{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SZvdVCjRo1tE"
   },
   "source": [
    "# **<center>Décision dans l'incertain</center>**\n",
    "\n",
    "\n",
    "## <center> La théorie du portefeuille de Markowitz (janv 2024)</center>\n",
    "$\\newcommand\\indi[1]{{\\mathbf 1}_{\\displaystyle #1}}$\n",
    "$\\newcommand\\inde[1]{{\\mathbf 1}_{\\displaystyle\\left\\{ #1 \\right\\}}}$\n",
    "$\\newcommand{\\ind}{\\inde}$\n",
    "$\\newcommand\\E{{\\mathbf E}}$\n",
    "$\\newcommand\\Cov{{\\mathrm Cov}}$\n",
    "$\\newcommand\\Var{{\\mathrm Var}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AZePCUPkotjl"
   },
   "source": [
    "# 1. Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "chL7VyMJotjm"
   },
   "source": [
    "On considere $d$ actifs dont les rendements sont donnés par\n",
    "$(R_1,\\ldots,R_d)$.  L'hypothèse de rendement signifie que si on\n",
    "détient à l'instant $0$ une quantité d'actif $i$ de valeur $V$, la\n",
    "valeur de cette même quantité d'actif à l'instant $T$ (égal à $T=1$ an\n",
    "par exemple) sera donnée par $V(1+R_i)$.\n",
    "\n",
    "On suppose de plus que ces rendements ont des caractéristiques de\n",
    "moyenne et de variance connue. On note $\\mu$ le vecteur des espérances\n",
    "$\\mu_i=\\E(R_i)$ et $\\Gamma$ la matrice de variance covariance, où\n",
    "$\\Gamma_{ij}=\\Cov(R_i,R_j)$. On note $\\sigma_i^2=\\Var(R_i)=\\Gamma_{ii}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZbbTA-WZotjn"
   },
   "source": [
    "Pour construire le modèle, on suppose que la matrice de corrélation $C$, i.e. la matrice définie par\n",
    "$$\n",
    "  C_{ij} = \\frac{\\Cov(R_i,R_j)}{\\sqrt{\\Var(R_i)}\\sqrt{\\Var(R_j)}},\n",
    "$$\n",
    "est de la forme\n",
    "$$\n",
    "  C= \\left(\n",
    "      \\begin{array}{lllll}\n",
    "         1    & \\rho & \\rho & \\dots & \\rho\\\\\n",
    "         \\rho & 1    & \\rho & \\dots & \\rho\\\\\n",
    "         \\rho & \\rho & 1    & \\dots & \\rho\\\\\n",
    "         \\vdots & \\ddots & \\ddots & \\ddots & \\vdots\\\\\n",
    "         \\rho & \\rho & \\ldots & \\rho & 1\n",
    "      \\end{array}\n",
    "    \\right).\n",
    "$$\n",
    "On fixe la constante $\\rho$ et le vecteur $\\sigma$ des écart-types des rendements défini pour tout $i$ par\n",
    "$$\n",
    "  \\sigma_i = \\sqrt{\\Var(R_i)}.\n",
    "$$\n",
    "Avec la matrice $C$, le vecteur $\\sigma$ (vecteur colonne) et sa transposée $\\sigma'$ on peut construire une matrice de variance-covariance $\\Gamma$ pour le vecteur $R$ en posant (exercice: il faut vérifier que $\\Gamma$ est bien une matrice symétrique et définie positive):\n",
    "$$\n",
    " \\Gamma_{ij} = \\sigma_i C_{ij} \\sigma_{j}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HZp9SbVXotjn"
   },
   "source": [
    "## 1.1. Le cas à deux actifs risqués"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MfyrebiNotjo"
   },
   "source": [
    "On suppose que $d=2$, que $\\mu_1=5\\%$ et $\\mu_2=15\\%$, que\n",
    "$\\sigma_1=10\\%$ et $\\sigma_2=30\\%$ et $\\rho$ étant un paramètre réel,\n",
    "$\\Gamma$ est donnée par\n",
    "$$\n",
    "   \\Gamma=\\left(\\begin{array}{cc}\n",
    "      \\sigma_1^2 & \\rho \\sigma_1 \\sigma_2\\\\\n",
    "      \\rho \\sigma_1 \\sigma_2 &  \\sigma_2^2 \n",
    "   \\end{array}\\right).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mpDmlt4Hotjr"
   },
   "source": [
    "---\n",
    "<font color=red>Question 1:</font>\n",
    "<br><font color='blue'>\n",
    " Que représente $\\rho$ ? A quelle condition sur $\\rho$ la matrice\n",
    "  $\\Gamma$ est la matrice de covariance d'un vecteur aléatoire ? \n",
    "</font>\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "\n",
    "  \n",
    "  Dans la suite, on prendra $\\rho=0$.\n",
    "\n",
    "  On constitue un portefeuille de valeur initiale $X_0=1$ constitué\n",
    "  d'une quantité $x_1$ d'actif $1$ et $x_2$ d'actif $2$ avec\n",
    "  $x_1\\geq 0$, $x_2\\geq 0$ et $X_0=x_1+x_2=1$ (i.e. on répartit $1$E\n",
    "  entre le deux actifs risqués). On note $X_T$ la valeur de ce\n",
    "  portefeuille en $T$\n",
    "\n",
    "  Vérifier que si le gain $G_T$ est défini par $G_T=X_T-X_0$,\n",
    "  $$\\E(G_T)=\\mu_1 x_1 + \\mu_2 x_2=\\mu_2 + x_1(\\mu_1-\\mu_2)$$ et\n",
    "  $$\\Var(G_T)=x.\\Gamma x=\\sigma_1^2 x_1^2 + \\sigma_2^2 (1-x_1)^2 + 2\n",
    "  \\rho \\sigma_1\\sigma_2 x_1 (1-x_1).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TgcOuYvlotjs"
   },
   "source": [
    "---\n",
    "<font color=red>Question 2:</font>\n",
    "<br><font color='blue'>\n",
    " Tracer les caractéristiques des actifs de base dans le plan (moyenne,écart type).\n",
    "</font>\n",
    "\n",
    "---\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "hZV0VyOUotjt",
    "outputId": "05f95e57-8766-4b3f-a252-2aa03bae20d0"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "#plt.style.use('dark_background') # Pour un background noir\n",
    "\n",
    "# On définit les caracteristiques des actifs\n",
    "d=2\n",
    "# On choisit les moyennes des actifs.\n",
    "mu=[0.05,0.15]\n",
    "# On choisit les variances des actifs.\n",
    "sigma=[0.10,0.30]\n",
    "\n",
    "# On choisit pour matrice de corrélation: des 1 sur la diagonale, des rho ailleurs\n",
    "# rho=0 : cas d'actifs décorrélés (en particulier cas indépendant) \n",
    "rho=0.0\n",
    "\n",
    "    ######  A vous de jouer  .....\n",
    "    # Construire la matrice C\n",
    "    # covariance = ...\n",
    "    # Construire la matrice Gamma\n",
    "    # Gamma = ...\n",
    "\n",
    "# Les caractéristiques des actifs de base\n",
    "moyenne_actif=mu\n",
    "std_actif=sigma\n",
    "\n",
    "# plot ###################################################################\n",
    "max_sigma=max(std_actif)\n",
    "max_esp=max(moyenne_actif)\n",
    "marge=0.03\n",
    "un_inche_en_cm=2.54 # 1 inche = 2.54 cm\n",
    "\n",
    "taille_h_cm=25\n",
    "taille_v_cm=20\n",
    "\n",
    "marker_size=100\n",
    "\n",
    "def plot1():\n",
    "    # On crée un figure dont on fixe la taille et dont on définit les axes\n",
    "    fig = plt.gcf()\n",
    "    fig.set_size_inches(taille_h_cm/un_inche_en_cm,taille_v_cm/un_inche_en_cm)\n",
    "    plt.axis([-marge, 2*max_sigma+marge, -marge, 2*max_esp+marge])\n",
    "    # On trace les points représentant les 2 actifs.\n",
    "    plt.scatter(sigma,mu, s=marker_size, c='b',marker='o')\n",
    "    plt.ylabel('Moyenne')\n",
    "    plt.xlabel('Ecart-type')\n",
    "    plt.title('diagamme (Ecart-type,Moyenne)')\n",
    "    #plt.text(60, .025, r'$\\mu=100,\\ \\sigma=15$')\n",
    "    plt.grid(True)\n",
    "\n",
    "plot1()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-pYAmSHfotjw"
   },
   "source": [
    "---\n",
    "<font color=red>Question 3:</font>\n",
    "<br><font color='blue'>\n",
    "Tracer la courbe $x_1\\in [0,1] \\to (\\E(G_T),\\sqrt{\\Var(G_T)})$.  \n",
    "Vérifier que l'on peut construire un portefeuille de même variance\n",
    "que l'actif $1$ mais dont l'espérance du rendement est supérieure à\n",
    "celle de cet actif. Est il rationnel d'investir dans l'actif $1$,\n",
    "si l'on cherche à minimiser son risque ?\n",
    "Quel sont les portefeuilles dans lesquels il paraît rationnel d'investir ?\n",
    "</font>\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "b7RlTsZWotjx",
    "outputId": "b74ea94c-0853-4cee-c865-b22915e024cc"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def frange(start, stop, step):\n",
    "#exemple:\n",
    "#for i in frange(0.5, 1.0, 0.1): print(i)\n",
    "    i = start\n",
    "    while i < stop:\n",
    "        yield i\n",
    "        i += step\n",
    "\n",
    "####################\n",
    "N=100\n",
    "moyenne_x=np.zeros(N)\n",
    "std_x=np.zeros(N)\n",
    "i=0\n",
    "for x_1 in frange(0.0,1.0,1.0/N):\n",
    "    current_x = [x_1,1-x_1]  # composition du portefeuille  x_1 + x_2 = 1\n",
    "\n",
    "    ######  A vous de jouer  .....\n",
    "    # moyenne_x[i] = ...   calcul de la moyenne du rendement du porfefeuille\n",
    "    # std_x[i]= ...        calcul de son écart-type\n",
    "    # np.dot(u,v) calcule le produit scalaire des vecteurs u et v\n",
    "    # np.dot(M,v) calcule le produit matriciel de M et du vecteur v\n",
    "    # math.sqrt(x) racine carrée de x\n",
    "    \n",
    "    i=i+1\n",
    "    \n",
    "# plot ###################################################################\n",
    "def plot2():\n",
    "    plot1()# le plot précédent\n",
    "    plt.plot(std_x,moyenne_x, 'r-')\n",
    "    \n",
    "plot2()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MKpuAT01otjy"
   },
   "source": [
    "---\n",
    "<font color=red>Question 4:</font>\n",
    "<br><font color='blue'>\n",
    "Vérifier que l'on peut construire un portefeuille de variance\n",
    "  minimum (et inférieure à celle de l'actif de variance\n",
    "  minimum). \n",
    "</font>\n",
    "\n",
    "---\n",
    "\n",
    "C'est un exemple de l'__effet de diversification__ dans\n",
    "  la théorie des portefeuille.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "AA3LRdmDotj1",
    "outputId": "cc23e99f-e026-4ae8-d311-982f61f88109"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot ###################################################################\n",
    "def plot3():\n",
    "    plot2()# le plot précédent\n",
    "\n",
    "    ######  A vous de jouer  .....\n",
    "    # calcul de l'indice du portefeuille de variance minimum\n",
    "    # Vecteur.argmin() renvoit l'indice du plus petit nombre du Vecteur\n",
    "    # imin = ...\n",
    "    \n",
    "    # on trace ce point en vert c='g' (couleur=vert)\n",
    "    plt.scatter(std_x[imin],moyenne_x[imin], s=marker_size, c='g',marker='o')\n",
    "\n",
    "plot3()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Hf4Skg1Kotj2"
   },
   "source": [
    "Nous relaxons la condition $x_1\\geq 0$, $x_2\\geq 0$ tout en\n",
    "  continuant à imposer $x_1+x_2=1$ (la valeur totale de notre\n",
    "  investissement initial reste égale à $1$). Nous allons faire varier\n",
    "  $x_1$ entre $-10$ et $0$ (lorsque $x_1$ est négatif, on emprunte une\n",
    "  quantité $|x_1|$ d'actif $1$, mais la valeur totale du portefeuille\n",
    "  doit toujours rester égale à $1$).\n",
    "\n",
    "\n",
    "---\n",
    "<font color=red>Question 5:</font>\n",
    "<br><font color='blue'>\n",
    " Tracer la courbe $x_1\\in [-5,0] \\to\n",
    " (\\E(G_T),\\sqrt{\\Var(G_T)})$. Vérifier que, si l'on accepte une\n",
