1933 lines
304 KiB
Plaintext
1933 lines
304 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Optimisation du Portefeuille"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\"Modern Portfolio Theory\" (MPT), une hypothèse avancée par Harry Markowitz dans son article \"Portfolio Selection\" (publié en 1952 par le Journal of Finance) est une théorie de l'investissement basée sur l'idée que les investisseurs peu enclins au risque peuvent construire des portefeuilles pour optimiser ou maximiser le rendement attendu en fonction d'un niveau de risque de marché donné, en soulignant que le risque est une partie inhérente à un rendement plus élevé. Il s'agit de l'une des théories économiques les plus importantes et les plus influentes en matière de finance et d'investissement.\n",
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"\n",
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"[Plus d'informations sur la théorie moderne du Portefeuille](https://fr.wikipedia.org/wiki/Th%C3%A9orie_moderne_du_portefeuille)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Simulation Monte Carlo pour la recherche d'optimisation\n",
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"\n",
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"\n",
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"Nous pourrions essayer de trouver au hasard l'équilibre optimal du portefeuille en utilisant la simulation de Monte Carlo"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"aapl = pd.read_csv('AAPL_CLOSE',index_col='Date',parse_dates=True)\n",
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"cisco = pd.read_csv('CISCO_CLOSE',index_col='Date',parse_dates=True)\n",
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"ibm = pd.read_csv('IBM_CLOSE',index_col='Date',parse_dates=True)\n",
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"amzn = pd.read_csv('AMZN_CLOSE',index_col='Date',parse_dates=True)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"stocks = pd.concat([aapl,cisco,ibm,amzn],axis=1)\n",
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"stocks.columns = ['aapl','cisco','ibm','amzn']"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>aapl</th>\n",
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" <th>cisco</th>\n",
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" <th>ibm</th>\n",
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" <th>amzn</th>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>Date</th>\n",
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" <th></th>\n",
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" <th></th>\n",
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" <th></th>\n",
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" <th></th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>2012-01-03</th>\n",
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" <td>52.848787</td>\n",
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" <td>15.617341</td>\n",
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" <td>157.578371</td>\n",
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" <td>179.03</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2012-01-04</th>\n",
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" <td>53.132802</td>\n",
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" <td>15.919125</td>\n",
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" <td>156.935540</td>\n",
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" <td>177.51</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2012-01-05</th>\n",
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" <td>53.722681</td>\n",
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" <td>15.860445</td>\n",
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" <td>156.191208</td>\n",
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" <td>177.61</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2012-01-06</th>\n",
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" <td>54.284287</td>\n",
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" <td>15.801764</td>\n",
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" <td>154.398046</td>\n",
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" <td>182.61</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2012-01-09</th>\n",
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" <td>54.198183</td>\n",
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" <td>15.902359</td>\n",
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" <td>153.594506</td>\n",
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" <td>178.56</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" aapl cisco ibm amzn\n",
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"Date \n",
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"2012-01-03 52.848787 15.617341 157.578371 179.03\n",
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"2012-01-04 53.132802 15.919125 156.935540 177.51\n",
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"2012-01-05 53.722681 15.860445 156.191208 177.61\n",
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"2012-01-06 54.284287 15.801764 154.398046 182.61\n",
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"2012-01-09 54.198183 15.902359 153.594506 178.56"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"stocks.head()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"aapl 0.000750\n",
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"cisco 0.000599\n",
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"ibm 0.000081\n",
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"amzn 0.001328\n",
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"dtype: float64"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"mean_daily_ret = stocks.pct_change(1).mean()\n",
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"mean_daily_ret"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>aapl</th>\n",
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" <th>cisco</th>\n",
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" <th>ibm</th>\n",
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" <th>amzn</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>aapl</th>\n",
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" <td>1.000000</td>\n",
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" <td>0.301990</td>\n",
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" <td>0.297498</td>\n",
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" <td>0.235487</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>cisco</th>\n",
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" <td>0.301990</td>\n",
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" <td>1.000000</td>\n",
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" <td>0.424672</td>\n",
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" <td>0.284470</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>ibm</th>\n",
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" <td>0.297498</td>\n",
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" <td>0.424672</td>\n",
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" <td>1.000000</td>\n",
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" <td>0.258492</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>amzn</th>\n",
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" <td>0.235487</td>\n",
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" <td>0.284470</td>\n",
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" <td>0.258492</td>\n",
