03_portfolio_optimizer.ipynb

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      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/github/jidemaestri/Financial-Markets/blob/master/03_portfolio_optimizer.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "## Markowitz Frontier"
      ],
      "metadata": {
        "id": "ggkNOyMWd_-Z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "La frontera de Markowitz se calcula para encontrar la combinación óptima de inversiones que ofrece el mejor rendimiento posible con un determinado nivel de riesgo. Esta frontera se basa en el modelo de Markowitz de selección de carteras, que es una forma de análisis de inversiones que toma en cuenta el riesgo y la rentabilidad potencial de diferentes activos financieros. La frontera de Markowitz se representa gráficamente como una curva que muestra la relación entre el rendimiento esperado y el riesgo de una cartera de inversiones. "
      ],
      "metadata": {
        "id": "CV86jBdhd5if"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install yfinance"
      ],
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          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting yfinance\n",
            "  Downloading yfinance-0.1.90-py2.py3-none-any.whl (29 kB)\n",
            "Requirement already satisfied: multitasking>=0.0.7 in /usr/local/lib/python3.8/dist-packages (from yfinance) (0.0.11)\n",
            "Collecting requests>=2.26\n",
            "  Downloading requests-2.28.1-py3-none-any.whl (62 kB)\n",
            "\u001b[K     |████████████████████████████████| 62 kB 1.4 MB/s \n",
            "\u001b[?25hRequirement already satisfied: appdirs>=1.4.4 in /usr/local/lib/python3.8/dist-packages (from yfinance) (1.4.4)\n",
            "Requirement already satisfied: lxml>=4.9.1 in /usr/local/lib/python3.8/dist-packages (from yfinance) (4.9.1)\n",
            "Requirement already satisfied: numpy>=1.16.5 in /usr/local/lib/python3.8/dist-packages (from yfinance) (1.21.6)\n",
            "Requirement already satisfied: pandas>=1.3.0 in /usr/local/lib/python3.8/dist-packages (from yfinance) (1.3.5)\n",
            "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.8/dist-packages (from pandas>=1.3.0->yfinance) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.8/dist-packages (from pandas>=1.3.0->yfinance) (2022.6)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.8/dist-packages (from python-dateutil>=2.7.3->pandas>=1.3.0->yfinance) (1.15.0)\n",
            "Requirement already satisfied: charset-normalizer<3,>=2 in /usr/local/lib/python3.8/dist-packages (from requests>=2.26->yfinance) (2.1.1)\n",
            "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /usr/local/lib/python3.8/dist-packages (from requests>=2.26->yfinance) (1.24.3)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.8/dist-packages (from requests>=2.26->yfinance) (2022.9.24)\n",
            "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.8/dist-packages (from requests>=2.26->yfinance) (2.10)\n",
            "Installing collected packages: requests, yfinance\n",
            "  Attempting uninstall: requests\n",
            "    Found existing installation: requests 2.23.0\n",
            "    Uninstalling requests-2.23.0:\n",
            "      Successfully uninstalled requests-2.23.0\n",
            "Successfully installed requests-2.28.1 yfinance-0.1.90\n"
          ]
        }
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    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import yfinance as yf\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n"
      ],
      "metadata": {
        "id": "UVCaPEPId6BX"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "tickers = [\"AAPL\", \"GOOG\", \"MSFT\", \"VALE\", \"MELI\", \"DIS\", \"KO\", \"MCD\", \"NVDA\", \"AMD\", \"PAM\", \"BBAR\", \"GGAL\", \"VIST\", \"JPM\", \"BRK\", \"PEP\", \"PBR\", \"BBD\", \"BABA\", \"GLOB\", \"TEO\", \"TGS\", \"CEPU\", \"LOMA\", \"CRESY\"]"
      ],
      "metadata": {
        "id": "dZH7nCBIeaYU"
      },
      "execution_count": 166,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data = yf.download(tickers, start=\"2009-01-01\", end=\"2022-12-31\")\n",
        "\n"
      ],
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        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UhC_cGI6e4s2",
        "outputId": "0a35a733-d2db-4fa6-ec95-c4d2c310308b"
      },
      "execution_count": 167,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  26 of 26 completed\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data[\"Adj Close\"].tail()"
      ],
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          "height": 398
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        "id": "V39B3GVdfn-o",
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              "                  AAPL        AMD       BABA  BBAR   BBD  BRK  CEPU  CRESY  \\\n",
              "Date                                                                         \n",
              "2022-12-07  140.940002  70.139999  88.330002  3.01  2.85  NaN  5.29   5.65   \n",
              "2022-12-08  142.649994  70.470001  94.169998  2.81  2.76  NaN  4.98   5.44   \n",
              "2022-12-09  142.160004  68.589996  91.339996  2.77  2.70  NaN  4.93   5.25   \n",
              "2022-12-12  144.490005  70.669998  89.410004  2.88  2.67  NaN  5.33   5.76   \n",
              "2022-12-13  145.470001  71.650002  91.410004  2.85  2.55  NaN  5.21   5.70   \n",
              "\n",
              "                  DIS  GGAL  ...        MELI        MSFT        NVDA  \\\n",
              "Date                         ...                                       \n",
              "2022-12-07  92.150002  7.95  ...  863.809998  244.369995  161.199997   \n",
              "2022-12-08  92.550003  7.51  ...  884.239990  247.399994  171.690002   \n",
              "2022-12-09  93.379997  7.44  ...  896.479980  245.419998  170.009995   \n",
              "2022-12-12  94.660004  7.76  ...  880.250000  252.509995  175.350006   \n",
              "2022-12-13  94.699997  7.62  ...  870.650024  256.920013  180.720001   \n",
              "\n",
              "                  PAM    PBR         PEP   TEO   TGS       VALE   VIST  \n",
              "Date                                                                    \n",
              "2022-12-07  27.639999  11.08  182.179993  4.56  9.44  16.170000  12.54  \n",
              "2022-12-08  26.180000  10.78  183.779999  4.61  8.94  16.430000  12.40  \n",
              "2022-12-09  25.980000  10.71  183.100006  4.45  8.52  16.940001  11.95  \n",
              "2022-12-12  26.450001  10.33  183.970001  4.60  9.28  16.230000  12.00  \n",
              "2022-12-13  26.010000  10.14  183.869995  4.34  9.00  16.180000  12.39  \n",
              "\n",
              "[5 rows x 26 columns]"
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              "      <th>AAPL</th>\n",
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              "      <th>CRESY</th>\n",
              "      <th>DIS</th>\n",
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              "      <th>MELI</th>\n",
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              "      <th>PAM</th>\n",
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              "      <th>2022-12-07</th>\n",
              "      <td>140.940002</td>\n",
              "      <td>70.139999</td>\n",
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              "      <td>3.01</td>\n",
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              "      <td>5.65</td>\n",
              "      <td>92.150002</td>\n",
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              "      <td>863.809998</td>\n",
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              "      <th>2022-12-08</th>\n",
              "      <td>142.649994</td>\n",
              "      <td>70.470001</td>\n",
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              "      <td>2.76</td>\n",
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              "      <td>4.98</td>\n",
