02_Comparing_Stock_Indices.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparing Stock Indices\n",
    "\n",
    "by [Magnus Erik Hvass Pedersen](http://www.hvass-labs.org/)\n",
    "/ [GitHub](https://github.com/Hvass-Labs/FinanceOps) / [Videos on YouTube](https://www.youtube.com/playlist?list=PL9Hr9sNUjfsmlHaWuVxIA0pKL1yjryR0Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "When comparing the historical returns on stock indices, it is a common mistake to only consider a single time-period.\n",
    "\n",
    "We will compare three well-known stock indices for USA: The S&P 500 for large-cap stocks, the S&P 400 for mid-cap stocks, and the S&P 600 for small-cap stocks. We show that there are periods where each of these stock indices was better than the others.\n",
    "\n",
    "So a more proper way of comparing stock indices is to consider **all** investment periods. For example, instead of just comparing the returns between 1. January 1990 to 1. January 2018, we consider all 1-year investment periods between 1990 and 2018. We also consider all 2-year investment periods, 3-year periods, and so on all the way up to 10-year investment periods. We then calculate and compare various statistics to assess which stock index was best.\n",
    "\n",
    "This methodology was also used in the paper [Comparison of U.S. Stock Indices](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2667556)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python Imports\n",
    "\n",
    "This Jupyter Notebook is implemented in Python v. 3.6 and requires various packages for numerical computations and plotting. See the installation instructions in the README-file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports from Python packages.\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import FuncFormatter\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports from FinanceOps.\n",
    "from data_keys import *\n",
    "from data import load_index_data, load_usa_cpi\n",
    "from data import load_usa_gov_bond_1year, common_period\n",
    "from returns import annualized_returns, bond_annualized_returns\n",
    "from recovery import prob_recovery"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data\n",
    "\n",
    "We now load all the financial data we will be using."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the ticker-names for the stocks we consider.\n",
    "ticker_SP500 = \"S&P 500\"\n",
    "ticker_SP400 = \"S&P 400\"\n",
    "ticker_SP600 = \"S&P 600\"\n",
    "\n",
    "# All tickers for the stocks.\n",
    "tickers = [ticker_SP500, ticker_SP400, ticker_SP600]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define longer names for the stocks.\n",
    "name_SP500 = \"S&P 500 (Large Cap)\"\n",
    "name_SP400 = \"S&P 400 (Mid Cap)\"\n",
    "name_SP600 = \"S&P 600 (Small Cap)\"\n",
    "\n",
    "# All names for the stocks.\n",
    "names = [name_SP500, name_SP400, name_SP600]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the financial data for the stock indices.\n",
    "df_SP500 = load_index_data(ticker=ticker_SP500)\n",
    "df_SP400 = load_index_data(ticker=ticker_SP400,\n",
    "                           sales=False, book_value=False)\n",
    "df_SP600 = load_index_data(ticker=ticker_SP600,\n",
    "                           sales=False, book_value=False)\n",
    "\n",
    "# All DataFrames for the stocks.\n",
    "dfs = [df_SP500, df_SP400, df_SP600]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1989-01-03 00:00:00 2018-07-06 00:00:00\n"
     ]
    }
   ],
   "source": [
    "# Common date-range for the stocks.\n",
    "start_date, end_date = common_period(dfs=dfs)\n",
    "print(start_date, end_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the US CPI inflation index.\n",
    "cpi = load_usa_cpi()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the yields for US Gov. Bonds with 1-year maturity.\n",
    "bond_yields = load_usa_gov_bond_1year()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Max number of investment years to consider.\n",
    "num_years = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare Total Returns\n",
    "\n",
    "The first plot shows the so-called Total Return of the stock indices, which is the investor's return when dividends are reinvested in the same stock index and taxes are ignored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_total_returns(dfs, names, start_date=None, end_date=None):\n",
    "    \"\"\"\n",
    "    Plot and compare the Total Returns for the given DataFrames.\n",
    "    \n",
    "    :param dfs: List of Pandas DataFrames with TOTAL_RETURN data.\n",
    "    :param names: Names of the stock indices.\n",
    "    :param start_date: Plot from this date.\n",
    "    :param end_date: Plot to this date.\n",
    "    :return: None.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Create a new Pandas DataFrame which will be used\n",
    "    # to combine the time-series and plot them.\n",
    "    df2 = pd.DataFrame()\n",
    "\n",
    "    # For all the given DataFrames and their names.\n",
    "    for df, name in zip(dfs, names):\n",
    "        # Get the Total Return for the period.\n",
    "        tot_ret = df[TOTAL_RETURN][start_date:end_date]\n",
    "        # Normalize it to start at 1.0\n",
    "        tot_ret /= tot_ret[0]\n",
    "\n",
    "        # Add it to the DataFrame.\n",
    "        # It will be plotted with the given name.\n",
    "        df2[name] = tot_ret\n",
    "\n",
    "    # Plot it all.\n",
    "    df2.plot(title=\"Total Return\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_total_returns(dfs=dfs, names=names,\n",
    "                   start_date=start_date, end_date=end_date)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot clearly shows that the S&P 400 (Mid-Cap) had a much higher Total Return than the S&P 500 (Large-Cap) and S&P 600 (Small-Cap), and the S&P 500 performed slightly worse than the S&P 600.\n",
    "\n",