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" <td>1.000000</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" aapl cisco ibm amzn\n",
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"aapl 1.000000 0.301990 0.297498 0.235487\n",
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"cisco 0.301990 1.000000 0.424672 0.284470\n",
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"ibm 0.297498 0.424672 1.000000 0.258492\n",
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"amzn 0.235487 0.284470 0.258492 1.000000"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"stocks.pct_change(1).corr()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Simulation de milliers de répartitions possibles"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>aapl</th>\n",
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" <th>cisco</th>\n",
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" <th>ibm</th>\n",
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" <th>amzn</th>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>Date</th>\n",
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" <th></th>\n",
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" <th></th>\n",
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" <th></th>\n",
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" <th></th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>2012-01-03</th>\n",
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" <td>52.848787</td>\n",
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" <td>15.617341</td>\n",
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" <td>157.578371</td>\n",
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" <td>179.03</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2012-01-04</th>\n",
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" <td>53.132802</td>\n",
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" <td>15.919125</td>\n",
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" <td>156.935540</td>\n",
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" <td>177.51</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2012-01-05</th>\n",
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" <td>53.722681</td>\n",
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" <td>15.860445</td>\n",
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" <td>156.191208</td>\n",
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" <td>177.61</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2012-01-06</th>\n",
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" <td>54.284287</td>\n",
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" <td>15.801764</td>\n",
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" <td>154.398046</td>\n",
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" <td>182.61</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2012-01-09</th>\n",
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" <td>54.198183</td>\n",
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" <td>15.902359</td>\n",
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" <td>153.594506</td>\n",
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" <td>178.56</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" aapl cisco ibm amzn\n",
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"Date \n",
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"2012-01-03 52.848787 15.617341 157.578371 179.03\n",
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"2012-01-04 53.132802 15.919125 156.935540 177.51\n",
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"2012-01-05 53.722681 15.860445 156.191208 177.61\n",
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"2012-01-06 54.284287 15.801764 154.398046 182.61\n",
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"2012-01-09 54.198183 15.902359 153.594506 178.56"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"stocks.head()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x115185a90>"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": 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\n",
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
|
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"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"stock_normed = stocks/stocks.iloc[0]\n",
|
|
"stock_normed.plot()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {},
|
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"outputs": [
|
|
{
|
|
"data": {
|
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"text/html": [
|
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"<div>\n",
|
|
"<style scoped>\n",
|
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|
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|
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" }\n",
|
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"\n",
|
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" .dataframe thead th {\n",
|
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" text-align: right;\n",
|
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" }\n",
|
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|
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"<table border=\"1\" class=\"dataframe\">\n",
|
|
" <thead>\n",
|
|
" <tr style=\"text-align: right;\">\n",
|
|
" <th></th>\n",
|
|
" <th>aapl</th>\n",
|
|
" <th>cisco</th>\n",
|
|
" <th>ibm</th>\n",
|
|
" <th>amzn</th>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>Date</th>\n",
|
|
" <th></th>\n",
|
|
" <th></th>\n",
|
|
" <th></th>\n",
|
|
" <th></th>\n",
|
|
" </tr>\n",
|
|
" </thead>\n",
|
|
" <tbody>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-03</th>\n",
|
|
" <td>NaN</td>\n",
|
|
" <td>NaN</td>\n",
|
|
" <td>NaN</td>\n",
|
|
" <td>NaN</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-04</th>\n",
|
|
" <td>0.005374</td>\n",
|
|
" <td>0.019324</td>\n",
|
|
" <td>-0.004079</td>\n",
|
|
" <td>-0.008490</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-05</th>\n",
|
|
" <td>0.011102</td>\n",
|
|
" <td>-0.003686</td>\n",
|
|
" <td>-0.004743</td>\n",
|
|
" <td>0.000563</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-06</th>\n",
|
|
" <td>0.010454</td>\n",
|
|
" <td>-0.003700</td>\n",
|
|
" <td>-0.011481</td>\n",
|
|
" <td>0.028152</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-09</th>\n",
|
|
" <td>-0.001586</td>\n",
|
|
" <td>0.006366</td>\n",
|
|
" <td>-0.005204</td>\n",
|
|
" <td>-0.022178</td>\n",
|
|
" </tr>\n",
|
|
" </tbody>\n",
|
|
"</table>\n",
|
|
"</div>"
|
|
],
|
|
"text/plain": [
|
|
" aapl cisco ibm amzn\n",
|
|
"Date \n",
|
|
"2012-01-03 NaN NaN NaN NaN\n",
|
|
"2012-01-04 0.005374 0.019324 -0.004079 -0.008490\n",
|
|
"2012-01-05 0.011102 -0.003686 -0.004743 0.000563\n",
|
|
"2012-01-06 0.010454 -0.003700 -0.011481 0.028152\n",
|
|
"2012-01-09 -0.001586 0.006366 -0.005204 -0.022178"
|
|
]
|
|
},
|
|
"execution_count": 10,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"stock_daily_ret = stocks.pct_change(1)\n",
|
|
"stock_daily_ret.head()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Rendements logarithmiques vs. Rendements arithmétiques\n",
|
|
"\n",
|
|
"Nous allons maintenant passer à l'utilisation de rendements logarithmiques au lieu de rendements arithmétiques, pour beaucoup de nos cas d'utilisation ce sont presque les mêmes, mais la plupart des analyses techniques nécessitent de normaliser les séries temporelles et l'utilisation de rendements logarithmiques est une bonne façon de le faire.\n",
|
|
"Les rendements logarithmiques sont pratiques à utiliser dans la plupart des algorithmes que nous rencontrerons.\n",
