PortOpt.MonteCarlo.RiskAdjusted.Returns.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load Packages and Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy as sp\n",
    "import statsmodels.api as sm\n",
    "%matplotlib inline\n",
    "\n",
    "#load csv containing return data on assets\n",
    "assets = pd.read_csv('/home/Portfolio_2.csv',header='infer',index_col='Date') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>FB</th>\n",
       "      <th>NFLX</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>BBBY</th>\n",
       "      <th>COST</th>\n",
       "      <th>DLTR</th>\n",
       "      <th>FOX</th>\n",
       "      <th>Gold</th>\n",
       "      <th>PEP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-04-01</th>\n",
       "      <td>549.489990</td>\n",
       "      <td>81.669998</td>\n",
       "      <td>59.017143</td>\n",
       "      <td>370.260010</td>\n",
       "      <td>73.779182</td>\n",
       "      <td>139.591400</td>\n",
       "      <td>81.300003</td>\n",
       "      <td>31.535204</td>\n",
       "      <td>68.523880</td>\n",
       "      <td>87.257195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-02</th>\n",
       "      <td>541.309998</td>\n",
       "      <td>81.559998</td>\n",
       "      <td>59.154285</td>\n",
       "      <td>372.250000</td>\n",
       "      <td>74.233482</td>\n",
       "      <td>140.882874</td>\n",
       "      <td>81.120003</td>\n",
       "      <td>32.055969</td>\n",
       "      <td>67.968102</td>\n",
       "      <td>87.807785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-06</th>\n",
       "      <td>543.950012</td>\n",
       "      <td>82.440002</td>\n",
       "      <td>60.330002</td>\n",
       "      <td>377.040009</td>\n",
       "      <td>74.900414</td>\n",
       "      <td>141.691223</td>\n",
       "      <td>80.980003</td>\n",
       "      <td>32.287418</td>\n",
       "      <td>69.050911</td>\n",
       "      <td>88.532707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-07</th>\n",
       "      <td>544.859985</td>\n",
       "      <td>82.320000</td>\n",
       "      <td>60.494286</td>\n",
       "      <td>374.410004</td>\n",
       "      <td>74.136803</td>\n",
       "      <td>141.022232</td>\n",
       "      <td>80.580002</td>\n",
       "      <td>32.104183</td>\n",
       "      <td>67.824371</td>\n",
       "      <td>88.284943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-08</th>\n",
       "      <td>548.840027</td>\n",
       "      <td>82.279999</td>\n",
       "      <td>63.049999</td>\n",
       "      <td>381.200012</td>\n",
       "      <td>75.084068</td>\n",
       "      <td>141.226639</td>\n",
       "      <td>83.529999</td>\n",
       "      <td>32.046318</td>\n",
       "      <td>67.345238</td>\n",
       "      <td>88.119774</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 GOOGL         FB       NFLX        AMZN       BBBY  \\\n",
       "Date                                                                  \n",
       "2015-04-01  549.489990  81.669998  59.017143  370.260010  73.779182   \n",
       "2015-04-02  541.309998  81.559998  59.154285  372.250000  74.233482   \n",
       "2015-04-06  543.950012  82.440002  60.330002  377.040009  74.900414   \n",
       "2015-04-07  544.859985  82.320000  60.494286  374.410004  74.136803   \n",
       "2015-04-08  548.840027  82.279999  63.049999  381.200012  75.084068   \n",
       "\n",
       "                  COST       DLTR        FOX       Gold        PEP  \n",
       "Date                                                                \n",
       "2015-04-01  139.591400  81.300003  31.535204  68.523880  87.257195  \n",
       "2015-04-02  140.882874  81.120003  32.055969  67.968102  87.807785  \n",
       "2015-04-06  141.691223  80.980003  32.287418  69.050911  88.532707  \n",
       "2015-04-07  141.022232  80.580002  32.104183  67.824371  88.284943  \n",
       "2015-04-08  141.226639  83.529999  32.046318  67.345238  88.119774  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "assets.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>FB</th>\n",
       "      <th>NFLX</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>BBBY</th>\n",
       "      <th>COST</th>\n",
       "      <th>DLTR</th>\n",
       "      <th>FOX</th>\n",
       "      <th>Gold</th>\n",
       "      <th>PEP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-03-23</th>\n",
       "      <td>1026.550049</td>\n",
       "      <td>159.389999</td>\n",
       "      <td>300.940002</td>\n",
       "      <td>1495.560059</td>\n",
       "      <td>21.299999</td>\n",
       "      <td>180.839996</td>\n",
       "      <td>91.949997</td>\n",
       "      <td>35.450001</td>\n",
       "      <td>83.919998</td>\n",
       "      <td>106.150002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-03-26</th>\n",
       "      <td>1054.089966</td>\n",
       "      <td>160.059998</td>\n",
       "      <td>320.350006</td>\n",
       "      <td>1555.859985</td>\n",
       "      <td>21.070000</td>\n",
       "      <td>187.220001</td>\n",
