python-pour-finance/09-Python-Finance-Fondamentaux/03-CAPM-Capital-Asset-Pricing-Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CAPM - Capital Asset Pricing Model \n",
    "## ou Le Modèle d'Evaluation Des Actifs Financiers (MEDAF)\n",
    "\n",
    "Regardez la vidéo pour un aperçu complet ou lis [ceci](https://fr.wikipedia.org/wiki/Mod%C3%A8le_d%27%C3%A9valuation_des_actifs_financiers)\n",
    "\n",
    "Rendements des portefeuilles:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $r_p(t) = \\sum\\limits_{i}^{n}w_i r_i(t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poids du Marché:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $ w_i = \\frac{MarketCap_i}{\\sum_{j}^{n}{MarketCap_j}} $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CAPM d'un portefeuille"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## $ r_p(t) = \\beta_pr_m(t) + \\sum\\limits_{i}^{n}w_i \\alpha_i(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Modèle CAPM en tant que simple régression linéaire"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function linregress in module scipy.stats._stats_mstats_common:\n",
      "\n",
      "linregress(x, y=None)\n",
      "    Calculate a linear least-squares regression for two sets of measurements.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    x, y : array_like\n",
      "        Two sets of measurements.  Both arrays should have the same length.  If\n",
      "        only `x` is given (and ``y=None``), then it must be a two-dimensional\n",
      "        array where one dimension has length 2.  The two sets of measurements\n",
      "        are then found by splitting the array along the length-2 dimension.  In\n",
      "        the case where ``y=None`` and `x` is a 2x2 array, ``linregress(x)`` is\n",
      "        equivalent to ``linregress(x[0], x[1])``.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    slope : float\n",
      "        Slope of the regression line.\n",
      "    intercept : float\n",
      "        Intercept of the regression line.\n",
      "    rvalue : float\n",
      "        Correlation coefficient.\n",
      "    pvalue : float\n",
      "        Two-sided p-value for a hypothesis test whose null hypothesis is\n",
      "        that the slope is zero, using Wald Test with t-distribution of\n",
      "        the test statistic.\n",
      "    stderr : float\n",
      "        Standard error of the estimated gradient.\n",
      "    \n",
      "    See also\n",
      "    --------\n",
      "    :func:`scipy.optimize.curve_fit` : Use non-linear\n",
      "     least squares to fit a function to data.\n",
      "    :func:`scipy.optimize.leastsq` : Minimize the sum of\n",
      "     squares of a set of equations.\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    Missing values are considered pair-wise: if a value is missing in `x`,\n",
      "    the corresponding value in `y` is masked.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> import matplotlib.pyplot as plt\n",
      "    >>> from scipy import stats\n",
      "    \n",
      "    Generate some data:\n",
      "    \n",
      "    >>> np.random.seed(12345678)\n",
      "    >>> x = np.random.random(10)\n",
      "    >>> y = 1.6*x + np.random.random(10)\n",
      "    \n",
      "    Perform the linear regression:\n",
      "    \n",
      "    >>> slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)\n",
      "    >>> print(\"slope: %f    intercept: %f\" % (slope, intercept))\n",
      "    slope: 1.944864    intercept: 0.268578\n",
      "    \n",
      "    To get coefficient of determination (R-squared):\n",
      "    \n",
      "    >>> print(\"R-squared: %f\" % r_value**2)\n",
      "    R-squared: 0.735498\n",
      "    \n",
      "    Plot the data along with the fitted line:\n",
      "    \n",
      "    >>> plt.plot(x, y, 'o', label='original data')\n",
      "    >>> plt.plot(x, intercept + slope*x, 'r', label='fitted line')\n",
      "    >>> plt.legend()\n",
      "    >>> plt.show()\n",
      "    \n",
      "    Example for the case where only x is provided as a 2x2 array:\n",
      "    \n",
      "    >>> x = np.array([[0, 1], [0, 2]])\n",
      "    >>> r = stats.linregress(x)\n",
      "    >>> r.slope, r.intercept\n",
      "    (2.0, 0.0)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(stats.linregress)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas_datareader as web"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "spy_etf = web.DataReader('SPY','yahoo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 1258 entries, 2015-01-23 to 2020-01-22\n",
      "Data columns (total 6 columns):\n",
      "High         1258 non-null float64\n",
      "Low          1258 non-null float64\n",
      "Open         1258 non-null float64\n",
