Bond Dedication and Asset Liability Cashflow Matching (LP).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a5ab6389",
   "metadata": {},
   "source": [
    "## 1b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "id": "6d43a87d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of variables = 2\n",
      "Number of constraints = 2\n",
      "Solution:\n",
      "Objective value = 4250.0\n",
      "x = 24.99999999999999\n",
      "y = 20.00000000000001\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from ortools.linear_solver import pywraplp\n",
    "\n",
    "\n",
    "def LinearProgrammingExample():\n",
    "    solver = pywraplp.Solver.CreateSolver('GLOP')\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    x = solver.NumVar(0, solver.infinity(), 'x')\n",
    "    y = solver.NumVar(0, solver.infinity(), 'y')\n",
    "  \n",
    "\n",
    "    print('Number of variables =', solver.NumVariables())\n",
    "\n",
    "    solver.Add(x + y <= 45.0)\n",
    "\n",
    "    solver.Add(6 * x + 10*y <= 350.0)\n",
    "\n",
    "\n",
    "    print('Number of constraints =', solver.NumConstraints())\n",
    "    \n",
    "    #Obj\n",
    "    solver.Maximize(90 * x + 100*y)\n",
    "\n",
    "    status = solver.Solve()\n",
    "\n",
    "    if status == pywraplp.Solver.OPTIMAL:\n",
    "        print('Solution:')\n",
    "        print('Objective value =', solver.Objective().Value())\n",
    "        print('x =', x.solution_value())\n",
    "        print('y =', y.solution_value())\n",
    "       \n",
    "    else:\n",
    "        print('No optimal solution.')\n",
    "LinearProgrammingExample()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec4b9666",
   "metadata": {},
   "source": [
    "## 1c "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "id": "b2d9dd58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective value when wheat is at $26 = $ 3624.9999999999995\n",
      "x = 12.500000000000002\n",
      "y = 27.499999999999996\n"
     ]
    }
   ],
   "source": [
    "from ortools.linear_solver import pywraplp\n",
    "\n",
    "\n",
    "def LinearProgrammingExample():\n",
    "    solver = pywraplp.Solver.CreateSolver('GLOP')\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    x = solver.NumVar(0, solver.infinity(), 'x')\n",
    "    y = solver.NumVar(0, solver.infinity(), 'y')\n",
    "  \n",
    "\n",
    "\n",
    "    solver.Add(x + y <= 40.0)\n",
    "\n",
    "    solver.Add(6 * x + 10*y <= 350.0)\n",
    "\n",
    "\n",
    "    \n",
    "    #Obj\n",
    "    solver.Maximize(70 * x + 100*y)\n",
    "\n",
    "    status = solver.Solve()\n",
    "\n",
    "    if status == pywraplp.Solver.OPTIMAL:\n",
    "        print('Objective value when wheat is at $26 = $', solver.Objective().Value())\n",
    "        print('x =', x.solution_value())\n",
    "        print('y =', y.solution_value())\n",
    "       \n",
    "    else:\n",
    "        print('No optimal solution.')\n",
    "LinearProgrammingExample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "id": "54451677",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution:\n",
      "Objective value when wheat constrant is at lower bound= 3525.0000000000005\n",
      "x = 24.99999999999999\n",
      "y = 20.00000000000001\n",
      "Solution:\n",
      "Objective value when wheat constrant is at upper bound= 4475.0\n",
      "x = 24.99999999999999\n",
      "y = 20.00000000000001\n"
     ]
    }
   ],
   "source": [
    "def LinearProgrammingExample():\n",
    "    solver = pywraplp.Solver.CreateSolver('GLOP')\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    x = solver.NumVar(0, solver.infinity(), 'x')\n",
    "    y = solver.NumVar(0, solver.infinity(), 'y')\n",
    "  \n",
    "    solver.Add(x + y <= 45.0)\n",
    "\n",
    "    solver.Add(6 * x + 10*y <= 350.0)\n",
    "\n",
    "    \n",
    "    #Obj\n",
    "    solver.Maximize(61 * x + 100*y)\n",
    "\n",
    "    status = solver.Solve()\n",
    "\n",
    "    if status == pywraplp.Solver.OPTIMAL:\n",
    "        print('Solution:')\n",
    "        print('Objective value when wheat constrant is at lower bound =', solver.Objective().Value())\n",
