{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Portfolio optimization\n",
    "\n",
    "This tutorial provides a guide to portfolio optimization in **Garpar**.\n",
    "\n",
    "Previously, we explored the different sections of the `StocksSet` representation. However, there's one key element we haven't discussed yet: the weights. These are located in the top section alongside each stock and are represented by `W`. They play a crucial role in the optimization process, as they define the percentage of the budget allocated to each stock.\n",
    "\n",
    "To start with the tutorial, suppose we have the following `StocksSet` instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class='portfolio'>\n",
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Stocks</th>\n",
       "      <th>S0[W 1.0, H 0.5]</th>\n",
       "      <th>S1[W 1.0, H 0.5]</th>\n",
       "      <th>S2[W 1.0, H 0.5]</th>\n",
       "      <th>S3[W 1.0, H 0.5]</th>\n",
       "      <th>S4[W 1.0, H 0.5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Days</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98.824038</td>\n",
       "      <td>101.124632</td>\n",
       "      <td>100.939574</td>\n",
       "      <td>100.867079</td>\n",
       "      <td>99.200673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97.617608</td>\n",
       "      <td>102.690200</td>\n",
       "      <td>100.080834</td>\n",
       "      <td>101.877495</td>\n",
       "      <td>98.395740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96.437211</td>\n",
       "      <td>101.683842</td>\n",
       "      <td>98.911027</td>\n",
       "      <td>102.603524</td>\n",
       "      <td>99.302223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.380756</td>\n",
       "      <td>102.877028</td>\n",
       "      <td>97.918415</td>\n",
       "      <td>101.580874</td>\n",
       "      <td>100.623724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>94.623557</td>\n",
       "      <td>101.729791</td>\n",
       "      <td>98.816100</td>\n",
       "      <td>102.412359</td>\n",
       "      <td>101.178809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.341120</td>\n",
       "      <td>100.597766</td>\n",
       "      <td>99.593006</td>\n",
       "      <td>101.869782</td>\n",
       "      <td>99.827506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.231449</td>\n",
       "      <td>101.330151</td>\n",
       "      <td>100.881106</td>\n",
       "      <td>100.822215</td>\n",
       "      <td>98.685957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>93.555166</td>\n",
       "      <td>102.478027</td>\n",
       "      <td>101.719552</td>\n",
       "      <td>99.749480</td>\n",
       "      <td>97.455211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>92.531113</td>\n",
       "      <td>103.317722</td>\n",
       "      <td>102.797938</td>\n",
       "      <td>98.803108</td>\n",
       "      <td>98.001995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>91.346297</td>\n",
       "      <td>104.206055</td>\n",
       "      <td>103.853711</td>\n",
       "      <td>99.987891</td>\n",
       "      <td>96.873211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><em class='portfolio-dim'>11 days x 5 stocks - W.Size 5</em>\n",
       "</div>"
      ],
      "text/plain": [
       "Stocks  S0[W 1.0, H 0.5]  S1[W 1.0, H 0.5]  S2[W 1.0, H 0.5]  \\\n",
       "Days                                                           \n",
       "0             100.000000        100.000000        100.000000   \n",
       "1              98.824038        101.124632        100.939574   \n",
       "2              97.617608        102.690200        100.080834   \n",
       "3              96.437211        101.683842         98.911027   \n",
       "4              95.380756        102.877028         97.918415   \n",
       "5              94.623557        101.729791         98.816100   \n",
       "6              93.341120        100.597766         99.593006   \n",
       "7              92.231449        101.330151        100.881106   \n",
       "8              93.555166        102.478027        101.719552   \n",
       "9              92.531113        103.317722        102.797938   \n",
       "10             91.346297        104.206055        103.853711   \n",
       "\n",
       "Stocks  S3[W 1.0, H 0.5]  S4[W 1.0, H 0.5]  \n",
       "Days                                        \n",
       "0             100.000000        100.000000  \n",
       "1             100.867079         99.200673  \n",
       "2             101.877495         98.395740  \n",
       "3             102.603524         99.302223  \n",
       "4             101.580874        100.623724  \n",
       "5             102.412359        101.178809  \n",
       "6             101.869782         99.827506  \n",
       "7             100.822215         98.685957  \n",
       "8              99.749480         97.455211  \n",
       "9              98.803108         98.001995  \n",
       "10             99.987891         96.873211  \n",
       "StocksSet [11 days x 5 stocks - W.Size 5]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from garpar.datasets.risso import make_risso_normal\n",
    "\n",
    "ss = make_risso_normal(days=10, stocks=5, random_state=702)\n",
    "ss\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the same prices throughout the tutorial. Note that the `W` value of each stock is `1.0` by default, this represents that we haven't applied an optimization model yet."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Your first optimization\n",
    "\n",
