mirror of
https://github.com/ArthurDanjou/ArtStudies.git
synced 2026-01-14 18:59:59 +01:00
Arthur DANJOU
8cf328e18a
- Updated import order in Point_Fixe.ipynb for consistency. - Changed lambda functions to regular function definitions for clarity in Point_Fixe.ipynb. - Added numpy import in TP1_EDO_EulerExp.ipynb, TP2_Lokta_Volterra.ipynb, and TP3_Convergence.ipynb for better readability. - Modified for loops in TP1_EDO_EulerExp.ipynb and TP2_Lokta_Volterra.ipynb to include strict=False for compatibility with future Python versions.
524 lines
16 KiB
Plaintext
524 lines
16 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "81049114d821d00e",
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"metadata": {},
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"source": [
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"# Project - Portfolio Management\n",
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"\n",
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"## Group: Danjou Arthur & Forest Thais\n",
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"\n",
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"### Time period studied from 2017-01-01 to 2018-01-01\n",
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"\n",
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"### Risk-free rate: 2%"
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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": 51,
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"id": "initial_id",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-11-25T13:43:46.298758Z",
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"start_time": "2024-11-25T13:43:46.293696Z"
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},
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"collapsed": true
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},
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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 yfinance as yf"
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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": 52,
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"id": "9f9fc36832c97e0",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-11-25T13:43:47.318911Z",
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"start_time": "2024-11-25T13:43:47.198820Z"
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}
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},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"[*********************100%***********************] 1 of 1 completed\n",
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"[*********************100%***********************] 1 of 1 completed\n",
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"[*********************100%***********************] 1 of 1 completed\n",
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"[*********************100%***********************] 1 of 1 completed\n",
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"/var/folders/tp/_ld5_pzs6nx6mv1pbjhq1l740000gn/T/ipykernel_92506/348989065.py:9: FutureWarning: DataFrame.interpolate with method=pad is deprecated and will raise in a future version. Use obj.ffill() or obj.bfill() instead.\n",
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" S = S.interpolate(method=\"pad\")\n"
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]
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},
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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 thead th {\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>^RUT</th>\n",
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" <th>^IXIC</th>\n",
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" <th>^GSPC</th>\n",
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" <th>XWD.TO</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>2017-01-03 00:00:00+00:00</th>\n",
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" <td>1365.489990</td>\n",
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" <td>5429.080078</td>\n",
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" <td>2257.830078</td>\n",
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" <td>38.499630</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2017-01-04 00:00:00+00:00</th>\n",
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" <td>1387.949951</td>\n",
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" <td>5477.000000</td>\n",
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" <td>2270.750000</td>\n",
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" <td>38.553375</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2017-01-05 00:00:00+00:00</th>\n",
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" <td>1371.939941</td>\n",
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" <td>5487.939941</td>\n",
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" <td>2269.000000</td>\n",
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" <td>38.481716</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2017-01-06 00:00:00+00:00</th>\n",
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" <td>1367.280029</td>\n",
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" <td>5521.060059</td>\n",
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" <td>2276.979980</td>\n",
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" <td>38.517544</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2017-01-09 00:00:00+00:00</th>\n",
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" <td>1357.489990</td>\n",
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" <td>5531.819824</td>\n",
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" <td>2268.899902</td>\n",
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" <td>38.383186</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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" ^RUT ^IXIC ^GSPC XWD.TO\n",
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"Date \n",
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"2017-01-03 00:00:00+00:00 1365.489990 5429.080078 2257.830078 38.499630\n",
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"2017-01-04 00:00:00+00:00 1387.949951 5477.000000 2270.750000 38.553375\n",
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"2017-01-05 00:00:00+00:00 1371.939941 5487.939941 2269.000000 38.481716\n",
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"2017-01-06 00:00:00+00:00 1367.280029 5521.060059 2276.979980 38.517544\n",
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"2017-01-09 00:00:00+00:00 1357.489990 5531.819824 2268.899902 38.383186"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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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>^RUT</th>\n",
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" <th>^IXIC</th>\n",
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" <th>^GSPC</th>\n",
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" <th>XWD.TO</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>2017-12-22 00:00:00+00:00</th>\n",
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" <td>1542.930054</td>\n",
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" <td>6959.959961</td>\n",
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" <td>2683.340088</td>\n",
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" <td>44.323349</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2017-12-26 00:00:00+00:00</th>\n",
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" <td>1544.229980</td>\n",
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" <td>6936.250000</td>\n",
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" <td>2680.500000</td>\n",
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" <td>44.323349</td>\n",
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" <tr>\n",
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" <th>2017-12-27 00:00:00+00:00</th>\n",
