{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "$\\newcommand\\indi[1]{{\\mathbf 1}_{\\displaystyle #1}}$\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": {}, "source": [ "# 1. Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "source": [ "Pour construire le modèle, on suppose que la matrice de corrélation, i.e. la matrice définie par\n", "$$\n", " \\rho_{ij} = \\frac{\\Cov(R_i,R_j)}{\\sqrt{\\Var(R_i)}\\sqrt{\\Var(R_j)}},\n", "$$\n", "est de la forme\n", "$$\n", " \\left(\n", " \\begin{array}{lllll}\n", " 1 & \\rho & \\rho & \\dots & \\rho\\\\\n", " \\rho & 1 & \\rho & \\dots & \\rho\\\\\n", " \\rho & \\rho & 1 & \\dots & \\rho\\\\\n", " \\vdots & \\ddots & \\ddots & \\ddots & \\vdots\\\\\n", " \\rho & \\rho & \\ldots & \\rho & 1\n", " \\end{array}\n", " \\right).\n", "$$\n", "Lorsque l'on fixe outre la matrice $\\rho$ un vecteur des écart-types des rendements $\\sigma_i$\n", "$$\n", " \\sigma_i = \\sqrt{\\Var(R_i)},\n", "$$\n", "($\\sigma$ est un vecteur colonne, $\\sigma'$ est le vecteur ligne correspondant) on peut construire une matrice de variance-covariance $\\Gamma$ \n", "pour le vecteur $R$ en posant (exercice: il faut vérifier que $\\Gamma$ est bien une matrice de\n", "symétrique et positive):\n", "$$\n", "\\Gamma = \\sigma' \\rho \\sigma'.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.1. Le cas à deux actifs risqués" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "source": [ "#### Question 1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Que représente $\\rho$ ? A quelle condition sur $\\rho$ la matrice\n", " $\\Gamma$ est la matrice de covariance d'un vecteur aléatoire ? Dans\n", " 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": {}, "source": [ "#### Question 2." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Tracer les caractéristiques des actifs de base dans le plan (moyenne,écart type)." ] }, { "cell_type": "code", "execution_count": 302, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np;\n", "import math;\n", "import random;\n", "import matplotlib.pyplot as plt;\n", "\n", "\n", "# On définit les caracteristiques des actifs\n", "d=2;\n", "mu=[0.05,0.15];\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", "covariance=rho*np.ones([d,d])+(1-rho)*np.eye(d);\n", "\n", "# On choisit les variances des actifs.\n", "sigma=[0.10,0.30];\n", "# On en déduit la matice de vairance-covariance\n", "Gamma = np.diag(sigma) * covariance * np.diag(sigma);\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", "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, max_sigma+marge, -marge, max_esp+marge]);\n", " # On trace les points représentant les 2 actifs.\n", " plt.plot(sigma,mu, 'bo');\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();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Question 3." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tracer la courbe $x_1\\in [0,1] \\to (\\E(G_T),\\sqrt{\\Var(G_T)})$.\n", " \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", "\n", " Quel sont les portefeuilles dans lesquels il paraît rationnel d'investir ?\n" ] }, { "cell_type": "code", "execution_count": 303, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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];\n", " # comment calculer la moyenne et la variance du portefeuille\n", " # np.dot(x,y) = produit scalaire de x et y\n", " \n", " ###### A vous de jouer .....\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();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. Vérifier que l'on peut construire un portefeuille de variance\n", " minimum (et inférieure à celle de l'actif de variance\n", " minimum). C'est un exemple de l'__effet de diversification__ dans\n", " la théorie des portefeuille." ] }, { "cell_type": "code", "execution_count": 304, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot ###################################################################\n", "def plot3():\n", " plot2();# le plot précédent\n", " \n", " # comment calculer le point de variance minimum\n", " # si v est un vecteur v.argmin() renvoit l'argmin\n", " ###### A vous de jouer .....\n", "\n", " \n", " plt.plot(std_x[imin],moyenne_x[imin], 'gx');\n", "\n", "plot3();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5. 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", " 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 !" ] }, { "cell_type": "code", "execution_count": 305, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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", " # On autorise une quantité négative (= emprunt) de l'actif 1\n", " # Donner des valeur negative à x_1, calculer x_2 \n", " ###### A vous de jouer .....\n", " x=[x_1,x_2];\n", " moyenne2_x[i]=np.dot(mu,x);\n", " std2_x[i]=math.sqrt(np.dot(x,np.dot(Gamma,x)));\n", "\n", "# plot ###################################################################\n", "def plot4():\n", " plot3();# le plot précédent\n", " plt.plot(std2_x, moyenne2_x,'g-');\n", " \n", "plot4();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6. 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!)." ] }, { "cell_type": "code", "execution_count": 306, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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", " # On autorise une quantité négative (= emprunt) de l'actif 2\n", " # Donner des valeur negative à x_2, calculer x_1 \n", " ###### A vous de jouer .....\n", " x=[x_1,x_2];\n", " moyenne3_x[i]=np.dot(mu,x)\n", " std3_x[i]=math.sqrt(np.dot(x,np.dot(Gamma,x)));\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": {}, "source": [ "## Introduction d'un actif sans risque" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "source": [ "8. Construire le vecteur de moyenne et la matrice de variance-covariance de ce nouveau vecteur des rendements." ] }, { "cell_type": "code", "execution_count": 307, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gamma_d=\n", "[[0. 0. 0. ]\n", " [0. 0.01 0. ]\n", " [0. 0. 0.09]]\n" ] } ], "source": [ "# Construction du vecteur des rendements.\n", "# On rajoute un actif de rendement sans risque (de variance nulle).\n", "r0=0;\n", "mu_d=np.append(r0,mu); # moyenne de l'actif sans rsique\n", "sigma_d=np.append(0,sigma); # variance (nulle) de l'actif sans risque\n", "\n", "# construction de la matrice de variance-covariance des actifs risqués\n", "rho=0.0;# -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", "\n", "# On rajoute l'actif non risqué. Comme le rendement est supposé deterministe, \n", "# la matrice de variance covariance se complete par une ligne et une colonne de 0\n", "# la syntaxe python est assez impénétrable désolé ...\n", "Gamma_d=np.vstack([np.zeros(d),Gamma])\n", "Gamma_d=np.c_[np.zeros(d+1),Gamma_d]\n", "\n", "print('Gamma_d=')\n", "print(Gamma_d)\n", "\n", "# Les vecteurs moyenne et variance des actifs\n", "moyenne_actif=mu_d;\n", "std_actif=np.sqrt(np.diag(Gamma_d));\n", "\n", "# On materialise les 3 actifs de base\n", "# plt.plot(std_actif, moyenne_actif, 'ro');" ] }, { "cell_type": "markdown", "metadata": {}, "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 $\\left\\{0\\leq x_i \\leq 1,i=1,2,3 \\mbox{ et }\n", " x_1+x_2+x_3=1\\right\\}$. La fonction $simplexe(d)$ fait ce travail." ] }, { "cell_type": "code", "execution_count": 308, "metadata": {}, "outputs": [], "source": [ "def simplexe(d):\n", "# Cette fonction tire \"au hasard\" de 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": {}, "source": [ " 8. Matérialiser, en tirant un grand nombre points au hasard, la nouvelle frontière\n", " efficiente. Vérifier que :\n", " \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", " \n", " -la variance reste bornée par la variance la plus grande\n", " (tant que l'on ne fait pas d'emprunt)." ] }, { "cell_type": "code", "execution_count": 220, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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", " \n", " # tirage au hasard dans le simplexe de dimension 3\n", " ###### A vous de jouer .....\n", " \n", " \n", " # comme d'habitude, on calcule la moyenne et l'écart-type du portefeuille\n", " moyenne_d_x[i] = np.dot(mu_d,x);\n", " std_d_x[i]=math.sqrt(np.dot(x,np.matmul(Gamma_d,x)));\n", "\n", "# plot ###################################################################\n", "def plot6():\n", " plot5();# le plot précédent\n", " # On materialise les 3 actifs de base en rouge\n", " plt.plot(std_actif, moyenne_actif, 'ro');\n", " plt.plot(std_d_x, moyenne_d_x,'b.',markersize=2);\n", "\n", "plot6();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Commentaire" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "source": [ " Question 9. 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." ] }, { "cell_type": "code", "execution_count": 221, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "r0=mu_d[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 cauluer le max des pentes ainsi obtenues.\n", "N=1000;\n", "moyenne_y=np.zeros(N);\n", "std_y=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", " # on calcule les moyennes et variances des portefeuilles y\n", " moyenne_y[i]=np.dot(mu_d,y);\n", " std_y[i]=math.sqrt(np.dot(y,np.matmul(Gamma_d,y)))\n", " \n", " # il faut calculer la pente et mettre à jour le maximum de cette pente\n", " ###### A vous de jouer .....\n", "\n", "\n", "# On calcule le point P maximise la pente\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\n", " plt.plot(sigma_P, x_P, 'go',markersize=10)\n", "\n", " # Tracé du segment \"Actif sans risque -> P\"\n", " plt.plot(np.array([sigma0,sigma_P]),np.array([r0,x_P]), 'g-');\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": {}, "source": [ "### Question 10." ] }, { "cell_type": "markdown", "metadata": {}, "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", " Tirer un grand nombre de portefeuille, calculer leurs moyennes et écarts-type,\n", " les tracer sur la figure." ] }, { "cell_type": "code", "execution_count": 222, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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", " x_0 = -4+ 5* np.random.rand(1);# x_0 dans [-4,1]\n", " s=simplexe(d);\n", " # tirage uniforme dans le simplexe de dim d (d=nbre actifs risqués, ici d=2).\n", " # On veut génèrer un portefeuille avec x_0 actifs sans risque\n", " # et de valeur totale |$x_0 + \\sum_{i=1,\\ldots,d} x_i = 1$|.