examples/Tutorial 22 - Logarithmic Mean Risk Optimization (Kelly Criterion).ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Riskfolio-Lib Tutorial: \n",
    "<br>__[Financionerioncios](https://financioneroncios.wordpress.com)__\n",
    "<br>__[Orenji](https://www.orenj-i.net)__\n",
    "<br>__[Riskfolio-Lib](https://riskfolio-lib.readthedocs.io/en/latest/)__\n",
    "<br>__[Dany Cajas](https://www.linkedin.com/in/dany-cajas/)__\n",
    "<a href='https://ko-fi.com/B0B833SXD' target='_blank'><img height='36' style='border:0px;height:36px;' src='https://cdn.ko-fi.com/cdn/kofi1.png?v=2' border='0' alt='Buy Me a Coffee at ko-fi.com' /></a> \n",
    "\n",
    "## Tutorial 22: Logarithmic Mean Risk Optimization (Kelly Criterion)\n",
    "\n",
    "## 1. Downloading the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  26 of 26 completed\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import yfinance as yf\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "pd.options.display.float_format = '{:.4%}'.format\n",
    "\n",
    "# Date range\n",
    "start = '2000-01-01'\n",
    "end = '2019-12-31'\n",
    "\n",
    "# Tickers of assets\n",
    "assets = ['AIG', 'AKAM', 'AMT', 'APA', 'BA', 'BAX', 'BKNG',\n",
    "          'BMY', 'CMCSA', 'CNP', 'CPB', 'DE', 'MO', 'MSFT', 'NI',\n",
    "          'NKTR', 'NTAP', 'PCAR', 'PSA', 'REGN', 'SBAC', 'SEE', 'T',\n",
    "          'TGT', 'TMO', 'TTWO']\n",
    "\n",
    "assets.sort()\n",
    "\n",
    "# Downloading data\n",
    "data = yf.download(assets, start = start, end = end)\n",
    "data = data.loc[:,('Adj Close', slice(None))]\n",
    "data.columns = assets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(239, 26)\n"
     ]
    },
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AIG</th>\n",
       "      <th>AKAM</th>\n",
       "      <th>AMT</th>\n",
       "      <th>APA</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAX</th>\n",
       "      <th>BKNG</th>\n",
       "      <th>BMY</th>\n",
       "      <th>CMCSA</th>\n",
       "      <th>CNP</th>\n",
       "      <th>...</th>\n",
       "      <th>NTAP</th>\n",
       "      <th>PCAR</th>\n",
       "      <th>PSA</th>\n",
       "      <th>REGN</th>\n",
       "      <th>SBAC</th>\n",
       "      <th>SEE</th>\n",
       "      <th>T</th>\n",
       "      <th>TGT</th>\n",
       "      <th>TMO</th>\n",
       "      <th>TTWO</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-02-29</th>\n",
       "      <td>-15.2695%</td>\n",
       "      <td>4.8670%</td>\n",
       "      <td>37.2823%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>-16.7100%</td>\n",
       "      <td>-14.6771%</td>\n",
       "      <td>-3.5560%</td>\n",
       "      <td>-13.5849%</td>\n",
       "      <td>-7.2463%</td>\n",
       "      <td>-8.3354%</td>\n",
       "      <td>...</td>\n",
       "      <td>88.0448%</td>\n",
       "      <td>4.6443%</td>\n",
       "      <td>-2.7548%</td>\n",
       "      <td>358.8832%</td>\n",
       "      <td>33.6082%</td>\n",
       "      <td>-11.4699%</td>\n",
       "      <td>-11.9534%</td>\n",
       "      <td>-10.2962%</td>\n",
       "      <td>-9.7473%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03-31</th>\n",
       "      <td>23.8863%</td>\n",
       "      <td>-38.4450%</td>\n",
       "      <td>0.2538%</td>\n",
       "      <td>36.5170%</td>\n",
       "      <td>2.3688%</td>\n",
       "      <td>15.0229%</td>\n",
       "      <td>43.0168%</td>\n",
       "      <td>-0.2183%</td>\n",
       "      <td>3.1250%</td>\n",
       "      <td>14.5896%</td>\n",
       "      <td>...</td>\n",
       "      <td>-12.3179%</td>\n",
       "      <td>16.1103%</td>\n",
       "      <td>-3.8081%</td>\n",
       "      <td>-47.6770%</td>\n",
       "      <td>8.6420%</td>\n",
       "      <td>9.3082%</td>\n",
       "      <td>11.5894%</td>\n",
       "      <td>26.6949%</td>\n",
       "      <td>30.4000%</td>\n",
       "      <td>6.5327%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-30</th>\n",
       "      <td>0.1712%</td>\n",
       "      <td>-38.5154%</td>\n",
       "      <td>-5.6962%</td>\n",
       "      <td>-2.6383%</td>\n",
       "      <td>4.9587%</td>\n",
       "      <td>8.5878%</td>\n",
       "      <td>-20.9375%</td>\n",
       "      <td>-7.8650%</td>\n",
       "      <td>-5.4546%</td>\n",
       "      <td>12.9974%</td>\n",
       "      <td>...</td>\n",
       "      <td>-10.6496%</td>\n",
       "      <td>-4.8750%</td>\n",
       "      <td>6.5476%</td>\n",
       "      <td>-3.3827%</td>\n",
       "      <td>-7.6705%</td>\n",
       "      <td>2.4165%</td>\n",
       "      <td>4.7667%</td>\n",
       "      <td>-10.9532%</td>\n",
       "      <td>-4.9079%</td>\n",
       "      <td>-27.3585%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-31</th>\n",
       "      <td>2.6662%</td>\n",
       "      <td>-32.4905%</td>\n",
       "      <td>-20.2685%</td>\n",
       "      <td>25.6130%</td>\n",
       "      <td>-1.2138%</td>\n",
       "      <td>2.1114%</td>\n",
       "      <td>-39.7233%</td>\n",
       "      <td>5.0060%</td>\n",
       "      <td>-3.6859%</td>\n",
       "      <td>8.7704%</td>\n",
       "      <td>...</td>\n",
       "      <td>-12.6796%</td>\n",
       "      <td>-11.3612%</td>\n",
       "      <td>-0.2794%</td>\n",
       "      <td>-28.6652%</td>\n",
       "      <td>-8.3077%</td>\n",
       "      <td>0.6742%</td>\n",
       "      <td>-0.2853%</td>\n",
       "      <td>-5.6896%</td>\n",
       "      <td>-4.1936%</td>\n",
       "      <td>-5.8442%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-06-30</th>\n",
       "      <td>4.3865%</td>\n",
       "      <td>77.8792%</td>\n",
       "      <td>12.2896%</td>\n",
       "      <td>-3.3385%</td>\n",
       "      <td>7.0400%</td>\n",
       "      <td>5.7330%</td>\n",
       "      <td>-0.3689%</td>\n",
       "      <td>5.7888%</td>\n",
       "      <td>3.4942%</td>\n",
       "      <td>3.5011%</td>\n",