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" <td>1543.939941</td>\n",
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" <td>6939.339844</td>\n",
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" <td>2682.620117</td>\n",
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" <td>44.052303</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2017-12-28 00:00:00+00:00</th>\n",
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" <td>1548.930054</td>\n",
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" <td>6950.160156</td>\n",
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" <td>2687.540039</td>\n",
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" <td>43.857414</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2017-12-29 00:00:00+00:00</th>\n",
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" <td>1535.510010</td>\n",
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" <td>6903.390137</td>\n",
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" <td>2673.610107</td>\n",
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" <td>43.784576</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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"text/plain": [
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" ^RUT ^IXIC ^GSPC XWD.TO\n",
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"Date \n",
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"2017-12-22 00:00:00+00:00 1542.930054 6959.959961 2683.340088 44.323349\n",
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"2017-12-26 00:00:00+00:00 1544.229980 6936.250000 2680.500000 44.323349\n",
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"2017-12-27 00:00:00+00:00 1543.939941 6939.339844 2682.620117 44.052303\n",
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"2017-12-28 00:00:00+00:00 1548.930054 6950.160156 2687.540039 43.857414\n",
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"2017-12-29 00:00:00+00:00 1535.510010 6903.390137 2673.610107 43.784576"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(251, 4)\n"
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]
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}
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],
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"source": [
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"# Data Extraction\n",
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"Tickers = [\"^RUT\", \"^IXIC\", \"^GSPC\", \"XWD.TO\"]\n",
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"start_input = \"2017-01-01\"\n",
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"end_input = \"2018-01-01\"\n",
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"S = pd.DataFrame()\n",
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"for t in Tickers:\n",
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" S[t] = yf.Tickers(t).history(start=start_input, end=end_input)[\"Close\"]\n",
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"\n",
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"S = S.interpolate(method=\"pad\")\n",
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"\n",
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"# Show the first five and last five values extracted\n",
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"display(S.head())\n",
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"display(S.tail())\n",
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"print(S.shape)"
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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": 53,
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"id": "53483cf3a925a4db",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-11-25T13:43:50.080380Z",
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"start_time": "2024-11-25T13:43:50.073119Z"
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}
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},
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"outputs": [],
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"source": [
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"R = S / S.shift() - 1\n",
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"R = R[1:]\n",
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"mean_d = R.mean()\n",
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"covar_d = R.cov()\n",
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"corr = R.corr()"
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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": 54,
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"id": "c327ed5967b1f442",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-11-25T13:43:50.965092Z",
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"start_time": "2024-11-25T13:43:50.961969Z"
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}
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},
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"outputs": [],
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"source": [
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"mean = mean_d * 252\n",
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"covar = covar_d * 252\n",
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"std = np.sqrt(np.diag(covar))"
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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": 55,
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"id": "6bc6a850bf06cc9d",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-11-25T13:43:51.701725Z",
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"start_time": "2024-11-25T13:43:51.695020Z"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Mean:\n",
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"\n",
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"^RUT 0.125501\n",
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"^IXIC 0.246863\n",
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"^GSPC 0.172641\n",
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"XWD.TO 0.133175\n",
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"dtype: float64\n",
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"\n",
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"Covariance:\n",
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"\n",
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" ^RUT ^IXIC ^GSPC XWD.TO\n",
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"^RUT 0.014417 0.008400 0.006485 0.004797\n",
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"^IXIC 0.008400 0.009182 0.005583 0.004337\n",
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"^GSPC 0.006485 0.005583 0.004426 0.003309\n",
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"XWD.TO 0.004797 0.004337 0.003309 0.006996\n",
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"\n",
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"Standard Deviation:\n",
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"\n",
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"[0.12007222 0.09582499 0.06653127 0.08364295]\n",
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"\n",
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"Correlation:\n",
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"\n",
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" ^RUT ^IXIC ^GSPC XWD.TO\n",
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"^RUT 1.000000 0.730047 0.811734 0.477668\n",
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"^IXIC 0.730047 1.000000 0.875687 0.541087\n",
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"^GSPC 0.811734 0.875687 1.000000 0.594658\n",
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"XWD.TO 0.477668 0.541087 0.594658 1.000000\n"
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]
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}
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],
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"source": [
