authors/fdabrandao/amplpyfinance/amplpyfinance_vs_amplpy.ipynb

{
  "cells": [
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Financial Portfolio Optimization with amplpy\n",
        "[![amplpyfinance_vs_amplpy.ipynb](https://img.shields.io/badge/github-%23121011.svg?logo=github)](https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/amplpyfinance/amplpyfinance_vs_amplpy.ipynb) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/amplpyfinance/amplpyfinance_vs_amplpy.ipynb) [![Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/amplpyfinance/amplpyfinance_vs_amplpy.ipynb) [![Gradient](https://assets.paperspace.io/img/gradient-badge.svg)](https://console.paperspace.com/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/amplpyfinance/amplpyfinance_vs_amplpy.ipynb) [![Open In SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/amplpyfinance/amplpyfinance_vs_amplpy.ipynb) [![Hits](https://h.ampl.com/https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/amplpyfinance/amplpyfinance_vs_amplpy.ipynb)](https://colab.ampl.com)\n",
        "\n",
        "Description: Financial Portfolio Optimization with amplpy and amplpyfinance\n",
        "\n",
        "Tags: amplpy, amplpyfinance, finance\n",
        "\n",
        "Notebook author: Filipe Brandão <<fdabrandao@gmail.com>>\n",
        "\n",
        "Model author: Harry Markowitz\n",
        "\n",
        "References:\n",
        "1. amplpy: https://amplpy.readthedocs.io/\n",
        "2. amplpyfinance: https://amplpyfinance.readthedocs.io/\n",
        "3. Cornuejols, G., and Tütüncü, R. (2018). *Optimization Methods in Finance* (2nd edition): Bond Dedication example. Cambridge University Press."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Install dependencies\n",
        "%pip install -q amplpy pandas matplotlib yfinance amplpyfinance"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Google Colab & Kaggle integration\n",
        "from amplpy import AMPL, ampl_notebook\n",
        "\n",
        "ampl = ampl_notebook(\n",
        "    modules=[\"gurobi\"],  # modules to install\n",
        "    license_uuid=\"default\",  # license to use\n",
        ")  # instantiate AMPL object and register magics"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Downloading data and callculate `mu` and `S`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[*********************100%***********************]  15 of 15 completed\n"
          ]
        }
      ],
      "source": [
        "from pypfopt import expected_returns, risk_models\n",
        "import yfinance as yf\n",
        "\n",
        "tickers = [\n",
        "    \"MSFT\",\n",
        "    \"AMZN\",\n",
        "    \"KO\",\n",
        "    \"MA\",\n",
        "    \"COST\",\n",
        "    \"LUV\",\n",
        "    \"XOM\",\n",
        "    \"PFE\",\n",
        "    \"JPM\",\n",
        "    \"UNH\",\n",
        "    \"ACN\",\n",
        "    \"DIS\",\n",
        "    \"GILD\",\n",
        "    \"F\",\n",
        "    \"TSLA\",\n",
        "]\n",
        "\n",
        "ohlc = yf.download(tickers, period=\"max\")\n",
        "prices = ohlc[\"Adj Close\"].dropna(how=\"all\")\n",
        "mu = expected_returns.capm_return(prices)\n",
        "S = risk_models.CovarianceShrinkage(prices).ledoit_wolf()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Minimize volatility \n",
        "\n",
        "Using `EfficientFrontierWithAMPL.min_volatility`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.01442725331\n",
            "11 barrier iterations\n",
            "No basis.\n",
            "Annual volatility: 12.0%\n"
          ]
        }
      ],
      "source": [
        "from amplpyfinance import EfficientFrontierWithAMPL\n",