       "      <td>...</td>\n",
       "      <td>24.6854%</td>\n",
       "      <td>-5.2239%</td>\n",
       "      <td>6.1300%</td>\n",
       "      <td>46.3190%</td>\n",
       "      <td>39.4295%</td>\n",
       "      <td>-6.4733%</td>\n",
       "      <td>0.7153%</td>\n",
       "      <td>-7.4776%</td>\n",
       "      <td>13.4680%</td>\n",
       "      <td>33.7931%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 AIG      AKAM       AMT      APA        BA       BAX  \\\n",
       "Date                                                                    \n",
       "2000-02-29 -15.2695%   4.8670%  37.2823%  0.0000% -16.7100% -14.6771%   \n",
       "2000-03-31  23.8863% -38.4450%   0.2538% 36.5170%   2.3688%  15.0229%   \n",
       "2000-04-30   0.1712% -38.5154%  -5.6962% -2.6383%   4.9587%   8.5878%   \n",
       "2000-05-31   2.6662% -32.4905% -20.2685% 25.6130%  -1.2138%   2.1114%   \n",
       "2000-06-30   4.3865%  77.8792%  12.2896% -3.3385%   7.0400%   5.7330%   \n",
       "\n",
       "                BKNG       BMY    CMCSA      CNP  ...      NTAP      PCAR  \\\n",
       "Date                                              ...                       \n",
       "2000-02-29  -3.5560% -13.5849% -7.2463% -8.3354%  ...  88.0448%   4.6443%   \n",
       "2000-03-31  43.0168%  -0.2183%  3.1250% 14.5896%  ... -12.3179%  16.1103%   \n",
       "2000-04-30 -20.9375%  -7.8650% -5.4546% 12.9974%  ... -10.6496%  -4.8750%   \n",
       "2000-05-31 -39.7233%   5.0060% -3.6859%  8.7704%  ... -12.6796% -11.3612%   \n",
       "2000-06-30  -0.3689%   5.7888%  3.4942%  3.5011%  ...  24.6854%  -5.2239%   \n",
       "\n",
       "                PSA      REGN     SBAC       SEE         T       TGT      TMO  \\\n",
       "Date                                                                            \n",
       "2000-02-29 -2.7548% 358.8832% 33.6082% -11.4699% -11.9534% -10.2962% -9.7473%   \n",
       "2000-03-31 -3.8081% -47.6770%  8.6420%   9.3082%  11.5894%  26.6949% 30.4000%   \n",
       "2000-04-30  6.5476%  -3.3827% -7.6705%   2.4165%   4.7667% -10.9532% -4.9079%   \n",
       "2000-05-31 -0.2794% -28.6652% -8.3077%   0.6742%  -0.2853%  -5.6896% -4.1936%   \n",
       "2000-06-30  6.1300%  46.3190% 39.4295%  -6.4733%   0.7153%  -7.4776% 13.4680%   \n",
       "\n",
       "                TTWO  \n",
       "Date                  \n",
       "2000-02-29   0.0000%  \n",
       "2000-03-31   6.5327%  \n",
       "2000-04-30 -27.3585%  \n",
       "2000-05-31  -5.8442%  \n",
       "2000-06-30  33.7931%  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculating returns\n",
    "\n",
    "#Y = data[assets].pct_change().dropna()\n",
    "Y = data[assets].copy()\n",
    "Y = Y.resample('M').last().pct_change().dropna()\n",
    "print(Y.shape)\n",
    "display(Y.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Estimating Logarithmic Mean Variance Portfolios\n",
    "\n",
    "### 2.1 Calculating the portfolio that maximizes Risk Adjusted Return."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>Arithmetic</th>\n",
       "      <th>Log Approx</th>\n",
       "      <th>Log Exact</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AIG</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AKAM</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AMT</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>APA</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>1.4589%</td>\n",
       "      <td>1.4586%</td>\n",
       "      <td>1.4465%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAX</th>\n",
       "      <td>1.3212%</td>\n",
       "      <td>1.8359%</td>\n",
       "      <td>1.8364%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BKNG</th>\n",
       "      <td>2.6984%</td>\n",
       "      <td>2.5664%</td>\n",
       "      <td>2.5803%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BMY</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0597%</td>\n",
       "      <td>0.1407%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CMCSA</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CNP</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0001%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CPB</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DE</th>\n",
       "      <td>2.7385%</td>\n",
       "      <td>2.7291%</td>\n",
       "      <td>2.6662%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MO</th>\n",
       "      <td>28.0287%</td>\n",
       "      <td>27.3152%</td>\n",
       "      <td>27.3182%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSFT</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NI</th>\n",
       "      <td>6.3848%</td>\n",
       "      <td>6.6816%</td>\n",
       "      <td>6.7298%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NKTR</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NTAP</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PCAR</th>\n",
       "      <td>7.1818%</td>\n",
       "      <td>6.9563%</td>\n",
       "      <td>6.9789%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PSA</th>\n",
       "      <td>30.2594%</td>\n",
       "      <td>30.1056%</td>\n",
       "      <td>30.0413%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>REGN</th>\n",
       "      <td>2.1683%</td>\n",
       "      <td>2.0841%</td>\n",
       "      <td>2.0812%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SBAC</th>\n",
       "      <td>2.6696%</td>\n",
       "      <td>2.4954%</td>\n",
       "      <td>2.5248%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SEE</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>T</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.8141%</td>\n",
       "      <td>0.8931%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TGT</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TMO</th>\n",
       "      <td>10.1668%</td>\n",
       "      <td>10.1240%</td>\n",
       "      <td>9.9982%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TTWO</th>\n",
