analysis (PCA) to deduce structure of portfolio returns.\n",
    "\n",
    "We work with S&P 500 index stock data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## About iPython Notebooks ##\n",
    "\n",
    "iPython Notebooks are interactive coding environments embedded in a webpage. You will be using iPython notebooks in this class. You only need to write code between the ### START CODE HERE ### and ### END CODE HERE ### comments. After writing your code, you can run the cell by either pressing \"SHIFT\"+\"ENTER\" or by clicking on \"Run Cell\" (denoted by a play symbol) in the upper bar of the notebook. \n",
    "\n",
    "We will often specify \"(≈ X lines of code)\" in the comments to tell you about how much code you need to write. It is just a rough estimate, so don't feel bad if your code is longer or shorter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  pandas: 0.19.2\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import os.path\n",
    "import numpy as np\n",
    "import datetime\n",
    "\n",
    "import sys\n",
    "sys.path.append(\"..\")\n",
    "import grading\n",
    "\n",
    "try:\n",
    "    import matplotlib.pyplot as plt\n",
    "    %matplotlib inline\n",
    "except:\n",
    "    pass\n",
    "\n",
    "try:\n",
    "    import pandas as pd\n",
    "    print(\"  pandas: %s\"% pd.__version__)\n",
    "except:\n",
    "    print(\"Missing pandas package\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### ONLY FOR GRADING. DO NOT EDIT ### \n",
    "submissions=dict()\n",
    "assignment_key=\"BBz-XobeEeegARIApDSa9g\" \n",
    "all_parts=[\"nvDA9\", \"ykDlW\", \"rpYVm\",\"oWy6l\",\"MWWt7\",\"3VyJD\"]\n",
    "### ONLY FOR GRADING. DO NOT EDIT ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "COURSERA_TOKEN = \" \"  # the key provided to the Student under his/her email on submission page\n",
    "COURSERA_EMAIL =  \" \"  # the email"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Asset prices shape (3493, 419)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>AA</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>ABC</th>\n",
       "      <th>ABT</th>\n",
       "      <th>ADBE</th>\n",
       "      <th>ADI</th>\n",
       "      <th>ADM</th>\n",
       "      <th>ADP</th>\n",
       "      <th>ADSK</th>\n",
       "      <th>AEE</th>\n",
       "      <th>AEP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-27</th>\n",
       "      <td>46.1112</td>\n",
       "      <td>78.9443</td>\n",
       "      <td>3.9286</td>\n",
       "      <td>4.5485</td>\n",
       "      <td>13.7898</td>\n",
       "      <td>15.6719</td>\n",
       "      <td>48.0313</td>\n",
       "      <td>10.8844</td>\n",
       "      <td>39.5477</td>\n",
       "      <td>8.1250</td>\n",
       "      <td>32.9375</td>\n",
       "      <td>33.5625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-28</th>\n",
       "      <td>45.8585</td>\n",
       "      <td>77.8245</td>\n",
       "      <td>3.6295</td>\n",
       "      <td>4.5485</td>\n",
       "      <td>14.2653</td>\n",
       "      <td>14.3906</td>\n",
       "      <td>47.7500</td>\n",
       "      <td>10.7143</td>\n",
       "      <td>38.5627</td>\n",
       "      <td>7.7188</td>\n",
       "      <td>32.3125</td>\n",
       "      <td>33.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-31</th>\n",
       "      <td>44.5952</td>\n",
       "      <td>78.0345</td>\n",
       "      <td>3.7054</td>\n",
       "      <td>4.3968</td>\n",
       "      <td>14.5730</td>\n",
       "      <td>13.7656</td>\n",
       "      <td>46.7500</td>\n",
       "      <td>10.6576</td>\n",
       "      <td>37.3807</td>\n",
       "      <td>7.6406</td>\n",
       "      <td>32.5625</td>\n",
       "      <td>33.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-01</th>\n",
       "      <td>47.8377</td>\n",
       "      <td>80.7640</td>\n",
       "      <td>3.5804</td>\n",
       "      <td>4.5333</td>\n",
       "      <td>14.7128</td>\n",
       "      <td>13.9688</td>\n",
       "      <td>49.0000</td>\n",
       "      <td>10.8844</td>\n",
       "      <td>37.9717</td>\n",
       "      <td>7.9219</td>\n",
       "      <td>32.5625</td>\n",
       "      <td>33.6875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-02</th>\n",
       "      <td>51.5434</td>\n",
       "      <td>83.4934</td>\n",
       "      <td>3.5290</td>\n",
       "      <td>4.5788</td>\n",
       "      <td>14.7968</td>\n",
       "      <td>15.3281</td>\n",
       "      <td>48.1250</td>\n",
       "      <td>10.6576</td>\n",
       "      <td>35.9032</td>\n",
       "      <td>7.9688</td>\n",
       "      <td>32.5625</td>\n",
       "      <td>33.6250</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  A       AA    AAPL     ABC      ABT     ADBE      ADI  \\\n",
       "2000-01-27  46.1112  78.9443  3.9286  4.5485  13.7898  15.6719  48.0313   \n",
       "2000-01-28  45.8585  77.8245  3.6295  4.5485  14.2653  14.3906  47.7500   \n",
       "2000-01-31  44.5952  78.0345  3.7054  4.3968  14.5730  13.7656  46.7500   \n",
       "2000-02-01  47.8377  80.7640  3.5804  4.5333  14.7128  13.9688  49.0000   \n",
       "2000-02-02  51.5434  83.4934  3.5290  4.5788  14.7968  15.3281  48.1250   \n",
       "\n",
       "                ADM      ADP    ADSK      AEE      AEP  \n",
       "2000-01-27  10.8844  39.5477  8.1250  32.9375  33.5625  \n",
       "2000-01-28  10.7143  38.5627  7.7188  32.3125  33.0000  \n",
       "2000-01-31  10.6576  37.3807  7.6406  32.5625  33.5000  \n",
       "2000-02-01  10.8844  37.9717  7.9219  32.5625  33.6875  \n",
       "2000-02-02  10.6576  35.9032  7.9688  32.5625  33.6250  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load dataset\n",
    "asset_prices = pd.read_csv(os.getcwd() + '/data/spx_holdings_and_spx_closeprice.csv',\n",
    "                     date_parser=lambda dt: pd.to_datetime(dt, format='%Y-%m-%d'),\n",
    "                     index_col = 0).dropna()\n",
    "n_stocks_show = 12\n",
    "print('Asset prices shape', asset_prices.shape)\n",
    "asset_prices.iloc[:, :n_stocks_show].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last column contains SPX index prices:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>STJ</th>\n",
       "      <th>SVU</th>\n",
       "      <th>SWY</th>\n",
       "      <th>TEG</th>\n",
       "      <th>TER</th>\n",
       "      <th>TGNA</th>\n",
       "      <th>THC</th>\n",
       "      <th>X</th>\n",
       "      <th>MAR.1</th>\n",
       "      <th>SPX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-27</th>\n",
       "      <td>5.5918</td>\n",
       "      <td>86.6178</td>\n",
       "      <td>26.3983</td>\n",
       "      <td>11.3873</td>\n",
       "      <td>65.8677</td>\n",
       "      <td>22.1921</td>\n",
       "      <td>60.9705</td>\n",
       "      <td>20.7086</td>\n",
       "      <td>12.2457</td>\n",
       "      <td>1398.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-28</th>\n",
       "      <td>5.4520</td>\n",
       "      <td>82.4218</td>\n",
       "      <td>27.4137</td>\n",
       "      <td>11.2230</td>\n",
       "      <td>60.3487</td>\n",
       "      <td>21.7558</td>\n",
       "      <td>62.3032</td>\n",
       "      <td>20.1183</td>\n",
       "      <td>12.0742</td>\n",
       "      <td>1360.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-31</th>\n",
       "      <td>5.5499</td>\n",
       "      <td>86.3181</td>\n",
       "      <td>28.2444</td>\n",
       "      <td>11.0862</td>\n",
       "      <td>62.1484</td>\n",
       "      <td>22.0533</td>\n",
       "      <td>60.6373</td>\n",
       "      <td>19.5772</td>\n",
       "      <td>12.1722</td>\n",
       "      <td>1394.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-01</th>\n",
       "      <td>5.4240</td>\n",
       "      <td>83.0212</td>\n",
       "      <td>28.7982</td>\n",
       "      <td>11.1683</td>\n",
       "      <td>67.3674</td>\n",
       "      <td>22.2120</td>\n",
       "      <td>60.4708</td>\n",
       "      <td>19.5772</td>\n",
       "      <td>12.5151</td>\n",
       "      <td>1409.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-02</th>\n",
       "      <td>5.3541</td>\n",
       "      <td>81.5226</td>\n",
       "      <td>28.6136</td>\n",
       "      <td>11.1956</td>\n",
       "      <td>68.9271</td>\n",
       "      <td>22.6483</td>\n",
       "      <td>62.4698</td>\n",
       "      <td>19.5281</td>\n",
       "      <td>12.3192</td>\n",
       "      <td>1409.12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               STJ      SVU      SWY      TEG      TER     TGNA      THC  \\\n",
       "2000-01-27  5.5918  86.6178  26.3983  11.3873  65.8677  22.1921  60.9705   \n",