       "      <td>95.209999</td>\n",
       "      <td>36.580002</td>\n",
       "      <td>85.220001</td>\n",
       "      <td>106.809998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-03-27</th>\n",
       "      <td>1006.940002</td>\n",
       "      <td>152.220001</td>\n",
       "      <td>300.690002</td>\n",
       "      <td>1497.050049</td>\n",
       "      <td>20.250000</td>\n",
       "      <td>183.149994</td>\n",
       "      <td>93.629997</td>\n",
       "      <td>36.080002</td>\n",
       "      <td>83.660004</td>\n",
       "      <td>107.639999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-03-28</th>\n",
       "      <td>1005.179993</td>\n",
       "      <td>153.029999</td>\n",
       "      <td>285.769989</td>\n",
       "      <td>1431.420044</td>\n",
       "      <td>20.610001</td>\n",
       "      <td>183.610001</td>\n",
       "      <td>93.910004</td>\n",
       "      <td>35.500000</td>\n",
       "      <td>82.320000</td>\n",
       "      <td>109.180000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-03-29</th>\n",
       "      <td>1037.140015</td>\n",
       "      <td>159.789993</td>\n",
       "      <td>295.350006</td>\n",
       "      <td>1447.339966</td>\n",
       "      <td>20.990000</td>\n",
       "      <td>188.429993</td>\n",
       "      <td>94.900002</td>\n",
       "      <td>36.369999</td>\n",
       "      <td>83.239998</td>\n",
       "      <td>109.150002</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "                  GOOGL          FB        NFLX         AMZN       BBBY  \\\n",
       "Date                                                                      \n",
       "2018-03-23  1026.550049  159.389999  300.940002  1495.560059  21.299999   \n",
       "2018-03-26  1054.089966  160.059998  320.350006  1555.859985  21.070000   \n",
       "2018-03-27  1006.940002  152.220001  300.690002  1497.050049  20.250000   \n",
       "2018-03-28  1005.179993  153.029999  285.769989  1431.420044  20.610001   \n",
       "2018-03-29  1037.140015  159.789993  295.350006  1447.339966  20.990000   \n",
       "\n",
       "                  COST       DLTR        FOX       Gold         PEP  \n",
       "Date                                                                 \n",
       "2018-03-23  180.839996  91.949997  35.450001  83.919998  106.150002  \n",
       "2018-03-26  187.220001  95.209999  36.580002  85.220001  106.809998  \n",
       "2018-03-27  183.149994  93.629997  36.080002  83.660004  107.639999  \n",
       "2018-03-28  183.610001  93.910004  35.500000  82.320000  109.180000  \n",
       "2018-03-29  188.429993  94.900002  36.369999  83.239998  109.150002  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "assets.tail(5) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate Daily Returns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>FB</th>\n",
       "      <th>NFLX</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>BBBY</th>\n",
       "      <th>COST</th>\n",
       "      <th>DLTR</th>\n",
       "      <th>FOX</th>\n",
       "      <th>Gold</th>\n",
       "      <th>PEP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-04-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-02</th>\n",
       "      <td>-0.014887</td>\n",
       "      <td>-0.001347</td>\n",
       "      <td>0.002324</td>\n",
       "      <td>0.005375</td>\n",
       "      <td>0.006158</td>\n",
       "      <td>0.009252</td>\n",
       "      <td>-0.002214</td>\n",
       "      <td>0.016514</td>\n",
       "      <td>-0.008111</td>\n",
       "      <td>0.006310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-06</th>\n",
       "      <td>0.004877</td>\n",
       "      <td>0.010790</td>\n",
       "      <td>0.019875</td>\n",
       "      <td>0.012868</td>\n",
       "      <td>0.008984</td>\n",
       "      <td>0.005738</td>\n",
       "      <td>-0.001726</td>\n",
       "      <td>0.007220</td>\n",
       "      <td>0.015931</td>\n",
       "      <td>0.008256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-07</th>\n",
       "      <td>0.001673</td>\n",
       "      <td>-0.001456</td>\n",
       "      <td>0.002723</td>\n",
       "      <td>-0.006975</td>\n",
       "      <td>-0.010195</td>\n",
       "      <td>-0.004721</td>\n",
       "      <td>-0.004940</td>\n",
       "      <td>-0.005675</td>\n",
       "      <td>-0.017763</td>\n",
       "      <td>-0.002799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-08</th>\n",
       "      <td>0.007305</td>\n",
       "      <td>-0.000486</td>\n",
       "      <td>0.042247</td>\n",
       "      <td>0.018135</td>\n",
       "      <td>0.012777</td>\n",
       "      <td>0.001449</td>\n",
       "      <td>0.036610</td>\n",
       "      <td>-0.001802</td>\n",
       "      <td>-0.007064</td>\n",
       "      <td>-0.001871</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "               GOOGL        FB      NFLX      AMZN      BBBY      COST  \\\n",
       "Date                                                                     \n",
