Stock Price VAR MMRisk.ipynb

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      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "np.random.seed(143)"
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      "source": [
        "stock_price = pd.read_csv(\"stock_data_2_yrs_daywise.csv\")\n",
        "stock_price.set_index('Date', inplace = True)\n",
        "\n",
        "returns = (stock_price - stock_price.shift(1))/stock_price.shift(1)\n",
        "returns.dropna(inplace = True)\n",
        "returns.head()"
      ],
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              "           AdaniPorts    Ambuja    Apollo  AxisBank     Bajaj       BoB  \\\n",
              "Date                                                                      \n",
              "01-Sep-23   -0.027492 -0.018092  0.007811 -0.018739  0.002547 -0.019895   \n",
              "31-Aug-23    0.029038  0.039667  0.012918  0.009138 -0.030779  0.024038   \n",
              "30-Aug-23    0.030337 -0.002032  0.004464 -0.001831 -0.015114  0.000261   \n",
              "29-Aug-23   -0.022914 -0.007691 -0.005333  0.010091  0.005899 -0.007823   \n",
              "28-Aug-23    0.006621 -0.005471 -0.006255 -0.008073 -0.007937 -0.001051   \n",
              "\n",
              "               Bata  BlueStar    Camlin   Castrol  ...  SteelAuth  sunPharma  \\\n",
              "Date                                               ...                         \n",
              "01-Sep-23 -0.001284 -0.004227 -0.000662  0.019359  ...  -0.066243   0.001982   \n",
              "31-Aug-23 -0.010797  0.003976  0.006623 -0.012086  ...   0.006699  -0.001079   \n",
              "30-Aug-23  0.000195 -0.006712 -0.030592  0.000699  ...  -0.033381   0.012511   \n",
              "29-Aug-23 -0.009419 -0.013447 -0.011876  0.014321  ...  -0.012527  -0.001244   \n",
              "28-Aug-23  0.005590 -0.035616 -0.016140 -0.000344  ...  -0.020571  -0.010413   \n",
              "\n",
              "           TataComm  TataSteel     Titan  Ultramarine     Wipro  Wonderla  \\\n",
              "Date                                                                        \n",
              "01-Sep-23 -0.037178  -0.042685 -0.001284    -0.001129 -0.026376  0.018740   \n",
              "31-Aug-23  0.002812  -0.005270 -0.010797    -0.037288  0.002463  0.002290   \n",
              "30-Aug-23 -0.007718  -0.020782  0.000195     0.017488  0.004913  0.008350   \n",
              "29-Aug-23  0.023641  -0.013733 -0.009419     0.003461  0.000000 -0.009843   \n",
              "28-Aug-23 -0.006478  -0.013080  0.005590    -0.062651  0.006845 -0.001815   \n",
              "\n",
              "            YesBank  Nilkamal  \n",
              "Date                           \n",
              "01-Sep-23 -0.030460  0.014803  \n",
              "31-Aug-23 -0.000593  0.019937  \n",
              "30-Aug-23  0.002966 -0.057087  \n",
              "29-Aug-23 -0.005914 -0.005775  \n",
              "28-Aug-23  0.005949 -0.009894  \n",
              "\n",
              "[5 rows x 50 columns]"
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          },
          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.optimize import minimize\n",
        "r = np.array(returns)\n",
        "\n",
        "exp_returns = r.mean(axis = 0)\n",
        "std_dev = r.std(axis = 0)\n",
        "cov_matrix = np.array(returns.cov())"
      ],
      "metadata": {
        "id": "IglQY-jUawOg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def VarRisk_minimization(shortsell = True):\n",
        "  def objective1(xi):\n",
        "    return np.dot(xi.T, np.dot(cov_matrix, xi))\n",
        "  def objective2(xi):\n",
        "    return np.dot(xi.T, exp_returns).sum()\n",
        "  objective = lambda xi: 0.5*objective1(xi) - 0.5*objective2(xi) #weighted sum = 0.5\n",
        "  initial_weights = [1/50]*50\n",
        "  constraints = [\n",
        "      {'type': 'eq', 'fun': lambda w: sum(w) - 1, 'args': ()},\n",
        "      # {'type': 'ineq', 'fun': lambda w: sum(w*exp_returns) - target_return}\n",
        "  ]\n",
        "  if not shortsell:\n",
        "    bounds = [(0., None)]*(len(initial_weights))\n",
        "    result = minimize(objective, initial_weights, constraints = constraints, bounds = bounds)\n",
        "  else:\n",
        "    result = minimize(objective, initial_weights, constraints = constraints)\n",
        "  return result.x\n"
      ],
      "metadata": {
        "id": "8cW2XfmubX7Y"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def risk_return(weights):\n",
        "  risk = np.dot(weights.T, np.dot(cov_matrix, weights))\n",
        "  returns = np.dot(weights.T, exp_returns)\n",
        "  return risk, returns"
      ],
      "metadata": {
        "id": "KMljGmrMpKL5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "results = VarRisk_minimization(True)\n",
        "total_capital = 100000\n",
        "investment = pd.DataFrame(results*total_capital)\n",
        "\n",
        "cols = returns.columns\n",
        "investment.set_index(cols, inplace = True)"
      ],
      "metadata": {
        "id": "mTJLFXr1lz_P"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "investment['Investment'] = investment[0]\n",
        "investment.drop([0],axis = 1, inplace = True)\n",
        "investment.round(3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "7J8wNnSHnAiy",
        "outputId": "870009e2-bef4-4714-dfa3-af87b3587f7b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                 Investment\n",
              "AdaniPorts        94074.387\n",
              "Ambuja            74141.319\n",
              "Apollo          -128057.386\n",
              "AxisBank         -28097.387\n",
              "Bajaj             15184.184\n",
              "BoB             -130552.271\n",
              "Bata            -107578.120\n",
              "BlueStar          44477.798\n",
              "Camlin           -90574.375\n",
              "Castrol          125427.460\n",
              "Cipla             30938.393\n",
              "Deccan Gold      -26948.710\n",
              "GreavesCotton     62256.917\n",
              "Fortis             8250.969\n",
              "Glenmark          55858.452\n",
              "GodfreyPhillips  -53988.156\n",
              "Godrej           145944.937\n",
              "HCLTech          -79296.097\n",
              "HDFCbank          65303.592\n",