    "        print('x =', x.solution_value())\n",
    "        print('y =', y.solution_value())\n",
    "       \n",
    "    else:\n",
    "        print('No optimal solution.')\n",
    "LinearProgrammingExample()\n",
    "\n",
    "def LinearProgrammingExample():\n",
    "    solver = pywraplp.Solver.CreateSolver('GLOP')\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    x = solver.NumVar(0, solver.infinity(), 'x')\n",
    "    y = solver.NumVar(0, solver.infinity(), 'y')\n",
    "  \n",
    "    solver.Add(x + y <= 45.0)\n",
    "\n",
    "    solver.Add(6 * x + 10*y <= 350.0)\n",
    "\n",
    "    \n",
    "    #Obj\n",
    "    solver.Maximize(99 * x + 100*y)\n",
    "\n",
    "    status = solver.Solve()\n",
    "\n",
    "    if status == pywraplp.Solver.OPTIMAL:\n",
    "        \n",
    "        print('Objective value when wheat constrant is at upper bound =', solver.Objective().Value())\n",
    "        print('x =', x.solution_value())\n",
    "        print('y =', y.solution_value())\n",
    "       \n",
    "    else:\n",
    "        print('No optimal solution.')\n",
    "LinearProgrammingExample()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71cd7d44",
   "metadata": {},
   "source": [
    "## 1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "id": "44d54960",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective value when 40 acres of land are available = 3875.0\n",
      "x = 12.500000000000002\n",
      "y = 27.499999999999996\n"
     ]
    }
   ],
   "source": [
    "def LinearProgrammingExample():\n",
    "    solver = pywraplp.Solver.CreateSolver('GLOP')\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    x = solver.NumVar(0, solver.infinity(), 'x')\n",
    "    y = solver.NumVar(0, solver.infinity(), 'y')\n",
    "  \n",
    "    solver.Add(x + y <= 40.0)\n",
    "\n",
    "    solver.Add(6 * x + 10*y <= 350.0)\n",
    "\n",
    "\n",
    "    \n",
    "    #Obj\n",
    "    solver.Maximize(90 * x + 100*y)\n",
    "\n",
    "    status = solver.Solve()\n",
    "\n",
    "    if status == pywraplp.Solver.OPTIMAL:\n",
    "    \n",
    "        print('Objective value when 40 acres of land are available =', solver.Objective().Value())\n",
    "        print('x =', x.solution_value())\n",
    "        print('y =', y.solution_value())\n",
    "       \n",
    "    else:\n",
    "        print('No optimal solution.')\n",
    "LinearProgrammingExample()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92c3ee8a",
   "metadata": {},
   "source": [
    "## 3.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "id": "c3c47225",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost of bond portfolio: $ 2754.2844571158134\n",
      "Amount saved from optimising instead of just depositing full cash flow amount: $ 945.7155428841866\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        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></th>\n",
       "      <th>Quantity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Bond1</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond3</th>\n",
       "      <td>11.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond5</th>\n",
       "      <td>6.645898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond6</th>\n",
       "      <td>0.609338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond7</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond8</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond9</th>\n",
       "      <td>6.119757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond10</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond11</th>\n",
       "      <td>0.108870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond12</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond13</th>\n",
       "      <td>3.108870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Surplus1</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Surplus2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Surplus3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Surplus4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Surplus5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Surplus6</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Quantity\n",