       "      <td>4.9237%</td>\n",
       "      <td>4.7738%</td>\n",
       "      <td>4.7644%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Arithmetic  Log Approx  Log Exact\n",
       "AIG       0.0000%     0.0000%    0.0000%\n",
       "AKAM      0.0000%     0.0000%    0.0000%\n",
       "AMT       0.0000%     0.0000%    0.0000%\n",
       "APA       0.0000%     0.0000%    0.0000%\n",
       "BA        1.4589%     1.4586%    1.4465%\n",
       "BAX       1.3212%     1.8359%    1.8364%\n",
       "BKNG      2.6984%     2.5664%    2.5803%\n",
       "BMY       0.0000%     0.0597%    0.1407%\n",
       "CMCSA     0.0000%     0.0000%    0.0000%\n",
       "CNP       0.0000%     0.0001%    0.0000%\n",
       "CPB       0.0000%     0.0000%    0.0000%\n",
       "DE        2.7385%     2.7291%    2.6662%\n",
       "MO       28.0287%    27.3152%   27.3182%\n",
       "MSFT      0.0000%     0.0000%    0.0000%\n",
       "NI        6.3848%     6.6816%    6.7298%\n",
       "NKTR      0.0000%     0.0000%    0.0000%\n",
       "NTAP      0.0000%     0.0000%    0.0000%\n",
       "PCAR      7.1818%     6.9563%    6.9789%\n",
       "PSA      30.2594%    30.1056%   30.0413%\n",
       "REGN      2.1683%     2.0841%    2.0812%\n",
       "SBAC      2.6696%     2.4954%    2.5248%\n",
       "SEE       0.0000%     0.0000%    0.0000%\n",
       "T         0.0000%     0.8141%    0.8931%\n",
       "TGT       0.0000%     0.0000%    0.0000%\n",
       "TMO      10.1668%    10.1240%    9.9982%\n",
       "TTWO      4.9237%     4.7738%    4.7644%"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import riskfolio as rp\n",
    "\n",
    "# Building the portfolio object\n",
    "port = rp.Portfolio(returns=Y)\n",
    "\n",
    "# Calculating optimal portfolio\n",
    "\n",
    "# Select method and estimate input parameters:\n",
    "\n",
    "method_mu='hist' # Method to estimate expected returns based on historical data.\n",
    "method_cov='hist' # Method to estimate covariance matrix based on historical data.\n",
    "\n",
    "port.assets_stats(method_mu=method_mu, method_cov=method_cov, d=0.94)\n",
    "\n",
    "# Estimate optimal portfolio:\n",
    "\n",
    "port.solvers = ['MOSEK']\n",
    "model='Classic' # Could be Classic (historical), BL (Black Litterman) or FM (Factor Model)\n",
    "rm = 'MV' # Risk measure used, this time will be variance\n",
    "obj = 'Sharpe' # Objective function, could be MinRisk, MaxRet, Utility or Sharpe\n",
    "hist = True # Use historical scenarios for risk measures that depend on scenarios\n",
    "rf = 0 # Risk free rate\n",
    "l = 0 # Risk aversion factor, only useful when obj is 'Utility'\n",
    "\n",
    "w_1 = port.optimization(model=model, rm=rm, obj=obj, kelly=False, rf=rf, l=l, hist=hist)\n",
    "w_2 = port.optimization(model=model, rm=rm, obj=obj, kelly='approx', rf=rf, l=l, hist=hist)\n",
    "w_3 = port.optimization(model=model, rm=rm, obj=obj, kelly='exact', rf=rf, l=l, hist=hist)\n",
    "\n",
    "w = pd.concat([w_1, w_2, w_3], axis=1)\n",
    "w.columns = ['Arithmetic', 'Log Approx', 'Log Exact']\n",
    "\n",
    "display(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14,6))\n",
    "w.plot(kind='bar', ax = ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Risk Adjusted Return:\n",
      "Arithmetic 1.2708631210924424\n",
      "Log Approx 1.2712397419739807\n",
      "Log Exact 1.2712465781050932\n"
     ]
    }
   ],
   "source": [
    "returns = port.returns\n",
    "cov = port.cov\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_1.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_1, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Risk Adjusted Return:\")\n",
    "print(\"Arithmetic\", (y/x).item() * 12**0.5)\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_2.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_2, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Log Approx\", (y/x).item() * 12**0.5)\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_3.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_3, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Log Exact\", (y/x).item() * 12**0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Calculate efficient frontier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>AIG</th>\n",
       "      <th>AKAM</th>\n",
       "      <th>AMT</th>\n",
       "      <th>APA</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAX</th>\n",
       "      <th>BKNG</th>\n",
       "      <th>BMY</th>\n",
       "      <th>CMCSA</th>\n",
       "      <th>CNP</th>\n",
       "      <th>...</th>\n",
       "      <th>NTAP</th>\n",
       "      <th>PCAR</th>\n",
       "      <th>PSA</th>\n",
       "      <th>REGN</th>\n",
       "      <th>SBAC</th>\n",
       "      <th>SEE</th>\n",
       "      <th>T</th>\n",
       "      <th>TGT</th>\n",
       "      <th>TMO</th>\n",
       "      <th>TTWO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.9497%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>6.4552%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>8.8793%</td>\n",
       "      <td>4.2373%</td>\n",
       "      <td>4.6782%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0469%</td>\n",
       "      <td>21.9202%</td>\n",
       "      <td>0.9367%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>8.8801%</td>\n",
       "      <td>2.6682%</td>\n",
       "      <td>1.3191%</td>\n",
       "      <td>1.8953%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.5034%</td>\n",
       "      <td>4.1813%</td>\n",
       "      <td>1.5452%</td>\n",
       "      <td>4.3751%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>2.5077%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>4.8895%</td>\n",
       "      <td>27.7197%</td>\n",
       "      <td>1.6074%</td>\n",
       "      <td>0.9938%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>5.0664%</td>\n",
       "      <td>0.0154%</td>\n",