    " variance grande, on peut constituer des portefeuilles d'espérance\n",
    " aussi grande que souhaitée (cet effet porte le nom d'__effet de\n",
    "   levier__ ou leverage effect). On comprend qu'il ne faille pas en\n",
    " abuser !\n",
    "</font>\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "nOkQQs2Totj3",
    "outputId": "e4e0a311-adc7-42b7-b9f0-83da924ae028"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On autorise l'emprunt de l'actif 1\n",
    "N=1000\n",
    "moyenne2_x=np.zeros(N)\n",
    "std2_x=np.zeros(N)\n",
    "for i in range(0,N):\n",
    "  \n",
    "    ######  A vous de jouer  .....\n",
    "    # prendre de valeurs negatives pour x_1 dans [-5,0], en déduire x_2\n",
    "    # x_1 = - ...\n",
    "    # x_2 = ...\n",
    "    # calcul de la moyenne et de l'écart-type de ce portefeuille\n",
    "    # x=[x_1,x_2]\n",
    "    # moyenne2_x[i]=...\n",
    "    # std2_x[i]=...\n",
    "    \n",
    "# plot ###################################################################\n",
    "def plot4():\n",
    "    plot3()# le plot précédent\n",
    "    plt.plot(std2_x, moyenne2_x,'g-')\n",
    "    \n",
    "plot4()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3eAq0uYZotj4"
   },
   "source": [
    "---\n",
    "<font color=red>Question 6:</font>\n",
    "<br><font color='blue'>\n",
    "Tracer la courbe $x_2\\in [-5,0] \\to\n",
    " (\\E(G_T),\\sqrt{\\Var(G_T)})$.\n",
    " Vérifier que lorsque l'on emprunte\n",
    " l'actif $2$ ($x_2$ négatif), l'on fait décroître l'espérance en\n",
    " augmentant la variance (ce qui est loin d'être optimal!).\n",
    "</font>\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "qHyQTkZVotj4",
    "outputId": "7b0f79dd-84ac-418d-dd5d-24ae777c5086"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BgwYJ3eLatm17z3lPPvmkxo0bp7179ybUIkmLFi2SzWZT06ZNE83v16+fWrRooVdeeUXOzs569dVXEz2e1u8jJZ555hmNHz9eZ8+eTXK7rD2xsbE6c+aMnn766QyoDkBmRFgCkC2MGTNGTz31lPz9/TVw4EDFxcUpODhYuXLleuBVj2eeeUYrVqxQ79691b59e505c0ZjxoxR0aJFdezYsYR5Tz31lPz8/DRw4EBFRkaqdu3a2r59uxYtWiRJifa0eeaZZ7Rw4UJVqFBB1apV0549ezRx4sQH3m6W0XLnzq0ZM2bolVde0eXLl9W+fXsVLlxYFy9e1IEDB3Tx4kXNnj37ns9/5JFHVLp0ae3YsUN9+/ZN8vitW7e0Y8cOu8+9cyVr9OjR+u677/T4449r2LBhqlq1qq5cuaLvv/9eAQEBqlChQrLX6H7y5MkjHx8frVq1Sk8++aTy58+vggUL3veqQpUqVSRJ8+bNU548eeTh4SFfX9+Eq0HOzs568803NXToUOXKleuenwsqVqyYnnvuOY0cOVJFixbVZ599ptDQUAUHBytnzpySpP79++urr77S448/rgEDBqhatWqKj4/X6dOntW7dOg0cOFD16tWTZLbSHjVq1ANvF5w/f/4Dvy8DBgzQokWL1Lp1a40ePVo+Pj5avXq1Zs2apTfeeEOPPvpoovn+/v6qVKmSfvzxx4R24/+WkveR1vz8/PTaa6+pW7du2r17tx5//HHlypVLYWFh2rJli6pWrZro/+g4ePCgbt68mSQQAshGLG4wAQAZ5r///a9RrVo1w83NzShZsqQxfvz4hC5a/2avG9748eONUqVKGe7u7kbFihWNDz/80O5zL1++bHTr1s3ImzevkTNnTsPf39/YsWOHIcmYNm1awry///7b6NGjh1G4cGEjZ86cRqNGjYzNmzcbTZo0MZo0aZIw7043vOXLlyd6nY8//tiQlKSj2L87nt0hyXjzzTcTzTt58mSS1tT3e72NGzcarVu3NvLnz2+4uroaxYsXN1q3bp1knj1vv/22kS9fPuP27duJxu/XDU+SERMTkzD3zJkzRvfu3Y0iRYoYrq6uRrFixYwOHToY58+fT5iT3DWy9/24Y/369UbNmjUNd3d3Q9J9uyLeERISYvj6+hrOzs6GJOPjjz9O9PipU6cMSUavXr3sPt/Hx8do3bq18eWXXxqVK1c23NzcjFKlShlTpkxJMvf69evGiBEjjPLlyxtubm6Gl5eXUbVqVWPAgAGJ2l4PHDjQsNlsCa3VDcP+nw177u6GZxiG8eeffxqdOnUyChQoYLi6uhrly5c3Jk6cmKjF+7+NHDnSkGTs2LHD7uPJfR/3Wqu7f0bv9d7u/Jz8u/ugYRjGggULjHr16hm5cuUycuTIYZQpU8bo0qWLsXv37kTz3n77baNgwYJJ/uwCyD5shpGMlj4AgFRbvHix/vOf/2jr1q1q2LCh1eVkuHPnzsnX11eLFi1Sx44drS4nw82YMUN9+/bVr7/+qsqVKyd5vFSpUqpSpUqSjVYfRt26deXj45PQiS+j1alTRzabLclnvbKSuLg4lS1bVp06ddL7779vdTkALMJteACQhpYsWaKzZ8+qatWqcnJy0o4dOzRx4kQ9/vjj2TIoSeYtZv3799f777+vF154IdHtiI5s3759OnnypEaPHq02bdrYDUrpITIyUgcOHNAnn3ySIa/379f99ddf9e2332rPnj1auXJlhr5+Wvvss890/fp1DR482OpSAFiIsAQAaShPnjxaunSp3nvvPd24cUNFixZV165d9d5771ldmqVGjBihnDlz6uzZsypRooTV5WSItm3bKjw8XI0bN9acOXMy7HU9PT3v2QUwPe3du1dNmzZVgQIF9O677+r555/P8BrSUnx8vD7//PNM1Z0SQMbjNjwAAAAAsCN73AsBAAAAAClEWAIAAAAAO/jMkh3x8fE6d+6c8uTJk6Jd3gEAAABkboZh6Nq1aypWrNgDmw4Rluw4d+5ctvkAMgAAAJAdnTlz5oGbwROW7MiTJ48k8xvo6elpaS0xMTFat26dWrRoIVdXV0trwcNjPR0Ha+lYWE/HwVo6FtbTcWSmtYyMjFSJEiUS/s1/P4QlO+7ceufp6ZkpwlLOnDnl6elp+R8sPDzW03Gwlo6F9XQcrKVjYT0dR2Zcy+R83IYGDwAAAABgB2EJAAAAAOwgLAEAAACAHYQlAAAAALCDsAQAAAAAdhCWAAAAAMAOwhIAAAAA2EFYAgAAAAA7CEsAAAAAYAdhCQAAAADsICwBAAAAgB2EJQAAAACwg7AEAAAAAHYQlgAAAADADsISAAAAANhBWAIAAAAAOwhLAAAAAGAHYQkAAAAA7CAsAQAAAIAdhCUAAAAAsIOwBAAAAAB2EJYAAAAAwA7CEgAAAADYQVgCAAAAADsISwAAAABgB2EJAAAAAOwgLAEAAACAHYQlAAAAALCDsAQAAAAAdhCWAAAAAMAOwhIAAAAA2EFYAgAAAAA7CEsAAAAAYAdhCQAAAADsICwBAAAAgB2EJQAAAACwg7AEAAAAAHYQlgAAAADADsISAAAAANhBWAIAAAAAOwhLAAAAAGAHYQkAAAAA7CAsAQAAAIAdhCUAAAAAsMPysDRr1iz5+vrKw8NDtWvX1ubNm+85d8uWLfLz81OBAgWUI0cOVahQQVOnTk0y76uvvlKlSpXk7u6uSpUqaeXKlen5FgAAAAA4IEvD0rJly9S/f38NHz5c+/btU+PGjdWqVSudPn3a7vxcuXLprbfe0qZNm3TkyBGNGDFCI0aM0Lx58xLmbN++XR07dlTnzp114MABde7cWR06dNDOnTsz6m0BAAAAcACWhqUpU6aoR48e6tmzpypWrKiQkBCVKFFCs2fPtju/Zs2aeumll1S5cmWVKlVKL7/8slq2bJnoalRISIj8/f0VFBSkChUqKCgoSE8++aRCQkIy6F0BAAAAcAQuVr1wdHS09uzZo8DAwETjLVq00LZt25J1jn379mnbtm167733Esa2b9+uAQMGJJrXsmXL+4alqKgoRUVFJRxHRkZKkmJiYhQTE5OsWtLLnde3ug6kDdbTcbCWjoX1dByspWNhPR1HZlrLlNRgWVi6dOmS4uLi5O3tnWjc29tb4eHh933uI488oosXLyo2NlYjR45Uz549Ex4LDw9P8TnHjRunUaNGJRlft26dcubMmZy3k+5CQ0OtLgFpiPV0HKylY2E9HQdr6VhYT8eRGdby5s2byZ5rWVi6w2azJTo2DCPJ2N02b96s69eva8eOHQoMDFTZsmX10ksvpfqcQUFBCggISDiOjIxUiRIl1KJFC3l6eqbk7aS5mJgYhYaGyt/fX66urpbWgofHejoO1tKxsJ6Og7V0LKyn48hMa3nnLrLksCwsFSxYUM7Ozkmu+Fy4cCHJlaG7+fr6SpKqVq2q8+fPa+TIkQlhqUiRIik+p7u7u9zd3ZOMu7q6Wr6Yd2SmWvDwWE/HwVo6FtbTcbCWjoX1dByZYS1T8vqWNXhwc3NT7dq1k1yKCw0NVcOGDZN9HsMwEn3eqEGDBknOuW7duhSdEwAAAAAsvQ0vICBAnTt3Vp06ddSgQQPNmzdPp0+fVq9evSSZt8edPXtWixYtkiTNnDlTJUuWVIUKFSSZ+y5NmjRJffr0SThnv3799Pjjjys4OFht2rTRqlWrtH79em3ZsiXj3yAAAACALMvSsNSxY0dFRERo9OjRCgsLU5UqVbRmzRr5+PhIksLCwhLtuRQfH6+goCCdPHlSLi4uKlOmjMaPH6/XX389YU7Dhg21dOlSjRgxQm+//bbKlCmjZcuWqV69ehn+/gAAAABkXZY3eOjdu7d69+5t97GFCxcmOu7Tp0+iq0j30r59e7Vv3z4tygMAAACQTVm6KS0AAAAAZFaEJQAAAACwg7AEAAAAAHYQlgAAAADADsISAAAAANhBWAIAAAAAOwhLAAAAAGAHYQkAAAAA7CAsAQAAAIAdhCUAAAAAsIOwBAAAAAB2EJYAAAAAwA7CEgAAAADYQVgCAAAAADsISwAAAABgB2EJAAAAAOwgLAEAAACAHYQlAAAAALCDsAQAAAAAdhCWAAAAAMAOwhIAAAAA2EFYAgAAAAA7CEsAAAAAYAdhCQAAAADsICwBAAAAgB2EJQAAAACwg7AEAAAAAHYQlgAAAADADsISAAAAANhBWAIAAAAAOwhLAAAAAGAHYQkAAAAA7CAsAQAAAIAdhCUAAAAAsIOwBAAAAAB2EJYAAAAAwA7CEgAAAADYQVgCAAAAADsISwAAAABgB2EJAAAAAOwgLAEAAACAHYQlAAAAALCDsAQAAAAAdhCWAAAAAMAOwhIAAAAA2EFYAgAAAAA7CEsAAAAAYAdhCQAAAADsICwBAAAAgB2EJQAAAACwg7AEAAAAAHYQlgAAAADADsISAAAAANhBWAIAAAAAOwhLAAAAAGAHYQkAAAAA7CAsAQAAAIAdhCUAAAAAsIOwBAAAAAB2EJYAAAAAwA7CEgAAAADYQVgCAAAAADsISwAAAABgB2EJAAAAAOwgLAEAAADIFm5E39DsXbOTPd8lHWsBAAAAAMtdunlJM3bO0Ae7PtDlvy8n+3mEJQAAAAAO6c8rf2ry9sn6aO9HuhV7S5Lkm89XJ3UyWc8nLAEAAABwKL+c/0UTtk3Qkl+WKM6IkyTVKlpLQ/2Gyr+4v/IPzZ+s8xCWAAAAADiELae3aPyW8Vp9bHXC2JO+TyqwUaCe9H1SNptNkZGRyT4fYQkAAABAlhVvxOvb379V8NZgbTuzTZJkk03tKrXTUL+hqlOsTqrPTVgCAAAAkOVEx0VryS9LNGHbBB2+eFiS5Obspleqv6JBDQfp0QKPPvRrEJYAAAAAZBnXo6/ro70fafL2yfor8i9Jkqe7p96o84b61eunonmKptlrEZYAAAAAZHp32n/P+HmG/r79tyTJO5e3BtQfoF51esnLwyvNX5OwBAAAACDTstf+u2z+shrccLC6VO8iDxePdHttp3Q7czLNmjVLvr6+8vDwUO3atbV58+Z7zl2xYoX8/f1VqFAheXp6qkGDBlq7dm2iOQsXLpTNZkvydfv27fR+KwAAAADSyC/nf9HLK15WmellNOPnGboVe0u1i9bWF+2/0G9v/qbXar+WrkFJsvjK0rJly9S/f3/NmjVLfn5+mjt3rlq1aqXDhw+rZMmSSeZv2rRJ/v7+Gjt2rPLmzauPP/5Yzz77rHbu3KmaNWsmzPP09NTRo0cTPdfDI32/kQAAAAAejmEYZvvvreO15tiahPHmpZsr0C9QzXybyWazZVg9loalKVOmqEePHurZs6ckKSQkRGvXrtXs2bM1bty4JPNDQkISHY8dO1arVq3SN998kygs2Ww2FSlSJNl1REVFKSoqKuH4Tu/1mJgYxcTEpOQtpbk7r291HUgbrKfjYC0dC+vpOFhLx8J6Oo4HrWW8Ea9vj32rSdsnacfZHZLM9t//V+H/NLjBYNUqWkuSFBsbm2a1JIdlYSk6Olp79uxRYGBgovEWLVpo27ZtyTpHfHy8rl27pvz5E+/Ae/36dfn4+CguLk41atTQmDFjEoWpu40bN06jRo1KMr5u3TrlzJkzWbWkt9DQUKtLQBpiPR0Ha+lYWE/HwVo6FtbTcdy9ljHxMdr09yatvLBSf0WZne1cbC5qlr+Zni/8vIq5F1P4vnCt2bfG3ulS5ebNm8mea1lYunTpkuLi4uTt7Z1o3NvbW+Hh4ck6x+TJk3Xjxg116NAhYaxChQpauHChqlatqsjISE2bNk1+fn46cOCAypUrZ/c8QUFBCggISDiOjIxUiRIl1KJFC3l6eqbi3aWdmJgYhYaGyt/fX66urpbWgofHejoO1tKxsJ6Og7V0LKyn47h7La9HX9f8/fM1bec0/XXtn/bfr9V6TX0e66OiudOu/ffd7txFlhyWd8O7+55DwzCSdR/ikiVLNHLkSK1atUqFCxdOGK9fv77q16+fcOzn56datWppxowZmj59ut1zubu7y93dPcm4q6trpvnBzEy14OGxno6DtXQsrKfjYC0dC+vpOK5EX9GcnXP0wc8fJLT/LpK7iAbUH6DXa7+eLu2/75aSP0uWhaWCBQvK2dk5yVWkCxcuJLnadLdly5apR48eWr58uZo3b37fuU5OTnrsscd07Nixh64ZAAAAQMqdunJK8/6ap5dmvpTQ/rtc/nIa3HCwOlfvnO5d7VLLstbhbm5uql27dpL7FkNDQ9WwYcN7Pm/JkiXq2rWrFi9erNatWz/wdQzD0P79+1W0aPpdygMAAACQ1MHzB/XyipdVcXZFrbm0Rrdib6lOsTpa/sJyHXnziF6t/WqmDUqSxbfhBQQEqHPnzqpTp44aNGigefPm6fTp0+rVq5ck87NEZ8+e1aJFiySZQalLly6aNm2a6tevn3BVKkeOHPLyMi/ZjRo1SvXr11e5cuUUGRmp6dOna//+/Zo5c6Y1bxIAAADIRgzD0ObTmxW8NThR++/qeaprwrMT5F/WP0Pbfz8MS8NSx44dFRERodGjRyssLExVqlTRmjVr5OPjI0kKCwvT6dOnE+bPnTtXsbGxevPNN/Xmm28mjL/yyitauHChJOnKlSt67bXXFB4eLi8vL9WsWVObNm1S3bp1M/S9AQAAANlJvBGvb45+o/Fbx2vHX2b7byebk9pXaq+B9QYqbG+YmpZqmmWCkpQJGjz07t1bvXv3tvvYnQB0x08//fTA802dOlVTp05Ng8oAAAAAPEh0XLQW/7JYE7ZO0JFLRyRJ7s7u6lqjqwY1HKSy+csqJiZGYQqzuNKUszwsAQAAAMh6rkVd04d7P9TUHVP1V+Q/7b971+mtfvX7qUjuIhZX+PAISwAAAACS7eKNi5q+c7pm7pqZ0P67aO6iZvvvOq/L093afUrTEmEJAAAAwAOdunJKk7dN1vx98xPafz9a4FGz/Xe1znJ3SbpvaVZHWAIAAABwT7+c/0XBW4O19NelijPiJEmPFXtMQ/2G6vkKz8vZydniCtMPYQkAAABAEltOb9H4LeO1+tjqhDH/0v4a6jdUzXybZamudqlFWAIAAAAgyWz/vfr31Rq/dby2ndkm6Z/230P9hqpW0VoWV5ixCEsAAABANhcTF6Olvy5V8NZgHbp4SJLk5uymrtXN9t/lCpSzuEJrEJYAAACAbOpG9A3N3zdfk7dP1umrpyVJedzyqPdjvdWvXj8VzVPU4gqtRVgCAAAAspmImxGauWumpu+crohbEZIk71ze6l+/v3rV6aW8HnmtLTCTICwBAAAA2cSZq2c0dcdUzdszTzdibkiSSucrrSENh+iVGq/Iw8XD4gozF8ISAAAA4OCOXDyiCdsm6LODnyk2PlaSVKNIDQX6BapdpXZycSIW2MN3BQAAAHBQO/7aoeCtwfr6t68Txp4o9YQC/QLVokyLbNH++2EQlgAAAAAHYhiG1h5fq/FbxmvjnxsTxttWaKuhfkNV75F6FlaXtRCWAAAAAAcQGx+rLw9/qfFbxuvA+QOSJFcnV71c7WUNbjhYFQtVtLjCrIewBAAAAGRht2Ju6ZMDn2jitok68fcJSVIu11x6vfbrGtBggB7xfMTiCrMuwhIAAACQBV25fUWzd81WyM4QXbhxQZJUIEcB9avXT2/WfVP5c+S3uMKsj7AEAAAAZCFh18IUsiNEs3fP1rXoa5Kkkl4lNajBIHWv2V253HJZXKHjICwBAAAAWcCxiGOauG2iPjnwiaLjoiVJlQtVVmCjQHWs3FGuzq4WV+h4CEsAAABAJrbn3B4Fbw3Wl4e/lCFDktSoZCMN9Ruqp8s9LSebk8UVOi7CEgAAAJDJGIahDSc3KHhrsEJPhCaMP/PoMxrqN1SNSjaysLrsg7AEAAAAZBJx8XH6+revNX7reO0+t1uS5GxzVqeqnTTEb4iqFK5icYXZC2EJAAAAsFhUbJQ+O/iZJmyboN8jfpck5XDJoZ61eiqgQYBK5S1lbYHZFGEJAAAAsMi1qGuau2eupu6YqnPXzkmS8nnk01t131Kfun1UKFchiyvM3ghLAAAAQAa7cOOCpu+crpm7ZurK7SuSpOJ5imtgg4F6tfaryu2W29oCIYmwBAAAAGSYk3+f1OTtkzV/33zdjr0tSSpfoLyG+g3Vf6r9R27ObhZXiH8jLAEAAADp7OD5gwreGqxlvy5TnBEnSapbvK4C/QLVpkIb2n9nUoQlAAAAIB0YhqEtp7do/NbxWnNsTcJ4yzItFdgoUE18mshms1lYIR6EsAQAAACkoXgjXt/+/q3Gbxmv7X9tlyQ52Zz0QqUXNNRvqGoWrWlxhUguwhIAAACQBmLiYrTk1yUK3hqswxcPS5Lcnd3VrUY3DWo4SGXyl7G4QqQUYQkAAAB4CDeib+ijvR9p8vbJOhN5RpLk6e6p3nV6q1/9fiqSu4jFFSK1CEsAAABAKkTcjNAHP3+gGT/PUMStCElSkdxFNKD+AL1e+3V5eXhZXCEeFmEJAAAASIEzV89oyvYpmrd3nm7G3JQklclXRkP8hqhL9S7ycPGwuEKkFcISAAAAkAyHLx7WhK0T9Pkvnys2PlaSVLNITQU2ClS7iu3k7ORscYVIa4QlAAAA4D52/LVD47eM16qjqxLGmvk2U6BfoJqXbk77bwdGWAIAAADuYhiGvv/jewVvDdbGPzdKkmyyqW3FthrqN1R1i9e1uEJkBMISAAAA8D+x8bFafmi5grcG68D5A5IkVydXdaneRYMbDlb5guUtrhAZibAEAACAbO9WzC0t3L9QE7dN1MkrJyVJud1y6/Xar2tA/QEq7lnc4gphBcISAAAAsq0rt69o1q5ZmrZzmi7cuCBJKpizoPrV66fej/VW/hz5La4QViIsAQAAINs5d+2cQnaEaM7uOboWfU2S5OPlo8ENB6tbzW7K6ZrT4gqRGRCWAAAAkG38HvG7Jm6dqEUHFyk6LlqSVKVwFQX6BapD5Q5ydXa1uEJkJoQlAAAAOLzd53YreGuwvjr8lQwZkqTGJRsrsFGgWpVtRftv2EVYAgAAgEMyDEM/nPxBwVuDtf7E+oTx58o/p6F+Q9WwREMLq0NWQFgCAACAQ4mLj9PK31Zq/Jbx2hO2R5Lk4uSiTlU7aUjDIapcuLLFFSKrICwBAADAIUTFRunTg59qwtYJOnb5mCQpp2tO9azZUwENAuST18fiCpHVEJYAAACQpUVGRWru7rmaumOqwq6HSZLy58ivPnX76K26b6lgzoIWV4isirAEAACALOn89fOavnO6Zu6aqatRVyVJj3g+ooENBqpnrZ7K7Zbb4gqR1RGWAAAAkKWc+PuEJm+brAX7F+h27G1JUsWCFTXEb4g6Ve0kN2c3iyuEoyAsAQAAIEs4EH5AwVuDtezQMsUb8ZKkesXrKahRkJ4t/6ycbE4WVwhHQ1gCAABApmUYhjaf3qxJOybpuz++Sxh/quxTCvQL1OM+j7NHEtINYQkAAACZTrwRr2+PfathfwzTbwd+kyQ52ZzUsXJHDfEbohpFalhbILIFwhIAAAAyjZi4GC07tEzBW4P164VfJUnuzu7qVqObBvsNVul8pS2uENkJYQkAAACWuxVzSwv2LdCk7ZN06sopSZKnu6f8vfw19cWpKpGvhLUFIlsiLAEAAMAyV25f0axdsxSyI0QXb16UJBXOVVgD6g9Qz+o9tXXDVhXJXcTiKpFdEZYAAACQ4cKuhSlkR4hm756ta9HXJEm+eX01uOFgda3RVTlccygmJsbiKpHdEZYAAACQYY5fPq6J2yZq4f6FioqLkiRVLVxVgY0C1aFyB7k48c9TZB78aQQAAEC62x++X8Fbg/XFoS8S9kjyK+GnoEZBerrc07T/RqZEWAIAAEC6uLNH0vgt4xPtkdS6XGsFNgpUo5KNLKwOeDDCEgAAANJUvBGv1b+v1vit47XtzDZJ5h5JL1Z5UUP9hqqadzWLKwSSh7AEAACANHGvPZK61+yuQQ0HsUcSshzCEgAAAB7KvfZI6l2nt/rV70frb2RZhCUAAACkyv32SHqjzhvy8vCyuELg4RCWAAAAkCL29kgqlbeUhjQckrBHEuAICEsAAABIFnt7JFUpXEWBfoHqWKUjeyTB4fAnGgAAAPdlb4+khiUaKqhRkFqXa80eSXBYhCUAAAAkca89kp4u97SCGgWxRxKyBcISAAAAEtxrj6SOlTtqqN9QVS9S3eIKgYxDWAIAAMA990jqVqObBvsNZo8kZEuEJQAAgGzM3h5JedzyqPdjvdW/fn/2SEK2RlgCAADIhu61R1L/ev31xmNvKK9HXmsLBDIBwhIAAEA2cq89kgY3HKxuNbqxRxLwL4QlAACAbIA9koCU46cCAADAgbFHEpB6hCUAAAAHwx5JQNpwsrqAWbNmydfXVx4eHqpdu7Y2b958z7krVqyQv7+/ChUqJE9PTzVo0EBr165NMu+rr75SpUqV5O7urkqVKmnlypXp+RYAAAAyhXgjXt8c/UaNPm6kJgub6Ls/vpOTzUkvVXlJ+1/fr9WdVhOUgBSwNCwtW7ZM/fv31/Dhw7Vv3z41btxYrVq10unTp+3O37Rpk/z9/bVmzRrt2bNHTZs21bPPPqt9+/YlzNm+fbs6duyozp0768CBA+rcubM6dOignTt3ZtTbAgAAyFAxcTH67OBnqja7mp5b+py2ndkmd2d39ardS8f6HNPidovZTBZIBUtvw5syZYp69Oihnj17SpJCQkK0du1azZ49W+PGjUsyPyQkJNHx2LFjtWrVKn3zzTeqWbNmwhx/f38FBQVJkoKCgrRx40aFhIRoyZIlduuIiopSVFRUwnFkZKQkKSYmRjExMQ/9Ph/Gnde3ug6kDdbTcbCWjoX1dBzZbS1vxtzUwgMLNXXnVP159U9J5h5Jr9d+XX0f65uwR1JW/X5kt/V0ZJlpLVNSg2VhKTo6Wnv27FFgYGCi8RYtWmjbtm3JOkd8fLyuXbum/PnzJ4xt375dAwYMSDSvZcuWSYLWv40bN06jRo1KMr5u3TrlzJkzWbWkt9DQUKtLQBpiPR0Ha+lYWE/H4ehreT32ur679J2+vfStrsZelSR5uXjp2ULP6qkCTyn3rdzau2mvxVWmHUdfz+wkM6zlzZs3kz3XsrB06dIlxcXFydvbO9G4t7e3wsPDk3WOyZMn68aNG+rQoUPCWHh4eIrPGRQUpICAgITjyMhIlShRQi1atJCnp2eyakkvMTExCg0Nlb+/v1xdXS2tBQ+P9XQcrKVjYT0dh6OvZdj1ME37eZo+3PvhP3skeZVSQP0AvVLtFYfbI8nR1zM7yUxreecusuSwvBve3e0qDcNIVgvLJUuWaOTIkVq1apUKFy78UOd0d3eXu7t7knFXV1fLF/OOzFQLHh7r6ThYS8fCejoOR1vLPy7/oYlbJ2rhgYWKjouWlL32SHK09czOMsNapuT1LfvJKliwoJydnZNc8blw4UKSK0N3W7ZsmXr06KHly5erefPmiR4rUqRIqs4JAACQ2ewP36/xW8Zr+eHl7JEEWMCybnhubm6qXbt2kvsWQ0ND1bBhw3s+b8mSJeratasWL16s1q1bJ3m8QYMGSc65bt26+54TAAAgszAMQ5v+3KRWn7dSzbk1tezQMsUb8Xq63NPa3G2ztnbfqmcefYagBGQAS6/ZBgQEqHPnzqpTp44aNGigefPm6fTp0+rVq5ck87NEZ8+e1aJFiySZQalLly6aNm2a6tevn3AFKUeOHPLy8pIk9evXT48//riCg4PVpk0brVq1SuvXr9eWLVuseZMAAADJEG/Ea/XvqzVuyzht/2u7JMnJ5qSOlTtqqN9QWn8DFrA0LHXs2FEREREaPXq0wsLCVKVKFa1Zs0Y+Pj6SpLCwsER7Ls2dO1exsbF688039eabbyaMv/LKK1q4cKEkqWHDhlq6dKlGjBiht99+W2XKlNGyZctUr169DH1vAAAAyRETF6Nlh5Zp/JbxOnTxkCTJ3dld3Wp002C/wSqdr7TFFQLZl+WfBuzdu7d69+5t97E7AeiOn376KVnnbN++vdq3b/+QlQEAAKSfmzE3tWDfAk3aNinRHkm9H+ut/vX7J+yRBMA6loclAACA7OTK7Sua+fNMTds5TRdvXpQkFc5VWP3r9dcbj72hvB55rS0QQALCEgAAQAYIuxamkB0hmr179j97JOUtpcENB6tbjW4Ot0cS4AgISwAAAOnoxN8nNHHrRH28/2NFxUVJyl57JAFZGT+dAAAA6eDXC79q/JbxWvrrUsUZcZLMPZIC/QLV+tHWcrJZtoMLgGQiLAEAAKShHX/t0NjNY/XN798kjLUs01LDGg9T45KN2R8JyEIISwAAAA/JMAyFngjVuC3j9NOpnyRJNtnUvlJ7BTYKVK2itawtEECqEJYAAABSKd6I18ojKzVuyzjtCdsjSXJ1clXnap01xG+Iyhcsb3GFAB4GYQkAACCFouOi9fnBzxW8NVhHI45KknK65tRrtV5TQIMAlfAqYXGFANICYQkAACCZbsbc1Ed7P9KkbZN0JvKMJCmvR171qdtHfev1VcGcBS2uEEBaIiwBAAA8wJ2NZEN2hujSzUuSpCK5iyigfoBer/O6PN09La4QQHogLAEAANxD+PVwTd0+NdFGsr55fTXEb4i61ugqDxcPiysEkJ4ISwAAAHc5+fdJTdw2UQv2LUi0kWxQoyB1qNyBjWSBbIKfdAAAgP85dOGQxm8dryW/LEnYSLbBIw0U1CiIjWSBbIiwBAAAsr0df+3QuC3j9N+j/00Ya1GmhYY1GqbHfR5nI1kgmyIsAQCAbMkwDK0/sV7jtozTj6d+lGRuJNuuUjsF+gWqdrHaFlcIwGqEJQAAkK3EG/H6+revNW7LOO0+t1uS5OLkkrCRbIWCFSyuEEBmQVgCAADZQkxcjD7/xdxI9rdLv0mScrjk0Ku1XtXAhgNV0qukxRUCyGwISwAAwKHdjLmp+Xvna9L2STp99bQkycvdS2/VfUv96vVToVyFLK4QQGZFWAIAAA7pyu0rmrVrlkJ2hOjizYuSJO9c3gpoEKBedXqxkSyAByIsAQAAh3Il5oqG/zhcc/fOVWRUpCSpVN5SGtJwiLrV7MZGsgCSjbAEAAAcwqkrpxS8OVgLDi9QtBEtSapcqLKCGgWpY5WObCQLIMX4rwYAAMjSDl04pOCtwVr8y+KEjWTrFqur4Y8P1zOPPsNGsgBSjbAEAACypJ1/7dS4LeO06uiqhLHmvs3VxKmJhnQYIjc3NwurA+AICEsAACDLMAxDP5z8QeO2jNOGkxskmRvJtq3YVkGNglS9UHWtWbNGNpvN4koBOALCEgAAyPTijXit+m2Vxm0Zp13ndkkyN5J9udrLGtJwiCoWqihJiomJsbJMAA6GsAQAADKtmLgYLf5lsYK3BuvIpSOSzI1ke9bqqUENB7GRLIB0RVgCAACZzq2YW5q/b74mbpuYaCPZNx97U/3q91PhXIUtrhBAdkBYAgAAmcbV21c1a9csTd0xNWEj2cK5CiugvrmRrJeHl8UVAshOCEsAAMBy56+fV8iOEM3aPSvRRrKDGw5WtxrdlMM1h8UVAsiOCEsAAMAyf175UxO3TdT8ffN1O/a2JKlSoUoK9AvUi1VelKuzq8UVAsjOCEsAACDDHb54OGEj2dj4WElS3eJ1NazRMD1b/lk2kgWQKRCWAABAhtl9brfGbh6rlb+tTBhrXrq5ghoFqWmppuyPBCBTISwBAIB0ZRiGNv25SWO3jNW64+sSxp+v8LyGNRqmx4o/ZmF1AHBvhCUAAJAuDMPQd398p7Gbx2rrma2SJGebszpV7aTARoGqVKiSxRUCwP0RlgAAQJqKi4/TiiMrNHbLWO0P3y9JcnN2U/ca3TXEb4h88/laWyAAJBNhCQAApImYuBh9dvAzjd86Xr9H/C5JyuWaS2/UeUMBDQJUNE9RiysEgJQhLAEAgIdyK+aW5u+br4nbJur01dOSpHwe+dS3Xl/1qdtHBXIWsLhCAEgdwhIAAEiVyKhIzd41W1N2TNGFGxckSd65vDWwwUD1qtNLedzzWFwhADwcwhIAAEiRSzcvadqOafpg1we6cvuKJMnHy0dD/YaqW81u8nDxsLZAAEgjhCUAAJAsZyPPavL2yZq7Z65uxtyUJFUoWEFBjYL0UpWX5OrsanGFAJC2CEsAAOC+jl8+rglbJ2jhgYWKjouWJNUqWkvDGg1T24pt5WRzsrhCAEgfhCUAAGDXrxd+1fgt47Xk1yWKN+IlSY1LNtawxsPUskxL2Ww2iysEgPRFWAIAAIn8fPZnjd08VquOrkoYe6rsUxrWaJga+zS2sDIAyFiEJQAAIMMw9NOpnzR2y1itP7FekmSTTe0qtVNQoyDVKlrL4goBIOMRlgAAyMYMw9DqY6s1dvNYbf9ruyTJ2easl6u9rKF+Q1WxUEWLKwQA6xCWAADIhuLi47T88HKN2zJOB88flCS5O7urR80eGuw3WKXylrK2QADIBAhLAABkI9Fx0fr0wKcav3W8/rj8hyQpt1tu9a7TWwMaDFCR3EUsrhAAMg/CEgAA2cDNmJv6aO9Hmrhtov6K/EuSlD9HfvWr109v1X1L+XPkt7hCAMh8CEsAADiwq7evatauWZq6Y6ou3rwoSSqau6gGNhio1+u8rtxuuS2uEAAyr1SHpStXrujLL7/U8ePHNXjwYOXPn1979+6Vt7e3ihcvnpY1AgCAFLp446JCdoTog10fKDIqUpLkm9dXQ/2G6pUar8jDxcPiCgEg80tVWDp48KCaN28uLy8vnTp1Sq+++qry58+vlStX6s8//9SiRYvSuk4AAJAMf0X+pUnbJmnennm6FXtLklSpUCUFNQrSi1VelIsTN5UAQHKl6r+YAQEB6tq1qyZMmKA8efIkjLdq1UqdOnVKs+IAAEDy/HH5DwVvCdYnBz5RTHyMJKl20doa3ni42lRoIyebk8UVAkDWk6qwtGvXLs2dOzfJePHixRUeHv7QRQEAgOT55fwvGrtlrL449IXijXhJUhOfJhreeLial24um81mcYUAkHWlKix5eHgoMjIyyfjRo0dVqFChhy4KAADc346/dmjs5rH65vdvEsaeLve0hjUaJr+SfhZWBgCOI1VhqU2bNho9erS++OILSZLNZtPp06cVGBiodu3apWmBAADAZBiGNpzcoLFbxmrDyQ2SJJtseqHyCwpqFKQaRWpYWyAAOJhUhaVJkybp6aefVuHChXXr1i01adJE4eHhatCggd5///20rhEAgGzNMAx9+/u3en/z+9p5dqckycXJRZ2rddZQv6EqX7C8xRUCgGNKVVjy9PTUli1btGHDBu3du1fx8fGqVauWmjdvntb1AQCQbcXFx+mrI1/p/c3v6+D5g5IkDxcP9azZU4P9BqukV0mLKwQAx/ZQ/UObNWumZs2apVUtAABAUkxcjBb/sljjtozT0YijkqTcbrnVu05vBTQIkHdub4srBIDsIdVh6YcfftAPP/ygCxcuKD4+PtFjCxYseOjCAADIbqJio/Tx/o8VvDVYp66ckiTl88infvX6qU+9PsqfI7+1BQJANpOqsDRq1CiNHj1aderUUdGiRWlLCgDAQ7gRfUPz9szTpO2TdO7aOUlS4VyFNbDBQL1R5w3lcc/zgDMAANJDqsLSnDlztHDhQnXu3Dmt6wEAINu4evuqZu2apSk7pujSzUuSpOJ5imuI3xD1rNVTOV1zWlwhAGRvqQpL0dHRatiwYVrXAgBAthBxM0LTdk7T9J3TdTXqqiSpdL7SCvQLVJfqXeTu4m5xhQAAKZVhqWfPnlq8eLHefvvttK4HAACHFX49XJO3Tdbs3bN1I+aGJKliwYoa1niYXqzyolycHqrvEgAgjaXqv8q3b9/WvHnztH79elWrVk2urq6JHp8yZUqaFAcAgCM4ffW0JmydoI/2fqSouChJUo0iNTSi8Qi1rdhWTjYniysEANiTqrB08OBB1ahRQ5L066+/JnqMZg8AAJj+uPyHxm8Zr08OfKLY+FhJUv1H6mtE4xF6utzT/J0JAJlcqsLSjz/+mNZ1AADgMA5dOKSxW8Zq6a9LFW+Y22s0LdVUIx4foaalmhKSACCL4OZoAADSyJ5ze/T+5ve18reVCWNPl3tawxsPV8MSNEYCgKwmVWHpxo0bGj9+/D03pT1x4kSaFAcAQFaw9fRWvbf5PX3/x/cJY+0qttOwxsNUq2gtCysDADyMVHfD27hxozp37symtACAbMkwDP1w8ge9v/l9/XTqJ0mSk81Jnap2UlCjIFUqVMnaAgEADy1VYem7777T6tWr5efnl9b1AACQoQxDiogwfx8RIXl7S/f7/wANw9C3v3+r9ze/r51nd0qSXJ1c9Ur1VzS00VCVzV82A6oGAGSEVPUqzZcvn/Lnz5/WtQAAkGGuXJGmTZPKlZNKlzbHSpc2j6dNMx//t7j4OC0/tFw159bUc0uf086zO+Xh4qE+dfvoeN/j+vC5DwlKAOBgUhWWxowZo3feeUc3b95M63oAAEh3a9dKjzwiDRgg3f0x2xMnzPFHHjHnxcTFaNGBRao8q7I6fNlBB84fUG633BrScIhO9Tul6a2mq4RXCWveCAAgXaXqNrzJkyfr+PHj8vb2VqlSpZJsSrt37940KQ4AgLS2dq3UurV5+51hJH38ztjN6Ci1enuhvPcFKzzqpCQpr0de9avXT33r9VX+HNxhAQCOLlVh6fnnn0+zAmbNmqWJEycqLCxMlStXVkhIiBo3bmx3blhYmAYOHKg9e/bo2LFj6tu3r0JCQhLNWbhwobp165bkubdu3ZKHh0ea1Q0AyHquXJHatTMD0V2NXP/helOqPU9Gw0mS51mFR0kFcxTSoIYD9cZjb8jT3TMjSwYAWChVYendd99NkxdftmyZ+vfvr1mzZsnPz09z585Vq1atdPjwYZUsWTLJ/KioKBUqVEjDhw/X1KlT73leT09PHT16NNEYQQkA8Mkn0s2b9q8o3Yy7qZh6E6THpkm5LpqDkcWlbYM19MVXNahRzowtFgBguVR9ZkmSrly5oo8++khBQUG6fPmyJPP2u7Nnzyb7HFOmTFGPHj3Us2dPVaxYUSEhISpRooRmz55td36pUqU0bdo0denSRV5eXvc8r81mU5EiRRJ9AQCyN8OQZsxIOu6V4w/Vb9BMrx/srtgnRphB6W9f6Zu50rTjsu3spzkzctoNWAAAx5aqK0sHDx5U8+bN5eXlpVOnTunVV19V/vz5tXLlSv35559atGjRA88RHR2tPXv2KDAwMNF4ixYttG3bttSUleD69evy8fFRXFycatSooTFjxqhmzZr3nB8VFaWoqKiE48jISElSTEyMYmJiHqqWh3Xn9a2uA2mD9XQcrGXWExEhnTsn3bnRoJBxQX1iQ3Sx/jRNeNxcR6fLj8p5W6CcD78om+EiuUlSjM6dky5ckGgEm/nxs+lYWE/HkZnWMiU1pCosBQQEqGvXrpowYYLy5MmTMN6qVSt16tQpWee4dOmS4uLi5O3tnWjc29tb4eHhqSlLklShQgUtXLhQVatWVWRkpKZNmyY/Pz8dOHBA5cqVs/uccePGadSoUUnG161bp5w5M8dtF6GhoVaXgDTEejoO1jJrWbJE8oiIUNmvv5bP2rVyiY3WxZ3SxgruapO3pco36SznZq6S1iV57o4dGV8vUo+fTcfCejqOzLCWKenonaqwtGvXLs2dOzfJePHixVMcdGx37fxnGEaSsZSoX7++6tevn3Ds5+enWrVqacaMGZo+fbrd5wQFBSkgICDhODIyUiVKlFCLFi3k6WntB3ljYmIUGhoqf3//JF0HkfWwno6Dtcx6/t7/p75uMEmvxH0sd0VLknbb6mh87DAdW9pClT5er+7d/XXrlv31PHmSK0tZAT+bjoX1dByZaS3v3EWWHKkKSx4eHnZf5OjRoypUqFCyzlGwYEE5OzsnCVcXLlxIcrXpYTg5Oemxxx7TsWPH7jnH3d1d7u7uScZdXV0tX8w7MlMteHisp+NgLbOAP/6Qxo1ToUWL9FpcrCRpsxrpPY3QOqOFFG1TDmfzloxbt1yThCWbzdystnBh8/fIGvjZdCysp+PIDGuZktdPVYOHNm3aaPTo0Qn3+9lsNp0+fVqBgYFq165dss7h5uam2rVrJ7kUFxoaqoYNG6amLLsMw9D+/ftVtGjRNDsnACALOHJEevllqXx5acEC2WJjdfrRJ/WEftLj2qx1aikpeemnb1+CEgBkR6kKS5MmTdLFixdVuHBh3bp1S02aNFHZsmWVJ08evf/++8k+T0BAgD766CMtWLBAR44c0YABA3T69Gn16tVLknl7XJcuXRI9Z//+/dq/f7+uX7+uixcvav/+/Tp8+HDC46NGjdLatWt14sQJ7d+/Xz169ND+/fsTzgkAcHAHD0odOkiVK0uff25uqPT009K2bfLcuV67czWRUzL/9nNyknLmlO76qwgAkE2k6jY8T09PbdmyRRs2bNDevXsVHx+vWrVqqXnz5ik6T8eOHRUREaHRo0crLCxMVapU0Zo1a+Tj4yPJ3IT29OnTiZ7z7652e/bs0eLFi+Xj46NTp05JMluav/baawoPD5eXl5dq1qypTZs2qW7duql5qwCArGLPHmnMGGnVqn/Gnn9eGjFCql1bkpRX0ldfSa1bm0HonhvTynzcZpNWrJDy5k3HugEAmVaqwtLJkyfl6+urZs2aqVmzZg9VQO/evdW7d2+7jy1cuDDJmPGAjS6mTp163w1rAQAOZvt2MyR99515bLNJL7xghqSqVZNMb9lSWr1aatfO3KD2bndut8uRwwxKLVqkY+0AgEwtVbfhlS1bVk2bNtVnn32m27dvp3VNAAA82MaNUvPmUsOGZlBydpY6d5YOHZKWLbMblO5o2VL66y8pJMRs3vBvpUub42fPEpQAILtLVVg6cOCAatasqYEDB6pIkSJ6/fXXtXPnzrSuDQCAxAxDWr9eevxx6YknpB9+kFxcpB49pKNHpUWLpIoVk3WqvHnNxg3HjpltwSXz12PHzHEvr3R7FwCALCJVYalKlSqaMmWKzp49q48//ljh4eFq3LixKleurClTpujixYtpXScAIDszDGnNGvMqkr+/tHmz5OYmvfGG2Rr8o4+kMmVSdWqb7Z/9k/Lnp+sdAOAfqQpLd7i4uKht27b64osvFBwcrOPHj2vQoEF65JFH1KVLF4WFhaVVnQCA7MgwzIYNjz1mdmXYsUPy8DAv/Zw4Ic2aJf2vKRAAAGntocLS7t271bt3bxUtWlRTpkzRoEGDdPz4cW3YsEFnz55VmzZt0qpOAEB2Eh8vffmlVKOG2dFuzx6zh/egQea9ctOmScWLW10lAMDBpaob3pQpU/Txxx/r6NGjevrpp7Vo0SI9/fTTcvrfxhW+vr6aO3euKlSokKbFAgAcXFyc9MUX0nvvSXf20MuTR3rrLWnAAKlQIWvrAwBkK6kKS7Nnz1b37t3VrVs3FSlSxO6ckiVLav78+Q9VHAAgm4iNlZYuNUPS0aPmmJeX1K+f+XXnQ0UAAGSgVIWlY8eOPXCOm5ubXnnlldScHgCQXcTESJ99Jr3/vnT8uDmWL58UECD16UNLOgCApVIVliTpypUrmj9/vo4cOSKbzaaKFSuqR48e8uIvNgDAg0RHS598Io0dK506ZY4VLCgNHCi9+aZ56x0AABZLVYOH3bt3q0yZMpo6daouX76sS5cuaerUqSpTpoz27t2b1jUCABxFVJQ0e7ZUtqz02mtmUPL2liZNMn8fGEhQAgBkGqm6sjRgwAA999xz+vDDD+XiYp4iNjZWPXv2VP/+/bVp06Y0LRIAkMXdumXuhRQcLJ09a44VKyYNGSK9+qrZ6Q4AgEwmVWFp9+7diYKSZO65NGTIENWpUyfNigMAZHE3b0pz50oTJkjh4ebYI4+YV5B69DD3TAIAIJNKVVjy9PTU6dOnk7QGP3PmjPJw+wQA4MYN83a7iROlCxfMsZIlpWHDpK5dJXd3S8sDACA5UhWWOnbsqB49emjSpElq2LChbDabtmzZosGDB+ull15K6xoBAFnFtWvSrFnmZ5AuXTLHfH3NkNSli+TmZm19AACkQKrC0qRJk2Sz2dSlSxfFxsbKMAy5ubnpjTfe0Pjx49O6RgBAZhcZKX3wgTRlihQRYY6VKSMNHy69/LLk6mptfQAApEKqwpKbm5umTZumcePG6fjx4zIMQ2XLllVOPqALANnL1avSjBnS1KnS5cvmWNmy0ogR0n/+I7mkeocKAAAsl6K/xbp3756seQsWLEhVMQCALOLqVWnaNDMkXblijpUvb4akF18kJAEAHEKK/jZbuHChfHx8VLNmTRmGkV41AQAyqytXpJAQ8+vqVXOsQgXp7beljh0lZ2cLiwMAIG2lKCz16tVLS5cu1YkTJ9S9e3e9/PLLyp8/f3rVBgDILP7+27yKNG2a+fkkSapUyQxJL7xASAIAOCSnlEyeNWuWwsLCNHToUH3zzTcqUaKEOnTooLVr13KlCQAc0eXLZiAqVUoaM8YMSpUrS8uWSb/8Yt5yR1ACADioFIUlSXJ3d9dLL72k0NBQHT58WJUrV1bv3r3l4+Oj69evp0eNAICMdvmy+fmjUqWk994zQ1LVqtLy5dLBg1KHDpJTiv8KAQAgS3moT+DabDbZbDYZhqH4+Pi0qgkAYJXLl83239Onm3smSVK1atK770rPP09AAgBkKyn+Wy8qKkpLliyRv7+/ypcvr19++UUffPCBTp8+rdy5c6dHjQCA9BYR8c+VpPffN4NS9erSV19J+/ZJ//d/BCUAQLaToitLvXv31tKlS1WyZEl169ZNS5cuVYECBdKrNgBAeouIMBs3/PtKUvXq5pWkNm0ISACAbC1FYWnOnDkqWbKkfH19tXHjRm3cuNHuvBUrVqRJcQCAdHKvkDRypPTcc4QkAACUwrDUpUsX2Wy29KoFAJDe7H0miStJAADYleJNaQEAWdDly//sk8SVJAAAkuWhuuEBADI5e5vJVqtmhiSuJAEAcF+EJQBwRFeuSCEh5tfVq+ZY1apmSKIFOAAAyUJYAgBHcvWqeRVp6lQzMElSlSpmSGrblpAEAEAKEJYAwBFERppNGyZP/ickVa5sNm5o146QBABAKhCWACAru3ZNmjHDDEmXL5tjFSuaIemFFwhJAAA8BMISAGRFN25IM2dKEyaYeyZJUvnyZkjq0EFydra2PgAAHABhCQCykps3pdmzpeBg6eJFc6xcOemdd6SXXiIkAQCQhghLAJAV3L4tzZ0rjRsnnT9vjpUubV5J6tRJcuE/5wAApDX+dgWAzCwqSpo/X3r/fencOXOsVClpxAipSxfJ1dXS8gAAcGSEJQDIjGJipIULpffek06fNsdKlDBDUteukpubldUBAJAtEJYAIDOJjZU++0waPVo6edIcK1ZMGjZM6tlTcne3tj4AALIRwhIAZAZxcdKyZdKoUdLvv5tjhQtLQUHS669LOXJYWx8AANkQYQkArBQfL61caXazO3zYHCtQQBo6VOrdW8qVy9r6AADIxghLAGAFw5C+/dYMSfv3m2N580qDBkl9+0p58lhZHQAAEGEJADKWYUihodLbb0s//2yO5ckjDRhgfuXNa2l5AADgH4QlAMgomzaZ3ew2bzaPc+aU+vSRBg82b70DAACZCmEJANLbzz+bISk01Dx2d5feeEMKDJS8va2tDQAA3BNhCQDSy8GDZkj65hvz2MVFevVVsw34I49YWxsAAHggwhIApLWjR6V33zVbgUuSk5PUubM55utrbW0AACDZCEsAkFb+/NPcJ+mTT8yW4JLUsaM0cqRUoYKlpQEAgJQjLAHAwwoPl95/X5o7V4qJMceefVYaM0aqXt3a2gAAQKoRlgAglVyvXZPTsGHSzJnSrVvm4JNPSu+9J9Wvb21xAADgoRGWACClrl2T0+TJ8p84Uc43b5pj9eubV5eaNbO2NgAAkGYISwCQXLdvS3PmSGPHyvniRTlLMqpWlW3sWKl1a8lms7pCAACQhghLAPAgsbFm04ZRo6QzZyRJRtmy2v3886rx3ntydXe3uEAAAJAenKwuAAAyrfh46YsvpMqVpZ49zaD0yCPSvHmKPXBA5xo1MtuCAwAAh8SVJQC4m2FI69ZJQUHSvn3mWMGC5mayb7wheXj80/UOAAA4LMISAPzbjh1mSPrpJ/M4Tx5p4EBpwADJ09PS0gAAQMYiLAGAJB0+LA0fLn39tXns7i717m0Gp0KFLC0NAABYg7AEIHv7809p5Ehp0SLzM0pOTlLXrtK770olS1pdHQAAsBBhCUD2dOmSNHasuaFsdLQ51ratuVdSxYrW1gYAADIFwhKA7OXGDSkkRJowQYqMNMeaNpXGjZPq1bO0NAAAkLkQlgBkDzEx0vz55l5J4eHmWI0a0vjxUosWbCgLAACSICwBcGyGIX31ldn2+9gxc6x0aem996SOHdknCQAA3BNhCYDj+uknaehQ6eefzeNChaR33pFee01yc7O0NAAAkPkRlgA4nl9/NUPSmjXmca5c5l5JgwaZ+yYBAAAkA2EJgOP46y+z5ffChWYbcGdn8yrSO+9IRYpYXR0AAMhiCEsAsr6rV83udlOnSrdumWPt2pmtwR991NraAABAlkVYApB1RUdLc+dKo0eb+yZJUqNG0sSJUv361tYGAACyPMISgKzHMKQVK6TAQOmPP8yx8uWl4GDpuedoAw4AANIEYQlA1rJjh9moYetW87hwYWnkSKlnT8nV1dLSAACAYyEsAcgaTpyQgoKkL74wj3PmNDvcDR5MhzsAAJAuCEsAMre//5bef1+aMcP8jJLNJnXvbn5OqVgxq6sDAAAOjLAEIHOKiZHmzDFvsbt82Rzz95cmTZKqVbO0NAAAkD0QlgBkLoYhffut+bmk3383xypXNkPSU09ZWxsAAMhWnKwuAAASHDxoXj167jkzKBUqJM2eLe3fT1ACAAAZzvKwNGvWLPn6+srDw0O1a9fW5s2b7zk3LCxMnTp1Uvny5eXk5KT+/fvbnffVV1+pUqVKcnd3V6VKlbRy5cp0qh5Amjh/XnrtNalmTemHHyQ3N2noULMteK9ekgsXwQEAQMazNCwtW7ZM/fv31/Dhw7Vv3z41btxYrVq10unTp+3Oj4qKUqFChTR8+HBVr17d7pzt27erY8eO6ty5sw4cOKDOnTurQ4cO2rlzZ3q+FQCpERUlTZgglSsnffihFB8vdegg/fabNH685OlpdYUAACAbszQsTZkyRT169FDPnj1VsWJFhYSEqESJEpo9e7bd+aVKldK0adPUpUsXeXl52Z0TEhIif39/BQUFqUKFCgoKCtKTTz6pkJCQdHwnAFLEMKSvvzY/izR0qHTtmlSnjrR5s7RsmeTra3WFAAAA1jV4iI6O1p49exQYGJhovEWLFtq2bVuqz7t9+3YNGDAg0VjLli3vG5aioqIUFRWVcBwZGSlJiomJUUxMTKprSQt3Xt/qOpA2WE9Jv/4q50GD5LRhgyTJKFpUce+9J+M//5GcnMwueFkAa+lYWE/HwVo6FtbTcWSmtUxJDZaFpUuXLikuLk7e3t6Jxr29vRUeHp7q84aHh6f4nOPGjdOoUaOSjK9bt045c+ZMdS1pKTQ01OoSkIay43q6XrumCkuWyPf772WLj1ecq6uOt2mj39u1U1yOHNL331tdYqpkx7V0ZKyn42AtHQvr6Tgyw1revHkz2XMt/9S0zWZLdGwYRpKx9D5nUFCQAgICEo4jIyNVokQJtWjRQp4Wf2YiJiZGoaGh8vf3l6urq6W14OFly/WMjZXTRx/JaeRI2f63X1J827aKHz9evr6+yqo33GXLtXRgrKfjYC0dC+vpODLTWt65iyw5LAtLBQsWlLOzc5IrPhcuXEhyZSglihQpkuJzuru7y93dPcm4q6ur5Yt5R2aqBQ8v26znpk1Snz5mS3BJqlJFmjZNTs2aWd+KM41km7XMJlhPx8FaOhbW03FkhrVMyetb9u8VNzc31a5dO8mluNDQUDVs2DDV523QoEGSc65bt+6hzgkghc6elTp1kpo0MYNSvnzSBx9I+/ZJzZpZXR0AAECyWHobXkBAgDp37qw6deqoQYMGmjdvnk6fPq1evXpJMm+PO3v2rBYtWpTwnP3790uSrl+/rosXL2r//v1yc3NTpUqVJEn9+vXT448/ruDgYLVp00arVq3S+vXrtWXLlgx/f0C2Ex0thYRIo0dLN25INpu5f9J770kFC1pdHQAAQIpYGpY6duyoiIgIjR49WmFhYapSpYrWrFkjHx8fSeYmtHfvuVSzZs2E3+/Zs0eLFy+Wj4+PTp06JUlq2LChli5dqhEjRujtt99WmTJltGzZMtWrVy/D3heQLYWGmrfcHT1qHjdoYF5NqlXL2roAAABSyfIGD71791bv3r3tPrZw4cIkY4ZhPPCc7du3V/v27R+2NADJ8ddfUkCAtHy5eeztbW40+/LLZitwAACALIp/yQBInZgYadIkqUIFMyg5OUl9+5pXlrp0ISgBAIAsz/IrSwCyoM2bpTfekA4dMo8bNpRmzZKqV7e2LgAAgDTE//ULIPkuXZK6d5cef9wMSgULSvPnm+GJoAQAABwMV5YAPJhhSAsXSoMHSxER5tirr0rjxkkFClhaGgAAQHohLAG4v6NHpddflzZuNI+rVpXmzjW73QEAADgwbsMDYF9UlDRqlFStmhmUcuaUJk6U9uwhKAEAgGyBK0sAktq61bzN7sgR87hVK7OBQ6lSlpYFAACQkbiyBOAfkZHSm29KjRqZQalwYWnpUmn1aoISAADIdriyBMC0Zo352aS//jKPu3c3b7vLn9/augAAACxCWAKyu4gIqX9/6bPPzOPSpaUPP5SaNbO0LAAAAKtxGx6Qna1cKVWubAYlJydp4EDpl18ISgAAAOLKEpA9RURIffpIS5aYxxUrSh9/LNWrZ21dAAAAmQhXloDs5ptvpCpVzKDk5CQFBUl79xKUAAAA7sKVJSC7iIw0P5v08cfmccWK0sKFUt26VlYFAACQaXFlCcgONm0yN5f9+GPJZpMGDTKvJhGUAAAA7okrS4Aji46W3n7bbAFuGJKvr/TJJ1LjxlZXBgAAkOkRlgBH9dtv0n/+Y15BkqQePaSpU6U8eaytCwAAIIvgNjzA0RiG9NFHUq1aZlAqUMBsEf7RRwQlAACAFODKEuBIrlyRXntNWr7cPG7e3LztrlgxS8sCAADIiriyBDiKXbvMq0nLl0suLtKECdLatQQlAACAVOLKEpDVGYY0fbo0eLAUE2M2cVi6lE53AAAAD4mwBGRlkZFm44YvvzSP27UzP5uUN6+lZQEAADgCwhKQVR0+LLVtK/3+u+TqKk2eLL31lrmPEgAAAB4aYQnIir78UuraVbpxQ3rkEfNzSvXrW10VAACAQ6HBA5CVxMdLI0ZIL7xgBqWmTc324AQlAACANMeVJSCruHZNevll6b//NY8DAqTgYLPzHQAAANIc/8oCsoLTp6VnnpF++UVyd5c+/FDq3NnqqgAAABwaYQnI7HbvNoPS+fOSt7d5ZYm24AAAAOmOzywBmdnq1VKTJmZQqlZN+vlnghIAAEAGISwBmdWCBVKbNtLNm1KLFtKWLVLJklZXBQAAkG0QloDMKDjY3Gw2Ls5sEf7tt1KePFZXBQAAkK0QloDMxDCk4cOlwEDzeOhQ8wqTq6u1dQEAAGRDNHgAMgvDkAYOlKZONY8nTJAGD7a2JgAAgGyMsARkBoZh7psUEmIez5wp9e5taUkAAADZHWEJsJphmLfd3QlK8+ZJr75qaUkAAADgM0uA9caONW+5k6Q5cwhKAAAAmQRhCbDShx9KI0aYv588WXr9dWvrAQAAQALCEmCV1aulXr3M3w8fbn5mCQAAAJkGYQmwwq+/Si++KMXHm/sojRljdUUAAAC4C2EJyGCu167JpV076fp1qWlTs6GDzWZ1WQAAALgLYQnISPHxqj11qmwnT0qlS0vLl7PhLAAAQCZFWAIykNPkyfLeu1dGjhzSihVSgQJWlwQAAIB7ICwBGWX3bjm9+64kKS4kRKpe3dp6AAAAcF+EJSAjREVJXbvKFhursw0byuja1eqKAAAA8ACEJSAjjB8vHToko3BhHejVi4YOAAAAWYCL1QUADu/kSWncOElS3JQpismd2+KCAAAAkBxcWQLSW2CgeRtes2YyXnjB6moAAACQTIQlID3t3St98YV5293Uqdx+BwAAkIUQloD0NHas+etLL0nVqllbCwAAAFKEsASkl+PHzb2UJGn4cGtrAQAAQIoRloD0Mm+eZBjSU09JlSpZXQ0AAABSiLAEpIe4OGnRIvP3r79ubS0AAABIFcISkMYMw9CVDWuk8HDF5/WS0aqV1SUBAAAgFQhLQBq5cvuKpu2YpnIzymnuqOckSZ+VvKpycytr2o5punL7irUFAgAAIEXYlBZIA2v/WKt2X7TTzZibkqQnTpnjoWWkE3+f0IC1AzR8w3B92e5L64oEAABAinBlCXhIa/9Yq9aLW+tWzC0ZMuQcZ6hmmPnY1hKS8b//3Yq5pReWsyktAABAVkFYAh7CldtX1O6LdjIMQ/GKlyQ9GiG5xUuRbtLJfP/MjVe8DMOQJF2NumpFuQAAAEgBwhLwED7Z/4luxtxMCEqSVOqK+evx/JJsieffmbfklyUZUyAAAABSjbAEpJJhGJrx84wk497XzV/P5bn3c+fsnpNwlQkAAACZE2EJSKWIWxE6/vdxGUocenLFmL9ed7v3c09eOanLty6nY3UAAAB4WIQlIJWuR1+3O+78vzvy4m12H05wLfpaGlcEAACAtERYAlIpt1tuu+M3Xc1fc8Tc//l53O5znx4AAAAsR1gCUqlAjgIqk6+MbHd1cYjIaf5a+Ma9n+ub11f5c+RPx+oAAADwsAhLQCrZbDb1qdsnyfgZT/NX3yv3fm6vOr1ksz3gPj0AAABYirAEPIRXaryinK455fSvH6XfCpq/Fr0uFbjr6pKTzZz3UtWXMqpEAAAApBJhCXgIeT3y6qsOX8lmsyUEpmse0rH/3WFX9+w/c53klHDLnpe7V0aXCgAAgBQiLAEPqWXZllrdabVyuOaQ7X//2+hjPtbspBLGcrjm0JcdvrS2WAAAACQbYQlIAy3LttRfAX8p5KkQlc5XWmvLmuNtjkql8/oq5KkQnQ04q2a+zawtFAAAAMnmYnUBgKPI65FXfev1VZ+6fXT5xdOK/6a8yl2O0rGGS2V77DFJUkzMA/qJAwAAINPgyhKQxmw2mwoU9pFT2/8zj+fPlyQZhhQRYc6JiDCPAQAAkHkRloD08uqrkiTj0081d2yEypWTSpc2HypdWipXTpo2TbpyxboSAQAAcG+EJSC9PPGEIsvUkO3mTZ0bPlMnTiR++MQJacAA6ZFHpLVrrSkRAAAA90ZYAtLJ2nU2vX4iUJIUoMnKZ0QketwwzK9bt6TWrQlMAAAAmY3lYWnWrFny9fWVh4eHateurc2bN993/saNG1W7dm15eHiodOnSmjNnTqLHFy5cKJvNluTr9u3b6fk2gESuXJHatZOW6wXtV3V5KVLvaLTdufHxZmhq145b8gAAADITS8PSsmXL1L9/fw0fPlz79u1T48aN1apVK50+fdru/JMnT+rpp59W48aNtW/fPg0bNkx9+/bVV199lWiep6enwsLCEn15eHhkxFsCJEmffCLdvCnFGU4arImSpDc1U5Xif7U7Pz7enL9oUUZWCQAAgPuxNCxNmTJFPXr0UM+ePVWxYkWFhISoRIkSmj17tt35c+bMUcmSJRUSEqKKFSuqZ8+e6t69uyZNmpRons1mU5EiRRJ9ARnFMKQZM/45Xi9/faX/k4vi9HTMN4qPv/dzp0+nSx4AAEBmYdk+S9HR0dqzZ48CAwMTjbdo0ULbtm2z+5zt27erRYsWicZatmyp+fPnKyYmRq6urpKk69evy8fHR3FxcapRo4bGjBmjmjVr3rOWqKgoRUVFJRxHRkZKMvfEsXpfnDuvb3UdSL6ICOncOenfFzOHxQdrSnSAtsX76ZVVh5Qjh/31PHdOunBByp8/g4pFqvGz6VhYT8fBWjoW1tNxZKa1TEkNloWlS5cuKS4uTt7e3onGvb29FR4ebvc54eHhdufHxsbq0qVLKlq0qCpUqKCFCxeqatWqioyM1LRp0+Tn56cDBw6oXLlyds87btw4jRo1Ksn4unXrlDNnzlS+w7QVGhpqdQlIgSVLko6tW+ejbbOkzz6rqHHjtujRR/+2+9wdO9K5OKQpfjYdC+vpOFhLx8J6Oo7MsJY3b95M9lzLwtIdNpst0bFhGEnGHjT/3+P169dX/fr1Ex738/NTrVq1NGPGDE2fPt3uOYOCghQQEJBwHBkZqRIlSqhFixby9PRM2RtKYzExMQoNDZW/v3/ClTNkbhER/+yn9G+GIbm5xSo62kWBgY3k5hYne3/UT57kylJWwM+mY2E9HQdr6VhYT8eRmdbyzl1kyWFZWCpYsKCcnZ2TXEW6cOFCkqtHdxQpUsTufBcXFxUoUMDuc5ycnPTYY4/p2LFj96zF3d1d7u7uScZdXV0tX8w7MlMtuD9vb6lYMXMfpbs/f+ThEaPChW/owoVcun078UcGbTYzZBUuLLshCpkTP5uOhfV0HKylY2E9HUdmWMuUvL5lDR7c3NxUu3btJJfiQkND1bBhQ7vPadCgQZL569atU506de75pg3D0P79+1W0aNG0KRx4AJtN6tPn3o8NGbJbkv0uDn37EpQAAAAyC0u74QUEBOijjz7SggULdOTIEQ0YMECnT59Wr169JJm3x3Xp0iVhfq9evfTnn38qICBAR44c0YIFCzR//nwNGjQoYc6oUaO0du1anThxQvv371ePHj20f//+hHMCGeGVV6ScOSUnOz9hZctekatrXKIxJydz/r/+uAMAAMBiln5mqWPHjoqIiNDo0aMVFhamKlWqaM2aNfLx8ZEkhYWFJdpzydfXV2vWrNGAAQM0c+ZMFStWTNOnT1e7du0S5ly5ckWvvfaawsPD5eXlpZo1a2rTpk2qW7duhr8/ZF9580pffSW1bm0Gobvbhbu4GLq7EcuKFebzAAAAkDlY3uChd+/e6t27t93HFi5cmGSsSZMm2rt37z3PN3XqVE2dOjWtygNSrWVLafVqqV07c8PZ+3FxkXLkyJi6AAAAkDyW3oYHOLqWLaW//pJCQpJ2yCtTRpoyxZwTHS09+6y0f78VVQIAAMAewhKQzvLmNRs3HDtmtgWXzF+PHZMGDJBWrpQaNZKuXpWefFK6z4VTAAAAZCDCEpBBbLZ/9k/Kn/+frnc5ckjffivVqyddvmwGpl27rKsTAAAAJsISkAl4eUnr1kl+ftKVK1Lz5tKOHVZXBQAAkL0RloBMwtNT+v576fHHpchIMzCtXWt1VQAAANkXYQnIRHLnltasMYPSjRvSM89In35qdVUAAADZE2EJyGRy5TJbjnfqJMXGmhvVTpggGYbVlQEAAGQvhCUgE3JzM68oDRxoHg8dKvXpY4YnAAAAZAzCEpBJOTlJkyaZezFJ0syZ0tNPS3//bW1dAAAA2QVhCcjk7uzFlCuXFBoq1a8v/f671VUBAAA4PsISkAU8/7y0datUooQZlOrVM4MTAAAA0g9hCcgiqlc3N6tt0MDci6llS+n996X4eKsrAwAAcEyEJSAL8faWNmyQevQwu+ONGCG1acPnmAAAANIDYQnIYjw8pI8+Mr/c3aVvv5Vq15b27bO6MgAAAMdCWAKyqB49pO3bJV9f6eRJ8/a8BQusrgoAAMBxEJaALKxmTWnPHumZZ6SoKDNAvfyyFBlpdWUAAABZH2EJyOLy5ZNWrTKbPTg7S59/boaonTutrgwAACBrIywBDsDJSRo2TNq0SfLxkU6ckBo1ksaPp1seAABAahGWAAfSsKG0f7/UsaMUGysFBUn+/tK5c1ZXBgAAkPUQlgAHkzevtGSJNH++lDOn2Wq8alXpiy+srgwAACBrISwBDshmk7p3l/buNT+/dPmyebXppZfM3wMAAODBCEuAAytfXtqxw9y81tlZWrpUqlJFWrPG6soAAAAyP8IS4ODc3KQxY6Rt26QKFaSwMKl1a+m116Rr16yuDgAAIPMiLAHZRN265m15/fubxx9+KFWrJm3caGlZAAAAmRZhCchGcuSQpk6VfvxRKlVKOnVKatpU6tOHq0wAAAB3IywB2dATT0gHD0o9e0qGIX3wgflZpu+/t7oyAACAzIOwBGRTefKYt+KFhkq+vtLp01KrVlKXLlJEhNXVAQAAWI+wBGRzzZtLv/wiDRggOTlJn34qVawoLVtmXnUCAADIrghLAJQrlzRlitkxr3Jl6eJF6cUXpTZtpL/+sro6AAAAaxCWACSoV8/smDdypOTqKn3zjRmePvhAiouzujoAAICMRVgCkIibm/Tuu9K+fWZ4iow0u+XVqyft2WN1dQAAABmHsATArsqVpa1bpVmzJC8vMyjVrSv17StdvWp1dQAAAOmPsATgnpydpTfekH77TerUSYqPl2bMMBtAfPEFDSAAAIBjIywBeKAiRaTPPzfbjJcrJ4WFSR07Sk89Jf3xh9XVAQAApA/CEoBka97c3Mx25Ejzs03r1pmb2Y4ZI0VFWV0dAABA2iIsAUgRDw+zAcSvv5rhKSpKeucdqWpVac0aq6sDAABIO4QlAKlSrpx5ZWnJEvM2vWPHpNatpeeek44ft7o6AACAh0dYApBqNpu5ee3Ro9LAgZKLyz97M40YId24YXWFAAAAqUdYAvDQPD2lSZPMzzP5+5u35r3/vtk1b/lyuuYBAICsibAEIM1UrCitXSutWCH5+EhnzkgdOkhPPikdOmR1dQAAAClDWAKQpmw2qW1b6fBhsxGEh4f0449S9epS//7SlStWVwgAAJA8hCUA6SJnTrPF+JEjZniKi5OmTZMefVRasMDc4BYAACAzIywBSFelSpm35a1bJ1WoIF28KPXoIT32mLRpk9XVAQAA3BthCUCG8PeXDhwwG0F4ekp790pNmkgvvCCdPGl1dQAAAEkRlgBkGDc3s8X4sWPS669LTk7Sl1+aV5wCA6XISKsrBAAA+AdhCUCGK1xYmjNH2r9fat5cio6WgoPNjW4//ND8fBMAAIDVCEsALFO1qvlZpm++MRs/XLggvfaaVKuWtGGD1dUBAIDsjrAEwFI2m/TMM9Ivv0ghIVLevObmtk8+KT3/vHnLHgAAgBUISwAyBTc3qV8/6Y8/pD59JGdnadUqqXJl83NOly9bXSEAAMhuCEsAMpUCBaTp080rTa1aSTEx0pQpUtmy0uTJUlSU1RUCAIDsgrAEIFOqWFFas0b6/nupShXp77+lQYPMznlLlrCpLQAASH+EJQCZWsuWZte8+fOlYsWkU6ekTp2k+vWljRutrg4AADgywhKATM/ZWereXfr9d2nMGCl3bmnXLumJJ6Q2baTffrO6QgAA4IgISwCyjFy5pBEjzCYQvXqZIeq//zVv03vjDen8easrBAAAjoSwBCDL8faWZs+Wfv1Veu45cxPbOXPMJhBjxkg3blhdIQAAcASEJQBZVoUKZnvxjRulxx6Trl+X3nnH3OB2/nwzRAEAAKQWYQlAlvf449KOHWaXvFKlpHPnpJ49perVzdv0DMPqCgEAQFZEWALgEJycpBdfNJs9TJ4s5csnHTpkNoBo3FjautXqCgEAQFZDWALgUNzdpYAA6fhxaehQycPDDEqNGpmfb/r1V6srBAAAWQVhCYBDypdPGj/e7Jz36qtm57xvvpGqVZO6dpX+/NPqCgEAQGZHWALg0IoXl+bNM68otWtnfn7pk0/MJhABAdKlS1ZXCAAAMivCEoBsoUIF6csvpZ07paZNpehoaepUqUwZ6b33aDcOAACSIiwByFbq1pV++EH6/nupRg0pMlJ6+21zj6bZs6WYGKsrBAAAmQVhCUC2Y7NJLVtKe/ZIixdLpUtL4eFS795SpUrSsmVSfLzVVQIAAKsRlgBkW05O0ksvSUeOSDNmSIULmw0hXnzR3OQ2NNTqCgEAgJUISwCyPTc36a23zHbjo0ZJuXNLe/dKLVpIzZubn3MCAADZD2EJAP4nd27pnXekEyekfv0kV1fz803160vPPy/98ovVFQIAgIxEWAKAuxQqJIWESL//bu7J5OQkrVolVa8u/ec/5q16AADA8RGWAOAeSpWSPv5YOnRIeuEFc4+mxYvNNuRvvOGsixc9rC4RAACkI8ISADxAhQrSF1+Yn2N6+mkpLk6aP99JvXs316BBTrpwweoKAQBAeiAsAUAy1awprV4tbdkiNW4cr5gYZ02f7qzSpc29mq5csbpCAACQlghLAJBCfn7S+vVxevfdbapVK143bkjvvWfu1zR+vHTjhtUVAgCAtEBYAoBUsNmkmjUvavv2OK1YYW5m+/ffUlCQVKaMuW9TVJTVVQIAgIdBWAKAh2CzSW3bSgcPSosWmVeXzp+X+vaVHn3UbBARG2t1lQAAIDUsD0uzZs2Sr6+vPDw8VLt2bW3evPm+8zdu3KjatWvLw8NDpUuX1pw5c5LM+eqrr1SpUiW5u7urUqVKWrlyZXqVDwCSJGdnqXNn6cgRafZsqVgx6fRpqXt3qUoVs0FEfLzVVQIAgJSwNCwtW7ZM/fv31/Dhw7Vv3z41btxYrVq10unTp+3OP3nypJ5++mk1btxY+/bt07Bhw9S3b1999dVXCXO2b9+ujh07qnPnzjpw4IA6d+6sDh06aOfOnRn1tgBkY25uUq9e5l5MkyZJBQpIR49KHTtKtWtL33xjtiAHAACZn4uVLz5lyhT16NFDPXv2lCSFhIRo7dq1mj17tsaNG5dk/pw5c1SyZEmFhIRIkipWrKjdu3dr0qRJateuXcI5/P39FRQUJEkKCgrSxo0bFRISoiVLltitIyoqSlH/+nBBZGSkJCkmJkYxMTFp9n5T487rW10H0gbr6TgetJYuLuateF27StOnOykkxEn799v03HPSY4/F69134+Xvb8hmy8CicU/8bDoO1tKxsJ6OIzOtZUpqsBmGNf8fZ3R0tHLmzKnly5erbdu2CeP9+vXT/v37tXHjxiTPefzxx1WzZk1NmzYtYWzlypXq0KGDbt68KVdXV5UsWVIDBgzQgAEDEuZMnTpVISEh+vPPP+3WMnLkSI0aNSrJ+OLFi5UzZ86HeZsAIEmKjHTV11+X0+rVvoqKMv9/qooVI/TSS7+pWrVLFlcHAED2cfPmTXXq1ElXr16Vp6fnfedadmXp0qVLiouLk7e3d6Jxb29vhYeH231OeHi43fmxsbG6dOmSihYtes859zqnZF59CggISDiOjIxUiRIl1KJFiwd+A9NbTEyMQkND5e/vL1dXV0trwcNjPR1HatbyxRel8+cNTZ4cpzlznHTkSAG9846fmjSJ18iR8fLz4/48q/Cz6ThYS8fCejqOzLSWd+4iSw5Lb8OTJNtd96AYhpFk7EHz7x5P6Tnd3d3l7u6eZNzV1dXyxbwjM9WCh8d6Oo6UruUjj0hTp0qDB0vjxknz5kkbNzqpaVMn+ftLY8ZI9eqlY8G4L342HQdr6VhYT8eRGdYyJa9vWYOHggULytnZOckVnwsXLiS5MnRHkSJF7M53cXFRgQIF7jvnXucEACsUK2buxfTHH9Lrr5ufcQoNlerXl555Rtqzx+oKAQCAZWHJzc1NtWvXVmhoaKLx0NBQNWzY0O5zGjRokGT+unXrVKdOnYSEeK859zonAFipRAlpzhzp99/NNuPOztLq1VKdOv/s3wQAAKxhaevwgIAAffTRR1qwYIGOHDmiAQMG6PTp0+rVq5ck87NEXbp0SZjfq1cv/fnnnwoICNCRI0e0YMECzZ8/X4MGDUqY069fP61bt07BwcH67bffFBwcrPXr16t///4Z/fYAINl8faX58819ml5+2dzs9uuvperVpQ4dpMOHra4QAIDsx9Kw1LFjR4WEhGj06NGqUaOGNm3apDVr1sjHx0eSFBYWlmjPJV9fX61Zs0Y//fSTatSooTFjxmj69OkJbcMlqWHDhlq6dKk+/vhjVatWTQsXLtSyZctUjw8BAMgCypWTPv1UOnTI3JtJkpYvNze2ffll8woUAADIGJY3eOjdu7d69+5t97GFCxcmGWvSpIn27t1733O2b99e7du3T4vyAMASFStKS5dKw4dL774rrVwpff65Oda5s/T221Lp0lZXCQCAY7P0yhIA4P6qVpVWrDAbPjzzjBQXJy1cKJUvL732mvSvi+8AACCNEZYAIAuoVUv65htpxw6pZUspNlb68EPztr233pLOnrW6QgAAHA9hCQCykHr1pO+/lzZvlpo1k6KjpZkzpTJlpP79pbAwqysEAMBxEJYAIAtq1Ej64Qfpxx/N30dFSdOmmZ9jGjCA0AQAQFogLAFAFvbEE9KmTdK6dVLDhtLt21JICKEJAIC0QFgCgCzOZpP8/aUtW8zQ1KBB4tAUECCFh1tdJQAAWQ9hCQAcxJ3QtHVr4tA0daq56S2hCQCAlCEsAYCD+XdoWrtWql+f0AQAQGoQlgDAQdlsUosW0rZtSUNT6dLSwIGEJgAA7oewBAAO7t+h6fvvzfbjt25JU6b8E5rOn7e6SgAAMh/CEgBkEzabuaHt9u1JQ5OvrzRoEKEJAIB/IywBQDbz79D03Xf/hKbJkwlNAAD8G2EJALIpm0166ql/QlPduoQmAAD+jbAEANncndC0Y4e0Zk3S0DR4sHThgtVVAgCQ8QhLAABJZmhq1eqf0PTYY2ZomjSJ0AQAyJ4ISwCARO6Epp07pdWrzdB08yahCQCQ/RCWAAB22WzS00//E5rq1PknNJUqxT5NAADHR1gCANzXndD088/St9/+c3venZbj/fpJZ89aXSUAAGmPsAQASBabTWrd2rzS9N13Uv360u3b0vTp5ua2b74pnTljdZUAAKQdwhIAIEXudM/btk0KDZUaNZKio6VZs6QyZaRevaRTp6yuEgCAh0dYAgCkis0mNW8ubdokbdggPfGEFBMjzZ0rlSsn9ewpnThhdZUAAKQeYQkA8FBsNqlpU+nHH6WNG80AFRsrzZ8vPfqo1K2bdOyY1VUCAJByhCUAQJp5/HHz1rytW6WWLaW4OGnhQqlCBalzZ+m336yuEACA5CMsAQDSXMOG0vffmxvctm4txcdLn30mVaokvfSSdOiQ1RUCAPBghCUAQLqpV89sN757t9SmjWQY0tKlUtWqUocO0sGDVlcIAMC9EZYAAOmudm3p66+lffuk//s/MzQtXy5Vr24e79tndYUAACRFWAIAZJgaNaSvvjKvKHXoYDaHWLlSqlVLeu45adcuqysEAOAfhCUAQIarWlVatkz69VepUyfJyUn65hupbl3p6afNzzoBAGA1whIAwDKVKkmffy4dPix16WKGpu++kxo0MLvpbd1qdYUAgOyMsAQAsFz58tInn0hHj5r7Mjk7S+vWSY0aSU8+ae7fBABARiMsAQAyjbJlpQULpN9/l159VXJxkTZskJ54QmrSxPy9YVhdJQAguyAsAQAyndKlpXnzpD/+kHr1klxdpU2bzKtMjRtLa9cSmgAA6Y+wBADItHx8pNmzpePHpbfektzdzc8xPfWUVL++2RSC0AQASC+EJQBApleihDRjhnTihNS/v5Qjh/Tzz2a78Zo1zT2b4uOtrhIA4GgISwCALKNYMWnqVOnkSWnoUCl3bunAAXPPpipVpM8+k2Jjra4SAOAoCEsAgCzH21saP146dUp65x3Jy0s6ckTq3FmqUEGaP1+Kjra6SgBAVkdYAgBkWQUKSKNGSX/+Kb3/vnl8/LjUs6dUrpw0a5Z0+7bVVQIAsirCEgAgy/PykoYNM680TZpkXnk6fVp6802zs97UqdKNG1ZXCQDIaghLAACHkTu3NHCg+ZmmGTOkRx6RwsKkgADJ19e8dS8y0uoqAQBZBWEJAOBwcuQwW40fP27u1+TrK128KAUFSaVKmbfu/f231VUCADI7whIAwGG5uUmvvir9/ru0aJFUvrwZkkaONPdwGjbMDFEAANhDWAIAODwXF7NT3qFD0rJlUtWq0rVr0rhx5pWmIUOcdPmyu9VlAgAyGRerC8iMjP9tBx+ZCW5sj4mJ0c2bNxUZGSlXV1ery8FDYj0dB2uZdT31lNSihfTdd9LEidK+fVJIiOTiUk9bt17XgAHOKlHC6iqRWvxsOhbW03FkprW882/8O//mvx+bkZxZ2cxff/2lEvxNCQAAADisM2fO6JFHHrnvHMKSHfHx8Tp37pzy5Mkjm81maS2RkZEqUaKEzpw5I09PT0trwcNjPR0Ha+lYWE/HwVo6FtbTcWSmtTQMQ9euXVOxYsXk5HT/TyVxG54dTk5OD0yZGc3T09PyP1hIO6yn42AtHQvr6ThYS8fCejqOzLKWXl5eyZpHgwcAAAAAsIOwBAAAAAB2EJYyOXd3d7377rtyd6elrSNgPR0Ha+lYWE/HwVo6FtbTcWTVtaTBAwAAAADYwZUlAAAAALCDsAQAAAAAdhCWAAAAAMAOwhIAAAAA2EFYygRmzZolX19feXh4qHbt2tq8efN952/cuFG1a9eWh4eHSpcurTlz5mRQpXiQlKxlWFiYOnXqpPLly8vJyUn9+/fPuEKRLClZzxUrVsjf31+FChWSp6enGjRooLVr12ZgtbiflKzlli1b5OfnpwIFCihHjhyqUKGCpk6dmoHV4kFS+vfmHVu3bpWLi4tq1KiRvgUiRVKynj/99JNsNluSr99++y0DK8a9pPRnMyoqSsOHD5ePj4/c3d1VpkwZLViwIIOqTSYDllq6dKnh6upqfPjhh8bhw4eNfv36Gbly5TL+/PNPu/NPnDhh5MyZ0+jXr59x+PBh48MPPzRcXV2NL7/8MoMrx91SupYnT540+vbta3zyySdGjRo1jH79+mVswbivlK5nv379jODgYOPnn382fv/9dyMoKMhwdXU19u7dm8GV424pXcu9e/caixcvNn799Vfj5MmTxqeffmrkzJnTmDt3bgZXDntSup53XLlyxShdurTRokULo3r16hlTLB4opev5448/GpKMo0ePGmFhYQlfsbGxGVw57paan83nnnvOqFevnhEaGmqcPHnS2Llzp7F169YMrPrBCEsWq1u3rtGrV69EYxUqVDACAwPtzh8yZIhRoUKFRGOvv/66Ub9+/XSrEcmT0rX8tyZNmhCWMpmHWc87KlWqZIwaNSqtS0MKpcVatm3b1nj55ZfTujSkQmrXs2PHjsaIESOMd999l7CUiaR0Pe+Epb///jsDqkNKpHQtv/vuO8PLy8uIiIjIiPJSjdvwLBQdHa09e/aoRYsWicZbtGihbdu22X3O9u3bk8xv2bKldu/erZiYmHSrFfeXmrVE5pUW6xkfH69r164pf/786VEi/r+9+41p4ozjAP6tngWEMJ1OKHahiwjiBllLF8UZUGARwwshGiJEY7N1bHEkQ2dcl22RxWxRJ3PZxtxchJghxBiDGoeOZopBiIuy1k0h1jiJktG56nCyP1Xrsxdos66H9Cqlzfb9JPfirs9dv9dfWvnl7h4DNBq1tNls6OzsRG5ubigikgLB1rO+vh4XL17Ehg0bQh2RFHiY76der4dGo0F+fj6OHTsWypgUgGBqefDgQRiNRmzZsgXTp09Hamoq1q1bhz///HMsIgdMCneA/zOXywWPx4OEhASf7QkJCXA6nbL7OJ1O2fF37tyBy+WCRqMJWV4aXjC1pMg1GvWsqanB77//jtLS0lBEpAA9TC21Wi1++eUX3LlzB9XV1TCbzaGMSgEIpp4XLlyAxWJBe3s7JIl/9kSSYOqp0WiwY8cOZGVlwe1248svv0R+fj7a2tqQk5MzFrFJRjC1/PHHH3HixAlER0ejubkZLpcLq1evxvXr1yPquSX+akQAlUrlsy6E8Ns20ni57TT2lNaSIluw9WxqakJ1dTUOHDiAadOmhSoeKRBMLdvb2zE4OIiTJ0/CYrEgJSUFZWVloYxJAQq0nh6PB+Xl5XjnnXeQmpo6VvFIISXfz7S0NKSlpXnXs7OzceXKFWzdupXNUgRQUsu7d+9CpVJh9+7deOSRRwAAH3zwAZYtW4ba2lrExMSEPG8g2CyF0dSpUzF+/Hi/jvvq1at+nfl9iYmJsuMlScKUKVNClpUeLJhaUuR6mHru2bMHL7zwAvbu3YuCgoJQxqQAPEwtn3jiCQBARkYGfv75Z1RXV7NZCjOl9bx58yZOnz4Nm82GyspKAEN/oAkhIEkSWltbkZeXNybZyd9o/ds5d+5cNDQ0jHY8UiCYWmo0GkyfPt3bKAFAeno6hBDo6+vDzJkzQ5o5UHxmKYzUajWysrJgtVp9tlutVsybN092n+zsbL/xra2tMBqNmDBhQsiy0oMFU0uKXMHWs6mpCSaTCY2NjSgqKgp1TArAaH03hRBwu92jHY8UUlrP+Ph4/PDDD7Db7d7l5ZdfRlpaGux2O+bMmTNW0UnGaH0/bTYbH0MIs2Bq+eyzz+Knn37C4OCgd5vD4cC4ceOg1WpDmleRME0sQffcn2Zx586doru7W1RVVYnY2FjR29srhBDCYrGIlStXesffnzp8zZo1oru7W+zcuZNTh0cIpbUUQgibzSZsNpvIysoS5eXlwmaziXPnzoUjPv2L0no2NjYKSZJEbW2tz3S2AwMD4ToFukdpLT/55BNx8OBB4XA4hMPhEHV1dSI+Pl68+eab4ToF+odgfmv/ibPhRRal9dy2bZtobm4WDodDnD17VlgsFgFA7Nu3L1ynQPcoreXNmzeFVqsVy5YtE+fOnRPHjx8XM2fOFGazOVynIIvNUgSora0VycnJQq1WC4PBII4fP+59bdWqVSI3N9dnfFtbm9Dr9UKtVgudTie2b98+xolpOEprCcBvSU5OHtvQNCwl9czNzZWt56pVq8Y+OPlRUsuPPvpIPPnkk2LixIkiPj5e6PV68emnnwqPxxOG5CRH6W/tP7FZijxK6rl582YxY8YMER0dLSZPnizmz58vvvrqqzCkJjlKv5s9PT2ioKBAxMTECK1WK9auXSv++OOPMU79YCoh7s0OQERERERERF58ZomIiIiIiEgGmyUiIiIiIiIZbJaIiIiIiIhksFkiIiIiIiKSwWaJiIiIiIhIBpslIiIiIiIiGWyWiIiIiIiIZLBZIiIiIiIiksFmiYiIiIiISAabJSIiChuTyQSVSuW3FBYWhvR9VSoV9u/fH1C+4uLikGYhIqLIJYU7ABER/b8VFhaivr7eZ1tUVFRI3uvWrVtQq9UhOTYREf338MoSERGFVVRUFBITE32WyZMnAwAGBgZQUVGBhIQEREdH46mnnsKhQ4cAANeuXUNZWRm0Wi0mTpyIjIwMNDU1+Rx7wYIFqKysxNq1azF16lQ899xz0Ol0AICSkhKoVCrv+r9VV1dj165dOHDggPeKV1tbG/Ly8lBZWekz9tq1a4iKisLRo0cBADqdDhs3bkR5eTni4uKQlJSEjz/+2GefGzduoKKiAtOmTUN8fDzy8vJw5syZh/04iYhoFLFZIiKiiHT37l0sXrwYnZ2daGhoQHd3NzZt2oTx48cDAP766y9kZWXh0KFDOHv2LCoqKrBy5Up8++23PsfZtWsXJElCR0cHPv/8c5w6dQoAUF9fj/7+fu/6v61btw6lpaUoLCxEf38/+vv7MW/ePJjNZjQ2NsLtdnvH7t69G0lJSVi4cKF32/vvv4/MzEx89913eOONN7BmzRpYrVYAgBACRUVFcDqdaGlpQVdXFwwGA/Lz83H9+vVR/RyJiCh4KiGECHcIIiL6fzKZTGhoaEB0dLTP9tdffx1z5szB4sWL0dPTg9TU1ICOV1RUhPT0dGzduhXA0JWlGzduwGaz+YxTqVRobm4e8Xkkk8mEgYEBn+eb3G43kpKSsH37dpSWlgIA9Ho9iouLsWHDBgBDV5bS09Nx+PBh737Lly/Hb7/9hpaWFhw9ehQlJSW4evWqzy2HKSkpWL9+PSoqKgI6XyIiCi1eWSIiorBauHAh7Ha7z/LKK6/AbrdDq9UO2yh5PB68++67yMzMxJQpUxAXF4fW1lZcvnzZZ5zRaBwxw+XLlxEXF+dd3nvvvWHHRkVFYcWKFairqwMA2O12nDlzBiaTyWdcdna233pPTw8AoKurC4ODg97c95dLly7h4sWLI+YlIqKxwQkeiIgorGJjY5GSkuK3PSYm5oH71dTUYNu2bfjwww+RkZGB2NhYVFVV4datW37HH0lSUhLsdrt3/dFHH33geLPZjKeffhp9fX2oq6tDfn4+kpOTR3wflUoFYOgWQ41Gg7a2Nr8xkyZNGvE4REQ0NtgsERFRRMrMzERfXx8cDofs1aX29nYsWbIEK1asADDUgFy4cAHp6ekjHnvChAnweDzedUmSZBs2tVrtM+6+jIwMGI1GfPHFF2hsbPSbvAEATp486bc+a9YsAIDBYIDT6YQkScNOMEFEROHH2/CIiCis3G43nE6nz+JyuZCbm4ucnBwsXboUVqsVly5dwuHDh3HkyBEAQ8/3WK1WdHZ2oqenBy+99BKcTmdA76nT6fDNN9/A6XTi119/feC477//HufPn4fL5cLt27e9r5nNZmzatAkejwclJSV++3Z0dGDLli1wOByora3F3r178eqrrwIACgoKkJ2djeLiYnz99dfo7e1FZ2cn3nrrLZw+fVrJx0dERCHEZomIiMLqyJEj0Gg0Psv8+fMBAPv27cMzzzyDsrIyzJ49G+vXr/de6Xn77bdhMBiwaNEiLFiwAImJiQH/B7I1NTWwWq14/PHHodfrhx334osvIi0tDUajEY899hg6Ojq8r5WVlUGSJJSXl/tNUAEAr732Grq6uqDX67Fx40bU1NRg0aJFAIZux2tpaUFOTg6ef/55pKamYvny5ejt7UVCQkKgHx0REYUYZ8MjIiIKwpUrV6DT6XDq1CkYDAaf13Q6HaqqqlBVVRWecERENCr4zBIREZECt2/fRn9/PywWC+bOnevXKBER0X8Hb8MjIiJSoKOjA8nJyejq6sJnn30W7jhERBRCvA2PiIiIiIhIBq8sERERERERyWCzREREREREJIPNEhERERERkQw2S0RERERERDLYLBEREREREclgs0RERERERCSDzRIREREREZEMNktEREREREQy/gYMXK/250hlkAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Que se passe t'il lorsque l'on emprunte l'actif 2 ?\n",