        "\n",
        "ef = EfficientFrontierWithAMPL(None, S, weight_bounds=(0, 1), solver=\"gurobi\")\n",
        "ef.min_volatility()\n",
        "_, sigma1, _ = ef.portfolio_performance(verbose=True)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Using `amplpy` directly:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.01442725331\n",
            "11 barrier iterations\n",
            "No basis.\n",
            "Annual volatility: 12.0%\n"
          ]
        }
      ],
      "source": [
        "from amplpy import AMPL\n",
        "import pandas as pd\n",
        "\n",
        "ampl = AMPL()\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    set A ordered;\n",
        "    param S{A, A};\n",
        "    param lb default 0;\n",
        "    param ub default 1;\n",
        "    var w{A} >= lb <= ub;\n",
        "    minimize portfolio_variance:\n",
        "        sum {i in A, j in A} w[i] * S[i, j] * w[j];\n",
        "    s.t. portfolio_weights:\n",
        "        sum {i in A} w[i] = 1;\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.set[\"A\"] = ef.tickers\n",
        "ampl.param[\"S\"] = pd.DataFrame(ef.cov_matrix, index=ef.tickers, columns=ef.tickers)\n",
        "ampl.option[\"solver\"] = \"gurobi\"\n",
        "ampl.solve()\n",
        "sigma = ampl.get_value(\"sqrt(sum {i in A, j in A} w[i] * S[i, j] * w[j])\")\n",
        "print(f\"Annual volatility: {sigma*100:.1f}%\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<AxesSubplot:>"
            ]
          },
          "execution_count": 30,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pd.Series(ef.clean_weights()).plot.barh()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Maximize return for a target risk\n",
        "\n",
        "Using `EfficientFrontierWithAMPL.efficient_risk`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.2821809144\n",
            "10 barrier iterations\n",
            "No basis.\n",
            "No dual variables returned.\n",
            "Expected annual return: 28.2%\n",
            "Annual volatility: 15.0%\n",
            "Sharpe Ratio: 1.75\n"
          ]
        }
      ],
      "source": [
        "from amplpyfinance import EfficientFrontierWithAMPL\n",
        "\n",
        "ef = EfficientFrontierWithAMPL(mu, S, solver=\"gurobi\")\n",
        "ef.efficient_risk(target_volatility=0.15)\n",
        "mu1, sigma1, sharpe1 = ef.portfolio_performance(verbose=True)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Using `amplpy` directly:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.2821809144\n",
            "10 barrier iterations\n",
            "No basis.\n",
            "No dual variables returned.\n",
            "Expected annual return: 28.2%\n",
            "Annual volatility: 15.0%\n",
            "Sharpe Ratio: 1.75\n"
          ]
        }
      ],
      "source": [
        "from amplpy import AMPL\n",
        "\n",
        "ampl = AMPL()\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    param target_volatility;\n",
        "    param market_neutral default 0;\n",
        "    set A ordered;\n",
        "    param S{A, A};\n",
        "    param mu{A} default 0;\n",
        "    \n",
        "    param lb default 0;\n",
        "    param ub default 1;\n",
        "    var w{A} >= lb <= ub;\n",
        "    maximize portfolio_return:\n",
        "        sum {i in A} mu[i] * w[i];\n",
        "    s.t. portfolio_variance:\n",
        "        sum {i in A, j in A} w[i] * S[i, j] * w[j] <= target_volatility^2;\n",
        "    s.t. portfolio_weights:\n",
        "        sum {i in A} w[i] = if market_neutral then 0 else 1;\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.set[\"A\"] = ef.tickers\n",