       "Bond1      0.000000\n",
       "Bond2      0.000000\n",
       "Bond3     11.111111\n",
       "Bond4      0.000000\n",
       "Bond5      6.645898\n",
       "Bond6      0.609338\n",
       "Bond7      0.000000\n",
       "Bond8      0.000000\n",
       "Bond9      6.119757\n",
       "Bond10     0.000000\n",
       "Bond11     0.108870\n",
       "Bond12     0.000000\n",
       "Bond13     3.108870\n",
       "Surplus1   0.000000\n",
       "Surplus2   0.000000\n",
       "Surplus3   0.000000\n",
       "Surplus4   0.000000\n",
       "Surplus5   0.000000\n",
       "Surplus6   0.000000"
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3.1a\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.optimize import linprog\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#objective function\n",
    "obj = [109, 94.8, 99.5, 93.1, 97.2, 96.3,92.9, 110, 104, 101, 107,102,95.2, 0, 0, 0, 0, 0, 0 ]\n",
    "\n",
    "#Constraints vector\n",
    "\n",
    "lhs_eq = [\n",
    "    [10, 7, 8, 6, 7,6, 5, 10, 8, 6,10,7,100, -1, 0, 0, 0, 0, 0],\n",
    "    [10, 7, 8, 6, 7,6, 5, 10, 8, 6,110,107,0, 1, -1, 0, 0, 0,0],\n",
    "    [10, 7, 8, 6, 7,6, 5, 110,108,106,0,0,0, 0, 1, -1, 0, 0,0],\n",
    "    [10, 7, 8, 6, 7,106, 105, 0,0,0,0,0,0, 0, 0, 1, -1,0,0],\n",
    "    [10, 7, 8, 106, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,1, -1, 0],\n",
    "    [110, 107, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0, 1, -1]\n",
    "]\n",
    "\n",
    "rhs_eq = [\n",
    "    500,\n",
    "    200,\n",
    "    800,\n",
    "    200,\n",
    "    800,\n",
    "    1200\n",
    "]\n",
    "\n",
    "#bounds and optimiser\n",
    "bounds = [(0, float(\"inf\")) for x in range(len(obj))]\n",
    "opt = linprog(c=obj,\n",
    "               A_eq=lhs_eq, b_eq=rhs_eq, bounds=bounds,\n",
    "               method=\"simplex\")\n",
    "\n",
    "holdings_array=opt.x\n",
    "original=opt.fun\n",
    "\n",
    "print('Cost of bond portfolio: $',opt.fun)\n",
    "print('Amount saved from optimising instead of just depositing full cash flow amount: $',sum(rhs_eq)-opt.fun)\n",
    "# Organise bond allocations into DataFrame\n",
    "holdings={}\n",
    "holdings_name=['Bond1','Bond2','Bond3','Bond4','Bond5',\n",
    "               'Bond6','Bond7','Bond8','Bond9','Bond10',\n",
    "               'Bond11','Bond12','Bond13','Surplus1','Surplus2','Surplus3',\n",
    "              'Surplus4','Surplus5','Surplus6']\n",
    "   \n",
    "for i in range(0,len(holdings_name)):\n",
    "    holdings[holdings_name[i]]=holdings_array[i]\n",
    "holdings\n",
    "\n",
    "df = pd.DataFrame.from_dict([holdings])\n",
    "df=df.T\n",
    "df.rename(columns={0: \"Quantity\"})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07452949",
   "metadata": {},
   "source": [
    "## 3.1c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "id": "98fc7894",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda list: [0.9519999999997708, 0.8861818181817398, 0.8268013468009485, 0.7576424623589446, 0.6845011271830117, 0.6170646848499928]\n",
      "Interest rate term structure: [0.05042016806747984, 0.06227896636433283, 0.0654496756964289, 0.07184978032989675, 0.07876082432950904, 0.08378936399849501]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11ea19250>]"
      ]
     },
     "execution_count": 338,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_list=[]\n",
    "rate_list=[]\n",
    "rhs_eq_shadow=rhs_eq\n",
    "\n",
    "for i in range(0,6):\n",
    "    rhs_eq = [500,200,800,200,800,1200]\n",
    "    rhs_eq[i]=rhs_eq[i]+1\n",
    "    bounds = [(0, float(\"inf\")) for x in range(len(obj))]\n",
    "    opt = linprog(c=obj,\n",
    "               A_eq=lhs_eq, b_eq=rhs_eq, bounds=bounds,\n",
    "               method=\"simplex\")\n",
    "    \n",
    "    lambda_=opt.fun-original\n",
    "    lambda_list.append(lambda_)\n",
    "    rate=(1/(lambda_**(1/(i+1))))-1\n",
    "    rate_list.append(rate)\n",
    "print('lambda list:',lambda_list)\n",