       "2000-01-28  5.4520  82.4218  27.4137  11.2230  60.3487  21.7558  62.3032   \n",
       "2000-01-31  5.5499  86.3181  28.2444  11.0862  62.1484  22.0533  60.6373   \n",
       "2000-02-01  5.4240  83.0212  28.7982  11.1683  67.3674  22.2120  60.4708   \n",
       "2000-02-02  5.3541  81.5226  28.6136  11.1956  68.9271  22.6483  62.4698   \n",
       "\n",
       "                  X    MAR.1      SPX  \n",
       "2000-01-27  20.7086  12.2457  1398.56  \n",
       "2000-01-28  20.1183  12.0742  1360.16  \n",
       "2000-01-31  19.5772  12.1722  1394.46  \n",
       "2000-02-01  19.5772  12.5151  1409.28  \n",
       "2000-02-02  19.5281  12.3192  1409.12  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Last column contains SPX index prices:')\n",
    "asset_prices.iloc[:, -10:].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part 1 (Asset Returns Calculation)\n",
    "**Instructions:**\n",
    "\n",
    "Calculate percent returns, also known as simple returns using asse_prices. assign the result to variable asset_returns. Keep only not-nan values in the resulting pandas.DataFrame\n",
    "\n",
    "Calculate de-meaned returns and scale them by standard deviation $\\sigma$. Assign result to normed_returns variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now compute stock returns and normalize stock returns data by subtracting the mean and dividing by standard diviation. This normalization is required by PCA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>STJ</th>\n",
       "      <th>SVU</th>\n",
       "      <th>SWY</th>\n",
       "      <th>TEG</th>\n",
       "      <th>TER</th>\n",
       "      <th>TGNA</th>\n",
       "      <th>THC</th>\n",
       "      <th>X</th>\n",
       "      <th>MAR.1</th>\n",
       "      <th>SPX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-12-16</th>\n",
       "      <td>0.852722</td>\n",
       "      <td>0.965219</td>\n",
       "      <td>-1.168885</td>\n",
       "      <td>0.884751</td>\n",
       "      <td>0.095865</td>\n",
       "      <td>0.656639</td>\n",
       "      <td>0.180014</td>\n",
       "      <td>-0.238498</td>\n",
       "      <td>0.465047</td>\n",
       "      <td>0.467931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-17</th>\n",
       "      <td>0.275173</td>\n",
       "      <td>0.517307</td>\n",
       "      <td>-0.086106</td>\n",
       "      <td>-0.306213</td>\n",
       "      <td>0.589689</td>\n",
       "      <td>-0.118610</td>\n",
       "      <td>-0.549523</td>\n",
       "      <td>0.025268</td>\n",
       "      <td>-0.260013</td>\n",
       "      <td>-0.247921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-18</th>\n",
       "      <td>0.864485</td>\n",
       "      <td>0.509435</td>\n",
       "      <td>0.600714</td>\n",
       "      <td>1.210605</td>\n",
       "      <td>-0.190024</td>\n",
       "      <td>0.925461</td>\n",
       "      <td>0.756998</td>\n",
       "      <td>0.058428</td>\n",
       "      <td>0.952458</td>\n",
       "      <td>1.252703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-19</th>\n",
       "      <td>0.210069</td>\n",
       "      <td>0.399574</td>\n",
       "      <td>-0.100159</td>\n",
       "      <td>-0.757419</td>\n",
       "      <td>-0.208023</td>\n",
       "      <td>0.304913</td>\n",
       "      <td>-0.772205</td>\n",
       "      <td>1.544228</td>\n",
       "      <td>-0.167775</td>\n",
       "      <td>-0.056358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-20</th>\n",
       "      <td>0.827306</td>\n",
       "      <td>0.748420</td>\n",
       "      <td>0.372443</td>\n",
       "      <td>1.048113</td>\n",
       "      <td>0.264046</td>\n",
       "      <td>0.436874</td>\n",
       "      <td>0.320641</td>\n",
       "      <td>-0.740854</td>\n",
       "      <td>0.373717</td>\n",
       "      <td>0.353859</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 STJ       SVU       SWY       TEG       TER      TGNA  \\\n",
       "2013-12-16  0.852722  0.965219 -1.168885  0.884751  0.095865  0.656639   \n",
       "2013-12-17  0.275173  0.517307 -0.086106 -0.306213  0.589689 -0.118610   \n",
       "2013-12-18  0.864485  0.509435  0.600714  1.210605 -0.190024  0.925461   \n",
       "2013-12-19  0.210069  0.399574 -0.100159 -0.757419 -0.208023  0.304913   \n",
       "2013-12-20  0.827306  0.748420  0.372443  1.048113  0.264046  0.436874   \n",
       "\n",
       "                 THC         X     MAR.1       SPX  \n",
       "2013-12-16  0.180014 -0.238498  0.465047  0.467931  \n",
       "2013-12-17 -0.549523  0.025268 -0.260013 -0.247921  \n",
       "2013-12-18  0.756998  0.058428  0.952458  1.252703  \n",
       "2013-12-19 -0.772205  1.544228 -0.167775 -0.056358  \n",
       "2013-12-20  0.320641 -0.740854  0.373717  0.353859  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asset_returns = pd.DataFrame(data=np.zeros(shape=(len(asset_prices.index), asset_prices.shape[1])), \n",
    "                             columns=asset_prices.columns.values,\n",
    "                             index=asset_prices.index)\n",
    "normed_returns = asset_returns\n",
    "### START CODE HERE ### (≈ 4 lines of code)\n",
    "# normed_returns is pandas.DataFrame that should contain normalized returns\n",
    "asset_returns = asset_prices.pct_change().dropna()\n",
    "normed_returns = (asset_returns - asset_returns.mean()) / asset_returns.std()\n",
    "### END CODE HERE ###\n",
    "\n",
    "\n",
    "normed_returns.iloc[-5:, -10:].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-0.19005437, -0.51371017, -2.71470869, -0.04977943,  2.18293305,\n",
       "       -2.68413088, -0.21246093, -0.76699639, -1.5407309 , -1.80394666,\n",
       "       -1.37299129, -0.99416907,  0.16136183,  0.72980366,  0.63485621,\n",
       "       -0.72131907, -0.01302927, -0.80797756,  0.39923062, -0.75893259,\n",
       "       -1.43444651, -1.12783867, -1.29385343, -0.44802859, -2.13973399,\n",
       "        0.58949813, -0.87826364,  0.31428572, -1.08060243, -0.31367868,\n",
       "        0.11819333, -1.8686777 , -1.87275168, -0.22608376, -0.04189121,\n",
       "       -0.02136145, -0.60458719, -1.43087396, -1.16679677, -1.65594274,\n",
       "       -0.50493241, -1.5196492 , -0.36359946, -0.58859176, -0.73289901,\n",
       "        0.87654672, -3.12410596, -1.33977245, -1.33866029, -0.53051976,\n",
       "       -1.28309222, -2.2171311 ,  1.75785074,  0.22815795, -0.48093428,\n",
       "       -0.21160476, -1.39163378, -1.8907977 , -1.26523275, -0.90790361,\n",
       "        1.20007622, -1.13783598, -1.06735573, -1.49029484,  1.65191927,\n",
       "       -0.94841616,  3.36936561, -0.82344479,  1.76591258,  0.0414378 ,\n",
       "       -2.73686257, -0.93544592,  0.02499427, -0.52726361, -0.34692757,\n",
       "       -3.31744267, -1.10532688, -0.797565  , -0.45450193,  1.58036671,\n",
       "       -1.05535759, -0.19732619, -0.85221605, -3.09447476, -2.41199636,\n",
       "       -0.9392503 , -1.88367011, -2.73709342, -2.97077299, -0.52321504,\n",
       "       -0.7113052 ,  2.02582123, -1.26160414, -3.24554378, -1.04361909,\n",
       "       -0.21374985,  0.86653839, -0.53475603,  0.92652973, -0.51024788])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "part_1=list(normed_returns.iloc[0,: 100].as_matrix().squeeze())\n",
    "try:\n",
    "    part1 = \" \".join(map(repr, part_1))\n",
    "except TypeError:\n",
    "    part1 = repr(part_1)\n",
    "submissions[all_parts[0]]=part1\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:1],all_parts,submissions)\n",
    "normed_returns.iloc[0,: 100].as_matrix().squeeze()\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train dataset: (3055, 419)\n",
      "Test dataset: (437, 419)\n"
     ]
    }
   ],
   "source": [
    "train_end = datetime.datetime(2012, 3, 26) \n",
    "\n",
    "df_train = None\n",
    "df_test = None\n",
    "df_raw_train = None\n",
    "df_raw_test = None\n",
    "\n",
    "df_train = normed_returns[normed_returns.index <= train_end].copy()\n",
    "df_test = normed_returns[normed_returns.index > train_end].copy()\n",
    "\n",
    "df_raw_train = asset_returns[asset_returns.index <= train_end].copy()\n",
    "df_raw_test = asset_returns[asset_returns.index > train_end].copy()\n",
    "\n",
    "print('Train dataset:', df_train.shape)\n",
    "print('Test dataset:', df_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we compute PCA using all available data. Once we do have PCA computed we fix variance explained at some number and see what is the smallest number of components needed to explain this variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part 2 (PCA fitting)\n",
    "**Instructions:**\n",