              "Hindalco          -6370.754\n",
              "HindustanPetrol  168527.802\n",
              "Imagica          -34834.245\n",
              "Infosys           45860.117\n",
              "IRCTC             10583.840\n",
              "ITC             -232462.700\n",
              "Kajaria           17648.202\n",
              "Kalyan           -74948.506\n",
              "Linc             -17622.686\n",
              "Lux              243965.291\n",
              "Max              -23330.565\n",
              "AndhraPaper      -83625.889\n",
              "Nerolac          133926.418\n",
              "ONGC            -119325.671\n",
              "Panasonic         10367.936\n",
              "Patanjali         47143.835\n",
              "Timex            -53073.541\n",
              "Raymond         -127203.355\n",
              "Reliance          51766.746\n",
              "Siemens         -101213.429\n",
              "SBI               40283.176\n",
              "SteelAuth        190399.563\n",
              "sunPharma       -124132.398\n",
              "TataComm         -46802.289\n",
              "TataSteel          4768.327\n",
              "Titan           -107578.127\n",
              "Ultramarine       11719.741\n",
              "Wipro            120386.663\n",
              "Wonderla         -36485.951\n",
              "YesBank           41683.389\n",
              "Nilkamal          73213.152"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-ded19b5f-d76d-4a7a-958b-a2bfff2835ff\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
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              "    .dataframe tbody tr th {\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Investment</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>AdaniPorts</th>\n",
              "      <td>94074.387</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ambuja</th>\n",
              "      <td>74141.319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Apollo</th>\n",
              "      <td>-128057.386</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AxisBank</th>\n",
              "      <td>-28097.387</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bajaj</th>\n",
              "      <td>15184.184</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BoB</th>\n",
              "      <td>-130552.271</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bata</th>\n",
              "      <td>-107578.120</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BlueStar</th>\n",
              "      <td>44477.798</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Camlin</th>\n",
              "      <td>-90574.375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Castrol</th>\n",
              "      <td>125427.460</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Cipla</th>\n",
              "      <td>30938.393</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Deccan Gold</th>\n",
              "      <td>-26948.710</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GreavesCotton</th>\n",
              "      <td>62256.917</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Fortis</th>\n",
              "      <td>8250.969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Glenmark</th>\n",
              "      <td>55858.452</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GodfreyPhillips</th>\n",
              "      <td>-53988.156</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Godrej</th>\n",
              "      <td>145944.937</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HCLTech</th>\n",
              "      <td>-79296.097</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HDFCbank</th>\n",
              "      <td>65303.592</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Hindalco</th>\n",
              "      <td>-6370.754</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HindustanPetrol</th>\n",
              "      <td>168527.802</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Imagica</th>\n",
              "      <td>-34834.245</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Infosys</th>\n",
              "      <td>45860.117</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>IRCTC</th>\n",
              "      <td>10583.840</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ITC</th>\n",
              "      <td>-232462.700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Kajaria</th>\n",
              "      <td>17648.202</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Kalyan</th>\n",
              "      <td>-74948.506</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Linc</th>\n",
              "      <td>-17622.686</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Lux</th>\n",
              "      <td>243965.291</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Max</th>\n",
              "      <td>-23330.565</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AndhraPaper</th>\n",
              "      <td>-83625.889</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Nerolac</th>\n",
              "      <td>133926.418</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ONGC</th>\n",
              "      <td>-119325.671</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Panasonic</th>\n",
              "      <td>10367.936</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Patanjali</th>\n",
              "      <td>47143.835</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Timex</th>\n",
              "      <td>-53073.541</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Raymond</th>\n",
              "      <td>-127203.355</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Reliance</th>\n",
              "      <td>51766.746</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Siemens</th>\n",
              "      <td>-101213.429</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>SBI</th>\n",
              "      <td>40283.176</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>SteelAuth</th>\n",
              "      <td>190399.563</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sunPharma</th>\n",
              "      <td>-124132.398</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TataComm</th>\n",
              "      <td>-46802.289</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TataSteel</th>\n",