    "N=1000\n",
    "moyenne3_x=np.zeros(N)\n",
    "std3_x=np.zeros(N)\n",
    "for i in range(0,N):\n",
    "\n",
    "    ######  A vous de jouer  .....\n",
    "    # prendre de valeurs negatives pour x_2 dans [-5,0], en déduire x_1\n",
    "    # x_2 = - ...\n",
    "    # x_1 = ...\n",
    "\n",
    "# plot ###################################################################\n",
    "def plot5():\n",
    "    plot4() # le plot précédent\n",
    "    plt.plot(std3_x, moyenne3_x,'b-')\n",
    "    \n",
    "plot5()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "21pVw4dVotj5"
   },
   "source": [
    "## Introduction d'un actif sans risque"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hEzaeE83otj6"
   },
   "source": [
    " Nous allons introduire un nouvel actif, l'actif sans risque, qui\n",
    "  comme son nom le suggère aura un rendement de variance nulle (ce qui\n",
    "  implique que ce rendement n'est pas aléatoire). On supposera que ce\n",
    "  rendement déterministe est inférieur à tous les rendements moyens\n",
    "  des actifs risqués (pourquoi est-ce une hypothèse raisonnable?). On\n",
    "  prendra, ici, ce rendement égal à $0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Y3tESug1otj7"
   },
   "source": [
    "---\n",
    "<font color=red>Question 7:</font>\n",
    "<br><font color='blue'>\n",
    "Construire le vecteur de moyenne et la matrice de variance-covariance de ce nouveau vecteur des rendements.\n",
    "</font>\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 334
    },
    "id": "1OmlcHbXotj7",
    "outputId": "80017f5f-bb2f-44e9-eabc-7a5e9b44e39f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gamma_3=\n",
      "[[0.   0.   0.  ]\n",
      " [0.   0.01 0.  ]\n",
      " [0.   0.   0.09]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f92f697f650>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JJ5/oq1/9qowxunLlir7zne9o/fr1g/alqqpKL774opPuAwCAcWpIN926XK6o18aYmLYb1f9h+5EjR/Tyyy+rurpaH3zwgQ4ePKh/+7d/00svvTToMSsqKtTb2xvZurq6hnIqAABgHHC0wpKeni632x2zmnL+/PmYVZRrpk2bFrc+KSlJU6ZMkSRt2rRJxcXFeu655yRJX/nKV/Tb3/5Wf/VXf6XKykpNmhSbqzwejzwej5PuAwCAccrRCktKSop8Pp8aGxuj2hsbG1VYWBh3n4KCgpj6w4cPKz8/X8nJyZKkzz77LCaUuN1uGWPk8J5gAAAwATm+JFReXq4333xTe/bsUUdHh8rKytTZ2amSkhJJA5dqVq1aFakvKSnR2bNnVV5ero6ODu3Zs0e1tbVau3ZtpObRRx9VTU2N9u/fr9OnT6uxsVGbNm3SY489JrfbPQynCQAAxjNHl4QkqaioSBcuXNCWLVsUDAaVl5enhoYGZWVlSZKCwWDUM1mys7PV0NCgsrIy7dixQzNmzND27du1YsWKSM3GjRvlcrm0ceNGnTt3TlOnTtWjjz6ql19+eRhOEQAAjHeOn8NiK57DAgDA+DMiz2EBAAAYCwQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGC9IQWW6upqZWdny+v1yufzqamp6br1R48elc/nk9fr1Zw5c7Rz586Ymk8//VTPP/+8pk+fLq/Xq5ycHDU0NAylewAAYIJxHFjq6upUWlqqyspKtbW1ye/3a8mSJers7Ixbf/r0aS1dulR+v19tbW3asGGDVq9erfr6+khNf3+/vv71r+vMmTM6cOCAPvzwQ+3evVszZ84c+pkBAIAJw2WMMU52WLBggebPn6+amppIW05OjpYtW6aqqqqY+nXr1unQoUPq6OiItJWUlOjEiRNqaWmRJO3cuVOvvfaa/vu//1vJyclDOpFQKKS0tDT19vYqNTV1SMcAAACjK9Hvb0crLP39/WptbVUgEIhqDwQCam5ujrtPS0tLTP3ixYt1/PhxXb58WZJ06NAhFRQU6Pnnn1dGRoby8vK0detWhcPhQfvS19enUCgUtQEAgInJUWDp6elROBxWRkZGVHtGRoa6u7vj7tPd3R23/sqVK+rp6ZEkffTRRzpw4IDC4bAaGhq0ceNGff/739fLL788aF+qqqqUlpYW2TIzM52cCgAAGEeGdNOty+WKem2MiWm7Uf0ftl+9elVf/vKXtWvXLvl8Pj311FOqrKyMuuz0eRUVFert7Y1sXV1dQzkVAAAwDiQ5KU5PT5fb7Y5ZTTl//nzMKso106ZNi1uflJSkKVOmSJKmT5+u5ORkud3uSE1OTo66u7vV39+vlJSUmON6PB55PB4n3QcAAOOUoxWWlJQU+Xw+NTY2RrU3NjaqsLAw7j4FBQUx9YcPH1Z+fn7kBtsHH3xQ//u//6urV69Gak6dOqXp06fHDSsAAODW4viSUHl5ud58803t2bNHHR0dKisrU2dnp0pKSiQNXKpZtWpVpL6kpERnz55VeXm5Ojo6tGfPHtXW1mrt2rWRmu985zu6cOGC1qxZo1OnTunf//3ftXXrVj3//PPDcIoAAGC8c3RJSJKKiop04cIFbdmyRcFgUHl5eWpoaFBWVpYkKRgMRj2TJTs7Ww0NDSorK9OOHTs0Y8YMbd++XStWrIjUZGZm6vDhwyorK9M999yjmTNnas2aNVq3bt0wnCIAABjvHD+HxVY8hwUAgPFnRJ7DAgAAMBYILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAeo7/lhCAYRAOS01NUjAoTZ8u+f2S2z3WvQIAaxFYgNF28KC0Zo30m9/8vm3WLOn116Xly8euXwBgMS4JAaPp4EHpiSeiw4oknTs30H7w4Nj0CwAsR2ABRks4PLCyEu8PpF9rKy0dqAMARCGwAKOlqSl2ZeUPGSN1dQ3UAQCiEFiA0RIMDm8dANxCCCzAaJk+fXjrAOAWQmABRovfP/BrIJcr/vsul5SZOVAHAIhCYAFGi9s98NNlKTa0XHu9bRvPYwGAOAgswGhavlw6cECaOTO6fdasgXaewwIAcfHgOGC0LV8uPf44T7oFAAcILMBYcLulhx4a614AwLjBJSEAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArDekwFJdXa3s7Gx5vV75fD41NTVdt/7o0aPy+Xzyer2aM2eOdu7cOWjt/v375XK5tGzZsqF0DQAATECOA0tdXZ1KS0tVWVmptrY2+f1+LVmyRJ2dnXHrT58+raVLl8rv96utrU0bNmzQ6tWrVV9fH1N79uxZrV27Vn6/3/mZAACACctljDFOdliwYIHmz5+vmpqaSFtOTo6WLVumqqqqmPp169bp0KFD6ujoiLSVlJToxIkTamlpibSFw2EtXLhQ3/72t9XU1KRPP/1U//qv/5pwv0KhkNLS0tTb26vU1FQnpwQAAMZIot/fjlZY+vv71draqkAgENUeCATU3Nwcd5+WlpaY+sWLF+v48eO6fPlypG3Lli2aOnWqnn322YT60tfXp1AoFLUBAICJyVFg6enpUTgcVkZGRlR7RkaGuru74+7T3d0dt/7KlSvq6emRJL377ruqra3V7t27E+5LVVWV0tLSIltmZqaTUwEAAOPIkG66dblcUa+NMTFtN6q/1n7x4kU988wz2r17t9LT0xPuQ0VFhXp7eyNbV1eXgzMAAADjSZKT4vT0dLnd7pjVlPPnz8esolwzbdq0uPVJSUmaMmWKfvWrX+nMmTN69NFHI+9fvXp1oHNJSfrwww919913xxzX4/HI4/E46T4AABinHK2wpKSkyOfzqbGxMaq9sbFRhYWFcfcpKCiIqT98+LDy8/OVnJysefPm6Ze//KXa29sj22OPPaaHH35Y7e3tXOoBAADOVlgkqby8XMXFxcrPz1dBQYF27dqlzs5OlZSUSBq4VHPu3Dm99dZbkgZ+EfTGG2+ovLxcf/mXf6mWlhbV1tZq3759kiSv16u8vLyoz/jSl74kSTHtAADg1uQ4sBQVFenChQvasmWLgsGg8vLy1NDQoKysLElSMBiMeiZLdna2GhoaVFZWph07dmjGjBnavn27VqxYMXxnAQAAJjTHz2GxFc9hAQBg/BmR57AAAACMBQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALDekAJLdXW1srOz5fV65fP51NTUdN36o0ePyufzyev1as6cOdq5c2fU+7t375bf79fkyZM1efJkLVq0SMeOHRtK1wAAwATkOLDU1dWptLRUlZWVamtrk9/v15IlS9TZ2Rm3/vTp01q6dKn8fr/a2tq0YcMGrV69WvX19ZGaI0eO6Omnn9bPf/5ztbS06K677lIgENC5c+eGfmYAAGDCcBljjJMdFixYoPnz56umpibSlpOTo2XLlqmqqiqmft26dTp06JA6OjoibSUlJTpx4oRaWlrifkY4HNbkyZP1xhtvaNWqVQn1KxQKKS0tTb29vUpNTXVySgAAYIwk+v3taIWlv79fra2tCgQCUe2BQEDNzc1x92lpaYmpX7x4sY4fP67Lly/H3eezzz7T5cuXdeeddw7al76+PoVCoagNAABMTI4CS09Pj8LhsDIyMqLaMzIy1N3dHXef7u7uuPVXrlxRT09P3H3Wr1+vmTNnatGiRYP2paqqSmlpaZEtMzPTyakAAIBxZEg33bpcrqjXxpiYthvVx2uXpFdffVX79u3TwYMH5fV6Bz1mRUWFent7I1tXV5eTUwAAAONIkpPi9PR0ud3umNWU8+fPx6yiXDNt2rS49UlJSZoyZUpU+/e+9z1t3bpVP/vZz3TPPfdcty8ej0cej8dJ9wEAwDjlaIUlJSVFPp9PjY2NUe2NjY0qLCyMu09BQUFM/eHDh5Wfn6/k5ORI22uvvaaXXnpJ77zzjvLz8510CwAATHCOLwmVl5frzTff1J49e9TR0aGysjJ1dnaqpKRE0sClmj/8ZU9JSYnOnj2r8vJydXR0aM+ePaqtrdXatWsjNa+++qo2btyoPXv2aPbs2eru7lZ3d7cuXbo0DKcIAADGO0eXhCSpqKhIFy5c0JYtWxQMBpWXl6eGhgZlZWVJkoLBYNQzWbKzs9XQ0KCysjLt2LFDM2bM0Pbt27VixYpITXV1tfr7+/XEE09EfdYLL7ygzZs3D/HUAADAROH4OSy24jksAACMPyPyHBYAAICxQGABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFgvaaw7YLVwWGpqkoJBafp0ye+X3O6x7hUAALecIa2wVFdXKzs7W16vVz6fT01NTdetP3r0qHw+n7xer+bMmaOdO3fG1NTX1ys3N1cej0e5ubl6++23h9K14XPwoDR7tvTww9LKlQP/O3v2QDsAABhVjgNLXV2dSktLVVlZqba2Nvn9fi1ZskSdnZ1x60+fPq2lS5fK7/erra1NGzZs0OrVq1VfXx+paWlpUVFRkYqLi3XixAkVFxfrySef1Pvvvz/0M7sZBw9KTzwh/eY30e3nzg20E1oAABhVLmOMcbLDggULNH/+fNXU1ETacnJytGzZMlVVVcXUr1u3TocOHVJHR0ekraSkRCdOnFBLS4skqaioSKFQSD/96U8jNY888ogmT56sffv2JdSvUCiktLQ09fb2KjU11ckpRQuHB1ZSPh9WrnG5pFmzpNOnuTwEAMBNSvT729EKS39/v1pbWxUIBKLaA4GAmpub4+7T0tISU7948WIdP35cly9fvm7NYMeUpL6+PoVCoahtWDQ1DR5WJMkYqatroA4AAIwKR4Glp6dH4XBYGRkZUe0ZGRnq7u6Ou093d3fc+itXrqinp+e6NYMdU5KqqqqUlpYW2TIzM52cyuCCweGtAwAAN21IN926XK6o18aYmLYb1X++3ekxKyoq1NvbG9m6uroS7v91TZ8+vHUAAOCmOfpZc3p6utxud8zKx/nz52NWSK6ZNm1a3PqkpCRNmTLlujWDHVOSPB6PPB6Pk+4nxu8fuEfl3LmByz+fd+0eFr9/+D8bAADE5WiFJSUlRT6fT42NjVHtjY2NKiwsjLtPQUFBTP3hw4eVn5+v5OTk69YMdswR5XZLr78+8O/Pr/Bce71tGzfcAgAwmoxD+/fvN8nJyaa2ttacPHnSlJaWmttvv92cOXPGGGPM+vXrTXFxcaT+o48+MrfddpspKyszJ0+eNLW1tSY5OdkcOHAgUvPuu+8at9ttXnnlFdPR0WFeeeUVk5SUZN57772E+9Xb22skmd7eXqenFF99vTGzZhkzsM4ysGVmDrQDAIBhkej3t+Mn3RYVFenChQvasmWLgsGg8vLy1NDQoKysLElSMBiMeiZLdna2GhoaVFZWph07dmjGjBnavn27VqxYEakpLCzU/v37tXHjRm3atEl333236urqtGDBgpsOZEO2fLn0+OM86RYAAAs4fg6LrYbtOSwAAGDUjMhzWAAAAMYCgQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsJ7jR/Pb6toDe0Oh0Bj3BAAAJOra9/aNHrw/YQLLxYsXJUmZmZlj3BMAAODUxYsXlZaWNuj7E+ZvCV29elUff/yx7rjjDrlcrmE7bigUUmZmprq6uvgbRTfAWDnDeCWOsUocY5U4xipxIzlWxhhdvHhRM2bM0KRJg9+pMmFWWCZNmqRZs2aN2PFTU1OZ0AlirJxhvBLHWCWOsUocY5W4kRqr662sXMNNtwAAwHoEFgAAYD0Cyw14PB698MIL8ng8Y90V6zFWzjBeiWOsEsdYJY6xSpwNYzVhbroFAAATFyssAADAegQWAABgPQILAACwHoEFAABY75YMLNXV1crOzpbX65XP51NTU9N1648ePSqfzyev16s5c+Zo586dMTX19fXKzc2Vx+NRbm6u3n777ZHq/qga7rH60Y9+JJfLFbP97ne/G8nTGBVOxioYDGrlypWaO3euJk2apNLS0rh1zKvExop5NeDgwYP6+te/rqlTpyo1NVUFBQX6j//4j5g65lViYzWR55XkbLx+8Ytf6MEHH9SUKVP0hS98QfPmzdMPfvCDmLoRnVvmFrN//36TnJxsdu/ebU6ePGnWrFljbr/9dnP27Nm49R999JG57bbbzJo1a8zJkyfN7t27TXJysjlw4ECkprm52bjdbrN161bT0dFhtm7dapKSksx77703Wqc1IkZirH74wx+a1NRUEwwGo7bxzulYnT592qxevdr80z/9k7nvvvvMmjVrYmqYVwMSGSvm1YA1a9aY7373u+bYsWPm1KlTpqKiwiQnJ5sPPvggUsO8GpDIWE3UeWWM8/H64IMPzN69e81//dd/mdOnT5t//ud/Nrfddpv5x3/8x0jNSM+tWy6w/Omf/qkpKSmJaps3b55Zv3593Pq/+7u/M/PmzYtq++u//mvzwAMPRF4/+eST5pFHHomqWbx4sXnqqaeGqddjYyTG6oc//KFJS0sb9r6ONadj9YcWLlwY90uYeRVrsLFiXg0uNzfXvPjii5HXzKvBfX6sJuq8MmZ4xuvP//zPzTPPPBN5PdJz65a6JNTf36/W1lYFAoGo9kAgoObm5rj7tLS0xNQvXrxYx48f1+XLl69bM9gxx4ORGitJunTpkrKysjRr1iz92Z/9mdra2ob/BEbRUMYqEcwrZ5hXsa5evaqLFy/qzjvvjLQxr+KLN1bSxJtX0vCMV1tbm5qbm7Vw4cJI20jPrVsqsPT09CgcDisjIyOqPSMjQ93d3XH36e7ujlt/5coV9fT0XLdmsGOOByM1VvPmzdOPfvQjHTp0SPv27ZPX69WDDz6o//mf/xmZExkFQxmrRDCvEse8iu/73/++fvvb3+rJJ5+MtDGv4os3VhNxXkk3N16zZs2Sx+NRfn6+nn/+eT333HOR90Z6bk2Yv9bshMvlinptjIlpu1H959udHnO8GO6xeuCBB/TAAw9E3n/wwQc1f/58/cM//IO2b98+XN0eEyMxB5hXiWFexdq3b582b96sn/zkJ/ryl788LMe03XCP1USeV9LQxqupqUmXLl3Se++9p/Xr1+uP/uiP9PTTT9/UMRN1SwWW9PR0ud3umLR3/vz5mFR4zbRp0+LWJyUlacqUKdetGeyY48FIjdXnTZo0SX/yJ38yrv8fy1DGKhHMq6G71edVXV2dnn32Wf34xz/WokWLot5jXkW73lh93kSYV9LNjVd2drYk6Stf+Yr+7//+T5s3b44ElpGeW7fUJaGUlBT5fD41NjZGtTc2NqqwsDDuPgUFBTH1hw8fVn5+vpKTk69bM9gxx4ORGqvPM8aovb1d06dPH56Oj4GhjFUimFdDdyvPq3379ulb3/qW9u7dq2984xsx7zOvfu9GY/V5E2FeScP336ExRn19fZHXIz63huXW3XHk2k+5amtrzcmTJ01paam5/fbbzZkzZ4wxxqxfv94UFxdH6q/9VLesrMycPHnS1NbWxvxU99133zVut9u88sorpqOjw7zyyisT6meCwzlWmzdvNu+884759a9/bdra2sy3v/1tk5SUZN5///1RP7/h5HSsjDGmra3NtLW1GZ/PZ1auXGna2trMr371q8j7zKvfu9FYMa8G7N271yQlJZkdO3ZE/Qz3008/jdQwrwYkMlYTdV4Z43y83njjDXPo0CFz6tQpc+rUKbNnzx6TmppqKisrIzUjPbduucBijDE7duwwWVlZJiUlxcyfP98cPXo08t43v/lNs3Dhwqj6I0eOmPvvv9+kpKSY2bNnm5qamphj/vjHPzZz5841ycnJZt68eaa+vn6kT2NUDPdYlZaWmrvuusukpKSYqVOnmkAgYJqbm0fjVEac07GSFLNlZWVF1TCvBtxorJhXAxYuXBh3rL75zW9GHZN5ldhYTeR5ZYyz8dq+fbv54z/+Y3PbbbeZ1NRUc//995vq6moTDoejjjmSc8tlzP+/KxIAAMBSt9Q9LAAAYHwisAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAev8P5ZWBuqvv8vUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Construction du vecteur des rendements.\n",