        "ampl.param[\"S\"] = pd.DataFrame(ef.cov_matrix, index=ef.tickers, columns=ef.tickers)\n",
        "ampl.param[\"mu\"] = ef.expected_returns\n",
        "ampl.param[\"target_volatility\"] = 0.15\n",
        "ampl.param[\"market_neutral\"] = False\n",
        "ampl.option[\"solver\"] = \"gurobi\"\n",
        "ampl.solve()\n",
        "sigma2 = ampl.get_value(\"sqrt(sum {i in A, j in A} w[i] * S[i, j] * w[j])\")\n",
        "mu2 = ampl.get_value(\"sum {i in A} mu[i] * w[i]\")\n",
        "risk_free_rate = 0.02\n",
        "sharpe2 = (mu2 - risk_free_rate) / sigma2\n",
        "print(f\"Expected annual return: {mu2*100:.1f}%\")\n",
        "print(f\"Annual volatility: {sigma2*100:.1f}%\")\n",
        "print(f\"Sharpe Ratio: {sharpe2:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<AxesSubplot:>"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pd.Series(ef.clean_weights()).plot.barh()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Minimizing volatility for a given target return\n",
        "\n",
        "Using `EfficientFrontierWithAMPL.efficient_return`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.7924129059\n",
            "1 simplex iterations\n",
            "Gurobi 9.5.1: optimal solution; objective 0.008882889913\n",
            "9 barrier iterations\n",
            "No basis.\n",
            "Expected annual return: 7.0%\n",
            "Annual volatility: 9.4%\n",
            "Sharpe Ratio: 0.53\n"
          ]
        }
      ],
      "source": [
        "from amplpyfinance import EfficientFrontierWithAMPL\n",
        "\n",
        "ef = EfficientFrontierWithAMPL(mu, S, weight_bounds=(None, None), solver=\"gurobi\")\n",
        "ef.efficient_return(target_return=0.07, market_neutral=True)\n",
        "mu1, sigma1, sharpe1 = ef.portfolio_performance(verbose=True)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Using `amplply` directly:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.008882889913\n",
            "9 barrier iterations\n",
            "No basis.\n",
            "Expected annual return: 7.0%\n",
            "Annual volatility: 9.4%\n",
            "Sharpe Ratio: 0.53\n"
          ]
        }
      ],
      "source": [
        "from amplpy import AMPL\n",
        "\n",
        "ampl = AMPL()\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    param target_return;\n",
        "    param market_neutral default 0;\n",
        "\n",
        "    set A ordered;\n",
        "    param S{A, A};\n",
        "    param mu{A} default 0;\n",
        "\n",
        "    param lb default 0;\n",
        "    param ub default 1;\n",
        "    var w{A} >= lb <= ub;\n",
        "\n",
        "    minimize portfolio_variance:\n",
        "        sum {i in A, j in A} w[i] * S[i, j] * w[j];\n",
        "    s.t. portfolio__return:\n",
        "        sum {i in A} mu[i] * w[i] >= target_return;\n",
        "    s.t. portfolio_weights:\n",
        "        sum {i in A} w[i] = if market_neutral then 0 else 1;\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.set[\"A\"] = ef.tickers\n",
        "ampl.param[\"S\"] = pd.DataFrame(ef.cov_matrix, index=ef.tickers, columns=ef.tickers)\n",
        "ampl.param[\"mu\"] = ef.expected_returns\n",
        "ampl.param[\"target_return\"] = 0.07\n",
        "ampl.param[\"market_neutral\"] = True\n",
        "ampl.param[\"lb\"] = -1\n",
        "ampl.option[\"solver\"] = \"gurobi\"\n",
        "ampl.solve()\n",
        "sigma2 = ampl.get_value(\"sqrt(sum {i in A, j in A} w[i] * S[i, j] * w[j])\")\n",
        "mu2 = ampl.get_value(\"sum {i in A} mu[i] * w[i]\")\n",
        "risk_free_rate = 0.02\n",
        "sharpe2 = (mu2 - risk_free_rate) / sigma2\n",