              "      <td>4768.327</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Titan</th>\n",
              "      <td>-107578.127</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ultramarine</th>\n",
              "      <td>11719.741</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Wipro</th>\n",
              "      <td>120386.663</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Wonderla</th>\n",
              "      <td>-36485.951</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>YesBank</th>\n",
              "      <td>41683.389</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Nilkamal</th>\n",
              "      <td>73213.152</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
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              "      border-radius: 50%;\n",
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
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              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-ded19b5f-d76d-4a7a-958b-a2bfff2835ff button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-ded19b5f-d76d-4a7a-958b-a2bfff2835ff');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
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              "\n",
              "\n",
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              "\n",
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              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
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              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
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              "    30% {\n",
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              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-53a6d001-8e65-447e-a713-aa0fff97ab9a button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 121
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w1 = VarRisk_minimization(True)\n",
        "risk_return(w1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wSjdtJgCpMHp",
        "outputId": "bc1672f4-5d4d-4b33-f5ec-f6ba893efa7b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.016789432839753395, 0.033040269595241735)"
            ]
          },
          "metadata": {},
          "execution_count": 122
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def MADRisk_minimization(shortsell = True):\n",
        "  def objective1(xi):\n",
        "    return (np.abs(((r - exp_returns)*xi)).sum(axis = 1)).sum()/r.shape[0]\n",
        "  def objective2(xi):\n",
        "    return np.dot(xi.T, exp_returns).sum()\n",
        "  objective = lambda xi: 0.5*objective1(xi) - 0.5*objective2(xi) #weighted sum = 0.5\n",
        "  initial_weights = [1/50]*50\n",
        "  constraints = [\n",
        "      {'type': 'eq', 'fun': lambda w: sum(w) - 1, 'args': ()},\n",
        "      # {'type': 'ineq', 'fun': lambda w: sum(exp_returns*w) - target_return}\n",
        "  ]\n",
        "  if not shortsell:\n",
        "    bounds = [(0., None)]*(len(initial_weights))\n",
        "    result = minimize(objective, initial_weights, constraints = constraints, bounds = bounds)\n",
        "  else:\n",
        "    result = minimize(objective, initial_weights, constraints = constraints)\n",
        "  return result.x"
      ],
      "metadata": {
        "id": "xBrFxLnWlfNO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "result_MAD = MADRisk_minimization(True)\n",
        "total_capital = 100000\n",
        "investment = pd.DataFrame(result_MAD*total_capital)\n",
        "\n",
        "cols = returns.columns\n",
        "investment.set_index(cols, inplace = True)\n",
        "\n",
        "investment['Investment'] = investment[0]\n",
        "investment.drop([0],axis = 1, inplace = True)\n",
        "investment.round(3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "MAAITwQRi9V5",
        "outputId": "d8326389-5334-463f-fcfd-93ae046fbb4f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                 Investment\n",
              "AdaniPorts          -42.311\n",
              "Ambuja               44.106\n",
              "Apollo              -18.464\n",
              "AxisBank           5280.937\n",
              "Bajaj                12.711\n",
              "BoB                  38.748\n",
              "Bata                 12.592\n",
              "BlueStar             51.020\n",
              "Camlin               38.110\n",
              "Castrol            7369.935\n",
              "Cipla             10957.682\n",
              "Deccan Gold          23.826\n",
              "GreavesCotton         4.136\n",
              "Fortis               -0.338\n",
              "Glenmark             22.065\n",
              "GodfreyPhillips       8.914\n",
              "Godrej               -0.667\n",
              "HCLTech            3500.222\n",
              "HDFCbank          16588.140\n",
              "Hindalco             -2.900\n",
              "HindustanPetrol      25.074\n",
              "Imagica               2.655\n",
              "Infosys           11046.463\n",
              "IRCTC                -0.228\n",
              "ITC                7520.843\n",
              "Kajaria              16.105\n",
              "Kalyan                5.691\n",
              "Linc                 -7.974\n",
              "Lux                  48.636\n",
              "Max                  -1.146\n",
              "AndhraPaper          46.300\n",
              "Nerolac              40.140\n",
              "ONGC                  9.918\n",
              "Panasonic             8.077\n",
              "Patanjali             6.607\n",
              "Timex                -6.058\n",
              "Raymond              20.189\n",
              "Reliance           6266.472\n",
              "Siemens              65.403\n",
              "SBI                6200.449\n",
              "SteelAuth            48.580\n",
              "sunPharma          9737.217\n",
              "TataComm             -3.211\n",
              "TataSteel            14.085\n",
              "Titan                12.592\n",
              "Ultramarine           0.347\n",
              "Wipro             14909.725\n",
              "Wonderla              2.030\n",
              "YesBank              69.510\n",
              "Nilkamal              7.046"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-52f6ae85-6914-4cfb-a3b0-bc6f096b8d4d\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