              "      <td>5.44</td>\n",
              "      <td>92.550003</td>\n",
              "      <td>7.51</td>\n",
              "      <td>...</td>\n",
              "      <td>884.239990</td>\n",
              "      <td>247.399994</td>\n",
              "      <td>171.690002</td>\n",
              "      <td>26.180000</td>\n",
              "      <td>10.78</td>\n",
              "      <td>183.779999</td>\n",
              "      <td>4.61</td>\n",
              "      <td>8.94</td>\n",
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              "      <td>12.40</td>\n",
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              "      <th>2022-12-09</th>\n",
              "      <td>142.160004</td>\n",
              "      <td>68.589996</td>\n",
              "      <td>91.339996</td>\n",
              "      <td>2.77</td>\n",
              "      <td>2.70</td>\n",
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              "      <td>7.44</td>\n",
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              "      <th>2022-12-12</th>\n",
              "      <td>144.490005</td>\n",
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              "      <td>2.67</td>\n",
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              "      <td>5.33</td>\n",
              "      <td>5.76</td>\n",
              "      <td>94.660004</td>\n",
              "      <td>7.76</td>\n",
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        "\n",
        "# Calcula los retornos de cada acción\n",
        "returns = data[\"Adj Close\"].pct_change().dropna()\n",
        "\n"
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              "                AAPL       AMD      BABA      BBAR  BRK      CEPU     CRESY  \\\n",
              "Date                                                                          \n",
              "2022-12-07 -0.013785 -0.001850 -0.034117  0.045139  0.0  0.058000  0.046296   \n",
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              "Date                                                                     \n",
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          "metadata": {},
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    {
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      "source": [
        "returns_pct = returns.mul(100)\n"
      ],
      "metadata": {
        "id": "i7tq6wsqlCIn"
      },
      "execution_count": 145,
      "outputs": []
    },
    {
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      "source": [
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          "height": 418
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        "id": "ggAl6BQelHEt",
        "outputId": "490d1c54-4268-4114-90cb-d30e3641468f"
      },
      "execution_count": 146,
      "outputs": [
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              "                AAPL       AMD      BABA      BBAR  BRK      CEPU     CRESY  \\\n",
              "Date                                                                          \n",
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              "                 DIS       DPZ      GGAL  ...       MCD      MELI      MSFT  \\\n",
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              "                NVDA       PAM       PEP       TEO       TGS      VALE  \\\n",
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              "2022-12-09 -3.629031  \n",
              "2022-12-12  0.418412  \n",
              "2022-12-13  3.250003  \n",
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              "      <th>2022-12-08</th>\n",
              "      <td>1.213276</td>\n",
              "      <td>0.470490</td>\n",
              "      <td>6.611566</td>\n",
              "      <td>-6.644520</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-5.860112</td>\n",
              "      <td>-3.716815</td>\n",
              "      <td>0.434077</td>\n",
              "      <td>0.752402</td>\n",
              "      <td>-5.534586</td>\n",
              "      <td>...</td>\n",
              "      <td>1.128216</td>\n",
              "      <td>2.365103</td>\n",
              "      <td>1.239923</td>\n",
              "      <td>6.507448</td>\n",
              "      <td>-5.282197</td>\n",
              "      <td>0.878256</td>\n",
              "      <td>1.096495</td>\n",
              "      <td>-5.296610</td>\n",
              "      <td>1.607917</td>\n",
              "      <td>-1.116430</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2022-12-09</th>\n",
              "      <td>-0.343491</td>\n",
              "      <td>-2.667809</td>\n",
              "      <td>-3.005205</td>\n",
              "      <td>-1.423486</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-1.004020</td>\n",
              "      <td>-3.492648</td>\n",
              "      <td>0.896806</td>\n",
              "      <td>-3.277860</td>\n",
              "      <td>-0.932093</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.493802</td>\n",
              "      <td>1.384238</td>\n",
              "      <td>-0.800322</td>\n",
              "      <td>-0.978512</td>\n",
              "      <td>-0.763945</td>\n",
              "      <td>-0.370004</td>\n",
              "      <td>-3.470723</td>\n",
              "      <td>-4.697977</td>\n",
              "      <td>3.104079</td>\n",
              "      <td>-3.629031</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2022-12-12</th>\n",
              "      <td>1.639000</td>\n",
              "      <td>3.032515</td>\n",
              "      <td>-2.112977</td>\n",
              "      <td>3.971124</td>\n",
              "      <td>0.0</td>\n",
              "      <td>8.113592</td>\n",
              "      <td>9.714290</td>\n",
              "      <td>1.370750</td>\n",
              "      <td>0.193027</td>\n",
              "      <td>4.301078</td>\n",
              "      <td>...</td>\n",
              "      <td>1.683571</td>\n",
              "      <td>-1.810412</td>\n",
              "      <td>2.888924</td>\n",
              "      <td>3.140999</td>\n",
              "      <td>1.809089</td>\n",
              "      <td>0.475148</td>\n",
              "      <td>3.370789</td>\n",
              "      <td>8.920179</td>\n",
              "      <td>-4.191269</td>\n",
              "      <td>0.418412</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2022-12-13</th>\n",
              "      <td>0.678245</td>\n",
              "      <td>1.386732</td>\n",
              "      <td>2.236886</td>\n",
              "      <td>-1.041674</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-2.251405</td>\n",
              "      <td>-1.041674</td>\n",
              "      <td>0.042249</td>\n",
              "      <td>-0.407324</td>\n",
              "      <td>-1.804128</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.845925</td>\n",
              "      <td>-1.090596</td>\n",
              "      <td>1.746473</td>\n",
              "      <td>3.062444</td>\n",
              "      <td>-1.663518</td>\n",
              "      <td>-0.054360</td>\n",
              "      <td>-5.652169</td>\n",
              "      <td>-3.017239</td>\n",
              "      <td>-0.308067</td>\n",
              "      <td>3.250003</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 25 columns</p>\n",
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            ]
          },
          "metadata": {},
          "execution_count": 146
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calcula la matriz de covarianzas de la cartera\n",
        "cov_matrix = np.cov(returns_pct)\n"
      ],
      "metadata": {
        "id": "XEnqSuy-fcUh"
      },
      "execution_count": 147,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "cov_matrix"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P2_tmrHCfzEF",
        "outputId": "15ed95eb-1121-408a-fdc6-e837218279e1"
      },
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[10.11585574,  2.16576382, -6.57189884, ...,  2.84264702,\n",
              "        -5.40891697, -0.84122502],\n",