    "print('Interest rate term structure:',rate_list)\n",
    "\n",
    "\n",
    "plt.plot([1,2,3,4,5,6],rate_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dd259e5",
   "metadata": {},
   "source": [
    "## 3.1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "id": "3452d632",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda list: [0.8387096774195015, 0.8387096774195015, 0.8387096774195015, 0.7649462365588988, 0.6925806451613425, 0.6260225103005723]\n",
      "Interest rate term structure: [0.1923076923074838, 0.0919284281982422, 0.060383062071035054, 0.06928203898812324, 0.07623207171752933, 0.08118914067292904]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11eb144f0>]"
      ]
     },
     "execution_count": 340,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#objective function\n",
    "obj = [109, 94.8, 99.5, 93.1, 97.2, 96.3,92.9, 110, 104, 101, 107,102,95.2, 0, 0, 0, 0, 0, 0 ]\n",
    "\n",
    "#lhs-equality\n",
    "lhs_eq = [\n",
    "    [10, 7, 8, 6, 7,6, 5, 10, 8, 6,10,7,100, -1, 0, 0, 0, 0, 0],\n",
    "    [10, 7, 8, 6, 7,6, 5, 10, 8, 6,110,107,0, 1, -1, 0, 0, 0,0],\n",
    "    [10, 7, 8, 6, 7,6, 5, 110,108,106,0,0,0, 0, 1, -1, 0, 0,0],\n",
    "    [10, 7, 8, 6, 7,106, 105, 0,0,0,0,0,0, 0, 0, 1, -1,0,0],\n",
    "    [10, 7, 8, 106, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,1, -1, 0],\n",
    "    [110, 107, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0, 1, -1]\n",
    "]\n",
    "\n",
    "#rhs-equality\n",
    "rhs_eq = [100,200,800,500,800,1200]\n",
    "\n",
    "#bounds\n",
    "bounds = [(0, float(\"inf\")) for x in range(len(obj))]\n",
    "opt2 = linprog(c=obj,\n",
    "               A_eq=lhs_eq, b_eq=rhs_eq, bounds=bounds,\n",
    "               method=\"simplex\")\n",
    "original=opt2.fun\n",
    "\n",
    "lambda_list=[]\n",
    "rate_list=[]\n",
    "\n",
    "original\n",
    "for i in range(0,6):\n",
    "    rhs_eq = [100,200,800,500,800,1200]\n",
    "    rhs_eq[i]=rhs_eq[i]+1\n",
    "    bounds = [(0, float(\"inf\")) for x in range(len(obj))]\n",
    "    opt2 = linprog(c=obj,\n",
    "               A_eq=lhs_eq, b_eq=rhs_eq, bounds=bounds,\n",
    "               method=\"simplex\")\n",
    "    lambda_=opt2.fun-original\n",
    "    lambda_list.append(lambda_)\n",
    "    rate=(1/(lambda_**(1/(i+1))))-1\n",
    "    rate_list.append(rate)\n",
    "\n",
    "print('lambda list:',lambda_list)\n",
    "print('Interest rate term structure:',rate_list)\n",
    "plt.plot([1,2,3,4,5,6],rate_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "197e0245",
   "metadata": {},
   "source": [
    "## 3.1f (Sum of cost of first 6 bonds has to be less than or equal half cost of total portfolio \n",
    "-> add an extra constraint sum of bonds 1-6 * their respective prices has to be <= to half portfolio value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "id": "d7710716",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost of bond portfolio: $ 2652.243431414401\n",
      "Amount saved from optimising instead of just depositing full cash flow amount: $ 847.7565685855989\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        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></th>\n",
       "      <th>Quantity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Bond1</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond3</th>\n",
       "      <td>8.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond5</th>\n",
       "      <td>5.919003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond6</th>\n",
       "      <td>2.753777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond7</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond8</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond9</th>\n",
       "      <td>6.253497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond10</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond11</th>\n",
       "      <td>0.230452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond12</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond13</th>\n",
       "      <td>3.230452</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Quantity\n",