       "      <td>7.7434%</td>\n",
       "      <td>3.7995%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.1276%</td>\n",
       "      <td>2.6421%</td>\n",
       "      <td>2.3361%</td>\n",
       "      <td>1.5717%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.5769%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>6.4586%</td>\n",
       "      <td>29.6415%</td>\n",
       "      <td>1.9030%</td>\n",
       "      <td>2.1597%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>2.5290%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>9.6799%</td>\n",
       "      <td>4.5687%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.1700%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.1115%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>7.3733%</td>\n",
       "      <td>30.3571%</td>\n",
       "      <td>2.4815%</td>\n",
       "      <td>3.3565%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>9.7306%</td>\n",
       "      <td>5.7699%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0296%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.9898%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>7.5012%</td>\n",
       "      <td>30.0468%</td>\n",
       "      <td>3.1727%</td>\n",
       "      <td>4.7569%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>8.3958%</td>\n",
       "      <td>7.7188%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      AIG    AKAM     AMT     APA      BA     BAX    BKNG     BMY   CMCSA  \\\n",
       "0 0.0000% 0.0000% 0.0000% 0.9497% 0.0000% 6.4552% 0.0000% 8.8793% 4.2373%   \n",
       "1 0.0000% 0.0000% 0.0000% 0.0000% 0.5034% 4.1813% 1.5452% 4.3751% 0.0000%   \n",
       "2 0.0000% 0.0000% 0.0000% 0.0000% 1.1276% 2.6421% 2.3361% 1.5717% 0.0000%   \n",
       "3 0.0000% 0.0000% 0.0000% 0.0000% 1.1700% 0.0000% 3.1115% 0.0000% 0.0000%   \n",
       "4 0.0000% 0.0000% 0.0000% 0.0000% 0.0296% 0.0000% 3.9898% 0.0000% 0.0000%   \n",
       "\n",
       "      CNP  ...    NTAP    PCAR      PSA    REGN    SBAC     SEE       T  \\\n",
       "0 4.6782%  ... 0.0000% 0.0469% 21.9202% 0.9367% 0.0000% 0.0000% 8.8801%   \n",
       "1 2.5077%  ... 0.0000% 4.8895% 27.7197% 1.6074% 0.9938% 0.0000% 5.0664%   \n",
       "2 0.5769%  ... 0.0000% 6.4586% 29.6415% 1.9030% 2.1597% 0.0000% 2.5290%   \n",
       "3 0.0000%  ... 0.0000% 7.3733% 30.3571% 2.4815% 3.3565% 0.0000% 0.0000%   \n",
       "4 0.0000%  ... 0.0000% 7.5012% 30.0468% 3.1727% 4.7569% 0.0000% 0.0000%   \n",
       "\n",
       "      TGT     TMO    TTWO  \n",
       "0 2.6682% 1.3191% 1.8953%  \n",
       "1 0.0154% 7.7434% 3.7995%  \n",
       "2 0.0000% 9.6799% 4.5687%  \n",
       "3 0.0000% 9.7306% 5.7699%  \n",
       "4 0.0000% 8.3958% 7.7188%  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = 40 # Number of points of the frontier\n",
    "\n",
    "frontier = port.efficient_frontier(model=model, rm=rm, kelly=\"exact\", points=points, rf=rf, hist=hist)\n",
    "\n",
    "display(frontier.T.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ffbc9fad9a0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the efficient frontier\n",
    "\n",
    "label = 'Max Risk Adjusted Log Return Portfolio' # Title of point\n",
    "mu = port.mu # Expected returns\n",
    "cov = port.cov # Covariance matrix\n",
    "returns = port.returns # Returns of the assets\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "rp.plot_frontier(w_frontier=frontier,\n",
    "                 mu=mu,\n",
    "                 cov=cov,\n",
    "                 returns=returns,\n",
    "                 rm=rm,\n",
    "                 kelly=True,\n",
    "                 rf=rf,\n",
    "                 alpha=0.05,\n",
    "                 cmap='viridis',\n",
    "                 w=w_3,\n",
    "                 label=label,\n",
    "                 marker='*',\n",
    "                 s=16,\n",
    "                 c='r',\n",
    "                 height=6,\n",
    "                 width=10,\n",
    "                 t_factor=12,\n",
    "                 ax=ax)\n",
    "\n",
    "y1 = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_1.to_numpy())) * 12 \n",
    "x1 = rp.Sharpe_Risk(w_1, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05) * 12**0.5\n",
    "\n",
    "y2 = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_2.to_numpy())) * 12 \n",
    "x2 = rp.Sharpe_Risk(w_2, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05) * 12**0.5\n",
    "\n",
    "ax.scatter(x=x1,\n",
    "           y=y1,\n",
    "           marker=\"^\",\n",
    "           s=8**2,\n",
    "           c=\"b\",\n",
    "           label=\"Max Risk Adjusted Arithmetic Return Portfolio\")\n",
    "ax.scatter(x=x2,\n",
    "           y=y2,\n",
    "           marker=\"v\",\n",
    "           s=8**2,\n",
    "           c=\"c\",\n",
    "           label=\"Max Risk Adjusted Approx Log Return Portfolio\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Estimating Logarithmic Mean EVaR Portfolios\n",
    "\n",
    "### 2.1 Calculating the portfolio that maximizes Risk Adjusted Return."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>Arithmetic</th>\n",
       "      <th>Log Approx</th>\n",
       "      <th>Log Exact</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AIG</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AKAM</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AMT</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>APA</th>\n",
       "      <td>6.6740%</td>\n",
       "      <td>3.2111%</td>\n",
       "      <td>3.5746%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAX</th>\n",
       "      <td>6.0638%</td>\n",
       "      <td>2.5271%</td>\n",
       "      <td>2.6328%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BKNG</th>\n",
       "      <td>6.9308%</td>\n",
       "      <td>5.1606%</td>\n",
       "      <td>5.3196%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BMY</th>\n",
       "      <td>4.7594%</td>\n",
       "      <td>6.8591%</td>\n",