    "The optimization process currently available in **Garpar** is based on mean-variance models. These models solve the problem of assigning weights by considering the mean and variance of the returns of asset prices. Mean-variance optimization is rooted in Harry Markowitz’s 1952 paper, *Portfolio Selection* ([available here](https://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1952.tb01525.x)), which revolutionized portfolio management, transforming it from an art into a science.\n",
    "\n",
    "For starters, we need an instance of an optimization model, also referred to as an optimizer. Currently, there are two classes that serve this purpose:\n",
    "\n",
    "- **MVOptimizer**: Applies one of several mean-variance models.\n",
    "- **Markowitz**: Specifically applies the Markowitz mean-variance model.\n",
    "\n",
    "We will begin with the `Markowitz` model. Later, we will explore the different mean-variance models that can be applied using `MVOptimizer`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from garpar.optimize.mean_variance import Markowitz\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Once we imported the `Markowitz` class, we have to instanciate it. This can be seen as defining parameters for the model. For example, in the Markowitz model, if we want to have a return of at least 15% we would instanciate the model as the following example shows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mk = Markowitz(target_return=0.15)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have both the instance of the model and the `StocksSet`. We can solve the optimization problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class='portfolio'>\n",
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Stocks</th>\n",
       "      <th>S0[W 0.180339, H 0.5]</th>\n",
       "      <th>S1[W 0.122161, H 0.5]</th>\n",
       "      <th>S2[W 0.236844, H 0.5]</th>\n",
       "      <th>S3[W 0.203510, H 0.5]</th>\n",
       "      <th>S4[W 0.257145, H 0.5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Days</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98.824038</td>\n",
       "      <td>101.124632</td>\n",
       "      <td>100.939574</td>\n",
       "      <td>100.867079</td>\n",
       "      <td>99.200673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97.617608</td>\n",
       "      <td>102.690200</td>\n",
       "      <td>100.080834</td>\n",
       "      <td>101.877495</td>\n",
       "      <td>98.395740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96.437211</td>\n",
       "      <td>101.683842</td>\n",
       "      <td>98.911027</td>\n",
       "      <td>102.603524</td>\n",
       "      <td>99.302223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.380756</td>\n",
       "      <td>102.877028</td>\n",
       "      <td>97.918415</td>\n",
       "      <td>101.580874</td>\n",
       "      <td>100.623724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>94.623557</td>\n",
       "      <td>101.729791</td>\n",
       "      <td>98.816100</td>\n",
       "      <td>102.412359</td>\n",
       "      <td>101.178809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.341120</td>\n",
       "      <td>100.597766</td>\n",
       "      <td>99.593006</td>\n",
       "      <td>101.869782</td>\n",
       "      <td>99.827506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.231449</td>\n",
       "      <td>101.330151</td>\n",
       "      <td>100.881106</td>\n",
       "      <td>100.822215</td>\n",
       "      <td>98.685957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>93.555166</td>\n",
       "      <td>102.478027</td>\n",
       "      <td>101.719552</td>\n",
       "      <td>99.749480</td>\n",
       "      <td>97.455211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>92.531113</td>\n",
       "      <td>103.317722</td>\n",
       "      <td>102.797938</td>\n",
       "      <td>98.803108</td>\n",
       "      <td>98.001995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>91.346297</td>\n",
       "      <td>104.206055</td>\n",
       "      <td>103.853711</td>\n",
       "      <td>99.987891</td>\n",
       "      <td>96.873211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><em class='portfolio-dim'>11 days x 5 stocks - W.Size 5</em>\n",
       "</div>"
      ],
      "text/plain": [
       "Stocks  S0[W 0.180339, H 0.5]  S1[W 0.122161, H 0.5]  S2[W 0.236844, H 0.5]  \\\n",
       "Days                                                                          \n",
       "0                  100.000000             100.000000             100.000000   \n",
       "1                   98.824038             101.124632             100.939574   \n",
       "2                   97.617608             102.690200             100.080834   \n",
       "3                   96.437211             101.683842              98.911027   \n",
       "4                   95.380756             102.877028              97.918415   \n",
       "5                   94.623557             101.729791              98.816100   \n",
       "6                   93.341120             100.597766              99.593006   \n",
       "7                   92.231449             101.330151             100.881106   \n",
       "8                   93.555166             102.478027             101.719552   \n",
       "9                   92.531113             103.317722             102.797938   \n",
       "10                  91.346297             104.206055             103.853711   \n",
       "\n",
       "Stocks  S3[W 0.203510, H 0.5]  S4[W 0.257145, H 0.5]  \n",
       "Days                                                  \n",
       "0                  100.000000             100.000000  \n",
       "1                  100.867079              99.200673  \n",
       "2                  101.877495              98.395740  \n",