\n", " x=np.append(x_0,(1-x_0)*s); # |$x_0 + (1- x_0) \\sum_{i=1,\\ldots,d} s_i = 1$| \n", "\n", " moyenne_x_d[i]= np.dot(mu_d,x);\n", " std_x_d[i]=math.sqrt(np.dot(x, np.matmul(Gamma_d,x)));\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": {}, "source": [ " 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", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Partie optionnelle: extensions du modèle à plus de 2 actifs risqués" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "source": [ "## 1. Le cas d'un corrélation non nulle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1.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", "\n", "Les scripts précédents fonctionnent dans ce cas. Nous vous laissons le soin d'expérimenter par vous même." ] }, { "cell_type": "code", "execution_count": 223, "metadata": {}, "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": {}, "source": [ "## 2. Le cas d'un nombre d'actifs risqués arbitraires" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "source": [ "##### Etape 1. Choix des actifs de base." ] }, { "cell_type": "code", "execution_count": 224, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# On définit les caracteristiques des actifs risqués\n", "d=3;rho=0.0;\n", "\n", "min_esp=0.05;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;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 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, max_sigma+marge, -marge, max_esp+marge]);\n", " # On trace les points représentant les actifs de risqués\n", " plt.plot(sigma,mu, 'bo');\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", "plot1();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Etape 2. Tirages des portefeuilles à coefficients positifs." ] }, { "cell_type": "code", "execution_count": 242, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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", " 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():\n", " plot1();# le plot précédent\n", " plt.plot(std1_d_x, moyenne1_d_x,'b.',markersize=2);\n", "\n", "plot2();" ] }, { "cell_type": "markdown", "metadata": {}, "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": 244, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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", "\n", " # On rajoute l'actif de moyenne et de variance maximum\n", " # pour avoir de plus jolis dessins !\n", " moyenne_x=np.append(moyenne_actif[np.size(moyenne_actif)-1],moyenne_x)\n", " std_x=np.append(std_actif[np.size(moyenne_actif)-1],std_x)\n", "\n", " liste=[];# indices des point de la frontiere courante, vide au debut\n", " N=moyenne_x.size;\n", " for i in range(N): # on parcours les points\n", " bool=False;\n", " # On regarde si on trouve un point de la frontiere courante\n", " # qui majore le point courant\n", " for j in range(len(liste)):\n", " if (moyenne_x[liste[j]] > moyenne_x[i]) & (std_x[liste[j]] < std_x[i]):\n", " bool=True;\n", " break; \n", " if bool:\n", " # si on a trouve un point de la frontiere courante\n", " # qui majore le point courant, il n'y a rien a faire, \n", " # la frontiere est a jour.\n", " pass\n", " else:\n", " # sinon on rajoute le point et on enleve tous les points qu'il domine\n", " # On identifie les points a enlever\n", " removeliste=[]\n", " for j in liste:\n", " if ((moyenne_x[j] < moyenne_x[i]) & (std_x[j] > std_x[i])):\n", " removeliste.append(j) \n", " # On enleve ces points\n", " for j in removeliste: liste.remove(j) \n", " liste.append(i);# on rajoute le point\n", " \n", " # on trie les points en fonction de la première coordonnée\n", " frontiere_m=moyenne_x[liste]\n", " frontiere_s=std_x[liste]\n", " L = [ (frontiere_m[i],i) for i in range(len(frontiere_m)) ]\n", " L.sort(); sorted_l,permutation = zip(*L)\n", " for i in range(len(frontiere_m)):\n", " frontiere_m[i]=moyenne_x[liste[permutation[i]]];\n", " frontiere_s[i]=std_x[liste[permutation[i]]];\n", " return [frontiere_m,frontiere_s]\n", " \n", "def plot2_1():\n", " plot2();# 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_1()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 3. Le point de variance minimum." ] }, { "cell_type": "code", "execution_count": 287, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.0157276,0.0374286,'Portefeuille de\\nvariance minimale')" ] }, "execution_count": 287, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Le point de variance minimum\n", "imin=std1_d_x.argmin();\n", "\n", "# plot ###################################################################\n", "def plot3():\n", " plot2_1();# le plot précédent\n", " plt.plot(std1_d_x[imin],moyenne1_d_x[imin], 'ro',markersize=6);\n", "\n", "plot3();\n", "dx=0.01;dy=0.01\n", "plt.arrow(std1_d_x[imin]-2*dx, moyenne1_d_x[imin]-2*dy, dx, dy,shape='full',head_length=0.01)\n", "plt.text(std1_d_x[imin]-0.07, moyenne1_d_x[imin] - 3*dy,'Portefeuille de\\nvariance minimale')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 4. On autorise l'emprunt de l'actif 1" ] }, { "cell_type": "code", "execution_count": 288, "metadata": {}, "outputs": [], "source": [ "def arbitraire(d,sigma): \n", "# tirages de valeurs de signe arbitraire\n", "# dont la somme vaut 1\n", "# -> l'emprunt est autorisé \n", " t=np.random.normal(0,sigma,d-1);\n", " n=np.random.randint(d-1);\n", " s=np.zeros(d);\n", " s[0:n]=t[0:n];\n", " s[n]=1-np.sum(t);\n", " s[n+1:d]=t[n:d-1];\n", " return s;\n", " " ] }, { "cell_type": "code", "execution_count": 289, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N=10000;\n", "moyenne2_d_x=np.zeros(N);\n", "std2_d_x=np.zeros(N);\n", "sigma_e=2;\n", "for i in range(0,N):\n", " x=arbitraire(d,sigma_e);\n", " moyenne2_d_x[i] = np.dot(mu,x);\n", " std2_d_x[i]=math.sqrt(np.dot(x,np.matmul(Gamma,x)));\n", "\n", "# plot ###################################################################\n", "def plot4():\n", " plot3();# le plot précédent\n", " plt.plot(std2_d_x, moyenne2_d_x,'g.',markersize=2);\n", " [frontiere_m_2,frontiere_s_2] = frontiere_efficiente(moyenne2_d_x,std2_d_x)\n", " plt.plot(frontiere_s_2, frontiere_m_2,'y-',markersize=2); \n", "\n", "plot4();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 5. On rajoute un actif sans risque de redement moyen nul." ] }, { "cell_type": "code", "execution_count": 290, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "# On rajoute un actif sans risque de moyenne nulle\n", "r0=0;\n", "mu_d=np.append(r0,mu);\n", "sigma_d=np.append(0,sigma);\n", "\n", "rho=0.0;# -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", "\n", "# comme ce rendement est suppose deterministe, la matrice de \n", "# variance covariance se complete par une ligne et une colonne de 0\n", "Gamma_d=np.vstack([np.zeros(d),Gamma])\n", "Gamma_d=np.c_[np.zeros(d+1),Gamma_d]\n", "\n", "moyenne_actif=mu_d;\n", "std_actif=np.sqrt(np.diag(Gamma_d));\n", "\n", "# On materialise les 3+1 actifs de base\n", "plt.plot(std_actif, moyenne_actif, 'ro');\n", "\n", "# 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+1\n", "N=1000;\n", "moyenne3_d_x=np.zeros(N);\n", "std3_d_x=np.zeros(N);\n", "for i in range(0,N):\n", " x=simplexe(d+1);# tirage au hasard dans le simplexe\n", " moyenne3_d_x[i] = np.dot(mu_d,x);\n", " std3_d_x[i]=math.sqrt(np.dot(x,np.matmul(Gamma_d,x)));\n", "\n", "# plot ###################################################################\n", "def plot6(): \n", " plot4()\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", "\n", " # On materialise les 4 actifs de base\n", " plt.plot(std_actif, moyenne_actif, 'bo');\n", "\n", " # et les portefeuilles tirés au hasard\n", " plt.plot(std3_d_x, moyenne3_d_x,'g.',markersize=2);\n", " \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", " [frontiere_m_3,frontiere_s_3] = frontiere_efficiente(moyenne3_d_x,std3_d_x)\n", " plt.plot(frontiere_s_3, frontiere_m_3,'b-',markersize=2); \n", "\n", "plot6();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 6. Identification du portefeuille de marché et de la droite de marché." ] }, { "cell_type": "code", "execution_count": 298, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.0233978,0.110858,'Portefeuille de\\nmarché')" ] }, "execution_count": 298, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# r0=mu_d[0];\n", "sigma0=math.sqrt(Gamma_d[0,0]);# sigma0 = Gamma(0,0) = 0\n", "\n", "# Calcul du point P qui maximise la pente de la droite \n", "# entre (sigma0=0, x_0=r0) et les portefeuilles\n", "# (ne faisant pas intervenir d'actif sans risque)\n", "N=1000;\n", "moyenne_d_x=np.zeros(N);\n", "std_d_x=np.zeros(N);\n", "pente=0;\n", "max_pente=0;\n", "\n", "for i in range(0,N):\n", " # tirage au hasard du portefeuille\n", " # dans le simplexe de dimension d. \n", " # On rajoute 0 comme quantité d'actif sans risque \n", " # car on ne considere dans la maximisation que \n", " # des portefeuilles sans actif sans risque\n", " x=np.append(0,simplexe(d));\n", " moyenne_d_x[i] = np.dot(mu_d,x);\n", " std_d_x[i]=math.sqrt(np.dot(x,np.matmul(Gamma_d,x)));\n", " pente=(moyenne_d_x[i] - r0) / (std_d_x[i] - sigma0);# calcul de la pente\n", " max_pente=max(pente,max_pente);\n", " if max_pente==pente:\n", " imax=i\n", "\n", "# Le point P maximise la pente de la droite entre (sigma0=0, x_0=r0) \n", "# et les portefeuilles y (sans actif sans risque)\n", "x_P=moyenne_d_x[imax];\n", "sigma_P=std_d_x[imax];\n", "\n", "# plot ###################################################################\n", "def plot7():\n", " plot6();# le plot précédent\n", "\n", " # Tracé du point P\n", " plt.plot(sigma_P, x_P, 'ro')\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]), 'r-');\n", "\n", "plot7();\n", "# annotation pour le portefeuille de marché\n", "dx=0.01;dy=0.01\n", "plt.arrow(sigma_P-2*dx, x_P+2*dy, dx, -dy,shape='full',head_length=0.01)\n", "plt.text(sigma_P-0.07, x_P + 3*dy,'Portefeuille de\\nmarché')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 7. Simulation de portefeuilles avec emprunt autorisé" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Avec actif sans risque et emprunt autorisé. On tire au hasard\n", " sans imposer le signe de l'actif sans risque mais en gardant \n", " la quantité de tous les actifs risqués positif. C'est fait par \n", " la primitive arbitraire(d,sigma_e) qui fait un choix\n", " (arbitraire) pour