              "       [ 2.16576382, 10.16248376, -6.94508429, ...,  2.45594866,\n",
              "        -2.90459381,  1.36800941],\n",
              "       [-6.57189884, -6.94508429,  9.77850831, ..., -3.1630933 ,\n",
              "         4.07781568, -0.16726995],\n",
              "       ...,\n",
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              "       [-5.40891697, -2.90459381,  4.07781568, ..., -2.93881815,\n",
              "         5.45946098,  1.85031614],\n",
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              "         1.85031614,  2.14889085]])"
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          },
          "metadata": {},
          "execution_count": 90
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "cov_matrix_df = pd.DataFrame(cov_matrix)"
      ],
      "metadata": {
        "id": "ANyWK1sOn9bR"
      },
      "execution_count": 91,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Crear una lista de posibles rendimientos esperados\n",
        "expected_returns = np.linspace(returns_pct.min(), returns_pct.max(), 100)\n"
      ],
      "metadata": {
        "id": "2FognrBXfhBI"
      },
      "execution_count": 148,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "expected_returns_df = pd.DataFrame(expected_returns)\n"
      ],
      "metadata": {
        "id": "F4Gf7a8DiX9I"
      },
      "execution_count": 149,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "expected_returns_df.tail()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "oAA3XsV8lw_v",
        "outputId": "94d2be45-38ce-4d49-c2cc-33b92eee05ff"
      },
      "execution_count": 150,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "           0          1          2          3    4          5          6   \\\n",
              "95  10.976977  15.243394  34.739450  17.834098  0.0  17.967582  36.652262   \n",
              "96  11.227942  15.557945  35.245573  18.609726  0.0  18.745295  37.439027   \n",
              "97  11.478907  15.872496  35.751695  19.385355  0.0  19.523008  38.225792   \n",
              "98  11.729872  16.187047  36.257818  20.160983  0.0  20.300722  39.012558   \n",
              "99  11.980837  16.501598  36.763940  20.936612  0.0  21.078435  39.799323   \n",
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              "           7          8          9   ...         15         16         17  \\\n",
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              "96  13.576693  24.534929  20.385867  ...  17.095121  18.531398  13.339437   \n",
              "97  13.855233  24.890217  21.182776  ...  17.438564  18.900255  13.631922   \n",
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              "99  14.412314  25.600792  22.776593  ...  18.125449  19.637969  14.216890   \n",
              "\n",
              "           18         19         20         21         22         23  \\\n",
              "95  15.717684  19.102708  11.952155  12.250538  13.333638  19.977975   \n",
              "96  16.077365  19.870268  12.198266  12.730815  13.979628  20.360579   \n",
              "97  16.437047  20.637828  12.444376  13.211092  14.625619  20.743182   \n",
              "98  16.796729  21.405388  12.690486  13.691369  15.271610  21.125786   \n",
              "99  17.156411  22.172948  12.936597  14.171646  15.917601  21.508389   \n",
              "\n",
              "           24  \n",
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              "96  28.119201  \n",
              "97  28.746132  \n",
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              "99  29.999992  \n",
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              "      <td>35.751695</td>\n",
              "      <td>19.385355</td>\n",
              "      <td>0.0</td>\n",
              "      <td>19.523008</td>\n",
              "      <td>38.225792</td>\n",
              "      <td>13.855233</td>\n",
              "      <td>24.890217</td>\n",
              "      <td>21.182776</td>\n",
              "      <td>...</td>\n",
              "      <td>17.438564</td>\n",
              "      <td>18.900255</td>\n",
              "      <td>13.631922</td>\n",
              "      <td>16.437047</td>\n",
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              "      <td>12.444376</td>\n",
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              "      <td>14.625619</td>\n",
              "      <td>20.743182</td>\n",
              "      <td>28.746132</td>\n",
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              "      <td>36.257818</td>\n",
              "      <td>20.160983</td>\n",
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              "      <td>14.133774</td>\n",
              "      <td>25.245504</td>\n",
              "      <td>21.979684</td>\n",
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              "      <td>17.782006</td>\n",
              "      <td>19.269112</td>\n",
              "      <td>13.924406</td>\n",
              "      <td>16.796729</td>\n",
              "      <td>21.405388</td>\n",
              "      <td>12.690486</td>\n",
              "      <td>13.691369</td>\n",
              "      <td>15.271610</td>\n",
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              "<p>5 rows × 25 columns</p>\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 150
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Crear una lista de posibles niveles de volatilidad\n",
        "volatilities = []\n"
      ],
      "metadata": {
        "id": "VLngUyqCiZCf"
      },
      "execution_count": 70,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "n = len(data[\"Adj Close\"].columns)\n",
        "\n",
        "# Crear un array de n elementos\n",
        "weights = np.ones(n)\n",
        "weights = weights / sum(weights)\n"
      ],
      "metadata": {
        "id": "POQcHLzKj_1n"
      },
      "execution_count": 151,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "weights\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vQRTtq7akERc",
        "outputId": "b2f12e76-c02d-4c9a-f134-0060b39d773b"
      },
      "execution_count": 152,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04,\n",
              "       0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04,\n",
              "       0.04, 0.04, 0.04])"
            ]
          },
          "metadata": {},
          "execution_count": 152
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Portfolio Optimizer"
      ],
      "metadata": {
        "id": "JIBkP8jgseys"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install PyPortfolioOpt"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8mn3hVC1o0WM",
        "outputId": "00a43b22-1ca5-48e7-e4b7-d18db5ac8571"
      },
      "execution_count": 154,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: PyPortfolioOpt in /usr/local/lib/python3.8/dist-packages (1.5.4)\n",
            "Requirement already satisfied: numpy<2.0.0,>=1.22.4 in /usr/local/lib/python3.8/dist-packages (from PyPortfolioOpt) (1.22.4)\n",
            "Requirement already satisfied: cvxpy<2.0.0,>=1.1.10 in /usr/local/lib/python3.8/dist-packages (from PyPortfolioOpt) (1.2.2)\n",
            "Requirement already satisfied: pandas>=0.19 in /usr/local/lib/python3.8/dist-packages (from PyPortfolioOpt) (1.3.5)\n",
            "Requirement already satisfied: scipy<2.0,>=1.3 in /usr/local/lib/python3.8/dist-packages (from PyPortfolioOpt) (1.7.3)\n",
            "Requirement already satisfied: osqp>=0.4.1 in /usr/local/lib/python3.8/dist-packages (from cvxpy<2.0.0,>=1.1.10->PyPortfolioOpt) (0.6.2.post0)\n",
            "Requirement already satisfied: ecos>=2 in /usr/local/lib/python3.8/dist-packages (from cvxpy<2.0.0,>=1.1.10->PyPortfolioOpt) (2.0.10)\n",
            "Requirement already satisfied: scs>=1.1.6 in /usr/local/lib/python3.8/dist-packages (from cvxpy<2.0.0,>=1.1.10->PyPortfolioOpt) (3.2.2)\n",
            "Requirement already satisfied: qdldl in /usr/local/lib/python3.8/dist-packages (from osqp>=0.4.1->cvxpy<2.0.0,>=1.1.10->PyPortfolioOpt) (0.1.5.post2)\n",