       "3                  102.603524              99.302223  \n",
       "4                  101.580874             100.623724  \n",
       "5                  102.412359             101.178809  \n",
       "6                  101.869782              99.827506  \n",
       "7                  100.822215              98.685957  \n",
       "8                   99.749480              97.455211  \n",
       "9                   98.803108              98.001995  \n",
       "10                  99.987891              96.873211  \n",
       "StocksSet [11 days x 5 stocks - W.Size 5]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mk.optimize(ss)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how the weights changed, lets see what happens when we try to optimize with a greater target return."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class='portfolio'>\n",
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Stocks</th>\n",
       "      <th>S0[W 0.180339, H 0.5]</th>\n",
       "      <th>S1[W 0.122161, H 0.5]</th>\n",
       "      <th>S2[W 0.236844, H 0.5]</th>\n",
       "      <th>S3[W 0.203510, H 0.5]</th>\n",
       "      <th>S4[W 0.257145, H 0.5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Days</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98.824038</td>\n",
       "      <td>101.124632</td>\n",
       "      <td>100.939574</td>\n",
       "      <td>100.867079</td>\n",
       "      <td>99.200673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97.617608</td>\n",
       "      <td>102.690200</td>\n",
       "      <td>100.080834</td>\n",
       "      <td>101.877495</td>\n",
       "      <td>98.395740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96.437211</td>\n",
       "      <td>101.683842</td>\n",
       "      <td>98.911027</td>\n",
       "      <td>102.603524</td>\n",
       "      <td>99.302223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.380756</td>\n",
       "      <td>102.877028</td>\n",
       "      <td>97.918415</td>\n",
       "      <td>101.580874</td>\n",
       "      <td>100.623724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>94.623557</td>\n",
       "      <td>101.729791</td>\n",
       "      <td>98.816100</td>\n",
       "      <td>102.412359</td>\n",
       "      <td>101.178809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.341120</td>\n",
       "      <td>100.597766</td>\n",
       "      <td>99.593006</td>\n",
       "      <td>101.869782</td>\n",
       "      <td>99.827506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.231449</td>\n",
       "      <td>101.330151</td>\n",
       "      <td>100.881106</td>\n",
       "      <td>100.822215</td>\n",
       "      <td>98.685957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>93.555166</td>\n",
       "      <td>102.478027</td>\n",
       "      <td>101.719552</td>\n",
       "      <td>99.749480</td>\n",
       "      <td>97.455211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>92.531113</td>\n",
       "      <td>103.317722</td>\n",
       "      <td>102.797938</td>\n",
       "      <td>98.803108</td>\n",
       "      <td>98.001995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>91.346297</td>\n",
       "      <td>104.206055</td>\n",
       "      <td>103.853711</td>\n",
       "      <td>99.987891</td>\n",
       "      <td>96.873211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><em class='portfolio-dim'>11 days x 5 stocks - W.Size 5</em>\n",
       "</div>"
      ],
      "text/plain": [
       "Stocks  S0[W 0.180339, H 0.5]  S1[W 0.122161, H 0.5]  S2[W 0.236844, H 0.5]  \\\n",
       "Days                                                                          \n",
       "0                  100.000000             100.000000             100.000000   \n",
       "1                   98.824038             101.124632             100.939574   \n",
       "2                   97.617608             102.690200             100.080834   \n",
       "3                   96.437211             101.683842              98.911027   \n",
       "4                   95.380756             102.877028              97.918415   \n",
       "5                   94.623557             101.729791              98.816100   \n",
       "6                   93.341120             100.597766              99.593006   \n",
       "7                   92.231449             101.330151             100.881106   \n",
       "8                   93.555166             102.478027             101.719552   \n",
       "9                   92.531113             103.317722             102.797938   \n",
       "10                  91.346297             104.206055             103.853711   \n",
       "\n",
       "Stocks  S3[W 0.203510, H 0.5]  S4[W 0.257145, H 0.5]  \n",
       "Days                                                  \n",
       "0                  100.000000             100.000000  \n",
       "1                  100.867079              99.200673  \n",
       "2                  101.877495              98.395740  \n",
       "3                  102.603524              99.302223  \n",
       "4                  101.580874             100.623724  \n",
       "5                  102.412359             101.178809  \n",
       "6                  101.869782              99.827506  \n",
       "7                  100.822215              98.685957  \n",
       "8                   99.749480              97.455211  \n",
       "9                   98.803108              98.001995  \n",
       "10                  99.987891              96.873211  \n",
       "StocksSet [11 days x 5 stocks - W.Size 5]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mk = Markowitz(target_return=0.20)\n",