    "But this period was nearly 30 years. What if we consider shorter investment periods with different start and end-dates? We need more detailed statistics to answer these questions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate Annualized Returns\n",
    "\n",
    "We calculate the annualized returns of the stock indices for **all** investment periods of durations from 1 to 10 years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_ann_returns(df, start_date, end_date, num_years):\n",
    "    \"\"\"\n",
    "    Calculate the annualized returns for the Total Return\n",
    "    of the given DataFrame.\n",
    "    \n",
    "    A list is returned so that ann_ret[0] is a Pandas Series\n",
    "    with the ann.returns for 1-year periods, and ann_ret[1]\n",
    "    are the ann.returns for 2-year periods, etc.\n",
    "    \n",
    "    :param df: Pandas DataFrame with TOTAL_RETURN data.\n",
    "    :param start_date: Start-date for the data.\n",
    "    :param end_date: End-date for the data.\n",
    "    :return: List of Pandas Series.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Get the Total Return for the given period.\n",
    "    tot_ret = df[TOTAL_RETURN][start_date:end_date]\n",
    "    \n",
    "    # Calculate the annualized returns for all\n",
    "    # investment periods between 1 and num_years.\n",
    "    ann_ret = [annualized_returns(series=tot_ret, years=years)\n",
    "               for years in range(1, num_years+1)]\n",
    "    \n",
    "    return ann_ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Annualized returns for the S&P 500.\n",
    "ann_ret_SP500 = calc_ann_returns(df=df_SP500,\n",
    "                                 start_date=start_date,\n",
    "                                 end_date=end_date,\n",
    "                                 num_years=num_years)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Annualized returns for the S&P 400.\n",
    "ann_ret_SP400 = calc_ann_returns(df=df_SP400,\n",
    "                                 start_date=start_date,\n",
    "                                 end_date=end_date,\n",
    "                                 num_years=num_years)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Annualized returns for the S&P 600.\n",
    "ann_ret_SP600 = calc_ann_returns(df=df_SP600,\n",
    "                                 start_date=start_date,\n",
    "                                 end_date=end_date,\n",
    "                                 num_years=num_years)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Annualized returns for investing and reinvesting in\n",
    "# US Gov. Bonds with 1-year maturity.\n",
    "ann_ret_bond = bond_annualized_returns(df=bond_yields,\n",
    "                                       num_years=num_years)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Annualized returns for the US CPI inflation index.\n",
    "cpi2 = cpi[start_date:end_date]\n",
    "ann_ret_cpi = [annualized_returns(series=cpi2, years=i+1)\n",
    "               for i in range(num_years)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examples of Annualized Returns\n",
    "\n",
    "The lists we have created above contain the annualized returns for the stock indices as well as US Government Bonds and the US CPI inflation index.\n",
    "\n",
    "Let us show the annualized returns of the S&P 500 for all 1-year periods. This is itself a time-series. It shows that the return was about 0.347 (or 34.7%) for the year between 3. January 1989 and 3. January 1990. The return was only about 31.6% between 4. January 1989 and 4. January 1990. And so on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "1989-01-03    0.347433\n",
       "1989-01-04    0.316132\n",
       "1989-01-05    0.300592\n",
       "1989-01-06    0.299486\n",
       "1989-01-07    0.300960\n",
       "1989-01-08    0.302432\n",
       "1989-01-09    0.286608\n",
       "1989-01-10    0.280842\n",
       "1989-01-11    0.277912\n",
       "1989-01-12    0.241273\n",
       "Name: Total Return, dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ann_ret_SP500[0].head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also show the summary statistics for the annualized returns of **all** 1-year periods of the S&P 500. Note that a mean of about 0.113 means an average 1-year return of 11.3%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    10412.000000\n",
       "mean         0.112986\n",
       "std          0.163164\n",
       "min         -0.475388\n",
       "25%          0.048051\n",
       "50%          0.134127\n",
       "75%          0.212517\n",
       "max          0.725738\n",
       "Name: Total Return, dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ann_ret_SP500[0].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also show the annualized returns of the S&P 500 for all 10-year periods. This shows that between 3. January 1989 and 1999 the annualized return was about 19.3%. Between 4. January 1989 and 1999 it was about 19.1%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "1989-01-03    0.192505\n",
       "1989-01-04    0.190708\n",
       "1989-01-05    0.192068\n",
       "1989-01-06    0.194400\n",
       "1989-01-07    0.194111\n",
       "1989-01-08    0.194570\n",
       "1989-01-09    0.194175\n",
       "1989-01-10    0.194079\n",
       "1989-01-11    0.193035\n",
       "1989-01-12    0.190226\n",
       "Name: Total Return, dtype: float64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ann_ret_SP500[9].head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are the summary statistics for **all** 10-year periods of the S&P 500, which show that it returned about 8.2% per year on average, for **all** 10-year periods between 1989 and 2018."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    7125.000000\n",
       "mean        0.082307\n",
       "std         0.052215\n",
       "min        -0.046228\n",
       "25%         0.062988\n",
       "50%         0.079510\n",
       "75%         0.106382\n",
       "max         0.199302\n",