la loi de la quantité d'actif sans risque." ] }, { "cell_type": "code", "execution_count": 299, "metadata": {}, "outputs": [ { "data": { "image/png": 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i1dW7WFj4CKdObV0nwK5kefkiz+UFYV9QZeixup9VvnAUFGjet5wc8+NEiAmCIAjWLF5MtmzJ6h/+mM89UqY8sDXU5SSCDJt6nUXntk67MoJcQ0xfTnV1GdeufZxTp7ZlPA4uWdKPZWUL/FVSRzp6QP0I5uTaa1ZtEiEmCIIgmLNpE3nMMeTRR/OV+zZ4HhyjzAEKM//JDDvREHR4LKwy3AjGp58u59q1T3Dq1HaMx8HFiy/jrl1zvVXsw56wygryePGIiRATBEHwTnk5efrpZIsW5MKFvgZHp7BOkHsg6uuys7mgQPNUFBT4q8+unFRPMlAN+akIxq1bd/OddwYzP799nQD7P65bNzttJlFY4da7Fvbx5MHXQYSYIAiCUJ/qavKyy7S8sHHjfBfnJAC8bvhtJuRUZ2cm6+zb13u7jG1IN0FibL9qnpP+75qavVy//llOm3Yk43Fw0aKLuXPnTNvynIhSoLrNLwzbg0Ye3G8ya1IQBEE4QCJB/vnP2mP/1VdDrcqvR8xJyEXhESsu9i4kw8ZrEvzgwWRmZhXffvsNTp/emfE4uHDhRdy5c7pt+aqkOgcs1fUf7BE7egMVtEuMpNqKZg2AXr16cd68eak2QxAEIf149lngX/8C7r5bW3EyjdGv1j9mjPnCnKqrqPth5Urgn//Uuu7EE8Opwy1e200msHr1h1i16iE0bboKrVr1Rvfuj6NNmwtSblsq6o/C1lis0WKy+jSn4zLCqV4QBEFIGz77TBNgV10FPPWUpyKSK8GvXKn9LCnxb1ayTGNZyVXKTzxR+2m38ry2lUw4jBmjbVs0ZozzsVZtcYtTOW7bTRIlJV9g3rzTsXHjjaipaY6lS7/AscdOD1SEhYWbfk3eNyrCKor7B6ipUTlKtjgSBEE4lJk9G/jtb4Gf/hR4910gw9v3b7d7Krop00tZUWyT5KaOoPbPdCrHjU07dsRRWHgfyspmoVmz47F69fu47bbrQGZg3z53dqp4kMLYQ9SuTD9erSDun6C8aiLEBEEQDlUKC4HLLwc6dQJGjwaaNfNcVHLA6tdPbU9FN2V6KSvIfRUB80HVTR1BCUO7clQH/rKyuSgsvB87dkxA48ad0bPnG+jY8fc47rhG2LDBm51uN762w42AsSvTj/DTX1uvgiow4amSSNZQXpKsLwiCUEdpKXnSSWSbNuS339b7KNXLL4RlRxhLcURVvwrJPRRzcsw/3717GZcu/TXjcXDatPZcv/5Z1tTsVS7fbhJAkG0LKqk+KJu8rK6v8rnqrEnxiAmCIBxqVFUBv/kNsHo1dn48AW9+cRIGtD/wbT+MEJIXnOwweiqcPBepDnV6rT+IENfGjS9g1aq7kJnZAt26PYxjjvkHsrJauSojaX9FBZCdrf18+GHts4ED67fJrc36iQ9BeQ+D8opa2eN0Pe3q13LaenRTMkBFrTWUl3jEBEE47EkkyJtu0r7iv/tuKHsSGlEpz+26T6T6ellu7AjyPGMZdqus26HqIbLzUM2dewbnzj2dVVUlSufbfa73vFkd79arFdT6bkbC9EL697CeSSpol5SLpyBfIsQEQTjsyc3VHu2PPEJSfZFLP2t/qQzKXrYF8rpelluCCJUly7ATL1b4XTy0urqM+fktuHLln5XP8WuPW2Ed1PpuRlK9dpgVxcVUXkcs5eIpyJcIMUEQDmtGjNAe67//veYZc0A/iCW9IH36uB/YvA7cdvZEid9cIP0xAwceEGR2ZViVqSrK9MetXPlnxuMx7tw5w1c7/Z5rvH5+F/b1apeXvg1D5EO2OBIEQTiMiMfJRo3ICy8kKyuVTtEPPkkhNnBgcOE9twLHrzjxerwTbgSiVUK9apjVrRgtLY0zHge///4faicoYHZdVHYZMHq9nHZIcGuTaujXS9+G8SVAhJggCMLhwooVZOvW5Mkns2TVjpTkSZkNZE6Dm+rg53aQDHpQddM3qmLSregsKnqXc+acytmzT+bs2Sdx1qwTOWvWCczPb8mZM49jTU2F9wYasBKNSZGlmjfmxSNm1f5k2WbX1SgAxSMmQkwQBCE6tmwhu3UjjzqKLCxMi/CecQC2GojdhuFUB3Q70RNmcndQVFfvYlnZQq5bN52vvfYNv//+PU6e3IRffvlDzp9/NZctu5bLll3H5ctv4IoV/VlevjjQ+u36z+7+CqJvrco3esT0dYU1EcAMN20UISYIgnCoU1FB/uQnZLNm5Jw5JNNDaKiG4fyW6+U8t2V4mTDg9RokEgkWFb3LqVPbMB5Hvdc33xzFNm2KUp6U7iUE7bd8M/Qh4LAmApjh5v5RFWKyjpggCEJDJJEAbroJmDtX20vyrLMAuFtbKayNj43rMkWx6rzTeRUV2uuGG9yVYVxLSv/3gAHm/Wdcj0ulf2trK7By5W3Ytu0DtGrVG8cc809UVLTC1183x69+1RyNGx+HQYOOCHVLJ8D8njC+Z7y/glyXTuX+LSkBpk8/8PeJJwJffumv3mS5Tv8PoWytpaLWGspLPGKCIBw2/Otf2lfz556r97Yb70C6Tv3XE9SMRn3CuJvEby9huuRnSa+NU/9WVHzPOXNOYTyewbVrH2ciUaPctqDxkusXtZ36nLUg60yW62UJEvLgfoCEJgVBEA5RXn5Ze3zfeedBy1S4yZdJhzCmE0Ek/BsHbrvEbzc4iV6V/i0pGcspU47ghAltWVj4jandUQplp9Cj13smFeFLr+WqCmgjxuslQkwQBOFQZOxYMiODvPxysqbmoI+DzJcJajkJL3V4/Vwlh0nFI6bSRq9CKZGo5Y4d+fz22z8wHgfHjj2dRx1VaOlZ82NjUNiJlDD7ys4WJy+o150OghKbIsQEQRAONRYsILOzyTPOIMvLQ6/OKlQT5KAatNcnyokBbgbsRKKG5eWLuXr1vZwxowvjcXDKlGZcufLP3Lp1j6eB38zGsMSZXdgu6L5StUXFC5pKj6KqEJNkfUEQhIbAhg3AZZcBbdsCY8cCLVrUSy4Ggk+8T5ZbUVE/GTvIhOWgk5/9lpfs0379nMtRSSwvK5uLNWvuwa5d00DWAMhE27YXo0eP/6BduyuQldUCgLckd7O2Ok0m8DpBQ1+X8TyVPg9qg27V+pITNMyOC2KSilUZ+v5XRkWtNZSXeMQEQTgk2bWL/NGPyFatyCVL9r/tZ1kGNzSEXLKg0Pej3xBVUVEJZ87sxunTO3HVqoHcvPm/rKzcGo7hhrqtJhP4vU8OhXvBrg9U2+c0UcONRywQAQTgUgArAawCcK/J578AsABADYCrDZ/VAlhU9xqje787gNkAvgfwIYDGTnaIEBME4ZCjqoq85BIyK4v8pn4yt1MS9aEwaBpx2yY/x3sVLYMH1/LSS9/mN9+0ZzyeydLSSSm5Fsk69Qvh+rUj6gkE771Hdu1KxmLaz/feUzvPrp12n6m2T6UfIxNiADIBrAbQA0BjAIsBnGw4phuAUwG8YyLEdluU+xGA6+t+fw3An5xsESEmCMIhRSJB3nab9qh+6y3Xp/udjk+mn5hzKwT8CAcvbS8vX8rZs89hPA7Onv2z/avee8mjCqrvo06UD6q8994jmzdnXa5XgoD2t4oY89rmINsXpRDrDWC87u9BAAZZHDtcRYgBiAEoAZBlVofVS4SYIAiHFE8+SQKcceF9jt4MO4+Y3XR8p4HHOKClWpiF7RFzSyKRYGlpHr///l9cvvx6xuOZnDq1HTdv/i8TiVpHO+w8cEEl46f6mtlhJZi279nO9r/4hPjVHcTfjiOOWrQ/+b5rV+dy06HNUQqxqwG8pfv7JgBDLY41E2I1AOYBmAXgyrr32gNYpTvmWADLLMq8ve78eV26dAmpOwVBECLmww9JgCt+fD1jqHXMA/Oa9+LkOTCeK7loGolEgiUlX3H+/N51MyCbcvr0ziwouJ1VVSXK5djlpJn1R9ShwbBJtnHjln2ctGYSB+UN4llvnMVYbozIBTGoJXHD5USn+fuFWCwWTJ0q95mfe1JViAUxazJm8h5dnN+F5OZYLNYDwKRYLLYUQJlqmSTfAPAGAPTq1ctNvYIgCOnJ9OnAzTcDP/85Oowahqc+yKg388tstpjdTDK7GWtOM9CM54ayxUsdQW6Vo4px9ltJCTB0qPbZnXcePKuOJLZv/xLr1j2C8vK5aNKkC0444VV06jQAGRlNXNdvnI2ob7fZdQuz/1UJYtZhggks2boEeWvykNdpAnLemoq9NXuRGcvEsbGzMfCsHIzI7YOt838CJBrVO7dLF382u7nPorgngxBiG6F5rJIcA2Cz6skkN9f9XBOLxSYDOB3ApwBax2KxLGrzfV2VKQiC0GBZtQq44gpttPn8c7Rv37TeAGA1GHhdHiAd9qZMot8TsqQknDqMmO0l+fDD2t/Z2Qf6hkygpGQ01q17FLt3L0TTpt3Rs+ebyMq6GSNGNPbcJ1b9b9XXQS4D4RUv4iTBBFaVrsK09dMwYc0ETFwzEcV7igEAJ3c4GbedcRv69OiDRaPPw0P/boX2g4Fn/g7cfjuwZ8+Bcpo1A3r3dn9/GJf10P+0w5/wzVLSWEEIsbkATojFYt0BbAJwPYAbVU6MxWJtAOwhWRmLxdoD+DmAwSQZi8Xi0MKeowD0BzA6AFsFQRDSl+3bgb59td/HjXM10oQtkkpKgP79NbOAAwNwkPW2b6+Jn3vuqS+CwsRsY3L9+lOJRDVKSj7DunWPo6JiKZo1Ox4nnTQcRx55IzIyGmHIkHA8JlZiJ+zrrIKTOCGJTeWbMHfTXMzZNAdzN8/FvM3zsKtyFwCgY4uOuOT4S/DLHr/ERd0vQudWnfef2/sWoGmsfvvuvx9Yv177btK7NzBqFHDGGe76287zaIfxWHf9f2Q7pUpU4pdOLwB9AXwHbfbk/XXvPQKgX93vZ0HznFUA2A5ged37PwOwFNpMy6UA/qArsweAOdCWxPgYQBMnOyRZXxCEBsveveQ555BNmpDTppF0Xp5CT9izA5PlGzdaDjpnKV3yxGpr93Ht2ic4fXqnuhmQJ3HLlvdYW1vt6rp4xarcKFaxd3t+SUUJv/r+Kz4y+RFe/v7l7Ph0Ry2/KxfMeiSLZ7x+Bu/44g6+Nf8tLtu6jNu2JRrsLF439zuQtYhRJOun00uEmCAIDZLaWvKGG7RH8qhR+992s2CrnwHKz+CuWm+qB1A3lJZO4qxZJzIeBxctuoQlJWOZSBzY1zOVCfNuRLPXBUud2ldUXsTnZj7H6z6+jj1e6LFfdCEXPGnoSbzps5v44qwXOXPDTO6t3ntQvUEsqBrEeWGfA9lrUhAEoYFw//3a4/iJJ+q9HaTnxesCl17LNNIQZvvV1Ozl99//g/E4OHPmcSwp+cr0OK/XJR3EglvRXVxMPvVUgrO//54jl4zkjZ/eyEaPNCJywS7PdeFVH17FB8c/yZtzJvLfOTstZ3zazQ61s0+1/V7ur7DvSRFigiAIDYH//ld7FN96q7aAqwu8CqFULBSazh6xsrL5/PbbP3DatA6Mx8HvvruTNTUV+z/3K2yMxxrDuyrnRBn63bZ7G8euHMuHJj3Eno9cQvy7zX6PV6snWvFv4/7GlSUrD7JRf3/17etNUHldLiUowRrkfSpCTBAEId2ZMEHbuujii7WtjEwoLtYWZM3J8ZYvpC9HJTTkBreDVrqIsaQd27bVct26wZw8OYtTprTkJ59cz8LCiQcdH1QozUygOFFQoJ1TUKB2vFsqqio4dd1UPjPjGV738XXs9ny3/aIr4+EM/vClU/mTR2/lI1++wbueXMyirdUHlWG8R70ITivs7n8vZTkJryCFrwgxQRCEdGbpUm0T7x/9SNvUm/YLeNptMKzfS1CFIAc3N6RKABoZOnQ+r7tuMEeP/gXjcXDp0qv4zDOlgectmeE2RBykMKipreHSrUv51vy3ePuY23naa6cx8+HM/cKr63Ndec1H13DI9CGcsnYKd1fu9mSHn/4Ksw/MynEbCpUcMRFigiAcCmzeTB57LNmpE7l+/f63zQYKFdGUjvkxZqgMYl6SyVUHx+rqnSwouJ3xOBiPg9OmdeHGja8ykUiEHqYyYizbylsWhA2zN87mecPOY/bj2ftF1xFPtGbPRy7mP8c+wDEFY1hUXuTK3rD2NzOuAAAgAElEQVSw+h/wkodn1sd+r7Gb/xsRYoIgCOnI7t3kmWeS2dnk/Pn1Pooiad5vXWGX7zaZXPWc1atHc/z4oxmPZ3DVqrtZWblN2RY/m6ab2Wtms9dwnko///bT37Llf1ryzi/v5LuL3+XKkpV88qnatJw84fe+1Per1y8bbr2WVogQEwRBSDdqasjLLyczMsgvvki1NY74GRT9DIJuw6Z2dlZWbuWyZdcxHgffeutUDh06V/n85PvJTdNVRZKKUFTx1qhg1c81tTWcs3EOn5z6JNs82YbXf3K9UptVSZd8PyN2HjHVfLugvMUixARBENKNv/5Ve+wOHZpqS5Tw4p1yel/l8yA8GYlEgkVF73Dq1LacPLkxly9/jEOGVLmuLykM+/RRt8lr6NQLByYeJLh823K+OOtFXjnqSrZ+svX+MOQpr5zCuZsOFqB+SEVo2wv6vk+Gfvv2VT/HDyLEBEEQ0onnn9ceuXfdlWpLSIaXr6Vat93sQT/eoUaN9vL118dx8eJLGY+D8+f35u7dKxztcRKFbsKTUXmL1u5Yy+en/JenP/pbHjW4037h1f357vzD6D/w/SXvc0v5Ft/1pDp/zg/6+9PoEQv7OqkKsSD2mhQEQRDsGD0auOsu4Ne/BoYMSbU1ANQ2blbZk8/LpsjDhml7Vvbta36el42ti4s/w0UXvY8zzhiPzMzd2LWrJY4//kV07vxnxGKZtufa1Wfco1CFIDfmrqiqwLaKbSjeU4ziimJs2b0FczbNwcTCiVi9Y7V20O4j8eMjLsRjl1+Ei7pfhO5tugdTeR1m94pZG4PYB9NqT1OvGO/P888H2tXtAOll83JVSkoA4OijVI4VISYIghAmc+cCN9wAnHUW8N57QKa9KIgKLwLKDC+iw4u4saOqqgTLl1+FRo2OwjHH3Ij27a9A69YXIjOz6UHHuhULQYoqO4x23T/xfjw36znsrdl70LGtmrTCeV3Pw19/8lec0eYizBz9Q9xySyy0TcBV75UghI2TSHeL/vrpN2hPbu6ekwP066d95uZ+dLqPhg0DgE7HqJQlQkwQBCEs1q4FLr8cOOooYMwYoHlzy0OD8Ca4ISqBEQROfVNTsx0AcPzxz+Coo35rW5aqWIj6eujt+tPfd+OF2S/g9E6no1/PfuiQ3QEdmnfAkdlHokN2B3Q5oguyMg4M3+feE65tqvdKEOI+aJFuVfawYcDDD2uCD9B+B9T/J5zuowEDgHvuKdqoUpYIMUEQhDDYuRO47DKgshKIxzUxZkPYYZKwRIWXst221en4mppdAIDMzCMcy7ITC/q2hHk9nOz67NvPUFFdgaf6PIVzupzju+xku/r1074PhCUugxD3VmUEfQ8PGABMnqx53846Cxg82J2AdBKdmo2btyoVppJI1lBekqwvCEJaUFlJXngh2agROWmS0ilhrgVmlVAfRLKy12R9N/UWF5PPPbeJy5bdx4KCW7l06VVcuPACzp17GmfM6MIpU7IZj4M7d04LbMkN1XLCSPi+aMRF7PFCDyZc7j1qxGz5Daf7IFXLUjjV62cGr1UZkqwvCIJwKEICd9wBTJoEDB8OXHCB0mlO3gQzj4Cq18bq23sQXh8v4Si3npPWrcvw859fguLib9G48ZHIymqDRo3aokmTY5GdfSqystqgadNj0bLlT/DMM97bZAyLBeGtM7Kneg++37gdwz/ajnMv3o7qRiXYvnc7tu/ZjpI92u+TCich57wcxGIxdw2wsC0nR/P49OunJavb3QdAOJ5AlZwqp1Cf/qcZbstIl/B8TBNthwa9evXivHnzUm2GIAiHM489Bjz4IPYMzMHLHXIdQymqIZdkovHgwQcGD7/hmqjzoLzYkEjUYNmyy7FjRx5OPfVrtGlzka/y/B5vZO7SnfjnI2tx85+L0KydJqi27z0gqvQCa/ue7abJ90laNWmFds3aoXOrzhh11Sh0btXZlS3Gtqi2TR+6/OAD7b0776x/jt9+Mrt/7Wz3UmfY97NV+Vbvx2Kx+SR7OZUrHjFBEISgGDkSePBB4Kab8HL7HCXPgopHpaTkwAwvvUfA7zd6t+eHMdDZtZ8kVq36O0pLv0bPnm84ijDAfZtU+r82UYtFWxZh+obpWLNjDdbuXLv/tatyF3AKMC3/wPExxNC2WVu0a94O7Zu3R5cjuuD0TqejXTPt7+qydvj8/Xa46472OP3EdmjXvB3aNmuLxpmN1Q1XaItqXySPGzJES1ofPPjg6+vXe6qSU2Us122dYXu4kvZMngyMGGHvmZblKwRBEKImPx+45RbgvPOAN9/EgPIYEHMO2amGXKwGyCgJI4Hdrv2bNr2EzZtfQVHRQJxyym3KZeoFI2AvHq3qL68sx5sL3kR8bRz56/JRVlkGAMhulI3ubbqjW+tuOLfLuejQqBtWzeuGGy4/Gsd10oRW66atkRHLsBSuubnAgpHAquOB352r3CxH/M5atDvfb9l+lzmxIkqvrj7Bf9iwA+0xs3PoUEB1+YqUJ9gH+ZJkfUEQUkJBAdmmDXnSSWRpaeDFp8u+flHZUVxMvv76F4zHM/jZZ1cyFqt1NRlAZeNns7YkEglu2LWBn3/7OS8acRGRC57w4gm8bcxtHLlkJDfs2uAqgd6q7mTyfE6OepsaElHer1FvtaTaNu0an0kqaJeUi6cgXyLEBEGInG3byB49yA4dyNWrQ6nC636Obo8Neuamanm1tZWsqdnN6updrKoq5csvz+C4cdkcO/YMbt2625dNVjYMHkyiRRF//8QXzInn8LKRl/GoIUft3yYo8+FMvjjrRfVKHexQed/rOX7xWrZt37oQR37uu4KC9PySUlxMAkdvoAgxQRCEENmzhzz7bLJpU3LWrNCqsRrY3Ax4Ksd68S7YnWP12c6d01lYmMslS67gjBldGI/joNf48Z25efMmkv5FSE1tDVeWrOTHyz/mQ5Me4hUfXMFOQzrvF10ZD2fwpBd/yDMf7c8nJr7EmRtmck/VHm+V+SSIa+22v7x6lYJaFiWo+y6Vy3CY2QNZvkIQBCFEEgng5puB2bOBjz8GfvrT0KqyypVxk7djdaw+x0blGGMejpu8orKyeSgsvB87dnwDIIZmzXriiCN+hubN/4CMjKaIxTIRi2UhFstCu3a/QtOmRwNwl5tWUVWBmRtnYunWpViybQmWbl2KFcUr9s9WzIhloGe7nrjouAvQq1MvnHn0mTit42l49YUWuOdB4LrBwNkX2tcRJMa+VbnWfpeCMOI1/8vqPLeLsnqp3+ycIJfhcJt75iuHTkWtNZSXeMQEQYiMgQO1r8BPP217mNM381Tkf+nrDMtTpmf37uVcuvQ3jMfBqVPbcf36p1ldXWZrl8r7SfZV7+Pn337O6z6+js0fb77f03XUkKP4y3d+yX9+/U8OWziM8zbN2+/pMgslpSLEFbQXkkyPnEIzG8LO5wrSI6Zqq109UPSIpVw8BfkSISYIQiS89pr2+PzTn0iH5G2nB3oQK4a7xe0K8m4Ekv69vXvXc8WKmxmPZzA/vyULC3NZXb1LyS4nW7ZsrWHe6jz+YfQf2PrJ1kQu2O6pdvzjF3/k+FXjuW33NuU+SAV+cpz83g9RCDWn0KEfu6Kw3++uFaQIMUEQhHD46isyM1PbL6a62vHwIAafoEVDEANZcbH5ljlJW198sYDTp3fklClNuWrV3aysdK7Mya5EIsG/PDGTuPRvbJnbkcgFG+e24LUf3MRx341jVU2VK/vDGMy9DOBBTpLwej8F3R9u7vvk78nZpE73udH+VHoAxSMmQkwQhChZtIhs0YI87TSyvDyyaoOezRgEycGwb9/6dWzdWsF33hnC/Py2nDbtSO7evcyXvcXF5D+fXMq/jxnE7s93J3LBrNwmvOyd3/B3//mYyNqTMq+WGV5CWkGGJ716WL3Y4Oce09eX/D0nx5tHLNXeTStEiAmCIATJhg1k587aa+PGlJjgZuAL24tm/LumZi83bHie06YdxXgcXLToYlZUFCi3Q29vdW01FxUt4uP5j7Pjw6doMxtzM3nJu5dw+MLh3Ll3p2U5qSYq0WyVD+W1T7ycp+KZUvHcpWOoNYgyRYgJgiAERVkZ+eMfky1bkosXB1as2zwhN+IqzLwyPbW1Vdy48RVOn96Z8Ti4cOEF3LFjqqVwKygwD2lu25bgHU9M5lUjb6yXcN8l5xz2zXmZK9ZtDaYhFqSjqFPF6tqE3SZj+WYL1aart8qJIOwWISYIghAE1dXk//2flhf29deBFq0P7/mdoaXyedBlFxeTo0b9jfE4OH/+z1laOmn/Z8aBzNjWvn3JBavXctjCYbz5fzfzmGePIXLBI544gnd8cQffX/I+73tyfWSDuGreVDoKNiubvIoJr200E2LpGFZXqU88YiLEBEFIBxIJ8o9/1B6Vr7/ueLjKw9ssJBPU6uB+vsV7OfeFF1ZxwoQsPv/8bdy2rf7sUSuP2KJle/irx59ht2eP2+/1aj+4Pa/56BqOWDSCFVUVlmWo4vY6WJ1j1icNYXsilfvKro/CFHBeJxOESVj1iRATBEHwy5Ah2mPy3/9WOlzlgR7mIBOmR0xPIlHDoqIRnDatC8ePb862bTebhsWeeirBwk3lXLtjLRdsXsBX577Kzs9oK9pfMPwCvjDrBS7ZsoS1idpA7QvqOpjV2RCEmN/2h+mR8trvYeL1C5TT8bLFkSAIgh8+/lh7RF57LVlbG9i3/YYQ7rKyJ5FIsKTkS86Z8yPG4+DcuWdy7dqp9Y7dU7WHX6z8gmc9+gfi7gN7NyZfZ791NuOFcdc2BZ0fF2VSe9SE1f4g2q6SvB902UGgv//Uha5s+i0IguCNmTO1/SN799b2k2S4nqx0S2g2s2fXrllcsOA8xuPgzJnHcevWD5mo82SVVJRw+MLh/PWoX+9PtG/5n1b88aPX8cHxT/LN+W/ysxWfcc7GOUw4LIBrRVTevijKaagk7wvVZSa8lK3qKVMNJauUpYLblALNI9ZzJxW0i+w1KQiCoGfNGqBfP6BzZ2D0aKBZMwA+95JzoF8/YPJk7Wc6kGzj7363GRs3foJt2z5EWdkMNGp0JE444WV06nQr1u7aiJGzXsDolaMxdf1UJJhA55ad0f/H/XHlSVfi/G7no3Fm48Bsstq/0ImSEqB/f2DcOO1vL2UkcbuH46FG8r6oqKjfD273ZbQr2+z/K1l+RQXw8MMH3jdeCzf/o26vpfH+GzgQGDLEugytH9asdS4ZIsQEQRD2U1oK9O0L1NZqI3eHDvs/8ioEVBgzRqvu/PNTP8BXVm5BZeWn6NPnQ6xcOQ0AkZ39Y3Tv/iQqm1+Ksetm4dNJv8KENRMAAKcceQoGnTMIV550Jc7sdCZisZhjHUEM3KoMG6b1bd++/kV0WII5iP6Iok+T/wMlJUB29oH+DEKgJjc8N2vD0KGaABs4EMjJ0QTZDTdon+mvqZv/0SC+WDmXUVOjUo4IMUEQBACorAR+/WugsBDIywN69oys6jC9bSqQxJYtI7B16wjs3DkFANGkyQ9xZOd/Y3F5a3yzoQATp72MDWX3AgCObnk07u59N/7Y6484ru1xrutLDqwVFUBubrBtMaLvW78ip7hYE3VVVcAHH/gTPHrhpBcyVmLEiSi9dUbBE9T969SG5s01AZg8Jjvbe11BfLEK6suZCDFBEAQSuPVWID8fGDkSOPfc0KqKyhukWk95+QIUFj6A0tKv0KxZT2za9CAeeOAanHn7LOTF7sauyl1o26wtLuh2AQadMwgXdr8QPdv1rOf5KinRxBUA3HnngfrSoa1uB0uzspICoU8f7e+8PO29oMKceiHjVVCpiiG7vvJyvYK8xlZtuPPO+h44oH541K149WOzu3Oz1DSWSiJZQ3lJsr4gCJ546CEty/exx0KvyiyhOIxkfacyy8oWcsmSKxiPg1OntuH69c+wtraWnyyYwK6P/IzIBc8bdh7nbJzjuLxEsi7VdkW16n9QZemTs3NytFdYif8q65v5Qd8+Y9le+jFVE030tru1wc8SJG7qkuUrBEEQVBg2THsU3nKLtoBryJjNuApysLWa0ZV8f8OGJVy69DeMx8H8/CO4ak0OF26cyuELh/Oct88hcsFjnj2Gb85/U2l9L1Krq08fcuDA1CzL4aYepxlvfpdXcDrObZ8ELXTsBEyqlrTwi1sb/AgxN3UBWYsoQkwQBMGGiRPJrCxNRVRVRVp1WJ4Eq3JffHEZc3KuqRNgrbik4F/sM/xsNnqk0f41vjo/05kvz3mZ+6r3eaozjGUNzPAz+CdtVd1Wynie0/FOx9l53NyugO+XdBBRXvBrd3Gxd8+mOyGmtrK+5IgJgnB4smIF8JvfACeeCHzyCdCokeeijHkjKnkkYSXoG8utqCjAunUP40c/+hC1tdnY3fh6fFPaBB/PGYmd+3birrPvwumdTsdpHU/DCW1PQGZGpuc6jcsaBIWxP5N5VBUVB3KHVHN9krb26wecdZZWRkmJ8/mq12vAAK1Mq3LNyrHLCwtztm6YZYeB2TIWVvY75Q0mk/6T949q3lcokyJU1FpDeYlHTBAEJYqKyK5dyY4dybVrfRdn9HKkwwKtVVXbuWLF7xiPZ3BivAmHjD2RnQZnE7lg9uPZvOrDqzhxzcRA6/Sa3+R0nFUILRli8trPqp68sMOJDdUzFTVuPK9O18BrjpmbrY4Q5V6TAC4FsBLAKgD3mnz+CwALANQAuFr3/mkAZgJYDmAJgOt0nw0HUAhgUd3rNCc7RIgJguBIRQV51llk8+bk3LmWh3nJOwo6wdprOeWV5RwxuQ/jcfCOd2I84nGw09OdeMcXd3Dcd+O4t3pvIPU4EVQ4L6xtcYyCrm9f8wE2LGHl1f6otwPyk/cW1DVym0sZ1rF6nHLsIhNiADIBrAbQA0BjAIsBnGw4phuAUwG8YxBiPQGcUPf70QCKALTmASF2tRtbRIgJgmBLTQ155ZVkLEaOHm17aJhJ0qq4tWH9zvUc+M1AHvHEEfzru+CXeRm8L+8+zt44m7UJ6/0yw/LghS1IgqK4uH7OmNHzMnOm9nlBQbD1ek2WD+J6uSnDS95bULYG0daw7i8nwa4qxILIEfsJgFUk1wBALBYbBeAKACt04c+1dZ8l9CeS/E73++ZYLLYNQAcAOwOwSxAEoT533w18/jnwwgtAv362eSRucrhU1mZSyWsx4pRvlCz/kbfmYlOX5zB61UcAgKtOvgrXdN+NrKrleLz34/uPtcpvCTJfzdgXXraPCRKVfL327YERIw4clySZ83bSSUBBQfA7Hxj7PXl9Jk/W7FHJL9S3L1mGSq6Tm2vuJe/NSz1+7UxilVMIqF0/r+uMeW6rilqzewG4GsBbur9vAjDU4tjhsPByQRN03wLI0B27ElrI8jkATSzOux3APADzunTpEqDWFQThkOKll7Svq3//+/63gvIEqXgE+vSxn6XlxVtVXVvNnz52B5ELNslpxV889i8uWL2WNTV7uWjRxZwz50e2dTgt5eAF/azEdMh58nON9Z6yKNpj9MypoG9fmH3vpR/N7ukowvZGWwsK3Hk07dqqn3HplKOICEOT15gIsZcsjjUVYgA61Ymusw3vxQA0ATACwENOtkhoUhAEU8aMITMyyCuu0MKTdXjNPzHilCOjMrharW1kVfaeqj284oNf8dinwD+92o9vDruXublXcdy4ExmPZzAeBxct+qWtvfrcqKBCk17ERPK8IBZLDTpfL+qwqdv6jPdwWMLRS56YmaCJ4stP0Dl+Zon9KpMGohRivQGM1/09CMAgi2MPEmIAWkFL5L/Gpo7zAYx1skWEmCAIBzFvnpaY36sXuXu35WFh5oSpDK6qi0xWVBRw8fIBfP/r5hw/EYzHk68Yv/rqBM6f/2uuWfMgt24dxcrKbaZlGHOgvHjEgk7Q1g9wUeU+RUEqhFyQwloVs3534xHzI0CdPvN7DfRtM/vCYFV+lEIsC8AaAN1xIFn/hxbH1hNidcdPBPAPk2M71f2MAXgewJNOtogQEwShHuvWaUtUdO2qLVlRR5ghkyR+v4UbKd0xjROnn89Jk2IcPxF86tMYv5x9BYuK3mFZ2XzW1OypV46duAqirWEI1zA8YqkkClEUxb2sgtvwnxFVIee1LD842WFVX2RCTKsLfQF8B2325P117z0CoF/d72cB2AigAsB2AMvr3v8dgGocWKJi/zIVACYBWApgGYD3ALRwskOEmCAI+9m5kzzlFPKII8hly+p9FIXXxOs3fL2ASiRqubTwDb43vh3jcXD0N+CA4eDpT5zDJVuWmJajzxPyu31NkO1rCBjFhN8cuijy5VTu5Shmr/r9n1INbXotK0xS7hFLp5cIMUEQSGrbFfXpo21flJd30MdB5YaZ4fdbvCagEnzstcf50TfZjMfBUV+Bg7/6Kd+cPowPPbXVtmwr8eAmpyaVpNIWfX4VaS1qVQmyLXYhPSdPomrY248XN4zrlk73pRdEiAmCcHiSSJB/+IP2eHv7bcfDg/KOmSXAu/GGJQfTWQumctj/ujIeB98Zl8HB4y/m3I2zHOt1yrmxG9SiDuXYEWSIyi3Gzcv9esSCxO4aOV0/VSHmtp+NuYZhhcG94DdEH4TdIsQEQTg8+c9/tEfbAw8oHR7UQKEflNx4UJJ5REccuZrPfHAW8yaBn38D5o45jWtKv1c616wuN+LKTR84eUHsbFKpJ8gQlReMidluQnpeBZvXfnH6LGwhafzyoSISo/AS6uu1+1+0s83qPnBjvwgxQRAOP95/X3us3Xij5hmLEH1+kZuH9ZAhlbz6bzfwi29izJsEPju2BxdsnKJUp10OUhADnpMoMhNIdjYFkfMTtofFajC2w28IMyyhGZWAdSMSg7TJKdyek6N5N63Ctna2Wd0HbuwXISYIwuHF1Klk48bkueeS+/ZFXr3bAaY2UcvP59/LT79pwXgcfOWLVpy95kNXdfr1pDjhFCa08oiFFe4x87aFKcycyjZ6nML0iHkhHXOs3ITM3ZZlxK13UyXM76YcIGsRRYgJgnBY8N13ZNu2ZM+e5PbtoVWjz+VS8UBZPbSLyor4whfaTMiRX2Uy58tLuKV8i2tbVAYwPx4Ir4OkW4GmWleyLfpdCqIMW1rZk4q6zbC7P9MRuzC2l7Ls7rlUhLeBozdQQbsEsdekIAhC6igpAfr2BTIygHHjgLZtQ6umf3+tCgDIznbet864x11ReRE++/YzvDv/P3jyB9uxq3EfXHvuF8jKbOraHtX98/zs9ed1D0i9bQMGqO21qdKeZBuSZWVnO7fP676BKgS5R2cQDBt2oI9V7s9UM2yY9v/Ut6//PjS7f/T3b5TXKlnHPfds2650gopaaygv8YgJwmHG3r3kz35GNmlCzpgRalVm3hizz/W5Uclv4oWbyvnPsQ8wK7cpkQveOvJIxuNgRcWBZHy33qeow05uQo5mngin7WDcJMa78fqElSweVdK523JS5RHz0oYo+jCV4VlIjpggCIc0tbXkdddpj7GPPgq9OpXQmjHMsnVbLa/9z3AeNbgTkQviqht495PfcunSqzljxrFM6CYUpENitR129jklTQc5ELrtp7CSxaNKOrfDjXgNW4y4zceKCtWlO8JAVYhJaFIQhIbJ/fcDH34IPPUUcM01pocEGZZyCtO1bw+MGHGgvmnrp+H6Ef/ApsR8dKv5Cb668jlsOLoZzjlnDEpKJqB9+ysRi8X2nx9V6EQ1pGnEzr4BA7RwYUWF1uf6vvYa3nRjh911bt/+QHh0wIDg+jl5fr9+wJAh3u6xpN39+nmzSfVaJo+bPFm7R4MO0QL1+9UsNK3vnzDDxQ0SFbXWUF7iEROEw4Q33tC+5t5xh+0yFXZLKQRN0gswb/UaXvPRNUQuePmbbTlqzHGMT26k25wbnD69E0tLD17x31hWWDMBwwhfpXPSfBi2Ja+R3RpaZsfr+9yvXW48YlFuBO6UJB/lvRKVd86sHkhoUhCEQ5Lx48nMTPLSS8nqattDoxyAnniqmvjFo8zKbczzXmnCMfGOjMfBWbN6cvXqe1lUNJy7ds3ili07lGcHhmVzmMIkzAHPax5QEMtmWImopKi1W69Kf7zVUiB+MS6lkS65UlazGZ2+DIS5rEUYmF1fWb5CEIRDj8WLyZYtyVNPJXftUjol7IdyIpHgJ8s/Yeenj+VZL4AfjG/LeBycObMHi4pGsLa2vlhUEUFh2xxG+VHnIXmxJ8j8ODOvj51tQfSPnYDRe3+j9kx6aVsYXky3XsogMW4YT1J5+YqUi6cgXyLEBOEQZtMm8phjyKOPJjdsqPdRKpODb/n8FjZ7FHzq8zaMx8EZM7py8+a3WFtbZXp8OiUy+8UqBBWWN8NNuXYhMbtQtRcBF9VsRTvBl0qPmB/RFKRHzOiltFtRP+jrJR4xEWKCcGhTXk6efjrZogW5cOFBH0edn1RVU8WJayZyUN4g/uAZ8IuJrRiPZ3DNmodYW1sZjRFpgJX40g+IQXtKVLESVE4eI6v6zTwefu3xUkZSQBgFl1P5Yf6PGEVgkDsNuOk3/TWya6+KB9MtkiMmQkwQDl2qq8nLLiMzMsgvvzQ9xM3D2s+AuHVbLX/7nw/Z47kTmJEL3vR2jBMnxTht+rHcsWOq+wIbOE45W15CRGF7l7x6YpICrm9fb/UGLYSMyzI4le/2vvfjkdL3lRcvqV7Iuwm1qnpl/d5jqm0RISYIQsMnkSD/8hftUfXqq/vf9iqmVDwiVmVPWD2BnR85k10Gg3cO78C8KUcxHgeXL7+eVVU7XDbs8MBvTtbAgf68UEHapuIRM5Zp5dlxCiOqYBRiQYcevYSarTxjxtC1E0YhrzrrOaqwv2pbRIgJgtDwefZZ7TF199313vbqXVDJETKW/V3Jd7z2g/N57VvgsC+Ty1BkcNGiX3Lr1o/rLcoaBYdSjpkVyTb26cODvL84LHQAACAASURBVFBBtT+MUJ2xTKs6gkisD+s+MBOJQfSVF3vT9V4Xj5gIMUE4PPjsMzIWI6+6SltFX4cfj5jTeclj1mws4/N5V/D5z2OcOElb/2vuvLO4YcML3LevyEOD/NmVxDgoBpXcHgRB12fmhfIjCrzmHnkp3+xv/XEqS16o1OH3OCNm/ZtKQRTFPRVWvSLEBEFouMyeTTZrRp59NrlnT+TVj17yPF8Z05jxOPh5XisuXXkP9+xZFVp9XsI2yQFCJSnZqyfD7WAUZkK43iav+T1W9qVCaOjzoNyIQ9U+9notosglc0PQ95Rqrl8Q9YoQEwShYbJmDXnkkWT37uTWrZ6K8Do4bC9fxxfG9WTeJHBsXibzl93DRKLGV5kqOH1L9+r18muz28EonXJ0zPrUyr4oBKQRswkNKnaE6RHzk6AfVt/Z5dN5mcnqxyPmtn9EiAmC0PAoLSV/8AOyTRvy2289F+N2cEgkEiwqeodj85pw4iTw/XgvVuytH370MuCoPridyk6FUCAbdo6Om1mObkLWYeVkJT1iUaxHZkWY97jqsW7Est+ZrG5x67mWBV0FQWhYVFaSF1xANmpETp7sq6iZM8mTTtJ+JrF6wJeXL+aCBecyHgdfGQ2+Ou0u0zL9eAucZn05lZ2ugiid8bvul5GgxLDTtTTOhvRTVtC2+a1TpQ/dhI8LCrQJHX/5SzTi1c09pbXjTFKEmCAIDYJEgrz5Zu2R9O67vosz+6ZsfMBXVe3gd9/9jfF4JidObsEr3shi35H/52kWpF1Sdiq2nEkVDX1yQBR1OYkRN0LMLM8sbMKeLOH2/aQ9YW8vpa9L3SPWcydFiAmC0CB4+GHtcfTww4EUZ5cftG1bLYuKhnPatCM5KR7jI5+1ZcvHwFNeOYXbdm/zVJ/dAzpoz0w6E3UINVUhWz8E6f1MhjKTy3yEFVIM4jwjbq+dnafMKZwblTfTiGxxJAhCw+Cdd7RHUf/+mmcsRJau/x9HTejAeBx8c2xjnvA0eOJLJ/L9Je+zprbGc7l2D2izQSBIT06Y4al0m0GX6vrSEbPwd5CzL6PIjfNyfNC5aWEgyfqCIKQ/8biWE3bhhVqOWEhUVZVy5qIbOHES+L/x4J0fHserP7qK7y1+z1KABZU4bVZOkLMR/X7bN5atLy+qGXGHs5Dyi1kfqoQ3g5pI4sdOP8eH/QUnCBtFiAmCkN6sWEG2bq3NktxhvkWQ3wdrbW0NX49fydHfZDBvEvi398CH8syT8Y3oc09UcnDciCW37bIbDO3K8uIZ8eMRU0FfZlhC73AXeG7yzJxIt1CknV1Ok2OCvi+cbBQhJghC+rJ1q7ZO2JFHkoWFlof5GajLyuZzxuwzGI+Db3zRmCPmPMhNZZvqHeMkYpKeLJXNq72KJRXMzg8q/OQ2OdoryfL0fRmWYHKbVN2QRJuKvenYprDC3MYvDnaTY4IW/k7/O5IjJghCerJnD/nTn2or58+ebXuol/BgIpHgt+vf5aR4BsdNbMpLXgVHLXnf9Ngg82TcepL8DpZ+RFZQ5XspL8yNvJO4aXeQYeIoSLcJCunSH0kvmF8PsRVe7ingmE0UISYIQlpRW0v+5jfaHpL/+5/SKXazpfQPxtpELd+Y9wZPebETPxsPDhsLtnhMS8Yv3FFoWnYYnio7m52OSacE5Cg8YmEThiBOtRAK4ro4lRGmkA0aMy+Y05ciLx5mL15WEWKCIKQf//qX9th59lnlU1TEzt69G5g77le85FVwxFctOTHemNNWjWTZvjLfJrvJ/VI5x+oYp7DKoYJfr0TSQ2q25Y2RMESCV/tT7TnS49Qv6RDa9fOlRG+/WQ6k2f+Zl5w0JyQ0KQhCevHKK9oj5847A1mmoriYfPrpCi5deg/j8UzG42A8Dk6enMWiIv+LwiYJM/fLrJ5k2M4o0qLI4/JLWGGhJAdCPmqiNQrvkSqp9hzpCdIjFhZB5TdaiTRjQn8YbZZkfUEQ0ocvvyQzMshf/Yqs8b5el56ysoWcObMH43Fw1Ie/56nPglc//VfW1OwJpPwkUYkgfXnGQchqUEqnwZ009z5YtckLqh6xIAVYUKFUL/mOKmWmwhulWm9Q3k+ncKHTFmIqNjmFM73YL3tNCoKQHixYQGZnk6efTpaX1/vI6wOvtDSP+fktOWPGMVy3ZTQ/XvANkQu+Mi04T5gTYYogs7ClVzHoN5SmEgK0qkvfR1F6WYK4Nskygtw+KMh7xirEFqTn0apc1XaoHqeSfmB1np1n1I2H1iyc6efaa2XIXpOCIKSaDRtY0/Fo7mp9LLcv3XTQx24feCOXjOQ9/zuTEybFOGJcFjs+mUnkYv9r/ub54bTDhHQKe9nhdVDRexu85gulKsQVRIg0aA+Jm7pVsPIGBeV5NNrpRVSrHmdls98vGnZ9Yee9tfKGurl+4hETBCH17NpFnnoq9zVpyVOwxPYbq1P4Z96meewzrC+veUvLA3t3fDv+afRNvC/vPj4/83mOXDKS09dPD3TD7iiIIrToNcTmxiMWdBgvTLz0ebqFgMlwQ+ZmZYQRWrWrL4hy7MpV2QPWKM7cTqaRHDFBEFJHVRV5ySVkZiZ3fjTe0bNg9X4iUcuXp97Fi16J8b73mzAeBz/69ArW1OwNzNRUDrJ+c2jcnOt3sFPxPAQZxgvCriCOVz0nlYLeL3ZhOj1+/lei9P6qeO3ctsVLPpoIMUEQUkMiQd5+u/Z4efPNeh+5efh9tyWf4/J77p8NGY/H+MEH/+C2bcEk+yfxm0Nl9Bo0pDyooOpLZehOpR+iFgENDaPICMPbFnb/GD12KvllYQt4EWKCIKSGp57SHi2DBh30kcrDrKqqlBPnXMyJk8Cv8sCbh7fkxII3A58N6RezB32Ug3HU4ieokJddeMtL/6nYpVpulB7KdMJL2M1LHWH2j9Ebpr/P3IQs3YTkzdCXLUJMEITo+fBD7bFy3XXaKvouWbXxA07Kb8e8SeC9H7Xhkk15nvK+VAgjVBfWYBNGuU55XWG0LzlYJsOYZjaFkYekareXhPRDhYbeXr39RuHt9LcevXfQi3jXly1CTBCEaJk+nWzShPz5z8m9zjlc+gfYvsod/HjK2YzHta2JTn42i/lr80M1N0jvld9v0U6E4WlzyutKCjS9YPLrsSouJvv0sRZiXusICrvBnFRL8LYrM50ISminY/ui9IgZ7xPxiIkQE4TU8P33ZPv25PHHKz+Rkw+w3Jfe46ffNObESeCTY3pwypoJ3Lp7q2+TnAaIID0+br9FuyVMj5hVmWZCLIgcLqcyvIidMDCzM3l9+/ZVLyeK3DoveAmtG0W1nUfVK0Hlp0XV73ZlRSrEAFwKYCWAVQDuNfn8FwAWAKgBcLXhs/4Avq979