    "mk.optimize(ss)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The weights changed quite a bit. That's how you can make your first optimization!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The available models\n",
    "\n",
    "Now that we saw how to optimize using the Markowitz mean-variance model, let's see how to repeat this process using other models of the same kind.\n",
    "\n",
    "The following models are available to use:\n",
    "\n",
    "* Min volatility: Minimize risk and don't take into account return.\n",
    "* Max Sharpe: Maximize Sharpe Ratio, [described here](https://www.degruyter.com/document/doi/10.1515/9781400829408-022/pdf?licenseType=restricted).\n",
    "* Max quadratic utility: Maximize quadratic utility [described here](https://d1wqtxts1xzle7.cloudfront.net/83844141/Mixture_Symmetry_and_Quadratic_Utility20220411-2705-1fslpew.pdf?1738490763=&response-content-disposition=inline%3B+filename%3DMixture_Symmetry_and_Quadratic_Utility.pdf&Expires=1739654891&Signature=RdB6j4s10PA~KDfm1iXMh274JDXKFilazXWjzKspjfiKIyGEB6EtejYtSaOPPRvSp~G~AdL3j0W3JoGl7kQCdTtT0reh-ESXbKHRwzrBYMMdik7d2mn2EoF1v4eykHpI7NEh5a4JfH-n5YeY1kaxzbuwzfOCAXw5jVLu-XISNzM~mYRI9b0baME0XZVTirfmmnTG~vVd~uwFte-Mssr9qC8q2aqIfwibfcRtTvBYiBfWSxSUGJZw~ClqCcsdDrRlfPaPg6LpU7Yddceqs0n-9jMvyOs-J-7JLUM1eT9P6Ig2RPW6NGKJZgYMvWkzSrJlxtGgQm0upk0jewmneNPyaA__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA).\n",
    "* Efficient risk: Minimize risk given a return value.\n",
    "* Efficient return: Maximize return given a risk value.\n",
    "\n",
    "We will show how two of these models behave and which values are required."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class='portfolio'>\n",
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       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Stocks</th>\n",
       "      <th>S0[W 0.000000, H 0.5]</th>\n",
       "      <th>S1[W 0.302386, H 0.5]</th>\n",
       "      <th>S2[W 0.382865, H 0.5]</th>\n",
       "      <th>S3[W 0.122339, H 0.5]</th>\n",
       "      <th>S4[W 0.192410, H 0.5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Days</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98.824038</td>\n",
       "      <td>101.124632</td>\n",
       "      <td>100.939574</td>\n",
       "      <td>100.867079</td>\n",
       "      <td>99.200673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97.617608</td>\n",
       "      <td>102.690200</td>\n",
       "      <td>100.080834</td>\n",
       "      <td>101.877495</td>\n",
       "      <td>98.395740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96.437211</td>\n",
       "      <td>101.683842</td>\n",
       "      <td>98.911027</td>\n",
       "      <td>102.603524</td>\n",
       "      <td>99.302223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.380756</td>\n",
       "      <td>102.877028</td>\n",
       "      <td>97.918415</td>\n",
       "      <td>101.580874</td>\n",
       "      <td>100.623724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>94.623557</td>\n",
       "      <td>101.729791</td>\n",
       "      <td>98.816100</td>\n",
       "      <td>102.412359</td>\n",
       "      <td>101.178809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.341120</td>\n",
       "      <td>100.597766</td>\n",
       "      <td>99.593006</td>\n",
       "      <td>101.869782</td>\n",
       "      <td>99.827506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.231449</td>\n",
       "      <td>101.330151</td>\n",
       "      <td>100.881106</td>\n",
       "      <td>100.822215</td>\n",
       "      <td>98.685957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>93.555166</td>\n",
       "      <td>102.478027</td>\n",
       "      <td>101.719552</td>\n",
       "      <td>99.749480</td>\n",
       "      <td>97.455211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>92.531113</td>\n",
       "      <td>103.317722</td>\n",
       "      <td>102.797938</td>\n",
       "      <td>98.803108</td>\n",
       "      <td>98.001995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>91.346297</td>\n",
       "      <td>104.206055</td>\n",
       "      <td>103.853711</td>\n",
       "      <td>99.987891</td>\n",
       "      <td>96.873211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><em class='portfolio-dim'>11 days x 5 stocks - W.Size 5</em>\n",
       "</div>"
      ],
      "text/plain": [
       "Stocks  S0[W 0.000000, H 0.5]  S1[W 0.302386, H 0.5]  S2[W 0.382865, H 0.5]  \\\n",
       "Days                                                                          \n",
       "0                  100.000000             100.000000             100.000000   \n",
       "1                   98.824038             101.124632             100.939574   \n",
       "2                   97.617608             102.690200             100.080834   \n",
       "3                   96.437211             101.683842              98.911027   \n",
       "4                   95.380756             102.877028              97.918415   \n",
       "5                   94.623557             101.729791              98.816100   \n",
       "6                   93.341120             100.597766              99.593006   \n",
       "7                   92.231449             101.330151             100.881106   \n",
       "8                   93.555166             102.478027             101.719552   \n",
       "9                   92.531113             103.317722             102.797938   \n",
       "10                  91.346297             104.206055             103.853711   \n",
       "\n",
       "Stocks  S3[W 0.122339, H 0.5]  S4[W 0.192410, H 0.5]  \n",
       "Days                                                  \n",
       "0                  100.000000             100.000000  \n",