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              "        vertical-align: middle;\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Investment</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>AdaniPorts</th>\n",
              "      <td>-42.311</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ambuja</th>\n",
              "      <td>44.106</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Apollo</th>\n",
              "      <td>-18.464</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AxisBank</th>\n",
              "      <td>5280.937</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bajaj</th>\n",
              "      <td>12.711</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BoB</th>\n",
              "      <td>38.748</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bata</th>\n",
              "      <td>12.592</td>\n",
              "    </tr>\n",
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              "      <th>BlueStar</th>\n",
              "      <td>51.020</td>\n",
              "    </tr>\n",
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              "      <th>Camlin</th>\n",
              "      <td>38.110</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Castrol</th>\n",
              "      <td>7369.935</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Cipla</th>\n",
              "      <td>10957.682</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Deccan Gold</th>\n",
              "      <td>23.826</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GreavesCotton</th>\n",
              "      <td>4.136</td>\n",
              "    </tr>\n",
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              "      <th>Fortis</th>\n",
              "      <td>-0.338</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Glenmark</th>\n",
              "      <td>22.065</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GodfreyPhillips</th>\n",
              "      <td>8.914</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Godrej</th>\n",
              "      <td>-0.667</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HCLTech</th>\n",
              "      <td>3500.222</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HDFCbank</th>\n",
              "      <td>16588.140</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Hindalco</th>\n",
              "      <td>-2.900</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HindustanPetrol</th>\n",
              "      <td>25.074</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Imagica</th>\n",
              "      <td>2.655</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Infosys</th>\n",
              "      <td>11046.463</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>IRCTC</th>\n",
              "      <td>-0.228</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ITC</th>\n",
              "      <td>7520.843</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Kajaria</th>\n",
              "      <td>16.105</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Kalyan</th>\n",
              "      <td>5.691</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Linc</th>\n",
              "      <td>-7.974</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Lux</th>\n",
              "      <td>48.636</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Max</th>\n",
              "      <td>-1.146</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AndhraPaper</th>\n",
              "      <td>46.300</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Nerolac</th>\n",
              "      <td>40.140</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ONGC</th>\n",
              "      <td>9.918</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Panasonic</th>\n",
              "      <td>8.077</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Patanjali</th>\n",
              "      <td>6.607</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Timex</th>\n",
              "      <td>-6.058</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Raymond</th>\n",
              "      <td>20.189</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Reliance</th>\n",
              "      <td>6266.472</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Siemens</th>\n",
              "      <td>65.403</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>SBI</th>\n",
              "      <td>6200.449</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>SteelAuth</th>\n",
              "      <td>48.580</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sunPharma</th>\n",
              "      <td>9737.217</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TataComm</th>\n",
              "      <td>-3.211</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TataSteel</th>\n",
              "      <td>14.085</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Titan</th>\n",
              "      <td>12.592</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ultramarine</th>\n",
              "      <td>0.347</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Wipro</th>\n",
              "      <td>14909.725</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Wonderla</th>\n",
              "      <td>2.030</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>YesBank</th>\n",
              "      <td>69.510</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Nilkamal</th>\n",
              "      <td>7.046</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "      margin-bottom: 4px;\n",
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              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
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              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-52f6ae85-6914-4cfb-a3b0-bc6f096b8d4d button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-52f6ae85-6914-4cfb-a3b0-bc6f096b8d4d');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
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              "\n",
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              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
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              "      --hover-bg-color: #E2EBFA;\n",
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              "      --disabled-fill-color: #AAA;\n",