      "Close        1258 non-null float64\n",
      "Volume       1258 non-null float64\n",
      "Adj Close    1258 non-null float64\n",
      "dtypes: float64(6)\n",
      "memory usage: 68.8 KB\n"
     ]
    }
   ],
   "source": [
    "spy_etf.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Low</th>\n",
       "      <th>Open</th>\n",
       "      <th>Close</th>\n",
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       "      <th>Adj Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-01-23</th>\n",
       "      <td>206.100006</td>\n",
       "      <td>204.809998</td>\n",
       "      <td>205.789993</td>\n",
       "      <td>204.970001</td>\n",
       "      <td>117516800.0</td>\n",
       "      <td>185.742508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-26</th>\n",
       "      <td>205.559998</td>\n",
       "      <td>203.850006</td>\n",
       "      <td>204.710007</td>\n",
       "      <td>205.449997</td>\n",
       "      <td>92009700.0</td>\n",
       "      <td>186.177475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-27</th>\n",
       "      <td>204.119995</td>\n",
       "      <td>201.740005</td>\n",
       "      <td>202.970001</td>\n",
       "      <td>202.740005</td>\n",
       "      <td>134044600.0</td>\n",
       "      <td>183.721680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-28</th>\n",
       "      <td>204.289993</td>\n",
       "      <td>199.910004</td>\n",
       "      <td>204.169998</td>\n",
       "      <td>200.139999</td>\n",
       "      <td>168514300.0</td>\n",
       "      <td>181.365585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-29</th>\n",
       "      <td>202.300003</td>\n",
       "      <td>198.679993</td>\n",
       "      <td>200.380005</td>\n",
       "      <td>201.990005</td>\n",
       "      <td>173585400.0</td>\n",
       "      <td>183.042038</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "                  High         Low        Open       Close       Volume  \\\n",
       "Date                                                                      \n",
       "2015-01-23  206.100006  204.809998  205.789993  204.970001  117516800.0   \n",
       "2015-01-26  205.559998  203.850006  204.710007  205.449997   92009700.0   \n",
       "2015-01-27  204.119995  201.740005  202.970001  202.740005  134044600.0   \n",
       "2015-01-28  204.289993  199.910004  204.169998  200.139999  168514300.0   \n",
       "2015-01-29  202.300003  198.679993  200.380005  201.990005  173585400.0   \n",
       "\n",
       "             Adj Close  \n",
       "Date                    \n",
       "2015-01-23  185.742508  \n",
       "2015-01-26  186.177475  \n",
       "2015-01-27  183.721680  \n",
       "2015-01-28  181.365585  \n",
       "2015-01-29  183.042038  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spy_etf.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prendre les dates du DatetimeIndex de spy_etf\n",
    "start = pd.to_datetime('2015-01-23')\n",
    "end = pd.to_datetime('2020-01-22')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "aapl = web.DataReader('AAPL','yahoo',start,end)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Low</th>\n",
       "      <th>Open</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Adj Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
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       "    <tr>\n",
       "      <th>2015-01-23</th>\n",
       "      <td>113.750000</td>\n",
       "      <td>111.529999</td>\n",
       "      <td>112.300003</td>\n",
       "      <td>112.980003</td>\n",
       "      <td>46464800.0</td>\n",
       "      <td>103.807991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-26</th>\n",
       "      <td>114.360001</td>\n",
       "      <td>112.800003</td>\n",
       "      <td>113.739998</td>\n",
       "      <td>113.099998</td>\n",
       "      <td>55615000.0</td>\n",
       "      <td>103.918228</td>\n",
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       "    <tr>\n",
       "      <th>2015-01-27</th>\n",
       "      <td>112.480003</td>\n",
       "      <td>109.029999</td>\n",
       "      <td>112.419998</td>\n",
       "      <td>109.139999</td>\n",
       "      <td>95568700.0</td>\n",
       "      <td>100.279716</td>\n",
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       "    <tr>\n",
       "      <th>2015-01-28</th>\n",
       "      <td>118.120003</td>\n",
       "      <td>115.309998</td>\n",
       "      <td>117.629997</td>\n",
       "      <td>115.309998</td>\n",
       "      <td>146477100.0</td>\n",
       "      <td>105.948822</td>\n",
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       "    <tr>\n",
       "      <th>2015-01-29</th>\n",
       "      <td>119.190002</td>\n",