       "Bond1   0.000000\n",
       "Bond2   0.000000\n",
       "Bond3   8.333333\n",
       "Bond4   0.000000\n",
       "Bond5   5.919003\n",
       "Bond6   2.753777\n",
       "Bond7   0.000000\n",
       "Bond8   0.000000\n",
       "Bond9   6.253497\n",
       "Bond10  0.000000\n",
       "Bond11  0.230452\n",
       "Bond12  0.000000\n",
       "Bond13  3.230452"
      ]
     },
     "execution_count": 354,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Constraints\n",
    "obj = [109, 94.8, 99.5, 93.1, 97.2, 96.3,92.9, 110, 104, 101, 107,102,95.2, 0, 0, 0, 0, 0, 0,0 ]\n",
    "#lhs-equality\n",
    "lhs_eq = [\n",
    "    [10, 7, 8, 6, 7,6, 5, 10, 8, 6,10,7,100, -1, 0, 0, 0, 0, 0,0],\n",
    "    [10, 7, 8, 6, 7,6, 5, 10, 8, 6,110,107,0, 1, -1, 0, 0, 0,0,0],\n",
    "    [10, 7, 8, 6, 7,6, 5, 110,108,106,0,0,0, 0, 1, -1, 0, 0,0,0],\n",
    "    [10, 7, 8, 6, 7,106, 105, 0,0,0,0,0,0, 0, 0, 1, -1,0,0,0],\n",
    "    [10, 7, 8, 106, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,1, -1, 0,0],\n",
    "    [110, 107, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0, 1, -1,0],\n",
    "    [1, 1, 1, 1, 1, 1,0,0,0,0,0, 0,0, 0, 0, 0, 0, 0, 0, 1]\n",
    "]\n",
    "\n",
    "#rhs-equality\n",
    "rhs_eq = [\n",
    "    500,\n",
    "    200,\n",
    "    800,\n",
    "    400,\n",
    "    700,\n",
    "    900,\n",
    "    1750\n",
    "]\n",
    "len(lhs_eq)\n",
    "#bounds\n",
    "bounds = [(0, float(\"inf\")) for x in range(len(obj))]\n",
    "opt = linprog(c=obj,\n",
    "               A_eq=lhs_eq, b_eq=rhs_eq, bounds=bounds,\n",
    "               method=\"simplex\")\n",
    "print('Cost of bond portfolio: $',opt.fun)\n",
    "print('Amount saved from optimising instead of just depositing full cash flow amount: $',sum(rhs_eq[0:6])-opt.fun)\n",
    "\n",
    "holdings_array=opt.x\n",
    "holdings={}\n",
    "holdings_name=['Bond1','Bond2','Bond3','Bond4','Bond5',\n",
    "               'Bond6','Bond7','Bond8','Bond9','Bond10',\n",
    "               'Bond11','Bond12','Bond13']\n",
    "   \n",
    "for i in range(0,len(holdings_name)):\n",
    "    holdings[holdings_name[i]]=holdings_array[i]\n",
    "holdings\n",
    "\n",
    "df = pd.DataFrame.from_dict([holdings])\n",
    "df=df.T\n",
    "df.rename(columns={0: \"Quantity\"})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14692c27",
   "metadata": {},
   "source": [
    "## 3.2a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "id": "9a66d9ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[103.313, 100.438, 102.746, 100.203, 104.066, 100.148, 104.7185, 100.141, 105.5235, 103.7185, 111.363, 105.445, 110.254, 101.9535]\n"
     ]
    }
   ],
   "source": [
    "# treasury bill dirty assuming its been 6 months since last interest payment with face value of 100\n",
    "\n",
    "dirty_price=[]\n",
    "clean_price=[101.563,100.188,101.746,100.078,102.941,100.023,103.656,100.016,104.461,103.031,109.738,104.570,108.879,101.516]\n",
    "coup=[3.5,0.5,2,.25,2.25,.25,2.125,.25,2.125,1.375,3.25,1.75,2.75,.875]\n",
    "for i in range (0,14):\n",
    "    dirty_price.append(((coup[i]/2))+clean_price[i])\n",
    "print(dirty_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "493bc5ea",
   "metadata": {},
   "source": [
    "## 3.2b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "id": "b0e61321",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost of bond portfolio: $ 80157383.82821563\n",
      "Amount saved from optimising instead of just depositing full cash flow amount: $ 3842616.171784371\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        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></th>\n",
       "      <th>Quantity in Millions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Bond1</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond4</th>\n",
       "      <td>0.236162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond6</th>\n",
       "      <td>0.170513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond7</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond8</th>\n",