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"print(\"Mean:\\n\")\n",
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"print(mean)\n",
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"print(\"\\nCovariance:\\n\")\n",
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"print(covar)\n",
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"print(\"\\nStandard Deviation:\\n\")\n",
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"print(std)\n",
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"print(\"\\nCorrelation:\\n\")\n",
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"print(corr)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fc4bec874f710f7c",
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"metadata": {},
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"source": "# Question 1"
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},
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{
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"cell_type": "code",
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"execution_count": 56,
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"id": "780c9cca6e0ed2d3",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-11-25T13:43:53.113423Z",
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"start_time": "2024-11-25T13:43:53.109514Z"
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}
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},
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"outputs": [],
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"source": [
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"r = 0.02\n",
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"d = len(Tickers)\n",
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"vec1 = np.linspace(1, 1, d)\n",
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"sigma = covar\n",
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"inv_sigma = np.linalg.inv(sigma)\n",
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"\n",
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"a = vec1.T.dot(inv_sigma).dot(vec1)\n",
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"b = mean.T.dot(inv_sigma).dot(vec1)"
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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": 57,
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"id": "81c956f147c68070",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-11-25T13:43:54.545400Z",
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"start_time": "2024-11-25T13:43:54.541579Z"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Expected return m_T: 0.2364033641931515\n",
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"Standard deviation sd_T: 0.07276528490265963\n",
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"Allocation pi_T: [-0.60853811 0.45748917 1.17944152 -0.02839259]\n",
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"We can verify that the allocation is possible as the sum of the allocations for the different indices is 0.9999999999999993, that is very close to 1\n"
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]
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}
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],
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"source": [
|
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"# Tangent portfolio\n",
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"pi_T = inv_sigma.dot(mean - r * vec1) / (b - r * a)\n",
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"sd_T = np.sqrt(pi_T.T.dot(sigma).dot(pi_T)) # Variance\n",
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"m_T = pi_T.T.dot(mean) # expected return\n",
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"\n",
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"print(f\"Expected return m_T: {m_T}\")\n",
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"print(f\"Standard deviation sd_T: {sd_T}\")\n",
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"print(f\"Allocation pi_T: {pi_T}\")\n",
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"print(\n",
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" f\"We can verify that the allocation is possible as the sum of the allocations for the different indices is {sum(pi_T)}, that is very close to 1\"\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2e121c2dfb946f3c",
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"metadata": {},
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"source": "# Question 2"
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},
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{
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"cell_type": "code",
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"execution_count": 58,
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"id": "c169808384ca1112",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-11-25T13:43:59.797115Z",
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"start_time": "2024-11-25T13:43:59.792462Z"
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}
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},
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"outputs": [
|
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The annualized volatilities of the index ^RUT is 0.12007221535411407\n",
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"The annualized expected returns of the index ^RUT is 0.12550141384538263\n",
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"\n",
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"The annualized volatilities of the index ^IXIC is 0.09582499431305072\n",
|
|
"The annualized expected returns of the index ^IXIC is 0.24686267015709437\n",
|
|
"\n",
|
|
"The annualized volatilities of the index ^GSPC is 0.06653126757186174\n",
|
|
"The annualized expected returns of the index ^GSPC is 0.17264098207081371\n",
|
|
"\n",
|
|
"The annualized volatilities of the index XWD.TO is 0.08364295296865466\n",
|
|
"The annualized expected returns of the index XWD.TO is 0.1331750489518068\n",
|
|
"\n",
|
|
"The annualized volatility of the Tangent Portfolio is 1.155113087587201\n",
|
|
"The annualized expected return of the Tangent Portfolio is 59.57364777667418\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"for i in range(len(std)):\n",
|
|
" print(f\"The annualized volatilities of the index {Tickers[i]} is {std[i]}\")\n",
|
|
" print(\n",
|
|
" f\"The annualized expected returns of the index {Tickers[i]} is {mean[Tickers[i]]}\"\n",
|
|
" )\n",
|
|
" print(\"\")\n",
|
|
"\n",
|
|
"print(f\"The annualized volatility of the Tangent Portfolio is {sd_T * np.sqrt(252)}\")\n",
|
|
"print(f\"The annualized expected return of the Tangent Portfolio is {m_T * 252}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "af8d29ecdbf2ae1",
|
|
"metadata": {},
|
|
"source": "# Question 3"
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 59,
|
|
"id": "2e0215ab7904906a",
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2024-11-25T13:44:01.393591Z",
|
|
"start_time": "2024-11-25T13:44:01.388830Z"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"sharpe ratio of the Tangent portfolio : 2.9739918490340687\n",
|
|
"the sharpe ratio of the index ^RUT is 0.8786496820620858\n",
|
|
"the sharpe ratio of the index ^IXIC is 2.3674686524473625\n",
|
|
"the sharpe ratio of the index ^GSPC is 2.294274371158541\n",
|
|
"the sharpe ratio of the index XWD.TO is 1.353073330567601\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(\"sharpe ratio of the Tangent portfolio :\", (m_T - r) / sd_T)\n",
|
|
"\n",
|
|
"for i in range(4):\n",
|
|
" print(\n",
|
|
" f\"the sharpe ratio of the index {Tickers[i]} is {(mean[Tickers[i]] - r) / std[i]}\"\n",
|
|
" )"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 2
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython2",
|
|
"version": "2.7.6"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|