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              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
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              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
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              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "    20% {\n",
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              "      border-left-color: var(--fill-color);\n",
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              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-928bf082-4757-4d7e-ba65-5970bc1b4dd8 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 124
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w2 = MADRisk_minimization(True)\n",
        "risk_return(w2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fy2bLBIgpY2M",
        "outputId": "fdd78fc3-35ce-4b1d-f6e3-7b6d36f2bb96"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(8.380932175360959e-05, -0.00013790756031195178)"
            ]
          },
          "metadata": {},
          "execution_count": 125
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def MMRisk_minimization(shortsell = True):\n",
        "  def objective1(xi):\n",
        "    return np.max(np.abs(xi - exp_returns))\n",
        "  def objective2(xi):\n",
        "    return np.dot(xi.T, exp_returns).sum()\n",
        "  objective = lambda xi: 0.5*objective1(xi) - 0.5*objective2(xi) #weighted sum = 0.5\n",
        "  initial_weights = [1/50]*50\n",
        "  constraints = [\n",
        "      {'type': 'eq', 'fun': lambda w: sum(w) - 1, 'args': ()},\n",
        "      # {'type': 'ineq', 'fun': lambda w: sum(w*exp_returns) - target_return}\n",
        "  ]\n",
        "  if not shortsell:\n",
        "    bounds = [(0., None)]*(len(initial_weights))\n",
        "    result = minimize(objective, initial_weights, constraints = constraints, bounds = bounds)\n",
        "  else:\n",
        "    result = minimize(objective, initial_weights, constraints = constraints)\n",
        "  return result.x"
      ],
      "metadata": {
        "id": "C6BVy43NrgW8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "result_MM = MMRisk_minimization(True)\n",
        "total_capital = 100000\n",
        "investment = pd.DataFrame(result_MM*total_capital)\n",
        "\n",
        "cols = returns.columns\n",
        "investment.set_index(cols, inplace = True)\n",
        "\n",
        "investment['Investment'] = investment[0]\n",
        "investment.drop([0],axis = 1, inplace = True)\n",
        "investment.round(3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "h-c94DruvbyR",
        "outputId": "5c4f1101-73ac-49b2-e2b6-872f135792d8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                 Investment\n",
              "AdaniPorts         2103.194\n",
              "Ambuja             2093.926\n",
              "Apollo             1997.462\n",
              "AxisBank           2053.056\n",
              "Bajaj              2102.790\n",
              "BoB                1890.451\n",
              "Bata               2003.592\n",
              "BlueStar           2107.740\n",
              "Camlin             1949.262\n",
              "Castrol            2103.487\n",
              "Cipla              2063.491\n",
              "Deccan Gold        1993.670\n",
              "GreavesCotton      2105.806\n",
              "Fortis             2082.141\n",
              "Glenmark           2102.580\n",
              "GodfreyPhillips    1945.622\n",
              "Godrej             2104.379\n",
              "HCLTech            2083.541\n",
              "HDFCbank           2102.661\n",
              "Hindalco           2088.656\n",
              "HindustanPetrol    2105.470\n",
              "Imagica            1420.867\n",
              "Infosys            2104.182\n",
              "IRCTC              2138.435\n",
              "ITC                1850.241\n",
              "Kajaria            2057.624\n",
              "Kalyan             1657.150\n",
              "Linc               1765.758\n",
              "Lux                2113.420\n",
              "Max                1934.985\n",
              "AndhraPaper        1992.408\n",
              "Nerolac            2109.339\n",
              "ONGC               2024.760\n",
              "Panasonic          2103.319\n",
              "Patanjali          2105.311\n",
              "Timex              1543.161\n",
              "Raymond            1278.859\n",
              "Reliance           2092.458\n",
              "Siemens            1928.775\n",
              "SBI                2047.974\n",
              "SteelAuth          2106.547\n",
              "sunPharma          1985.711\n",
              "TataComm           2060.666\n",
              "TataSteel          2184.937\n",
              "Titan              2003.592\n",
              "Ultramarine        2089.421\n",
              "Wipro              2105.777\n",
              "Wonderla           1809.566\n",
              "YesBank            2098.174\n",
              "Nilkamal           2103.607"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-c6c354b9-d60c-440c-93e2-82a32db31e38\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Investment</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>AdaniPorts</th>\n",
              "      <td>2103.194</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ambuja</th>\n",
              "      <td>2093.926</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Apollo</th>\n",
              "      <td>1997.462</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AxisBank</th>\n",
              "      <td>2053.056</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bajaj</th>\n",
              "      <td>2102.790</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BoB</th>\n",
              "      <td>1890.451</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bata</th>\n",
              "      <td>2003.592</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>BlueStar</th>\n",
              "      <td>2107.740</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Camlin</th>\n",
              "      <td>1949.262</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Castrol</th>\n",
              "      <td>2103.487</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Cipla</th>\n",