    "- Calculate covariance matrix using training data set, i.e. **df_train** for all assets.  Assign results to **cov_matrix**.\n",
    "- Calculate covariance matrix using training data set, i.e. **df_raw_train** for all assets.  Assign results to **cov_matrix_raw**.\n",
    "- Use scikit-learn PCA to fit PCA model to **cov_matrix**. Assign fitted model to **pca**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 components explain 80.00% of variance\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "import seaborn as sns\n",
    "\n",
    "stock_tickers = normed_returns.columns.values[:-1]\n",
    "assert 'SPX' not in stock_tickers, \"By accident included SPX index\"\n",
    "\n",
    "n_tickers = len(stock_tickers)\n",
    "pca = None\n",
    "cov_matrix = pd.DataFrame(data=np.ones(shape=(n_tickers, n_tickers)), columns=stock_tickers)\n",
    "cov_matrix_raw = cov_matrix\n",
    "\n",
    "if df_train is not None and df_raw_train is not None:\n",
    "    stock_tickers = asset_returns.columns.values[:-1]\n",
    "    assert 'SPX' not in stock_tickers, \"By accident included SPX index\"\n",
    "\n",
    "    ### START CODE HERE ### (≈ 2-3 lines of code)\n",
    "    cov_matrix = df_train.loc[:, df_train.columns != 'SPX'].cov()    \n",
    "    # computing PCA on S&P 500 stocks\n",
    "    pca = PCA().fit(cov_matrix)\n",
    "    # not normed covariance matrix\n",
    "    cov_matrix_raw = df_raw_train.loc[:, df_raw_train.columns != 'SPX'].cov()  \n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    cov_raw_df = pd.DataFrame({'Variance': np.diag(cov_matrix_raw)}, index=stock_tickers)    \n",
    "    # cumulative variance explained\n",
    "    var_threshold = 0.8\n",
    "    var_explained = np.cumsum(pca.explained_variance_ratio_)\n",
    "    num_comp = np.where(np.logical_not(var_explained < var_threshold))[0][0] + 1  # +1 due to zero based-arrays\n",
    "    print('%d components explain %.2f%% of variance' %(num_comp, 100* var_threshold))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 1.10446611,  1.09424087,  1.08190134,  1.10517006,  1.06941473,\n",
       "        1.10597862,  1.11869287,  1.0839399 ,  1.09803084,  1.06590728,\n",
       "        1.07798702,  1.107393  ,  1.12418337,  1.10412774,  1.07721126,\n",
       "        1.11952577,  1.11507312,  1.10687469,  1.04827028,  1.10800935,\n",
       "        1.10480045,  1.04297489,  1.07466613,  1.12510255,  1.10831513,\n",
       "        1.09118222,  1.08418296,  1.02668336,  1.09808835,  1.08506552,\n",
       "        1.08022595,  1.08116796,  1.09591114,  0.99807688,  1.11068716,\n",
       "        1.01433366,  1.10360906,  1.06598755,  1.11003861,  1.0879927 ,\n",
       "        1.08236593,  1.093903  ,  1.08489115,  1.1050359 ,  0.99850151,\n",
       "        1.08347058,  1.1019318 ,  1.08932552,  1.08876911,  1.09560839,\n",
       "        1.1027858 ,  1.09150807,  1.07067427,  1.1119615 ,  1.07304668,\n",
       "        1.10625388,  1.10454709,  1.11531806,  1.06707655,  1.08925028,\n",
       "        1.07207857,  1.08151718,  1.11539438,  1.09563297,  1.09915349,\n",
       "        1.10098573,  1.09770417,  1.05315411,  1.08235287,  1.10420203,\n",
       "        1.10765821,  1.08524638,  1.02531398,  1.10595498,  1.10337109,\n",
       "        1.10913785,  1.08713617,  1.11825335,  1.11819787,  1.08122381,\n",
       "        1.11686164,  1.0559472 ,  1.09614651,  1.10212167,  1.06172191,\n",
       "        1.09017849,  1.09338258,  1.11186398,  1.04779305,  1.0920264 ,\n",
       "        1.09189706,  1.10245445,  1.09369637,  1.09399401,  1.09920198,\n",
       "        0.92356831,  1.0993287 ,  1.05898641,  1.08077773,  1.09900737])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "part_2 = np.diag(cov_matrix[: 100])\n",
    "try:\n",
    "    part2 = \" \".join(map(repr, part_2))\n",
    "except TypeError:\n",
    "    part2 = repr(part_2)\n",
    "submissions[all_parts[1]]=part2\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:2],all_parts,submissions)\n",
    "### GRADED PART (DO NOT EDIT) ###\n",
    "np.diag(cov_matrix[: 100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wDKOgDSZMmICXl5e5Ee7duzd+fn7UqFHDvM2iRYv49ttvefXVVxk0aFCBA2Zk\nZGJjY30PUr9zpq13HmO0vddZiIiIiMiDVqQ1wTnl1TMPGjSIV199lYEDB/Lkk0/y5JNP5hsfG5t8\np0PeQ853FRUVlXBXcS4uzhYT+6jlq9i/J/ZRy1exD/eYin34Yx+1fBX7cI95L7i45N/7FbocwtXV\nlejoaPPjyMhI85KH69evs2/fPgDs7e1p06YNBw8e/Kv5ioiIiIjcV4U2wS1btmTDhg0ABAUF4erq\nipOTEwAZGRm8//77JCUlAXDs2LFcyyRERERERB5GhS6HaNy4MfXr16dnz56YTCYmTpyIv78/zs7O\n+Pj4MGTIEF599VVsbGyoXbs2HTp0+DvyFhERERG5a0VaEzxq1Khcj+vUqWP+umvXrnTt2vXeZiUi\nIiIich/pL8aJiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdN\nsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVR\nEywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx\n1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhY\nHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIi\nFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMWxKcpG06ZN48iRI5hMJsaOHYuHh4f5uT179jBr1iys\nrKyoUaMGfn5+WFmptxYRERGRh1eh3WpgYCChoaGsWrUKPz8//Pz8cj3/4YcfMnfuXFauXElSUhI7\nduy4b8mKiIiIiNwLhTbBAQEBeHt7A+Du7k5cXByJiYnm5/39/SlfvjwApUuXJjY29j6lKiIiIiJy\nb5gMwzAK2mDChAl4eXmZG+HevXvj5+dHjRo1cm0XGRlJnz59WL16NaVKlcp3fxkZmdjYWN+D1O+c\naeudxxht73UWIiIiIvKgFWlNcE559czXrl3jzTffZOLEiQU2wACxscl3OuQ95HxXUVFRCXcV5+Li\nbDGxj1q+iv17Yh+1fBX7cI+p2Ic/9lHLV7EP95j3gotL/r1foU2wq6sr0dHR5seRkZG4uLiYHycm\nJjJw4EDDIs5CAAAgAElEQVRGjBhBq1at/mKqDy/XoDtvoHUWWUREROThVOia4JYtW7JhwwYAgoKC\ncHV1xcnJyfz8jBkzeO2112jTps39y1JERERE5B4q9Exw48aNqV+/Pj179sRkMjFx4kT8/f1xdnam\nVatWrFu3jtDQUNasWQPAc889R48ePe574iIiIiIid6tIa4JHjRqV63GdOnXMXx8/fvzeZiQiIiIi\ncp/pr1qIiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiI\niIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywi\nIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASL\niIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXB\nIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMWxedAJ/K9zDXK+\nqzij7b3NQ0RERET+S2eCRURERMTiqAkWEREREYtTpCZ42rRp9OjRg549e3L06NFcz6WmpjJmzBi6\ndu16XxIUEREREbnXCm2CAwMDCQ0NZdWqVfj5+eHn55fr+Y8//pi6devetwRFRERERO61QpvggIAA\nvL29AXB3dycuLo7ExETz8yNHjjQ/LyIiIiLyKDAZhmEUtMGECRPw8vIyN7q9e/fGz8+PGjVqmLe5\nfPkyb7/9Nv7+/oUOmJGRiY2N9V9M++6Ytt55TPanNNxt7N3E5RxXRERERO69O/6ItEJ65kLFxib/\npfi/5u4+riwqKuGuY/+Km+PeORcX57899kGMqdiHP/ZRy1exD/eYin34Yx+1fBX7cI95L7i45N+/\nFbocwtXVlejoaPPjyMhIXFxc7k1mIiIiIiIPQKFNcMuWLdmwYQMAQUFBuLq64uTkdN8TExERERG5\nXwpdDtG4cWPq169Pz549MZlMTJw4EX9/f5ydnfHx8eHtt98mPDyc8+fP07dvX7p3787zzz//d+Qu\nIiIiInJXirQmeNSoUbke16lTx/z13Llz721GIiIiIiL3mf5inIiIiIhYHDXBIiIiImJx1ASLiIiI\niMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIi\nImJx1ASLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMVREywiIiIiFsfmQScg\n+XMNcr6rOKPtvc1DRERE5H+NzgSLiIiIiMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiI\niMVREywiIiIiFkdNsIiIiIhYHDXBIiIiImJx1ASLiIiIiMXRX4z7H6W/NiciIiKSP50JFhERERGL\noyZYRERERCyOmmARERERsThqgkVERETE4qgJFhERERGLoyZYRERERCyOPiJNbnM3H6+mj1YTERGR\nR4nOBIuIiIiIxVETLCIiIiIWR8sh5J76K0spHlSsiIiIWJ4inQmeNm0aPXr0oGfPnhw9ejTXc7t3\n7+all16iR48ezJ8//74kKSIiIiJyLxV6JjgwMJDQ0FBWrVrF2bNnGTt2LKtWrTI/P3XqVJYsWUK5\ncuV45ZVX8PX1pWbNmvc1aZF76W7PIt9N3IOOFRERkZsKbYIDAgLw9vYGwN3dnbi4OBITE3FycuLS\npUuULFmSChUqAODl5UVAQICaYJGH1N/dfD/opS4PIvZR/OXoUZvjBxX7KL0+Dyr2UX1t/0rso/T6\n/JXY/8XlhybDMIyCNpgwYQJeXl7mRrh37974+flRo0YNDh48yJIlS8zLIP71r39x6dIl3nnnnfuf\nuYiIiIjIXbrjT4copGcWEREREXnoFdoEu7q6Eh0dbX4cGRmJi4tLns9FRETg6up6H9IUEREREbl3\nCm2CW7ZsyYYNGwAICgrC1dUVJycnACpXrkxiYiKXL18mIyODLVu20LJly/ubsYiIiIjIX1TommCA\nTz/9lP3792MymZg4cSInTpzA2dkZHx8f9u3bx6effgpAx44dGTBgwH1PWkRERETkryhSEywiIiIi\n8r9EfzZZRERERCyOmmARERERsThqgvMQFxdHQkLCXcVmZmbeVVxkZCSXLl26q9ioqCiuXr16V7Fn\nz57l4sWLdxV78OBBtm7delexkZGRhIeH31Xs5s2bmTFjxl3FXrt2jYiIiLuKTUxMJC0t7a5iHyZ/\n5wqoux0rJSXlHmdSNHdbk5bs715Rp5r63/co1JTq6X+D9UcfffTRg07iYbJt2zamTJnCvn372Ldv\nH23atClybGBgILt376ZixYo4ODgUOW7r1q1MnjyZHTt2sHPnTjp27Fjk2B07djBp0iR27tzJgQMH\naNeuXZHisrKySEhIoE+fPiQmJlKuXDnKlClT5HH37NnDF198QYcOHShXrlyR4wA2bdrElClTOHPm\nDCVKlKBSpUpFjg0MDOTLL78kMjIST09PSpcuXeTYnTt3MmXKFHbt2kVgYCDt27cvcuy2bduYPn06\nx48f59ChQzRv3rzIsdlOnDhBREQEqamplCxZErj55msymQqNzczMxMrKiqysrCJtn9OhQ4c4c+YM\nUVFRVKxYscjxR44c4dy5c8TGxt7xa7x9+3ZOnz6Nu7t7kY8xW0BAANu2baNOnTrY2BT6Ry1zOXTo\nEKGhoRiGYZ7jotq3bx8zZ86kbt26d/R/AeDo0aOEhoYSGxt7xx8TGRISQkxMDBkZGeZP3inKnD1q\n9QSqqaJ6EPUEqqmijvuo1RM8mjX1d1ATnMPly5eZPXs248aNo2vXrqxYsYKjR4/i4eFRpKZ2xowZ\nhIWFkZ6eToUKFYoUEx4ezuzZs5k6dSr9+vXjq6++Ij09HQ8Pj0Jjg4ODmTVrFh9++CG9evViw4YN\ntG3btkj/KU0mE8WKFePs2bMkJSWRmZmJjY2N+TOgCxIQEMBHH33Exx9/TN26dUlOTiYtLQ07O7tC\nY5OTk5k/fz7Dhw+nd+/eVKpUibS0NKytrQuN3bt3L7Nnz2bMmDG4uLhga2tL5cqVC40DOHXqlHmu\n+vXrx08//USrVq0oVqxYobGhoaF8+umnjB07ls6dO7No0SJ27NhBu3btipQ33GzAZ82axcWLFzly\n5AghISE0adIEk8lU6BtCYGAgw4cP59lnn6VYsWJ39ENm9+7dzJo1i4yMDPbv309SUhJ16tQpUr5z\n5swhISGB48eP4+7ufkdv2P/85z+ZOXMmTz31FJUqVTKfaSks74CAAObNm0eXLl2oWrVqrucKm6e9\ne/cyZcoUUlNTqVKlCuXLly9ybEBAAJ9//jlOTk64u7vfNnZBsucqPj6e48ePU6VKlSL/cpYde+XK\nFUJCQggJCcHT07PQunjU6innsaqmCvZX6mnHjh3MnTv3juspe1zVVOE19ajVEzyaNfV30XKIHBwc\nHLC2tsbW1hYHBwe++uorEhISmDt3bpHiixUrRvny5Tl79ix//PEHMTExhcbY2tqSmpqKldXNl2Lg\nwIFkZGQUaTw7Ozvc3NyoU6cOYWFhnDx5klmzZjFp0qQixQO4ublhZWVFTEwMhw8fZvPmzZw6dSrf\n7Q3D4NKlSzz22GPY29tz48YNRowYwejRoxk7dmyhl4hMJhOxsbFkZGSQmJjIm2++yYgRIxg3blyB\ncWlpaRw6dIgPPvgAT09PXFxcWLFiRZHmGG7Os5ubGxUrViQ2NpZjx44xd+5cpk6dWmisvb09jo6O\n2NvbY2tri5+fH0FBQSxYsKDQWMMwSEtLY8WKFQwePJjp06fTq1cvjh8/zscff2yek/xi4eZyl4iI\nCEaNGkViYqL5bEth42ZkZPDPf/6T//u//2PMmDE0a9asSEtfEhMTWbZsGe+//z4TJkwgPT2d5ORk\nYmNjb8stPx4eHtSrV4/Ro0ezadMmTCZToW94x48fZ9q0aQwYMIAnn3ySmJgYTp06xenTpwHMb5x5\nHSvAhg0b6NWrF+PHj6dWrVqcPXuWs2fPFhgLN38wzZ8/n6lTp/L+++/z448/Eh8fX6RLpAkJCSxd\nupT333+fcePGYW1tTVxcHImJiQXGGYbBjRs3+P777xk8eDAffvghHTp0YPPmzSxevNicc17S0tJY\nuXIlb7zxxh3VU7Zr165x5cqVO6onuHmmb+XKlQwePPiO6glu1tS3337L6NGj77qmGjRocMc1FRQU\nxPTp0+nXr98d1VS2jRs30r179zuuqcDAQBYsWMDkyZPvqKYSExNZvnw577333h3VE0BqaiorVqzg\njTfeuKN6gv/W1MCBA++qpqKjoy2iph5UPe3du/eu6gn+Wk3duHGDFStWMHDgwDuuqfT0dFauXMmg\nQYPuqqb+LjoTnIO9vT0RERHmyyrOzs60a9eOpUuXEhwcTOvWrQuMb9CgAU8//TRpaWmcOHGC6Oho\nKlWqhIODQ76/9WSfzaxfvz4AZ86cYc+ePfj6+gKQkZFhbpBvZWNjQ8mSJalSpQrr16+nWrVqvPrq\nq6xdu5Y9e/bg7e2db67Z+dja2mJtbU3//v1ZsWIFixcvxtPTk1q1auUZZzKZcHd3x9HRkcWLF+Pv\n70+3bt144403+P333wkICChwXFtbW+zt7dmxYwd//vkn3t7eDBgwgLVr17J37146dOiQZ5y1tTUe\nHh5UqlSJzMxMKlWqxKVLl6hWrRqPPfaY+VJcfqytrTl27Bh//PEHixcv5uWXX6Zv374sXryYY8eO\nFbg0ws7OjosXL3L69GmsrKzYu3cvbm5uBAYGEhYWRtOmTfONzczMxNbWlpMnT+Lm5kblypUpU6YM\njRo14rfffiMsLIzGjRvnG2tlZUVISAhdunQhOjqa5cuX07Fjx0LPtmSf2d+5cydNmzbF1dUVW1tb\nfvrpJ9q2bYutrW2esdn5btu2jZdffpnMzEw++eQTwsLC2LVrF2fPnjX/Jp9fvgBWVlaUL1+eXr16\nMXHiRFJSUggKCqJRo0b5/l/IPtPQpEkTkpOTmTJlCkFBQezevZvg4GCaN29e4LjR0dEkJydTsWJF\nhg8fTlBQEIGBgZw/f55//OMf+c7VlStXaN26NfXq1cPKyopTp07RuHFjHBwcCp1jKysrNm3aRJs2\nbUhNTWXhwoWEhIRw5MgRwsLC8r2ik5WVhZ2dHYGBgXh4eFC+fHlcXFw4ffo0p0+fJikpyfyekFNE\nRAQJCQnEx8dTq1YtypcvX+R6ioiIICkpiYSEBLp27crly5f57rvvilRPERERXL9+ndDQUJ566inK\nlClTpHrKjo2MjCQ0NJQePXqQlJTEZ599VqSaioiIICYmhpIlS1K8eHHKlClD7969i1RT165dIzAw\nkIyMDJo2bUpsbCxTp04tUk1lX761sbEhJSWFsmXLMmLEiCLVVExMDHv37qVv377UrFmTrKwsQkJC\nCq2piIgIrl69ypkzZ/Dy8iIuLo6vv/66SPWUPU8RERF4enpStmzZItUT3Lw/Izk5mevXr+Pu7n5H\nNRUZGcmNGzeIi4uja9euXLlyhW+//bZINRUZGUliYiLnz5+/45qKiooiOjqa8+fP0717d5KTk/n0\n00+LVFNRUVFcv36dEiVK4ODgUOSaiomJ4cCBA6SmpvKPf/yD69evF7meIiMjSU9Px8rKipSUFFxc\nXIpcT9evX2f//v306dOHmjVrYhgGwcHBRXqPyj6Bcvr0aby8vIiPjy9yTUVGRhIfH8/Vq1fx8PDA\nxcWlyDV19uxZUlJSiIqKwt3dnYoVKxa5pv5uaoJzMJlMuLi48Ouvv2JlZUXJkiVxdnamTZs27Ny5\nkzZt2hTYaDk6OmIymXBzcyMpKYmTJ0+SkZFBYGAghw4dwtPT87YYa2trqlSpYn58+fJlzp49i4+P\nD+vWrWPnzp00btw4zyIvVqyYOdbT05OmTZvi6OjICy+8wKpVq2jVqlW+SzKy95eZmcnvv/+OyWTi\nl19+4YknnqB48eLmHzh5sbGxoVq1amRkZJCWlsZrr72Go6MjnTp1YvXq1QWOC1CmTBlOnjzJxYsX\n6dSpE1WqVDHn3KJFC4oXL55nXPbSAysrK2xsbNi7dy/r16/nmWeeKXQtmr29PY0aNaJhw4YEBQXx\n+uuv4+rqSpcuXfj5558LXBphbW1NtWrVuHDhAhs2bCAxMZH333+f5s2bc/jwYVq0aJFnXPYa8Vq1\nahEXF8cnn3xChw4dcHZ2xtHRkQoVKnDgwAEaNmx423xlx1avXp0KFSrw+OOP4+XlxeHDh3M1LqGh\noTz22GN5xtauXZvq1atTt25dsrKySExMZNeuXXTp0gUrKysuXLiQKzYwMJCAgADq1atHjRo1qFCh\nAsHBwXh6ejJw4EAqVqzI5s2bqVKlym3LZm5dD5+VlcX8+fMZNGgQmZmZzJkzh7p169KsWTMg91mA\nvXv3EhAQQNu2bXFxcWH16tVs3boVX19fRowYQZ06ddiwYQOVK1e+bc1fznkymUysXLmS2NhYWrdu\nzdChQ6lSpQp//vknlStXvm0dXPa4zZs3p1q1amRlZWFvb09gYCDr16+nU6dO+V62y56rBg0aEBcX\nx/r161m+fDmdOnVi3LhxFC9enN27d+Pm5kapUqXyjK1Vqxbx8fHMnTsXGxsb1q5dC0Dnzp05ceIE\nTz75ZK7lNlu3bmXKlCkcOHCAFStWcOHCBdq0aYOjo2Oh9ZQdu2vXLnbu3MmwYcNo164dBw8e5Pvv\nvy+wnrJjDx06xP79+xkxYgQA8fHxBdZTztiTJ0+yb98++vXrx/nz5/Hw8Ci0prJjd+7cSUBAAC+8\n8AJffPEFAwYMKLSmsu+zuHbtGlu2bMHKysr8S/fIkSMLrKnscXfs2MGaNWvMv2C1aNGCYcOGFVhT\nW7ZsYfLkyYSFhXH69Gnat2+Pg4OD+b0qv5rKHjM4OJh///vfZGZmsmzZMnx8fBg/fnyB9ZQde+TI\nEdasWWO+wXrVqlWYTKZ86wluXuqePHmyuQ5CQkJo3bp1kd6jsmN3797NgQMHePPNN2nbti0HDhzg\nhx9+KLCmsmMPHz7MsWPHGDJkCIZhFKmmsu+DCQ4OJigoiD59+nDmzBkaNWpUaE1lx+7atYvDhw/j\n6+vL7NmzC32f2r59O5MmTSI2Npa9e/eSmprKpk2b8PHxKbSeso91586d/Pvf/yYlJYXIyEhatmxZ\naD1t376djz76iPDwcC5fvkzr1q1xcHBgz549/PzzzwW+R2Uf6+nTp1m/fj2pqal88803dOzYsdCa\nys756NGjrF69mnPnzmEYBqtXry6wpnLea5SZmUliYiIrV66kXbt2ODk5FVpTD4KWQ9yiatWq9OvX\njz179rBx40ZOnTrF4cOHCQsLK/STH6ysrMyXJ3x9ffH29mb16tXm5q4oypQpQ82aNTl8+DDr1q2j\nffv2RbpskJaWRnh4OFFRUWzbto3k5OQirdF1dXXF2tqaOXPmMHbsWD744ANu3LhB2bJlC4yzt7en\nS5cujBgxAnt7e1JSUti+fTspKSnY2toWGFu6dGl69epF9erV2bp1K4cOHWLbtm2kpKQUaY1u9hwP\nHToUBwcHxowZA1DgLygATk5OVK5cmWrVqrFv3z6uXbvG7t27SUhIKHRtb/ny5enfvz9z5szBz8+P\n1NRU9u7dS0hICGlpaXlelvruu+/YvXs369ev5/nnn6dHjx688sorhIeHY21tjaenJ9HR0Vy/fj3P\n2ICAAH777bdcxzV58mTc3NwYMWIE69at48svv7ztk0yyx123bp35dbSyssLBwQFbW1usrKz49ddf\nmTVrFnFxcbnidu3ahb+/v/nNuF69enh7e2NjY0PDhg0pVqwYN27cyDPfPXv2sGnTJqKjoylbtixN\nmjRh/fr1bN++naFDh7JixQp27NhxWz1///337Ny5E39/f5o2bUqfPn1o2LCh+cqLm5sbJUqUyHOZ\nUM55atSoES+++CL+/v6kp6cDUL9+fRwdHfPM+fvvv2fXrl389ttvxMTEmOd5xIgRlCtXjl9//RXI\n+7Jd9lytXbuWnj178tlnn/HMM8/QqlUr7OzseOqpp0hPTycpKSnf2J9++omuXbsydOhQUlJSKFOm\nDOPGjaN58+acOnUq12Xd8PBwvvvuO2bOnMmCBQto27YtZ8+eLVI95Yz9+uuvSUtLY9myZQBMnTq1\nwHrKjp0xYwbz5s3DycmJH374AYDixYtjZ2eXbz3ljJ07dy4lS5Zk1apV1K5du9Cayo79+OOPWbZs\nGcHBwfj7+9OkSRN++umnAmsqO3b69OnMnTuXRo0acfnyZTw8PMw3OudXU7fOVe3atTl16hT+/v7m\nbfOrqfDwcL7//ntmzpzJ4sWLOXHiBMuXLwdg5MiR+dZUznmaM2cOzZs3p0qVKjz99NO0bt26wHq6\n9fXx8vIiKSmJ5ORkypYtm289wc17ShYuXMjEiROZOXMmr7/+Os2aNeONN94gJiamwJrKjv3oo4+Y\nNWsWpUqVMufm5+dHjRo18q2pnOPOmDGDmjVrkpaWhslkolSpUgXWVM5YPz8/atWqRVZWFvXq1cPH\nx6fAmsqZ8xdffEFsbCzFihWjdevW/P7772zZsiXPmgoODmbRokV8+OGH+Pn54e3tTZs2bWjWrJn5\nymV+9ZRzzNmzZ9OmTRuefPJJNmzYYP6Zk189ZY87ceJEZs2axbVr10hOTgbg3XffxcXFhV9++eW2\nesprnnr16sXo0aPp1q0b3t7eBdbUrXXx2muv0blzZ0wmE5UqVSqwpqysrChRogQtWrQgIiKCp556\nisqVK9OvXz+ioqIK/bn3INzZbY0WombNmgwcOJA///yTzz77DDs7O8aMGVOkBi3nb2WJiYlERkYy\nb9483NzcijR2mTJlWLBgAb///juffvppkePS0tJYt24dx44d48aNG3z00UfmuzgLYm1tTe/evXn6\n6adp0qQJAP379y9SA21ra0vp0qXZtGkTv/32G5GRkUycOLFI45YrV47Bgwebz0CYTCbGjRtXpFiT\nyURWVhZWVla88847LF68mJiYmCIt9DeZTHTp0oVvv/2WLVu2EB8fbz5zVxQmk4mDBw8yb948MjMz\nGT9+fL5zVaxYMVxcXAgODmb16tX069ePrKwsBgwYwMiRI4mOjiY+Ph5HR8d8Y8+cOUNmZiYdO3Y0\nH9/kyZN5+eWX+fzzz/nmm29wdnYuMNbX15dSpUpha2trXsayc+dOPvzww1w3kWTHnT17NteY27Zt\no3LlyoSEhHDp0qU8b57MGZuVlUW3bt0oVaoUfn5+zJw5k7Zt2+Lh4UGFChXyjQ0JCWHt2rV07twZ\nT09PbGxsiI2NZd++fYSGhhY4bkhICKtXr6Z79+5kZmbi7++Po6Mj4eHhnD59Os+7oW/NOft4MzIy\nqFevHgcPHqRq1ao0aNCgwHH/9a9/0blzZ0qVKsXIkSNZtGgRp0+fJioqKs+avLUunnnmGXPdnz9/\nnoCAANLT03P9Mpl970D2D84XX3yRzp07ExsbyxtvvMHIkSOJiorKs55ujR04cGCujwksqJ6yY7Nv\nts0Za2dnh6OjI0uWLGH79u1MnDgxVz3lFRsZGQncPNNUsWLFfGvq1nslBg8eTFJSEmXKlGH69OnM\nnDkTLy+vPGvq1nF79OhBfHw83bt3B25eXg4MDMyzpm6dq5dfftl8GXvNmjU4OjqaLy/fWlN53d+R\nPVdZWVnUr1+fQ4cO3VZTt+bbvXt34uLisLe355133imwnm6NffHFF4mJiaFXr14AXLhwgd27d99W\nT9mvn5ubG3Xr1iU4OJgdO3bQtWtXzpw5w/Dhwxk0aBCXLl3Ks6Zy3o9y5swZTp48ydy5c83LmKZM\nmUK3bt3yrKmc42bHZt8YN2TIEEqXLs2iRYvYvXv3be9ROWPPnj3LqVOnmDFjBjdu3KBLly64uLhw\n7NixPGvq1pxDQkKYO3cuCxYsoGrVqkyaNInmzZvfVlM5xwwJCSEwMJCSJUty5coV+vfvT1JSEtu3\nb+fixYsFjhkSEmK+onH69GlWrlxJ8eLFCQ0NzbOe8prjOXPmcOPGDcaPH0/jxo0JDAykWrVqt71H\n3Zrz3r17WbRoEQsXLqRKlSosXbqUo0eP5llTt9bFzp07sbOzIysri/fee48rV66wZcuWPGsqW82a\nNTlx4gTBwcF07dqVpUuXMnz4cAYPHkxYWFi+P/ceBC2HyEfJkiXx9PSkXbt2dOjQgYoVKxY51mQy\nkZmZSWhoKK+88go1atQocqyTkxMZGRkMHz78juLs7OyoU6cOLVq0wMfHJ9cSi8KULl2aihUrmpv3\non7iQTZXV1c8PT3p1KnTHd2xWrx4cdzd3fHy8qJdu3Z5Nkj5yf7N19nZmebNmxepec5WunRpmjZt\nypNPPknHjh3vKGeAChUq0KpVK3x9fQv8dIrsNeLp6ekcOXKEq1ev0rdvX9zc3Dh//jynTp1i+PDh\neb5WBa0vP3HiBCdOnGD69Om4u7sXGBsUFER0dLR5nd+PP/7IyZMnzWeU84pLTU01j+nm5saVK1dY\ntmwZZ86cYfTo0XnWZc4xjx8/TkREBD4+PgwePNi8jq1KlSq3Xdq8dZ6OHTtGeHg4VapUISwsjE8+\n+YSjR4/ywQcfFDhuzjl++eWXqVu3LuHh4Zw7d45hw4ZRvXr1Is1xxYoVcXJywsXFhXPnztG8efM8\nL9nlHPf48eNERUXRo0cPHB0d+eWXXzhx4gSjRo0qcNzs442MjKRSpUokJSWxdu1ajhw5wjvvvJOr\nLm69dyA4OJitW7fy7rvvUrZsWa5cucLJkycZMWLEbfVU2H0HQUFB+dZTQbH29vb8f3vnF9LUG8bx\nr6muDqsAAAa6SURBVMPSSgpXl8Ywyi4bK6rbIPJWoSXLycDqwrKBDUvapKJIsp0VrZAILwqkMjNj\nzjBkElgwzTP/sBP9IwlL0alrs1bTtt9F6O/85tl2zsx/vz2f+w/vc877nPe855z3eU9DQwM4jsOl\nS5fm9I+Q63Q6ceDAAfT396Ourg4fPnzAmTNn4rrv379HR0cH9Ho98vPzZ5f4COVUpPvu3bvZrSd7\ne3thsVjQ29sLo9E4p3+EzvOLFy9w4sQJZGVlYXx8HB8/foRer4/r8s+VTCaDXC4XzCmhY3316hX0\nej1CoRCeP38Ot9uN8vJyKBSKuMf68uVL5ObmYmBgAE1NTYL5BPy3pqS5uRlZWVlQq9UYGxtDR0cH\nlEol+vr6UFZWFtPl16M8efIETqcT2dnZ6OnpwZUrV+bklJBbVFSE+vp6dHV1QSaTgWVZwZyK1q7d\nbgfDMPD5fHC73aioqBDlHj58GIODg0hPT0dpaalgTvE9m80GhUIBjUYDm80Gi8WCr1+/orOzE2fP\nnp2TE5Hu5s2bUVBQAI/Hg56eHuzfvx8cxwnmU7RjbWxsRF9fH4qLi8FxnOAYJRSzVquF1+uF0+lE\nKBQCy7I4ffr0nJyKzAuFQoHCwkI8ePAAtbW1SEtLg9PphMFgmJMX/FqjVatWQafToba2dnYburS0\nNHAcJzhOLRUp4cXelTqJSHQLkOnpacl7DxLLj5m31cCfnQu6urqwc+dOTE5OIjU1Ffn5+aJdlmWx\nY8cO+Hw+vH37FiUlJVH3eozmBoNBNDQ04OLFi4ITykivu7sbKpUKwWAQfr8fGo0m6pITIVepVGJi\nYgJTU1PQ6XRRrwWheJVKJaampjA0NASdTof09HRR7uvXr6FSqeD3+yGTyXDw4EFBL9Z58ng8WLdu\nHfLy8qI+EAr17a5du/Dr1y/4fD5oNJqo13C04/3x4wcCgQAKCgriLilqb29Hc3MzGIZBS0sLvn//\nDrVaHdPhu8+ePUN1dTVsNhs6OztRWloqao9VvtvW1oY7d+7g8uXLgg9jQm5LSwuuXr0Kh8OBz58/\no6ioSNRDN99tamrCyMgIiouLRY2T/JgdDgf6+/tx7NgxUV9/2tvbYbfbYTabYbfbMTk5iUOHDoka\n1/ntNjY24ufPn1Cr1ZL6tq2tDYODgygsLIzrRbbZ2tqKL1++QKvVivqyx+fkyZOoqqrC2rVr4y4z\ni6SkpARarXa2yE4KZWVl2L17N/bu3SvpJRDwZ4lARUUFMjMzJd8/jx49iurqamRmZkq6ZxsMBpw6\ndQqbNm0S9aWYz/Hjx2GxWKKObbE4cuQIampqkJqaKrl/DAYDysvLIZfLJeeFXq/HhQsXkJGRETMf\nh4aGcPv2bezbtw/Xr19HTk4OVCoV9uzZA4VCsWx2hgBoOcSCkmhH0wT4/8HMGvGUlBTk5uZCLpfj\n5s2bmJiYgNlsTsj1er2wWCwxNzsXcq1WK759+4Zr165FvblE87xeL8xmc8zBVsi9desWxsfHwTBM\nzGshVrsMw8S8ScQ6xwzDRPXExBxrchYv5ljXcDxXzGRn48aN2L59O1wuFx4+fAiTyRTX4btbt26F\ny+XC48ePUVlZKfonAzMuy7Koq6tDVVWVpKVe27ZtA8uyuHv3Lkwmk+ivTpG1EiaTSfQ4yY/53r17\ns0VBYt2cnBy4XC7U19fDZDKJHtf5MT99+hSVlZWS+nZmqZjRaBTl8dtkWRb379+H0WgUNdEJBoOz\n64A5jsPY2BiA+HUWQq7P55stsJbiut1ujI6OIi8vT1TBVKQ7PDyMNWvWiMoLvvvmzRsEAgGsXr06\nbt8KtblhwwZRE+DI8+T1ekVvhxrpBgIB0XvzC8WckZGRcF7MvOWNBb/WyGg0Ijs7G48ePcL69euX\n1QQYoEkwQSwokWvER0dHRa8RF3KtVquot26RrsfjgdVqjduukJdovFLWw//NdudzjpcqZiku8G/t\nwJYtWyTVDqxkt6amBq2trSsq5kTqO5Yi3siakpm3fYm458+fF/2QEemeO3dO9I4BidbBzMf9m23O\n5xzPt38W2p1PrdGiEyYIYsGZnp4OOxyO8KdPn1aEu9LiTTb39+/f4Rs3boQHBgYkt0nu8naXKl6/\n3x8eHh4Oj4yMkLvM2lypbjgcDodCoYS8xYLWBBPEIhGex28il8JdafEmmzuf2gFyl7e7VPESRLJB\nk2CCIAiCIAgi6aCfZRAEQRAEQRBJB02CCYIgCIIgiKSDJsEEQRAEQRBE0kGTYIIgCIIgCCLpoEkw\nQRAEQRAEkXTQJJggCIIgCIJIOv4BaUp3LS4PXKcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7db1e350b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if pca is not None:\n",
    "    bar_width = 0.9\n",
    "    n_asset = int((1 / 10) * normed_returns.shape[1])\n",
    "    x_indx = np.arange(n_asset)\n",
    "    fig, ax = plt.subplots()\n",
    "    fig.set_size_inches(12, 4)\n",
    "    # Eigenvalues are measured as percentage of explained variance.\n",
    "    rects = ax.bar(x_indx, pca.explained_variance_ratio_[:n_asset], bar_width, color='deepskyblue')\n",
    "    ax.set_xticks(x_indx + bar_width / 2)\n",
    "    ax.set_xticklabels(list(range(n_asset)), rotation=45)\n",
    "    ax.set_title('Percent variance explained')\n",
    "    ax.legend((rects[0],), ('Percent variance explained by principal components',))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "if pca is not None:\n",
    "    projected = pca.fit_transform(cov_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part 3 (Eigen-portfolios construction)\n",
    "\n",
    "**Instructions:**\n",
    "\n",
    "We now look a the first two eigen portfolios. We use definition of eigen portfolios as provided by Avellaneda \n",
    "http://math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb20090616.pdf\n",
    "\n",
    "Following Avellaneda we define eigen portfolio weights as:\n",
    "$$Q_i^{(j)} = \\frac{v_i^{(j)}}{\\sigma_i}$$\n",
    "\n",
    "where $j$ is the index of eigen portfolio and $v_i$ is the i-th element of j-th eigen vector.\n",
    "\n",
    "In the code the pca.components_ are the Principal axes in feature space, representing the directions of maximum variance in the data. The components are sorted by explained_variance_.\n",
    "\n",
    "**Hint:** do not forget to normalize portfolio wieghts such they sum up to 1.\n",
    "\n",
    "Assign **pc_w** to be weights of the first eigen portfolio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of weights of first eigen-portfolio: 100.00\n"
     ]
    },
    {
     "data": {
      "image/png": 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+QKntJBV53RR53Vx+wUCqGwP839p9fLCnpsM1sXiClRsPsaW4lm9cP6HD0m0i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\njY1QV1dHT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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7d80eee588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the first two eigen-portfolio weights# the fi \n",
    "# first component\n",
    "# get the Principal components\n",
    "pc_w = np.zeros(len(stock_tickers))\n",
    "eigen_prtf1 = pd.DataFrame(data ={'weights': pc_w.squeeze()*100}, index = stock_tickers)\n",
    "if pca is not None:\n",
    "    pcs = pca.components_\n",
    "\n",
    "    ### START CODE HERE ### (≈ 1-2 lines of code)\n",
    "    # normalized to 1 \n",
    "    pc_w = pcs[:, 0] / sum(pcs[:, 0])\n",
    "    \n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    eigen_prtf1 = pd.DataFrame(data ={'weights': pc_w.squeeze()*100}, index = stock_tickers)\n",
    "    eigen_prtf1.sort_values(by=['weights'], ascending=False, inplace=True)\n",
    "    print('Sum of weights of first eigen-portfolio: %.2f' % np.sum(eigen_prtf1))\n",
    "    eigen_prtf1.plot(title='First eigen-portfolio weights', \n",
    "                     figsize=(12,6), \n",
    "                     xticks=range(0, len(stock_tickers),10), \n",
    "                     rot=45, \n",
    "                     linewidth=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 32.15627636,  30.933928  ,  25.50776408,  22.16747872,\n",
       "        18.00892145,  17.79316587,  17.76782255,  16.81928891,\n",
       "        16.18087374,  15.83795897,  15.80665872,  15.43552731,\n",
       "        15.08220124,  14.72631873,  14.69273653,  14.01762469,\n",
       "        13.94532135,  13.82765547,  13.79929467,  13.50835772,\n",
       "        13.22735361,  13.07723085,  12.6101472 ,  12.49384414,\n",
       "        12.49071201,  12.13649924,  11.93252738,  11.25794592,\n",
       "        11.18841954,  11.09494289,  10.92729081,  10.82338093,\n",
       "        10.81882089,  10.64506427,  10.42304627,  10.32449474,\n",
       "        10.25693633,   9.99434957,   9.97161064,   9.96682527,\n",
       "         9.93480531,   9.86884924,   9.80240134,   9.71265744,\n",
       "         9.6591354 ,   9.62279386,   9.55800793,   9.33991524,\n",
       "         9.31636337,   9.29680255,   9.17862032,   9.15001613,\n",
       "         8.96845462,   8.91793278,   8.91342386,   8.89668537,\n",
       "         8.8801725 ,   8.75420601,   8.7305932 ,   8.66536223,\n",
       "         8.59827941,   8.56445122,   8.49320556,   8.34214463,\n",
       "         8.31702119,   8.30595091,   8.2435913 ,   8.01729508,\n",
       "         8.01116225,   7.95202673,   7.92653242,   7.89411659,\n",
       "         7.82607966,   7.77944802,   7.73992992,   7.7104847 ,\n",
       "         7.67636914,   7.65524306,   7.4606705 ,   7.1692165 ,\n",
       "         7.16514262,   7.07709956,   6.88773062,   6.7971531 ,\n",
       "         6.57188438,   6.51131209,   6.35928881,   6.34822256,\n",
       "         6.29609156,   6.26489402,   5.9178115 ,   5.88005587,\n",
       "         5.83164358,   5.75464697,   5.751713  ,   5.6780948 ,\n",
       "         5.66534148,   5.63171516,   5.58108367,   5.52824121,\n",
       "         5.48679532,   5.4295469 ,   5.38997364,   5.38548353,\n",
       "         5.38021992,   5.33471658,   5.32436336,   5.12059851,\n",
       "         5.11212257,   5.08363416,   4.94687645,   4.9419909 ,\n",
       "         4.89848515,   4.87187476,   4.69646802,   4.61296522,\n",
       "         4.56002204,   4.54205748,   4.52356808,   4.50206086,\n",
       "         4.44237392,   4.39524874,   4.18702601,   4.11514071,\n",
       "         4.10328863,   4.0795515 ,   3.98378154,   3.98242273,\n",
       "         3.95138962,   3.91404548,   3.88759381,   3.8452876 ,\n",
       "         3.806866  ,   3.78288618,   3.70341557,   3.6867927 ,\n",
       "         3.66238738,   3.64811561,   3.61886522,   3.61576454,\n",
       "         3.60244652,   3.53737689,   3.53415434,   3.45098448,\n",
       "         3.41455925,   3.36513668,   3.3625489 ,   3.3191274 ,\n",
       "         3.24158055,   3.19570771,   3.18552748,   3.12815354,\n",
       "         3.05870406,   3.04515239,   3.02934119,   2.98816968,\n",
       "         2.81980822,   2.77921913,   2.74139179,   2.6059568 ,\n",
       "         2.52151711,   2.50986115,   2.4747736 ,   2.45968604,\n",
       "         2.44460196,   2.33681242,   2.3221179 ,   2.29982764,\n",
       "         2.22892247,   2.21395704,   2.19525634,   2.13304931,\n",
       "         2.05499157,   1.99194993,   1.91187091,   1.812632  ,\n",
       "         1.74310967,   1.71497934,   1.70530273,   1.5769675 ,\n",
       "         1.54524789,   1.51493611,   1.42286668,   1.42179869,\n",
       "         1.35881444,   1.30386817,   1.26820852,   1.22983483,\n",
       "         1.18231373,   1.17456906,   1.11103599,   1.09741697,\n",
       "         1.05291044,   1.03669352,   1.00895468,   1.00588621,\n",
       "         0.97293487,   0.81706987,   0.81123455,   0.7368411 ,\n",
       "         0.72750008,   0.5982855 ,   0.52125733,   0.51458962,\n",
       "         0.4600874 ,   0.3615934 ,   0.34609816,   0.2924146 ,\n",