de9fyaApXVlvggg5mSHCDFBSAElJeQJJ5Dt2pHffad82vqiPbzrjUs5fiL44dcZ/HTBw4GGIb14Vrx6Y8L2iKUClcHqvffIrl21Pdy7dtX+9lKOnqg8Yl4GY68eMatwaxBt9SoqvHwR0dvr5FH1ilWfuM3zs/tftCoraGEMNFvKKIQYgEwAqwH0ANAYwGIAJxuO6QbgVADv6IUYgLYA1tT9bFP3e5u6z+YA6A0gBuArAP/nZIsIMUGImH37yHPP1UKS06Ypn5a36mvmftKK8Tg48pujuXXX956qVwkxNPQwSyqx64/33iObN+f+nC9A+9tMjAVVpxucRFOUIVArr2AQwj0qUWEsM+x8SNX9Vo2oXFersoK+J4CeOxmREOsNYLzu70EABlkcO9wgxG4A8Lru79fr3usEoMDqOKuXCDFBiJDaWvKGG7THyKhRSqfsrtzN33/+e948TFuSYtL865lIeF+OIpX5RIcDdv3btWt9EZZ8de0atZUH0A+wTmHEKEW3XUK3H1vC9rZFhVn7/XqnvVzXoMKiSaL0iF0N4C3d3zcBGGpxrFGI3Q3gAd3fD9a91wtAnu79cwGMtSjzdgDzAMzr0qWLu14SBME799+vPUL+8x+lw8v2lfH0105n9yExTpyUwSVLr/Vtgniw1AnaQxiLmQsxIHXXQz94Jz1iM2em3z1iJ8zcXKd0zT9zg14069uRTvZ7FYWR5YgBuMZEiL1kcaxRiA00EWL/AnCWiRD7wskW8YgJQkT897/a4+PWW7UFXG0o3VPKhyY9xHZPtWMsF/xySg9OndqWlZX+E/LTBb+DRhSDjlMIyypMVlCgzXQcOLB+SOqYY6yFWKq8MEF6VsK2y+pzN/amk1jxSrK9ZivWB+2h8opbOw5cx6xFjEiISWhSEA4nJkwgs7LIiy/WtjKyYfr66ezyXBfGcmO8aMRFHD1nAONxsKhoRETGRoPXwdPtzLMwwi76gdDMhuT7xiTt668/OEesWTPtfRX7vCSLeyEMkaxaZjJ0mFyyQyUUmS6zRqPCri/8Ju6HjZN9kW36DSCrLsm+uy5Z/4cWxxqFWFsAhXWJ+m3qfm9b99lcAGfrkvX7OtkiQkwQQmbpUrJVK/KUU8idOy0Pq03U8ompTzDz4Ux2f74752ycw7171zM/vwUXLfplaIu0pgqv4SS3M8/C8JZ49YgVF6vNmrSyyawtfhKt3eIn+VvVTr2I1Xt87M4PQ2SEMXElrMR9lXKN76fKM2gl0pN5e5F5xKiJpr4AvoM2e/L+uvceAdCv7vezAGwEUAFgO4DlunNvgbZExSoAA3Tv9wKwrK7MoZDlKwQhtWzeTHbpQnbqRK5bZ3nYprJNPOftc4hc8NqPr+XOvTtZXr6Ic+eezilTmnPPnjURGu2esB/qfgawoPKHUoVZLpReAKq0L6i8KNX+8eoRS5bfp8/ByfR254cRjjNrq1N5Tv1j9oUiiFw1t19OVGx1Isj/eb0tkeWIpdNLhJgghMTu3eSZZ5LZ2eT8+aaH1NTW8PH8x5n9eDaRC/7m8de4fHkZP/jgX4zHMzltWgcWF3/u2YSovvWmo4DxQhhekKDK14svt/1t58FLVX6VmYfGy1ZNbsJ0fq+VU185fWFQ/ULh9fq6WSjW77U0+4Lg1dOnP0eEmCAIwVBTQ15+OZmRQX7xhekhG3Zt4HnDziNywSs+uIJ/eWIme/cew88/78J4HPzww9tYVbXdlxleBJJ+0FYdGFMV5kgH3PSxH9FjNfBZHa8qJLwKIL8YbfF6r9rtzGDXh16Iyrvq9f8pTKFs97neI+d3NqcIMUEQguFvf9MeFUOHmn78v2//x7ZPtWX249kcvnA49+5dz/nzf814HJw69Yd85ZWpkTxMzUg+VK1ydYT6hOURc+vNURE2VmWkwqMZRM6S/l4NyyPpFZW60s0ePV6+NCQ9csbr4SakHVmyfjq9RIgJQsA8/7z2mLjrroM+qqiq4B1f3EHkgr3eOJNL173PFSt+x8mTm3DKlGZcu/YJ1tZWHnReKh7YSY+YcfZaKom6H4yeoigHV7d1+RE2YYdkw8IYcm1o22U5eTnDqsuJoMPEdqHxg208kxQhJgiCZz7/XJsO9+tfa+FJHYuKFvEHQ3/A7EfBl/Mu4qzZJzMeB/PzW3Hlyj/bJuSnMgcrHQbcJGH0g5OXyG34LMpr5Sf07OV66gfUsDZr94LRi5sONqlgFt4LK5QZVVjVT7niERMEwR9z52qLRJ11FllRUe+jUUs+4KnPNWLOx804aXITxuPgvHm9uHnzW6yp2X1QUUGEbfySTgIsSRg2WQ0OQXvEghgsgwznefHCGAVPKkPWZt7AsD1iQYhY1WvrBhWB46bssP73VcqVHDFBELyxdi151FFkt27kli37366s3sMXJvySb4zR9omcMqU5CwpuZ1mZ+SzKJKn0gKWTDVEQleAMwpuWzMHJyfFuhx8vjKrgiaJPU3F/+qkzTHvd5g+GjZ/rL0JMEAT37NhBnnwyecQR5PLl+99eUzyXb49ryXgc/F9eO65d/yKrq3cpFZkO3qh0TiQOmzDs8esRKy4+kK/nR4i5tckLxoE/iHoaupc4bHud7h2Vur3aaDzPj/ATISYIgjsqK8mLLiIbNSInTtz/9ldLn+Jn42P8Og/8fO6fQ1sVP90EjFfsHtypSCRPR2+gPiwY9fX2G9oKwpMXhbhLd8zsTb43cGDwfez1vCg8YlkQBEEggT/+EZg4ERg+HLjwQlTXVuO/ky/GCRmTUYYmOPakT3Fy58tcFVtSAgwbBgwYALRvb3/ssGHAPfdovw8c6K0Z6cCAAUBFhfYqKanfbqc2mvWX334ZMKD+z7BRueZJW/r1U78/gsJtf7ZvH/z9aLwmQdz7Uf//uPnfNsPM3uR7ffr4t8/rfW88L4zrfxAqaq2hvMQjJggeefRR7WvgQw+RJNeVruDQse0Yj4PvTOjO8r1bXRdZXGw988vu23BYIYcocZM0b3ee0/HGstOhX9x4IpLHutnOxg9u+tOujFSEeqO0S6Usv15Nu2dAQ1u6Q4++XZDQpCAISowcqT0KbrqJTCQ4s3AMR3yZybxJ4OjZvzMNRarMprN7UKdrorBfVAYSN6FLL6LGabZZ2OtUuREEyWPdbGfjh3S+d5JEIajNZmnq69P3k93/ekNbYiMK9M+9SDf9TpeXCDFBcMmUKWTjxuR555H79vG7LZM46usMjsuLcXHhcMvTrAY0lQc46TzYBJGsa0XSKzJwYPBb4agM9F6EiptjrQRW/QHC3XY6YRNVfVGLHC9EIRb1dZj9z6ruBZouXth0Qj8RBThmE0WICYJgSUEB2aYNeeKJZGkpy8oW8su8Jvz8G3DFBvvNuVU8Yn4IczBKlm1c4DQI0iG8ahcWVfWIpZPnKIhwYpT47btUesTMbA/ii8/hItaMkw1EiAmCYM22bWSPHmSHDuTq1SwtzeOkyc056ivw2Sl3pdwjEqbQ8+oR8+rJcgr9BE265Rv5LU8vnKMWhip22927fvOggroOqfyCEMS9ng5fcNzkzSVzHiU0KQiCOXv2kL17k02bsnZGPletGsh4PMb3v2rCM14+lnur9/pOxHWL6sM6iKUDvKJqozF3JgwvQ6rwaref8FZYHjEvA6tb76HZZ8YQsd39lLzfBw4MPtxpJxLdCp4wUwms7Derw2qj7iBsUnn2GMtVTdaX5SsE4XAikQD69wdmzcK+d5/Fosy/YN+GpZi8vRWeWlGGD68diqZZTTFgADB5MjBunDalPOzp21EvseAFu2Up9AwbpvVb377126P/PZIp8SHgdYkEu+urUmZ29oFlEvTLJiTP97KEgkq9yToqKqyPtWub2T3Tr5/2v/Xgg8D556vd8wsXAnl59rbaYbSxpER7DIwbV79M1etrPC7spTOcng/J+nNytP87p+dWkPYal/HwVJ6KWmsoL/GICYID99xDAtz00F/49cTG/N94sPdL4M/++zOOXTm23qHp6LVJtU1O+VdW4Si3pLqdVoSRL+RUprHPrRLN3dbtNdSsitFLY7TfzmvjJp/PC1Y2hOERiyLf0Or/TyXFwawtZh5Yq7Ls2gdZvkIQhHq8/joJsPLWG/n22MacOAkcNO5aLt6yONWWNRi8PIy9kE7J8kHipV1uc7CCrNvJFpX6+vQ5eLN1p/X1wl7Ow48o9VtXlGWpXHMroa+ahmAXNhchJgjCAb76iszM5O4Lz+CX4zM5dgI4bPqtJMPLwTmc8OMxCSuvJh1J5YAfRa6SsT43Cxrry3da4DZor6uxXV7Fbtj3rVsxrWKPqkfM7Bw7wVxcTAJHb6AIMUEQuGgREy1asLjnMfz40xhHjovx44XP7v/YzTdAIThUE5CDEnd+CXuQ9Vu+vj/DslUl1KXyvtvyjQTh3bPrL9Xwr915YZAuX1CsvJ0HH3MmKUJMEA5zNm5k7dFHs7Rdc94xBIzHwfnfP13vEL8esSg8EQ2FIL0HXga1MAfCsAdZv+XbeXjCJur6Cgo0b1tBgfcyVD2ybvK/ovhfTwcP/v+3d+7xdlXVvf+t5CSB8CaIECBARBtBWhEspZS21lMfacX2ih/RW6W2Xkql7b1WTwtFbyj2Wh99WbEXr5ZPq7lVlNtavdSLoicPQh4kkJAEE0hCMCGQHPIihDzOY9w/zl5kZmU95mPMx9p7fD+f8znn7L3WnGM+1py/NcbYa9d5O9VjxCMmCL3OCy/Q6M9cTIePz+ih/zUuwpYuvZRGRw+xVtO0Cbl4Ktom4jg35G73iPnMUwo5b3wIA12RXhbCtAl52/ZXkyD0MQ6xPfh5m9QPUFS1U3LEBKGXGR6m/f2/QKMTQEs/Bfrkv51DTz37f2lsbJS9KhOPmKlQsRU2sQScqUcs9p19THx5kbjzp5rw0Q7dsLX6bCuda6zqPds2mNyE6dIk0NXrRvfTpGXjaTtPytpUdbMpQkwQepWxMdrzweuJAFrzEdCv/+N59PXVX49tFRGF84iFDhURmdvqcmffJs9X6Hq486eaMPFA6bZZ97jcI5V/pY4qBNatO1bou3rETNtjM8Z53+eP1qgaC53wYLFMHfHURJOoU8sVISYIPcrQHX9KBNDT14OWrPt0bHOi4LLJc4k/nU3K1iMWMxcs9XBxaI9YHcW+5B63uhCljxAeh4dL53hVYFWdn9uiJsybCM0y8dT0aVXT9ooQE4Qe5Ll/+iIRQNt/CfTDpR9hLdv1rtGmnBjYekOK7fIplnz2r25+Ulm7Uh/bkJQJbe7+aZoHdULfxhYXD5fJ9aT7PZxz5owLMZsH/JbVy/38NhFigtBjbL3/Xjo4CbT7YtDtt/fTZz87xlq+ySJXdqyvxY4brvygWJ4Z32HZOq+DbqiIq06u47ko87KE+r7WMhvqqArNhRSLdTbpUOxj3zchpogQE4QeYvuqxfT8iRNo31mghf9+Jv31X+9mX/xdPWKc7v9U8L3hhwgFceFTeJiGS32L0SqK4saXMDWxQcdzqp4Tq++I9D+FWfzqJ46vgFq8mGjWrPHfXIgQE4ReYedO2nbOybT/RNCSr2a0Z8+DsS0qJaWwVUq21BEj1822Dp/1NW3Qpvl5vijWG8OOKoGle45Pj5hL2Ft9vyhwOcTjrFnjZcyaZV+GyniOmDxHTBC6n4MH6aWrr6RDfaBHPg+aO/e/sy76ITeSkHXFuOsPvSnrtNFV6IXy+Jh6xIRxXAQWV5+aeNua6qzKIeMISd58M9FFF+l7xPREpTxZXxC6k7lzic4/nwigsalTiQBaMJDRd+/7KZowYZh1UwwpWELWFWPjDi3+dNroYlPIHKhuElqxQ8em+Veu87VMDHKEEjmxaWvZOcW2ikdMELqRuXOJOuLrECYRAXR4ImjtbaANG+5hWdxChZu4wjht2aTrktxDhhC56uawm+OrejjtCUGsHCxXjxhn/3L3QYwk/Xzufu97R+ZwMT9PhJggdCMdT9hCXE0E0F6cSATQwbP62J6aH2qj4KonZnKxCVWLfYj8Jts6fIubPLQ5e7Z7WRz9yHlO0+upeYXKsMk3My2X43gf3rsm8jrz3DL1AbRH+ktCk4LQfWQZPYLX02H00QpcRocxkQigsSxzLjr0BsG1ybfdE1K034ewrKqj7rsK8zt+nyLXxCOmmz+0ePGxT5vXpapf6uquGq8mYWg6znU2+BCdxRxA7uvMRvTY5pbpYhJuL8634hwWj5ggdClPnnEl7cHJ9AQuoj04ifJHZ4/NmOFcdsw73l5AN9QTMlRZ9kw3dTMyzQHzabvu/Mzt7u/XFy7Fm5DidzjWPftOdxxdPXZ17efKcSp731cOoInNodaTovh0RR5fIQhdxo7Vz9HTE2bQcziTtmD6ERF2/OTx3DFHUs4B6Ubq+ijkxlPnETO1wee46/aJjpetaGeVSCr7Um3f9tuc78sjZhNyjSnaOcp0KaN4rggxQegi9g/tp1XHv4FexFQauPIyOnTO2TSWdXLD5n71mONje6Ri198GbMJdXOVznsN5fihieSerhK/td47GQDcUG4PYNhTrFyEmCF3CyKERWnz2b9AoMrrhLW+l5/Y9R9u330ODg6Dnnvt66TmxFyTBDQ4BUDYHQiU969IW4cZFWf/mr/l65luo3K6QHi4bG1w8vU1lVx0jQkwQuoTBN3yECKA/nPWL9OmFn6axsVFauvQSWrr0tTQ2NlJ6Tq9tcMKxlM2BUEnPunAJv7bMdxePmG1ftfmmzMX7VpWjZ5sDZtOPIsQEoQuYd90XiAD6l5nvItwO2rx7M+3d+zANDoK2bbu79BzdTSnG5uW7TpO2+w4HpSgOUrOJy55UE79DeKJC2xGyHhfvW1ne35w545+mHRjQv/aLnjQTj5oIMUFoOYMf/S6NYAINTnsLTfh4Rr/z7d8hIqLNm/+CBgdBhw5tLz1Pd1PivlO2WRy5MW27aejOhy0xCC3IQgtw3/l3OqQ2/tzJ/sXz2tBeG69YsV0m7RQhJggt5vG5K+hFTKVl2WV0ysfOoJ/98s/SgeEDRET0yCPX0MMPv6HyXHUB8rH4VmETLuDG1SNmk1flaovp+b7yx2xs8VWfK3X16V4frqTmfazrE46wZwwPoOlYmuSJVR1r0s6gQgzA2wCsB7ABwC0l708BcE/n/aUALui8/p8BrFR+xgC8vvPevE6Z+XtnNtkhQkzoBrY+9DQ9O+Fs2jJxBp1101l0+qen0da9W4mIaHh4L82b10cbN95aem5VXkSIDTBEuM8Gk4XTJq/KFy75MU2YbpqudTbV52sTb9pw1cdTdDu2N2Uhb+ZUdOacekxRFLquRbZzXu2TYEIMwEQAGwHMBDAZwCoAFxeO+TCAuzp/Xw/gnpJyLgWwSfl/HoArTGwRISa0nT1P76EnpryO9uBk+uPbbqa+O/po466NL78/NPRtGhwE7do1WHp+WV5EyLtyTo+ST5tMiGW/i0cslfwkXXyJ3aZyOYSYTd/EviZMiHUj4uIRq0o94K6/DLW/QgqxqwDcr/x/K4BbC8fcD+Cqzt99AJ4HkBWO+RSA/6H8L0JM6CkO7z9My0//xhCt/AAAIABJREFUVTqMPvrRJ/8P4XbQ73339446Zv3636cFC06k0dFDpWVwLfAc4bj877qnkoegTZteE7ptqdo8U+0LX3Y1eUZCh3nLrolUxySnaJ+LvcVzOb70vcyesnEP0c/FekMKsesAfEX5//0A7iwcswbAucr/GwGcUThmI4DXKf/PA7C6E5b8RFG4KcfdCGA5gOUzGL7mRRBiMDY6RvN/6kNEAC344N30nm+9h3A7aMmWJUeOGRuhxYsvoMcee4d3e9SkVlfXPsdTyW1JfZMzRXdcqtody7vhQur5aSb2lV0TKY2JTltc7C2ey/Gl77r2uNitO8ZFD2tIIfbuEiH2hcIxa0uE2DTl/ysBrC6cc07n90kAvg/gA022iEdMaCuDb/kUEUCDv/Bx2v7idpp0xyS68Ts3HnXMtm130+AgaPv2e4jIf6Kx63eupSCCfGxyMdtVNy4xQpYhcE0IDxWmte1/To+TDWUhvbrrRacNuufaesSqQpImdZug62GOKcScQ5MA/hbAn9XU8dtFL1vZjwgxoY0s+sOvEwH04Pnvo7HRMfrcos8Rbgc9vuPxl48ZHt5HixadRStWXEVjY2NElNadvk0ZoUIF3PXH9mD49nalJtZMhYJvqmzIN+GLLtITFpzjyCUymsqpEo3c6QdNQiv0PNAdq+JxIYVYH4BNAC5UkvUvKRxzcyFZ/5vKexMAbAUws1DmGZ2/JwG4F8BNTbaIEBPaxqovLqQDmEIrT76GDu49SEREl911GV355SuPOm7Tpo/T4CBoz57FL7+W2oZZRt2CGXtTNa0/72/br0ixxfaOPzWh2ZSvpVtGiL63EfC5GNENtXHm8TUJgjpM5lfRG+sr/UBtT1k/pbL2Na0JwYTYeF2YDeCJTsjxts5rdwC4tvP3cQC+hfHHVywriK5fBrCkUN4JAFYAeKwT1vw8gIlNdogQE9rEU99/gnZmp9OmSa+mXU8+T0REm3ZtItwO+tyiz7183IEDT9P8+cfR2rXvjWWqNS4eKd+LrWn5sR51YCuMbM/z1e+5PSl6E4s09V1ZSG1oaPyJ7f39bh6xuvd0X/chpvMy83b7vCmxCT261OFKVX8HFWKp/IgQE9rC8+uG6KlJF9FQdgZtfuDJl1//q0V/RbgdRz2yYu3a62n+/OPowIGng9lnu0iFWNw4bLHJ88mF2MCAfY6MDSmMBQccHjFXdOdUU99xJJnXUWUnl/02pBYiroJLbJuUWfU+0LeSRIgJQnoc2H2AVp10NR3AFHrsS4uOeu/N//xmuvQfLn35/5/85K9pcBD01FO3B7UxtBemDBuxpGuLenevm3tSlw+T8sbULZiKi7LjubywHI9dsLEzFXEd4ubAd2jdpHzb6xuYvoVEiAlCWowOj9Ki895DBNBDH/nmUe8dHD5IJ/yPE+jm+24mIqLt279Bg4OgNWuuo7GxkaB22m5YIRZojoW2mO9ikv9ls8Gb2BaSGHbYhp1MN0ObzZMzb8u1zpTgar9JW9VjQwi4uvJsPbniEROEBBm86lYigAbf/plj3vvqyq8Sbgfdv+F+2rVrkObNm0yPPHINjYwciGBpPdybB2eYQJeYoRbbTcanHTHq9DnuNv1aPKfOC8pdh0kIPTRc88RWUMUUqy51S46YICTGgg98mQig+a+9kcZGx455f+D7AzTlk1No7wsracGCU2jp0tfS4cM7I1jajI+7zpgbTtXm6JKMrLvBxtxkfORtmXhTY497E/nYVH0qkNPr5nqsDm3NN+QKKfuouw4RYoKQEMs/dT8NYyI9fMZbafjAcOkx1379Wrr6S6+hRYvOoUWLpgdLzo+9yKZIvgHOmmW2EdoIrNj9H9O7WSR2XxRp8l5xeMS4jtUhpOgPMZZ1HssU5pIIMUFIhPX3PkZ7cRKtO+6nae+WvZXH/fSdM+lbPziZFiw4ifbtW+lcr+5dZKjvguTOK/OJmkNm8jVPqeS1mGAbGrMZz6Z2ppgvZSquU5zPOT5sMw3nupavUuextJ1LnH0kQkwQEuDZFc/Q1onn0bYJ02nbsi2Vxw2PvER/82+gH/5oAu3a9QBL3U0LUVPYhZsqe2Jtvj7CHbaLeKg+MLWvzi4fYbkURYypuA4ZTgyRN9d0XrG93OtKXf/X3QzYhtw58+HkU5OCEJl9z+6jx4+/jPbhBFr39Udqj917YBd99H+D/nHB+4iIZ0NqKoPzI/gu9nBtvpwig7MejjK55oPp94dyigDbczjPD1EnR/hShVMM2875uvO42quzPuiKvBTC4+M2XE4kQkwQ4jByaISWnvnrNIIJtOz2+xqPf+aFZwi3g+56+C4iCuMhsQ2jNRFCRJZh2mepe6+468zLMAm1pkaMDdY1xOza76l7xLjK0PnmCt2wJ7cYtkE8YoIQkbHRMZp36R8QATT/+n/QOuelwy/RfU/cR5t3byaiMAuHae6LLpyiwaSMUIttqM2vrAxfn+JsCy5t8OEN0jnWxhOpQwjvokuIr0hTP+biqr+/uS5TuzjDjSZ9LjlighCJwXf+LRFA8674aGxTtAntEQsRiksFTlEZwxvngzaEGE3OaxLKPtrrOhd0zs+PCSFiTAWrSft5w436fSFCTBAisPhP/pVGkdFD57yLRodHY5uTLN0iKHSoC5OYCq5YYd8mTPMNQ46/z1y2vN0DA+Hnc9s8Ylw22RzLVbd4xESICYmz5u6ltB/H0+oTrqSXdr7kta4UPEYuNqRgfyiKbVVFSFX+kM/+8SGCTL8EO+T427