       "Name: Total Return, dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ann_ret_SP500[9].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For US Government Bonds we only consider bonds with 1-year maturity, so for multi-year periods we assume the return is reinvested in new 1-year bonds. Reinvesting in gov. bonds gave an average return of about 5.7% for **all** 10-year periods between 1962 and 2018."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    17372.000000\n",
       "mean         0.056716\n",
       "std          0.027343\n",
       "min          0.004515\n",
       "25%          0.038709\n",
       "50%          0.058005\n",
       "75%          0.076294\n",
       "max          0.104418\n",
       "Name: Bond Yield, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ann_ret_bond[9].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples of Good and Bad Periods\n",
    "\n",
    "Using the annualized returns we have just calculated, we can now easily find investment periods where one stock index was better than another."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_better(df1, df2, ann_ret1, ann_ret2,\n",
    "                name1, name2, years):\n",
    "    \"\"\"\n",
    "    Plot the Total Return for a period of the given number\n",
    "    of years where the return on stock 1 > stock 2.\n",
    "\n",
    "    If this does not exist, then plot for the period where\n",
    "    the return of stock 1 was closest to that of stock 2.\n",
    "    \n",
    "    :param df1: Pandas DataFrame for stock 1.\n",
    "    :param df2: Pandas DataFrame for stock 2.\n",
    "    :param ann_ret1: List of ann.returns for stock 1.\n",
    "    :param ann_ret2: List of ann.returns for stock 2.\n",
    "    :param name1: Name of stock 1.\n",
    "    :param name2: Name of stock 2.\n",
    "    :param years: Investment period in years.\n",
    "    :return: None.\n",
    "    \"\"\"\n",
    "\n",
    "    # Convert number of years to index.\n",
    "    i = years - 1\n",
    "\n",
    "    # Difference of annualized returns.\n",
    "    ann_ret_dif = ann_ret1[i] - ann_ret2[i]\n",
    "\n",
    "    # Find the biggest return difference and use its\n",
    "    # index as the start-date for the period to be plotted.\n",
    "    start_date = ann_ret_dif.idxmax()\n",
    "    \n",
    "    # The end-date for the period to be plotted.\n",
    "    days = int(years * 365.25)\n",
    "    end_date = start_date + pd.Timedelta(days=days)\n",
    "    \n",
    "    # Create a Pandas DataFrame with stock 1,\n",
    "    # whose Total Return is normalized to start at 1.0\n",
    "    df = pd.DataFrame()\n",
    "    tot_ret1 = df1[start_date:end_date][TOTAL_RETURN]\n",
    "    df[name1] = tot_ret1 / tot_ret1[0]\n",
    "\n",
    "    # Add stock 2 to the DataFrame.\n",
    "    tot_ret2 = df2[start_date:end_date][TOTAL_RETURN]\n",
    "    df[name2] = tot_ret2 / tot_ret2[0]\n",
    "\n",
    "    # Plot the two stocks' Total Return for this period.\n",
    "    df.plot(title=\"Total Return\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we show a 3-year period where the S&P 500 was better than the S&P 400."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_better(df1=df_SP500, df2=df_SP400,\n",
    "            ann_ret1=ann_ret_SP500,\n",
    "            ann_ret2=ann_ret_SP400,\n",
    "            name1=name_SP500,\n",
    "            name2=name_SP400,\n",
    "            years=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we show a 3-year period where the S&P 400 was better than the S&P 500."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_better(df1=df_SP400, df2=df_SP500,\n",
    "            ann_ret1=ann_ret_SP400,\n",
    "            ann_ret2=ann_ret_SP500,\n",
    "            name1=name_SP400,\n",
    "            name2=name_SP500,\n",
    "            years=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we show a 3-year period where the S&P 600 was better than the S&P 400."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_better(df1=df_SP600, df2=df_SP400,\n",
    "            ann_ret1=ann_ret_SP600,\n",
    "            ann_ret2=ann_ret_SP400,\n",
    "            name1=name_SP600,\n",
    "            name2=name_SP400,\n",
    "            years=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we show a 3-year period where the S&P 400 was better than the S&P 600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_better(df1=df_SP400, df2=df_SP600,\n",
    "            ann_ret1=ann_ret_SP400,\n",
    "            ann_ret2=ann_ret_SP600,\n",
    "            name1=name_SP400,\n",
    "            name2=name_SP600,\n",
    "            years=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistics for Annualized Returns\n",
    "\n",
    "We can also print summary statistics for the annualized returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_return_stats():\n",
    "    \"\"\"\n",
    "    Print basic statistics for the annualized returns.\n",
    "    \"\"\"\n",
    "\n",
    "    # For each period-duration.\n",
    "    for i in range(num_years):\n",
    "        years = i + 1\n",
    "        print(years, \"Year Investment Periods:\")\n",
    "\n",
    "        # Create a new DataFrame.\n",
    "        df = pd.DataFrame()\n",
    "        \n",
    "        # Add the basic statistics for each stock.\n",
    "        df[name_SP500] = ann_ret_SP500[i].describe()\n",
    "        df[name_SP400] = ann_ret_SP400[i].describe()\n",
    "        df[name_SP600] = ann_ret_SP600[i].describe()\n",
    "\n",
    "        # Print it.\n",
    "        print(df)\n",
    "        print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we print the summary statistics for the stock indices, we see that for 1-year investment periods the S&P 500 returned about 11.3% on average, while the S&P 400 returned about 14.0%, and the S&P 600 returned about 12.4%.\n",
    "\n",
    "For longer investment periods the average returns decrease. For 10-year investment periods the S&P 500 returned about 8.2% per year on average, the S&P 400 returned about 11.6% on average, and the S&P 600 returned about 10.3% on average.\n",