       "2015-04-01       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "2015-04-02 -0.014887 -0.001347  0.002324  0.005375  0.006158  0.009252   \n",
       "2015-04-06  0.004877  0.010790  0.019875  0.012868  0.008984  0.005738   \n",
       "2015-04-07  0.001673 -0.001456  0.002723 -0.006975 -0.010195 -0.004721   \n",
       "2015-04-08  0.007305 -0.000486  0.042247  0.018135  0.012777  0.001449   \n",
       "\n",
       "                DLTR       FOX      Gold       PEP  \n",
       "Date                                                \n",
       "2015-04-01       NaN       NaN       NaN       NaN  \n",
       "2015-04-02 -0.002214  0.016514 -0.008111  0.006310  \n",
       "2015-04-06 -0.001726  0.007220  0.015931  0.008256  \n",
       "2015-04-07 -0.004940 -0.005675 -0.017763 -0.002799  \n",
       "2015-04-08  0.036610 -0.001802 -0.007064 -0.001871  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns = (assets/assets.shift(1))-1\n",
    "returns.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Check Distribution of Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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p1i1lLVqM89It8WpEZZ6ajnEnz+gecsgh1m7z589v+zSalUfZ6PCT7kaKcZHj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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8acc583128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "returns.hist(bins=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate Log Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "log_returns = np.log((assets/assets.shift(1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>FB</th>\n",
       "      <th>NFLX</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>BBBY</th>\n",
       "      <th>COST</th>\n",
       "      <th>DLTR</th>\n",
       "      <th>FOX</th>\n",
       "      <th>Gold</th>\n",
       "      <th>PEP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-04-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-02</th>\n",
       "      <td>-0.014998</td>\n",
       "      <td>-0.001348</td>\n",
       "      <td>0.002321</td>\n",
       "      <td>0.005360</td>\n",
       "      <td>0.006139</td>\n",
       "      <td>0.009209</td>\n",
       "      <td>-0.002216</td>\n",
       "      <td>0.016379</td>\n",
       "      <td>-0.008144</td>\n",
       "      <td>0.006290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-06</th>\n",
       "      <td>0.004865</td>\n",
       "      <td>0.010732</td>\n",
       "      <td>0.019680</td>\n",
       "      <td>0.012786</td>\n",
       "      <td>0.008944</td>\n",
       "      <td>0.005721</td>\n",
       "      <td>-0.001727</td>\n",
       "      <td>0.007194</td>\n",
       "      <td>0.015806</td>\n",
       "      <td>0.008222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-07</th>\n",
       "      <td>0.001672</td>\n",
       "      <td>-0.001457</td>\n",
       "      <td>0.002719</td>\n",
       "      <td>-0.007000</td>\n",
       "      <td>-0.010247</td>\n",
       "      <td>-0.004733</td>\n",
       "      <td>-0.004952</td>\n",
       "      <td>-0.005691</td>\n",
       "      <td>-0.017922</td>\n",
       "      <td>-0.002802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-08</th>\n",
       "      <td>0.007278</td>\n",
       "      <td>-0.000486</td>\n",
       "      <td>0.041379</td>\n",
       "      <td>0.017973</td>\n",
       "      <td>0.012696</td>\n",
       "      <td>0.001448</td>\n",
       "      <td>0.035955</td>\n",
       "      <td>-0.001804</td>\n",
       "      <td>-0.007089</td>\n",
       "      <td>-0.001873</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               GOOGL        FB      NFLX      AMZN      BBBY      COST  \\\n",
       "Date                                                                     \n",
       "2015-04-01       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "2015-04-02 -0.014998 -0.001348  0.002321  0.005360  0.006139  0.009209   \n",
       "2015-04-06  0.004865  0.010732  0.019680  0.012786  0.008944  0.005721   \n",
       "2015-04-07  0.001672 -0.001457  0.002719 -0.007000 -0.010247 -0.004733   \n",
       "2015-04-08  0.007278 -0.000486  0.041379  0.017973  0.012696  0.001448   \n",
       "\n",
       "                DLTR       FOX      Gold       PEP  \n",
       "Date                                                \n",
       "2015-04-01       NaN       NaN       NaN       NaN  \n",
       "2015-04-02 -0.002216  0.016379 -0.008144  0.006290  \n",
       "2015-04-06 -0.001727  0.007194  0.015806  0.008222  \n",
       "2015-04-07 -0.004952 -0.005691 -0.017922 -0.002802  \n",
       "2015-04-08  0.035955 -0.001804 -0.007089 -0.001873  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GOOGL    0.212306\n",
       "FB       0.224318\n",
       "NFLX     0.538202\n",
       "AMZN     0.455631\n",
       "BBBY    -0.420122\n",
       "COST     0.100268\n",
       "DLTR     0.051696\n",
       "FOX      0.047673\n",
       "Gold     0.065021\n",
       "PEP      0.074819\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_returns_means= log_returns.mean()*252\n",
    "log_returns_means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>FB</th>\n",