       "         0.26727967,   0.26190696,   0.17730959,   0.15125563,\n",
       "         0.10723449,   0.08654033,   0.0597015 ,  -0.0557358 ,\n",
       "        -0.08692647,  -0.11206998,  -0.15121343,  -0.18790832,\n",
       "        -0.21548668,  -0.21631904,  -0.23281801,  -0.24094782,\n",
       "        -0.32807204,  -0.46561326,  -0.5320355 ,  -0.62555696,\n",
       "        -0.64875481,  -0.67846195,  -0.68742399,  -0.7202875 ,\n",
       "        -0.74365652,  -0.80234017,  -0.81926408,  -1.04241588,\n",
       "        -1.05620274,  -1.21894655,  -1.27563693,  -1.29541343,\n",
       "        -1.29812308,  -1.34256956,  -1.38818191,  -1.41697038,\n",
       "        -1.51100807,  -1.59597119,  -1.60330609,  -1.65659672,\n",
       "        -1.75410943,  -1.75917702,  -2.04606048,  -2.0465409 ,\n",
       "        -2.10907307,  -2.14474455,  -2.22803484,  -2.22943001,\n",
       "        -2.29888029,  -2.31460232,  -2.35367212,  -2.42836882,\n",
       "        -2.49384416,  -2.51557327,  -2.55189638,  -2.57184377,\n",
       "        -2.57892112,  -2.59479446,  -2.65391145,  -2.65594557,\n",
       "        -2.67815035,  -2.67819484,  -2.79741082,  -2.8160212 ,\n",
       "        -2.86855778,  -2.87291304,  -2.87832079,  -2.88938517,\n",
       "        -2.94101885,  -2.95450215,  -2.95630914,  -2.97900869,\n",
       "        -3.09023062,  -3.12574211,  -3.2053992 ,  -3.40985894,\n",
       "        -3.43672823,  -3.48775542,  -3.50664183,  -3.57241786,\n",
       "        -3.57407899,  -3.63658212,  -3.66220695,  -3.6978119 ,\n",
       "        -3.71078064,  -3.7540065 ,  -3.7871498 ,  -3.78886105,\n",
       "        -3.85146459,  -3.87653019,  -3.92668502,  -4.0896392 ,\n",
       "        -4.24201923,  -4.24697029,  -4.25243107,  -4.49493243,\n",
       "        -4.50392189,  -4.53222319,  -4.53712082,  -4.55964191,\n",
       "        -4.57491027,  -4.67137914,  -4.71198908,  -4.71302006,\n",
       "        -4.73363279,  -4.75173183,  -4.78598877,  -4.87544271,\n",
       "        -4.94834241,  -4.96539629,  -4.99123477,  -4.99908917,\n",
       "        -5.07711316,  -5.09577626,  -5.17424435,  -5.1843572 ,\n",
       "        -5.18764847,  -5.22835566,  -5.23852723,  -5.30139067,\n",
       "        -5.48553464,  -5.53526614,  -5.55627871,  -5.64957709,\n",
       "        -5.69071538,  -5.69387325,  -5.83713928,  -5.92627383,\n",
       "        -6.07701325,  -6.18955893,  -6.24396636,  -6.2490045 ,\n",
       "        -6.33103449,  -6.35300848,  -6.78733658,  -6.83534616,\n",
       "        -6.93671333,  -7.0955804 ,  -7.25835221,  -7.30938741,\n",
       "        -7.45799232,  -7.58359386,  -7.63607691,  -7.71934206,\n",
       "        -7.88876604,  -7.89500746,  -8.06174906,  -8.0678495 ,\n",
       "        -8.14725187,  -8.34405988,  -8.44670927,  -8.82389528,\n",
       "        -8.97050342,  -9.12295329,  -9.13890405,  -9.17737275,\n",
       "        -9.18297553,  -9.24627595,  -9.2867669 ,  -9.39608929,\n",
       "        -9.46310214,  -9.5180178 ,  -9.54215838,  -9.81277016,\n",
       "        -9.81750221,  -9.81955017,  -9.90111576, -10.17353046,\n",
       "       -10.29779865, -10.66189804, -10.68262901, -10.9296642 ,\n",
       "       -10.94297036, -11.04055867, -11.04260035, -11.32856023,\n",
       "       -11.61560743, -11.81154341, -11.86495788, -11.86567688,\n",
       "       -11.98486517, -12.16750417, -12.41881119, -12.44057146,\n",
       "       -12.63399896, -12.68060184, -12.68608292, -12.86036696,\n",
       "       -12.8764651 , -12.96922261, -13.06289534, -13.07823812,\n",
       "       -13.87902318, -14.31115145, -14.34953669, -14.61440766,\n",
       "       -14.65627554, -14.99342457, -15.02195634, -15.37738891,\n",
       "       -15.6738353 , -15.79055611, -15.93681142, -16.22246156,\n",
       "       -16.77791626, -17.31352144, -17.60067165, -17.79578107,\n",
       "       -21.00138056, -21.04210789])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "part_3 = list(eigen_prtf1.squeeze().values)\n",
    "try:\n",
    "    part3 = \" \".join(map(repr, part_3))\n",
    "except TypeError:\n",
    "    part3 = repr(part_3)\n",
    "submissions[all_parts[2]]=part3\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:3],all_parts,submissions)\n",
    "eigen_prtf1.squeeze().values\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We sort the first two eigen portfolio weights and plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of weights of second eigen-portfolio: 100.00\n"
     ]
    },
    {
     "data": {
      "image/png": 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qJipqA0RjmqFCRERE5ExTD/EZkppi5TtXj6HaF+RP/9rGrmIfhgGPvbjxsHMs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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7d80cff3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pc_w = np.zeros(len(stock_tickers))\n",
    "eigen_prtf2 = pd.DataFrame(data ={'weights': pc_w.squeeze()*100}, index = stock_tickers)\n",
    "\n",
    "if pca is not None:\n",
    "    pcs = pca.components_\n",
    "    \n",
    "    ### START CODE HERE ### (≈ 1-2 lines of code)\n",
    "    # normalized to 1 \n",
    "    pc_w = pcs[:, 1] / sum(pcs[:, 1])\n",
    "    \n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    eigen_prtf2 = pd.DataFrame(data ={'weights': pc_w.squeeze()*100}, index = stock_tickers)\n",
    "    eigen_prtf2.sort_values(by=['weights'], ascending=False, inplace=True)\n",
    "    print('Sum of weights of second eigen-portfolio: %.2f' % np.sum(eigen_prtf2))\n",
    "    eigen_prtf2.plot(title='Second eigen-portfolio weights',\n",
    "                     figsize=(12,6), \n",
    "                     xticks=range(0, len(stock_tickers),10), \n",
    "                     rot=45, \n",
    "                     linewidth=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 27.53031336,  27.44303101,  26.92015668,  25.4310494 ,\n",
       "        25.03044897,  24.12127012,  23.62909928,  23.13646227,\n",
       "        21.73518084,  21.3899741 ,  21.10378786,  20.86975774,\n",
       "        20.56977124,  20.26750658,  19.9710755 ,  19.41651496,\n",
       "        18.77730475,  18.51765116,  18.49095368,  18.25276419,\n",
       "        16.39168846,  16.25426255,  15.97969732,  15.96457002,\n",
       "        15.63103436,  15.40186792,  15.34420783,  15.25021659,\n",
       "        14.77661408,  14.73123119,  14.70789736,  14.63359636,\n",
       "        14.31750245,  14.21219482,  14.08577939,  14.08395854,\n",
       "        14.01547523,  13.91722912,  13.63007081,  13.53974902,\n",
       "        13.13074358,  13.07617812,  13.07322375,  12.96274837,\n",
       "        12.77003598,  12.73471508,  12.5667775 ,  12.47796756,\n",
       "        12.29056859,  12.04541745,  11.96601592,  11.93996984,\n",
       "        11.79293162,  11.50831821,  11.45618398,  11.45151495,\n",
       "        11.20146656,  11.14579526,  11.1357662 ,  11.0945854 ,\n",
       "        10.99734798,  10.91045933,  10.78097499,  10.74314901,\n",
       "        10.72078183,  10.67801201,  10.50463204,  10.46149178,\n",
       "        10.43159287,  10.26087759,  10.08394312,   9.9609939 ,\n",
       "         9.86182923,   9.76396495,   9.63650882,   9.63004769,\n",
       "         9.50466844,   9.49864483,   9.4957028 ,   9.4703881 ,\n",
       "         9.3941701 ,   9.31171419,   9.14361585,   9.08169237,\n",
       "         8.68245288,   8.65412772,   8.62048511,   8.52003903,\n",
       "         8.37839441,   7.99133823,   7.79946679,   7.57260774,\n",
       "         7.35288001,   7.33939776,   7.30067078,   6.93373317,\n",
       "         6.86419914,   6.83250721,   6.82884836,   6.80372355,\n",
       "         6.76185388,   6.75965892,   6.69159231,   6.68643616,\n",
       "         6.64537488,   6.5516704 ,   6.53342164,   6.43976482,\n",
       "         6.34857817,   6.32610806,   6.15118462,   6.12894593,\n",
       "         6.01615886,   5.90917836,   5.66915694,   5.62308417,\n",
       "         5.62034367,   5.58230684,   5.54576126,   5.42484044,\n",
       "         5.41215222,   5.34383525,   5.25534923,   5.24655677,\n",
       "         5.12282146,   5.12250845,   5.11237952,   5.11150717,\n",
       "         5.01559552,   4.94211285,   4.91390062,   4.81946811,\n",
       "         4.81749083,   4.7459741 ,   4.67075723,   4.61996263,\n",
       "         4.45603814,   4.29761458,   4.27250743,   4.22510039,\n",
       "         4.18212156,   4.18007646,   4.15940821,   4.03964224,\n",
       "         3.92161175,   3.87527802,   3.87136317,   3.77679406,\n",
       "         3.62925732,   3.55483188,   3.51472534,   3.42643802,\n",
       "         3.37957108,   3.36669628,   3.17837066,   3.1545631 ,\n",