    "\n",
    "It can be a bit confusing to view all the summary statistics like this and it is better to show selected data in a table, as was done in the paper [Comparison of U.S. Stock Indices](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2667556)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count         10412.000000       10412.000000         10412.000000\n",
      "mean              0.112986           0.139816             0.124422\n",
      "std               0.163164           0.169569             0.182067\n",
      "min              -0.475388          -0.486201            -0.480795\n",
      "25%               0.048051           0.051591             0.017765\n",
      "50%               0.134127           0.152299             0.138376\n",
      "75%               0.212517           0.233438             0.238640\n",
      "max               0.725738           0.940194             0.980847\n",
      "\n",
      "2 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count         10047.000000       10047.000000         10047.000000\n",
      "mean              0.106581           0.132753             0.118638\n",
      "std               0.127940           0.110371             0.115345\n",
      "min              -0.290626          -0.292739            -0.319836\n",
      "25%               0.064603           0.084897             0.057287\n",
      "50%               0.117945           0.144117             0.125716\n",
      "75%               0.186966           0.198057             0.197526\n",
      "max               0.427370           0.567336             0.567132\n",
      "\n",
      "3 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count          9682.000000        9682.000000          9682.000000\n",
      "mean              0.102499           0.128249             0.116065\n",
      "std               0.109208           0.083235             0.085480\n",
      "min              -0.174875          -0.179764            -0.205387\n",
      "25%               0.035026           0.089267             0.075811\n",
      "50%               0.114638           0.139113             0.123830\n",
      "75%               0.166633           0.182907             0.165271\n",
      "max               0.333561           0.360864             0.366621\n",
      "\n",
      "4 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count          9316.000000        9316.000000          9316.000000\n",
      "mean              0.100798           0.126808             0.115251\n",
      "std               0.096932           0.067837             0.066867\n",
      "min              -0.119021          -0.109266            -0.130330\n",
      "25%               0.010796           0.083519             0.078164\n",
      "50%               0.122646           0.136477             0.124898\n",
      "75%               0.157617           0.177959             0.161976\n",
      "max               0.315208           0.312517             0.319759\n",
      "\n",
      "5 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count          8951.000000        8951.000000          8951.000000\n",
      "mean              0.098910           0.125713             0.114381\n",
      "std               0.086653           0.060182             0.060642\n",
      "min              -0.082479          -0.066485            -0.076961\n",
      "25%               0.011236           0.081825             0.080427\n",
      "50%               0.109953           0.134945             0.120274\n",
      "75%               0.158924           0.168750             0.158512\n",
      "max               0.285207           0.297958             0.317837\n",
      "\n",
      "6 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count          8586.000000        8586.000000          8586.000000\n",
      "mean              0.096727           0.124291             0.112477\n",
      "std               0.074872           0.049256             0.047576\n",
      "min              -0.017193           0.001454             0.004222\n",
      "25%               0.028761           0.088841             0.069622\n",
      "50%               0.082208           0.118801             0.118331\n",
      "75%               0.157388           0.163534             0.142846\n",
      "max               0.251919           0.261439             0.267713\n",
      "\n",
      "7 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count          8221.000000        8221.000000          8221.000000\n",
      "mean              0.093989           0.122882             0.110610\n",
      "std               0.066929           0.045170             0.040869\n",
      "min              -0.057312          -0.027798            -0.031855\n",
      "25%               0.037935           0.088598             0.080493\n",
      "50%               0.070826           0.118456             0.112046\n",
      "75%               0.150195           0.162904             0.139893\n",
      "max               0.218949           0.241754             0.242934\n",
      "\n",
      "8 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count          7855.000000        7855.000000          7855.000000\n",
      "mean              0.091149           0.121829             0.108708\n",
      "std               0.062544           0.043995             0.035950\n",
      "min              -0.057814          -0.016115            -0.013276\n",
      "25%               0.046099           0.086711             0.082492\n",
      "50%               0.074485           0.124011             0.106222\n",
      "75%               0.146414           0.160711             0.135071\n",
      "max               0.221715           0.215918             0.223878\n",
      "\n",
      "9 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count          7490.000000        7490.000000          7490.000000\n",
      "mean              0.087202           0.119475             0.105844\n",
      "std               0.058660           0.042426             0.032688\n",