       "      <th>NFLX</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>BBBY</th>\n",
       "      <th>COST</th>\n",
       "      <th>DLTR</th>\n",
       "      <th>FOX</th>\n",
       "      <th>Gold</th>\n",
       "      <th>PEP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>GOOGL</th>\n",
       "      <td>0.051703</td>\n",
       "      <td>0.037923</td>\n",
       "      <td>0.040084</td>\n",
       "      <td>0.037761</td>\n",
       "      <td>0.006759</td>\n",
       "      <td>0.014809</td>\n",
       "      <td>0.017474</td>\n",
       "      <td>0.016526</td>\n",
       "      <td>0.003415</td>\n",
       "      <td>0.011622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FB</th>\n",
       "      <td>0.037923</td>\n",
       "      <td>0.063865</td>\n",
       "      <td>0.041359</td>\n",
       "      <td>0.041199</td>\n",
       "      <td>0.006268</td>\n",
       "      <td>0.012379</td>\n",
       "      <td>0.015795</td>\n",
       "      <td>0.018267</td>\n",
       "      <td>0.004893</td>\n",
       "      <td>0.011475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NFLX</th>\n",
       "      <td>0.040084</td>\n",
       "      <td>0.041359</td>\n",
       "      <td>0.174764</td>\n",
       "      <td>0.048329</td>\n",
       "      <td>0.011944</td>\n",
       "      <td>0.016129</td>\n",
       "      <td>0.022053</td>\n",
       "      <td>0.023956</td>\n",
       "      <td>0.009260</td>\n",
       "      <td>0.011262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AMZN</th>\n",
       "      <td>0.037761</td>\n",
       "      <td>0.041199</td>\n",
       "      <td>0.048329</td>\n",
       "      <td>0.077447</td>\n",
       "      <td>0.004387</td>\n",
       "      <td>0.013007</td>\n",
       "      <td>0.015140</td>\n",
       "      <td>0.020239</td>\n",
       "      <td>0.005545</td>\n",
       "      <td>0.010551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BBBY</th>\n",
       "      <td>0.006759</td>\n",
       "      <td>0.006268</td>\n",
       "      <td>0.011944</td>\n",
       "      <td>0.004387</td>\n",
       "      <td>0.099406</td>\n",
       "      <td>0.016719</td>\n",
       "      <td>0.031556</td>\n",
       "      <td>0.020358</td>\n",
       "      <td>0.002565</td>\n",
       "      <td>0.004672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>COST</th>\n",
       "      <td>0.014809</td>\n",
       "      <td>0.012379</td>\n",
       "      <td>0.016129</td>\n",
       "      <td>0.013007</td>\n",
       "      <td>0.016719</td>\n",
       "      <td>0.034535</td>\n",
       "      <td>0.021681</td>\n",
       "      <td>0.011282</td>\n",
       "      <td>-0.002043</td>\n",
       "      <td>0.010648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DLTR</th>\n",
       "      <td>0.017474</td>\n",
       "      <td>0.015795</td>\n",
       "      <td>0.022053</td>\n",
       "      <td>0.015140</td>\n",
       "      <td>0.031556</td>\n",
       "      <td>0.021681</td>\n",
       "      <td>0.079864</td>\n",
       "      <td>0.018325</td>\n",
       "      <td>-0.000960</td>\n",
       "      <td>0.010233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FOX</th>\n",
       "      <td>0.016526</td>\n",
       "      <td>0.018267</td>\n",
       "      <td>0.023956</td>\n",
       "      <td>0.020239</td>\n",
       "      <td>0.020358</td>\n",
       "      <td>0.011282</td>\n",
       "      <td>0.018325</td>\n",
       "      <td>0.060808</td>\n",
       "      <td>0.000715</td>\n",
       "      <td>0.008245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gold</th>\n",
       "      <td>0.003415</td>\n",
       "      <td>0.004893</td>\n",
       "      <td>0.009260</td>\n",
       "      <td>0.005545</td>\n",
       "      <td>0.002565</td>\n",
       "      <td>-0.002043</td>\n",
       "      <td>-0.000960</td>\n",
       "      <td>0.000715</td>\n",
       "      <td>0.127163</td>\n",
       "      <td>0.006395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PEP</th>\n",
       "      <td>0.011622</td>\n",
       "      <td>0.011475</td>\n",
       "      <td>0.011262</td>\n",
       "      <td>0.010551</td>\n",
       "      <td>0.004672</td>\n",
       "      <td>0.010648</td>\n",
       "      <td>0.010233</td>\n",
       "      <td>0.008245</td>\n",
       "      <td>0.006395</td>\n",
       "      <td>0.017353</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          GOOGL        FB      NFLX      AMZN      BBBY      COST      DLTR  \\\n",
       "GOOGL  0.051703  0.037923  0.040084  0.037761  0.006759  0.014809  0.017474   \n",
       "FB     0.037923  0.063865  0.041359  0.041199  0.006268  0.012379  0.015795   \n",
       "NFLX   0.040084  0.041359  0.174764  0.048329  0.011944  0.016129  0.022053   \n",
       "AMZN   0.037761  0.041199  0.048329  0.077447  0.004387  0.013007  0.015140   \n",
       "BBBY   0.006759  0.006268  0.011944  0.004387  0.099406  0.016719  0.031556   \n",
       "COST   0.014809  0.012379  0.016129  0.013007  0.016719  0.034535  0.021681   \n",