            "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.8/dist-packages (from pandas>=0.19->PyPortfolioOpt) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.8/dist-packages (from pandas>=0.19->PyPortfolioOpt) (2022.6)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.8/dist-packages (from python-dateutil>=2.7.3->pandas>=0.19->PyPortfolioOpt) (1.15.0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from pypfopt import EfficientFrontier\n",
        "from pypfopt import risk_models\n",
        "from pypfopt import expected_returns\n",
        "\n"
      ],
      "metadata": {
        "id": "Scm3iBH4py_d"
      },
      "execution_count": 169,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "portfolio = data[\"Adj Close\"]"
      ],
      "metadata": {
        "id": "IcciKoeuq221"
      },
      "execution_count": 170,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "mu = expected_returns.mean_historical_return(portfolio)\n",
        "S = risk_models.sample_cov(portfolio)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JmGqmN9gorGE",
        "outputId": "d078d493-df5f-4ed1-dd5d-5928c90e7b6e"
      },
      "execution_count": 171,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/pypfopt/risk_models.py:68: UserWarning: The covariance matrix is non positive semidefinite. Amending eigenvalues.\n",
            "  warnings.warn(\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mu"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vfTiT3WEq1B8",
        "outputId": "f7796687-cec6-49cb-c8cb-768ba35aa3ef"
      },
      "execution_count": 172,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "AAPL     0.329091\n",
              "AMD      0.276816\n",
              "BABA    -0.003249\n",
              "BBAR     0.023754\n",
              "BBD     -0.030168\n",
              "BRK     -0.198114\n",
              "CEPU    -0.213677\n",
              "CRESY   -0.012435\n",
              "DIS      0.115715\n",
              "GGAL     0.094788\n",
              "GLOB     0.397033\n",
              "GOOG     0.195081\n",
              "JPM      0.137170\n",
              "KO       0.110601\n",
              "LOMA    -0.214043\n",
              "MCD      0.142948\n",
              "MELI     0.326254\n",
              "MSFT     0.224998\n",
              "NVDA     0.381701\n",
              "PAM      0.057195\n",
              "PBR     -0.004182\n",
              "PEP      0.121747\n",
              "TEO     -0.004831\n",
              "TGS      0.173810\n",
              "VALE     0.065283\n",
              "VIST     0.095459\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 172
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "S"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "rhpH1-pErDHC",
        "outputId": "cc1b644b-ab65-44fe-fb4f-ffabc8447a11"
      },
      "execution_count": 173,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           AAPL       AMD      BABA      BBAR       BBD           BRK  \\\n",
              "AAPL   0.084654  0.068348  0.047588  0.042443  0.041607  3.883429e-01   \n",
              "AMD    0.068348  0.342217  0.077670  0.055276  0.067481  9.610440e-01   \n",
              "BABA   0.047588  0.077670  0.175929  0.045831  0.047027  3.262279e-01   \n",
              "BBAR   0.042443  0.055276  0.045831  0.336643  0.099234 -1.352410e-01   \n",
              "BBD    0.041607  0.067481  0.047027  0.099234  0.192760 -2.847818e-01   \n",
              "BRK    0.388343  0.961044  0.326228 -0.135241 -0.284782  2.947748e+03   \n",
              "CEPU   0.051155  0.068549  0.052167  0.305033  0.112745 -1.877193e-04   \n",
              "CRESY  0.033638  0.049038  0.038053  0.138557  0.070810  2.426819e-01   \n",
              "DIS    0.034519  0.053903  0.033082  0.047015  0.050847  2.184654e-01   \n",
              "GGAL   0.043965  0.059396  0.044354  0.256647  0.095339 -8.946165e-02   \n",
              "GLOB   0.057601  0.100818  0.067037  0.060011  0.046453  3.345050e-01   \n",
              "GOOG   0.045661  0.057828  0.047659  0.041864  0.041167  1.922735e-01   \n",
              "JPM    0.042584  0.065831  0.033463  0.066902  0.073174  3.460840e-01   \n",
              "KO     0.018466  0.024527  0.011690  0.025561  0.029525  1.242727e-01   \n",
              "LOMA   0.044956  0.067144  0.051409  0.263595  0.106165 -6.546805e-04   \n",
              "MCD    0.022752  0.029145  0.017399  0.029928  0.028844  2.532004e-01   \n",
              "MELI   0.061122  0.106688  0.090030  0.078291  0.072802  3.724412e-01   \n",
              "MSFT   0.045172  0.064483  0.046182  0.041985  0.042354  1.408996e-01   \n",
              "NVDA   0.067793  0.146284  0.079455  0.057976  0.058602  8.395696e-01   \n",
              "PAM    0.030767  0.035823  0.036229  0.185625  0.065845  9.462959e-02   \n",
              "PBR    0.047047  0.083044  0.050184  0.106085  0.164185 -1.514022e-01   \n",
              "PEP    0.020434  0.025141  0.012610  0.021085  0.026100  7.083149e-02   \n",
              "TEO    0.023926  0.038135  0.026447  0.127632  0.059691 -1.685349e-01   \n",
              "TGS    0.025615  0.037671  0.033587  0.155326  0.058527 -3.008070e-01   \n",
              "VALE   0.049002  0.088941  0.063939  0.083580  0.124766 -1.509427e-01   \n",
              "VIST   0.075493  0.095291  0.071604  0.234361  0.144738 -3.928763e-07   \n",
              "\n",
              "           CEPU     CRESY       DIS      GGAL  ...      MELI      MSFT  \\\n",
              "AAPL   0.051155  0.033638  0.034519  0.043965  ...  0.061122  0.045172   \n",
              "AMD    0.068549  0.049038  0.053903  0.059396  ...  0.106688  0.064483   \n",
              "BABA   0.052167  0.038053  0.033082  0.044354  ...  0.090030  0.046182   \n",
              "BBAR   0.305033  0.138557  0.047015  0.256647  ...  0.078291  0.041985   \n",
              "BBD    0.112745  0.070810  0.050847  0.095339  ...  0.072802  0.042354   \n",
              "BRK   -0.000188  0.242682  0.218465 -0.089462  ...  0.372441  0.140900   \n",
              "CEPU   0.444770  0.199128  0.052794  0.300827  ...  0.084585  0.050148   \n",
              "CRESY  0.199128  0.233812  0.038482  0.136996  ...  0.058266  0.032013   \n",
              "DIS    0.052794  0.038482  0.075082  0.049701  ...  0.057656  0.036142   \n",
              "GGAL   0.300827  0.136996  0.049701  0.321388  ...  0.075040  0.042608   \n",
              "GLOB   0.063942  0.042529  0.047051  0.053317  ...  0.109915  0.060464   \n",
              "GOOG   0.045697  0.032503  0.036079  0.043997  ...  0.062989  0.046633   \n",
              "JPM    0.065699  0.046301  0.054213  0.068133  ...  0.064212  0.043742   \n",
              "KO     0.026711  0.022607  0.022944  0.024518  ...  0.024249  0.020368   \n",
              "LOMA   0.277253  0.169737  0.051852  0.265931  ...  0.090743  0.047308   \n",
              "MCD    0.035949  0.023396  0.024437  0.031956  ...  0.027815  0.023524   \n",
              "MELI   0.084585  0.058266  0.057656  0.075040  ...  0.250451  0.062221   \n",
              "MSFT   0.050148  0.032013  0.036142  0.042608  ...  0.062221  0.072578   \n",
              "NVDA   0.069837  0.049343  0.051986  0.060520  ...  0.104462  0.068352   \n",
              "PAM    0.259109  0.117570  0.030312  0.185091  ...  0.053501  0.031439   \n",
              "PBR    0.124103  0.080317  0.054546  0.103730  ...  0.081892  0.048860   \n",
              "PEP    0.025461  0.017599  0.020593  0.021187  ...  0.024001  0.022911   \n",
              "TEO    0.160716  0.085055  0.032383  0.129753  ...  0.046240  0.021969   \n",
              "TGS    0.240729  0.110832  0.029072  0.158055  ...  0.044630  0.025799   \n",
              "VALE   0.096994  0.070089  0.050019  0.080177  ...  0.080645  0.048567   \n",
              "VIST   0.227352  0.191638  0.090323  0.234808  ...  0.113852  0.069892   \n",
              "\n",
              "           NVDA       PAM       PBR       PEP       TEO       TGS      VALE  \\\n",
              "AAPL   0.067793  0.030767  0.047047  0.020434  0.023926  0.025615  0.049002   \n",
              "AMD    0.146284  0.035823  0.083044  0.025141  0.038135  0.037671  0.088941   \n",