       "         3.14759078,   3.14110355,   3.10089143,   3.04229264,\n",
       "         2.8908103 ,   2.86709806,   2.83207955,   2.7405512 ,\n",
       "         2.55098267,   2.54731302,   2.50924445,   2.38649765,\n",
       "         2.34661498,   2.33828808,   2.3316228 ,   2.23586861,\n",
       "         2.22452326,   2.2138903 ,   2.1540927 ,   2.0636746 ,\n",
       "         1.79629483,   1.78096309,   1.77540758,   1.76643907,\n",
       "         1.7487678 ,   1.74241004,   1.70905534,   1.66062031,\n",
       "         1.60810452,   1.60708039,   1.49939442,   1.44505791,\n",
       "         1.37853864,   1.3427175 ,   1.31523359,   1.17971819,\n",
       "         1.0689228 ,   0.94968933,   0.91405518,   0.90345156,\n",
       "         0.87726586,   0.84206071,   0.76114543,   0.66349731,\n",
       "         0.64490199,   0.6056523 ,   0.59829791,   0.56974935,\n",
       "         0.56062364,   0.51316831,   0.5072826 ,   0.49061942,\n",
       "         0.44739042,   0.44575907,   0.35986181,   0.2244308 ,\n",
       "         0.15289962,   0.10523638,   0.08442007,  -0.06922596,\n",
       "        -0.08264087,  -0.13604063,  -0.13848862,  -0.14340122,\n",
       "        -0.17758784,  -0.20937016,  -0.24110603,  -0.32821667,\n",
       "        -0.39524778,  -0.48437771,  -0.54934386,  -0.57920837,\n",
       "        -0.59195883,  -0.60826219,  -0.71402152,  -0.77244242,\n",
       "        -0.83678351,  -0.99919211,  -1.19684113,  -1.25542595,\n",
       "        -1.27328751,  -1.28626492,  -1.30765915,  -1.34999235,\n",
       "        -1.38768349,  -1.44995527,  -1.49616718,  -1.59863266,\n",
       "        -1.6151748 ,  -1.64604519,  -1.65687562,  -1.79219817,\n",
       "        -1.82935763,  -1.87309535,  -1.90995093,  -1.93195537,\n",
       "        -1.93406615,  -1.9950288 ,  -2.05814617,  -2.14045012,\n",
       "        -2.17157674,  -2.18586761,  -2.25096975,  -2.31295378,\n",
       "        -2.3848644 ,  -2.41325419,  -2.43382476,  -2.47888688,\n",
       "        -2.72898462,  -2.74958125,  -2.86606204,  -2.92175855,\n",
       "        -3.17222143,  -3.54024415,  -3.65383342,  -3.74044297,\n",
       "        -3.77890186,  -3.7906216 ,  -3.82178724,  -3.83076534,\n",
       "        -3.8808885 ,  -3.89014202,  -3.98923981,  -4.04239777,\n",
       "        -4.06875243,  -4.22500533,  -4.31113533,  -4.44475693,\n",
       "        -4.48514079,  -4.62357889,  -4.68715274,  -4.69055963,\n",
       "        -4.71498031,  -4.7388593 ,  -4.78665783,  -4.79506315,\n",
       "        -4.84080404,  -4.9463238 ,  -4.96863853,  -4.97880824,\n",
       "        -4.98467908,  -5.13193765,  -5.13841775,  -5.22479417,\n",
       "        -5.3299395 ,  -5.3509973 ,  -5.39164525,  -5.40541501,\n",
       "        -5.44419132,  -5.56293087,  -5.6089496 ,  -5.711541  ,\n",
       "        -5.77341293,  -5.79981169,  -5.96099501,  -5.99663691,\n",
       "        -6.17214175,  -6.17715124,  -6.27317934,  -6.27963382,\n",
       "        -6.30551099,  -6.33362791,  -6.33531977,  -6.35011287,\n",
       "        -6.46015663,  -6.49909982,  -6.59631923,  -6.60860519,\n",
       "        -6.9912739 ,  -7.02155377,  -7.11244457,  -7.33323449,\n",
       "        -7.48903655,  -7.58651288,  -7.6091664 ,  -7.70481273,\n",
       "        -7.74936346,  -7.78657882,  -7.80950439,  -7.87491615,\n",
       "        -7.87498827,  -7.95252638,  -8.09514874,  -8.13069207,\n",
       "        -8.18003935,  -8.21838164,  -8.25111808,  -8.49197299,\n",
       "        -8.51751981,  -8.52169152,  -8.58301075,  -8.5875456 ,\n",
       "        -8.9974824 ,  -9.03994749,  -9.09555791,  -9.15749336,\n",
       "        -9.17420706,  -9.21076096,  -9.26583559,  -9.63636144,\n",
       "        -9.66700172,  -9.75542795,  -9.8225125 ,  -9.87907527,\n",
       "        -9.95561572, -10.13038866, -10.15211806, -10.15909807,\n",
       "       -10.33947034, -10.51475891, -10.53577983, -10.66690814,\n",
       "       -10.7585451 , -10.96655041, -11.02521309, -11.16919069,\n",
       "       -11.19154488, -11.34578475, -11.62614273, -12.14767145,\n",
       "       -12.23541092, -12.46824707, -12.51057085, -12.87699868,\n",
       "       -13.2331274 , -13.35529279, -13.40052933, -13.70009205,\n",
       "       -13.71781767, -14.02202044, -14.39984146, -14.58819737,\n",
       "       -15.32871122, -15.59575095, -15.65026676, -15.87551601,\n",
       "       -16.02614228, -16.10217363, -17.08467598, -17.26678038,\n",
       "       -17.36490516, -17.78117739, -18.01583006, -18.38291172,\n",
       "       -18.40663005, -18.76725963, -19.43166057, -20.05927005,\n",
       "       -20.83294877, -21.14534698, -21.32065422, -21.4458864 ,\n",
       "       -23.0226232 , -23.11954752, -24.63871717, -24.93168371,\n",
       "       -25.46098173, -25.56237365, -27.06112175, -27.0785548 ,\n",
       "       -28.39508025, -30.44951689])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "part_4 = list(eigen_prtf2.as_matrix().squeeze())\n",
    "try:\n",
    "    part4 = \" \".join(map(repr, part_4))\n",
    "except TypeError:\n",
    "    part4 = repr(part_4)\n",
    "submissions[all_parts[3]]=part4\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:4],all_parts,submissions)\n",
    "eigen_prtf2.as_matrix().squeeze()\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part 4 (Compute performance of several eigen portfolios)\n",
    "\n",
    "**Instructions:**\n",
    "- Implement sharpe_ratio() function. The function takes ts_returns argument of type pd.Series and returns a tuple of annualized return, annualized vol, and annualized sharpe ratio, where sharpe ratio is defined as annualized return divided by annualized volatility \n",
    "- find portfolio (an index into sharpe_metric) that has the highest sharpe ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sharpe_ratio(ts_returns, periods_per_year=252):\n",
    "    \"\"\"\n",
    "    sharpe_ratio - Calculates annualized return, annualized vol, and annualized sharpe ratio, \n",
    "                    where sharpe ratio is defined as annualized return divided by annualized volatility \n",
    "                    \n",
    "    Arguments:\n",
    "    ts_returns - pd.Series of returns of a single eigen portfolio\n",
    "    \n",
    "    Return:\n",
    "    a tuple of three doubles: annualized return, volatility, and sharpe ratio\n",
    "    \"\"\"\n",
    "    \n",
    "    annualized_return = 0.\n",
    "    annualized_vol = 0.\n",
    "    annualized_sharpe = 0.\n",
    "    \n",
    "    ### START CODE HERE ### (≈ 4-5 lines of code)\n",
    "    ### ...\n",
    "    n_years = ts_returns.shape[0] / periods_per_year\n",
    "    annualized_return = np.power(np.prod(1 + ts_returns),(1 / n_years)) - 1\n",
    "    annualized_vol = ts_returns.std() * np.sqrt(periods_per_year)\n",
    "    annualized_sharpe = annualized_return / annualized_vol\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return annualized_return, annualized_vol, annualized_sharpe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We compute the annualized return, volatility, and Sharpe ratio of the first two eigen portfolios."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First eigen-portfolio:\n",
      "Return = 41.39%\n",
      "Volatility = 31.50%\n",
      "Sharpe = 1.31\n"
     ]
    },
    {
     "data": {
      "image/png": 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Zg9mzZyM2NhbR0dEICQnB9OnT8dRTT1X7WEuXLsXSpUul2/7+/sjLy5Nu5+TkwN3dHatW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/ETI8adsw0ZwSn8o/QbwLEbl3NHrpPNpVS2VnFP8u09CuHs9Ei+PlBJUWUzVpudDduK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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7d80cdf898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if df_raw_test is not None:\n",
    "    eigen_prtf1_returns = np.dot(df_raw_test.loc[:, eigen_prtf1.index], eigen_prtf1 / 100)\n",
    "    eigen_prtf1_returns = pd.Series(eigen_prtf1_returns.squeeze(), index=df_test.index)\n",
    "    er, vol, sharpe = sharpe_ratio(eigen_prtf1_returns)\n",
    "    print('First eigen-portfolio:\\nReturn = %.2f%%\\nVolatility = %.2f%%\\nSharpe = %.2f' % (er*100, vol*100, sharpe))\n",
    "    year_frac = (eigen_prtf1_returns.index[-1] - eigen_prtf1_returns.index[0]).days / 252\n",
    "\n",
    "    df_plot = pd.DataFrame({'PC1': eigen_prtf1_returns, 'SPX': df_raw_test.loc[:, 'SPX']}, index=df_test.index)\n",
    "    np.cumprod(df_plot + 1).plot(title='Returns of the market-cap weighted index vs. First eigen-portfolio', \n",
    "                             figsize=(12,6), linewidth=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Second eigen-portfolio:\n",
      "Return = 15.76%\n",
      "Volatility = 42.84%\n",