|
|
"\n",
|
|
"\n",
|
|
"Pour une analyse complète des raisons pour lesquelles nous utilisons les rendements logarithmiques, consultez [ce super article](https://quantivity.wordpress.com/2011/02/21/why-log-returns/).\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/html": [
|
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|
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"<style scoped>\n",
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|
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|
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|
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|
|
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|
|
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|
|
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|
|
" text-align: right;\n",
|
|
" }\n",
|
|
"</style>\n",
|
|
"<table border=\"1\" class=\"dataframe\">\n",
|
|
" <thead>\n",
|
|
" <tr style=\"text-align: right;\">\n",
|
|
" <th></th>\n",
|
|
" <th>aapl</th>\n",
|
|
" <th>cisco</th>\n",
|
|
" <th>ibm</th>\n",
|
|
" <th>amzn</th>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>Date</th>\n",
|
|
" <th></th>\n",
|
|
" <th></th>\n",
|
|
" <th></th>\n",
|
|
" <th></th>\n",
|
|
" </tr>\n",
|
|
" </thead>\n",
|
|
" <tbody>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-03</th>\n",
|
|
" <td>NaN</td>\n",
|
|
" <td>NaN</td>\n",
|
|
" <td>NaN</td>\n",
|
|
" <td>NaN</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-04</th>\n",
|
|
" <td>0.005360</td>\n",
|
|
" <td>0.019139</td>\n",
|
|
" <td>-0.004088</td>\n",
|
|
" <td>-0.008526</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-05</th>\n",
|
|
" <td>0.011041</td>\n",
|
|
" <td>-0.003693</td>\n",
|
|
" <td>-0.004754</td>\n",
|
|
" <td>0.000563</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-06</th>\n",
|
|
" <td>0.010400</td>\n",
|
|
" <td>-0.003707</td>\n",
|
|
" <td>-0.011547</td>\n",
|
|
" <td>0.027763</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>2012-01-09</th>\n",
|
|
" <td>-0.001587</td>\n",
|
|
" <td>0.006346</td>\n",
|
|
" <td>-0.005218</td>\n",
|
|
" <td>-0.022428</td>\n",
|
|
" </tr>\n",
|
|
" </tbody>\n",
|
|
"</table>\n",
|
|
"</div>"
|
|
],
|
|
"text/plain": [
|
|
" aapl cisco ibm amzn\n",
|
|
"Date \n",
|
|
"2012-01-03 NaN NaN NaN NaN\n",
|
|
"2012-01-04 0.005360 0.019139 -0.004088 -0.008526\n",
|
|
"2012-01-05 0.011041 -0.003693 -0.004754 0.000563\n",
|
|
"2012-01-06 0.010400 -0.003707 -0.011547 0.027763\n",
|
|
"2012-01-09 -0.001587 0.006346 -0.005218 -0.022428"
|
|
]
|
|
},
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"log_ret = np.log(stocks/stocks.shift(1))\n",
|
|
"log_ret.head()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
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\n",
|
|
"text/plain": [
|
|
"<Figure size 864x432 with 4 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"log_ret.hist(bins=100,figsize=(12,6));\n",
|
|
"plt.tight_layout()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/html": [
|
|
"<div>\n",
|
|
"<style scoped>\n",
|
|
" .dataframe tbody tr th:only-of-type {\n",
|
|
" vertical-align: middle;\n",
|
|
" }\n",
|
|
"\n",
|
|
" .dataframe tbody tr th {\n",
|
|
" vertical-align: top;\n",
|
|
" }\n",
|
|
"\n",
|
|
" .dataframe thead th {\n",
|
|
" text-align: right;\n",
|
|
" }\n",
|
|
"</style>\n",
|
|
"<table border=\"1\" class=\"dataframe\">\n",
|
|
" <thead>\n",
|
|
" <tr style=\"text-align: right;\">\n",
|
|
" <th></th>\n",
|
|
" <th>count</th>\n",
|
|
" <th>mean</th>\n",
|
|
" <th>std</th>\n",
|
|
" <th>min</th>\n",
|
|
" <th>25%</th>\n",
|
|
" <th>50%</th>\n",
|
|
" <th>75%</th>\n",
|
|
" <th>max</th>\n",
|
|
" </tr>\n",
|
|
" </thead>\n",
|
|
" <tbody>\n",
|
|
" <tr>\n",
|
|
" <th>aapl</th>\n",
|
|
" <td>1257.0</td>\n",
|
|
" <td>0.000614</td>\n",
|
|
" <td>0.016466</td>\n",
|
|
" <td>-0.131875</td>\n",
|
|
" <td>-0.007358</td>\n",
|
|
" <td>0.000455</td>\n",
|
|
" <td>0.009724</td>\n",
|
|
" <td>0.085022</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>cisco</th>\n",
|
|
" <td>1257.0</td>\n",
|
|
" <td>0.000497</td>\n",
|
|
" <td>0.014279</td>\n",
|
|
" <td>-0.116091</td>\n",
|
|
" <td>-0.006240</td>\n",
|
|
" <td>0.000213</td>\n",
|
|
" <td>0.007634</td>\n",
|
|
" <td>0.118862</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>ibm</th>\n",
|
|
" <td>1257.0</td>\n",
|
|
" <td>0.000011</td>\n",
|
|
" <td>0.011819</td>\n",
|
|
" <td>-0.086419</td>\n",
|
|
" <td>-0.005873</td>\n",
|
|
" <td>0.000049</td>\n",
|
|
" <td>0.006477</td>\n",
|
|
" <td>0.049130</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>amzn</th>\n",
|
|
" <td>1257.0</td>\n",
|
|
" <td>0.001139</td>\n",
|
|
" <td>0.019362</td>\n",
|
|
" <td>-0.116503</td>\n",
|
|
" <td>-0.008534</td>\n",
|
|
" <td>0.000563</td>\n",
|
|
" <td>0.011407</td>\n",
|
|
" <td>0.146225</td>\n",
|
|
" </tr>\n",
|
|
" </tbody>\n",
|
|
"</table>\n",
|
|
"</div>"
|
|
],
|
|
"text/plain": [
|
|
" count mean std min 25% 50% 75% \\\n",
|
|
"aapl 1257.0 0.000614 0.016466 -0.131875 -0.007358 0.000455 0.009724 \n",
|
|
"cisco 1257.0 0.000497 0.014279 -0.116091 -0.006240 0.000213 0.007634 \n",
|
|
"ibm 1257.0 0.000011 0.011819 -0.086419 -0.005873 0.000049 0.006477 \n",
|
|
"amzn 1257.0 0.001139 0.019362 -0.116503 -0.008534 0.000563 0.011407 \n",
|
|
"\n",
|
|
" max \n",
|
|
"aapl 0.085022 \n",
|
|
"cisco 0.118862 \n",
|
|
"ibm 0.049130 \n",
|
|
"amzn 0.146225 "
|
|
]
|
|
},
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"log_ret.describe().transpose()"
|
|
]
|
|
},
|
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{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
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"metadata": {},
|
|
"outputs": [
|
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{
|
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"data": {
|
|
"text/plain": [
|
|
"aapl 0.154803\n",
|
|
"cisco 0.125291\n",
|
|
"ibm 0.002788\n",
|
|
"amzn 0.287153\n",
|
|
"dtype: float64"
|
|
]
|
|
},
|
|
"execution_count": 14,
|
|
"metadata": {},
|
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"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"log_ret.mean() * 252"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
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"metadata": {},
|
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"outputs": [
|
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{
|
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"data": {
|
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"text/html": [
|
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"<div>\n",
|
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"<style scoped>\n",
|
|
" .dataframe tbody tr th:only-of-type {\n",
|
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" vertical-align: middle;\n",
|
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" }\n",
|
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"\n",
|
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
|
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" }\n",
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"\n",
|
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" .dataframe thead th {\n",
|
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" text-align: right;\n",
|
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" }\n",
|
|
"</style>\n",
|
|
"<table border=\"1\" class=\"dataframe\">\n",
|
|
" <thead>\n",
|
|
" <tr style=\"text-align: right;\">\n",
|
|
" <th></th>\n",
|
|
" <th>aapl</th>\n",
|
|
" <th>cisco</th>\n",
|
|
" <th>ibm</th>\n",