       "1                  100.867079              99.200673  \n",
       "2                  101.877495              98.395740  \n",
       "3                  102.603524              99.302223  \n",
       "4                  101.580874             100.623724  \n",
       "5                  102.412359             101.178809  \n",
       "6                  101.869782              99.827506  \n",
       "7                  100.822215              98.685957  \n",
       "8                   99.749480              97.455211  \n",
       "9                   98.803108              98.001995  \n",
       "10                  99.987891              96.873211  \n",
       "StocksSet [11 days x 5 stocks - W.Size 5]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from garpar.optimize.mean_variance import MVOptimizer\n",
    "\n",
    "max_sharpe_model = MVOptimizer(model=\"max_sharpe\", risk_free_rate=0.01)\n",
    "max_sharpe_model.optimize(ss)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have a named parameter `risk_free_rate` that represents a rate of return received at zero-risk assets. You can consult [here](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1317436) for details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class='portfolio'>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Stocks</th>\n",
       "      <th>S0[W-0.000003, H 0.5]</th>\n",
       "      <th>S1[W 1.000000, H 0.5]</th>\n",
       "      <th>S2[W 0.000003, H 0.5]</th>\n",
       "      <th>S3[W-0.000001, H 0.5]</th>\n",
       "      <th>S4[W 0.000001, H 0.5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Days</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98.824038</td>\n",
       "      <td>101.124632</td>\n",
       "      <td>100.939574</td>\n",
       "      <td>100.867079</td>\n",
       "      <td>99.200673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97.617608</td>\n",
       "      <td>102.690200</td>\n",
       "      <td>100.080834</td>\n",
       "      <td>101.877495</td>\n",
       "      <td>98.395740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96.437211</td>\n",
       "      <td>101.683842</td>\n",
       "      <td>98.911027</td>\n",
       "      <td>102.603524</td>\n",
       "      <td>99.302223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.380756</td>\n",
       "      <td>102.877028</td>\n",
       "      <td>97.918415</td>\n",
       "      <td>101.580874</td>\n",
       "      <td>100.623724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>94.623557</td>\n",
       "      <td>101.729791</td>\n",
       "      <td>98.816100</td>\n",
       "      <td>102.412359</td>\n",
       "      <td>101.178809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.341120</td>\n",
       "      <td>100.597766</td>\n",
       "      <td>99.593006</td>\n",
       "      <td>101.869782</td>\n",
       "      <td>99.827506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.231449</td>\n",
       "      <td>101.330151</td>\n",
       "      <td>100.881106</td>\n",
       "      <td>100.822215</td>\n",
       "      <td>98.685957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>93.555166</td>\n",
       "      <td>102.478027</td>\n",
       "      <td>101.719552</td>\n",
       "      <td>99.749480</td>\n",
       "      <td>97.455211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>92.531113</td>\n",
       "      <td>103.317722</td>\n",
       "      <td>102.797938</td>\n",
       "      <td>98.803108</td>\n",
       "      <td>98.001995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>91.346297</td>\n",
       "      <td>104.206055</td>\n",
       "      <td>103.853711</td>\n",
       "      <td>99.987891</td>\n",
       "      <td>96.873211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><em class='portfolio-dim'>11 days x 5 stocks - W.Size 5</em>\n",
       "</div>"
      ],
      "text/plain": [
       "Stocks  S0[W-0.000003, H 0.5]  S1[W 1.000000, H 0.5]  S2[W 0.000003, H 0.5]  \\\n",
       "Days                                                                          \n",
       "0                  100.000000             100.000000             100.000000   \n",
       "1                   98.824038             101.124632             100.939574   \n",
       "2                   97.617608             102.690200             100.080834   \n",
       "3                   96.437211             101.683842              98.911027   \n",
       "4                   95.380756             102.877028              97.918415   \n",
       "5                   94.623557             101.729791              98.816100   \n",
       "6                   93.341120             100.597766              99.593006   \n",
       "7                   92.231449             101.330151             100.881106   \n",
       "8                   93.555166             102.478027             101.719552   \n",
       "9                   92.531113             103.317722             102.797938   \n",
       "10                  91.346297             104.206055             103.853711   \n",
       "\n",
       "Stocks  S3[W-0.000001, H 0.5]  S4[W 0.000001, H 0.5]  \n",
       "Days                                                  \n",
       "0                  100.000000             100.000000  \n",
       "1                  100.867079              99.200673  \n",
       "2                  101.877495              98.395740  \n",
       "3                  102.603524              99.302223  \n",
       "4                  101.580874             100.623724  \n",
       "5                  102.412359             101.178809  \n",
       "6                  101.869782              99.827506  \n",
