{ "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", "$\\newcommand\\Var{{\\mathrm Var}}$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1. Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On considere $d$ actifs dont les rendements sont donnés pas\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": [ "## 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", " $$\n", " X_T=x_1(1+R_1)+x_2(1+R_2)\n", " $$\n", "\n", " Vérifier que si le gain $G_T$ est défini par $G_T=X_T-X_0$,\n", " $$\n", " G_T=X_T-X_0=x_1R_1+x_2R_2\n", " $$\n", " $$\\E(G_T)=\\mu_1 x_1 + \\mu_2 x_2=\\mu_2 + x_1(\\mu_1-\\mu_2)=x.\\mu$$ et\n", " $$\\Var(G_T)=x.\\Gamma x=\\sigma_1^2 x_1^2 + \\sigma_2^2 (1-x_1)^2 + 2\n", " \\rho \\sigma_1\\sigma_2 x_1 (1-x_1),$$\n", " car $x_2=1-x_1$.\n", " \n", " \n", " On rappelle que $x=(x_1,x_2)$ et $y=(y_1,y_2)$ le produit scalaire euclidien est noté $x.y=x_1y_1+x_2y_2$." ] }, { "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": 176, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "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", "# Matrice de covariance: des 1 sur la diagonale, des rho ailleurs\n", "rho=0.0\n", "\n", "# Compléter\n", "covariance= np.eye(d) + (rho * (np.ones((d,d)) - np.eye(d)))\n", "\n", "sigma= np.array([0.1, 0.3])\n", "Gamma = np.dot(np.dot(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 une 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", "\n", "plot1()\n" ] }, { "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": 177, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def frange(start, stop, step):\n", "#exemple:\n", "#for i in frange(0.5, 1.0, 0.1): print(i)\n", " i = start\n", " while i < stop:\n", " yield i\n", " i += step\n", " \n", "#On peut remplacer par np.linspace(0.0,1.0,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];# startégie \n", " #Compléter\n", " moyenne_x[i]= np.dot(current_x, mu)\n", " std_x[i]= math.sqrt(np.dot(np.dot(current_x, Gamma), current_x))\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": 178, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot ###################################################################\n", "def plot3():\n", " plot2();# le plot précédent\n", " #Compléter\n", " \n", " plt.plot(min(std_x), moyenne_x[np.argmin(std_x)], 'go') # point de variance minimale\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": 179, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# On autorise l'emprunt de l'actif 1\n", "N=100\n", "moyenne2_x=np.zeros(N)\n", "std2_x=np.zeros(N)\n", "\n", "for i in range(0,N): # on s'arrete à N-1 pour avoir N terme en tout comme moyenne et std\n", " # quantité négative = emprunt de l'actif 1\n", " #QUESTION: x_1= # QUE VAUT x_1; \n", " x_1= -5 + i * (5.0/(N - 1))\n", " x_2= 1 - x_1\n", " x=[x_1,x_2]; #stratégie \n", " moyenne2_x[i]= np.dot(x, mu)\n", " std2_x[i]= np.sqrt(np.dot(np.dot(x, Gamma), x))\n", "# plot ###################################################################\n", "def plot4():\n", " plot3();# on garde le plot en rouge 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": 180, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Que se passe t'il lorsque l'on emprunte l'actif 2 ?\n", "N=1000\n", "moyenne3_x=np.zeros(N)\n", "std3_x=np.zeros(N)\n", "for i in range(0,N):\n", " #quantité négative = emprunt de l'actif 2\n", " #QUESTION: x_2 = # QUE VAUT x_2;\n", " x_2= -5 + i * (5.0/(N - 1))\n", " x_1= 1 - x_2\n", " x=[x_1,x_2]\n", " moyenne3_x[i]= np.dot(x, mu)\n", " std3_x[i]= np.sqrt(np.dot(np.dot(x, Gamma), x))\n", "\n", "# plot ###################################################################\n", "def plot5():\n", " plot4();# le plot précédent\n", " #Faites le plot en 'b-'\n", " plt.plot(std3_x,moyenne3_x, 'b-')\n", "plot5()" ] }, { "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 $0$.\n", "\n", " 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 $simplexe(d)$ figurant dans\n", " \"utils.sci\" pour $d=3$ fait ce travail." ] }, { "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": 181, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.01563159 0.28129922 0.70306919]\n" ] } ], "source": [ "import numpy as np\n", "\n", "\n", "def simplexe(d):\n", "# tirages de d nombre positifs\n", "# de somme egale 1\n", " t=np.random.rand(d-1); \n", " \n", " t=np.sort(t)[::-1] # classer t dans l'ordre décroissant\n", " t=np.append(1,t)\n", " t=np.append(t,0)\n", "\n", " \n", " s=np.zeros(d) # initialisation [0,0,0] \n", " for i in range(d-1,-1,-1): # range(start, end-1, step) exple d=3 on a range(2,-1,-1)---> (2,1,0)\n", " # compléter\n", " s[i] = t[i] - t[i+1]\n", " \n", " return s\n", "\n", "#on tire deux points au hasard entre 0 et 1 puis on les range dans un ordre croissant x_1" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# On rajoute un actif sans risque de moyenne nulle\n", "r0=0.0\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", "# comme ce rendement est suppose deterministe, la matrice de \n", "# variance covariance se complete par une ligne et une colonne de 0\n", "#QUESTION: Gamma= # QUE VAUT GAMMA DANS CE CAS\n", "#REPONSE: \n", "\n", "#Gamma = np.insert(len(Gamma), Gamma, )\n", "Gamma_d = np.vstack((np.zeros(d), Gamma))\n", "Gamma_d = np.c_[np.zeros((d+1, 1)), Gamma_d]\n", "\n", "x=simplexe(d+1)# tirage au hasard de la stratégie dans le simplexe\n", "moyenne_actif= np.dot(mu_d, x)\n", "std_actif = np.sqrt(np.dot(np.dot(x, Gamma_d), x))\n", "\n", "# On materialise les 3 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\n", "N=1000\n", "moyenne_d_x=np.zeros(N);# initialisation à 0\n", "std_d_x=np.zeros(N);# initialisation à 0\n", "for i in range(0,N):\n", " #Compléter \n", " x=simplexe(d+1)# tirage au hasard de la stratégie dans le simplexe\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", " 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": 183, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.8719353]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# On genere des portefeuilles sans actifs sans risque\n", "N=1000\n", "r0=mu_d[0]\n", "sigma0=sigma_d[0];# sigma0 = Gamma_d(1,1) = 0\n", "\n", "moyenne_y=np.zeros(N)\n", "std_y=np.zeros(N)\n", "max_pente=0\n", "for i in range(1,N):\n", " # cas d=2\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", " #Compléter \n", " moyenne_y[i]= np.dot(mu_d, y)\n", " std_y[i]= math.sqrt(np.dot(y, np.matmul(Gamma_d, y)))\n", " pente = (moyenne_y[i] - r0) / (std_y[i] - sigma0) # calcul de la pente\n", " if max_pente <= pente:\n", " imax = i\n", " max_pente = pente\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", "#Compléter \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, 'ro')\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()\n", "print(np.random.rand(1))" ] }, { "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": 184, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# L'emprunt en actif sans risque est autorisé\n", "N=1000; #nombre de stratégies\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)\n", " s=simplexe(d)\n", " # tirage uniforme dans le simplexe de dim |$d$|.\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)\n", " # |$x_0 + (1- x_0) \\sum_{i=1,\\ldots,d} s_i = 1$| \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 le 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": [ "# Extensions du modèle" ] }, { "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": [ "7. 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": 185, "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", "\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": 186, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "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", "\n", "plot1();\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Etape 2. Tirages des portefeuilles à coefficients positifs." ] }, { "cell_type": "code", "execution_count": 187, "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (3740242663.py, line 8)", "output_type": "error", "traceback": [ " \u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[187]\u001b[39m\u001b[32m, line 8\u001b[39m\n\u001b[31m \u001b[39m\u001b[31mx=?# tirage au hasard dans le simplexe\u001b[39m\n ^\n\u001b[31mSyntaxError\u001b[39m\u001b[31m:\u001b[39m invalid syntax\n" ] } ], "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", "moyenne_x=np.zeros(N);\n", "std_x=np.zeros(N);\n", "for i in range(0,N):\n", " x=?# tirage au hasard dans le simplexe\n", " moyenne_x[i] = ?\n", " std_x[i]=? \n", "\n", "# plot ###################################################################\n", "def plot2():\n", " plot1();# le plot précédent\n", " plt.plot(std_x, moyenne_x,'b.',markersize=2);\n", "\n", "plot2();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 3. Le point de variance minimum." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Le point de variance minimum\n", "\n", "# plot ###################################################################\n", "def plot3():\n", " plot2();# le plot précédent\n", " imin= ?\n", " plt.plot(std_x[imin],moyenne_x[imin], 'ro',markersize=6);\n", "\n", "plot3();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 4. On autorise l'emprunt de l'actif 1" ] }, { "cell_type": "code", "execution_count": null, "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]=? \n", " s[n]=?\n", " s[n+1:d]=?\n", " return s;\n", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "N=10000;\n", "moyenne_x_1=np.zeros(N);\n", "std_x_1=np.zeros(N);\n", "sigma_e=2;\n", "for i in range(0,N):\n", " x=?\n", " moyenne_x_1[i] = ?\n", " std_x_1[i]=?\n", "\n", "# plot ###################################################################\n", "def plot4():\n", " plot3();# le plot précédent\n", " plt.plot(std_x_1, moyenne_x_1,'g.',markersize=2);\n", "\n", "plot4();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 5. On rajoute un actif sans risque de moyenne nulle." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 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", "moyenne_d_x=np.zeros(N);\n", "std_d_x=np.zeros(N);\n", "for i in range(0,N):\n", " x=?# tirage au hasard dans le simplexe\n", " moyenne_d_x[i] = ?\n", " std_d_x[i]=?\n", "\n", "# plot ###################################################################\n", "def plot6(): \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(std_d_x, moyenne_d_x,'g.',markersize=2);\n", "\n", "plot6();\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 6. Identification du portefeuille de marché et de la droite de marché." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# r0=mu_d[0];\n", "sigma0=math.sqrt(Gamma_d[0,0]);# sigma0 = Gamma(0,0) = 0\n", "pente=0;\n", "max_pente=0;\n", "\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", " x=?;# tirage au hasard dans le simplexe de dimension d, n rajoute 0\n", " moyenne_d_x[i] = ?\n", " std_d_x[i]=?\n", " pente=?# 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=?\n", "sigma_P=?\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();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Etape 7. Simulation de portefeuilles avec emprunt de cash 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": null, "metadata": {}, "outputs": [], "source": [ "N=50000;\n", "sigma_e=2.0;\n", "moyenne_d_x=np.zeros(N);\n", "std_d_x=np.zeros(N);\n", "for i in range(0,N):\n", " x=?# tirage au hasard dans le simplexe\n", " moyenne_d_x[i] = ?\n", " std_d_x[i]=?\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", " # et les portefeuilles tirés au hasard\n", " plt.plot(std_d_x, moyenne_d_x,'g.',markersize=2);\n", "\n", "plot8();\n", "\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": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 2 }