MINMAX MAD Visualization.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)"
      ]
    },
    {
      "cell_type": "code",
      "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(axis = 0, inplace = True)\n",
        "returns.head()"
      ],
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          "height": 460
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        "outputId": "c43519e6-0bb3-4b01-9233-4560908b0710"
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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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              "      <th>Ambuja</th>\n",
              "      <th>Apollo</th>\n",
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              "      <th>Titan</th>\n",
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              "      <th></th>\n",
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              "      <th>01-Sep-23</th>\n",
              "      <td>-0.027492</td>\n",
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              "      <td>0.007811</td>\n",
              "      <td>-0.018739</td>\n",
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              "      <td>-0.004227</td>\n",
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              "      <td>0.019359</td>\n",
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              "      <th>30-Aug-23</th>\n",
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              "      <td>0.004464</td>\n",
              "      <td>-0.001831</td>\n",
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              "      <th>29-Aug-23</th>\n",
              "      <td>-0.022914</td>\n",
              "      <td>-0.007691</td>\n",
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              "      <td>0.010091</td>\n",
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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",
        "stddev_returns = r.std(axis = 0)\n",
        "covariance_matrix = np.array(returns.cov())\n",
        "\n",
        "def obj_function(xi) :\n",
        "  return (((r - exp_returns)*xi).sum(axis = 1)).sum()/r.shape[0]\n",
        "target_return = 0.1\n",
        "initial_weights = [1/50]*50\n",
        "\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",
        "]"
      ],
      "metadata": {
        "id": "0yKjO0ced6y_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "result = minimize(obj_function, initial_weights, constraints = constraints)\n",
        "print(\"MinMax portfolio weights: \")\n",
        "print(result.x)\n",
        "print(\"MinMax portfolio returns: \", np.sum(result.x * exp_returns))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aZU6uhS1CiSR",
        "outputId": "e49a122c-2d6c-4026-c1b0-eedea3878b21"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MinMax portfolio weights: \n",
            "[ 0.0129876  -0.04334112 -0.21803611 -0.12525076 -0.00944126 -0.34883747\n",
            " -0.27321623  0.26558921 -0.28713481  0.02926611 -0.10521753 -0.22292945\n",
            "  0.15815926 -0.07328493 -0.02115295 -0.29019922  0.0788211  -0.07024152\n",
            " -0.01665831 -0.05708962  0.13947384 -0.60765399  0.06789657  1.97134744\n",
            " -0.3861272  -0.11655545 -0.50366799 -0.43772872  0.58127121 -0.29947802\n",
            " -0.22314652  0.3544886  -0.17447109  0.01991356  0.13061054 -0.55791868\n",
            " -0.68174526 -0.04685016 -0.30669612 -0.13300273  0.19928509 -0.23304004\n",
            " -0.11130592  4.5555207  -0.27321623 -0.055262    0.15650304 -0.41352946\n",
            " -0.03362818  0.03592119]\n",
            "MinMax portfolio returns:  0.0999999972694877\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def MAD_portfolio(target_return, shortsell = True):\n",
        "  obj_fn = lambda xi: (((r - exp_returns)*xi).sum(axis = 1)).sum()/r.shape[0]\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)) #all positive\n",
        "    result = minimize(obj_fn, initial_weights, constraints = constraints, bounds = bounds)\n",
        "  else:\n",
        "    result = minimize(obj_fn, initial_weights, constraints = constraints)\n",
        "  return result.x\n",
        "\n",
        "def Minmax_portfolio(target_return, shortsell = True):\n",
        "  obj_fn = lambda xi: np.max(np.abs(xi - exp_returns))\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)) #all positive\n",
        "    result = minimize(obj_fn, initial_weights, constraints = constraints, bounds = bounds)\n",
        "  else:\n",
        "    result = minimize(obj_fn, initial_weights, constraints = constraints)\n",
        "  return result.x"
      ],
      "metadata": {
        "id": "fhIzTt-iFhQ2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def Markowitz_portfolio(target_return, shortsell = True):\n",
        "  obj_fn = lambda xi: np.dot(xi.T, np.dot(covariance_matrix, xi))\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)) #all positive\n",
        "    result = minimize(obj_fn, initial_weights, constraints = constraints, bounds = bounds)\n",
        "  else:\n",
        "    result = minimize(obj_fn, initial_weights, constraints = constraints)\n",
        "  return result.x"
      ],
      "metadata": {
        "id": "f4kLX05YLbVc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def risk_return(weights):\n",
        "  risk = np.dot(weights.T, np.dot(covariance_matrix, weights))\n",
        "  returns = np.dot(weights.T, exp_returns)\n",
        "  return risk, returns"
      ],
      "metadata": {
        "id": "Ig689QYtMOOs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w1 = MAD_portfolio(0.1, True)\n",
        "risk_return(w1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hGHOlS6LMfLI",
        "outputId": "087949f6-75bd-4251-cb39-e93a87cbf127"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3.056213993941731, 0.0999999972694877)"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w2 = Minmax_portfolio(0.1)\n",
        "risk_return(w2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y_EKycYvMlRR",
        "outputId": "a13e05d7-6a5b-42db-a7d3-9aa794a0b072"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.8044797851168234, 0.10000000035520415)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w3 = Markowitz_portfolio(0,1)\n",
        "risk_return(w3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0AOJa1mOMqGf",
        "outputId": "38648ac2-bfdd-4d10-85f9-4cdfa5edfdb6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(9.770191275263425e-05, 2.956279962651865e-05)"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Visualizing MinMax, Markowitz, MAD models"
      ],
      "metadata": {
        "id": "zU7pTtKfM6Yx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "markowitz = []\n",
        "minmax = []\n",
        "mad = []\n",
        "\n",
        "for i in range(5, 35, 2):\n",
        "  markowitz += [risk_return(Markowitz_portfolio(i/100))]\n",
        "  minmax += [risk_return(Minmax_portfolio(i/100))]\n",
        "  mad += [risk_return(MAD_portfolio(i/100))]"
      ],
      "metadata": {
        "id": "k6wvJzhPMx4L"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_line(tuples, colour):\n",
        "  x_values = [tuple[0] for tuple in tuples]\n",
        "  y_values = [tuple[1] for tuple in tuples]\n",
        "  plt.plot(x_values, y_values, color = colour)\n",
        "\n",
        "plot_line(markowitz, 'red')\n",
        "plot_line(minmax, 'green')\n",
        "plot_line(mad, 'blue')\n",
        "\n",
        "plt.legend(['Markowitz', 'Minmax', 'MAD'])\n",
        "plt.xlabel('Risk')\n",
        "plt.ylabel('Returns')\n",
        "plt.title('Portfolio Visualization')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "T4DPLr74NlUN",
        "outputId": "d5694d1f-6613-4229-b311-cb76d221183f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "VjSEGaa0OFOV"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}