      "min              -0.061491          -0.007457            -0.013526\n",
      "25%               0.055023           0.090126             0.084489\n",
      "50%               0.077352           0.114463             0.102917\n",
      "75%               0.123626           0.153306             0.127317\n",
      "max               0.215052           0.209029             0.219871\n",
      "\n",
      "10 Year Investment Periods:\n",
      "       S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "count          7125.000000        7125.000000          7125.000000\n",
      "mean              0.082307           0.116262             0.102765\n",
      "std               0.052215           0.038534             0.027056\n",
      "min              -0.046228           0.022417             0.019949\n",
      "25%               0.062988           0.087941             0.083334\n",
      "50%               0.079510           0.109439             0.104170\n",
      "75%               0.106382           0.144599             0.121255\n",
      "max               0.199302           0.217551             0.183106\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print_return_stats()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability of Loss\n",
    "\n",
    "Another useful statistic is the historical probability of loss for different investment periods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prob_loss(ann_ret):\n",
    "    \"\"\"\n",
    "    Calculate the probability of negative ann.returns (losses).\n",
    "    \"\"\"\n",
    "\n",
    "    # Remove rows with NA.\n",
    "    ann_ret = ann_ret.dropna()\n",
    "    \n",
    "    # Calculate the probability using a boolean mask.\n",
    "    mask = (ann_ret < 0.0)\n",
    "    prob = np.sum(mask) / len(mask)\n",
    "\n",
    "    return prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_prob_loss():\n",
    "    \"\"\"\n",
    "    Print the probability of loss for increasing investment\n",
    "    periods for all the stocks.\n",
    "    \"\"\"\n",
    "\n",
    "    # Create a new DataFrame.\n",
    "    df = pd.DataFrame()\n",
    "\n",
    "    # Add a column with the probability of loss for S&P 500.\n",
    "    df[name_SP500] = [prob_loss(ann_ret_SP500[i])\n",
    "                      for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the probability of loss for S&P 400.\n",
    "    df[name_SP400] = [prob_loss(ann_ret_SP400[i])\n",
    "                      for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the probability of loss for S&P 600.\n",
    "    df[name_SP600] = [prob_loss(ann_ret_SP600[i])\n",
    "                      for i in range(num_years)]\n",
    "\n",
    "    # Set the index.\n",
    "    df.index = [\"{} Years\".format(i+1) for i in range(num_years)]\n",
    "    \n",
    "    print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows the probability of loss for the stock-indices for investment periods between 1 and 10 years.\n",
    "\n",
    "For example, the S&P 500 had a loss in about 17.8% of all 1-year investment periods, while the S&P 400 had a loss in about 18.1% of all 1-year periods, and the S&P 600 had a loss in about 22.3% of all 1-year periods.\n",
    "\n",
    "The probability of loss generally decreases as the investment period increases.\n",
    "\n",
    "For example, the S&P 500 had a loss in about 9.6% of all 10-year investment periods, while the S&P 400 and S&P 600 did not have a loss in any of the 10-year periods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          S&P 500 (Large Cap)  S&P 400 (Mid Cap)  S&P 600 (Small Cap)\n",
      "1 Years              0.178352           0.181137             0.223300\n",
      "2 Years              0.174978           0.105803             0.147109\n",
      "3 Years              0.189837           0.096364             0.090787\n",
      "4 Years              0.230893           0.044976             0.075247\n",
      "5 Years              0.174841           0.019327             0.031505\n",
      "6 Years              0.049033           0.000000             0.000000\n",
      "7 Years              0.027491           0.004136             0.004622\n",
      "8 Years              0.051305           0.002164             0.001400\n",
      "9 Years              0.065554           0.000935             0.001469\n",
      "10 Years             0.096281           0.000000             0.000000\n"
     ]
    }
   ],
   "source": [
    "print_prob_loss()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compared to Inflation\n",
    "\n",
    "It is also useful to consider the probability of a stock index performing better than inflation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prob_better(ann_ret1, ann_ret2):\n",
    "    \"\"\"\n",
    "    Calculate the probability that the ann.returns of stock 1\n",
    "    were better than the ann.returns of stock 2.\n",
    "\n",
    "    This does not assume the index-dates are identical.\n",
    "\n",
    "    :param ann_ret1: Pandas Series with ann.returns for stock 1.\n",
    "    :param ann_ret2: Pandas Series with ann.returns for stock 2.\n",
    "    :return: Probability.\n",
    "    \"\"\"\n",
    "\n",
    "    # Create a new DataFrame.\n",
    "    df = pd.DataFrame()\n",
    "\n",
    "    # Add the ann.returns for the two stocks.\n",
    "    df[\"ann_ret1\"] = ann_ret1\n",
    "    df[\"ann_ret2\"] = ann_ret2\n",
    "\n",
    "    # Remove all rows with NA.\n",
    "    df.dropna(inplace=True)\n",
    "\n",
    "    # Calculate the probability using a boolean mask.\n",
    "    mask = (df[\"ann_ret1\"] > df[\"ann_ret2\"])\n",
    "    prob = np.sum(mask) / len(mask)\n",
    "\n",
    "    return prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_prob_better_than_inflation():\n",
    "    \"\"\"\n",
    "    Print the probability of the stocks performing better\n",
    "    than inflation for increasing investment periods.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Create a new DataFrame.\n",