|
|
" <th>amzn</th>\n",
|
|
" </tr>\n",
|
|
" </thead>\n",
|
|
" <tbody>\n",
|
|
" <tr>\n",
|
|
" <th>aapl</th>\n",
|
|
" <td>0.000271</td>\n",
|
|
" <td>0.000071</td>\n",
|
|
" <td>0.000057</td>\n",
|
|
" <td>0.000075</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>cisco</th>\n",
|
|
" <td>0.000071</td>\n",
|
|
" <td>0.000204</td>\n",
|
|
" <td>0.000072</td>\n",
|
|
" <td>0.000079</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>ibm</th>\n",
|
|
" <td>0.000057</td>\n",
|
|
" <td>0.000072</td>\n",
|
|
" <td>0.000140</td>\n",
|
|
" <td>0.000059</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>amzn</th>\n",
|
|
" <td>0.000075</td>\n",
|
|
" <td>0.000079</td>\n",
|
|
" <td>0.000059</td>\n",
|
|
" <td>0.000375</td>\n",
|
|
" </tr>\n",
|
|
" </tbody>\n",
|
|
"</table>\n",
|
|
"</div>"
|
|
],
|
|
"text/plain": [
|
|
" aapl cisco ibm amzn\n",
|
|
"aapl 0.000271 0.000071 0.000057 0.000075\n",
|
|
"cisco 0.000071 0.000204 0.000072 0.000079\n",
|
|
"ibm 0.000057 0.000072 0.000140 0.000059\n",
|
|
"amzn 0.000075 0.000079 0.000059 0.000375"
|
|
]
|
|
},
|
|
"execution_count": 15,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Calculer la covariance des colonnes par paires\n",
|
|
"log_ret.cov()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"metadata": {},
|
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"outputs": [
|
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{
|
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"data": {
|
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"text/html": [
|
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"<div>\n",
|
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"<style scoped>\n",
|
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" .dataframe tbody tr th:only-of-type {\n",
|
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" vertical-align: middle;\n",
|
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" }\n",
|
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"\n",
|
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" .dataframe tbody tr th {\n",
|
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" vertical-align: top;\n",
|
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" }\n",
|
|
"\n",
|
|
" .dataframe thead th {\n",
|
|
" text-align: right;\n",
|
|
" }\n",
|
|
"</style>\n",
|
|
"<table border=\"1\" class=\"dataframe\">\n",
|
|
" <thead>\n",
|
|
" <tr style=\"text-align: right;\">\n",
|
|
" <th></th>\n",
|
|
" <th>aapl</th>\n",
|
|
" <th>cisco</th>\n",
|
|
" <th>ibm</th>\n",
|
|
" <th>amzn</th>\n",
|
|
" </tr>\n",
|
|
" </thead>\n",
|
|
" <tbody>\n",
|
|
" <tr>\n",
|
|
" <th>aapl</th>\n",
|
|
" <td>0.068326</td>\n",
|
|
" <td>0.017854</td>\n",
|
|
" <td>0.014464</td>\n",
|
|
" <td>0.018986</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>cisco</th>\n",
|
|
" <td>0.017854</td>\n",
|
|
" <td>0.051381</td>\n",
|
|
" <td>0.018029</td>\n",
|
|
" <td>0.019956</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>ibm</th>\n",
|
|
" <td>0.014464</td>\n",
|
|
" <td>0.018029</td>\n",
|
|
" <td>0.035203</td>\n",
|
|
" <td>0.014939</td>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <th>amzn</th>\n",
|
|
" <td>0.018986</td>\n",
|
|
" <td>0.019956</td>\n",
|
|
" <td>0.014939</td>\n",
|
|
" <td>0.094470</td>\n",
|
|
" </tr>\n",
|
|
" </tbody>\n",
|
|
"</table>\n",
|
|
"</div>"
|
|
],
|
|
"text/plain": [
|
|
" aapl cisco ibm amzn\n",
|
|
"aapl 0.068326 0.017854 0.014464 0.018986\n",
|
|
"cisco 0.017854 0.051381 0.018029 0.019956\n",
|
|
"ibm 0.014464 0.018029 0.035203 0.014939\n",
|
|
"amzn 0.018986 0.019956 0.014939 0.094470"
|
|
]
|
|
},
|
|
"execution_count": 16,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"log_ret.cov()*252 # multiplier par les jours ouvrables"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Exécution pour une certaine répartition aléatoire"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Stocks\n",
|
|
"Index(['aapl', 'cisco', 'ibm', 'amzn'], dtype='object')\n",
|
|
"\n",
|
|
"\n",
|
|
"Creating Random Weights\n",
|
|
"[0.51639863 0.57066759 0.02847423 0.17152166]\n",
|
|
"\n",
|
|
"\n",
|
|
"Rebalance to sum to 1.0\n",
|
|
"[0.40122278 0.44338777 0.02212343 0.13326603]\n",
|
|
"\n",
|
|
"\n",
|
|
"Expected Portfolio Return\n",
|
|
"0.1559927204963252\n",
|
|
"\n",
|
|
"\n",
|
|
"Expected Volatility\n",
|
|
"0.1850264956590895\n",
|
|
"\n",
|
|
"\n",
|
|
"Sharpe Ratio\n",
|
|
"0.8430831483926556\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Règlage du seed (optionnel)\n",
|
|
"np.random.seed(101)\n",
|
|
"\n",
|
|
"# Colonnes d'actions (Stocks)\n",
|
|
"print('Stocks')\n",
|
|
"print(stocks.columns)\n",
|
|
"print('\\n')\n",
|
|
"\n",
|
|
"# Créer des poids aléatoires\n",
|
|
"print('Creating Random Weights')\n",
|
|
"weights = np.array(np.random.random(4))\n",
|
|
"print(weights)\n",
|
|
"print('\\n')\n",
|
|
"\n",
|
|
"# Re-pondération des Poids\n",
|
|
"print('Rebalance to sum to 1.0')\n",
|
|
"weights = weights / np.sum(weights)\n",
|
|
"print(weights)\n",
|
|
"print('\\n')\n",
|
|
"\n",
|
|
"# Rendement attendu ou escompté\n",
|
|
"print('Expected Portfolio Return')\n",
|
|
"exp_ret = np.sum(log_ret.mean() * weights) *252\n",
|
|
"print(exp_ret)\n",
|
|
"print('\\n')\n",
|
|
"\n",
|
|
"# variance attendue ou escomptée\n",
|
|
"print('Expected Volatility')\n",
|
|
"exp_vol = np.sqrt(np.dot(weights.T, np.dot(log_ret.cov() * 252, weights)))\n",
|
|
"print(exp_vol)\n",
|
|
"print('\\n')\n",
|
|
"\n",
|
|
"# Ratio de Sharpe\n",
|
|
"SR = exp_ret/exp_vol\n",
|
|
"print('Sharpe Ratio')\n",
|
|
"print(SR)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Super ! Maintenant, on peut l'éxécuter plein de fois !"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"num_ports = 15000\n",
|
|
"\n",
|
|
"all_weights = np.zeros((num_ports,len(stocks.columns)))\n",
|
|
"ret_arr = np.zeros(num_ports)\n",
|
|
"vol_arr = np.zeros(num_ports)\n",
|
|
"sharpe_arr = np.zeros(num_ports)\n",
|
|
"\n",
|
|
"for ind in range(num_ports):\n",
|
|
"\n",
|
|
" # Créer des poids aléatoires\n",
|
|
" weights = np.array(np.random.random(4))\n",
|
|
"\n",
|
|
" # (re)Pondération des poids\n",
|
|
" weights = weights / np.sum(weights)\n",
|
|
" \n",
|
|
" # Sauvegarde des Poids\n",
|
|
" all_weights[ind,:] = weights\n",
|
|
"\n",
|
|
" # rendement attendu\n",
|
|
" ret_arr[ind] = np.sum((log_ret.mean() * weights) *252)\n",
|
|
"\n",
|
|
" # variance Attendue\n",
|
|
" vol_arr[ind] = np.sqrt(np.dot(weights.T, np.dot(log_ret.cov() * 252, weights)))\n",
|
|
"\n",
|
|
" # Ratio de Sharpe\n",
|
|
" sharpe_arr[ind] = ret_arr[ind]/vol_arr[ind]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"1.030326055127131"
|
|
]
|
|
},
|
|
"execution_count": 19,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"sharpe_arr.max()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"1419"
|
|
]
|
|
},
|
|
"execution_count": 20,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"sharpe_arr.argmax()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([0.26188068, 0.20759516, 0.00110226, 0.5294219 ])"
|
|
]
|
|
},
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"all_weights[1419,:]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 22,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"max_sr_ret = ret_arr[1419]\n",
|
|
"max_sr_vol = vol_arr[1419]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Tracer les données"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 23,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<matplotlib.collections.PathCollection at 0x115e86e10>"
|
|
]
|
|
},
|
|