    "# On rajoute un actif de rendement sans risque (de variance nulle).\n",
    "\n",
    "# Pour la moyenne des rendements il suffit de rajouter le rendement sans risque\n",
    "# au vecteur des rendements\n",
    "r0=0\n",
    "mu_3=np.append(r0,mu)\n",
    "# On rajoute 0 au vecteur des variances \n",
    "sigma_3=np.append(0,sigma) # variance (nulle) de l'actif sans risque\n",
    "\n",
    "######  A vous de jouer  .....\n",
    "# Construire la nouvelle matrice Gamma_3 pour les trois actifs.\n",
    "\n",
    "\n",
    "print('Gamma_3=');print(Gamma_3)\n",
    "\n",
    "# Les vecteurs moyenne et variance des actifs\n",
    "moyenne_actif=mu_3\n",
    "std_actif=np.sqrt(np.diag(Gamma_3))\n",
    "\n",
    "# On peut aussi materialise les 3 actifs de base\n",
    "plt.plot(std_actif, moyenne_actif, 'ro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MWqfdgnZotj8"
   },
   "source": [
    "On constitue des portefeuilles avec les 3 actifs (1 non risqué, 2\n",
    "  risqués) en tirant au hasard des coefficients $(x_1,x_2,x_3)$ dans\n",
    "  le simplexe $\\left \\{(x_1, x_2, x_3) \\in \\mathbb{R}^3 | \\forall i\\in \\{1,2, 3\\} \\ 0 \\leq x_i \\leq 1 \\ \\text{et} \\ x_1+x_2+x_3=1 \\right \\}$. \n",
    "\n",
    "La fonction `simplexe(d)` fait ce travail. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "ORl0khsDotj8"
   },
   "outputs": [],
   "source": [
    "def simplexe(d):\n",
    "# Cette fonction tire \"au hasard\"  d nombre positifs\n",
    "# de somme egale 1 (= dans le simplexe)\n",
    "    t=np.random.rand(d-1)\n",
    "    t=np.sort(t)[::-1]\n",
    "    t=np.append(1,t)\n",
    "    t=np.append(t,0)\n",
    "    s=np.zeros(d)\n",
    "    for i in range(d-1,-1,-1):\n",
    "        s[i]=t[i]-t[i+1]\n",
    "    return s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Xy1RvsbAotj9"
   },
   "source": [
    "---\n",
    "<font color=red>Question 8:</font>\n",
    "<br><font color='blue'>\n",
    "Matérialiser, en tirant un grand nombre de points au hasard, la nouvelle frontière efficiente. \n",
    "</font>\n",
    "<br><font color='blue'>\n",
    "Vérifier que :\n",
    "  * La nouvelle frontière efficiente étend l'ancienne par de\n",
    "    nouveaux points \"non dominés\" entre l'actif sans risque et un\n",
    "    portefeuille tangent à l'ancienne frontière $P$.\n",
    "  * La variance reste bornée par la variance la plus grande\n",
    "    (tant que l'on ne fait pas d'emprunt).\n",
    "</font>\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "6dx2CWKZotj-",
    "outputId": "d5ce9622-3214-4ccd-90a4-cc4ad9d6a15d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On considère des portefeuilles *incluant l'actif sans risque*\n",
    "# mais *sans emprunt*. On tire \"au hasard\" des portefeuilles \n",
    "# dans le simplexe de dimension 3\n",
    "N=1000\n",
    "moyenne_d_x=np.zeros(N)\n",
    "std_d_x=np.zeros(N)\n",
    "for i in range(0,N):\n",
    "    # tirage au hasard dans le simplexe, d=2 et d+1=3 !\n",
    "    ######  A vous de jouer  .....\n",
    "    \n",
    "# plot ###################################################################\n",
    "def plot6():\n",
    "    plot5()# le plot précédent\n",
    "    # On rajoute en bleu ('b') les points ('.') représentant \n",
    "    # les portefeuilles tirés au hasard\n",
    "    plt.plot(std_d_x, moyenne_d_x,'b.',markersize=2)\n",
    "\n",
    "plot6()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UZxxyiW7otj_"
   },
   "source": [
    "# Commentaire"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "o0ii3mBHotkA"
   },
   "source": [
    "On obtient de nouveaux points \"non\n",
    "  dominés\" entre l'actif sans risque et un portefeuille tangent.  La\n",
    "  variance reste bornée par la variance de l'actifs de plus grande\n",
    "  variance tant que l'on n'emprunte pas.\n",
    "\n",
    "On va identifier un portefeuille particulier $P$, le \"portefeuille de\n",
    "  marché\".  $P$ est le portefeuille correspondant au point de\n",
    "  tangence de la droite passant par l'actif sans risque et de\n",
    "  l'ensemble de tous les portefeuilles a coefficients positifs de la\n",
    "  question précédente.\n",
    "\n",
    "  Le point $P$ est caractérisé par le fait qu'il maximise la pente des\n",
    "  droites reliant le point $(\\sigma_0=0, r_0=0)$ et les points\n",
    "  correspondants à des portefeuilles $y$ ne faisant pas intervenir\n",
    "  d'actif sans risque.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uz_1gTZyotkI"
   },
   "source": [
    "---\n",
    "<font color=red>Question 9:</font>\n",
    "<br><font color='blue'>\n",
    "Toujours en procédant par simulation dans le simplexe, calculer $P$\n",
    "  (en fait une approximation de $P$).\n",
    "\n",
    "  Vérifier que le portefeuille $P$ fait intervenir les $2$ actifs\n",
    "  risqués.\n",
    "</font>\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "hW4yus88otkI",
    "outputId": "f8ff6b54-e994-447c-f0d5-711d18867fb6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r0=mu_3[0]\n",
    "sigma0=0\n",
    "\n",
    "# On veut calculer le point P qui maximise la pente de la droite \n",
    "# entre (sigma0=0, x_0=r0) et les portefeuilles sans actif sans risque.\n",
    "# Pour cela, on va genere des portefeuilles sans actifs sans risque\n",
    "# et calculer le max des pentes ainsi obtenues.\n",
    "N=1000\n",
    "moyenne_y=np.zeros(N)\n",
    "std_y=np.zeros(N)\n",
    "pente=np.zeros(N)\n",
    "max_pente=0\n",
    "for i in range(1,N):\n",
    "    y = np.array([0,i/N,1-i/N]) # on  rajoute O en actif sans risque\n",
    "    ######  A vous de jouer  .....\n",
    "    # pente[i] = ....   pente associée au i-ième point\n",
    "\n",
    "# On calcule le point P maximise la pente\n",
    "imax=pente.argmax()\n",
    "x_P=moyenne_y[imax]\n",
    "sigma_P=std_y[imax]\n",
    "\n",
    "# plot ###################################################################\n",
    "def plot7():\n",
    "    plot6()# le plot précédent\n",
    "    \n",
    "    # Tracé du point P en rouge ('r')\n",
    "    plt.scatter(sigma_P, x_P, s=marker_size, c='r', marker='o')\n",
    "\n",
    "    # Tracé du segment \"Actif sans risque -> P\"\n",
    "    plt.plot(np.array([sigma0,sigma_P]),np.array([r0,x_P]), 'r-')\n",
    "\n",
    "    # Tracé de la droite \"actif sans risque -> P\" au dela de P\n",
    "    lambd=(x_P-r0)/(sigma_P-sigma0)# pente de la droite\n",
    "    sigma_infinity=2.0# arbitraire mais \"grand\"\n",
    "    x_infinity=r0+lambd*(sigma_infinity-sigma0)\n",
    "    plt.plot(np.array([sigma0,sigma_infinity]),np.array([r0,x_infinity]), 'g-')\n",
    "\n",
    "plot7()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HMLDcF1totkK"
   },
   "source": [
    "On autorise la détention d'une quantité de signe arbitraire\n",
    "  d'actif sans risque (cela correspond soit à un emprunt, soit à un\n",
    "  placement). Pour cela on vous suggère de tirer la quantité d'actif\n",
    "  sans risque $x_0$ entre $[-4,1]$ (on peut emprunter jusqu'à $4$ fois\n",
    "  ce que l'on possède). Puis on tire, les quantités d'actifs\n",
    "  risqués uniformément sur le simplexe $\\{x_1+x_2=1-x_0\\}$.\n",
    "\n",
    "---\n",
    "<font color=red>Question 10:</font>\n",
    "<br><font color='blue'>\n",
    "  Tirer un grand nombre de portefeuille, calculer leurs moyennes et écarts-type,\n",
    "  les tracer sur la figure.\n",
    "</font>\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "IKBPOS5motkK",
    "outputId": "b26ef40e-2b05-4019-9c39-3d094c7ed780"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# L'emprunt en actif sans risque est autorisé\n",
    "N=1000\n",
    "moyenne_x_d=np.zeros(N+1)\n",
    "std_x_d=np.zeros(N+1)\n",
    "for i in range(1,N):\n",
    "    # On génère des portefeuilles dont la quantité \n",
    "    # d'actif sans risque est uniforme sur [-4,1]\n",
    "    ######  A vous de jouer  .....\n",
    "    \n",
    "# plot ###################################################################\n",
    "def plot8():\n",
    "    plot7()# le plot précédent\n",
    "\n",
    "    # Tracé des points tirés au hazard    \n",
    "    plt.plot(std_x_d,moyenne_x_d,'mo',markersize=2)\n",
    "\n",
    "plot8()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ll2A-StQotkL"
   },
   "source": [
    "---\n",
    "<font color=red>Question 11:</font>\n",
    "<br><font color='blue'>\n",
    "  Vérifier que:\n",
    "  1. l'on obtient de nouveaux points \"non dominés\" au delà du\n",
    "    portefeuille tangent.\n",
    "  2. le rendement (mais aussi la variance) peut devenir aussi\n",
    "    grand que souhaité: __effet de levier__.\n",
    "  3. un emprunt permet de construire des portefeuilles dont la\n",
    "    moyenne des rendements est plus élevée à variance égale:\n",
    "      __emprunter permet d'augmenter la moyenne du rendement__.\n",
    "  4. l'emprunt permet de construire des portefeuilles de même\n",
    "    moyenne mais de variance inférieure: __emprunter permet de\n",
    "      réduire le risque__.  Il existe en particulier un portefeuille\n",
    "    dont la variance est égale à celle de l'actif 2 (l'actif de\n",
    "    rendement maximum) mais de rendement supérieur.\n",
    "  5. le seul point de la \"frontière sans emprunt\" qui n'est pas\n",
    "    dominé par un point de la \"frontière avec emprunt\" est le point\n",
    "    $P$: si l'on ne souhaite pas emprunter, \"le seul point\n",
    "      rationnel est\" $P$.\n",
    "  6. le portefeuille $P$ fait intervenir l'ensemble des actifs de\n",
    "    base risqués (en dehors des actifs de base dominés par d'autres\n",
    "    actifs de base).\n",
    "</font>\n",
    "\n",
    "---\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dXdRlkrkotkL"
   },
   "source": [
    "# Partie optionnelle: extensions du modèle à plus de 2 actifs risqués"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-frJHum3otkM"
   },
   "source": [
    "Le modèle de Markowitz vient d'être illustré dans le cas où l'on considère deux actifs risqués décorrélés ($\\rho=0$)\n",