       "DLTR   0.017474  0.015795  0.022053  0.015140  0.031556  0.021681  0.079864   \n",
       "FOX    0.016526  0.018267  0.023956  0.020239  0.020358  0.011282  0.018325   \n",
       "Gold   0.003415  0.004893  0.009260  0.005545  0.002565 -0.002043 -0.000960   \n",
       "PEP    0.011622  0.011475  0.011262  0.010551  0.004672  0.010648  0.010233   \n",
       "\n",
       "            FOX      Gold       PEP  \n",
       "GOOGL  0.016526  0.003415  0.011622  \n",
       "FB     0.018267  0.004893  0.011475  \n",
       "NFLX   0.023956  0.009260  0.011262  \n",
       "AMZN   0.020239  0.005545  0.010551  \n",
       "BBBY   0.020358  0.002565  0.004672  \n",
       "COST   0.011282 -0.002043  0.010648  \n",
       "DLTR   0.018325 -0.000960  0.010233  \n",
       "FOX    0.060808  0.000715  0.008245  \n",
       "Gold   0.000715  0.127163  0.006395  \n",
       "PEP    0.008245  0.006395  0.017353  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov_mat = log_returns.cov()*252\n",
    "cov_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>FB</th>\n",
       "      <th>NFLX</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>BBBY</th>\n",
       "      <th>COST</th>\n",
       "      <th>DLTR</th>\n",
       "      <th>FOX</th>\n",
       "      <th>Gold</th>\n",
       "      <th>PEP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>GOOGL</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.659948</td>\n",
       "      <td>0.421682</td>\n",
       "      <td>0.596727</td>\n",
       "      <td>0.094283</td>\n",
       "      <td>0.350461</td>\n",
       "      <td>0.271933</td>\n",
       "      <td>0.294732</td>\n",
       "      <td>0.042117</td>\n",
       "      <td>0.388017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FB</th>\n",
       "      <td>0.659948</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.391481</td>\n",
       "      <td>0.585806</td>\n",
       "      <td>0.078667</td>\n",
       "      <td>0.263593</td>\n",
       "      <td>0.221170</td>\n",
       "      <td>0.293131</td>\n",
       "      <td>0.054295</td>\n",
       "      <td>0.344700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NFLX</th>\n",
       "      <td>0.421682</td>\n",
       "      <td>0.391481</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.415408</td>\n",
       "      <td>0.090621</td>\n",
       "      <td>0.207611</td>\n",
       "      <td>0.186670</td>\n",
       "      <td>0.232387</td>\n",
       "      <td>0.062117</td>\n",
       "      <td>0.204512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AMZN</th>\n",
       "      <td>0.596727</td>\n",
       "      <td>0.585806</td>\n",
       "      <td>0.415408</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.050001</td>\n",
       "      <td>0.251497</td>\n",
       "      <td>0.192502</td>\n",
       "      <td>0.294913</td>\n",
       "      <td>0.055871</td>\n",
       "      <td>0.287823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BBBY</th>\n",
       "      <td>0.094283</td>\n",
       "      <td>0.078667</td>\n",
       "      <td>0.090621</td>\n",
       "      <td>0.050001</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.285347</td>\n",
       "      <td>0.354165</td>\n",
       "      <td>0.261850</td>\n",
       "      <td>0.022818</td>\n",
       "      <td>0.112488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>COST</th>\n",
       "      <td>0.350461</td>\n",
       "      <td>0.263593</td>\n",
       "      <td>0.207611</td>\n",
       "      <td>0.251497</td>\n",
       "      <td>0.285347</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.412833</td>\n",
       "      <td>0.246201</td>\n",
       "      <td>-0.030832</td>\n",
       "      <td>0.434950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DLTR</th>\n",
       "      <td>0.271933</td>\n",
       "      <td>0.221170</td>\n",
       "      <td>0.186670</td>\n",
       "      <td>0.192502</td>\n",
       "      <td>0.354165</td>\n",
       "      <td>0.412833</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.262965</td>\n",
       "      <td>-0.009527</td>\n",
       "      <td>0.274878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FOX</th>\n",
       "      <td>0.294732</td>\n",
       "      <td>0.293131</td>\n",
       "      <td>0.232387</td>\n",
       "      <td>0.294913</td>\n",
       "      <td>0.261850</td>\n",
       "      <td>0.246201</td>\n",
       "      <td>0.262965</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.008136</td>\n",
       "      <td>0.253833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gold</th>\n",
       "      <td>0.042117</td>\n",
       "      <td>0.054295</td>\n",
       "      <td>0.062117</td>\n",
       "      <td>0.055871</td>\n",
       "      <td>0.022818</td>\n",
       "      <td>-0.030832</td>\n",
       "      <td>-0.009527</td>\n",
       "      <td>0.008136</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.136136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PEP</th>\n",
       "      <td>0.388017</td>\n",
       "      <td>0.344700</td>\n",
       "      <td>0.204512</td>\n",