"execution_count": 23,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 864x576 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure(figsize=(12,8))\n",
|
|
"plt.scatter(vol_arr,ret_arr,c=sharpe_arr,cmap='plasma')\n",
|
|
"plt.colorbar(label='Sharpe Ratio')\n",
|
|
"plt.xlabel('Volatility')\n",
|
|
"plt.ylabel('Return')\n",
|
|
"\n",
|
|
"# Ajouter un point rouge pour le SR max\n",
|
|
"plt.scatter(max_sr_vol,max_sr_ret,c='red',s=50,edgecolors='black')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Optimisation mathématique\n",
|
|
"\n",
|
|
"Il y a de bien meilleures façons de trouver de bons poids de répartition que de simplement deviner et vérifier ! Nous pouvons utiliser des fonctions d'optimisation pour trouver les poids idéaux mathématiquement !"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Fonctionnaliser les opérations de rendement et de SR"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 24,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def get_ret_vol_sr(weights):\n",
|
|
" \"\"\"\n",
|
|
" Prends en argument les poids, retourne un tableau de rendement,\n",
|
|
" volatilité et Ratio de Sharpe\n",
|
|
" \"\"\"\n",
|
|
" weights = np.array(weights)\n",
|
|
" ret = np.sum(log_ret.mean() * weights) * 252\n",
|
|
" vol = np.sqrt(np.dot(weights.T, np.dot(log_ret.cov() * 252, weights)))\n",
|
|
" sr = ret/vol\n",
|
|
" return np.array([ret,vol,sr])"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"from scipy.optimize import minimize"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Pour bien comprendre tous les paramètres, regardez:\n",
|
|
"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 26,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Help on function minimize in module scipy.optimize._minimize:\n",
|
|
"\n",
|
|
"minimize(fun, x0, args=(), method=None, jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None)\n",
|
|
" Minimization of scalar function of one or more variables.\n",
|
|
" \n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" fun : callable\n",
|
|
" The objective function to be minimized.\n",
|
|
" \n",
|
|
" ``fun(x, *args) -> float``\n",
|
|
" \n",
|
|
" where x is an 1-D array with shape (n,) and `args`\n",
|
|
" is a tuple of the fixed parameters needed to completely\n",
|
|
" specify the function.\n",
|
|
" x0 : ndarray, shape (n,)\n",
|
|
" Initial guess. Array of real elements of size (n,),\n",
|
|
" where 'n' is the number of independent variables.\n",
|
|
" args : tuple, optional\n",
|
|
" Extra arguments passed to the objective function and its\n",
|
|
" derivatives (`fun`, `jac` and `hess` functions).\n",
|
|
" method : str or callable, optional\n",
|
|
" Type of solver. Should be one of\n",
|
|
" \n",
|
|
" - 'Nelder-Mead' :ref:`(see here) <optimize.minimize-neldermead>`\n",
|
|
" - 'Powell' :ref:`(see here) <optimize.minimize-powell>`\n",
|
|
" - 'CG' :ref:`(see here) <optimize.minimize-cg>`\n",
|
|
" - 'BFGS' :ref:`(see here) <optimize.minimize-bfgs>`\n",
|
|
" - 'Newton-CG' :ref:`(see here) <optimize.minimize-newtoncg>`\n",
|
|
" - 'L-BFGS-B' :ref:`(see here) <optimize.minimize-lbfgsb>`\n",
|
|
" - 'TNC' :ref:`(see here) <optimize.minimize-tnc>`\n",
|
|
" - 'COBYLA' :ref:`(see here) <optimize.minimize-cobyla>`\n",
|
|
" - 'SLSQP' :ref:`(see here) <optimize.minimize-slsqp>`\n",
|
|
" - 'trust-constr':ref:`(see here) <optimize.minimize-trustconstr>`\n",
|
|
" - 'dogleg' :ref:`(see here) <optimize.minimize-dogleg>`\n",
|
|
" - 'trust-ncg' :ref:`(see here) <optimize.minimize-trustncg>`\n",
|
|
" - 'trust-exact' :ref:`(see here) <optimize.minimize-trustexact>`\n",
|
|
" - 'trust-krylov' :ref:`(see here) <optimize.minimize-trustkrylov>`\n",
|
|
" - custom - a callable object (added in version 0.14.0),\n",
|
|
" see below for description.\n",
|
|
" \n",
|
|
" If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``,\n",
|
|
" depending if the problem has constraints or bounds.\n",
|
|
" jac : {callable, '2-point', '3-point', 'cs', bool}, optional\n",
|
|
" Method for computing the gradient vector. Only for CG, BFGS,\n",
|
|
" Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov,\n",
|
|
" trust-exact and trust-constr. If it is a callable, it should be a\n",
|
|
" function that returns the gradient vector:\n",
|
|
" \n",
|
|
" ``jac(x, *args) -> array_like, shape (n,)``\n",
|
|
" \n",
|
|
" where x is an array with shape (n,) and `args` is a tuple with\n",
|
|
" the fixed parameters. Alternatively, the keywords\n",
|
|
" {'2-point', '3-point', 'cs'} select a finite\n",
|
|
" difference scheme for numerical estimation of the gradient. Options\n",
|
|
" '3-point' and 'cs' are available only to 'trust-constr'.\n",
|
|
" If `jac` is a Boolean and is True, `fun` is assumed to return the\n",
|
|
" gradient along with the objective function. If False, the gradient\n",
|
|
" will be estimated using '2-point' finite difference estimation.\n",
|
|
" hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy}, optional\n",
|
|
" Method for computing the Hessian matrix. Only for Newton-CG, dogleg,\n",
|
|
" trust-ncg, trust-krylov, trust-exact and trust-constr. If it is\n",
|
|
" callable, it should return the Hessian matrix:\n",
|
|
" \n",
|
|
" ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)``\n",
|
|
" \n",
|
|
" where x is a (n,) ndarray and `args` is a tuple with the fixed\n",
|
|
" parameters. LinearOperator and sparse matrix returns are\n",
|
|
" allowed only for 'trust-constr' method. Alternatively, the keywords\n",
|
|
" {'2-point', '3-point', 'cs'} select a finite difference scheme\n",
|
|
" for numerical estimation. Or, objects implementing\n",
|
|
" `HessianUpdateStrategy` interface can be used to approximate\n",
|
|
" the Hessian. Available quasi-Newton methods implementing\n",
|
|
" this interface are:\n",
|
|
" \n",
|
|
" - `BFGS`;\n",
|
|
" - `SR1`.\n",
|
|
" \n",
|
|
" Whenever the gradient is estimated via finite-differences,\n",
|
|
" the Hessian cannot be estimated with options\n",
|
|
" {'2-point', '3-point', 'cs'} and needs to be\n",
|
|
" estimated using one of the quasi-Newton strategies.\n",
|
|
" Finite-difference options {'2-point', '3-point', 'cs'} and\n",
|
|
" `HessianUpdateStrategy` are available only for 'trust-constr' method.\n",
|
|
" hessp : callable, optional\n",
|
|
" Hessian of objective function times an arbitrary vector p. Only for\n",
|
|
" Newton-CG, trust-ncg, trust-krylov, trust-constr.\n",
|
|
" Only one of `hessp` or `hess` needs to be given. If `hess` is\n",
|
|
" provided, then `hessp` will be ignored. `hessp` must compute the\n",
|
|
" Hessian times an arbitrary vector:\n",
|
|
" \n",
|
|
" ``hessp(x, p, *args) -> ndarray shape (n,)``\n",
|
|
" \n",
|
|
" where x is a (n,) ndarray, p is an arbitrary vector with\n",
|
|
" dimension (n,) and `args` is a tuple with the fixed\n",
|
|
" parameters.\n",
|
|
" bounds : sequence or `Bounds`, optional\n",
|
|
" Bounds on variables for L-BFGS-B, TNC, SLSQP and\n",
|
|
" trust-constr methods. There are two ways to specify the bounds:\n",
|
|
" \n",
|
|
" 1. Instance of `Bounds` class.\n",
|
|
" 2. Sequence of ``(min, max)`` pairs for each element in `x`. None\n",
|
|
" is used to specify no bound.\n",
|
|
" \n",
|
|
" constraints : {Constraint, dict} or List of {Constraint, dict}, optional\n",
|
|
" Constraints definition (only for COBYLA, SLSQP and trust-constr).\n",
|
|
" Constraints for 'trust-constr' are defined as a single object or a\n",
|
|
" list of objects specifying constraints to the optimization problem.\n",
|
|
" Available constraints are:\n",
|
|
" \n",
|
|
" - `LinearConstraint`\n",
|
|
" - `NonlinearConstraint`\n",