    "    df = pd.DataFrame()\n",
    "\n",
    "    # Add a column with the probabilities for the S&P 500.\n",
    "    name = ticker_SP500 + \" > CPI\"\n",
    "    df[name] = [prob_better(ann_ret_SP500[i], ann_ret_cpi[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the probabilities for the S&P 400.\n",
    "    name = ticker_SP400 + \" > CPI\"\n",
    "    df[name] = [prob_better(ann_ret_SP400[i], ann_ret_cpi[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the probabilities for the S&P 600.\n",
    "    name = ticker_SP600 + \" > CPI\"\n",
    "    df[name] = [prob_better(ann_ret_SP600[i], ann_ret_cpi[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Set the index.\n",
    "    df.index = [\"{} Years\".format(i+1) for i in range(num_years)]\n",
    "    \n",
    "    print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows the probability of each stock index having a higher return than inflation for investment periods between 1 and 10 years. All taxes are ignored.\n",
    "\n",
    "For example, both the S&P 500 and S&P 400 had a higher return than inflation in about 79% of all 1-year investment periods, while the S&P 600 only exceeded inflation in about 73.6% of all 1-year periods.\n",
    "\n",
    "For investment periods of 6 years or more, the S&P 400 and S&P 600 performed better than inflation for almost all investment periods. But the S&P 500 only exceeded inflation in about 86% of all 10-year periods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          S&P 500 > CPI  S&P 400 > CPI  S&P 600 > CPI\n",
      "1 Years        0.789484       0.786101       0.736033\n",
      "2 Years        0.803727       0.876966       0.812945\n",
      "3 Years        0.771319       0.882488       0.866889\n",
      "4 Years        0.731892       0.921514       0.884432\n",
      "5 Years        0.695104       0.960270       0.896455\n",
      "6 Years        0.794249       0.998005       0.995305\n",
      "7 Years        0.850153       0.975720       0.979277\n",
      "8 Years        0.873154       0.975350       0.989087\n",
      "9 Years        0.868534       0.989494       0.992726\n",
      "10 Years       0.858904       0.999292       0.999292\n"
     ]
    }
   ],
   "source": [
    "print_prob_better_than_inflation()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compared to Bonds\n",
    "\n",
    "It is also useful to compare the returns of the stock indices to risk-free government bonds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_prob_better_than_bonds():\n",
    "    \"\"\"\n",
    "    Print the probability of the stocks performing better\n",
    "    than US Gov. Bonds for increasing investment periods.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Create a new DataFrame.\n",
    "    df = pd.DataFrame()\n",
    "\n",
    "    # Add a column with the probabilities for the S&P 500.\n",
    "    name = ticker_SP500 + \" > Bonds\"\n",
    "    df[name] = [prob_better(ann_ret_SP500[i], ann_ret_bond[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the probabilities for the S&P 400.\n",
    "    name = ticker_SP400 + \" > Bonds\"\n",
    "    df[name] = [prob_better(ann_ret_SP400[i], ann_ret_bond[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the probabilities for the S&P 600.\n",
    "    name = ticker_SP600 + \" > Bonds\"\n",
    "    df[name] = [prob_better(ann_ret_SP600[i], ann_ret_bond[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Set the index.\n",
    "    df.index = [\"{} Years\".format(i+1) for i in range(num_years)]\n",
    "    \n",
    "    print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows the probability of each stock index having a higher return than risk-free government bonds, for investment periods between 1 and 10 years. We consider annual reinvestment in bonds with 1-year maturity. All taxes are ignored.\n",
    "\n",
    "For example, the S&P 500 returned more than government bonds in about 79% of all 1-year periods, while it was 78% for the S&P 400 and 73% for the S&P 600.\n",
    "\n",
    "For investment periods of 6 years or more, the S&P 400 and S&P 600 nearly always returned more than government bonds. But the S&P 500 only returned more than bonds in about 84% of all 10-year periods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          S&P 500 > Bonds  S&P 400 > Bonds  S&P 600 > Bonds\n",
      "1 Years          0.792451         0.782655         0.731464\n",
      "2 Years          0.794864         0.867324         0.787797\n",
      "3 Years          0.764925         0.869758         0.830097\n",
      "4 Years          0.727458         0.896415         0.869794\n",
      "5 Years          0.694448         0.942129         0.869512\n",
      "6 Years          0.730608         0.996389         0.987072\n",
      "7 Years          0.816567         0.974577         0.976645\n",
      "8 Years          0.838956         0.965500         0.980267\n",
      "9 Years          0.866489         0.970494         0.985314\n",
      "10 Years         0.843789         0.997193         0.997193\n"
     ]
    }
   ],
   "source": [
    "print_prob_better_than_bonds()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compared to Other Stock Indices\n",
    "\n",
    "Now we will compare the stock indices directly against each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_prob_better():\n",
    "    \"\"\"\n",
    "    Print the probability of one stock index performing better\n",
    "    than another stock index for increasing investment periods.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Create a new DataFrame.\n",
    "    df = pd.DataFrame()\n",
    "\n",
    "    # Add a column with the probabilities for S&P 500 > S&P 400.\n",
    "    name = ticker_SP500 + \" > \" + ticker_SP400\n",
    "    df[name] = [prob_better(ann_ret_SP500[i], ann_ret_SP400[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the probabilities for S&P 500 > S&P 600.\n",
    "    name = ticker_SP500 + \" > \" + ticker_SP600\n",