       "      <td>0.093359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond9</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond10</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond11</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond12</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond13</th>\n",
       "      <td>0.294915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bond14</th>\n",
       "      <td>18.671745</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Quantity in Millions\n",
       "Bond1               0.000000\n",
       "Bond2               0.000000\n",
       "Bond3               0.000000\n",
       "Bond4               0.236162\n",
       "Bond5               0.000000\n",
       "Bond6               0.170513\n",
       "Bond7               0.000000\n",
       "Bond8               0.093359\n",
       "Bond9               0.000000\n",
       "Bond10              0.000000\n",
       "Bond11              0.000000\n",
       "Bond12              0.000000\n",
       "Bond13              0.294915\n",
       "Bond14             18.671745"
      ]
     },
     "execution_count": 370,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#treasury 3.2 b\n",
    "while len(dirty_price)<22:\n",
    "    dirty_price.append(0)\n",
    "obj=dirty_price\n",
    "\n",
    "lhs_eq = [\n",
    "    [.4375, 1.375, 0.875, 1.625, .685,1.0625, .125, 1.0625,.125,1.125,.125,1,100.25,101.75, -1, 0, 0, 0, 0, 0,0,0],\n",
    "    [.4375, 1.375, 0.875, 1.625, .685,1.0625, .125, 1.0625,.125,1.125,100.125,101, 0,0,1, -1, 0, 0, 0,0,0,0],\n",
    "    [.4375, 1.375, 0.875, 1.625, .685,1.0625, .125, 1.0625,100.125,101.125,0,0,0, 0, 0,1, -1, 0, 0,0,0,0],\n",
    "    [.4375, 1.375, 0.875, 1.625, .685, 1.0625, 100.125,101.0625,0,0,0,0, 0, 0,0,0, 1, -1,0,0,0,0],\n",
    "    [.4375, 1.375, 0.875, 1.625, .685, 101.0625, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0,1, -1, 0,0,0],\n",
    "    [.4375, 1.375, 0.875, 1.625, 100.685, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0,0, 1, -1,0,0],\n",
    "    [.4375, 1.375, 100.875, 101.625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0,0,0, 1, -1,0],\n",
    "    [100.4375, 101.375, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0, 1, -1]\n",
    "]\n",
    "\n",
    "rhs_eq = [12000000,10000000,10000000,10000000,9000000,9000000,9000000,15000000]\n",
    "\n",
    "#bounds\n",
    "bounds = [(0, float(\"inf\")) for x in range(len(obj))]\n",
    "opt_treasure = linprog(c=obj,\n",
    "               A_eq=lhs_eq, b_eq=rhs_eq, bounds=bounds,\n",
    "               method=\"simplex\")\n",
    "original=opt_treasure.fun\n",
    "\n",
    "print('Cost of bond portfolio: $',original)\n",
    "print('Amount saved from optimising instead of just depositing full cash flow amount: $',sum(rhs_eq)-original)\n",
    "\n",
    "holdings_array=(opt_treasure.x)/1000000\n",
    "holdings={}\n",
    "holdings_name=['Bond1','Bond2','Bond3','Bond4','Bond5',\n",
    "               'Bond6','Bond7','Bond8','Bond9','Bond10',\n",
    "               'Bond11','Bond12','Bond13','Bond13','Bond14']\n",
    "   \n",
    "for i in range(0,len(holdings_name)):\n",
    "    holdings[holdings_name[i]]=holdings_array[i]\n",
    "holdings\n",
    "\n",
    "df = pd.DataFrame.from_dict([holdings])\n",
    "df=df.T\n",
    "df.rename(columns={0: \"Quantity in Millions\"})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "582bd708",
   "metadata": {},
   "source": [
    "## 3.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "id": "694d95d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of variables = 22\n",
      "Number of constraints = 8\n",
      "Solution:\n",
      "Objective value = 471.3459717977485\n",
      "x1 = 424.40992891312027\n",
      "y1 = 0.0\n",
      "y2 = 178.21212073144528\n",
      "y3 = 0.0\n",
      "y4 = 0.0\n",
      "y5 = 0.0\n",
      "y6 = 0.0\n"
     ]
    }
   ],
   "source": [
    "#3.5\n",
    "from ortools.linear_solver import pywraplp\n",
    "\n",
    "\n",
    "def LinearProgrammingExample():\n",
    "    solver = pywraplp.Solver.CreateSolver('GLOP')\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    x1 = solver.NumVar(0, solver.infinity(), 'x1')\n",