              "BABA   0.079455  0.036229  0.050184  0.012610  0.026447  0.033587  0.063939   \n",
              "BBAR   0.057976  0.185625  0.106085  0.021085  0.127632  0.155326  0.083580   \n",
              "BBD    0.058602  0.065845  0.164185  0.026100  0.059691  0.058527  0.124766   \n",
              "BRK    0.839570  0.094630 -0.151402  0.070831 -0.168535 -0.300807 -0.150943   \n",
              "CEPU   0.069837  0.259109  0.124103  0.025461  0.160716  0.240729  0.096994   \n",
              "CRESY  0.049343  0.117570  0.080317  0.017599  0.085055  0.110832  0.070089   \n",
              "DIS    0.051986  0.030312  0.054546  0.020593  0.032383  0.029072  0.050019   \n",
              "GGAL   0.060520  0.185091  0.103730  0.021187  0.129753  0.158055  0.080177   \n",
              "GLOB   0.097228  0.046422  0.054122  0.024539  0.029639  0.039140  0.050690   \n",
              "GOOG   0.064689  0.029540  0.044460  0.019217  0.024658  0.024946  0.044911   \n",
              "JPM    0.060457  0.035671  0.077534  0.024329  0.037740  0.029547  0.073672   \n",
              "KO     0.021774  0.017004  0.030612  0.022470  0.015016  0.014074  0.026313   \n",
              "LOMA   0.064075  0.213479  0.115752  0.026485  0.142811  0.203940  0.084720   \n",
              "MCD    0.028775  0.023530  0.033028  0.017070  0.017514  0.021371  0.025651   \n",
              "MELI   0.104462  0.053501  0.081892  0.024001  0.046240  0.044630  0.080645   \n",
              "MSFT   0.068352  0.031439  0.048860  0.022911  0.021969  0.025799  0.048567   \n",
              "NVDA   0.208481  0.038599  0.063946  0.024870  0.038040  0.038099  0.071801   \n",
              "PAM    0.038599  0.248821  0.082445  0.015924  0.100268  0.157039  0.059250   \n",
              "PBR    0.063946  0.082445  0.267128  0.026963  0.068359  0.073065  0.161068   \n",
              "PEP    0.024870  0.015924  0.026963  0.032040  0.011323  0.014841  0.023780   \n",
              "TEO    0.038040  0.100268  0.068359  0.011323  0.175840  0.090493  0.054109   \n",
              "TGS    0.038099  0.157039  0.073065  0.014841  0.090493  0.275143  0.056785   \n",
              "VALE   0.071801  0.059250  0.161068  0.023780  0.054109  0.056785  0.221467   \n",
              "VIST   0.106086  0.190582  0.209140  0.037288  0.137990  0.197603  0.153299   \n",
              "\n",
              "               VIST  \n",
              "AAPL   7.549279e-02  \n",
              "AMD    9.529119e-02  \n",
              "BABA   7.160391e-02  \n",
              "BBAR   2.343605e-01  \n",
              "BBD    1.447379e-01  \n",
              "BRK   -3.928763e-07  \n",
              "CEPU   2.273520e-01  \n",
              "CRESY  1.916377e-01  \n",
              "DIS    9.032264e-02  \n",
              "GGAL   2.348076e-01  \n",
              "GLOB   8.658171e-02  \n",
              "GOOG   7.696566e-02  \n",
              "JPM    1.075265e-01  \n",
              "KO     4.581635e-02  \n",
              "LOMA   1.865976e-01  \n",
              "MCD    5.288797e-02  \n",
              "MELI   1.138525e-01  \n",
              "MSFT   6.989166e-02  \n",
              "NVDA   1.060857e-01  \n",
              "PAM    1.905823e-01  \n",
              "PBR    2.091398e-01  \n",
              "PEP    3.728833e-02  \n",
              "TEO    1.379896e-01  \n",
              "TGS    1.976028e-01  \n",
              "VALE   1.532993e-01  \n",
              "VIST   5.240321e-01  \n",
              "\n",
              "[26 rows x 26 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-fea68be0-0587-4830-8f43-9d4374ffd6de\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>AAPL</th>\n",
              "      <th>AMD</th>\n",
              "      <th>BABA</th>\n",
              "      <th>BBAR</th>\n",
              "      <th>BBD</th>\n",
              "      <th>BRK</th>\n",
              "      <th>CEPU</th>\n",
              "      <th>CRESY</th>\n",
              "      <th>DIS</th>\n",
              "      <th>GGAL</th>\n",
              "      <th>...</th>\n",
              "      <th>MELI</th>\n",
              "      <th>MSFT</th>\n",
              "      <th>NVDA</th>\n",
              "      <th>PAM</th>\n",
              "      <th>PBR</th>\n",
              "      <th>PEP</th>\n",
              "      <th>TEO</th>\n",
              "      <th>TGS</th>\n",
              "      <th>VALE</th>\n",
              "      <th>VIST</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>AAPL</th>\n",
              "      <td>0.084654</td>\n",
              "      <td>0.068348</td>\n",
              "      <td>0.047588</td>\n",
              "      <td>0.042443</td>\n",
              "      <td>0.041607</td>\n",
              "      <td>3.883429e-01</td>\n",
              "      <td>0.051155</td>\n",
              "      <td>0.033638</td>\n",
              "      <td>0.034519</td>\n",
              "      <td>0.043965</td>\n",
              "      <td>...</td>\n",
              "      <td>0.061122</td>\n",
              "      <td>0.045172</td>\n",
              "      <td>0.067793</td>\n",
              "      <td>0.030767</td>\n",
              "      <td>0.047047</td>\n",
              "      <td>0.020434</td>\n",
              "      <td>0.023926</td>\n",
              "      <td>0.025615</td>\n",
              "      <td>0.049002</td>\n",
              "      <td>7.549279e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AMD</th>\n",
              "      <td>0.068348</td>\n",
              "      <td>0.342217</td>\n",
              "      <td>0.077670</td>\n",
              "      <td>0.055276</td>\n",
              "      <td>0.067481</td>\n",
              "      <td>9.610440e-01</td>\n",
              "      <td>0.068549</td>\n",
              "      <td>0.049038</td>\n",
              "      <td>0.053903</td>\n",
              "      <td>0.059396</td>\n",
              "      <td>...</td>\n",
              "      <td>0.106688</td>\n",
              "      <td>0.064483</td>\n",
              "      <td>0.146284</td>\n",
              "      <td>0.035823</td>\n",
              "      <td>0.083044</td>\n",
              "      <td>0.025141</td>\n",
              "      <td>0.038135</td>\n",
              "      <td>0.037671</td>\n",
              "      <td>0.088941</td>\n",
              "      <td>9.529119e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BABA</th>\n",
              "      <td>0.047588</td>\n",
              "      <td>0.077670</td>\n",
              "      <td>0.175929</td>\n",
              "      <td>0.045831</td>\n",
              "      <td>0.047027</td>\n",
              "      <td>3.262279e-01</td>\n",
              "      <td>0.052167</td>\n",
              "      <td>0.038053</td>\n",
              "      <td>0.033082</td>\n",
              "      <td>0.044354</td>\n",
              "      <td>...</td>\n",
              "      <td>0.090030</td>\n",
              "      <td>0.046182</td>\n",
              "      <td>0.079455</td>\n",
              "      <td>0.036229</td>\n",
              "      <td>0.050184</td>\n",
              "      <td>0.012610</td>\n",
              "      <td>0.026447</td>\n",
              "      <td>0.033587</td>\n",
              "      <td>0.063939</td>\n",
              "      <td>7.160391e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BBAR</th>\n",
              "      <td>0.042443</td>\n",
              "      <td>0.055276</td>\n",
              "      <td>0.045831</td>\n",
              "      <td>0.336643</td>\n",
              "      <td>0.099234</td>\n",
              "      <td>-1.352410e-01</td>\n",
              "      <td>0.305033</td>\n",
              "      <td>0.138557</td>\n",
              "      <td>0.047015</td>\n",
              "      <td>0.256647</td>\n",
              "      <td>...</td>\n",
              "      <td>0.078291</td>\n",
              "      <td>0.041985</td>\n",
              "      <td>0.057976</td>\n",
              "      <td>0.185625</td>\n",
              "      <td>0.106085</td>\n",
              "      <td>0.021085</td>\n",
              "      <td>0.127632</td>\n",