       "7                  100.822215              98.685957  \n",
       "8                   99.749480              97.455211  \n",
       "9                   98.803108              98.001995  \n",
       "10                  99.987891              96.873211  \n",
       "StocksSet [11 days x 5 stocks - W.Size 5]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_quadratic_utility_model = MVOptimizer(model=\"max_quadratic_utility\", risk_aversion=0.65)\n",
    "max_quadratic_utility_model.optimize(ss)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model uses the parameter `risk_aversion`, which represents how much an investor prefers outcomes with low uncertainty. You can learn more about risk aversion [here](https://scholar.google.com/scholar_url?url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1540-6261.1983.tb02291.x%3Fcasa_token%3DfAcRdkc8w3sAAAAA:XLknTwxobkFK76KtIRpytNAYH6GkjxIsapdXkMtWyUyXL8I6v1j0aX7tpCoT_AwjTJNGUpGnHEsCue-WJw&hl=es&sa=T&oi=gsb&ct=res&cd=2&d=12100987240872776321&ei=1PuxZ5PpBOehieoP4b3H4A0&scisig=AFWwaeZGLl6QLFyi0fhPHZZiz3dY).\n",
    "\n",
    "In some cases a market neutral strategy can be used. Allowing a profit with the increase or decrease of a stock value. By default the weights are bounded to be between 0 and 1. This can be changed by defining the attribute `weight_bounds`. Allowing the usage of market neutral models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Stocks</th>\n",
       "      <th>S0[W-1.0, H 0.5]</th>\n",
       "      <th>S1[W 1.0, H 0.5]</th>\n",
       "      <th>S2[W 1.0, H 0.5]</th>\n",
       "      <th>S3[W 0.0, H 0.5]</th>\n",
       "      <th>S4[W-1.0, H 0.5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Days</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98.824038</td>\n",
       "      <td>101.124632</td>\n",
       "      <td>100.939574</td>\n",
       "      <td>100.867079</td>\n",
       "      <td>99.200673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97.617608</td>\n",
       "      <td>102.690200</td>\n",
       "      <td>100.080834</td>\n",
       "      <td>101.877495</td>\n",
       "      <td>98.395740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96.437211</td>\n",
       "      <td>101.683842</td>\n",
       "      <td>98.911027</td>\n",
       "      <td>102.603524</td>\n",
       "      <td>99.302223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.380756</td>\n",
       "      <td>102.877028</td>\n",
       "      <td>97.918415</td>\n",
       "      <td>101.580874</td>\n",
       "      <td>100.623724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>94.623557</td>\n",
       "      <td>101.729791</td>\n",
       "      <td>98.816100</td>\n",
       "      <td>102.412359</td>\n",
       "      <td>101.178809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.341120</td>\n",
       "      <td>100.597766</td>\n",
       "      <td>99.593006</td>\n",
       "      <td>101.869782</td>\n",
       "      <td>99.827506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.231449</td>\n",
       "      <td>101.330151</td>\n",
       "      <td>100.881106</td>\n",
       "      <td>100.822215</td>\n",
       "      <td>98.685957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>93.555166</td>\n",
       "      <td>102.478027</td>\n",
       "      <td>101.719552</td>\n",
       "      <td>99.749480</td>\n",
       "      <td>97.455211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>92.531113</td>\n",
       "      <td>103.317722</td>\n",
       "      <td>102.797938</td>\n",
       "      <td>98.803108</td>\n",
       "      <td>98.001995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>91.346297</td>\n",
       "      <td>104.206055</td>\n",
       "      <td>103.853711</td>\n",
       "      <td>99.987891</td>\n",
       "      <td>96.873211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><em class='portfolio-dim'>11 days x 5 stocks - W.Size 5</em>\n",
       "</div>"
      ],
      "text/plain": [
       "Stocks  S0[W-1.0, H 0.5]  S1[W 1.0, H 0.5]  S2[W 1.0, H 0.5]  \\\n",
       "Days                                                           \n",
       "0             100.000000        100.000000        100.000000   \n",
       "1              98.824038        101.124632        100.939574   \n",
       "2              97.617608        102.690200        100.080834   \n",
       "3              96.437211        101.683842         98.911027   \n",
       "4              95.380756        102.877028         97.918415   \n",
       "5              94.623557        101.729791         98.816100   \n",
       "6              93.341120        100.597766         99.593006   \n",
       "7              92.231449        101.330151        100.881106   \n",
       "8              93.555166        102.478027        101.719552   \n",
       "9              92.531113        103.317722        102.797938   \n",
       "10             91.346297        104.206055        103.853711   \n",
       "\n",
       "Stocks  S3[W 0.0, H 0.5]  S4[W-1.0, H 0.5]  \n",
       "Days                                        \n",
       "0             100.000000        100.000000  \n",
       "1             100.867079         99.200673  \n",
       "2             101.877495         98.395740  \n",
       "3             102.603524         99.302223  \n",
       "4             101.580874        100.623724  \n",
       "5             102.412359        101.178809  \n",
       "6             101.869782         99.827506  \n",
       "7             100.822215         98.685957  \n",
       "8              99.749480         97.455211  \n",
       "9              98.803108         98.001995  \n",
       "10             99.987891         96.873211  \n",
