{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean variance optimization set up example\n",
    "\n",
    "Frans de Ruiter, CQM\n",
    "For assignment and data, see https://www.fransderuiter.com/JADS/\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup\n",
    "Make sure you have installed all the packages listed below, as well as the ipopt solver (see installation instructions from previous class)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pyomo.environ import *\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = \"https://www.fransderuiter.com/JADS/Meanvariance/MeanVarPortfolio.xlsx\"\n",
    "# Create pandas table\n",
    "df_input = pd.read_excel(data_path, sheet_name=0, header=1, skiprows=4, index_col=0)\n",
    "\n",
    "# Show table\n",
    "df_input.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "## Rename the first two columns\n",
    "\n",
    "newcolumn_values = df_input.columns.values\n",
    "newcolumn_values[0] = 'Mean'\n",
    "newcolumn_values[1] = 'Variance'\n",
    "\n",
    "df_input.columns = newcolumn_values\n",
    "\n",
    "# Show table with removed column\n",
    "df_input.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set with assets (indices)\n",
    "assets = df_input.columns[2:] # first two columns are only mean and variance\n",
    "\n",
    "# risk parameter\n",
    "alpha = 0.012"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot means and variances of portfolios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize plot\n",
    "fig=plt.figure(figsize=(16,16))\n",
    "\n",
    "# Plot mean returns and variances of individual assets\n",
    "plt.scatter([df_input.loc[i,'Variance'] for i in assets], \n",
    "            [100*df_input.loc[i,'Mean'] for i in assets], \n",
    "            s = 200*np.ones(assets.size),\n",
    "            alpha=0.9)\n",
    "\n",
    "plt.title(\"Mean-Variance portfolios\")\n",
    "plt.xlabel(\"Variance\")\n",
    "plt.ylabel(\"Mean return (\\%)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Tips:\n",
    "# acces the mean of asset\n",
    "i = 'ME1 INV2'\n",
    "# by:\n",
    "return_example = df_input.loc[i,'Mean']\n",
    "\n",
    "# acces the covariance of two assets by\n",
    "i = 'ME1 INV2'\n",
    "j = 'ME1 INV3'\n",
    "\n",
    "variance_example = df_input.loc[i,j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## TODO: fill in the dots\n",
    "\n",
    "def MeanVarModelConstruction(alpha,df_input):\n",
    "    # Create model\n",
    "    m = ConcreteModel()\n",
    "\n",
    "    # TODO: Add variables, objective and constraints to the model. \n",
    "    # In the objective you have to specify the direction (sense): is this a minimization or maximization problem?\n",
    "    \n",
    "    # Variables\n",
    "    m.amount = Var(...) # note that short sellings is not allowed, what does that mean for the range of values that he variable can take?\n",
    "\n",
    "    # Objective\n",
    "    m.value = Objective(..., sense =...)\n",
    "\n",
    "    # Constraints on budget\n",
    "    m.budget = Constraint(....)\n",
    "\n",
    "    return m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function to solve the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OptimizeMeanVarModel(m,printResults,showprogress = False):\n",
    "    # Optimize\n",
    "    solver = SolverFactory('ipopt') # Take the ipopt solver for nonlinear problems\n",
    "    status = solver.solve(m,tee=showprogress,)\n",
    "\n",
    "    # Print the status of the solved model\n",
    "    \n",
    "    if printResults:\n",
    "        print(\"Risk aversion parameter = %s \\n\" % alpha)\n",
    "        print(\"Status = %s \\n\" % status.solver.termination_condition)\n",
    "    \n",
    "    obj_opt = value(m.value)\n",
    "    mean_opt = sum([value(m.amount[i]*df_input.loc[i,'Mean']) for i in assets])\n",
    "    variance_opt = sum(df_input.loc[i,j]*value(m.amount[i])*value(m.amount[j]) for i in assets for j in assets)\n",
    "    \n",
    "    return (obj_opt, mean_opt, variance_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot and show the solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Construct model with chosen alpha\n",
    "m = MeanVarModelConstruction(alpha,df_input)\n",
    "# Optimize\n",
    "obj_opt, mean_opt, variance_opt = OptimizeMeanVarModel(m,True,False)\n",
    "\n",
    "print(\"Objective value model \\t= %.3f\" % obj_opt)\n",
    "print(\"\\t Mean return \\t= %.3f\" % mean_opt)\n",
    "print(\"\\t Variance \\t= %.3f\\n\" % variance_opt)\n",
    "\n",
    "print(\"Assets invested in (and amount):\")\n",
    "print(\"Portfolio composition:\")\n",
    "for i in assets:\n",
    "    if value(m.amount[i] > 0.0001):\n",
    "        print(\"\\t\"+ i + \" : \\t\" + str(value(m.amount[i]))) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize plot\n",
    "fig=plt.figure(figsize=(16,16))\n",
    "\n",
    "# Plot mean returns and variances of individual assets\n",
    "plt.scatter([df_input.loc[i,'Variance'] for i in assets], \n",
    "            [100*df_input.loc[i,'Mean'] for i in assets], \n",
    "            s = 200*np.ones(assets.size),\n",
    "            alpha=0.9)\n",
    "# Plot mean returns and variances of new optimal portfolio\n",
    "plt.scatter(variance_opt, \n",
    "            100*mean_opt, \n",
    "            s = 200*np.ones(assets.size),\n",
    "            c = 'red',\n",
    "            alpha=0.9)\n",
    "\n",
    "plt.title(\"Mean-Variance portfolios\")\n",
    "plt.xlabel(\"Variance\")\n",
    "plt.ylabel(\"Mean return (\\%)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bonus question:\n",
    "Suppose we allow for short selling, short position cannot be more than 10% of your long position. How can we incorporate this in our model?\n",
    "\n",
    "Hint 1: First try to write this new constraint on paper before you try to implement it.\n",
    "\n",
    "Hint 2: Introduce two new parameters $x_long \\geq 0$ and $x_short \\geq 0$ that indicate the short and long position. So the total position is $x = x_long - x_short$. How do you incorporate the 10% requirement constraint?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO:\n",
    "# 1) write down the new constraint on paper.\n",
    "# 2) Make new optimization model for the mean-variance problem that allows for short-selling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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