RX95y83f39ac7nmDlhtrgI53XrjhWOumF97utCcsQEITA/mb+JdmRn0tN9F9KONduJqH2baco2uOZlxdxYiv1U9IiVfedlqNxAjuOIwn8C1wSbPtVtT8rtJgqTF1eHTd+7COf8Wip7nEZT2JMjD/NYm+RTk4IQhN2bdtGGya+l3dmptPG+H7/8uk+hkoJHKWQYwTRUVzzedSx8ef+KoZ8UBHaOiy0pCeEq6myybXtqHih1fpkIjFg5VbZ1c3jETGzWDWOKR0wQAnBo3yF65NQ30SFMokf/bt5R76W4+cTClxCq8jYVF93QQtC23JTmjIst3EK4DtvcnjqbbNvuwwPlKmp1PUI+aON81jlOd5wlR0wQPDM2OkYLX3UDEUAP3vS12OYkjS/vWV3+FSe6QpCr3LZTFMRc4Z4ydMag7JgmT2VIz1ad16Zou87ztnTL5iT19AGTa7XJFl1bRYgJgmcG3/TnRMD4b4ENzpCYb7pVSHERwuNn6xGrw3eI2ETYF481FWKhMBW7vrymVXl7JnOAyxYRYoLgkQdv+hoRQAtfdQONjY7FNoeNFIRFCjYI+ph4lkKGYn3l9XFQtdHrJP+ndH2otuiEf+uObypLF9NP8Da1y+S9IiLEBMETj/7dPDqESeO5YfsOEVFai6MLvj0BqdMt4xgSm5BPHiZr+qoan3bFHGtfoW4bO1yeE6bmn9kI8aZy646r6kObT7KahCJV25rOEyEmCB7YeN+PaXd2Km2Y/Fra89Sul1/vFgGTuhAJ5alo8/cxhsZmTPJ+bvryZhdbmuxK8ZoNff3lfWD7ycZc9HA/4Z4zYd62LB3x1WSDCDFBYGbHmu3jzwnLzqQtC5866r3UBIyPvBmuc10IkbujhjZSGU9dfI0Ld7m+7FSFdFNyuqs3qBuw6QP1GtHxCpWdz/HhAd01TsfWsjCpzXnF10SICQIjL+18iVafcCXtx/G05u6lsc1pREewuIiaWN6EEAKwuAj7KN9XG3yNi49yffSDOnazZvm9BlK7+aqC205Xr7F6vu81pGir7gcdXNqozikRYoLAxOjw6Ph3RyKjJX/6r7HN0cKHR4wrmZYD3/XHEkuuXkpfHh4f/eFLNJp4NZv6rK7dqeWgVdVn+7iLquvcdR3g8oiZ1JXXodsXXNECEWKCwMTgFR8jAmjwnX/jva7YAqeOlHJqTGxJrU9dNvc6UhofHXyOi0nZdflBdR8mSC0Hrao+UyGmltOUy+frpsIXoW0SISYIDMy//h+IAJp/6c1BHlOR8maa0sLqutGmShvz9rjhbIeJZ1j10DQJEJ26Qn8PpW0eU105TYKU86aCe/6GLK/qPRFiguDIstvvoxFMoKVn/jqNHBwOUme3bKZVxGhft/dpt6G7geuMq4kYUD1HNnOmWFedp833XOT21rmEIHXP4b5hKpana0/VcXXiXK1LQpMixAQm1n3jUXoBJ9Ljx19G+57dF9ucrqFN3ikdbDfWpvNSF48+PXe6ZevMJRM7XZ9YX6yrrO5Q4iy1/DUdbMVeVY5fsTzdtafquDrvoFqXer4IMUGwZNuyLbRtwnTaOvE8enbFM7HN6Sp8CZfQ6OQQ1dG0KTRtBj49Ezpw5rJxzglfApGrD3XFmStl4cW2iv468utP94MZJuFY2/4Sj5gIMcGRvVv20rrjfpr24iRaf+9jlceltHj53CRSwWSzCtEOmxwilab8oabwiImI8b3Rm1JsO6d9nGVVeTm48T1fq8JmZe9zEUr85ULsoovs2zA05O9RGiLEBMGQ4QPDtOyMt9EwJtLyT91fe2zMEJuty72JUG3i8uo0iRXdr12xwbUM2762GXuTu/0QcHnEyuD0iKl2cifec4+DrreHIzTKIf5N539VnfnrZY/C0A1bNq0XLogQEwQDxkbHaP6sG4kAWvCBLzceH3ND09nIUglh+bwDrwvf1d3hNnkIdNvhQiwvJmfI05YUxGAZddcV901KrPI4+t5U/Ne9r/ssMZv+ys8pO89mDSjarnO8CDFBMGDw7Z8hAmjwqltjm9JIrHCUDRx34FXoegHq3tPtp1T6U4emtg8MEPX3H+3d8ekVsKHYhhDizXY+2ZTrU9j77ivOsfEhIHPv5eLF9R4xk4cf24pyEWKCoMlDH/kmEUCLznsPjQ6PWpWhs4iHeJK0jj0hScWOKprGLV+sYzwF3JamjaK/f/z9/v6j6y7zIsYav2IbuIUwpzhqOi+0yA190+BSn4/5pX6rQh0mdtt60ESICYIGj921iA5gCq066Wo6sPuAdTl1F7W6ENu6wwU+dPu+LrThA64NtKl9AwPj9QwMNJ/HEYaywbdHrKxdtv1fF+6dM+eIBzLUPPIZavNxPnf5uvl8JuXaCncRYoLQwOYfbqCh7Ax6atJF9Pw6t1XE1CNmG7LjDpG0GdPwQo5JOMTXdzdW1RdifFw3oCJN/ekr5FeFjgc6hEdMFfJln65NZbxtw4O69rv2dZ19HH1oW4ZOv4kQE4Qadj7xPG2a9Bp6PptGT33/Cfbymy5uW++Dy6Zn614PhalNth6rFNvuk9Aei+L/Ot5iTk9RmQfaBK7+ahLyIUKIxZBzmUg19RCbhotdvY918ysvx/YxMia2FD1t4hETISY4cHDvQVp58jV0EJNp1RcXeqnDZpHl8Ijp3j2G2ARMMbWpaaPrNcFVReixLtaXokeszo7c/v5+P95QG/tsUUWp2rYmkarjxdK92ax6tASHcMrLsX2wsokturlnKiLEBKGEsdExevD89xEBtOiPvu6tnlgiwCVcYFM+Zzu5n9WUotiMQei56FNc+WpDcXPPN10f8yfkvFT7Tb1xaRKBNjdFNh5+G8rqUj8pabr+6c4tm/VJhJgglDD4Cx8nAmjwLZ+KbUorsQ1P2JTtSupiODZtsZPIv3gpu8HwlR/I2e9cuVauNpaVHXJ+mYajVXt9pmyIEBOEAgs+eDcRQAte87s0NjoW25xWYuIRM13UuBfBWEIjtGiwpU0eQ5s2u4TO2oKJAPJ5PcQW9aZjWeUR003t0EWEmCAorPjMD+gw+mj5tF+lw/sPB6tXJ9eiW4m90ceqP2QYzQUXO2OHO3Xqb9pU1Zyf1ASpS4pB7OuuiZTXvzrbbPo1qBAD8DYA6wFsAHBLyftTANzTeX8pgAs6r18A4ACAlZ2fu5RzLgewunPO3wPImuwQISaU8eS319AenExPTHkd7Xl6T9C6yy7eUAvl3LlE5547XtfZZxNdf33YxS/2ghu7fh1shLpOrkrKYtAmidsmJK6zqeZ5Ra65idz9bRIuqxKppp6+UNeL6/oXKwcxaY8YgIkANgKYCWAygFUALi4c8+FcZAG4HsA9dESIrakodxmAqwBkAL4H4O1NtogQE4psX/UsbZk4g56bcBZtfejp4PXH8ojNnUs0dSq9nHCc/1x/vb86BXNMhbrqyanbyJo2O9c56BLWq8vnqbLbxiOmY39TOEqX/FN7c+bYl2FrX9X7pu3S6XuOtcu1PB9z29fNcUghdhWA+5X/bwVwa+GY+wFc1fm7D8DzHYFVKsQAnA1gnfL/ewF8qckWEWKCyovbX6S1Uy+nfTiBHp+7IrY5xrjkxeSesOLPuef6s7eXsd2gTIW6KmJc7t65Np5iOSaehSqPWFOSfIq5hEUhxmmjiUfMReToeCO5BYtNeT7mtq+b45BC7DoAX1H+fz+AOwvHrAFwrvL/RgBndITYfgCPApgP4JrO+1cAeEA5/hoA/7ei/hsBLAewfMaMGby9KLSWkUMjtOSsa2kEE2jpJ74b2xwrbBaU/JyqnyzzZ28suO/YbQgVbuZqn69yTASJbhiySJPHsKxM3+GsYvkcoVsbW01Cmjb2pCiCbcoMtU6EFGLvLhFiXygcs7ZEiE3r5I5N67x2OYAtAE4G8MYSIfbdJlvEIybkzHv9fyUCaP67v2B0XqyNnMuWJo/Y+efz2ROjr8rq9HnH7mJXG+twpSjE6sZDNwxZRMdjWHzSuo3nrok60ePijdKZwzqCkztc2nZUT2xdeJ9TwALTt1AgIWYdmiwpa17HGyahScGaef/p80QADb7hI8bnxrqT5aYsR2zq1PHXbSn2TQzRU1ZnCh6xEJj0dyzPmYkgcbWxLqxbfNI6p8eqrH7X8tTzdT6MoVNfNwoxDm+h+mnZOjHvOjfG67mcKJAQ6wOwCcCFSrL+JYVjbi4k63+z8/crAEzs/D0TwDMATu/8/zCAn1OS9Wc32SJCTFjyZ/9Oo8ho8dm/SSOHRozP5woLxEK1f+7ccQ9Ylo3/dhFhxbLL/g9BSkIrtC269R3ZBNznoo9QlytVYqvsGBuvmotNHKLSxSPGaVNodOzluFFu+oAJp7cUeM0eCiHEaFw0zQbwRCfkeFvntTsAXNv5+zgA38L4oyiWAZjZef1dnbDlKgCPAHiHUuYVndyyjQDuLPOgFX9EiPU2a//5YXoRU2nNCW+k/UP7a4+NlZvgmxTEoG9cNlnOMYrR1yabVVNCv2l9vtprOiZV4cduIYV1JCQ6wrp4bOp9c+R66VtJoYRYKj8ixHqXLQ9upu0TXkk/6buAdqx+rvH4FO/0i7jkiHHeKfuywxTdBbsu94jz4Z0x5o2rt8TFZl/tNRV4qV6vvY7tuHSzsA6WrJ/Sjwix3mTP03voiSmX0B6cQk/++1qtc0Lc6bviyy7Tcm3s4AqvlJVZtWDXhR5UEcbhKYqFqwhJca6LsOoObOdWN4+/CDGhJzi07xCtOO3NdBh99Mhf/dCqDNuFwPcC4qv8VDxi3J6QuvLqwnXdtBGEzo1qM2pftKFfUrdxaMjfF6W3FRFiQtczNjpGC179QSKAFn7on4LXn6J3oUjKizfXwq2ThFvXDzHHkXt82jAnuXC9QVD7qg391qs2priG6dokQkzoegb7/4IIoMFf/O9R6o+5QOjWnfribWJfVZtd2xhzHG1sD/VhhNRxCZnnj4cw9YhxH2dCscwQY+3qPeewMcU1TNcmEWJCV7PoD/6FCKCFF/4WjY2OsZadaqhSRXchSH1jNrGvLgk/5TYSVXvtbGxPcWOKga1HzOUDG7p9XxcK5yLEPHCtg+NGg+v65lwndJ71RiRCTOhiVn5hAR3EZHr0lF+ig3sPspdftnhUXcSxkv5jiY+Yi2KbBFdxExkYGJ8b/f12c6Rt+UwpY9uXJqF0V8Gng+s80Dnf1QNY9rpLrqcLnOXmZTV90lOEmNCVbPp/62lndjptnPxTtHvTLi91lC0UVRex+novbJBci1mxnG7pu2K78v9zATYwYNdO8YK5wRHWNh2D1Oe0D2Hi0o86uZ4ucI5HXlbTo3REiAldx9DjO2hz36toR/YKenpwY9i6Ne74Ul94OfDlEesWoVHlEXPdXDi9F71I1Q2TqUfMV/+65v3F9jCbzHMOUZwKTX0oQkzoKl7a+RI9duJV9BKOo9VfXhzbnFLauJDY4GNDSkVEpGKHDb0y/2yIlULQZEtOnZdIJ8TJ0SaOue9iR4xrz0bkmtgpQkzoGkaHR+mhc99No8jooY/dG9ucStq8iZvQbSEaldibtAup9HMqdlQR2z6THFQ1tF2XmxZbRHHaERKdNlelG+j0kwgxoWsYvPJPiQAa/LXPxTYlCqktbqb26Ca2xsDlbtek3G5At01tFrMhaArjlYVOdb6HUbdeXTHXjXO4iHjERIgJGsz/z18iAmj+Jb/P/piKttD2jY1zM+HGV9+mNmYhPSbdsoH7bkdVf5p4zDjqczk+xFjHrMO1bvnSb6H1PPzJ79EwJtKyV8ym4QPDsc2Jhmxs/vBlU2ptLW6qsZO7fcHp1bEV00NDeo+5qPKMpTIndY6v6yOuDxmY3ACo/W7SXhNRbAIwfQuJEBPayvpvraK9OIl+fPzr6YVnXohtjnfasMkJ7aU4v1Lz2HHhks9TxPaazOv09ViMlKjrI5v8K9M61GPyDzXYfG0Vl0eseLx4xITWsu3hrfTMxHNp24RzaNvDW2ObEwSORSM2qdllaw9nO1Lrk5zQdul6iTjqcfUuuW6+Q0Pjz4vr729+8rqtjbHh8nZxtb3sQw0x+rW4josQE1rJC8+8MO4Fw4m07p6Vsc0JhsmikedazZnj2yozUruzt7XHNdzCYYMuITcbjjBfWV/ofl2MD8raZJtLpX6dUehrIbTocG0fd5g0FTF7rEdMQpNCyxg+MDyeD4aJ9PAnvxfbnGRJVYiFWgx167G9I3cNt9jYakuoDV8N/dgkkdd5xPJyZ8/mtvpYG3REV37c4sVHC8S68FWxb0KLy5jCryrXra4PTG92XPL1Ygo08YgJrWJsdIzmX/L7RMD4JyUTIfaFXEbZIpiSfb5xEaKuuVIcoS9OQtVf9Prk9RY/CWsjktetGw8pDQz4DWOpY10lHlSKAtFEPKTqEfMRqlXnhtrmOoFterNjO/axvfTy+AqhVQz++l8RATT4s38S25SjiH0hN5G6fT7Iv0B7YMD83GJ/cW7u3UyV0Cg+G063P4rH6ZzHGQ7TKavo0THxsKb6fYk2Yfema8bGI1YHZ26Zblm+8hdFiAmt4aGP3Tv+1Pxz302jw6OxzTmK2B6PJrjtS729RLweMVdS7C+TcKut/a7lNXkWTUPGpvgatyaB51v4N5VfJzqqyi4KqhRuPjhtyMvy0SYRYkIrWP2VJfQSjhv/HsmdL8U2JzqxN3buRVZnY+AOlfgk9vjoUAwjqq8VxzWFTbWMVO1qQjeMx+HVsy2/LERbl+ZQFZaOeQ1w5uCJR0yEWE/z9OBG2pG9gjb3zaShx3fENicJYm9A3ItsU3tSzaWpog3jMzR0bL6OrQcr1qabwmbvA9/tMg3r6cznsvkUm9jXoS4ixISk2b1pF22YPIt2ZafRxv+I8Ln1RElxA3KxKbWN3rdHwjdl3q4yuOy0ySlqs8cy9viGxlcOle8wMlf5vsdbhJiQLAf3HqRHTv1lOojJtPLv58c2xwvdtKDHvvtsQ25QKHx6J8rCVHVJ57rhTlMx7jJGZTaZlBd7rjdhm4Pngk2f+Mjh8jEmednFD51wIUJMSJKx0TFaOPP9RAA9+OH/Hdscb6S4oHMnZofCti/bln+mS4hEc92QlY5HrMmrVhSWJuOtI+JcyksN3bZwrj+xryOdPDbbevPji49hMbWrChFiQpIM/tIcIoAG3/zJ2KZ4JYUF3WRDrDsvNrb2xL6TT6kfTXOHQnkhy0Kt3B6sbgpX6o5RSjbncNjUNN4hb9p06hIhJiTHwg/9ExFACy/6bRobHWMrV0JX5RQXCt1PGunmIaWOyUalE4prKrNISl5R1ZaU5rirh0PXK+dCSuOokqpdVXDYazIffM9z8YiJEGsdj/z1j+gQJtGK095Mh188xFp2W/IRQuPiEUvtU1LcFPuiKXymCpgQYS7uTaSuDSkJsyK216Nr7o/Ohm6ar7VuHe9jEoaGeMrjKkenHhNR7TovY3m31WNFiAnJsOG7j9MenEJPTrmY9mzezV6+b49YqhuVbT6EzlO/U20zF8WNtm4jCuFNshXNqdflgo5AaBJJNrk/RHp9oiv2VA8z94NDXcdOveny/QGQJnRujmwFkSsm/aweK0JMSIIdq5+jn/RdQNsnvJK2PLg5tjlWhNyoQoS+Ut14y7ANNXD2YwhRGtNLlaroNhFDumNn6sXSuVlpEntNHjEXT5FJ+L2MvP/6+/14xFw8yGX2x1qLxSMmQqy17B/aT2tOeCO9iKm09p8fjm2OFrE9YiFCX6luvGWoX2dke1fahO2Cy0lbxiQ1gWhqT9W8cGmXiafZxKaq93Xnts5xpn1s64Xnmi+prsVViBATojJyaIQWn/2bNIqMltz67djmaBPbW+S60MReKLlRhViIsITu+Kfeb76IfX24UjVuHO2yLcPFI+ZSri5qu1xvFE3bGhMOW0SICVEZvPyPiQCa95t/d9TrKV1oZaRuXxOmm0HqG6vNeHB4N5rONe23FOYVhw0ptIOT/JPEixe7ebWIqvsmxHz0Wa6tR6ws3N70IaDU1yNTRIgJ0Zj37jvHRdjP/NEx73XbhdZE6I2r2zxiNoSYY1whsZCkYIMvbOd9fz+9nEhP5KePXEKEnPaodZSJJO51oFhmXmfdY3HatB7p2CpCTIjC0k98l0YwgZacdS2NHBo55v02XWgcdPPmVySVsU3FDpW25qGl2Jdl6GzyZcehF0FBAAAgAElEQVTffDPRrFnjHjGiMIKkzh7O3LViGeqHCqpEUko3LyFwyUPU6TMRYkJwHp+7gvbhBFo79XJ6cfuL2ueleIFy0ca2+c6v6nXq+olrvvjID0oZnbBX8fiiOHGpO+WQbz6GdY/Z4LxRsD2fO4Sr85rO/HYRySLEhKA8s+Qn9OyEs2nLxBm0feU2o3PbstiHJpaIsx2PFEVnbpNL7o8vm8ps4fKMcF1TKY5pFS4eP5eHrYYQ1i7Yzh3bh+GWhT11+tZlzpadq/Oai0dMBxFiQjD2btlL64+7lPbgZHry22uMz09hsUqRWAK1m8ZDDVm5PvgyxF0+V66QrzFsU1jVpIy8f21EsI2wDontHBwYOCLIXOqr69uy82xummw9Yr7I6wH6VpIIMcE3h/cfpoenvYUOo49WfOYHsc0Jgs88EnURqqunm8QSN2VhFlOPh04IwyX3x5RUxjuWsHCpVycMWee14ag75rjZ2q8+OobI7WbE5NozsTeF/lUpzjVg+hYSISb4ZGx0jOb/1IeIAFr4wX+MbU4wXDejssXD1HOTwp12TrE9vhfHpvKr+sakz3RCGDrlpbZRFOHy2Pmu26XefJwGBvS+9J6z7hTg8uY2zXcXz6Hpcbm4yz/1auIp9vG9mkUBduQB1OIREzwz+Na/JAJo8OrbYpsSFNeFuS6HQtctn9LmUGxPlYjhytOy3RBM+ix/vlTdpp3SGJShs+m45gO54CqQdGnyiLmOo8v5PucQV9nF67fqOq67LoeG3NMDyuoy+aRs8TwTO3Rv/orXkeSICV5Z9EffIAJo0fnvpbHRsdjmvEzqmyOR+Z1m6hTbo4oYdQHmWoh175hdvC2hx8THvFU3nSqhpRO280Ved/FZXmXH+PTAqWNtU5/LXPE5z7jKrrrRKs6pur5TPf5cY2nj2bI9z/bmL6gQA/A2AOsBbABwS8n7UwDc03l/KYALOq//KoAVAFZ3fv+Kcs68TpkrOz9nNtkhQiwMq/7hQTqAKbTy5Gvo4N6Dsc05ipAbKPcdZ+hwjy/UMVAXYJdPpjXhIm7Ljg3djz7mrbrp6H4x9eLFfr1TZdR5H0Ncz+pY29TXKx6xouAyEe+x0xVilR9MiAGYCGAjgJkAJgNYBeDiwjEfBnBX5+/rAdzT+fsyANM7f78OwDPKOfMAXGFiiwgx/2x+4El6PptGmya9mnY+8XwSG79KSHtCiT6Tu7jQG0lTeTYCySa0WBUOtfWI2WJbbyobieq9jEXIfqmru1cZGhoPF/f3H/nqp7L+8C0ifSX4m9jg2r6QQuwqAPcr/98K4NbCMfcDuKrzdx+A5wFkhWMyADsBTCERYkny/LohemrSRTSUnUGbH3iSiNofVnMh1KJtktcQOrSiSzHPpM6+4qe1dOxMZQNtmyeuiE5uXBFum2OtKbH7PhXU9eaii8LdbJbdsMX0uJnMw+ihSQDXAfiK8v/7AdxZOGYNgHOV/zcCOKOknAeU/+d1QpYrAXyiKNyU424EsBzA8hkzZpj0s2DAgd0HaNVJV9MBTKHH7lr08uuyePmh6BXwFdIr1uXrfJNFrUqI+Qi1cHvDXB6RQdTOG5uqnCFbQq0pVZs/Vx5TU30plpvP4Z//+fG+uPlm/2MxNHRs/qjutWRz42Bil27bq67bkELs3SVC7AuFY9aWCLFpyv+XdF57lfLaOZ3fJwH4PoAPNNkiHjE/jA6P0qIZ1xMB9NBHvhnbHBZSF5Bt2pBdwo1lx3A/Bb8uPMrZzxxlxZyXtnXb5Az5RLcdZeFszk/2NdUXolzTMeUQ1bZ16gjgYtn5eM2aFcbWqjKqRGNrQpMAzgXwBICra+r47aKXrexHhJgfBn/+z4gAGnz7p2ObwkbqQid1oajCZWuojcqnRyzVMdOxrcoTyVmHL9S6dedRmb2+855Ce8RMrylXMa72v66Yq6pTx2O8bt24CIv5qdW69SWkEOsDsAnAhUqy/iWFY24uJOt/s/P3qZ3j31VS5hmdvycBuBfATU22iBDjZ8EHvkwE0PxZNyb1mApXUt40Y6PbN9x92IbQTVvR2XByITYwkGZ/6QoOGe8jhOoLVXzpflK3yU7dHEqXNnJ5xKo87sGEGI2Lpdkdr9ZGALd1XrsDwLWdv48D8C2MP75iGYCZndc/DmA/jjyiYiWAMwGcgPHHWTzWCWt+HsDEJjtEiPGy/C+/T8OYSA9PeysNHxiObY7ggTK3uu5dYupexSZMFuG2b+4moeFUQoxFOENwAi9lc8c1x6qtY6rmrQUVYqn8iBDj44l/XU17cDKtP+5S2rtlb2xzeobQi0++ANo8+sHH3WTIMkyEZNtFpwkxNkATocjl+WjrRh+bun7jCG36JEQ90TxiqfyIEOPh2RXP0NaJ59G2CdPpmSU/iW1Oa7FZsEJv+HWJpiHwkaOhS9s8YinYUCT1/MC68rnmTdtD6qZrQIw1iqsf6vK5uOqNkiOW0o8IMXf2PbuPHj/+DbQPJ9CP/+WR2OYcRYobUR11C1b+XvGTQm1rYxkcAqdtIikENnlQvvNnuDZlrjFsmk/qJ3K5PKlV17IroQRPmVe8Dp+PjCjDtB/UcS0Tzaro1FmjXfIORYgJxowcGqElr3wHjWACLbv9vtjmHEMbwkN1i0DxOJOPyrdJbOiOU12bUh/rkONRJiJ0N4mqfrQRWb7Cez49Hqbv11E2DvnrTdeyTRtDesTyJ+lXiSvVllDXZlV/N5HbN2dO+bjoXjscbRYhJhgxNjpG8y79AyKA5r3ni7HNKaUNYsTkgjVpT+rCREW3XXVtSn2sQ45HWV26m0RVGE0nIb94rq82c5Zr4hHjtLNpvjaNIRdcXr66932HYvMxKpujOnUX5zhH1EE8YiLEgjDvN/6WCKDByz/68mupb4Yp0vZ8EU6abNb1HqZIDI+YTj82oXoLYnto6sSRrqdC1zYOsefS/rJwng9ha/ssOM45ZkveH7kXq2yO+rrR9YUIMUGbJbf8G40io8XT/xONDo++/HqbvDDdQgqLBxcm86fb5lqqoaiU5pcqGop21QmKsrnSNH98hVWr0PEm+qjf9aG8NnC1Q8dr6Xv+cpcvQkzQYu0/LaP9OJ5Wn3Al7R/af9R7KS3avUI3CRKT+ePL2xJr7tqMY1vG3lVk5n8PDNBRng+17XWCwkZUlb3vs7+LZbvMx5jXkU6Z+Vj196d9rescZzsnqsoWISY0smXhU7QjO5Oe7ruQdqzZHtscgeILiBSx6ZMYosY11NqWsXcVmWXh0WLbufsilEfKR9mx53KTly1/39b77eqt1O0f9biqT37ajpsaVlXPFSEm1LJn827aMPm1tDs7lTZ89/HY5nijLZubUI3NRsQ57roioS0eLVe4PGJ15+cCgOv5djHWAa7HPPiYy00fWlDncpMQMx0rnbCtj1ww9bg8D2327ObydVDLVG0WISZUcmjfIVpx2q/QIUyiR/92MLY5XumVzbGbsU0k5trAinOoak6lJPpTssWGvI9Tv3br+pl7s+dA9dzo5NStW+f/gc++8/fKyvLxLLSymw2gbyWJEBOKjI2O0cJX3UAE0IM3fS22Od5JbUNKzZ5UsBFb+WtV32/HJcJ9hc18zoW23YCU9bEPARAi5JkT+sGnOuh6xHLaNo/KiNGGIzcS07eQCDGhyOCv3EEE0OAv3x7blJ6kGxY2HzT1S1l4pCzXSC0nddHrcy6EajuXNzLUdcFdTwpzzJcNXGKYM5neZ/0+6hSPmHAMD970NSKAFs78AI2NjsU2pydJYeFOkaZ+KRNivkMavrENucamzOtYfOZT1es6ZYayPWS9VfVzYCsum2zhEq265cR49IZvJEdMOIpH/24eHcIkeuTUN9GhfYdimyMIRqQqSoj0vEI29ofyErl4r8rCw2qZOk/wj0loD7WP/ELbc5vaznWjoHsclxDzuVaYli1CTHiZjf+xjnZlp9GGybNo96Zdsc0JTsqbeDfC3d+pj1/Vhqa+brPhh2q3qW0mnsiUNkVfZdjW5yOfUbdu9X/br30q2uzal1zn+xT/puMkQkwgIqIda7bT5r6ZtCM7k34yf1Nsc6IgeVlh4e7v1MfPl0fMN64bcUyGhpo/+cdZl4/+Ued1iMR+nRsGE4r94us61e1/03C4L1vUY0SICfTSzpfosRN/jvbjeFpz99LY5jjhkg+U4iaYIlz9ZLpYhbJLh9hzJWT9KQhc17Ba8QGaPmzy5c3UybWzpewmYPFi3oeY1tXJSVkovOymx/djNor1VbVVtVeS9Xuc0eFReuicd41/h+Sf/Gtsc5wpWwxT2EjKiL2Z29oQsj9THbvYdoWsP4UQMpc3hrMtdSE3U++MabiXI6xW9BaqojXGJ0Y5Q5bcXj1uO4rHyeMrepzBN45/kdvgO/8mtiksuHjEQqO7KPi032Rhcg1R2bQj1bCYy5i0MWeJE1+eI1915/UXPSl1YULf1zZHfxS9heq1VuU1chHRTV5JTpGkkwbgCx3PXBHxiPUw89/7P4kAmnfpzfKYigj4umv2YQOHHS7nx/ZAcdJNbbEhpoi09ZDlY1b2zQllAsO0jTH6RDdspvN6Uz06XrY231yo2HhGJUesR1n25/9BI5hAS8/8NRo+MBzbHKGGVBYoztCBy7kh+sNnHZxlpzI32oqJ56roJdIVGJx2VNnGPQe4PUqpzdNQ9uiOqwixHmTdNx6lF3AiPX78ZbTv2X2xzYlK3QXZ9g2/LZj2QQiPUkpeKxvPhc86feK73jKPWJnA0rWB61hbTx1RWnOVC9/zQKfPdG0om0M6ZajviRDrMbYt20LbJkynrRPPo2dXPBPbnOjUXZC9tuHHwrQPUhPIMTcNX3XHenq57+uhrPzia67zsWpMiuVyCexuvJnzPQ90+kzXhrKwtU4davkixHqIF555gdYd9zO0FyfR+nsfi21OEohHTM+OtoTqYpDCpsFNLCEWyiOmfvjDxRtFpC/kiuXGENhtoM7DVDzOZdx07HDxiDWtC+IR60EhNnxgmJad8TYaxkRa/qn7Y5sjBITj7s9kUQlhb0qY2tuG9ulshm1oRxWc4rlOEMS+0ePERJi4tMvUE2XryfSNST+IEOsBxkbHaP5rf48IoAUf+HJsc4QaOBZnkztv3XpN3OyuqGW1bbPSIbUNowpXcZ4yoeZVm/qI6xrXPa6qPlvBF8qb6qN8EWI9wODs8Stj8OduiW2K0ADHwm2Si8KFL49YqI0spOBri5ckZriam1i2pjKvdODyeusel9K1XXZM0bPJ8QnZKltEiHU5D33km0QALTrvPTQ6PBrbHKEBHx6xNhH6LjcnFc9FKnakjM2c6IV+dW1j6HXDtr4m0VREp1/KjlFfy/8uPvzWxPY6MSdCrIt57EsP0QFMoVUnXU0Hdh+IbY7QxZgsTK6LJpcdHOdxk4odKWMzR3ohhzFVu3Qwsb1JNJWVbZPvWJfrV1WfztpW9gBgEWJdyuYfbqCh7Ax6atJF9Py6dlyZbV5I2oDtXRx3mKHuE3mhEn0FPVK8JmPb1JY5Fsu7bINJn5Z9tVSdaDItv1ieyfu2a5sIsS5k14adtGnSa+j5bBo99f0nYpujTVsWuLZi07+uibdl+Hw0QsqbTRkp5GH58lC2bSx0aUu7imNX55GJjatHrOl90zGznfe2a5t812SXcXDvQVp58jV0EJNp1RcXxjbHiLYscFWkbr9Pj5hvO1LAh902m4oOXBubS5u5bqx6Yb74vM7yZ6blniSdhHz1OWupYXrzEnLdsz0PmL6FRIh1B2OjY/Tg+e8jAmjRH349tjk9B6dHz2VhbuvGlTo+PLa+PGImttbVkcI8bGqLL/tdyzEZA5/RALXspnaoXrO2RCd025RKW8rsFY9YFzF4zSeIABp8y6dim9Jz6CSEmuCyeMReeFISgpy2pNSuJrjyg2LPJSK3jZbLfhsxGNsj5mJHyh6xIi5CXed9bsrslRyxLmHBB+8mAmjBa36XxkbHYpvTc3BvWCl4ImxJYfNO0ZaYhAhxxiIFj1g3zLPQ4TguXOvXEXKcN9nlHjERYq1nxWcfoMPoo+Wn/yod3n84tjlBib0IpGaHLr7vwG2+K84HbRsXW1K76+8WdPutjSKmWLetmGy7CNUV2T6/hF2EWMt58ttraA9OoSemvI72PL0ntjnBafsi4JuqRcF3v+mU38tjx70Bu/SlqS0piQff9eSfgot5nZTB0Q/FukOIyTbeEJh6xMrGtKndIsRazPZVz9KWiTPouQln0daHno5tThTacGH7vquuo2qh991vOuW3SQBwMjTEnwzt0jemYiCGgA4ljHLyNs6ZE/86KYNjDGJcTynefNmEtuvEWdk5de0eGiL51GRbeXH7i7R26hX0IqbS419bHtscoQbdxcfHIqUuCm0XMlzPH+PO+TAlH+dUnudkI4hD918oYZST+rWSun1VxLK7rt66dbfqPTVcqXMdN9d/OZEIsXYxcmiElpz1ThrBBFr68e/ENqdn8O26971IpXg3agKXEKvK+Qgd9mqzOPZ902DynsBHt/Zzk0dKx7tV/HvOHKL+fvfrQDxiLWXe6/8rEUDzrvsCa7ndehFy0XYh4yNcGBIu26oWXp1PT4UKHacO11xSj2lrX/gk9PUYWmCHoknk54Kq7ibPJvdLF8kRaxnz3vX34yLssv/GXrYshPWksKD4xmQOdFt/NLWnWzcpX5h+YCOFvEXfdZnaEHpNDn2zkcL8Vz3kdULMp61BhRiAtwFYD2ADgFtK3p8C4J7O+0sBXKC8d2vn9fUA3qpbZtlP24TY3LlE559P9A78O41gAg2e8k4aOTTCXo/rREvhohLcMBnDbtgk2lQ/NykIH04bYgjpKppyi3RtaNucK7PXNj8rFENDRAMD414x9YvEi8f4HIdgQgzARAAbAcwEMBnAKgAXF475MIC7On9fD+Cezt8Xd46fAuDCTjkTdcos+2mTEJs7l2jqVKI3YDm9iKm0FG+kace9SHPnxrbsWGJdVG1brLqFbgib1NGGeeViYwqbICcmoWWbfjM5h8MjxuVVC0lbhWaT3b694SGF2FUA7lf+vxXArYVj7gdwVefvPgDPA8iKx+bH6ZRZ9tMmIXb++UQn4gV6BmfTUzifzsRzBIy/nhqxLqpu21B0SCHMEhrfm2eRNswrFxtDjasPr1fZV/DYeHNNPrkaej5wedVC0taoSlO9vkO2IYXYdQC+ovz/fgB3Fo5ZA+Bc5f+NAM4AcCeA31Je/8dOeY1lKu/dCGA5gOUzZszg603PZNl471+Pf6HXYu3Lsewsi21ZOqQiFEKSQpglFLHEVBvmVRts5Jw/qoDSKbPOq2T6LLfQfa3jEfNpU7Fs3bpcbphCPScuBWJ5xN5dIpq+UDhmbYkQmwbgiyVC7F06ZZb9tM0jlosv9SdFj5jQDNfC2UsesXzz7e83f3ZVbNuFcB6xMkIninNf303t9HmTVCxbty4bm/JzQj0njhvXcZfQZOLkOWKqCJs6lZLMEROa8Z1rwHFcaqjeC9e+W7duvKyqpNxUSWnsTMUQV3029XBfG03HmVzfdZ4tXc9ft3nEXNoRylNYhuu6HlKI9QHY1Em2zxPrLykcc3MhWf+bnb8vKSTrb+ok6jeWWfbTJiFGdORTk1k2/ltEWHhS9mT5vFNNhaEhu6e5F/s739hmz/ZhpT9SGjvT8CBXfT7rqaqjSiBxCCO1rGK5ocVuaHyvg6Gvl9Z4xMbrwmwAT3RCjrd1XrsDwLWdv48D8C2MP4piGYCZyrm3dc5bD+DtdWU2/bRNiAnxsb3TDYGPO9WUPDAqpnYVx63JI9Yt7TY5z7Ts1D1inB6ZKoHEGWaN4cGpsyUEusLXBNP+rDsmdJQhqBBL5UeEmGCK7Z1uW0m1DaZ2mS6oNsnCsTfROnT6K9WxtkENY3O0J8Wx5Q7jEYWfA1U3RCHtUD27TQK8qYym48rGTH1NhJggMOPrrjkkqW5Avr5s2iVZOGUh48MjljJ1mysHPkSQKRxeOo4yXLxGph4xW29+k9erSrRze8Ty9qofOFL7QISYICSMzSbfTRurik/BwxUS4So/pTFMyZYmfNvKMQddy+DwZnH0k66YK7PPNcVA99im80J9eEcVfWVf6SVCTBAShuNu17ac1GhzG0w3S99etl4Ltevg03voMx/M93Wh66XykfdlU4ZOX5ukInD1b51HX4SYIFRge/HHxiQUIBzB5xjmZesmuPuyxTQXzjUcnNJ1UYZqn89rpM3Xn264lyt1IMSc0U1FqAtf2lJs37hHbPoWEiEmCMdi6w5PkdQ3xBQIMYa+c5h069fNhXPtk1DXhe38Vu0zCVO5hppjXo9NeVPF90zESAqhWx1Mc7s4r9di+8b/v5xIhJggHEtbPWKCHSHGcN06olmzjl6Ibeo1CXXZhMWqPHip5rrZbt62HjFugRpyramzvUqo64Zt6zxipnMvhdCtj/krHjERYoIgRKTsDttmUzdJSHYpv+gJqCurypviIjJ9nuNShmt9TflVdeWbjKfpmLjkTjXNDdWrFvLGtcwurrmqg05dkiMmCJHpNm9a6PZU1ceVs8JlT9V7pscXXzfxiJm0oSwcVVdWvnnPmXPkNVeR6ZOUwoOmokbXbtO+rPKE6pStIx5zYe9zjOv6tk5o+rKprNziayLEBCEyoTaeUHCEiTjqy18PfRfOOZ4x54Zpf5UJMRfvVpMY8Bmi802TiOGaq6bluHrbdI/1eS3WtSGfowMD8TxiZTeIIsQEwZCUchhShFtQ2dZXXPDa6Glp09zQsZXLm1PlseO21xcmHrCYdqWKjReZiP9mwUaElo21CDFBMCSVRbPbcNkEuEWA0IxNf3J5XPINtb+/O8azzXNTRxTphDp9hlzr6uAKn1fZrxPCFSEmCIa0edG0oQ0eHk5xHHJ82zCXdDcYl7JMKfNspEIKHvOQ86puHqi5YU2PgWiaT2W5Xhw3bTY3cWXhxSr7dcoXISYIkUl9M25DzhPnV5WoNvoeG5/eVZfwiY6Npn1TdrytJzPla4Z7TLk8Ni7YhgJVj1hTKLlpTF3blJev+zDjprp1PF26iBAThMikHuoM7RHjDnm5CAbfY+NTUJjYHiKJWWczqzvP5gvZY8DluSkrz+c5dXDcnLja5Hpj4TKPfN8MiBATepKU7qhTssWElMKMNh4d13JjYLMZ6TyUVc250v3qI1+bWVXoqM6TETscWNUO7q/HcbXT9ryqm5NYItHGe5batawiQkzoSVL3QuWkvHj46kObHA6T8kLDaT9HmKpuk1q3Tu/Zaz6vH5tQqK9woJrTZFp/WRnc2Lab6+YkVti0qYymay72mlBEhJjQk6R2IVZhsmiFblOo+rg9ZKFxvTvn9kBw5OL49MRwe1l0yyuGFIverLp+8RG68tVXOufpzJmhoXLRHkIEuZahftiDw/vpiggxoWfh9rz4wHbD7iZsxiWUt073nDlzxvOvbJ5pFnqe+iw/hJfIts7imMReH2Jezzpe1Cr7QtjNKcRM7bVtX53NIsQEI2KKFe66dRabNpGikKzDp70+PBRE9l6RfOHn+DSmqccqpXlR5mnKX+cWPWq4VSdXK6V+IvJnj42nzeR64vwEcxWugr7u+vDl0au7bkWICUakdJdWhslFEvuOVwefG1TsMkLPJY766tpd5zXIQzgc33ups9GptqR2g1Fmv8lNke7cU8tI8doORbHtvudDKI9YUVybCsyq42N400WICUak7hFLbdNR4QixcbSvrAxT23yLGh/ECOn5yD9ps0eMqHn+5aHcKtGqO/dSa3csiv2Vemhb93wbgalzgxJj3ogQE7qKlBdfG/ESyiNmalsK/VxnQwr22dA0Dk0ipQ00jY1OH5iObarzocouTntTbXsVtjd5XB6xGIgQE4RApHThF0nZtirqFuzUPKO2d/lFUmsXJ3nbdb6X0JRUPbi5XcVcp24e5zrKbjRCCO/Y658IMSEZYlwMPhd/nXp91udSR6yFyaReE49YbA8D18Yae8OowtRTx+GVNamDo99y+zif8D80pPfhhRCkMLfK5oDNvDD9LlKXuWfqiStDhJiQDCHvAvMLI79guZ+AHcuzoW6INt+p5ts+X/WG7G+OEHO3kfeJbr805Ylx2sR9TbtcV3Xlxp4bPkOCLmXZeLfyb4jQfU6YbRt0hXSTiBchJiRDyAWpeGFwe8R85LmY1Ot6594Gj5iKTX+7LL4pbJwp2cLhEbOtlyNP0NexuoQaR67+Uo83EaYhPNPFcK/Pm0rd0HJTX4kQE3oS3wtfTCETOpk7BTEQM1xoCmd/9WouUQ5X+129nK5CP9Q4+vAMm9zwhfBMq2ug7ld25eeZXpdVc6BqPlTZIkJMECpIQWCYEMvetooB14XXFs7+SnWOpuDh8V2OOo6uuU0u7fDpzeP0oBHxPuy1rn7VU+USLjeh6fy690WICUIBX7kgvukGD08MQnsuUu8vH2KTMzScCkUPiMun/Vz6IkTorS7/qeq10Laq5IJv8eIwY7Bu3Xhe2sDAsefn5dalv4gQE4QCNi73FGj7xhYLdXNo6sOmO/o2jUFTjo3uZqmzMbt6jGzawX1OUxku7XE512feVVnZLmMZ6voIfVOae976+/X6q4gIMaFVhLiQOd33LuUKYVDHxSW8oPO+rh0hqMuxMbFDp80+PWI2fc6xUet4/XRJZW0INZa+2+ur/Kpy8xu0gYFj+0/HFhFiQqtIMTSka1Os0KGgT9PccH2/jqb5we354PhQB1c5LtjcCPnwiHERs0+7wWPlsw3c1+iRm7++lSRCTGgLPvJXQtmUyl2vKW29e20bTf1gM2+bwo8mX0auG6ZKjdxum5xP27nJIciLDyTltCX2NRdTLLnY4+smHpi+hUSICb1E7EWobZjkULmWrwO3N6Mt88FmQ20KP+biRCcnslhWXYJySqiiU3ecXcSbWqdpiCo/TgfpkgAAAAvySURBVH0gaV2ZTfZXhdtTDaHH8lTq9oerfUVvp3jEBCEgITb7vA7uh9M2Leqc5de9lsOd39MGr46KyXjohFJ1v4mhWFaeoDx7tmODGuDY/Gw3ZtsP7Lh6D129WE03Ty7eNe5vIVFx7XdbdPvDda1QvZ1qGZIjJggBcNkwTRcJnwtlCjkkHM8iMvWIpeQ18+WhNC3LdBxsbY0hlH2E80J6knzVpa4xPtuR6qODuD1iOSLEhKRJaQN0wTaE1PReWR2hv8DcB749Yqa4hJq4qVrMU8f2ZiSUyGiyJ2XPKZdtOh7UUH3fxjleRVO/iRATkiblxa8O0wWLwyPGQSp21BHDDtdQU1NZpscW6/bdJ5y5O1U3Crptqut3zn7w1ce6gpOjTN1zUvRExVr7fXg+m9oiQkxImlQ2f1PaKiA5PHMpETIcpFufST9WHRvaW8NZvmub6sLKNnaaCiPXOVVlYy6C1AR9n6j15TapuVkx196YHjHXuW7jPRchJgTH1wKXEm1ti4lHrA1tDC0ederj8Ii5lGkDZ/mcbeLwWpnOEdc5VWVjLowGBsJcV6oQq/PiqPlgoa550z7mDKm6zk+bPhIhJgSn6iJro8ell2nDeIUWiyFzaGKIYM4NL4Q9Psrw1cbQ4UGdsSx+8KfotfM1H0zPa1qLfKxVnGJRhJjAis4F1AsesV4gtLdG5scRykJJOvgKq9W9L+Nmhs366LLumthSFGJN8yFUuDXGDYJphKCur4IIMQCnA/gBgCc7v0+rOO6GzjFPArih89pUAPcBWAdgLYBPK8f/NoAhACs7Px/SsUeEmD/a4CWJQds2o9zeqsRqk/ZwzYm2zS3XjbOuzHxcdL0nXN4Wmw2vbeOWKnX9qL5XNUYc4zA0VP5A0qr5EDrvLSZN/av2VbHfQgmxzwK4pfP3LQA+U3LM6QA2dX6f1vn7tI4Qe1PnmMkAFgJ4Ox0RYnea2iNCzB9tExyc1LXd92bE3e9qfohrGDmURyy1uae7cbqUqdtmWw8aB6mNSxMu9vpsq66wLxvrooBygfvab9v8qMJkfSr2YSghth7A2Z2/zwawvuSY9wL4kvL/lwC8t+S4zwP4LyRCTEiMugXK92LDLfSaPGIcD1XlJjXPC7dHzGUzTWGzS8EGHVzmEWfekO25Zd5PDrua1gRbUrtufVHntQwlxPYU/t9dcszHAHxc+f8TAD5WOObUjqdsJh0RYs8CeAzAvQDOq7HhRgDLASyfMWOGh24Wep2YG03oulNcPDnv+lMkxT43oS32u1xLpjcoJuEsl3NN21RWtq/xa4tAd6WunWxCDMADANaU/LxTU4gNlAixjyr/9wH4HoD/prw2DcCUzt83AfiRTmPEIyYIbqS6eLZls7eBo89dc9Ni1N0mTEPAugneZV8pFDoMqltfk6eum8ffltaEJgHcDeDva+qYCGCvjj0ixASBh9QW15D2pNZ2Hbhy02zh7rPUxsDmQxFNIWyO747NvcUDA8d6jLmFU9Vc6aabJO55F0qIfa6QrP/