        "print(f\"Expected annual return: {mu2*100:.1f}%\")\n",
        "print(f\"Annual volatility: {sigma2*100:.1f}%\")\n",
        "print(f\"Sharpe Ratio: {sharpe2:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<AxesSubplot:>"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pd.Series(ef.clean_weights()).plot.barh()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Maximize the Sharpe Ratio\n",
        "\n",
        "Using `EfficientFrontierWithAMPL.max_sharpe`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.3017535499\n",
            "13 barrier iterations\n",
            "No basis.\n",
            "Expected annual return: 25.5%\n",
            "Annual volatility: 12.9%\n",
            "Sharpe Ratio: 1.82\n"
          ]
        }
      ],
      "source": [
        "from amplpyfinance import EfficientFrontierWithAMPL\n",
        "\n",
        "ef = EfficientFrontierWithAMPL(mu, S, solver=\"gurobi\")\n",
        "ef.max_sharpe()\n",
        "mu1, sigma1, sharpe1 = ef.portfolio_performance(verbose=True)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Using `amplpy` directly:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.3017535499\n",
            "13 barrier iterations\n",
            "No basis.\n",
            "Expected annual return: 25.5%\n",
            "Annual volatility: 12.9%\n",
            "Sharpe Ratio: 1.82\n"
          ]
        }
      ],
      "source": [
        "from amplpy import AMPL\n",
        "\n",
        "ampl = AMPL()\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    param risk_free_rate default 0.02;\n",
        "\n",
        "    set A ordered;\n",
        "    param S{A, A};\n",
        "    param mu{A} default 0;\n",
        "\n",
        "    var k >= 0;\n",
        "    var z{i in A} >= 0;  # scaled weights\n",
        "    var w{i in A} = z[i] / k;\n",
        "\n",
        "    minimize portfolio_sharpe:\n",
        "        sum {i in A, j in A} z[i] * S[i, j] * z[j];\n",
        "    s.t. muz:\n",
        "        sum {i in A} (mu[i] - risk_free_rate) * z[i] = 1;\n",
        "    s.t. portfolio_weights:\n",
        "        sum {i in A}  z[i] = k;\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.set[\"A\"] = ef.tickers\n",
        "ampl.param[\"S\"] = pd.DataFrame(ef.cov_matrix, index=ef.tickers, columns=ef.tickers)\n",
        "ampl.param[\"mu\"] = ef.expected_returns\n",
        "ampl.option[\"solver\"] = \"gurobi\"\n",
        "ampl.solve()\n",
        "sigma2 = ampl.get_value(\"sqrt(sum {i in A, j in A} w[i] * S[i, j] * w[j])\")\n",
        "mu2 = ampl.get_value(\"sum {i in A} mu[i] * w[i]\")\n",
        "risk_free_rate = 0.02\n",
        "sharpe2 = (mu2 - risk_free_rate) / sigma2\n",
        "print(f\"Expected annual return: {mu2*100:.1f}%\")\n",
        "print(f\"Annual volatility: {sigma2*100:.1f}%\")\n",
        "print(f\"Sharpe Ratio: {sharpe2:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<AxesSubplot:>"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pd.Series(ef.clean_weights()).plot.barh()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Maximize quadratic utility\n",
        "\n",
        "Quadratic utility: $\\max_w w^T \\mu - \\frac \\delta 2 w^T \\Sigma w$\n",
        "\n",
        "Using `EfficientFrontierWithAMPL.max_quadratic_utility`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.2710034744\n",
            "11 barrier iterations\n",
            "No basis.\n",
            "Expected annual return: 31.2%\n",
            "Annual volatility: 20.1%\n",
            "Sharpe Ratio: 1.45\n"
          ]
        }
      ],
      "source": [
        "ef = EfficientFrontierWithAMPL(mu, S, weight_bounds=(0, 1), solver=\"gurobi\")\n",