       "      <td>6.9081%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CMCSA</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CNP</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>2.3999%</td>\n",
       "      <td>2.2606%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CPB</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DE</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0001%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MO</th>\n",
       "      <td>16.0365%</td>\n",
       "      <td>21.2115%</td>\n",
       "      <td>20.9253%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSFT</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NI</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NKTR</th>\n",
       "      <td>6.8735%</td>\n",
       "      <td>7.8037%</td>\n",
       "      <td>7.7487%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NTAP</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PCAR</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0001%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PSA</th>\n",
       "      <td>26.3963%</td>\n",
       "      <td>29.7631%</td>\n",
       "      <td>29.5170%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>REGN</th>\n",
       "      <td>13.6260%</td>\n",
       "      <td>4.4503%</td>\n",
       "      <td>5.0530%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SBAC</th>\n",
       "      <td>5.2176%</td>\n",
       "      <td>5.4909%</td>\n",
       "      <td>5.4697%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SEE</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>T</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.3653%</td>\n",
       "      <td>0.1755%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TGT</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TMO</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TTWO</th>\n",
       "      <td>7.4222%</td>\n",
       "      <td>10.7570%</td>\n",
       "      <td>10.4152%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Arithmetic  Log Approx  Log Exact\n",
       "AIG       0.0000%     0.0000%    0.0000%\n",
       "AKAM      0.0000%     0.0000%    0.0000%\n",
       "AMT       0.0000%     0.0000%    0.0000%\n",
       "APA       6.6740%     3.2111%    3.5746%\n",
       "BA        0.0000%     0.0000%    0.0000%\n",
       "BAX       6.0638%     2.5271%    2.6328%\n",
       "BKNG      6.9308%     5.1606%    5.3196%\n",
       "BMY       4.7594%     6.8591%    6.9081%\n",
       "CMCSA     0.0000%     0.0000%    0.0000%\n",
       "CNP       0.0000%     2.3999%    2.2606%\n",
       "CPB       0.0000%     0.0000%    0.0000%\n",
       "DE        0.0000%     0.0001%    0.0000%\n",
       "MO       16.0365%    21.2115%   20.9253%\n",
       "MSFT      0.0000%     0.0000%    0.0000%\n",
       "NI        0.0000%     0.0000%    0.0000%\n",
       "NKTR      6.8735%     7.8037%    7.7487%\n",
       "NTAP      0.0000%     0.0000%    0.0000%\n",
       "PCAR      0.0000%     0.0001%    0.0000%\n",
       "PSA      26.3963%    29.7631%   29.5170%\n",
       "REGN     13.6260%     4.4503%    5.0530%\n",
       "SBAC      5.2176%     5.4909%    5.4697%\n",
       "SEE       0.0000%     0.0000%    0.0000%\n",
       "T         0.0000%     0.3653%    0.1755%\n",
       "TGT       0.0000%     0.0000%    0.0000%\n",
       "TMO       0.0000%     0.0000%    0.0000%\n",
       "TTWO      7.4222%    10.7570%   10.4152%"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rm = 'EVaR' # Risk measure\n",
    "\n",
    "w_1 = port.optimization(model=model, rm=rm, obj=obj, kelly=False, rf=rf, l=l, hist=hist)\n",
    "w_2 = port.optimization(model=model, rm=rm, obj=obj, kelly='approx', rf=rf, l=l, hist=hist)\n",
    "w_3 = port.optimization(model=model, rm=rm, obj=obj, kelly='exact', rf=rf, l=l, hist=hist)\n",
    "\n",
    "w = pd.concat([w_1, w_2, w_3], axis=1)\n",
    "w.columns = ['Arithmetic', 'Log Approx', 'Log Exact']\n",
    "\n",
    "display(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14,6))\n",
    "w.plot(kind='bar', ax = ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Risk Adjusted Return:\n",
      "Arithmetic 0.6328345241128857\n",
      "Log Approx 0.645853935415245\n",
      "Log Exact 0.6459339768016784\n"
     ]
    }
   ],
   "source": [
    "returns = port.returns\n",
    "cov = port.cov\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_1.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_1, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Risk Adjusted Return:\")\n",
    "print(\"Arithmetic\", (y/x).item() * 12**0.5)\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_2.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_2, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Log Approx\", (y/x).item() * 12**0.5)\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_3.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_3, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Log Exact\", (y/x).item() * 12**0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Calculate efficient frontier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        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>AIG</th>\n",
       "      <th>AKAM</th>\n",
       "      <th>AMT</th>\n",
       "      <th>APA</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAX</th>\n",
       "      <th>BKNG</th>\n",
       "      <th>BMY</th>\n",
       "      <th>CMCSA</th>\n",
       "      <th>CNP</th>\n",
       "      <th>...</th>\n",
       "      <th>NTAP</th>\n",
       "      <th>PCAR</th>\n",
       "      <th>PSA</th>\n",
       "      <th>REGN</th>\n",
       "      <th>SBAC</th>\n",
       "      <th>SEE</th>\n",
       "      <th>T</th>\n",
       "      <th>TGT</th>\n",
       "      <th>TMO</th>\n",
       "      <th>TTWO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>2.8293%</td>\n",
       "      <td>2.3021%</td>\n",