              "      <td>0.155326</td>\n",
              "      <td>0.083580</td>\n",
              "      <td>2.343605e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BBD</th>\n",
              "      <td>0.041607</td>\n",
              "      <td>0.067481</td>\n",
              "      <td>0.047027</td>\n",
              "      <td>0.099234</td>\n",
              "      <td>0.192760</td>\n",
              "      <td>-2.847818e-01</td>\n",
              "      <td>0.112745</td>\n",
              "      <td>0.070810</td>\n",
              "      <td>0.050847</td>\n",
              "      <td>0.095339</td>\n",
              "      <td>...</td>\n",
              "      <td>0.072802</td>\n",
              "      <td>0.042354</td>\n",
              "      <td>0.058602</td>\n",
              "      <td>0.065845</td>\n",
              "      <td>0.164185</td>\n",
              "      <td>0.026100</td>\n",
              "      <td>0.059691</td>\n",
              "      <td>0.058527</td>\n",
              "      <td>0.124766</td>\n",
              "      <td>1.447379e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BRK</th>\n",
              "      <td>0.388343</td>\n",
              "      <td>0.961044</td>\n",
              "      <td>0.326228</td>\n",
              "      <td>-0.135241</td>\n",
              "      <td>-0.284782</td>\n",
              "      <td>2.947748e+03</td>\n",
              "      <td>-0.000188</td>\n",
              "      <td>0.242682</td>\n",
              "      <td>0.218465</td>\n",
              "      <td>-0.089462</td>\n",
              "      <td>...</td>\n",
              "      <td>0.372441</td>\n",
              "      <td>0.140900</td>\n",
              "      <td>0.839570</td>\n",
              "      <td>0.094630</td>\n",
              "      <td>-0.151402</td>\n",
              "      <td>0.070831</td>\n",
              "      <td>-0.168535</td>\n",
              "      <td>-0.300807</td>\n",
              "      <td>-0.150943</td>\n",
              "      <td>-3.928763e-07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>CEPU</th>\n",
              "      <td>0.051155</td>\n",
              "      <td>0.068549</td>\n",
              "      <td>0.052167</td>\n",
              "      <td>0.305033</td>\n",
              "      <td>0.112745</td>\n",
              "      <td>-1.877193e-04</td>\n",
              "      <td>0.444770</td>\n",
              "      <td>0.199128</td>\n",
              "      <td>0.052794</td>\n",
              "      <td>0.300827</td>\n",
              "      <td>...</td>\n",
              "      <td>0.084585</td>\n",
              "      <td>0.050148</td>\n",
              "      <td>0.069837</td>\n",
              "      <td>0.259109</td>\n",
              "      <td>0.124103</td>\n",
              "      <td>0.025461</td>\n",
              "      <td>0.160716</td>\n",
              "      <td>0.240729</td>\n",
              "      <td>0.096994</td>\n",
              "      <td>2.273520e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>CRESY</th>\n",
              "      <td>0.033638</td>\n",
              "      <td>0.049038</td>\n",
              "      <td>0.038053</td>\n",
              "      <td>0.138557</td>\n",
              "      <td>0.070810</td>\n",
              "      <td>2.426819e-01</td>\n",
              "      <td>0.199128</td>\n",
              "      <td>0.233812</td>\n",
              "      <td>0.038482</td>\n",
              "      <td>0.136996</td>\n",
              "      <td>...</td>\n",
              "      <td>0.058266</td>\n",
              "      <td>0.032013</td>\n",
              "      <td>0.049343</td>\n",
              "      <td>0.117570</td>\n",
              "      <td>0.080317</td>\n",
              "      <td>0.017599</td>\n",
              "      <td>0.085055</td>\n",
              "      <td>0.110832</td>\n",
              "      <td>0.070089</td>\n",
              "      <td>1.916377e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>DIS</th>\n",
              "      <td>0.034519</td>\n",
              "      <td>0.053903</td>\n",
              "      <td>0.033082</td>\n",
              "      <td>0.047015</td>\n",
              "      <td>0.050847</td>\n",
              "      <td>2.184654e-01</td>\n",
              "      <td>0.052794</td>\n",
              "      <td>0.038482</td>\n",
              "      <td>0.075082</td>\n",
              "      <td>0.049701</td>\n",
              "      <td>...</td>\n",
              "      <td>0.057656</td>\n",
              "      <td>0.036142</td>\n",
              "      <td>0.051986</td>\n",
              "      <td>0.030312</td>\n",
              "      <td>0.054546</td>\n",
              "      <td>0.020593</td>\n",
              "      <td>0.032383</td>\n",
              "      <td>0.029072</td>\n",
              "      <td>0.050019</td>\n",
              "      <td>9.032264e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GGAL</th>\n",
              "      <td>0.043965</td>\n",
              "      <td>0.059396</td>\n",
              "      <td>0.044354</td>\n",
              "      <td>0.256647</td>\n",
              "      <td>0.095339</td>\n",
              "      <td>-8.946165e-02</td>\n",
              "      <td>0.300827</td>\n",
              "      <td>0.136996</td>\n",
              "      <td>0.049701</td>\n",
              "      <td>0.321388</td>\n",
              "      <td>...</td>\n",
              "      <td>0.075040</td>\n",
              "      <td>0.042608</td>\n",
              "      <td>0.060520</td>\n",
              "      <td>0.185091</td>\n",
              "      <td>0.103730</td>\n",
              "      <td>0.021187</td>\n",
              "      <td>0.129753</td>\n",
              "      <td>0.158055</td>\n",
              "      <td>0.080177</td>\n",
              "      <td>2.348076e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GLOB</th>\n",
              "      <td>0.057601</td>\n",
              "      <td>0.100818</td>\n",
              "      <td>0.067037</td>\n",
              "      <td>0.060011</td>\n",
              "      <td>0.046453</td>\n",
              "      <td>3.345050e-01</td>\n",
              "      <td>0.063942</td>\n",
              "      <td>0.042529</td>\n",
              "      <td>0.047051</td>\n",
              "      <td>0.053317</td>\n",
              "      <td>...</td>\n",
              "      <td>0.109915</td>\n",
              "      <td>0.060464</td>\n",
              "      <td>0.097228</td>\n",
              "      <td>0.046422</td>\n",
              "      <td>0.054122</td>\n",
              "      <td>0.024539</td>\n",
              "      <td>0.029639</td>\n",
              "      <td>0.039140</td>\n",
              "      <td>0.050690</td>\n",
              "      <td>8.658171e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GOOG</th>\n",
              "      <td>0.045661</td>\n",
              "      <td>0.057828</td>\n",
              "      <td>0.047659</td>\n",
              "      <td>0.041864</td>\n",
              "      <td>0.041167</td>\n",
              "      <td>1.922735e-01</td>\n",
              "      <td>0.045697</td>\n",
              "      <td>0.032503</td>\n",
              "      <td>0.036079</td>\n",
              "      <td>0.043997</td>\n",
              "      <td>...</td>\n",
              "      <td>0.062989</td>\n",
              "      <td>0.046633</td>\n",
              "      <td>0.064689</td>\n",
              "      <td>0.029540</td>\n",
              "      <td>0.044460</td>\n",
              "      <td>0.019217</td>\n",
              "      <td>0.024658</td>\n",
              "      <td>0.024946</td>\n",
              "      <td>0.044911</td>\n",
              "      <td>7.696566e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>JPM</th>\n",
              "      <td>0.042584</td>\n",
              "      <td>0.065831</td>\n",
              "      <td>0.033463</td>\n",
              "      <td>0.066902</td>\n",
              "      <td>0.073174</td>\n",
              "      <td>3.460840e-01</td>\n",
              "      <td>0.065699</td>\n",