        "ef.max_quadratic_utility(risk_aversion=2, market_neutral=False)\n",
        "mu1, sigma1, sharpe1 = ef.portfolio_performance(verbose=True)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Using `amplpy` directly:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.2710034744\n",
            "11 barrier iterations\n",
            "No basis.\n",
            "Expected annual return: 31.2%\n",
            "Annual volatility: 20.1%\n",
            "Sharpe Ratio: 1.45\n"
          ]
        }
      ],
      "source": [
        "from amplpy import AMPL\n",
        "\n",
        "ampl = AMPL()\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    param risk_aversion default 1;\n",
        "    param market_neutral default 0;\n",
        "\n",
        "    set A ordered;\n",
        "    param S{A, A};\n",
        "    param mu{A} default 0;\n",
        "    \n",
        "    param lb default 0;\n",
        "    param ub default 1;\n",
        "    var w{A} >= lb <= ub;\n",
        "\n",
        "    maximize quadratic_utility:\n",
        "        sum {i in A} mu[i] * w[i]\n",
        "        - 0.5 * risk_aversion * sum {i in A, j in A} w[i] * S[i, j] * w[j];\n",
        "    s.t. portfolio_weights:\n",
        "        sum {i in A} w[i] = if market_neutral then 0 else 1;\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.set[\"A\"] = ef.tickers\n",
        "ampl.param[\"S\"] = pd.DataFrame(ef.cov_matrix, index=ef.tickers, columns=ef.tickers)\n",
        "ampl.param[\"mu\"] = ef.expected_returns\n",
        "ampl.param[\"risk_aversion\"] = 2\n",
        "ampl.param[\"market_neutral\"] = False\n",
        "ampl.option[\"solver\"] = \"gurobi\"\n",
        "ampl.solve()\n",
        "sigma2 = ampl.get_value(\"sqrt(sum {i in A, j in A} w[i] * S[i, j] * w[j])\")\n",
        "mu2 = ampl.get_value(\"sum {i in A} mu[i] * w[i]\")\n",
        "risk_free_rate = 0.02\n",
        "sharpe2 = (mu2 - risk_free_rate) / sigma2\n",
        "print(f\"Expected annual return: {mu2*100:.1f}%\")\n",
        "print(f\"Annual volatility: {sigma2*100:.1f}%\")\n",
        "print(f\"Sharpe Ratio: {sharpe2:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<AxesSubplot:>"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pd.Series(ef.clean_weights()).plot.barh()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Maximize return for a target risk with sector constraints\n",
        "\n",
        "Using `EfficientFrontierWithAMPL.add_sector_constraints`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {},
      "outputs": [],
      "source": [
        "sector_mapper = {\n",
        "    \"MSFT\": \"Tech\",\n",
        "    \"AMZN\": \"Consumer Discretionary\",\n",
        "    \"KO\": \"Consumer Staples\",\n",
        "    \"MA\": \"Financial Services\",\n",
        "    \"COST\": \"Consumer Staples\",\n",
        "    \"LUV\": \"Aerospace\",\n",
        "    \"XOM\": \"Energy\",\n",
        "    \"PFE\": \"Healthcare\",\n",
        "    \"JPM\": \"Financial Services\",\n",
        "    \"UNH\": \"Healthcare\",\n",
        "    \"ACN\": \"Misc\",\n",
        "    \"DIS\": \"Media\",\n",
        "    \"GILD\": \"Healthcare\",\n",
        "    \"F\": \"Auto\",\n",
        "    \"TSLA\": \"Auto\",\n",
        "}\n",
        "\n",
        "sector_lower = {\n",
        "    \"Consumer Staples\": 0.1,  # at least 10% to staples\n",
        "    \"Tech\": 0.05  # at least 5% to tech\n",
        "    # For all other sectors, it will be assumed there is no lower bound\n",
        "}\n",
        "\n",
        "sector_upper = {\"Tech\": 0.2, \"Aerospace\": 0.1, \"Energy\": 0.1, \"Auto\": 0.15}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.2768198377\n",