       "      <td>0.287823</td>\n",
       "      <td>0.112488</td>\n",
       "      <td>0.434950</td>\n",
       "      <td>0.274878</td>\n",
       "      <td>0.253833</td>\n",
       "      <td>0.136136</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          GOOGL        FB      NFLX      AMZN      BBBY      COST      DLTR  \\\n",
       "GOOGL  1.000000  0.659948  0.421682  0.596727  0.094283  0.350461  0.271933   \n",
       "FB     0.659948  1.000000  0.391481  0.585806  0.078667  0.263593  0.221170   \n",
       "NFLX   0.421682  0.391481  1.000000  0.415408  0.090621  0.207611  0.186670   \n",
       "AMZN   0.596727  0.585806  0.415408  1.000000  0.050001  0.251497  0.192502   \n",
       "BBBY   0.094283  0.078667  0.090621  0.050001  1.000000  0.285347  0.354165   \n",
       "COST   0.350461  0.263593  0.207611  0.251497  0.285347  1.000000  0.412833   \n",
       "DLTR   0.271933  0.221170  0.186670  0.192502  0.354165  0.412833  1.000000   \n",
       "FOX    0.294732  0.293131  0.232387  0.294913  0.261850  0.246201  0.262965   \n",
       "Gold   0.042117  0.054295  0.062117  0.055871  0.022818 -0.030832 -0.009527   \n",
       "PEP    0.388017  0.344700  0.204512  0.287823  0.112488  0.434950  0.274878   \n",
       "\n",
       "            FOX      Gold       PEP  \n",
       "GOOGL  0.294732  0.042117  0.388017  \n",
       "FB     0.293131  0.054295  0.344700  \n",
       "NFLX   0.232387  0.062117  0.204512  \n",
       "AMZN   0.294913  0.055871  0.287823  \n",
       "BBBY   0.261850  0.022818  0.112488  \n",
       "COST   0.246201 -0.030832  0.434950  \n",
       "DLTR   0.262965 -0.009527  0.274878  \n",
       "FOX    1.000000  0.008136  0.253833  \n",
       "Gold   0.008136  1.000000  0.136136  \n",
       "PEP    0.253833  0.136136  1.000000  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corr_mat = log_returns.corr()\n",
    "corr_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random Weights via Monte Carlo Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max Sharpe Ratio: 1.5130528738159625 Min Vol: 0.12654536358254154\n"
     ]
    }
   ],
   "source": [
    "#set seed for reproduceable results\n",
    "np.random.seed(600)\n",
    "number_port = 25000\n",
    "number_assets = len(assets.columns)\n",
    "\n",
    "#array to store weights\n",
    "weights_store = np.zeros((number_port,len(assets.columns)))\n",
    "\n",
    "#array to store returns\n",
    "returns_store = np.zeros(number_port)\n",
    "\n",
    "#array to store returns\n",
    "vol_store = np.zeros(number_port)\n",
    "\n",
    "#array to store Sharpe Ratio info\n",
    "sharpe_store=np.zeros(number_port)\n",
    "\n",
    "#set Riskfree Rate, necessary for sharpe ratio\n",
    "Rf = .015\n",
    "\n",
    "for x in range(number_port):\n",
    "    #Weights\n",
    "    weights = np.array(np.random.random(number_assets))\n",
    "    weights /= np.sum(weights)\n",
    "    #Save Weights\n",
    "    weights_store[x,:] = weights\n",
    "    \n",
    "    #Save Expected Returns\n",
    "    returns_store[x] = np.sum(weights*log_returns.mean())*252\n",
    "   \n",
    "    #Save Expected Volatility\n",
    "    vol_store[x] = np.sqrt(np.dot(weights.T,np.dot(log_returns.cov()*252, weights)))\n",
    "   \n",
    "    #Save Sharpe Ratio\n",
    "    sharpe_store[x] = (returns_store[x] - Rf)/vol_store[x]\n",
    "    \n",
    "print('Max Sharpe Ratio:',sharpe_store.max(),'Min Vol:',vol_store.min())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        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>GOOGL</th>\n",
       "      <th>FB</th>\n",
       "      <th>NFLX</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>BBBY</th>\n",
       "      <th>COST</th>\n",
       "      <th>DLTR</th>\n",
       "      <th>FOX</th>\n",
       "      <th>Gold</th>\n",
       "      <th>PEP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Max_Sharpe_Allocation</th>\n",
       "      <td>7.7</td>\n",
       "      <td>12.1</td>\n",
       "      <td>23.12</td>\n",
       "      <td>23.94</td>\n",
       "      <td>0.43</td>\n",
       "      <td>2.93</td>\n",
       "      <td>2.58</td>\n",
       "      <td>0.51</td>\n",
       "      <td>3.67</td>\n",
       "      <td>23.03</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       GOOGL    FB   NFLX   AMZN  BBBY  COST  DLTR   FOX  \\\n",
       "Max_Sharpe_Allocation    7.7  12.1  23.12  23.94  0.43  2.93  2.58  0.51   \n",
       "\n",
       "                       Gold    PEP  \n",
       "Max_Sharpe_Allocation  3.67  23.03  "
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Find location and allocation of Max Sharpe portfolio\n",
    "max_sharpe_idx = np.argmax(sharpe_store)\n",
    "max_sharpe_return = returns_store[max_sharpe_idx]\n",
    "max_sharpe_vol = vol_store[max_sharpe_idx]\n",
    "max_sharpe_wght = weights_store[max_sharpe_idx]\n",
    "\n",
    "max_sharpe_allocation = pd.DataFrame(weights_store[max_sharpe_idx],index=returns.columns,columns=['Max_Sharpe_Allocation'])\n",
    "max_sharpe_allocation.Max_Sharpe_Allocation = [round(i*100,2)for i in max_sharpe_allocation.Max_Sharpe_Allocation]\n",