       "      <td>115.559998</td>\n",
       "      <td>116.320000</td>\n",
       "      <td>118.900002</td>\n",
       "      <td>84436400.0</td>\n",
       "      <td>109.247391</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "                  High         Low        Open       Close       Volume  \\\n",
       "Date                                                                      \n",
       "2015-01-23  113.750000  111.529999  112.300003  112.980003   46464800.0   \n",
       "2015-01-26  114.360001  112.800003  113.739998  113.099998   55615000.0   \n",
       "2015-01-27  112.480003  109.029999  112.419998  109.139999   95568700.0   \n",
       "2015-01-28  118.120003  115.309998  117.629997  115.309998  146477100.0   \n",
       "2015-01-29  119.190002  115.559998  116.320000  118.900002   84436400.0   \n",
       "\n",
       "             Adj Close  \n",
       "Date                    \n",
       "2015-01-23  103.807991  \n",
       "2015-01-26  103.918228  \n",
       "2015-01-27  100.279716  \n",
       "2015-01-28  105.948822  \n",
       "2015-01-29  109.247391  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aapl.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a215f0090>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "aapl['Close'].plot(label='AAPL',figsize=(10,8))\n",
    "spy_etf['Close'].plot(label='SPY Index')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compaison de Rendements Cumulatifs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "aapl['Cumulative'] = aapl['Close']/aapl['Close'].iloc[0]\n",
    "spy_etf['Cumulative'] = spy_etf['Close']/spy_etf['Close'].iloc[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Cumulative Return')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "aapl['Cumulative'].plot(label='AAPL',figsize=(10,8))\n",
    "spy_etf['Cumulative'].plot(label='SPY Index')\n",
    "plt.legend()\n",
    "plt.title('Cumulative Return')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Obtenir un Rendement Quotidien"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "aapl['Daily Return'] = aapl['Close'].pct_change(1)\n",
    "spy_etf['Daily Return'] = spy_etf['Close'].pct_change(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a21c53c10>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(aapl['Daily Return'],spy_etf['Daily Return'],alpha=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a21c7e4d0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "aapl['Daily Return'].hist(bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a21d5cd90>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "spy_etf['Daily Return'].hist(bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta,alpha,r_value,p_value,std_err = stats.linregress(aapl['Daily Return'].iloc[1:],spy_etf['Daily Return'].iloc[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36427945112845933"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.509655057407941e-05"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6716569379192504"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Et si nos actions étaient entièrement lié au SP500 ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2015-01-23         NaN\n",
       "2015-01-26    0.002342\n",
       "2015-01-27   -0.013191\n",
       "2015-01-28   -0.012824\n",
       "2015-01-29    0.009244\n",
       "Name: Daily Return, dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spy_etf['Daily Return'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = np.random.normal(0,0.001,len(spy_etf['Daily Return'].iloc[1:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7.33560734e-05, -1.10514969e-03,  3.59585924e-04, ...,\n",
       "        2.50719947e-04, -4.33730167e-05,  3.05482906e-04])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2015-01-26    0.002415\n",
       "2015-01-27   -0.014296\n",
       "2015-01-28   -0.012465\n",
       "2015-01-29    0.009031\n",
       "2015-01-30   -0.010271\n",
       "                ...   \n",
       "2020-01-15    0.000974\n",
       "2020-01-16    0.007649\n",
       "2020-01-17    0.003363\n",
       "2020-01-21   -0.002002\n",
       "2020-01-22    0.002298\n",
       "Name: Daily Return, Length: 1257, dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spy_etf['Daily Return'].iloc[1:] + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta,alpha,r_value,p_value,std_err = stats.linregress(spy_etf['Daily Return'].iloc[1:]+noise,spy_etf['Daily Return'].iloc[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9856347921712466"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-5.02497565290158e-06"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On dirait que notre compréhension est correcte !"
   ]
  }
 ],
 "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}