      "Sharpe = 0.37\n"
     ]
    }
   ],
   "source": [
    "if df_raw_test is not None:\n",
    "    eigen_prtf2_returns = np.dot(df_raw_test.loc[:, eigen_prtf2.index], eigen_prtf2 / 100)\n",
    "    eigen_prtf2_returns = pd.Series(eigen_prtf2_returns.squeeze(), index=df_test.index)\n",
    "    er, vol, sharpe = sharpe_ratio(eigen_prtf2_returns)\n",
    "    print('Second eigen-portfolio:\\nReturn = %.2f%%\\nVolatility = %.2f%%\\nSharpe = %.2f' % (er*100, vol*100, sharpe))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We repeat the exercise of computing Sharpe ratio for the first N portfolios and select portfolio with the highest postive Sharpe ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.6/site-packages/ipykernel/__main__.py:21: RuntimeWarning: invalid value encountered in power\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigen portfolio #42 with the highest Sharpe. Return 61.14%, vol = 22.80%, Sharpe = 2.68\n"
     ]
    },
    {
     "data": {
      "image/png": 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MerXKbfsIRyW5pJPVYkZtFVdTWcc74SM9Xmzb60Y0xvCXLZ26jUMNISnRYREy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\n/wGdo8yI1PJR1wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7d80ba5400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_portfolios = 120\n",
    "annualized_ret = np.array([0.] * n_portfolios)\n",
    "sharpe_metric = np.array([0.] * n_portfolios)\n",
    "annualized_vol = np.array([0.] * n_portfolios)\n",
    "idx_highest_sharpe = 0 # index into sharpe_metric which identifies a portfolio with rhe highest Sharpe ratio\n",
    "    \n",
    "if pca is not None:\n",
    "    for ix in range(n_portfolios):\n",
    "        \n",
    "        ### START CODE HERE ### (≈ 4-5 lines of code)\n",
    "        pc_w = pcs[:, ix] / sum(pcs[:, ix])\n",
    "        eigen_prtfix = pd.DataFrame(data ={'weights': pc_w.squeeze()*100}, index = stock_tickers)\n",
    "        eigen_prtfix.sort_values(by=['weights'], ascending=False, inplace=True)\n",
    "        \n",
    "        eigen_prtix_returns = np.dot(df_raw_test.loc[:, eigen_prtfix.index], eigen_prtfix / 100)\n",
    "        eigen_prtix_returns = pd.Series(eigen_prtix_returns.squeeze(), index=df_test.index)\n",
    "        er, vol, sharpe = sharpe_ratio(eigen_prtix_returns)\n",
    "        annualized_ret[ix] = er\n",
    "        annualized_vol[ix] = vol\n",
    "        sharpe_metric[ix] = sharpe\n",
    "    \n",
    "        ### END CODE HERE ###\n",
    "    \n",
    "    \n",
    "    # find portfolio with the highest Sharpe ratio\n",
    "    ### START CODE HERE ### (≈ 2-3 lines of code)\n",
    "    ### ...\n",
    "    idx_highest_sharpe = np.nanargmax(sharpe_metric)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    print('Eigen portfolio #%d with the highest Sharpe. Return %.2f%%, vol = %.2f%%, Sharpe = %.2f' % \n",
    "          (idx_highest_sharpe,\n",
    "           annualized_ret[idx_highest_sharpe]*100, \n",
    "           annualized_vol[idx_highest_sharpe]*100, \n",
    "           sharpe_metric[idx_highest_sharpe]))\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    fig.set_size_inches(12, 4)\n",
    "    ax.plot(sharpe_metric, linewidth=3)\n",
    "    ax.set_title('Sharpe ratio of eigen-portfolios')\n",
    "    ax.set_ylabel('Sharpe ratio')\n",
    "    ax.set_xlabel('Portfolios')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Return</th>\n",
       "      <th>Sharpe</th>\n",
       "      <th>Vol</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0.611437</td>\n",
       "      <td>2.681354</td>\n",
       "      <td>0.228033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.032178</td>\n",
       "      <td>2.431344</td>\n",
       "      <td>0.424530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104</th>\n",
       "      <td>0.512464</td>\n",
       "      <td>2.398724</td>\n",
       "      <td>0.213640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>1.425562</td>\n",
       "      <td>2.337929</td>\n",
       "      <td>0.609754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.753548</td>\n",
       "      <td>2.306601</td>\n",
       "      <td>0.326692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.502025</td>\n",
       "      <td>2.221589</td>\n",
       "      <td>0.225976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>0.601081</td>\n",
       "      <td>2.216774</td>\n",
       "      <td>0.271151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.453437</td>\n",
       "      <td>2.198512</td>\n",
       "      <td>0.206247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>0.274142</td>\n",
       "      <td>1.813008</td>\n",
       "      <td>0.151208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>0.874381</td>\n",
       "      <td>1.793422</td>\n",
       "      <td>0.487549</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Return    Sharpe       Vol\n",
       "42   0.611437  2.681354  0.228033\n",
       "24   1.032178  2.431344  0.424530\n",
       "104  0.512464  2.398724  0.213640\n",
       "97   1.425562  2.337929  0.609754\n",
       "9    0.753548  2.306601  0.326692\n",
       "94   0.502025  2.221589  0.225976\n",
       "93   0.601081  2.216774  0.271151\n",
       "2    0.453437  2.198512  0.206247\n",
       "102  0.274142  1.813008  0.151208\n",
       "118  0.874381  1.793422  0.487549"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = pd.DataFrame(data={'Return': annualized_ret, 'Vol': annualized_vol, 'Sharpe': sharpe_metric})\n",
    "results.dropna(inplace=True)\n",
    "results.sort_values(by=['Sharpe'], ascending=False, inplace=True)\n",
    "results.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 2.68135386,  2.43134379,  2.39872442,  2.33792864,  2.30660114,\n",
       "        2.22158907,  2.2167735 ,  2.19851244,  1.81300846,  1.79342192,\n",
       "        1.76312136,  1.61426685,  1.31394555,  1.30788062,  1.26660256,\n",
       "        1.25888541,  1.18687021,  1.17034684,  1.1646922 ,  1.06187713,\n",
       "        1.05581668,  1.05503146,  1.04881373,  1.02165359,  1.01830316,\n",
       "        1.00829296,  0.99498987,  0.9752889 ,  0.958144  ,  0.92726752,\n",
       "        0.92483757,  0.90418802,  0.89253674,  0.88640631,  0.86855843,\n",
       "        0.8428844 ,  0.79154999,  0.7280406 ,  0.68482477,  0.66834314,\n",
       "        0.64094412,  0.62471951,  0.6200365 ,  0.60334151,  0.60021067,\n",
       "        0.5947495 ,  0.5909932 ,  0.48427946,  0.47798503,  0.47444463,\n",
       "        0.47279705,  0.46333553,  0.46119478,  0.4259212 ,  0.42363749,\n",
       "        0.4154423 ,  0.41218842,  0.36779464,  0.30061885,  0.29467637,\n",
       "        0.27703449,  0.25218081,  0.24689467,  0.23703113,  0.23105779,\n",
       "        0.22907762,  0.20739231,  0.14234158,  0.1409318 ,  0.14041686,\n",
       "        0.12992353,  0.11648127,  0.10386079,  0.06260278,  0.05659276,\n",
       "        0.04381381,  0.03635583,  0.02334462,  0.01970139, -0.02079731,\n",
       "       -0.02326461, -0.05238554, -0.07089928, -0.07540045, -0.08174287,\n",
       "       -0.09489727, -0.09821993, -0.10092825, -0.14388953, -0.20465891,\n",
       "       -0.21335143, -0.21535573, -0.21826577, -0.26268148, -0.28928421,\n",
       "       -0.29044099, -0.33644553, -0.3399915 , -0.34757978, -0.34789059,\n",
       "       -0.36090558, -0.41387712, -0.42602414, -0.42603886, -0.42931113,\n",
       "       -0.50531371, -0.50667481, -0.5444063 , -0.56360796, -0.68829347,\n",
       "       -0.69692501, -0.7294767 , -0.73094093, -0.82976161, -0.89658555,\n",
       "       -1.09025839, -1.21303625])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "part_5 = list(results.iloc[:, 1].values.squeeze())\n",
    "try:\n",
    "    part5 = \" \".join(map(repr, part_5))\n",
    "except TypeError:\n",
    "    part5 = repr(part_5)\n",
    "submissions[all_parts[4]]=part5\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:5],all_parts,submissions)\n",
    "results.iloc[:, 1].values.squeeze()\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submission successful, please check on the coursera grader page for the status\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### GRADED PART (DO NOT EDIT) ###\n",
    "part6 = str(idx_highest_sharpe)\n",
    "submissions[all_parts[5]]=part6\n",
    "grading.submit(COURSERA_EMAIL, COURSERA_TOKEN, assignment_key,all_parts[:6],all_parts,submissions)\n",
    "idx_highest_sharpe\n",
    "### GRADED PART (DO NOT EDIT) ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "coursera": {
   "course_slug": "machine-learning-in-finance"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
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}