              "      <td>0.046301</td>\n",
              "      <td>0.054213</td>\n",
              "      <td>0.068133</td>\n",
              "      <td>...</td>\n",
              "      <td>0.064212</td>\n",
              "      <td>0.043742</td>\n",
              "      <td>0.060457</td>\n",
              "      <td>0.035671</td>\n",
              "      <td>0.077534</td>\n",
              "      <td>0.024329</td>\n",
              "      <td>0.037740</td>\n",
              "      <td>0.029547</td>\n",
              "      <td>0.073672</td>\n",
              "      <td>1.075265e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>KO</th>\n",
              "      <td>0.018466</td>\n",
              "      <td>0.024527</td>\n",
              "      <td>0.011690</td>\n",
              "      <td>0.025561</td>\n",
              "      <td>0.029525</td>\n",
              "      <td>1.242727e-01</td>\n",
              "      <td>0.026711</td>\n",
              "      <td>0.022607</td>\n",
              "      <td>0.022944</td>\n",
              "      <td>0.024518</td>\n",
              "      <td>...</td>\n",
              "      <td>0.024249</td>\n",
              "      <td>0.020368</td>\n",
              "      <td>0.021774</td>\n",
              "      <td>0.017004</td>\n",
              "      <td>0.030612</td>\n",
              "      <td>0.022470</td>\n",
              "      <td>0.015016</td>\n",
              "      <td>0.014074</td>\n",
              "      <td>0.026313</td>\n",
              "      <td>4.581635e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LOMA</th>\n",
              "      <td>0.044956</td>\n",
              "      <td>0.067144</td>\n",
              "      <td>0.051409</td>\n",
              "      <td>0.263595</td>\n",
              "      <td>0.106165</td>\n",
              "      <td>-6.546805e-04</td>\n",
              "      <td>0.277253</td>\n",
              "      <td>0.169737</td>\n",
              "      <td>0.051852</td>\n",
              "      <td>0.265931</td>\n",
              "      <td>...</td>\n",
              "      <td>0.090743</td>\n",
              "      <td>0.047308</td>\n",
              "      <td>0.064075</td>\n",
              "      <td>0.213479</td>\n",
              "      <td>0.115752</td>\n",
              "      <td>0.026485</td>\n",
              "      <td>0.142811</td>\n",
              "      <td>0.203940</td>\n",
              "      <td>0.084720</td>\n",
              "      <td>1.865976e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>MCD</th>\n",
              "      <td>0.022752</td>\n",
              "      <td>0.029145</td>\n",
              "      <td>0.017399</td>\n",
              "      <td>0.029928</td>\n",
              "      <td>0.028844</td>\n",
              "      <td>2.532004e-01</td>\n",
              "      <td>0.035949</td>\n",
              "      <td>0.023396</td>\n",
              "      <td>0.024437</td>\n",
              "      <td>0.031956</td>\n",
              "      <td>...</td>\n",
              "      <td>0.027815</td>\n",
              "      <td>0.023524</td>\n",
              "      <td>0.028775</td>\n",
              "      <td>0.023530</td>\n",
              "      <td>0.033028</td>\n",
              "      <td>0.017070</td>\n",
              "      <td>0.017514</td>\n",
              "      <td>0.021371</td>\n",
              "      <td>0.025651</td>\n",
              "      <td>5.288797e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>MELI</th>\n",
              "      <td>0.061122</td>\n",
              "      <td>0.106688</td>\n",
              "      <td>0.090030</td>\n",
              "      <td>0.078291</td>\n",
              "      <td>0.072802</td>\n",
              "      <td>3.724412e-01</td>\n",
              "      <td>0.084585</td>\n",
              "      <td>0.058266</td>\n",
              "      <td>0.057656</td>\n",
              "      <td>0.075040</td>\n",
              "      <td>...</td>\n",
              "      <td>0.250451</td>\n",
              "      <td>0.062221</td>\n",
              "      <td>0.104462</td>\n",
              "      <td>0.053501</td>\n",
              "      <td>0.081892</td>\n",
              "      <td>0.024001</td>\n",
              "      <td>0.046240</td>\n",
              "      <td>0.044630</td>\n",
              "      <td>0.080645</td>\n",
              "      <td>1.138525e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>MSFT</th>\n",
              "      <td>0.045172</td>\n",
              "      <td>0.064483</td>\n",
              "      <td>0.046182</td>\n",
              "      <td>0.041985</td>\n",
              "      <td>0.042354</td>\n",
              "      <td>1.408996e-01</td>\n",
              "      <td>0.050148</td>\n",
              "      <td>0.032013</td>\n",
              "      <td>0.036142</td>\n",
              "      <td>0.042608</td>\n",
              "      <td>...</td>\n",
              "      <td>0.062221</td>\n",
              "      <td>0.072578</td>\n",
              "      <td>0.068352</td>\n",
              "      <td>0.031439</td>\n",
              "      <td>0.048860</td>\n",
              "      <td>0.022911</td>\n",
              "      <td>0.021969</td>\n",
              "      <td>0.025799</td>\n",
              "      <td>0.048567</td>\n",
              "      <td>6.989166e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NVDA</th>\n",
              "      <td>0.067793</td>\n",
              "      <td>0.146284</td>\n",
              "      <td>0.079455</td>\n",
              "      <td>0.057976</td>\n",
              "      <td>0.058602</td>\n",
              "      <td>8.395696e-01</td>\n",
              "      <td>0.069837</td>\n",
              "      <td>0.049343</td>\n",
              "      <td>0.051986</td>\n",
              "      <td>0.060520</td>\n",
              "      <td>...</td>\n",
              "      <td>0.104462</td>\n",
              "      <td>0.068352</td>\n",
              "      <td>0.208481</td>\n",
              "      <td>0.038599</td>\n",
              "      <td>0.063946</td>\n",
              "      <td>0.024870</td>\n",
              "      <td>0.038040</td>\n",
              "      <td>0.038099</td>\n",
              "      <td>0.071801</td>\n",
              "      <td>1.060857e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>PAM</th>\n",
              "      <td>0.030767</td>\n",
              "      <td>0.035823</td>\n",
              "      <td>0.036229</td>\n",
              "      <td>0.185625</td>\n",
              "      <td>0.065845</td>\n",
              "      <td>9.462959e-02</td>\n",
              "      <td>0.259109</td>\n",
              "      <td>0.117570</td>\n",
              "      <td>0.030312</td>\n",
              "      <td>0.185091</td>\n",
              "      <td>...</td>\n",
              "      <td>0.053501</td>\n",
              "      <td>0.031439</td>\n",
              "      <td>0.038599</td>\n",
              "      <td>0.248821</td>\n",
              "      <td>0.082445</td>\n",
              "      <td>0.015924</td>\n",
              "      <td>0.100268</td>\n",
              "      <td>0.157039</td>\n",
              "      <td>0.059250</td>\n",
              "      <td>1.905823e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>PBR</th>\n",
              "      <td>0.047047</td>\n",
              "      <td>0.083044</td>\n",
              "      <td>0.050184</td>\n",
              "      <td>0.106085</td>\n",
              "      <td>0.164185</td>\n",
              "      <td>-1.514022e-01</td>\n",
              "      <td>0.124103</td>\n",
              "      <td>0.080317</td>\n",
              "      <td>0.054546</td>\n",
              "      <td>0.103730</td>\n",
              "      <td>...</td>\n",
              "      <td>0.081892</td>\n",
              "      <td>0.048860</td>\n",
              "      <td>0.063946</td>\n",
              "      <td>0.082445</td>\n",
              "      <td>0.267128</td>\n",
              "      <td>0.026963</td>\n",
              "      <td>0.068359</td>\n",
              "      <td>0.073065</td>\n",