       "StocksSet [11 days x 5 stocks - W.Size 5]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_quadratic_utility_neutral = MVOptimizer(model=\"max_quadratic_utility\", risk_aversion=10, market_neutral=True, weight_bounds=(-1, 1))\n",
    "max_quadratic_utility_neutral.optimize(ss)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we don't change this, the system will show a warning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ebner/.pyenv/versions/garpar/lib/python3.13/site-packages/pypfopt/efficient_frontier/efficient_frontier.py:172: RuntimeWarning: Market neutrality requires shorting - bounds have been amended\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th>Stocks</th>\n",
       "      <th>S0[W-1.0, H 0.5]</th>\n",
       "      <th>S1[W 1.0, H 0.5]</th>\n",
       "      <th>S2[W 1.0, H 0.5]</th>\n",
       "      <th>S3[W 0.0, H 0.5]</th>\n",
       "      <th>S4[W-1.0, H 0.5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Days</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98.824038</td>\n",
       "      <td>101.124632</td>\n",
       "      <td>100.939574</td>\n",
       "      <td>100.867079</td>\n",
       "      <td>99.200673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97.617608</td>\n",
       "      <td>102.690200</td>\n",
       "      <td>100.080834</td>\n",
       "      <td>101.877495</td>\n",
       "      <td>98.395740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96.437211</td>\n",
       "      <td>101.683842</td>\n",
       "      <td>98.911027</td>\n",
       "      <td>102.603524</td>\n",
       "      <td>99.302223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.380756</td>\n",
       "      <td>102.877028</td>\n",
       "      <td>97.918415</td>\n",
       "      <td>101.580874</td>\n",
       "      <td>100.623724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>94.623557</td>\n",
       "      <td>101.729791</td>\n",
       "      <td>98.816100</td>\n",
       "      <td>102.412359</td>\n",
       "      <td>101.178809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.341120</td>\n",
       "      <td>100.597766</td>\n",
       "      <td>99.593006</td>\n",
       "      <td>101.869782</td>\n",
       "      <td>99.827506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.231449</td>\n",
       "      <td>101.330151</td>\n",
       "      <td>100.881106</td>\n",
       "      <td>100.822215</td>\n",
       "      <td>98.685957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>93.555166</td>\n",
       "      <td>102.478027</td>\n",
       "      <td>101.719552</td>\n",
       "      <td>99.749480</td>\n",
       "      <td>97.455211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>92.531113</td>\n",
       "      <td>103.317722</td>\n",
       "      <td>102.797938</td>\n",
       "      <td>98.803108</td>\n",
       "      <td>98.001995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>91.346297</td>\n",
       "      <td>104.206055</td>\n",
       "      <td>103.853711</td>\n",
       "      <td>99.987891</td>\n",
       "      <td>96.873211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><em class='portfolio-dim'>11 days x 5 stocks - W.Size 5</em>\n",
       "</div>"
      ],
      "text/plain": [
       "Stocks  S0[W-1.0, H 0.5]  S1[W 1.0, H 0.5]  S2[W 1.0, H 0.5]  \\\n",
       "Days                                                           \n",
       "0             100.000000        100.000000        100.000000   \n",
       "1              98.824038        101.124632        100.939574   \n",
       "2              97.617608        102.690200        100.080834   \n",
       "3              96.437211        101.683842         98.911027   \n",
       "4              95.380756        102.877028         97.918415   \n",
       "5              94.623557        101.729791         98.816100   \n",
       "6              93.341120        100.597766         99.593006   \n",
       "7              92.231449        101.330151        100.881106   \n",
       "8              93.555166        102.478027        101.719552   \n",
       "9              92.531113        103.317722        102.797938   \n",
       "10             91.346297        104.206055        103.853711   \n",
       "\n",
       "Stocks  S3[W 0.0, H 0.5]  S4[W-1.0, H 0.5]  \n",
       "Days                                        \n",
       "0             100.000000        100.000000  \n",
       "1             100.867079         99.200673  \n",
       "2             101.877495         98.395740  \n",
       "3             102.603524         99.302223  \n",
       "4             101.580874        100.623724  \n",
       "5             102.412359        101.178809  \n",
       "6             101.869782         99.827506  \n",
       "7             100.822215         98.685957  \n",
       "8              99.749480         97.455211  \n",
       "9              98.803108         98.001995  \n",
       "10             99.987891         96.873211  \n",
       "StocksSet [11 days x 5 stocks - W.Size 5]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_quadratic_utility_neutral = MVOptimizer(model=\"max_quadratic_utility\", risk_aversion=10, market_neutral=True)\n",
    "max_quadratic_utility_neutral.optimize(ss)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The warning names the concept \"shorting\", in this context shorting means that the weights can be negative. More about how shorting works [here](https://www.sciencedirect.com/science/article/pii/S0304405X0200226X?casa_token=J97TfsEiGVUAAAAA:lgV9gs3Z1Ta4syU0iL9o6JY6cxf3f1Ld9FEzpgl3aJyDRIniZ2ZKtaksSFFepwxj8IXBZRq1htcQ).\n",
    "\n",