    "    y1 = solver.NumVar(0, solver.infinity(), 'y1')\n",
    "    y2= solver.NumVar(0, solver.infinity(), 'y2')\n",
    "    y3 = solver.NumVar(0, solver.infinity(), 'y3')\n",
    "    y4 = solver.NumVar(0, solver.infinity(), 'y4')\n",
    "    y5 = solver.NumVar(0, solver.infinity(), 'y5')\n",
    "    y6 = solver.NumVar(0, solver.infinity(), 'y6')\n",
    "    \n",
    "    z1=solver.NumVar(0, solver.infinity(), 'z1')\n",
    "    z2=solver.NumVar(0, solver.infinity(), 'z2')\n",
    "    z3=solver.NumVar(0, solver.infinity(), 'z3')\n",
    "    z4=solver.NumVar(0, solver.infinity(), 'z4')\n",
    "    z5=solver.NumVar(0, solver.infinity(), 'z5')\n",
    "    z6=solver.NumVar(0, solver.infinity(), 'z6')\n",
    "    z7=solver.NumVar(0, solver.infinity(), 'z7')\n",
    "    \n",
    "    c1=solver.NumVar(0, solver.infinity(), 'c1')\n",
    "    c2=solver.NumVar(0, solver.infinity(), 'c2')\n",
    "    c3=solver.NumVar(0, solver.infinity(), 'c3')\n",
    "    c4=solver.NumVar(0, solver.infinity(), 'c4')\n",
    "    c5=solver.NumVar(0, solver.infinity(), 'c5')\n",
    "    c6=solver.NumVar(0, solver.infinity(), 'c6')\n",
    "    c7=solver.NumVar(0, solver.infinity(), 'c7')\n",
    "    vf=solver.NumVar(0,solver.infinity(), 'vf')\n",
    "  \n",
    "\n",
    "    print('Number of variables =', solver.NumVariables())\n",
    "\n",
    "    solver.Add(x1 + y1+z1-c1 == 100)\n",
    "\n",
    "    solver.Add(-0.01*x1-0.018*y1+y2+z2-1.025*z1-c2+1.005*c1 == 500)\n",
    "    \n",
    "    solver.Add((-0.01*x1)+y3-(.018)*y2-1.018*y1+z3-1.025*z2-c3+1.005*c2==100)\n",
    "    \n",
    "    solver.Add(-0.01*x1+y4-(.018)*y3 -1.018*y2+z4 - 1.025*z3-c4+1.005*c3==-600)\n",
    "    \n",
    "    solver.Add(-0.01*x1+y5-(.018)*y4-1.018*y3+z5-1.025*z4-c5+1.005*c4 == -500)\n",
    "    \n",
    "    solver.Add(-0.01*x1+y6-(.018)*y5-1.018*y4+z6-1.025*z5-c6+1.005*c5==200)\n",
    "    \n",
    "    solver.Add(-0.01*x1-(.018)*y6-1.018*y5+z7-1.025*z6-c7+1.005*c6==600)\n",
    "    \n",
    "    solver.Add(-(1.01)*x1-(1.018)*y6 - 1.025*z7+1.005*c7-vf==-900)\n",
    "\n",
    "\n",
    "    print('Number of constraints =', solver.NumConstraints())\n",
    "    \n",
    "    #Obj\n",
    "    solver.Maximize(vf)\n",
    "\n",
    "    status = solver.Solve()\n",
    "\n",
    "    if status == pywraplp.Solver.OPTIMAL:\n",
    "        print('Solution:')\n",
    "        print('Objective value =', solver.Objective().Value())\n",
    "        print('x1 =', x1.solution_value())\n",
    "        print('y1 =', y1.solution_value())\n",
    "        print('y2 =', y2.solution_value())\n",
    "        print('y3 =', y3.solution_value())\n",
    "        print('y4 =', y4.solution_value())\n",
    "        print('y5 =', y5.solution_value())\n",
    "        print('y6 =', y6.solution_value())\n",
    "        \n",
    "    else:\n",
    "        print('No optimal solution.')\n",
    "LinearProgrammingExample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "id": "ba81a505",
   "metadata": {},
   "outputs": [
    {
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
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       "      <td>471.345972</td>\n",
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       "      <th>z3 quantity</th>\n",
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       "      <th>z4 quantity</th>\n",
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       "      <th>z7 quantity</th>\n",
       "      <td>0.000000</td>\n",
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       "</table>\n",
       "</div>"
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       "                       \n",
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       "      <td>0.000000</td>\n",
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       "      <th>z7 quantity</th>\n",
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       "                       \n",
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       "y4 quantity    0.000000\n",
       "y5 quantity    0.000000\n",
       "y6 quantity    0.000000\n",
       "z1 quantity    0.000000\n",