|
|
" \n",
|
|
" Constraints for COBYLA, SLSQP are defined as a list of dictionaries.\n",
|
|
" Each dictionary with fields:\n",
|
|
" \n",
|
|
" type : str\n",
|
|
" Constraint type: 'eq' for equality, 'ineq' for inequality.\n",
|
|
" fun : callable\n",
|
|
" The function defining the constraint.\n",
|
|
" jac : callable, optional\n",
|
|
" The Jacobian of `fun` (only for SLSQP).\n",
|
|
" args : sequence, optional\n",
|
|
" Extra arguments to be passed to the function and Jacobian.\n",
|
|
" \n",
|
|
" Equality constraint means that the constraint function result is to\n",
|
|
" be zero whereas inequality means that it is to be non-negative.\n",
|
|
" Note that COBYLA only supports inequality constraints.\n",
|
|
" tol : float, optional\n",
|
|
" Tolerance for termination. For detailed control, use solver-specific\n",
|
|
" options.\n",
|
|
" options : dict, optional\n",
|
|
" A dictionary of solver options. All methods accept the following\n",
|
|
" generic options:\n",
|
|
" \n",
|
|
" maxiter : int\n",
|
|
" Maximum number of iterations to perform.\n",
|
|
" disp : bool\n",
|
|
" Set to True to print convergence messages.\n",
|
|
" \n",
|
|
" For method-specific options, see :func:`show_options()`.\n",
|
|
" callback : callable, optional\n",
|
|
" Called after each iteration. For 'trust-constr' it is a callable with\n",
|
|
" the signature:\n",
|
|
" \n",
|
|
" ``callback(xk, OptimizeResult state) -> bool``\n",
|
|
" \n",
|
|
" where ``xk`` is the current parameter vector. and ``state``\n",
|
|
" is an `OptimizeResult` object, with the same fields\n",
|
|
" as the ones from the return. If callback returns True\n",
|
|
" the algorithm execution is terminated.\n",
|
|
" For all the other methods, the signature is:\n",
|
|
" \n",
|
|
" ``callback(xk)``\n",
|
|
" \n",
|
|
" where ``xk`` is the current parameter vector.\n",
|
|
" \n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" res : OptimizeResult\n",
|
|
" The optimization result represented as a ``OptimizeResult`` object.\n",
|
|
" Important attributes are: ``x`` the solution array, ``success`` a\n",
|
|
" Boolean flag indicating if the optimizer exited successfully and\n",
|
|
" ``message`` which describes the cause of the termination. See\n",
|
|
" `OptimizeResult` for a description of other attributes.\n",
|
|
" \n",
|
|
" See also\n",
|
|
" --------\n",
|
|
" minimize_scalar : Interface to minimization algorithms for scalar\n",
|
|
" univariate functions\n",
|
|
" show_options : Additional options accepted by the solvers\n",
|
|
" \n",
|
|
" Notes\n",
|
|
" -----\n",
|
|
" This section describes the available solvers that can be selected by the\n",
|
|
" 'method' parameter. The default method is *BFGS*.\n",
|
|
" \n",
|
|
" **Unconstrained minimization**\n",
|
|
" \n",
|
|
" Method :ref:`Nelder-Mead <optimize.minimize-neldermead>` uses the\n",
|
|
" Simplex algorithm [1]_, [2]_. This algorithm is robust in many\n",
|
|
" applications. However, if numerical computation of derivative can be\n",
|
|
" trusted, other algorithms using the first and/or second derivatives\n",
|
|
" information might be preferred for their better performance in\n",
|
|
" general.\n",
|
|
" \n",
|
|
" Method :ref:`Powell <optimize.minimize-powell>` is a modification\n",
|
|
" of Powell's method [3]_, [4]_ which is a conjugate direction\n",
|
|
" method. It performs sequential one-dimensional minimizations along\n",
|
|
" each vector of the directions set (`direc` field in `options` and\n",
|
|
" `info`), which is updated at each iteration of the main\n",
|
|
" minimization loop. The function need not be differentiable, and no\n",
|
|
" derivatives are taken.\n",
|
|
" \n",
|
|
" Method :ref:`CG <optimize.minimize-cg>` uses a nonlinear conjugate\n",
|
|
" gradient algorithm by Polak and Ribiere, a variant of the\n",
|
|
" Fletcher-Reeves method described in [5]_ pp. 120-122. Only the\n",
|
|
" first derivatives are used.\n",
|
|
" \n",
|
|
" Method :ref:`BFGS <optimize.minimize-bfgs>` uses the quasi-Newton\n",
|
|
" method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) [5]_\n",
|
|
" pp. 136. It uses the first derivatives only. BFGS has proven good\n",
|
|
" performance even for non-smooth optimizations. This method also\n",
|
|
" returns an approximation of the Hessian inverse, stored as\n",
|
|
" `hess_inv` in the OptimizeResult object.\n",
|
|
" \n",
|
|
" Method :ref:`Newton-CG <optimize.minimize-newtoncg>` uses a\n",
|
|
" Newton-CG algorithm [5]_ pp. 168 (also known as the truncated\n",
|
|
" Newton method). It uses a CG method to the compute the search\n",
|
|
" direction. See also *TNC* method for a box-constrained\n",
|
|
" minimization with a similar algorithm. Suitable for large-scale\n",
|
|
" problems.\n",
|
|
" \n",
|
|
" Method :ref:`dogleg <optimize.minimize-dogleg>` uses the dog-leg\n",
|
|
" trust-region algorithm [5]_ for unconstrained minimization. This\n",
|
|
" algorithm requires the gradient and Hessian; furthermore the\n",
|
|
" Hessian is required to be positive definite.\n",
|
|
" \n",
|
|
" Method :ref:`trust-ncg <optimize.minimize-trustncg>` uses the\n",
|
|
" Newton conjugate gradient trust-region algorithm [5]_ for\n",
|
|
" unconstrained minimization. This algorithm requires the gradient\n",
|
|
" and either the Hessian or a function that computes the product of\n",
|
|
" the Hessian with a given vector. Suitable for large-scale problems.\n",
|
|
" \n",
|
|
" Method :ref:`trust-krylov <optimize.minimize-trustkrylov>` uses\n",
|
|
" the Newton GLTR trust-region algorithm [14]_, [15]_ for unconstrained\n",
|
|
" minimization. This algorithm requires the gradient\n",
|
|
" and either the Hessian or a function that computes the product of\n",
|
|
" the Hessian with a given vector. Suitable for large-scale problems.\n",
|
|
" On indefinite problems it requires usually less iterations than the\n",
|
|
" `trust-ncg` method and is recommended for medium and large-scale problems.\n",
|
|
" \n",
|
|
" Method :ref:`trust-exact <optimize.minimize-trustexact>`\n",
|
|
" is a trust-region method for unconstrained minimization in which\n",
|
|
" quadratic subproblems are solved almost exactly [13]_. This\n",
|
|
" algorithm requires the gradient and the Hessian (which is\n",
|
|
" *not* required to be positive definite). It is, in many\n",
|
|
" situations, the Newton method to converge in fewer iteraction\n",
|
|
" and the most recommended for small and medium-size problems.\n",
|
|
" \n",
|
|
" **Bound-Constrained minimization**\n",
|
|
" \n",
|
|
" Method :ref:`L-BFGS-B <optimize.minimize-lbfgsb>` uses the L-BFGS-B\n",
|
|
" algorithm [6]_, [7]_ for bound constrained minimization.\n",
|
|
" \n",
|
|
" Method :ref:`TNC <optimize.minimize-tnc>` uses a truncated Newton\n",
|
|
" algorithm [5]_, [8]_ to minimize a function with variables subject\n",
|
|
" to bounds. This algorithm uses gradient information; it is also\n",
|
|
" called Newton Conjugate-Gradient. It differs from the *Newton-CG*\n",
|
|
" method described above as it wraps a C implementation and allows\n",
|
|
" each variable to be given upper and lower bounds.\n",
|
|
" \n",
|
|
" **Constrained Minimization**\n",
|
|
" \n",
|
|
" Method :ref:`COBYLA <optimize.minimize-cobyla>` uses the\n",
|
|
" Constrained Optimization BY Linear Approximation (COBYLA) method\n",
|
|
" [9]_, [10]_, [11]_. The algorithm is based on linear\n",
|
|
" approximations to the objective function and each constraint. The\n",
|
|
" method wraps a FORTRAN implementation of the algorithm. The\n",
|
|
" constraints functions 'fun' may return either a single number\n",