    "    df[name] = [prob_better(ann_ret_SP500[i], ann_ret_SP600[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the probabilities for S&P 600 > S&P 400.\n",
    "    name = ticker_SP600 + \" > \" + ticker_SP400\n",
    "    df[name] = [prob_better(ann_ret_SP600[i], ann_ret_SP400[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Set the index.\n",
    "    df.index = [\"{} Years\".format(i+1) for i in range(num_years)]\n",
    "    \n",
    "    print(df)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows the probability of one stock index performing better than another for investment periods between 1 and 10 years. All taxes are ignored.\n",
    "\n",
    "For example, the S&P 500 (Large-Cap) performed better than the S&P 400 (Mid-Cap) in about 42% of all 1-year periods. Similarly, the S&P 500 performed better than the S&P 600 (Small-Cap) in almost 45% of all 1-year periods.\n",
    "\n",
    "For longer investment periods the S&P 500 generally performed worse than the S&P 400 and S&P 600. For example, the S&P 500 only performed better than the S&P 400 in about 6% of all 10-year periods, and it was better than the S&P 600 in about 15% of the 10-year periods. Similarly, the S&P 600 was better than the S&P 400 in only about 21% of all 10-year periods.\n",
    "\n",
    "This shows that for longer investment periods the S&P 400 (Mid-Cap) mostly had a higher return than both the S&P 500 (Large-Cap) and S&P 600 (Small-Cap)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          S&P 500 > S&P 400  S&P 500 > S&P 600  S&P 600 > S&P 400\n",
      "1 Years            0.424894           0.446024           0.495102\n",
      "2 Years            0.362297           0.413656           0.518961\n",
      "3 Years            0.336501           0.385561           0.516629\n",
      "4 Years            0.305389           0.336840           0.485831\n",
      "5 Years            0.259524           0.299631           0.458943\n",
      "6 Years            0.252737           0.269509           0.411134\n",
      "7 Years            0.182460           0.265175           0.302153\n",
      "8 Years            0.128708           0.252451           0.239975\n",
      "9 Years            0.107210           0.241522           0.181976\n",
      "10 Years           0.061895           0.153123           0.210246\n"
     ]
    }
   ],
   "source": [
    "print_prob_better()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlation\n",
    "\n",
    "It is also useful to consider the statistical correlation between the returns of stock indices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_correlation():\n",
    "    \"\"\"\n",
    "    Print the correlation between the stock indices\n",
    "    for increasing investment periods.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Create a new DataFrame.\n",
    "    df = pd.DataFrame()\n",
    "\n",
    "    # Add a column with the correlations for S&P 500 vs. S&P 400.\n",
    "    name = ticker_SP500 + \" vs. \" + ticker_SP400\n",
    "    df[name] = [ann_ret_SP500[i].corr(ann_ret_SP400[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the correlations for S&P 500 vs. S&P 600.\n",
    "    name = ticker_SP500 + \" vs. \" + ticker_SP600\n",
    "    df[name] = [ann_ret_SP500[i].corr(ann_ret_SP600[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Add a column with the correlations for S&P 600 vs. S&P 400.\n",
    "    name = ticker_SP600 + \" vs. \" + ticker_SP400\n",
    "    df[name] = [ann_ret_SP600[i].corr(ann_ret_SP400[i])\n",
    "                for i in range(num_years)]\n",
    "\n",
    "    # Set the index.\n",
    "    df.index = [\"{} Years\".format(i+1) for i in range(num_years)]\n",
    "    \n",
    "    print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows the correlation coefficient (Pearson) between the returns on the stock indices for investment periods between 1 and 10 years.\n",
    "\n",
    "For example, the correlation was about 0.88 between the S&P 500 and S&P 400 for all 1-year investment periods, while it was only 0.77 for the S&P 500 and S&P 600, and 0.92 for the S&P 600 and S&P 400.\n",
    "\n",
    "For longer investment periods the correlation coefficient generally increases. For example, the correlation was about 0.93 between the S&P 500 and S&P 400 for all 10-year investment periods, while it was about 0.85 between the S&P 500 and S&P 600, and it was almost 0.94 between the S&P 600 and S&P 400.\n",
    "\n",
    "This shows that the return on these three stock indices are all highly correlated, so that they have a strong tendency to show losses or gains for the same periods.\n",
    "\n",
    "It might also be useful to consider the correlation for shorter investment periods, e.g. monthly, weekly or even daily, because a low correlation between stock indices might be useful for rebalancing the investment portfolio when one stock index is down and another is up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          S&P 500 vs. S&P 400  S&P 500 vs. S&P 600  S&P 600 vs. S&P 400\n",
      "1 Years              0.881041             0.773324             0.921980\n",
      "2 Years              0.872209             0.730016             0.882637\n",
      "3 Years              0.875349             0.728040             0.873453\n",
      "4 Years              0.887510             0.758450             0.877225\n",
      "5 Years              0.887614             0.756654             0.889081\n",
      "6 Years              0.890631             0.749908             0.874440\n",
      "7 Years              0.890307             0.771255             0.899970\n",
      "8 Years              0.912973             0.837214             0.936627\n",
      "9 Years              0.930655             0.857917             0.945555\n",
      "10 Years             0.929490             0.846769             0.935134\n"
     ]
    }
   ],
   "source": [
    "print_correlation()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recovery Times\n",
    "\n",