    "max_sharpe_allocation = max_sharpe_allocation.T\n",
    "\n",
    "max_sharpe_allocation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max Sharpe Portfolio Returns =  0.299334925592094\n",
      "Max Sharpe Portfolio Vol =  0.18792134135735336\n"
     ]
    }
   ],
   "source": [
    "print('Max Sharpe Portfolio Returns = ',max_sharpe_return)\n",
    "print('Max Sharpe Portfolio Vol = ',max_sharpe_vol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "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>GOOGL</th>\n",
       "      <th>FB</th>\n",
       "      <th>NFLX</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>BBBY</th>\n",
       "      <th>COST</th>\n",
       "      <th>DLTR</th>\n",
       "      <th>FOX</th>\n",
       "      <th>Gold</th>\n",
       "      <th>PEP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Min_Vol_Allocation</th>\n",
       "      <td>4.63</td>\n",
       "      <td>1.38</td>\n",
       "      <td>0.5</td>\n",
       "      <td>6.62</td>\n",
       "      <td>4.95</td>\n",
       "      <td>19.43</td>\n",
       "      <td>7.17</td>\n",
       "      <td>10.93</td>\n",
       "      <td>17.16</td>\n",
       "      <td>27.22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    GOOGL    FB  NFLX  AMZN  BBBY   COST  DLTR    FOX   Gold  \\\n",
       "Min_Vol_Allocation   4.63  1.38   0.5  6.62  4.95  19.43  7.17  10.93  17.16   \n",
       "\n",
       "                      PEP  \n",
       "Min_Vol_Allocation  27.22  "
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Find location and allocation of Min Vol portfolio\n",
    "min_vol_idx = np.argmin(vol_store)\n",
    "min_vol_return = returns_store[min_vol_idx]\n",
    "min_vol_vol = vol_store[min_vol_idx]\n",
    "min_vol_allocation = pd.DataFrame(weights_store[min_vol_idx],index=returns.columns,columns=['Min_Vol_Allocation'])\n",
    "min_vol_allocation.Min_Vol_Allocation = [round(i*100,2)for i in min_vol_allocation.Min_Vol_Allocation]\n",
    "min_vol_allocation = min_vol_allocation.T\n",
    "\n",
    "min_vol_allocation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min Vol Portfolio Returns =  0.08490098513644295\n",
      "Min Vol Portfolio Vol =  0.12654536358254154\n"
     ]
    }
   ],
   "source": [
    "print('Min Vol Portfolio Returns = ',min_vol_return)\n",
    "print('Min Vol Portfolio Vol = ',min_vol_vol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CggJKS0uzfgnGYjBnjtn0uqgIJk2KsmJF7TYzhxwCK1bAeeeZelWYPZuMbOqW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\ncwJWfq+V591Ub7H5PdVZvJD5p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8TYgfLBI35/t/T10lv+8Amd+85CKXU6sBz4HxHZ7p87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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a8de4b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 7))\n",
    "#Assign data to axis, Vol,Returns, C= Sharpe Ratio, Cmap = 'Style'\n",
    "plt.scatter(vol_store,returns_store,c=sharpe_store,cmap='plasma')\n",
    "#Label Colorbar\n",
    "plt.colorbar(label='Sharpe Ratio')\n",
    "#Label Maximum Sharpe and Minimum Vol\n",
    "plt.scatter(max_sharpe_vol,max_sharpe_return,marker='*',color='r',s=500, label='Maximum Sharpe ratio')\n",
    "plt.scatter(min_vol_vol,min_vol_return,marker='*',color='b',s=500, label='Minimum volatility')\n",
    "#Provide a title\n",
    "plt.title('Portfolio Optimization - Efficient Frontier')\n",
    "plt.grid(True)\n",
    "#Label X and Y Access\n",
    "plt.xlabel('Volatility')\n",
    "plt.ylabel('Returns')\n",
    "plt.legend(labelspacing=0.8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a Benchmark/Market Returns (S&P500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>GSPC</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-04-01</th>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-02</th>\n",
       "      <td>0.003523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-06</th>\n",
       "      <td>0.006587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-07</th>\n",
       "      <td>-0.002064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-08</th>\n",
       "      <td>0.002679</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                GSPC\n",
       "Date                \n",
       "2015-04-01       NaN\n",
       "2015-04-02  0.003523\n",
       "2015-04-06  0.006587\n",
       "2015-04-07 -0.002064\n",
       "2015-04-08  0.002679"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SP500 Serves as our Benchmark\n",
    "benchmark = pd.read_csv('/home/riverstone/GSPC_Benchmark.csv',header='infer',index_col='Date')\n",
    "benchmark_ret = (benchmark/benchmark.shift(1))-1\n",
    "log_benchmark_ret = np.log(benchmark/benchmark.shift(1)) \n",
    "SP500_ret = log_benchmark_ret\n",
    "SP500_ret.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate Portfolio Beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0200115301040453\n"
     ]
    }
   ],
   "source": [
    "#Calculate Betas for each individual asset \n",
    "\n",
    "#Create a list to hold Betas\n",
    "outputs=[]\n",
    "\n",