            "9 barrier iterations\n",
            "No basis.\n",
            "No dual variables returned.\n",
            "Expected annual return: 27.7%\n",
            "Annual volatility: 15.0%\n",
            "Sharpe Ratio: 1.71\n"
          ]
        }
      ],
      "source": [
        "ef = EfficientFrontierWithAMPL(mu, S)\n",
        "ef.add_sector_constraints(sector_mapper, sector_lower, sector_upper)\n",
        "ef.efficient_risk(target_volatility=0.15)\n",
        "mu1, sigma1, sharpe1 = ef.portfolio_performance(verbose=True)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Using `amplpy` directly:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.2768198377\n",
            "9 barrier iterations\n",
            "No basis.\n",
            "No dual variables returned.\n",
            "Expected annual return: 27.7%\n",
            "Annual volatility: 15.0%\n",
            "Sharpe Ratio: 1.71\n"
          ]
        }
      ],
      "source": [
        "from amplpy import AMPL\n",
        "\n",
        "ampl = AMPL()\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    param target_volatility;\n",
        "    param market_neutral default 0;\n",
        "\n",
        "    set A ordered;\n",
        "    param S{A, A};\n",
        "    param mu{A} default 0;\n",
        "\n",
        "    param lb default 0;\n",
        "    param ub default 1;\n",
        "    var w{A} >= lb <= ub;\n",
        "    \n",
        "    maximize portfolio_return:\n",
        "        sum {i in A} mu[i] * w[i];\n",
        "    s.t. portfolio_variance:\n",
        "        sum {i in A, j in A} w[i] * S[i, j] * w[j] <= target_volatility^2;\n",
        "    s.t. portfolio_weights:\n",
        "        sum {i in A} w[i] = 1;\n",
        "\n",
        "    set SECTORS default {};\n",
        "    set SECTOR_MEMBERS{SECTORS};\n",
        "    param sector_lower{SECTORS} default -Infinity;\n",
        "    param sector_upper{SECTORS} default Infinity;\n",
        "    s.t. sector_constraints_lower{s in SECTORS: sector_lower[s] != -Infinity}:\n",
        "        sum {i in SECTOR_MEMBERS[s]} w[i] >= sector_lower[s];\n",
        "    s.t. sector_constraints_upper{s in SECTORS: sector_upper[s] != Infinity}:\n",
        "        sum {i in SECTOR_MEMBERS[s]} w[i] <= sector_upper[s];\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.set[\"A\"] = ef.tickers\n",
        "ampl.param[\"S\"] = pd.DataFrame(ef.cov_matrix, index=ef.tickers, columns=ef.tickers)\n",
        "ampl.param[\"mu\"] = ef.expected_returns\n",
        "ampl.param[\"target_volatility\"] = 0.15\n",
        "sectors = set(sector_mapper.values())\n",
        "ampl.set[\"SECTORS\"] = sectors\n",
        "for sector in sectors:\n",
        "    ampl.set[\"SECTOR_MEMBERS\"][sector] = [\n",
        "        ticker for ticker, s in sector_mapper.items() if s == sector\n",
        "    ]\n",
        "ampl.param[\"sector_lower\"] = sector_lower\n",
        "ampl.param[\"sector_upper\"] = sector_upper\n",
        "ampl.option[\"solver\"] = \"gurobi\"\n",
        "ampl.solve()\n",
        "sigma2 = ampl.get_value(\"sqrt(sum {i in A, j in A} w[i] * S[i, j] * w[j])\")\n",
        "mu2 = ampl.get_value(\"sum {i in A} mu[i] * w[i]\")\n",
        "risk_free_rate = 0.02\n",
        "sharpe2 = (mu2 - risk_free_rate) / sigma2\n",
        "print(f\"Expected annual return: {mu2*100:.1f}%\")\n",
        "print(f\"Annual volatility: {sigma2*100:.1f}%\")\n",
        "print(f\"Sharpe Ratio: {sharpe2:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<AxesSubplot:>"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pd.Series(ef.clean_weights()).plot.barh()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Maximize return for a target risk with cardinality constraints\n",