    "et un actif sans risque. On peut évidemment généraliser l'approche au cas d'actifs corrélés et en faisant intervenir\n",
    "un nombre arbitraire d'actifs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8-qTHaTXotkM"
   },
   "source": [
    "## 1. Le cas d'un corrélation non nulle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TqhmE7VeotkM"
   },
   "source": [
    "---\n",
    "<font color=red>Question 12:</font>\n",
    "<br><font color='blue'>\n",
    "Recommencer l'expérience précédente avec des valeurs de $\\rho$\n",
    "  non nulle.  Prendre par exemple \n",
    "$$\n",
    "\\rho=-0.5\\quad\\mbox{et}\\quad \\rho=0.5\n",
    "$$ \n",
    "</font>\n",
    "\n",
    "---\n",
    "\n",
    "Les scripts précédents fonctionnent dans ce cas. Nous vous laissons le soin d'expérimenter par vous même."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "id": "fEpt-dCkotkM"
   },
   "outputs": [],
   "source": [
    "# Matrice de covariance: des 1 sur la diagonale, des rho ailleurs\n",
    "rho=0.5# -0.5\n",
    "covariance=rho*np.ones([d,d])+(1-rho)*np.eye(d)\n",
    "Gamma = np.matmul(np.matmul(np.diag(sigma),covariance), np.diag(sigma))\n",
    "# etc ...\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NRMKZEuYotkM"
   },
   "source": [
    "## 2. Le cas d'un nombre  d'actifs risqués arbitraires"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PWoH4KkHotkN"
   },
   "source": [
    "Lorsque $d>2$ les phénomènes sont identiques mais moins explicites. On\n",
    "peut recommencer ce qui précède mais il faudra généraliser le choix de\n",
    "la matrice de variance covariance et procéder par simulation dans tous\n",
    "les cas.\n",
    "\n",
    "Les programmes fournis en correction fonctionnent (le plus souvent) en \n",
    "dimension arbitraire.\n",
    "\n",
    "A titre indicatif voici un exemple du cas $d=3$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XCbbs7wkotkN"
   },
   "source": [
    "##### Etape 1. Choix des actifs de base."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "PTL-HltkotkN",
    "outputId": "9fd3504d-96b9-4ad9-ad9c-147ca62ad355"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On définit les caracteristiques des actifs risqués\n",
    "d=3\n",
    "rho=0.0\n",
    "\n",
    "min_esp=0.05\n",
    "max_esp=0.15\n",
    "mu=np.linspace(min_esp,max_esp,d)\n",
    "\n",
    "# On suppose que tous les actifs risqués ont une \n",
    "# corrélation constante égale à |$\\rho$|.\n",
    "# On doit forcement avoir |$\\rho >= -(1/(d-1))$|, \n",
    "# sinon la matrice n'est pas une matrice de covariance (exercice!).\n",
    "covariance=rho*np.ones([d,d])+(1-rho)*np.eye(d)\n",
    "\n",
    "# On choisit un ecart type croissant en fonction de l'actif\n",
    "min_sigma=0.1\n",
    "max_sigma=0.3\n",
    "sigma=np.linspace(min_sigma,max_sigma,d)\n",
    "\n",
    "# La matrice de variance covariance se calcule par :\n",
    "Gamma = np.diag(sigma) * covariance * np.diag(sigma)\n",
    "\n",
    "# Les caractéristiques des actifs de base\n",
    "moyenne_actif=mu\n",
    "std_actif=np.sqrt(np.diag(Gamma))\n",
    "\n",
    "# plot ###################################################################\n",
    "\n",
    "# Tracé des actifs dans le plan (ecart-type,moyenne)\n",
    "max_sigma=max(std_actif)\n",
    "max_esp=max(moyenne_actif)\n",
    "marge=0.03\n",
    "un_inche_en_cm=2.54 # 1 inche = 2.54 cm\n",
    "\n",
    "taille_h_cm=25\n",
    "taille_v_cm=20\n",
    "\n",
    "def plot2_1():\n",
    "    # On crée un figure dont on fixe la taille et dont on définit les axes\n",
    "    fig = plt.gcf()\n",
    "    fig.set_size_inches(taille_h_cm/un_inche_en_cm,taille_v_cm/un_inche_en_cm)\n",
    "    plt.axis([-marge, max_sigma+marge, -marge, max_esp+marge])\n",
    "    # On trace les points représentant les actifs de risqués\n",
    "    plt.scatter(sigma,mu, s=marker_size, c='b', marker='o')\n",
    "    plt.ylabel('Moyenne')\n",
    "    plt.xlabel('Ecart-type')\n",
    "    plt.title('Rendements : diagramme (Ecart-type,Moyenne)')\n",
    "    #plt.text(60, .025, r'$\\mu=100,\\ \\sigma=15$')\n",
    "    plt.grid(True)\n",
    "\n",
    "\n",
    "plot2_1()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_myvUEelotkN"
   },
   "source": [
    "#####  Etape 2. Tirages des portefeuilles à coefficients positifs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "ACA1bVOVotkO",
    "outputId": "0bd7c68f-ac95-439d-9d28-da54a4a4c031"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On considère des portefeuilles *avec l'actif sans risque*\n",
    "# mais *sans emprunt*. On les tire au hasard dans le simplexe\n",
    "# de dimension 3\n",
    "N=1000\n",
    "moyenne1_d_x=np.zeros(N)\n",
    "std1_d_x=np.zeros(N)\n",
    "for i in range(0,N):\n",
    "    \n",
    "    ######  A vous de jouer  .....\n",
    "   \n",
    "    \n",
    "    x=simplexe(d)# tirage au hasard dans le simplexe\n",
    "    moyenne1_d_x[i] = np.dot(mu,x)\n",
    "    std1_d_x[i]=math.sqrt(np.dot(x,np.matmul(Gamma,x)))\n",
    "\n",
    "# plot ###################################################################\n",
    "def plot2_2():\n",
    "    plot2_1()# le plot précédent\n",
    "    plt.plot(std1_d_x, moyenne1_d_x,'b.',markersize=2)\n",
    "\n",
    "plot2_2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lYJIse6WotkO"
   },
   "source": [
    "    On peut estimer la frontière efficiente à partir de ces tirages. Il suffit de ne garder que les\n",
    "    points non dominés parmis les tirages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "id": "xRzrSqVpotkP",
    "outputId": "b61fc573-dc2a-411f-8eb0-a37237b45a02"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 984.252x787.402 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def frontiere_efficiente(moyenne_x,std_x):\n",
    "# Calcule la fontiere efficiente\n",
    "# a partir des points de R^2 ((moyenne_x(i),std_x(i)),1<=i<=N)\n",
    "    ######  A vous de jouer  .....\n",
    "\n",
    "\n",
    "def plot2_3():\n",
    "    plot2_2();# le plot précédent\n",
    "    [frontiere_m_1,frontiere_s_1] = frontiere_efficiente(moyenne1_d_x,std1_d_x) # calcul de la frontière\n",
    "    plt.plot(frontiere_s_1, frontiere_m_1,'r-',markersize=2)\n",
    "    \n",
    "plot2_3()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OH9avmqVotkX"
   },
   "source": [
    "## Partie optionnelle: solution des problèmes d'optimisation associés"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QKBfMIKuotkX"
   },
   "source": [
    "Les complèments qui suivent sont optionnels. Ils montrent cmment calculer par diverses méthodes la frontière \n",
    "efficiente ainsi que le portefeuille de marché."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wy-LPKEWotkX"
   },
   "source": [
    "### Calcul du portefeuille de marché par optimisation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yuT7y9f3otkY"
   },
   "source": [
    " Le calcul du portefeuille de marché $P$, s'exprime sous la forme\n",
    "  d'un problème d'optimisation avec contrainte.\n",
    "\n",
    "  Ce poblème se résout avec des techniques classiques implémentées\n",
    "  dans __Python__ et qui utilisent vos cours d'optimisation de 1A\n",
    "  (passé) et de 2A (futur!).\n",
    "\n",
    "  La fonction _minimize_ de _scipy_ minimise une fonction, si\n",
    "  on lui fournit une fonction _cost_ qui renvoie la valeur du coût ainsi que de\n",
    "  la dérivée du coût en fonction des paramètres. $x_0$ est la\n",
    "  valeur initiale de l'algorithme. _minimize_  renvoie la valeur de l'optimum\n",
    "  dans f et le minimiseur dans _xopt_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "lYd3mOxeotkY",
    "outputId": "9711a525-baaf-49ce-a4aa-6d9f9b445914"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: -0.750000\n",
      "         Iterations: 7\n",
      "         Function evaluations: 11\n",
      "         Gradient evaluations: 11\n",
      "Lorsque rho=0, vérfiez que ce qui suit est petit, sinon vous avez un problème ...\n",
      "1.6104417260799285e-07\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "# Choix des caracteristiques des actifs sans risque\n",
    "d=3\n",
    "rho=0.0\n",
    "min_esp=0.05;max_esp=0.15\n",
    "mu=np.linspace(min_esp,max_esp,d)\n",
    "min_sigma=0.1;max_sigma=0.3\n",
    "sigma=np.linspace(min_sigma,max_sigma,d)\n",
    "correlation =rho*np.ones([d,d])+(1-rho)*np.eye(d)\n",
    "Gamma = np.diag(sigma) * correlation * np.diag(sigma)\n",
    "\n",
    "# Définition de la fonction de coût et de sa dérivée\n",
    "# en utilisant la contrainte |$\\sum_{i=1}^d \\lambda_i=1$|\n",
    "\n",
    "def cost(x):\n",
    "    # Renvoie la valeur de la fonction a minimiser\n",
    "    # On maximise \n",
    "    #       f = (mu*lambd)^2 / lambd'*Gamma*lambd\n",
    "    # sous la contrainte |$\\sum_{i=1}^d \\lambda_i=1$|, |$x=\\lambd(2:d)$|\n",
    "    # x_1 est calculé en fonction de |$\\lambd$| à partir de x(2:d)\n",
    "    # en utilisant la contrainte |$\\sum_{i=1}^d \\lambd_i = 1$|\n",
    "    \n",
    "def cost_der(x):\n",
    "    # le dérivée du coût en fonction de lambda\n",
    "    # x_1 est calculé en fonction de |$\\lambd$| à partir de x(2:d)\n",
    "    # en utilisant la contrainte |$\\sum_{i=1}^d \\lambd_i = 1$|\n",
    "    \n",
    "x0=np.ones(d-1)/d\n",
    "xopt = minimize(cost, x0, method='BFGS', jac=cost_der, options={'disp': True})\n",
    "Xopt=np.append(1-sum(xopt.x),xopt.x)\n",
    "Fopt=math.sqrt(-xopt.fun)\n",
    "\n",
    "# Est on bien entre |$0$| et |$1$| ? C'est toujours le cas pour \n",
    "# Rho diagonale mais pas toujours dans le cas non diagonal\n",
    "# ok = and(0<=Xopt) & and(Xopt<=1)\n",
    "\n",
    "# Lorsque rho=0, il y a une solution explicite (exercice)\n",
    "# lambda_i = alpha * mu_i/sigma_i^2, renormalisé\n",
    "# On verifie ...\n",
    "sigma=np.transpose(np.sqrt(np.diag(Gamma)))\n",
    "x= np.divide(mu, np.multiply(sigma,sigma))\n",
    "x=x/np.sum(x)# normalisation\n",
    "x=np.transpose(x)\n",
    "print('Lorsque rho=0, vérfiez que ce qui suit est petit, sinon vous avez un problème ...')\n",
    "print(np.linalg.norm(x - Xopt)) # lorsque la matrice Rho est diagonale \n",
    "                          # ça devrait etre petit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "colab": {
   "collapsed_sections": [],
   "name": "TD1_master.ipynb",
   "provenance": []
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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