              "      <td>0.161068</td>\n",
              "      <td>2.091398e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>PEP</th>\n",
              "      <td>0.020434</td>\n",
              "      <td>0.025141</td>\n",
              "      <td>0.012610</td>\n",
              "      <td>0.021085</td>\n",
              "      <td>0.026100</td>\n",
              "      <td>7.083149e-02</td>\n",
              "      <td>0.025461</td>\n",
              "      <td>0.017599</td>\n",
              "      <td>0.020593</td>\n",
              "      <td>0.021187</td>\n",
              "      <td>...</td>\n",
              "      <td>0.024001</td>\n",
              "      <td>0.022911</td>\n",
              "      <td>0.024870</td>\n",
              "      <td>0.015924</td>\n",
              "      <td>0.026963</td>\n",
              "      <td>0.032040</td>\n",
              "      <td>0.011323</td>\n",
              "      <td>0.014841</td>\n",
              "      <td>0.023780</td>\n",
              "      <td>3.728833e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TEO</th>\n",
              "      <td>0.023926</td>\n",
              "      <td>0.038135</td>\n",
              "      <td>0.026447</td>\n",
              "      <td>0.127632</td>\n",
              "      <td>0.059691</td>\n",
              "      <td>-1.685349e-01</td>\n",
              "      <td>0.160716</td>\n",
              "      <td>0.085055</td>\n",
              "      <td>0.032383</td>\n",
              "      <td>0.129753</td>\n",
              "      <td>...</td>\n",
              "      <td>0.046240</td>\n",
              "      <td>0.021969</td>\n",
              "      <td>0.038040</td>\n",
              "      <td>0.100268</td>\n",
              "      <td>0.068359</td>\n",
              "      <td>0.011323</td>\n",
              "      <td>0.175840</td>\n",
              "      <td>0.090493</td>\n",
              "      <td>0.054109</td>\n",
              "      <td>1.379896e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TGS</th>\n",
              "      <td>0.025615</td>\n",
              "      <td>0.037671</td>\n",
              "      <td>0.033587</td>\n",
              "      <td>0.155326</td>\n",
              "      <td>0.058527</td>\n",
              "      <td>-3.008070e-01</td>\n",
              "      <td>0.240729</td>\n",
              "      <td>0.110832</td>\n",
              "      <td>0.029072</td>\n",
              "      <td>0.158055</td>\n",
              "      <td>...</td>\n",
              "      <td>0.044630</td>\n",
              "      <td>0.025799</td>\n",
              "      <td>0.038099</td>\n",
              "      <td>0.157039</td>\n",
              "      <td>0.073065</td>\n",
              "      <td>0.014841</td>\n",
              "      <td>0.090493</td>\n",
              "      <td>0.275143</td>\n",
              "      <td>0.056785</td>\n",
              "      <td>1.976028e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>VALE</th>\n",
              "      <td>0.049002</td>\n",
              "      <td>0.088941</td>\n",
              "      <td>0.063939</td>\n",
              "      <td>0.083580</td>\n",
              "      <td>0.124766</td>\n",
              "      <td>-1.509427e-01</td>\n",
              "      <td>0.096994</td>\n",
              "      <td>0.070089</td>\n",
              "      <td>0.050019</td>\n",
              "      <td>0.080177</td>\n",
              "      <td>...</td>\n",
              "      <td>0.080645</td>\n",
              "      <td>0.048567</td>\n",
              "      <td>0.071801</td>\n",
              "      <td>0.059250</td>\n",
              "      <td>0.161068</td>\n",
              "      <td>0.023780</td>\n",
              "      <td>0.054109</td>\n",
              "      <td>0.056785</td>\n",
              "      <td>0.221467</td>\n",
              "      <td>1.532993e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>VIST</th>\n",
              "      <td>0.075493</td>\n",
              "      <td>0.095291</td>\n",
              "      <td>0.071604</td>\n",
              "      <td>0.234361</td>\n",
              "      <td>0.144738</td>\n",
              "      <td>-3.928763e-07</td>\n",
              "      <td>0.227352</td>\n",
              "      <td>0.191638</td>\n",
              "      <td>0.090323</td>\n",
              "      <td>0.234808</td>\n",
              "      <td>...</td>\n",
              "      <td>0.113852</td>\n",
              "      <td>0.069892</td>\n",
              "      <td>0.106086</td>\n",
              "      <td>0.190582</td>\n",
              "      <td>0.209140</td>\n",
              "      <td>0.037288</td>\n",
              "      <td>0.137990</td>\n",
              "      <td>0.197603</td>\n",
              "      <td>0.153299</td>\n",
              "      <td>5.240321e-01</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>26 rows × 26 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-fea68be0-0587-4830-8f43-9d4374ffd6de')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "  <style>\n",
              "    .colab-df-container {\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "    [theme=dark] .colab-df-convert {\n",
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              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 173
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Optimize for maximal Sharpe ratio\n",
        "ef = EfficientFrontier(mu, S)\n",
        "raw_weights = ef.max_sharpe()"
      ],
      "metadata": {
        "id": "ctxBKRHWrOt4"
      },
      "execution_count": 174,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "cleaned_weights = ef.clean_weights()\n",
        "ef.save_weights_to_file(\"weights.csv\")  # saves to file\n",
        "print(cleaned_weights)\n",
        "ef.portfolio_performance(verbose=True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DOH7P3MirRC1",
        "outputId": "6f083662-a19f-4374-9f7b-a90b559fbfc2"
      },
      "execution_count": 176,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "OrderedDict([('AAPL', 0.53394), ('AMD', 0.0), ('BABA', 0.0), ('BBAR', 0.0), ('BBD', 0.0), ('BRK', 0.0), ('CEPU', 0.0), ('CRESY', 0.0), ('DIS', 0.0), ('GGAL', 0.0), ('GLOB', 0.16017), ('GOOG', 0.0), ('JPM', 0.0), ('KO', 0.0), ('LOMA', 0.0), ('MCD', 0.1459), ('MELI', 0.0), ('MSFT', 0.0), ('NVDA', 0.08826), ('PAM', 0.0), ('PBR', 0.0), ('PEP', 0.0525), ('TEO', 0.0), ('TGS', 0.01921), ('VALE', 0.0), ('VIST', 0.0)])\n",
            "Expected annual return: 30.4%\n",
            "Annual volatility: 24.5%\n",
            "Sharpe Ratio: 1.16\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.3035887753644613, 0.2447604385145533, 1.1586381242228379)"
            ]
          },
          "metadata": {},
          "execution_count": 176
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from pypfopt.discrete_allocation import DiscreteAllocation, get_latest_prices\n",
        "\n"
      ],
      "metadata": {
        "id": "oZ-2IugBrTBY"
      },
      "execution_count": 177,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "latest_prices = get_latest_prices(portfolio)\n"
      ],
      "metadata": {
        "id": "_wxHCh5lrdN9"
      },
      "execution_count": 178,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "da = DiscreteAllocation(cleaned_weights, latest_prices, total_portfolio_value=15000)\n",
        "allocation, leftover = da.greedy_portfolio()\n"
      ],
      "metadata": {
        "id": "xpGvzSMSrm9B"
      },
      "execution_count": 179,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Total Stocks: \", allocation)\n",
        "print(\"Funds remaining: ${:.2f}\".format(leftover))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W__xRfHerqih",
        "outputId": "31660230-7b1c-432f-fe1f-0983c1a813bd"
      },
      "execution_count": 180,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Total Stocks:  {'AAPL': 55, 'GLOB': 13, 'MCD': 8, 'NVDA': 7, 'PEP': 4, 'TGS': 32}\n",
            "Funds remaining: $90.07\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Jw9-tcexsMuS"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}