        "\n",
        "Using `EfficientFrontierWithAMPL`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.2665926133\n",
            "926 simplex iterations\n",
            "204 branch-and-cut nodes\n",
            "No dual variables returned.\n",
            "Expected annual return: 26.7%\n",
            "Annual volatility: 15.0%\n",
            "Sharpe Ratio: 1.64\n"
          ]
        }
      ],
      "source": [
        "ef = EfficientFrontierWithAMPL(mu, S)\n",
        "ef.ampl.param[\"card_ub\"] = 3\n",
        "ef.efficient_risk(target_volatility=0.15)\n",
        "mu1, sigma1, sharpe1 = ef.portfolio_performance(verbose=True)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Using `amplpy` directly:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 9.5.1: optimal solution; objective 0.2665926133\n",
            "926 simplex iterations\n",
            "204 branch-and-cut nodes\n",
            "No dual variables returned.\n",
            "Expected annual return: 26.7%\n",
            "Annual volatility: 15.0%\n",
            "Sharpe Ratio: 1.64\n"
          ]
        }
      ],
      "source": [
        "from amplpy import AMPL\n",
        "\n",
        "ampl = AMPL()\n",
        "ampl.eval(\n",
        "    r\"\"\"\n",
        "    param target_volatility;\n",
        "    param market_neutral default 0;\n",
        "\n",
        "    set A ordered;\n",
        "    param S{A, A};\n",
        "    param mu{A} default 0;\n",
        "    \n",
        "    param lb default 0;\n",
        "    param ub default 1;\n",
        "    var w{A} >= lb <= ub;\n",
        "    \n",
        "    maximize portfolio_return:\n",
        "        sum {i in A} mu[i] * w[i];\n",
        "    s.t. portfolio_variance:\n",
        "        sum {i in A, j in A} w[i] * S[i, j] * w[j] <= target_volatility^2;\n",
        "    s.t. portfolio_weights:\n",
        "        sum {i in A} w[i] = if market_neutral then 0 else 1;\n",
        "    \n",
        "    var y{A} binary;\n",
        "    s.t. w_lower{i in A}:\n",
        "        lb * y[i] <= w[i];\n",
        "    s.t. w_upper{i in A}:\n",
        "        w[i] <= ub * y[i];\n",
        "\n",
        "    param card_ub default Infinity;\n",
        "    s.t. card_limit:\n",
        "        sum {i in A} y[i] <= card_ub;\n",
        "    \"\"\"\n",
        ")\n",
        "ampl.set[\"A\"] = ef.tickers\n",
        "ampl.param[\"S\"] = pd.DataFrame(ef.cov_matrix, index=ef.tickers, columns=ef.tickers)\n",
        "ampl.param[\"mu\"] = ef.expected_returns\n",
        "ampl.param[\"card_ub\"] = 3\n",
        "ampl.param[\"target_volatility\"] = 0.15\n",
        "ampl.option[\"solver\"] = \"gurobi\"\n",
        "ampl.solve()\n",
        "sigma2 = ampl.get_value(\"sqrt(sum {i in A, j in A} w[i] * S[i, j] * w[j])\")\n",
        "mu2 = ampl.get_value(\"sum {i in A} mu[i] * w[i]\")\n",
        "risk_free_rate = 0.02\n",
        "sharpe2 = (mu2 - risk_free_rate) / sigma2\n",
        "print(f\"Expected annual return: {mu2*100:.1f}%\")\n",
        "print(f\"Annual volatility: {sigma2*100:.1f}%\")\n",
        "print(f\"Sharpe Ratio: {sharpe2:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<AxesSubplot:>"
            ]
          },
          "execution_count": 49,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pd.Series(ef.clean_weights()).plot.barh()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3.9.13 ('venv': venv)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.13"
    },
    "vscode": {
      "interpreter": {
        "hash": "f848cddd71240b43e0ed72421413d4d333821702b87f1d51f57304cea288bd62"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}