    "If we don't define a value that is required by the model, the system will also raise a warning and the optimization process will follow with a coerced value. We can see an example in the following code fragment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ebner/FAMAF/Tesis/garpar/garpar/optimize/mean_variance.py:259: UserWarning: No risk_free_rate specified, coercing it\n",
      "  warnings.warn(\"No risk_free_rate specified, coercing it\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class='portfolio'>\n",
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       "    }\n",
       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Stocks</th>\n",
       "      <th>S0[W 0.000000, H 0.5]</th>\n",
       "      <th>S1[W 0.278483, H 0.5]</th>\n",
       "      <th>S2[W 0.369474, H 0.5]</th>\n",
       "      <th>S3[W 0.137504, H 0.5]</th>\n",
       "      <th>S4[W 0.214540, H 0.5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Days</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98.824038</td>\n",
       "      <td>101.124632</td>\n",
       "      <td>100.939574</td>\n",
       "      <td>100.867079</td>\n",
       "      <td>99.200673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97.617608</td>\n",
       "      <td>102.690200</td>\n",
       "      <td>100.080834</td>\n",
       "      <td>101.877495</td>\n",
       "      <td>98.395740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96.437211</td>\n",
       "      <td>101.683842</td>\n",
       "      <td>98.911027</td>\n",
       "      <td>102.603524</td>\n",
       "      <td>99.302223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.380756</td>\n",
       "      <td>102.877028</td>\n",
       "      <td>97.918415</td>\n",
       "      <td>101.580874</td>\n",
       "      <td>100.623724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>94.623557</td>\n",
       "      <td>101.729791</td>\n",
       "      <td>98.816100</td>\n",
       "      <td>102.412359</td>\n",
       "      <td>101.178809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.341120</td>\n",
       "      <td>100.597766</td>\n",
       "      <td>99.593006</td>\n",
       "      <td>101.869782</td>\n",
       "      <td>99.827506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.231449</td>\n",
       "      <td>101.330151</td>\n",
       "      <td>100.881106</td>\n",
       "      <td>100.822215</td>\n",
       "      <td>98.685957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>93.555166</td>\n",
       "      <td>102.478027</td>\n",
       "      <td>101.719552</td>\n",
       "      <td>99.749480</td>\n",
       "      <td>97.455211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>92.531113</td>\n",
       "      <td>103.317722</td>\n",
       "      <td>102.797938</td>\n",
       "      <td>98.803108</td>\n",
       "      <td>98.001995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>91.346297</td>\n",
       "      <td>104.206055</td>\n",
       "      <td>103.853711</td>\n",
       "      <td>99.987891</td>\n",
       "      <td>96.873211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><em class='portfolio-dim'>11 days x 5 stocks - W.Size 5</em>\n",
       "</div>"
      ],
      "text/plain": [
       "Stocks  S0[W 0.000000, H 0.5]  S1[W 0.278483, H 0.5]  S2[W 0.369474, H 0.5]  \\\n",
       "Days                                                                          \n",
       "0                  100.000000             100.000000             100.000000   \n",
       "1                   98.824038             101.124632             100.939574   \n",
       "2                   97.617608             102.690200             100.080834   \n",
       "3                   96.437211             101.683842              98.911027   \n",
       "4                   95.380756             102.877028              97.918415   \n",
       "5                   94.623557             101.729791              98.816100   \n",
       "6                   93.341120             100.597766              99.593006   \n",
       "7                   92.231449             101.330151             100.881106   \n",
       "8                   93.555166             102.478027             101.719552   \n",
       "9                   92.531113             103.317722             102.797938   \n",
       "10                  91.346297             104.206055             103.853711   \n",
       "\n",
       "Stocks  S3[W 0.137504, H 0.5]  S4[W 0.214540, H 0.5]  \n",
       "Days                                                  \n",
       "0                  100.000000             100.000000  \n",
       "1                  100.867079              99.200673  \n",
       "2                  101.877495              98.395740  \n",
       "3                  102.603524              99.302223  \n",
       "4                  101.580874             100.623724  \n",
       "5                  102.412359             101.178809  \n",
       "6                  101.869782              99.827506  \n",
       "7                  100.822215              98.685957  \n",
       "8                   99.749480              97.455211  \n",
       "9                   98.803108              98.001995  \n",
       "10                  99.987891              96.873211  \n",
       "StocksSet [11 days x 5 stocks - W.Size 5]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_sharpe_coerced = MVOptimizer(model=\"max_sharpe\")\n",
    "max_sharpe_coerced.optimize(ss)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This concludes the portfolio optimization tutorial. Please refer to the [**API section**](../api/garpar.optimize.rst) for more information.\n",
    "\n",
    "There is one more tutorial that consists of creating a custom optimizer. You can find it [here](optimizer_creation.ipynb)."
   ]
  }
 ],
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