|
|
" or an array or list of numbers.\n",
|
|
" \n",
|
|
" Method :ref:`SLSQP <optimize.minimize-slsqp>` uses Sequential\n",
|
|
" Least SQuares Programming to minimize a function of several\n",
|
|
" variables with any combination of bounds, equality and inequality\n",
|
|
" constraints. The method wraps the SLSQP Optimization subroutine\n",
|
|
" originally implemented by Dieter Kraft [12]_. Note that the\n",
|
|
" wrapper handles infinite values in bounds by converting them into\n",
|
|
" large floating values.\n",
|
|
" \n",
|
|
" Method :ref:`trust-constr <optimize.minimize-trustconstr>` is a\n",
|
|
" trust-region algorithm for constrained optimization. It swiches\n",
|
|
" between two implementations depending on the problem definition.\n",
|
|
" It is the most versatile constrained minimization algorithm\n",
|
|
" implemented in SciPy and the most appropriate for large-scale problems.\n",
|
|
" For equality constrained problems it is an implementation of Byrd-Omojokun\n",
|
|
" Trust-Region SQP method described in [17]_ and in [5]_, p. 549. When\n",
|
|
" inequality constraints are imposed as well, it swiches to the trust-region\n",
|
|
" interior point method described in [16]_. This interior point algorithm,\n",
|
|
" in turn, solves inequality constraints by introducing slack variables\n",
|
|
" and solving a sequence of equality-constrained barrier problems\n",
|
|
" for progressively smaller values of the barrier parameter.\n",
|
|
" The previously described equality constrained SQP method is\n",
|
|
" used to solve the subproblems with increasing levels of accuracy\n",
|
|
" as the iterate gets closer to a solution.\n",
|
|
" \n",
|
|
" **Finite-Difference Options**\n",
|
|
" \n",
|
|
" For Method :ref:`trust-constr <optimize.minimize-trustconstr>`\n",
|
|
" the gradient and the Hessian may be approximated using\n",
|
|
" three finite-difference schemes: {'2-point', '3-point', 'cs'}.\n",
|
|
" The scheme 'cs' is, potentially, the most accurate but it\n",
|
|
" requires the function to correctly handles complex inputs and to\n",
|
|
" be differentiable in the complex plane. The scheme '3-point' is more\n",
|
|
" accurate than '2-point' but requires twice as much operations.\n",
|
|
" \n",
|
|
" **Custom minimizers**\n",
|
|
" \n",
|
|
" It may be useful to pass a custom minimization method, for example\n",
|
|
" when using a frontend to this method such as `scipy.optimize.basinhopping`\n",
|
|
" or a different library. You can simply pass a callable as the ``method``\n",
|
|
" parameter.\n",
|
|
" \n",
|
|
" The callable is called as ``method(fun, x0, args, **kwargs, **options)``\n",
|
|
" where ``kwargs`` corresponds to any other parameters passed to `minimize`\n",
|
|
" (such as `callback`, `hess`, etc.), except the `options` dict, which has\n",
|
|
" its contents also passed as `method` parameters pair by pair. Also, if\n",
|
|
" `jac` has been passed as a bool type, `jac` and `fun` are mangled so that\n",
|
|
" `fun` returns just the function values and `jac` is converted to a function\n",
|
|
" returning the Jacobian. The method shall return an `OptimizeResult`\n",
|
|
" object.\n",
|
|
" \n",
|
|
" The provided `method` callable must be able to accept (and possibly ignore)\n",
|
|
" arbitrary parameters; the set of parameters accepted by `minimize` may\n",
|
|
" expand in future versions and then these parameters will be passed to\n",
|
|
" the method. You can find an example in the scipy.optimize tutorial.\n",
|
|
" \n",
|
|
" .. versionadded:: 0.11.0\n",
|
|
" \n",
|
|
" References\n",
|
|
" ----------\n",
|
|
" .. [1] Nelder, J A, and R Mead. 1965. A Simplex Method for Function\n",
|
|
" Minimization. The Computer Journal 7: 308-13.\n",
|
|
" .. [2] Wright M H. 1996. Direct search methods: Once scorned, now\n",
|
|
" respectable, in Numerical Analysis 1995: Proceedings of the 1995\n",
|
|
" Dundee Biennial Conference in Numerical Analysis (Eds. D F\n",
|
|
" Griffiths and G A Watson). Addison Wesley Longman, Harlow, UK.\n",
|
|
" 191-208.\n",
|
|
" .. [3] Powell, M J D. 1964. An efficient method for finding the minimum of\n",
|
|
" a function of several variables without calculating derivatives. The\n",
|
|
" Computer Journal 7: 155-162.\n",
|
|
" .. [4] Press W, S A Teukolsky, W T Vetterling and B P Flannery.\n",
|
|
" Numerical Recipes (any edition), Cambridge University Press.\n",
|
|
" .. [5] Nocedal, J, and S J Wright. 2006. Numerical Optimization.\n",
|
|
" Springer New York.\n",
|
|
" .. [6] Byrd, R H and P Lu and J. Nocedal. 1995. A Limited Memory\n",
|
|
" Algorithm for Bound Constrained Optimization. SIAM Journal on\n",
|
|
" Scientific and Statistical Computing 16 (5): 1190-1208.\n",
|
|
" .. [7] Zhu, C and R H Byrd and J Nocedal. 1997. L-BFGS-B: Algorithm\n",
|
|
" 778: L-BFGS-B, FORTRAN routines for large scale bound constrained\n",
|
|
" optimization. ACM Transactions on Mathematical Software 23 (4):\n",
|
|
" 550-560.\n",
|
|
" .. [8] Nash, S G. Newton-Type Minimization Via the Lanczos Method.\n",
|
|
" 1984. SIAM Journal of Numerical Analysis 21: 770-778.\n",
|
|
" .. [9] Powell, M J D. A direct search optimization method that models\n",
|
|
" the objective and constraint functions by linear interpolation.\n",
|
|
" 1994. Advances in Optimization and Numerical Analysis, eds. S. Gomez\n",
|
|
" and J-P Hennart, Kluwer Academic (Dordrecht), 51-67.\n",
|
|
" .. [10] Powell M J D. Direct search algorithms for optimization\n",
|
|
" calculations. 1998. Acta Numerica 7: 287-336.\n",
|
|
" .. [11] Powell M J D. A view of algorithms for optimization without\n",
|
|
" derivatives. 2007.Cambridge University Technical Report DAMTP\n",
|
|
" 2007/NA03\n",
|
|
" .. [12] Kraft, D. A software package for sequential quadratic\n",
|
|
" programming. 1988. Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace\n",
|
|
" Center -- Institute for Flight Mechanics, Koln, Germany.\n",
|
|
" .. [13] Conn, A. R., Gould, N. I., and Toint, P. L.\n",
|
|
" Trust region methods. 2000. Siam. pp. 169-200.\n",
|
|
" .. [14] F. Lenders, C. Kirches, A. Potschka: \"trlib: A vector-free\n",
|
|
" implementation of the GLTR method for iterative solution of\n",
|
|
" the trust region problem\", https://arxiv.org/abs/1611.04718\n",
|
|
" .. [15] N. Gould, S. Lucidi, M. Roma, P. Toint: \"Solving the\n",
|
|
" Trust-Region Subproblem using the Lanczos Method\",\n",
|
|
" SIAM J. Optim., 9(2), 504--525, (1999).\n",
|
|
" .. [16] Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal. 1999.\n",
|
|
" An interior point algorithm for large-scale nonlinear programming.\n",
|
|
" SIAM Journal on Optimization 9.4: 877-900.\n",
|
|
" .. [17] Lalee, Marucha, Jorge Nocedal, and Todd Plantega. 1998. On the\n",
|
|
" implementation of an algorithm for large-scale equality constrained\n",
|
|
" optimization. SIAM Journal on Optimization 8.3: 682-706.\n",
|
|
" \n",
|
|
" Examples\n",
|
|
" --------\n",
|
|
" Let us consider the problem of minimizing the Rosenbrock function. This\n",
|
|
" function (and its respective derivatives) is implemented in `rosen`\n",
|
|
" (resp. `rosen_der`, `rosen_hess`) in the `scipy.optimize`.\n",
|
|
" \n",
|
|
" >>> from scipy.optimize import minimize, rosen, rosen_der\n",
|
|
" \n",
|
|
" A simple application of the *Nelder-Mead* method is:\n",
|
|
" \n",
|
|
" >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]\n",
|
|
" >>> res = minimize(rosen, x0, method='Nelder-Mead', tol=1e-6)\n",
|
|
" >>> res.x\n",
|
|
" array([ 1., 1., 1., 1., 1.])\n",
|
|
" \n",
|
|
" Now using the *BFGS* algorithm, using the first derivative and a few\n",