              "      <td>2063.491</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Deccan Gold</th>\n",
              "      <td>1993.670</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GreavesCotton</th>\n",
              "      <td>2105.806</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Fortis</th>\n",
              "      <td>2082.141</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Glenmark</th>\n",
              "      <td>2102.580</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GodfreyPhillips</th>\n",
              "      <td>1945.622</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Godrej</th>\n",
              "      <td>2104.379</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HCLTech</th>\n",
              "      <td>2083.541</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HDFCbank</th>\n",
              "      <td>2102.661</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Hindalco</th>\n",
              "      <td>2088.656</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HindustanPetrol</th>\n",
              "      <td>2105.470</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Imagica</th>\n",
              "      <td>1420.867</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Infosys</th>\n",
              "      <td>2104.182</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>IRCTC</th>\n",
              "      <td>2138.435</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ITC</th>\n",
              "      <td>1850.241</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Kajaria</th>\n",
              "      <td>2057.624</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Kalyan</th>\n",
              "      <td>1657.150</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Linc</th>\n",
              "      <td>1765.758</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Lux</th>\n",
              "      <td>2113.420</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Max</th>\n",
              "      <td>1934.985</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AndhraPaper</th>\n",
              "      <td>1992.408</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Nerolac</th>\n",
              "      <td>2109.339</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ONGC</th>\n",
              "      <td>2024.760</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Panasonic</th>\n",
              "      <td>2103.319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Patanjali</th>\n",
              "      <td>2105.311</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Timex</th>\n",
              "      <td>1543.161</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Raymond</th>\n",
              "      <td>1278.859</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Reliance</th>\n",
              "      <td>2092.458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Siemens</th>\n",
              "      <td>1928.775</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>SBI</th>\n",
              "      <td>2047.974</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>SteelAuth</th>\n",
              "      <td>2106.547</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sunPharma</th>\n",
              "      <td>1985.711</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TataComm</th>\n",
              "      <td>2060.666</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TataSteel</th>\n",
              "      <td>2184.937</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Titan</th>\n",
              "      <td>2003.592</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ultramarine</th>\n",
              "      <td>2089.421</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Wipro</th>\n",
              "      <td>2105.777</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Wonderla</th>\n",
              "      <td>1809.566</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>YesBank</th>\n",
              "      <td>2098.174</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Nilkamal</th>\n",
              "      <td>2103.607</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "  <style>\n",
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              "      width: 32px;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
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              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "  </style>\n",
              "\n",
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              "      const buttonEl =\n",
              "        document.querySelector('#df-c6c354b9-d60c-440c-93e2-82a32db31e38 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-c6c354b9-d60c-440c-93e2-82a32db31e38');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "        element.appendChild(docLink);\n",
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              "\n",
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              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
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              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
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              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
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              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
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              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
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              "    30% {\n",
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              "      border-left-color: var(--fill-color);\n",
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              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-07e74b58-ee5d-4926-92f0-378e54bd1462 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 127
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w3 = MMRisk_minimization(True)\n",
        "risk_return(w3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iXh74eOqvgIS",
        "outputId": "000ac639-0869-4368-ef0c-d73b59401072"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0001857579506295628, 0.00022352436848140566)"
            ]
          },
          "metadata": {},
          "execution_count": 128
        }
      ]
    }
  ]
}