    "It is also useful to consider how quickly the stock indices typically recover from losses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_recovery_days():\n",
    "    \"\"\"\n",
    "    Print the probability of the stocks recovering from losses\n",
    "    for increasing number of days.\n",
    "    \"\"\"\n",
    "\n",
    "    # Print the probability for these days.\n",
    "    num_days = [7, 30, 90, 180, 365, 2*365, 5*365]\n",
    "    \n",
    "    # Create a new DataFrame.\n",
    "    df = pd.DataFrame()\n",
    "    \n",
    "    # Add a column with the probabilities for the S&P 500.\n",
    "    df[ticker_SP500] = prob_recovery(df=df_SP500, num_days=num_days,\n",
    "                                     start_date=start_date,\n",
    "                                     end_date=end_date)\n",
    "\n",
    "    # Add a column with the probabilities for the S&P 400.\n",
    "    df[ticker_SP400] = prob_recovery(df=df_SP400, num_days=num_days,\n",
    "                                     start_date=start_date,\n",
    "                                     end_date=end_date)\n",
    "\n",
    "    # Add a column with the probabilities for the S&P 600.\n",
    "    df[ticker_SP600] = prob_recovery(df=df_SP600, num_days=num_days,\n",
    "                                     start_date=start_date,\n",
    "                                     end_date=end_date)\n",
    "\n",
    "    # Set the index.\n",
    "    df.index = [\"{} Days\".format(days) for days in num_days]\n",
    "    \n",
    "    print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows the probability that each stock index has recovered from losses within a given number of days.\n",
    "\n",
    "For example, all three stock indices recovered from about 80-83% of all losses within just a week. The probability goes up for longer investment periods. For example, for 5-year investment periods the S&P 500 had recovered from about 99.8% of all losses, while the S&P 400 and S&P 600 had recovered from all losses in 5 years.\n",
    "\n",
    "Note that this only measures the number of days until the stock index recovered the first time. It is possible that a stock index decreases again in the future. This can be seen from the non-zero probabilities of loss shown further above, where the S&P 400 and S&P 600 had losses in some 7, 8, and 9 year investment periods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            S&P 500   S&P 400   S&P 600\n",
      "7 Days     0.826761  0.814791  0.804398\n",
      "30 Days    0.938016  0.931985  0.921128\n",
      "90 Days    0.975503  0.968915  0.962698\n",
      "180 Days   0.984411  0.984597  0.982370\n",
      "365 Days   0.988865  0.994340  0.991278\n",
      "730 Days   0.992113  0.999165  0.998423\n",
      "1825 Days  0.997773  1.000000  1.000000\n"
     ]
    }
   ],
   "source": [
    "print_recovery_days()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion\n",
    "\n",
    "From the above statistics we saw that the S&P 400 (Mid-Cap) was generally better than the S&P 600 (Small-Cap), which was generally better than the S&P 500 (Large-Cap), especially for longer investment periods.\n",
    "\n",
    "For all 10-year investment periods between 1989 and 2018, the S&P 400 returned 11.6% per year on average, while the S&P 600 returned 10.3% on average, and the S&P 500 only returned 8.2% on average.\n",
    "\n",
    "Furthermore, the S&P 400 and 600 almost never had losses for investment periods of 6 years or more, while the S&P 500 had losses in about 9.6% of all 10-year investment periods.\n",
    "\n",
    "Obviously the S&P 400 (Mid-Cap) would have been a better investment for most longer periods between 1989 and 2018. The question is whether this superiority will continue in the future?\n",
    "\n",
    "### Forecasting Future Returns\n",
    "\n",
    "It is easy to imagine, that if many investors were to believe that the S&P 400 was generally a superior investment to the S&P 500, then the price of the S&P 400 would be bid up to the point where its future earnings growth could no longer justify its price and the S&P 400 would therefore end up under-performing the S&P 500 in the long-term.\n",
    "\n",
    "We therefore need to forecast the future returns of the S&P 400 and S&P 600 similarly to how we did that for the S&P 500 in the [previous paper](https://github.com/Hvass-Labs/FinanceOps/blob/master/01_Forecasting_Long-Term_Stock_Returns.ipynb). The problem is that we do not have the P/Sales or P/Book data for the S&P 400 and S&P 600. This data can be purchased from Standard & Poor's but it is quite expensive.\n",
    "\n",
    "What we have instead are the dividend payouts for the S&P 400 and 600, which can be used to calculate the P/Dividend ratio or its reciprocal value called the Dividend Yield. You are encouraged to try and run the previous Python Notebook with this data to see if you can forecast the future returns of the S&P 400 and 600 from their dividend yields.\n",
    "\n",
    "Once you have forecasted the future returns of the three indices you can guage whether the indices are mispriced, so that one index might currently be preferred over the others.\n",
    "\n",
    "### Cause of Growth\n",
    "\n",
    "We have not considered the underlying cause of growth for these three indices. It would be of great importance to know whether the superior returns on the S&P 400 were caused by superior growth in sales and earnings, and whether we might expect such growth to continue in the future. More detailed financial data is needed for this analysis, which unfortunately can be difficult and expensive to obtain for many stock indices."
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    "## License (MIT)\n",
    "\n",
    "Copyright (c) 2015-18 by [Magnus Erik Hvass Pedersen](http://www.hvass-labs.org/)\n",
    "\n",
    "Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n",
    "\n",
    "The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n",
    "\n",
    "THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE."
   ]
  }
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