    "for column in log_returns:\n",
    "    #concatentate market and log_returns[column] in to one dataframe\n",
    "    df = pd.DataFrame({'Benchmark':SP500_ret['GSPC'].dropna(),'Return':log_returns[column].dropna()})\n",
    "    \n",
    "    #Conduct Linear Regression to find Beta\n",
    "    rgress = sm.OLS(df.Return,sm.tools.add_constant(df.Benchmark)).fit()\n",
    "    \n",
    "    #Collect individual Regressions \n",
    "    outputs.append(rgress.params[1]) \n",
    "\n",
    "#Calculate Weighted Average of Betas    \n",
    "port_beta= np.sum(np.dot(outputs,(max_sharpe_allocation.T)/100))\n",
    "print(port_beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Treynor Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max Sharpe Treynor =  0.26405086378251114\n",
      "Min Vol Treynor =  0.05382388680532153\n"
     ]
    }
   ],
   "source": [
    "#Assign Riskfree Rate or Threshold\n",
    "rf = .03\n",
    "\n",
    "#Calculate Treynor Ratio\n",
    "#Beta used to adjust for market risk\n",
    "ms_Treynor = (max_sharpe_return - rf)/port_beta\n",
    "\n",
    "mv_Treynor = (min_vol_return - rf)/port_beta\n",
    "\n",
    "print('Max Sharpe Treynor = ', ms_Treynor)\n",
    "print('Min Vol Treynor = ', mv_Treynor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Information Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max Sharpe Info Ratio =  [1.59111934]\n",
      "Min Vol Info Ratio =  [0.66830848]\n"
     ]
    }
   ],
   "source": [
    "#Find excess returns less the Market Benchmark\n",
    "ms_ret_less_bench = max_sharpe_return - SP500_ret.mean()\n",
    "ms_info_ratio = ms_ret_less_bench/max_sharpe_vol\n",
    "\n",
    "mv_ret_less_bench = min_vol_return - SP500_ret.mean()\n",
    "mv_info_ratio = mv_ret_less_bench/min_vol_vol\n",
    "\n",
    "print('Max Sharpe Info Ratio = ',ms_info_ratio.values)\n",
    "print('Min Vol Info Ratio = ', mv_info_ratio.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lower Partial Moment "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            LPM\n",
      "GOOGL  0.001050\n",
      "FB     0.001108\n",
      "NFLX   0.001497\n",
      "AMZN   0.001095\n",
      "BBBY   0.001454\n",
      "COST   0.001027\n",
      "DLTR   0.001223\n",
      "FOX    0.001154\n",
      "Gold   0.001483\n",
      "PEP    0.000954\n",
      "Weighted Average LPM= 0.001170901106613874\n"
     ]
    }
   ],
   "source": [
    "#Lower Partial Moment\n",
    "_LPM=[]\n",
    "for column in log_returns:\n",
    "    y=log_returns[column][log_returns[column]-rf<0]\n",
    "    m=len(y)\n",
    "    total=0.0\n",
    "    for i in sp.arange(m):\n",
    "        total+=(y[i]-rf)**2\n",
    "    _LPM.append(total/(m-1))\n",
    "    \n",
    "\n",
    "lpmf = pd.DataFrame(_LPM,index=returns.columns,columns=['LPM'])\n",
    "print(lpmf)\n",
    "Weighted_Avg_LPM= np.sum(np.dot(_LPM,(max_sharpe_allocation.T)/100))\n",
    "print(\"Weighted Average LPM=\",Weighted_Avg_LPM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Omega Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min Vol Omega Ratio =  46.88780702856365\n",
      "Max Sharpe Omega Ratio = 230.0236322869171\n"
     ]
    }
   ],
   "source": [
    "#First Order Lower Partial Moment\n",
    "#A larger ratio indicates that the asset provides more gains relative to losses for some threshold r \n",
    "#and so would be preferred by an investor\n",
    "\n",
    "ms_omega_ratio = (max_sharpe_return - rf) / Weighted_Avg_LPM\n",
    "mv_omega_ratio = (min_vol_return -rf)/ Weighted_Avg_LPM\n",
    "\n",
    "print('Min Vol Omega Ratio = ',mv_omega_ratio)\n",
    "print('Max Sharpe Omega Ratio =',ms_omega_ratio)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sortino Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Portfolio Standard Deviation =  0.18792134135735336\n",
      "Target Downside Deviation =  0.034218432264115695\n",
      "Max Sharpe Sortino Ratio =  7.871048080555728\n",
      "Min Volatility Sortino Ratio =  1.604427248819833\n"
     ]
    }
   ],
   "source": [
    "#Second Order Lower Partial moment\n",
    "TDD = np.sqrt(Weighted_Avg_LPM) \n",
    "ms_sortino_ratio = (max_sharpe_return - rf) /TDD\n",
    "ms_sortino_ratio\n",
    "\n",
    "mv_sortino_ratio = (min_vol_return - rf) /TDD\n",
    "mv_sortino_ratio\n",
    "print('Portfolio Standard Deviation = ',max_sharpe_vol)\n",
    "print('Target Downside Deviation = ',TDD)\n",
    "print('Max Sharpe Sortino Ratio = ',ms_sortino_ratio)\n",
    "print('Min Volatility Sortino Ratio = ',mv_sortino_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max_Sharpe_Kappa_Ratio =  2.5553629951828674\n",
      "Min_Vol_Kappa_Ratio =  0.5208828580561519\n"
     ]
    }
   ],
   "source": [
    "#Third Partial Moment\n",
    "ms_kappa_ratio = (max_sharpe_return - rf) / np.power(Weighted_Avg_LPM,float(1/3))\n",
    "mv_kappa_ratio = (min_vol_return - rf) / np.power(Weighted_Avg_LPM,float(1/3))\n",
    "\n",
    "print('Max_Sharpe_Kappa_Ratio = ',ms_kappa_ratio)\n",
    "print('Min_Vol_Kappa_Ratio = ',mv_kappa_ratio)"
   ]
  }
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