       "z2 quantity    0.000000\n",
       "z3 quantity  105.522801\n",
       "z4 quantity    0.000000\n",
       "z5 quantity    0.000000\n",
       "z6 quantity    0.000000\n",
       "z7 quantity    0.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(None, None)"
      ]
     },
     "execution_count": 399,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3.5\n",
    "def short_term_cashflow(i):\n",
    "    def LinearProgrammingExample():\n",
    "        solver = pywraplp.Solver.CreateSolver('GLOP')\n",
    "        if not solver:\n",
    "            return\n",
    "\n",
    "        x1 = solver.NumVar(0, solver.infinity(), 'x1')\n",
    "        y1 = solver.NumVar(0, solver.infinity(), 'y1')\n",
    "        y2= solver.NumVar(0, solver.infinity(), 'y2')\n",
    "        y3 = solver.NumVar(0, solver.infinity(), 'y3')\n",
    "        y4 = solver.NumVar(0, solver.infinity(), 'y4')\n",
    "        y5 = solver.NumVar(0, solver.infinity(), 'y5')\n",
    "        y6 = solver.NumVar(0, solver.infinity(), 'y6')\n",
    "\n",
    "        z1=solver.NumVar(0, solver.infinity(), 'z1')\n",
    "        z2=solver.NumVar(0, solver.infinity(), 'z2')\n",
    "        z3=solver.NumVar(0, solver.infinity(), 'z3')\n",
    "        z4=solver.NumVar(0, solver.infinity(), 'z4')\n",
    "        z5=solver.NumVar(0, solver.infinity(), 'z5')\n",
    "        z6=solver.NumVar(0, solver.infinity(), 'z6')\n",
    "        z7=solver.NumVar(0, solver.infinity(), 'z7')\n",
    "\n",
    "        c1=solver.NumVar(0, solver.infinity(), 'c1')\n",
    "        c2=solver.NumVar(0, solver.infinity(), 'c2')\n",
    "        c3=solver.NumVar(0, solver.infinity(), 'c3')\n",
    "        c4=solver.NumVar(0, solver.infinity(), 'c4')\n",
    "        c5=solver.NumVar(0, solver.infinity(), 'c5')\n",
    "        c6=solver.NumVar(0, solver.infinity(), 'c6')\n",
    "        c7=solver.NumVar(0, solver.infinity(), 'c7')\n",
    "        vf=solver.NumVar(0,solver.infinity(), 'vf')\n",
    "\n",
    "\n",
    "        solver.Add(x1 + y1+z1-c1 == 100)\n",
    "\n",
    "        solver.Add(-0.01*x1-0.018*y1+y2+z2-1.025*z1-c2+1.005*c1 == i)\n",
    "\n",
    "        solver.Add((-0.01*x1)+y3-(.018)*y2-1.018*y1+z3-1.025*z2-c3+1.005*c2==100)\n",
    "\n",
    "        solver.Add(-0.01*x1+y4-(.018)*y3 -1.018*y2+z4 - 1.025*z3-c4+1.005*c3==-600)\n",
    "\n",
    "        solver.Add(-0.01*x1+y5-(.018)*y4-1.018*y3+z5-1.025*z4-c5+1.005*c4 == -500)\n",
    "\n",
    "        solver.Add(-0.01*x1+y6-(.018)*y5-1.018*y4+z6-1.025*z5-c6+1.005*c5==200)\n",
    "\n",
    "        solver.Add(-0.01*x1-(.018)*y6-1.018*y5+z7-1.025*z6-c7+1.005*c6==600)\n",
    "\n",
    "        solver.Add(-(1.01)*x1-(1.018)*y6 - 1.025*z7+1.005*c7-vf==-900)\n",
    "\n",
    "\n",
    "        #Obj\n",
    "        solver.Maximize(vf)\n",
    "\n",
    "        status = solver.Solve()\n",
    "\n",
    "        if status == pywraplp.Solver.OPTIMAL:\n",
    "            df_dict={'Cost':solver.Objective().Value(),'x1 quantity' : x1.solution_value(),\n",
    "                           'y1 quantity':y1.solution_value(),'y2 quantity':y2.solution_value(),\n",
    "                           'y3 quantity':y3.solution_value(), 'y4 quantity':y4.solution_value(),\n",
    "                           'y5 quantity':y5.solution_value(),'y6 quantity':y6.solution_value(),\n",
    "                           'z1 quantity':z1.solution_value(), 'z2 quantity':z2.solution_value(),\n",
    "                           'z3 quantity':z3.solution_value(), 'z4 quantity':z4.solution_value(),\n",
    "                           'z5 quantity':z5.solution_value(),'z6 quantity':z6.solution_value(), \n",
    "                           'z7 quantity':z7.solution_value()}\n",
    "            df=pd.DataFrame(df_dict,index=[0])\n",
    "            display(df.T.rename(columns={0: \"\"}))\n",
    "            \n",
    "                    \n",
    "\n",
    "        else:\n",
    "            print('No optimal solution.')\n",
    "    return LinearProgrammingExample()\n",
    "\n",
    "short_term_cashflow(500),short_term_cashflow(300)"
   ]
  }
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