       "      <td>18.2682%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.9354%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>17.2214%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>5.2722%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>6.7943%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>7.5230%</td>\n",
       "      <td>8.0869%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.4832%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.9411%</td>\n",
       "      <td>3.1868%</td>\n",
       "      <td>11.6400%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.6459%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>25.2858%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>7.1268%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>4.4858%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>11.6264%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>4.3953%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.0234%</td>\n",
       "      <td>3.8072%</td>\n",
       "      <td>10.2550%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.3127%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>27.4594%</td>\n",
       "      <td>1.2358%</td>\n",
       "      <td>6.6436%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.9048%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>11.3907%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>4.0924%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.0385%</td>\n",
       "      <td>4.7244%</td>\n",
       "      <td>8.0627%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>2.6206%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>28.5343%</td>\n",
       "      <td>3.7233%</td>\n",
       "      <td>5.8076%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.9777%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>10.7467%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.2559%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>2.4338%</td>\n",
       "      <td>5.5133%</td>\n",
       "      <td>6.3207%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>2.1010%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>29.9199%</td>\n",
       "      <td>5.5798%</td>\n",
       "      <td>5.3796%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>10.3803%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      AIG    AKAM     AMT     APA      BA     BAX    BKNG      BMY   CMCSA  \\\n",
       "0 0.0000% 0.0000% 0.0000% 0.0000% 0.0000% 2.8293% 2.3021% 18.2682% 0.0000%   \n",
       "1 0.0000% 0.0000% 0.0000% 3.4832% 0.0000% 3.9411% 3.1868% 11.6400% 0.0000%   \n",
       "2 0.0000% 0.0000% 0.0000% 4.3953% 0.0000% 3.0234% 3.8072% 10.2550% 0.0000%   \n",
       "3 0.0000% 0.0000% 0.0000% 4.0924% 0.0000% 3.0385% 4.7244%  8.0627% 0.0000%   \n",
       "4 0.0000% 0.0000% 0.0000% 3.2559% 0.0000% 2.4338% 5.5133%  6.3207% 0.0000%   \n",
       "\n",
       "      CNP  ...    NTAP    PCAR      PSA    REGN    SBAC     SEE       T  \\\n",
       "0 1.9354%  ... 0.0000% 0.0000% 17.2214% 0.0000% 5.2722% 0.0000% 6.7943%   \n",
       "1 3.6459%  ... 0.0000% 0.0000% 25.2858% 0.0000% 7.1268% 0.0000% 4.4858%   \n",
       "2 3.3127%  ... 0.0000% 0.0000% 27.4594% 1.2358% 6.6436% 0.0000% 1.9048%   \n",
       "3 2.6206%  ... 0.0000% 0.0000% 28.5343% 3.7233% 5.8076% 0.0000% 0.9777%   \n",
       "4 2.1010%  ... 0.0000% 0.0000% 29.9199% 5.5798% 5.3796% 0.0000% 0.0000%   \n",
       "\n",
       "      TGT     TMO     TTWO  \n",
       "0 0.0000% 7.5230%  8.0869%  \n",
       "1 0.0000% 0.0000% 11.6264%  \n",
       "2 0.0000% 0.0000% 11.3907%  \n",
       "3 0.0000% 0.0000% 10.7467%  \n",
       "4 0.0000% 0.0000% 10.3803%  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = 40 # Number of points of the frontier\n",
    "\n",
    "frontier = port.efficient_frontier(model=model, rm=rm, kelly=\"exact\", points=points, rf=rf, hist=hist)\n",
    "\n",
    "display(frontier.T.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ffbc9ff7ee0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the efficient frontier\n",
    "\n",
    "label = 'Max Risk Adjusted Log Return Portfolio' # Title of point\n",
    "mu = port.mu # Expected returns\n",
    "cov = port.cov # Covariance matrix\n",
    "returns = port.returns # Returns of the assets\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "rp.plot_frontier(w_frontier=frontier,\n",
    "                 mu=mu,\n",
    "                 cov=cov,\n",
    "                 returns=returns,\n",
    "                 rm=rm,\n",
    "                 kelly=True,\n",
    "                 rf=rf,\n",
    "                 alpha=0.05,\n",
    "                 cmap='viridis',\n",
    "                 w=w_3,\n",
    "                 label=label,\n",
    "                 marker='*',\n",
    "                 s=16,\n",
    "                 c='r',\n",
    "                 height=6,\n",
    "                 width=10,\n",
    "                 t_factor=12,\n",
    "                 ax=ax)\n",
    "\n",
    "y1 = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_1.to_numpy())) * 12\n",
    "x1 = rp.Sharpe_Risk(w_1, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05) * 12**0.5\n",
    "\n",
    "y2 = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_2.to_numpy())) * 12\n",
    "x2 = rp.Sharpe_Risk(w_2, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05) * 12**0.5\n",
    "\n",
    "ax.scatter(x=x1,\n",
    "           y=y1,\n",
    "           marker=\"^\",\n",
    "           s=8**2,\n",
    "           c=\"b\",\n",
    "           label=\"Max Risk Adjusted Arithmetic Return Portfolio\")\n",
    "ax.scatter(x=x2,\n",
    "           y=y2,\n",
    "           marker=\"v\",\n",
    "           s=8**2,\n",
    "           c=\"c\",\n",
    "           label=\"Max Risk Adjusted Approx Log Return Portfolio\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Estimating Logarithmic Mean EDaR Portfolios\n",
    "\n",
    "### 3.1 Calculating the portfolio that maximizes Risk Adjusted Return."