ZkmNOB/BUJ0H/tM7fp3fe+wsA/wfAhMI5Zyt//yaAJTr2iBAThHFcF5RuWlxNSbXt3LlpLucV4e6zGB8a0cGkrqY2cORj5nXkP+qHPTg+kKOiI+x8j4VJ+TYpDa59U8yzCyXEpgH4IcYfS/FDRWBdAeArynG/A2BD5+eDndfOBUAAfozCYyoA/CXGH2mxCsAggFk69ogQE9pOKhtjah6JkKTa9lQFIhH/Js0peHTwMea64UkfHrG87P5+fU+Zbn2+21RHXflF21SRWjzel7cwF795yDmIEEvtR4SY0HZSDRV1G75EgU9i22GTS6TOZ5NNlGN8Qos5U1xzs3LKPGs2oVQdTD5I4IMqz1OZbXUeMfVYzjzJfCzyskWICUIEXC/q2JttHSnZxh16rSvPREDYEKtfTevVFStVm5xJH3MIo1TDm6Y0tUP1whThbhdXea7iuaxPdM4tE3Lc80Q9RoSY0BX4vvA5qPIAxIZbJKTUNu7Qq63YCi0YONGtt84LUXe8ybxz8YjplFlWXlu8ojYeMZ3zYlI190znpG0I0VTAFc+v+vRssSwRYkIScHsubOv2udlxu7l92MVRRkptS+VOvxc8YjoilfthoNyUtcHk+gghlrnngW9R4wJHONmmLq6IRVXIt9jnIsSEJOD2XNjWrbNhuGzGnA8c5drcOWxKSXylju9NJFZZOh7BWbP8CxUX2uAR4/7+xjqbTW5S274G+BDRukIS6FtJGtolIyJ0C1mWDQF4OrYdFpwB4PnYRvihrw84cxqwYycwMsJUqGZ/ldU9/ZXA2ecCz24Ftm0/+vi695qoO9e0D1zsKC1jFF07v7xhcU1yjJvPMpvKsrlW+/qAmRcAJ50C7NsLbNpsdp17WR9aUHfZ/Dr3bOCV04Ht24Ctz/qtXp0LO3Ye2w9q35w5jXde52Xv3gOcdqpB/1vuk1XjHGL8j59F9NKJTUd1lRBrK1mWLSeiK2Lb0Rakv8yQ/jJH+swM6S8zpL/M6eY+mxDbAEEQBEEQhF5FhJggCIIgCEIkRIilwf+KbUDLkP4yQ/rLHOkzM6S/zJD+Mqdr+0xyxARBEARBECIhHjFBEARBEIRIiBATBEEQBEGIhAgxj2RZ9rYsy9ZnWbYhy7JbSt6fkmXZPZ33l2ZZdoHy3q2d19dnWfbWkHbHxLbPsiy7IMuyA1mWrez83BXa9hho9NcvZln2SJZlI1mWXVd474Ysy57s/NwQzup4OPbXqDK/vhPO6rho9NkfZ1n2eJZlj2VZ9sMsy85X3pM5duz7df3Vc3NMo79uyrJsdadPHsyy7GLlve7YJ3We+io/5j8AJgLYCGAmgMkAVgG4uHDMhwHc1fn7egD3dP6+uHP8FAAXdsqZGLtNiffZBQDWxG5Dgv11AYCfBvBVANcpr58OYFPn92mdv0+L3aZU+6vz3oux25Bon70JwNTO37+vXJMyxwz6qxfnmGZ/naz8fS2A/9f5u2v2SfGI+eNnAWwgok1EdBjANwC8s3DMOwH8c+fvewG8OcuyrPP6N4joEBE9BWBDp7xux6XPepHG/iKizUT0GICxwrlvBfADItpFRLsB/ADA20IYHRGX/upVdPpskIhe6vy7BMC5nb9ljpn1Vy+i018vKP+eACD/hGHX7JMixPxxDoAtyv9bO6+VHkNEIwD2ApimeW434tJnAHBhlmWPZlk2P8uya3wbmwAu86QX55hrm4/Lsmx5lmVLsiz7DV7TksW0z34XwPcsz+0GXPoL6L05ptVfWZbdnGXZRgCfBfBHJue2gb7YBnQxZV6a4rNCqo7RObcbcemzZwHMIKKdWZZdDuDbWZZdUrib6jZc5kkvzjHXNs8gom1Zls0E8KMsy1YT0UYm21JFu8+yLPstAFcA+CXTc7sIl/4Cem+OafUXEX0RwBezLHsfgI8DuEH33DYgHjF/bAVwnvL/uQC2VR2TZVkfgFMA7NI8txux7rOOe3onABDRCoznC7zGu8VxcZknvTjHnNpMRNs6vzcBmAfgMk7jEkWrz7Is6wdwG4BrieiQybldhkt/9eIcM50j3wCQewq7Zn6JEPPHwwBenWXZhVmWTcZ4YnnxUzDfwbiyB4DrAPyIxrMQvwPg+s4nBC8E8GoAywLZHRPrPsuy7BVZlk0EgM7d5Ksxnhzczej0VxX3A3hLlmWnZVl2GoC3dF7rZqz7q9NPUzp/nwHgagCPe7M0HRr7LMuyywB8CeOiYofylswxg/7q0Tmm01+vVv79NQBPdv7unn0y9qcFuvkHwGwAT2DcO3Nb57U7MH4BAsBxAL6F8STDZQBmKufe1jlvPYC3x25L6n0G4F0A1mL8UzSPAHhH7LYk0l9vxPid434AOwGsVc79nU4/bgDwwdhtSbm/APw8gNWd+bUawO/GbktCffYAgO0AVnZ+viNzzLy/enWOafTX5ztr+0oAgwAuUc7tin1SvuJIEARBEAQhEhKaFARBEARBiIQIMUEQBEEQhEiIEBMEQRAEQYiECDFBEARBEIRIiBATBEEQBEGIhAgxQRAEQRCESIgQEwRBEARBiMT/B9POiPuqssD7AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N=50000;\n", "sigma_e=2.0;\n", "moyenne4_d_x=np.zeros(N);\n", "std4_d_x=np.zeros(N);\n", "for i in range(0,N):\n", " x=arbitraire(d+1,sigma_e);# tirage au hasard dans le simplexe\n", " moyenne4_d_x[i] = np.dot(mu_d,x);\n", " std4_d_x[i]=math.sqrt(np.dot(x,np.matmul(Gamma_d,x)));\n", "\n", "# plot ###################################################################\n", "def plot8(): \n", " #plot7();\n", " \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", "\n", " # On materialise les 4 actifs de base\n", " plt.plot(std_actif, moyenne_actif, 'bo');\n", "\n", " # les portefeuilles tirés au hasard\n", " plt.plot(std4_d_x, moyenne4_d_x,'b.',markersize=2);\n", " \n", " # la frontière sans aucun emprunt\n", " [frontiere_m_1,frontiere_s_1] = frontiere_efficiente(moyenne_d_x,std_d_x)\n", " plt.plot(frontiere_s_1, frontiere_m_1,'-g',markersize=2); \n", " \n", " # la frontière où l'on peut emprunter l'actif 1\n", " [frontiere_m_2,frontiere_s_2] = frontiere_efficiente(moyenne2_d_x,std2_d_x)\n", " plt.plot(frontiere_s_2, frontiere_m_2,'y-',markersize=2); \n", " \n", " # La frontière définie par la droite de marché où l'on peut emprunter l'actif sans risque\n", " plt.plot(sigma_P, x_P, 'ro')\n", " plt.plot(np.array([sigma0,sigma_P]),np.array([r0,x_P]), 'b-');\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]), 'r-');\n", "\n", "plot8();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut vérifier que tous les portefeuilles restent en dessous de la droite de marché." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ce programme est paramétrable pour des valeurs de $d$ et $\\rho$\n", "arbitraires, si vous souhaitez expérimenter par vous même. Toutefois\n", "des problèmes d'échantillonage se pose lorsque $d$ devient grand (au\n", "delà de $5$, la loi uniforme sur le simplexe \"a du mal à visiter les\n", "coins du simplexe\", c'est une réalité géométrique incontournable)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Partie optionnelle: solution des problèmes d'optimisation associés" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "source": [ "### Calcul du portefeuille de marché par optimisation" ] }, { "cell_type": "markdown", "metadata": {}, "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": 300, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: -7.500000\n", " Iterations: 38\n", " Function evaluations: 57\n", " Gradient evaluations: 57\n", "Lorsque rho=0, vérfiez que ce qui suit est petit, sinon vous avez un problème ...\n", "1.2941033662151341e-08\n" ] } ], "source": [ "from scipy.optimize import minimize\n", "\n", "# Choix des caracteristiques des actifs sans risque\n", "d=30;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", "def cost(x):\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", " lambd=np.append(1-sum(x),x);\n", " ps=np.dot(mu,lambd);\n", " var=np.dot(lambd, np.matmul(Gamma,lambd));\n", " # On cherche à minimiser (lambd.mu)^2 / lambd'.Gamma.lambd \n", " f = ps*ps / var;\n", " return -f; # On maximise mais Python suppose que l'on minimise ...\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", " lambd=np.append(1-sum(x),x);\n", " ps=np.dot(mu,lambd);\n", " var=np.dot(lambd, np.matmul(Gamma,lambd));\n", " k=(2*ps/var)*mu - (2*ps*ps/(var*var)*np.matmul(np.transpose(lambd),Gamma));\n", " # Calcul de la dérivée par rapport a |$x$| \n", " # en fonction de la derivee en |$\\lambda$|.\n", " p=np.size(x)+1;# dimension de |$\\lambda = 1+dim(x)$|\n", " g=k[1:p]-k[0];\n", " return -g; # On maximise mais Python suppose que l'on minimise ...\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": "markdown", "metadata": {}, "source": [ "### Calcul numérique de la frontière efficiente (Work in progress !)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La frontière efficiente peut se calculer en résolvant une famille de\n", "problème d'optimisation classique~: minimisation de variance à espérance fixée\n", "et/ou maximisation d'espérance à variance fixée." ] }, { "cell_type": "code", "execution_count": 301, "metadata": { "scrolled": true }, "outputs": [], "source": [ "def x2lambda(x,R,mu):\n", " # construction de lambda a partir de x\n", " # en tenant compte des contraintes |$\\sum_i \\lambda_i =1$|, |$r^T \\lambda = R$|\n", " p=np.size(x)+2;# dimension de lambda = 2+dim x\n", " alpha0=1-np.sum(x);\n", " beta0=R-np.matmul(mu[0:p-2],x);\n", " lambda_n_1 = (mu[d]*alpha0 - beta0) / (mu[d] - mu[d-1]);\n", " lambda_n = (beta0 - mu[d-1] * alpha0) / (mu[d] - mu[d-1]);\n", " lambd=nappend(np.append(x,lambda_n_1),lambda_n);\n", " return lambd;\n", "\n", "def cost(x):\n", "# On minimise la variance \n", "# f = lambda'*Gamma*lambda\n", "# sous les contraintes |$\\sum(\\lambda)=1$|, |$r^T \\lambda = R$|\n", " p=np.size(x)+2;# dimension de lambda = 2+dim x\n", " lambd=x2lambda(x,R,mu);\n", " k=np.matmul(Gamma,lambd);# derive en fonction de lambda\n", " lambd = np.transpose(lambd);\n", " f = np.matmul(lambd,k);\n", " return f;\n", "\n", "def cost_der(x):\n", "# On minimise la variance \n", "# f = lambda'*Gamma*lambda\n", "# sous les contraintes |$\\sum(\\lambda)=1$|, |$r^T \\lambda = R$|\n", " p=np.size(x)+2;# dimension de lambda = 2+dim x\n", " lambd=x2lambda(x,R,mu);\n", " k=np.matmul(Gamma,lambd);# derive en fonction de lambda\n", " for i in range(0,p-2):\n", " # derivee par rapport a x (et non lambd)\n", " g[i]=k[i] + (k[p-1] * (- mu[p] + mu[i]) + k[p] * (- mu[i] + mu[p-1])) / (mu[d] - mu[d-1]);\n", " return g;\n", "\n", "\n", "# Choix des caracteristiques des actifs sans risque\n", "d=30;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", "x0=np.ones(d-2)/d;\n", "i=0;abscisse=np.zeros(1000);0;ordonnee=np.zeros(1000);\n", "for R in frange(0.05,0.001,0.15):\n", " xopt=minimize(cost, x0, method='BFGS', jac=cost_der, options={'disp': True});\n", " Xopt=x2lambda(xopt.x,R,mu);\n", " i=i+1;\n", " abscisse[i]=sqrt(xopt.fun);\n", " ordonnee[i]=R;\n", "\n", "#plt.plot(abscisse,ordonnee);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calcul explicite de la frontière efficiente" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Toujours en ignorant les contraintes de positivités, on peut\n", "obtenir une forme quasi explicite pour la frontière de Pareto, en utilisant\n", "deux multiplicateurs de Lagrange (l'un pour $\\sum_{i=1}^d \\lambda_i=1$, l'autre\n", "pour $\\sum_{i=1}^d \\mu_i \\lambda_i = r$).\n", "\n", "On obtient après quelques calculs simples, si\n", "$$\n", " A=\\mu' \\Sigma^{-1} \\mu,\\; B=\\mu' \\Sigma^{-1} {\\mathbf 1},\\; C=\n", " {\\mathbf 1}' \\Sigma^{-1} {\\mathbf 1}, \\;D= AC - B^2,\n", "$$\n", "la paramètrisation suivante de la frontière de Pareto~:\n", "$(\\lambda'\\mu,\\lambda'\\Sigma\\lambda)$ où $\\lambda$ est la fonction de\n", "$r$ suivante~:\n", "$$\n", " \\lambda=\\frac{BC}{D} \\left(r - \\frac{B}{C}\\right) (\\lambda_\\mu -\n", " \\lambda_g) + \\lambda_g,\n", "$$\n", "où $\\lambda_g = \\Sigma^{-1} {\\mathbf 1}/C$ et\n", "$\\lambda_\\mu = \\Sigma^{-1} \\mu/B$. On peut vérifier que seule la\n", "partie de cette courbe correspondant à $r \\geq \\frac{B}{C}$\n", "appartient à la frontière de Pareto.\n", "\n", "On pourra se convaincre que $\\lambda_g$ est le point qui __minimise__ \n", "la variance des portefeuilles sous la seule contrainte\n", "que $\\sum_{i=1}^d \\lambda_i=1$ et que $\\lambda_\\mu$ est le point qui\n", "__maximise__ le ratio de Sharpe\n", "$\\mu' \\lambda / \\sqrt{\\lambda' \\Sigma \\lambda}$ sous la même\n", "contrainte (utiliser Cauchy-Schwartz pour s'en convaincre).\n", "\n", "Voir T.J. Brennan and A.W. Lo, 2010, \"Impossible frontiers\" ou Merton, R., 1972, \"An analytic derivation of the \n", "Efficient Portfolio Frontier\"." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 2 }