python/notebooks/ch3_data_preparation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LaTeX macros (hidden cell)\n",
    "$\n",
    "\\newcommand{\\Q}{\\mathcal{Q}}\n",
    "\\newcommand{\\ECov}{\\boldsymbol{\\Sigma}}\n",
    "\\newcommand{\\EMean}{\\boldsymbol{\\mu}}\n",
    "\\newcommand{\\EAlpha}{\\boldsymbol{\\alpha}}\n",
    "\\newcommand{\\EBeta}{\\boldsymbol{\\beta}}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imports and configuration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "import os\n",
    "import re\n",
    "import datetime as dt\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import LinearSegmentedColormap\n",
    "\n",
    "from notebook.services.config import ConfigManager\n",
    "\n",
    "from portfolio_tools import data_download, DataReader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6.9 (default, Jan 26 2021, 15:33:00) \n",
      "[GCC 8.4.0]\n",
      "matplotlib: 3.3.4\n"
     ]
    }
   ],
   "source": [
    "# Version checks\n",
    "print(sys.version)\n",
    "print('matplotlib: {}'.format(matplotlib.__version__))\n",
    "\n",
    "# Jupyter configuration\n",
    "c = ConfigManager()\n",
    "c.update('notebook', {\"CodeCell\": {\"cm_config\": {\"autoCloseBrackets\": False}}})  \n",
    "\n",
    "# Numpy options\n",
    "np.set_printoptions(precision=5, linewidth=120, suppress=True)\n",
    "\n",
    "# Pandas options\n",
    "pd.set_option('display.max_rows', None)\n",
    "\n",
    "# Matplotlib options\n",
    "plt.rcParams['figure.figsize'] = [12, 8]\n",
    "plt.rcParams['figure.dpi'] = 200"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prepare input data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we compute the optimization input variables, the vector $\\EMean$ of expected returns, and the covariance matrix $\\ECov$, from raw data. The data consists of daily stock prices of $8$ stocks from the US market. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Download data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data downloading:\n",
    "# If the user has an API key for alphavantage.co, then this code part will download the data. \n",
    "# The code can be modified to download from other sources. To be able to run the examples, \n",
    "# and reproduce results in the cookbook, the files have to have the following format and content:\n",
    "# - File name pattern: \"daily_adjusted_[TICKER].csv\", where TICKER is the symbol of a stock. \n",
    "# - The file contains at least columns \"timestamp\", \"adjusted_close\", and \"volume\".\n",
    "# - The data is daily price/volume, covering at least the period from 2016-03-18 until 2021-03-18, \n",
    "# - Files are for the stocks PM, LMT, MCD, MMM, AAPL, MSFT, TXN, CSCO.\n",
    "list_stocks = [\"PM\", \"LMT\", \"MCD\", \"MMM\", \"AAPL\", \"MSFT\", \"TXN\", \"CSCO\"]\n",
    "list_factors = []\n",
    "alphaToken = None\n",
    " \n",
    "list_tickers = list_stocks + list_factors\n",
    "if alphaToken is not None:\n",
    "    data_download(list_tickers, alphaToken)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We load the daily stock price data from the downloaded CSV files. The data is adjusted for splits and dividends. Then a selected time period is taken from the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "investment_start = \"2016-03-18\"\n",
    "investment_end = \"2021-03-18\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found data files: \n",
      "stock_data/daily_adjusted_AAPL.csv\n",
      "stock_data/daily_adjusted_PM.csv\n",
      "stock_data/daily_adjusted_CSCO.csv\n",
      "stock_data/daily_adjusted_TXN.csv\n",
      "stock_data/daily_adjusted_MMM.csv\n",
      "stock_data/daily_adjusted_MCD.csv\n",
      "stock_data/daily_adjusted_SPY.csv\n",
      "stock_data/daily_adjusted_MSFT.csv\n",
      "stock_data/daily_adjusted_LMT.csv\n",
      "\n",
      "Using data files: \n",
      "stock_data/daily_adjusted_PM.csv\n",
      "stock_data/daily_adjusted_LMT.csv\n",
      "stock_data/daily_adjusted_MCD.csv\n",
      "stock_data/daily_adjusted_MMM.csv\n",
      "stock_data/daily_adjusted_AAPL.csv\n",
      "stock_data/daily_adjusted_MSFT.csv\n",
      "stock_data/daily_adjusted_TXN.csv\n",
      "stock_data/daily_adjusted_CSCO.csv\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# The files are in \"stock_data\" folder, named as \"daily_adjusted_[TICKER].csv\"\n",
    "dr = DataReader(folder_path=\"stock_data\", symbol_list=list_tickers)\n",
    "dr.read_data()\n",
    "df_prices, _ = dr.get_period(start_date=investment_start, end_date=investment_end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute yearly return statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we use the loaded daily price data to compute the corresponding yearly mean return and covariance matrix. The below logic is implemented also in the `portfolio_tools` module as a function. It is used in the other notebooks.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Compute weekly logarithmic return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we convert the daily prices to weekly prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df_weekly_prices = df_prices.resample('W').last()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert the weekly prices to weekly logarithmic return."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_weekly_log_returns = np.log(df_weekly_prices) - np.log(df_weekly_prices.shift(1))\n",
    "df_weekly_log_returns = df_weekly_log_returns.dropna(how='all')\n",
    "df_weekly_log_returns = df_weekly_log_returns.fillna(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see based on the histograms that the distribution of weekly logarithmic return is approximately normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:title={'center':'PM'}>, <AxesSubplot:title={'center':'LMT'}>,\n",
       "        <AxesSubplot:title={'center':'MCD'}>],\n",
       "       [<AxesSubplot:title={'center':'MMM'}>, <AxesSubplot:title={'center':'AAPL'}>,\n",
       "        <AxesSubplot:title={'center':'MSFT'}>],\n",
       "       [<AxesSubplot:title={'center':'TXN'}>, <AxesSubplot:title={'center':'CSCO'}>, <AxesSubplot:>]], dtype=object)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 2400x1600 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_weekly_log_returns.hist(bins=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Compute the distribution of weekly logarithmic return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming that the distribution is normal, we estimate the mean and covariance of the weekly logarithmic return."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "return_array = df_weekly_log_returns.to_numpy()\n",
    "T = return_array.shape[0]\n",
    "m_weekly_log = np.mean(return_array, axis=0)\n",
    "S_weekly_log = np.cov(return_array.transpose())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Project the distribution to the investment horizon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we project the logarithmic return statistics to the investment horizon of 1 year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "m_log = 52 * m_weekly_log\n",
    "S_log = 52 * S_weekly_log"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Compute the distribution of yearly linear return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We recover the distribution of prices from the distribution of logarithmic returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_0 = df_weekly_prices.iloc[0].to_numpy()\n",
    "m_P = p_0 * np.exp(m_log + 1/2*np.diag(S_log))\n",
    "S_P = np.outer(m_P, m_P) * (np.exp(S_log) - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we convert the distribution of prices to the distribution of yearly linear returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 1 / p_0 * m_P - 1\n",
    "S = 1 / np.outer(p_0, p_0) * S_P"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}