   ]
  },
  {
   "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>Arithmetic</th>\n",
       "      <th>Log Approx</th>\n",
       "      <th>Log Exact</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AIG</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AKAM</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AMT</th>\n",
       "      <td>2.8670%</td>\n",
       "      <td>0.3727%</td>\n",
       "      <td>0.5224%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>APA</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAX</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BKNG</th>\n",
       "      <td>3.0492%</td>\n",
       "      <td>1.4551%</td>\n",
       "      <td>1.6956%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BMY</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CMCSA</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CNP</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CPB</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DE</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MO</th>\n",
       "      <td>27.1690%</td>\n",
       "      <td>34.2848%</td>\n",
       "      <td>33.5919%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSFT</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NI</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NKTR</th>\n",
       "      <td>12.5570%</td>\n",
       "      <td>9.2335%</td>\n",
       "      <td>10.2399%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NTAP</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PCAR</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0002%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PSA</th>\n",
       "      <td>25.6707%</td>\n",
       "      <td>33.9465%</td>\n",
       "      <td>30.4418%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>REGN</th>\n",
       "      <td>19.7833%</td>\n",
       "      <td>12.5667%</td>\n",
       "      <td>14.1518%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SBAC</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.8721%</td>\n",
       "      <td>3.7937%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SEE</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>T</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TGT</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TMO</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0001%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TTWO</th>\n",
       "      <td>8.9038%</td>\n",
       "      <td>4.2680%</td>\n",
       "      <td>5.5630%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Arithmetic  Log Approx  Log Exact\n",
       "AIG       0.0000%     0.0000%    0.0000%\n",
       "AKAM      0.0000%     0.0000%    0.0000%\n",
       "AMT       2.8670%     0.3727%    0.5224%\n",
       "APA       0.0000%     0.0000%    0.0000%\n",
       "BA        0.0000%     0.0000%    0.0000%\n",
       "BAX       0.0000%     0.0000%    0.0000%\n",
       "BKNG      3.0492%     1.4551%    1.6956%\n",
       "BMY       0.0000%     0.0000%    0.0000%\n",
       "CMCSA     0.0000%     0.0000%    0.0000%\n",
       "CNP       0.0000%     0.0000%    0.0000%\n",
       "CPB       0.0000%     0.0000%    0.0000%\n",
       "DE        0.0000%     0.0000%    0.0000%\n",
       "MO       27.1690%    34.2848%   33.5919%\n",
       "MSFT      0.0000%     0.0000%    0.0000%\n",
       "NI        0.0000%     0.0000%    0.0000%\n",
       "NKTR     12.5570%     9.2335%   10.2399%\n",
       "NTAP      0.0000%     0.0000%    0.0000%\n",
       "PCAR      0.0000%     0.0002%    0.0000%\n",
       "PSA      25.6707%    33.9465%   30.4418%\n",
       "REGN     19.7833%    12.5667%   14.1518%\n",
       "SBAC      0.0000%     3.8721%    3.7937%\n",
       "SEE       0.0000%     0.0000%    0.0000%\n",
       "T         0.0000%     0.0000%    0.0000%\n",
       "TGT       0.0000%     0.0000%    0.0000%\n",
       "TMO       0.0000%     0.0001%    0.0000%\n",
       "TTWO      8.9038%     4.2680%    5.5630%"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rm = 'EDaR' # Risk measure\n",
    "\n",
    "w_1 = port.optimization(model=model, rm=rm, obj=obj, kelly=False, rf=rf, l=l, hist=hist)\n",
    "w_2 = port.optimization(model=model, rm=rm, obj=obj, kelly='approx', rf=rf, l=l, hist=hist)\n",
    "w_3 = port.optimization(model=model, rm=rm, obj=obj, kelly='exact', rf=rf, l=l, hist=hist)\n",
    "\n",
    "w = pd.concat([w_1, w_2, w_3], axis=1)\n",
    "w.columns = ['Arithmetic', 'Log Approx', 'Log Exact']\n",
    "\n",
    "display(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14,6))\n",
    "w.plot(kind='bar', ax = ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Risk Adjusted Return:\n",
      "Arithmetic 0.8286219613071538\n",
      "Log Approx 0.8435798738462544\n",
      "Log Exact 0.8449873687053613\n"
     ]
    }
   ],
   "source": [
    "returns = port.returns\n",
    "cov = port.cov\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_1.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_1, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Risk Adjusted Return:\")\n",
    "print(\"Arithmetic\", (y/x).item() * 12)\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_2.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_2, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Log Approx\", (y/x).item() * 12)\n",
    "\n",
    "y = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_3.to_numpy()))\n",
    "x = rp.Sharpe_Risk(w_3, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "print(\"Log Exact\", (y/x).item() * 12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Calculate efficient frontier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>AIG</th>\n",