|
|
" options:\n",
|
|
" \n",
|
|
" >>> res = minimize(rosen, x0, method='BFGS', jac=rosen_der,\n",
|
|
" ... options={'gtol': 1e-6, 'disp': True})\n",
|
|
" Optimization terminated successfully.\n",
|
|
" Current function value: 0.000000\n",
|
|
" Iterations: 26\n",
|
|
" Function evaluations: 31\n",
|
|
" Gradient evaluations: 31\n",
|
|
" >>> res.x\n",
|
|
" array([ 1., 1., 1., 1., 1.])\n",
|
|
" >>> print(res.message)\n",
|
|
" Optimization terminated successfully.\n",
|
|
" >>> res.hess_inv\n",
|
|
" array([[ 0.00749589, 0.01255155, 0.02396251, 0.04750988, 0.09495377], # may vary\n",
|
|
" [ 0.01255155, 0.02510441, 0.04794055, 0.09502834, 0.18996269],\n",
|
|
" [ 0.02396251, 0.04794055, 0.09631614, 0.19092151, 0.38165151],\n",
|
|
" [ 0.04750988, 0.09502834, 0.19092151, 0.38341252, 0.7664427 ],\n",
|
|
" [ 0.09495377, 0.18996269, 0.38165151, 0.7664427, 1.53713523]])\n",
|
|
" \n",
|
|
" \n",
|
|
" Next, consider a minimization problem with several constraints (namely\n",
|
|
" Example 16.4 from [5]_). The objective function is:\n",
|
|
" \n",
|
|
" >>> fun = lambda x: (x[0] - 1)**2 + (x[1] - 2.5)**2\n",
|
|
" \n",
|
|
" There are three constraints defined as:\n",
|
|
" \n",
|
|
" >>> cons = ({'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2},\n",
|
|
" ... {'type': 'ineq', 'fun': lambda x: -x[0] - 2 * x[1] + 6},\n",
|
|
" ... {'type': 'ineq', 'fun': lambda x: -x[0] + 2 * x[1] + 2})\n",
|
|
" \n",
|
|
" And variables must be positive, hence the following bounds:\n",
|
|
" \n",
|
|
" >>> bnds = ((0, None), (0, None))\n",
|
|
" \n",
|
|
" The optimization problem is solved using the SLSQP method as:\n",
|
|
" \n",
|
|
" >>> res = minimize(fun, (2, 0), method='SLSQP', bounds=bnds,\n",
|
|
" ... constraints=cons)\n",
|
|
" \n",
|
|
" It should converge to the theoretical solution (1.4 ,1.7).\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"help(minimize)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"L'optimisation fonctionne comme une fonction de minimisation, puisque nous voulons en fait maximiser le ratio de Sharpe, nous devrons le rendre négatif afin de pouvoir minimiser le sharpe négatif (comme pour maximiser le sharpe positif)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 27,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def neg_sharpe(weights):\n",
|
|
" return get_ret_vol_sr(weights)[2] * -1"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 28,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Contraintes\n",
|
|
"def check_sum(weights):\n",
|
|
" '''\n",
|
|
" Retourne 0 si la somme des poids vaut 1.0\n",
|
|
" '''\n",
|
|
" return np.sum(weights) - 1"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 29,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Par convention de fonction de minimisation, il devrait s'agir d'une fonction qui retourne zéro pour certaines conditions\n",
|
|
"cons = ({'type':'eq','fun': check_sum})"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 30,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# 0-1 pour chaque poids\n",
|
|
"bounds = ((0, 1), (0, 1), (0, 1), (0, 1))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 31,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Hypothèse initiale (répartition égale)\n",
|
|
"init_guess = [0.25,0.25,0.25,0.25]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 32,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Sequential Least Squares Programming (SLSQP)\n",
|
|
"# Programmation séquentielle des moindres carrés\n",
|
|
"opt_results = minimize(neg_sharpe,init_guess,method='SLSQP',bounds=bounds,constraints=cons)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 33,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
" fun: -1.0307168703356593\n",
|
|
" jac: array([ 5.64157963e-05, 4.18424606e-05, 3.39921728e-01, -4.44948673e-05])\n",
|
|
" message: 'Optimization terminated successfully.'\n",
|
|
" nfev: 42\n",
|
|
" nit: 7\n",
|
|
" njev: 7\n",
|
|
" status: 0\n",
|
|
" success: True\n",
|
|
" x: array([0.26628976, 0.20418983, 0. , 0.52952041])"
|
|
]
|
|
},
|
|
"execution_count": 33,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"opt_results"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 34,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([0.26628976, 0.20418983, 0. , 0.52952041])"
|
|
]
|
|
},
|
|
"execution_count": 34,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"opt_results.x"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 35,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([0.21885915, 0.21233683, 1.03071687])"
|
|
]
|
|
},
|
|
"execution_count": 35,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"get_ret_vol_sr(opt_results.x)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Portefeuilles Optimaux (Frontière Efficiente)\n",
|
|
"\n",
|
|
"La frontière efficiente est l'ensemble des portefeuilles optimaux qui offrent le rendement attendu le plus élevé pour un niveau de risque défini ou le risque le plus faible pour un niveau de rendement attendu donné. Les portefeuilles qui se situent sous la frontière efficiente sont sous-optimaux, car ils n'offrent pas un rendement suffisant pour le niveau de risque. Les portefeuilles qui se regroupent à droite de la frontière efficiente sont également sous-optimaux, car ils présentent un niveau de risque plus élevé pour le taux de rendement défini.\n",
|
|
"\n",
|
|
"En résumé, la frontière efficiente est composée de l'ensemble des portefeuilles (combinaisons de titres) qui présentent la meilleure rentabilité pour un niveau de risque donné.\n",
|
|
"\n",
|
|
"Frontière Efficiente https://epargne.ooreka.fr/astuce/voir/678865/frontiere-efficiente"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 36,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Nos rendements vont de 0 à 0.3\n",
|
|
"# Créer un nombre de points linéairement espacés pour calculer x dessus\n",
|
|
"frontier_y = np.linspace(0,0.3,100) # Changez 100 à un chiffre inférieur pour les ordinateurs plus lents !"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 37,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def minimize_volatility(weights):\n",
|
|
" return get_ret_vol_sr(weights)[1] "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 38,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"frontier_volatility = []\n",
|
|
"\n",
|
|
"for possible_return in frontier_y:\n",
|
|
" # contraintes\n",
|
|
" cons = ({'type':'eq','fun': check_sum},\n",
|
|
" {'type':'eq','fun': lambda w: get_ret_vol_sr(w)[0] - possible_return})\n",
|
|
" \n",
|
|
" result = minimize(minimize_volatility,init_guess,method='SLSQP',bounds=bounds,constraints=cons)\n",
|
|
" \n",
|
|
" frontier_volatility.append(result['fun'])"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 39,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"[<matplotlib.lines.Line2D at 0x115951ad0>]"
|
|
]
|
|
},
|
|
"execution_count": 39,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 864x576 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure(figsize=(12,8))\n",
|
|
"plt.scatter(vol_arr,ret_arr,c=sharpe_arr,cmap='plasma')\n",
|
|
"plt.colorbar(label='Sharpe Ratio')\n",
|
|
"plt.xlabel('Volatility')\n",
|
|
"plt.ylabel('Return')\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"# Ajouter une ligne de frontière\n",
|
|
"plt.plot(frontier_volatility,frontier_y,'g--',linewidth=3)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Bon Travail!"
|
|
]
|
|
}
|
|
],
|
|
"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": "3.8.5-final"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
} |