       "      <th>AKAM</th>\n",
       "      <th>AMT</th>\n",
       "      <th>APA</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAX</th>\n",
       "      <th>BKNG</th>\n",
       "      <th>BMY</th>\n",
       "      <th>CMCSA</th>\n",
       "      <th>CNP</th>\n",
       "      <th>...</th>\n",
       "      <th>NTAP</th>\n",
       "      <th>PCAR</th>\n",
       "      <th>PSA</th>\n",
       "      <th>REGN</th>\n",
       "      <th>SBAC</th>\n",
       "      <th>SEE</th>\n",
       "      <th>T</th>\n",
       "      <th>TGT</th>\n",
       "      <th>TMO</th>\n",
       "      <th>TTWO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.9618%</td>\n",
       "      <td>5.5780%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.9596%</td>\n",
       "      <td>2.3327%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>23.2489%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>2.5703%</td>\n",
       "      <td>3.6696%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.9192%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>31.4908%</td>\n",
       "      <td>5.8684%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.2751%</td>\n",
       "      <td>1.2159%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.3203%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>36.5053%</td>\n",
       "      <td>8.0955%</td>\n",
       "      <td>0.4379%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.7603%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.6927%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.2423%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>34.9685%</td>\n",
       "      <td>12.1344%</td>\n",
       "      <td>2.4517%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>3.5029%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.8850%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>1.8558%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>27.4040%</td>\n",
       "      <td>15.3669%</td>\n",
       "      <td>3.4524%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>0.0000%</td>\n",
       "      <td>6.5588%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      AIG    AKAM     AMT     APA      BA     BAX    BKNG     BMY   CMCSA  \\\n",
       "0 0.0000% 0.0000% 1.9618% 5.5780% 0.0000% 0.0000% 1.9596% 2.3327% 0.0000%   \n",
       "1 0.0000% 0.0000% 2.5703% 3.6696% 0.0000% 0.0000% 0.9192% 0.0000% 0.0000%   \n",
       "2 0.0000% 0.0000% 3.2751% 1.2159% 0.0000% 0.0000% 0.3203% 0.0000% 0.0000%   \n",
       "3 0.0000% 0.0000% 1.6927% 0.0000% 0.0000% 0.0000% 1.2423% 0.0000% 0.0000%   \n",
       "4 0.0000% 0.0000% 0.8850% 0.0000% 0.0000% 0.0000% 1.8558% 0.0000% 0.0000%   \n",
       "\n",
       "      CNP  ...    NTAP    PCAR      PSA     REGN    SBAC     SEE       T  \\\n",
       "0 0.0000%  ... 0.0000% 0.0000% 23.2489%  0.0000% 0.0000% 0.0000% 0.0000%   \n",
       "1 0.0000%  ... 0.0000% 0.0000% 31.4908%  5.8684% 0.0000% 0.0000% 0.0000%   \n",
       "2 0.0000%  ... 0.0000% 0.0000% 36.5053%  8.0955% 0.4379% 0.0000% 0.0000%   \n",
       "3 0.0000%  ... 0.0000% 0.0000% 34.9685% 12.1344% 2.4517% 0.0000% 0.0000%   \n",
       "4 0.0000%  ... 0.0000% 0.0000% 27.4040% 15.3669% 3.4524% 0.0000% 0.0000%   \n",
       "\n",
       "      TGT     TMO    TTWO  \n",
       "0 0.0000% 0.0000% 0.0000%  \n",
       "1 0.0000% 0.0000% 0.0000%  \n",
       "2 0.0000% 0.0000% 0.7603%  \n",
       "3 0.0000% 0.0000% 3.5029%  \n",
       "4 0.0000% 0.0000% 6.5588%  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = 40 # Number of points of the frontier\n",
    "\n",
    "frontier = port.efficient_frontier(model=model, rm=rm, kelly=\"exact\", points=points, rf=rf, hist=hist)\n",
    "\n",
    "display(frontier.T.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ffbcb317190>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the efficient frontier\n",
    "\n",
    "label = 'Max Risk Adjusted Log Return Portfolio' # Title of point\n",
    "mu = port.mu # Expected returns\n",
    "cov = port.cov # Covariance matrix\n",
    "returns = port.returns # Returns of the assets\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "rp.plot_frontier(w_frontier=frontier,\n",
    "                 mu=mu,\n",
    "                 cov=cov,\n",
    "                 returns=returns,\n",
    "                 rm=rm,\n",
    "                 kelly=True,\n",
    "                 rf=rf,\n",
    "                 alpha=0.05,\n",
    "                 cmap='viridis',\n",
    "                 w=w_3,\n",
    "                 label=label,\n",
    "                 marker='*',\n",
    "                 s=16,\n",
    "                 c='r',\n",
    "                 height=6,\n",
    "                 width=10,\n",
    "                 t_factor=12,\n",
    "                 ax=ax)\n",
    "\n",
    "y1 = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_1.to_numpy())) * 12\n",
    "x1 = rp.Sharpe_Risk(w_1, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "\n",
    "y2 = 1/(returns.shape[0]) * np.sum(np.log(1 + returns @ w_2.to_numpy())) * 12\n",
    "x2 = rp.Sharpe_Risk(w_2, cov=cov, returns=returns, rm=rm, rf=rf, alpha=0.05)\n",
    "\n",
    "ax.scatter(x=x1,\n",
    "           y=y1,\n",
    "           marker=\"^\",\n",
    "           s=8**2,\n",
    "           c=\"b\",\n",
    "           label=\"Max Risk Adjusted Arithmetic Return Portfolio\")\n",
    "ax.scatter(x=x2,\n",
    "           y=y2,\n",
    "           marker=\"v\",\n",
    "           s=8**2,\n",
    "           c=\"c\",\n",
    "           label=\"Max Risk Adjusted Approx Log Return Portfolio\")\n",
    "plt.legend()"
   ]
  }
 ],
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