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": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the US CPI inflation index.\n",
    "cpi = load_usa_cpi()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": [
    {
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69+5NSoqmfSOE4LHHDDKbubm5BAYGMnToUAB+/PFHFixYYHEsY7uMiY2N5eGHH6Zp06Z0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\nUIWuKIrSRvh/bFFNdlduTMsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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",
       "Freq: B, 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",
       "Freq: B, 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": {
    "collapsed": true
   },
   "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 = np.argmax(ann_ret_dif)\n",
    "    \n",
    "    # The end-date for the period to be plotted.\n",
    "    end_date = start_date + int(years * 365.25)\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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ll5CXl0dFRQWzZ8+mffv29TDK2nPs2DHmzJlz0rH3Gs3poKLKilVCaJA/Gx4ZB0Bqvop3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\nRkz6jgVq234AXDNfzdjB98I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xUSy6+zzaepkZ3zE6ni/+fA7D4jykyteCOVckEt0iiNJK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\nuNx+cwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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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k20yy9EGK1Ri1IXl72XK4AVMe/Q6PL9oOh9snzxoArTJma+GOh/pi2hmGHRDG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\nnZ1Neno6NWvWdJTbpKamus2d25QvX56LFy9SLkc0XVJSEo888girV6/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rUnn58O+vOdDM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\ncTcYDIYg5P8BA3BI1YOjDKMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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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V0Y68ojIKSsrIKy6jXwdvos5msTs209T+5wOJDA2v+Y2/OkJ9XTmVmk+5QXLfqI48Ma5b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\nSqkgoMFeKaWCgAZ7pZQKAv8PqnZ8h8H3+WAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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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yEPAn0wxNoVBcyeQWa8leHg7WzBnZixuH1D7Fu9lbcX2oj2HiH9RDk1d2srFg\n5e54amokhxNzic8qZv7YgHp9CyEY3NOZ2eG9iEzIpaZGkphdwjubz/BHbBYAw/2vLGXOjqBZF5CU\ncqcQIqCJJncC30kpE3XtM0wzNIVCcSWTV6pl7LrYWfLWrWH1zkcM8OLrSE2b5++zBhPk5cAPR1N5\n8fsoMovKOZmq6e+PaaLIyjB/F9YeTCIxp4S/b4hm22lt+vF0tCbQo/FwT4WGKTaB+wOuQogdQohD\nQoh5JuhToVBc4eTp5B5cGpFRuLqfh+Hnvh4OONlY0tNFk19OzSvlcGIu7vZWeDs1rsMzQFeY5XRa\nIXFZtcll1w/2Uf7+FmCKTWALYARwLWAL7BVC7JNSnr24oRDiQeBBAH9//4tPKxSKLsKbv5zio9/j\nABrV0XGyseSa/p7EpBfirJNg0LctKKtiT0w2V/fzaFI0rr+3A0JoeQXxRgZgmlGoqKJxTGEAkoFs\nKWUxUCyE2AkMAeoZACnlcmA5QHh4eMMpfAqF4opASklpZTV2F2noF5ZVGib/ob1cmpRvXnXPSCqM\nooUcdSGeH2yPIauonBG9XZscg52VBb3d7PjuiJYP8M6fhlBUVsmYPldWacaOwhQuoB+Aq4UQFkII\nO2A0cKqZaxQKxRXO6z+fIuSlzazYFVfneEKWJt627K7hfP/ncYZQzIYwMxN1tPQddWqc++O1TOGW\nlFgc6ONkUAidEuzNPeP6KPdPC2lJGOgaYC8wQAiRLIS4TwjxsBDiYQAp5SlgE3AcOACskFI2GjKq\nUCi6BlGpmijbst9j68T8X8jXsnB7urQ+6cpYjG1ILxcG+jo20Vqjn7e22Rvk5WBwJSlaRkuigO5o\nQZu3gbdNMiKFQnFFUFhWBUBWUQV747INcfZ5pbrN3zZMxna6ert3jvbnjZtDm2mtETHAk//+FsP9\nV/dp9f26OyoTWKFQtInCsiqmDfJhd0wWm6LSDAYgv6TtBkAIwem/T2tVfd0Rvd3Y9deJ+Lk2LvOs\naBilBaRQKNpEYVklHo5W2FiasXp/Ij/ohNnySiswNxMNlldsCTaW5q324fdys2tViUmFhjIACoWi\n1UgpKSqvwtHGkqwibQP2wx1aucdz6UV4OlirCfkKQLmAFApFq9l1LovKaskA79pN2tNphQQ8+zMA\nD00I7KihKVqBMgAKhaLVrNgdj5ejNdNDfenlZssvJ9L4dG8CldVaes+8BvR7FJ0PZQAUCkWrqKqu\nYW9sFvdcFYCVhRkjersxorcbcVnF/HY6g/fnDG2y7q6i86AMgEKhaBWpeWVUVst6tXX/dVsY206l\nM9NI9VPRuVGbwAqFolnKKquttKdlAAAgAElEQVT54WgK6QVlxGdrmjsB7vZ12ng4WDN7pL/a/L2C\nUCsAhULRJKPf2Ep6gVa68aahPfjhaCoAfTzsm7pMcQWgVgAKhaJRSiqqDJM/YJj8AUO9XcWVizIA\nCoWiUb7RFWwBsLKoO10oV8+Vj3IBKRSKRjmcmIu5mWDlPSMpLKvk413xHEvKU+6fLoIyAAqFolFO\npOQzaaAXE/prOj8zwnqQV1JRbzWguDJRf0WFQtEgReVVxGcVE9rTuc5xFzurekVgFFcm6q+oUCga\nZPDLmwHqGQBF10GtABQKRT3Kq6oNP4f5KQPQVVEGQKFQ1ENfYhFosqav4spGGQCFQlGPbJ3E80d3\nj+jgkSjaE2UAFApFPTKLtOQvD/X036VRBkChaAYpZUcP4bKjXwF4OFh18EgU7YkyAApFI8RkFDH5\n3d+Z/dG+jh7KZSdbrQC6BSoMVKFohOU7Y4nJKAIgr6QCF7vu8zScWViOjaUZdlbmHT0URTuiVgCK\nbsmmqDRDEfPGOJ1WiLmuOPmRpLzLMaxOw8nUAvp5OSq9ny6OMgCKbsPuc1lc9eY2fjyWysNfHOKJ\ntUcpLq9qsG11jeRMWiG3h/thJuBIYvcxAFXVNRxLzmO4v0tHD0XRzjRrAIQQK4UQGUKIqGbajRRC\nVAkhbjPd8BQK0yCl5M1fTpGaX8Y/fzltOP7Z3vMNtj+fXUx5VQ3D/V0Z4OPEkcTcyzXUDudsehEl\nFdUM83ft6KEo2pmWrABWAdOaaiCEMAf+CfxqgjEpFCZnX1wOJ1MLsLYwIyWv1HB866n0Ou1+PJbK\n/Z8eZOp7OwEY6OPEMH8XjibmUVPTPaKBolLzAQhVGcBdnmYNgJRyJ5DTTLPHgW+BDFMMSqEwNUeS\ntCf4564fCGjRLX+e2JfDiblkFmoRL1uj01m45ghbT2VQpZvs+3k7MNzflcLyKmIyizpm8JeZ6NQC\nbC3N65V8VHQ9LjkKSAjRE7gZmAiMvOQRKRTtQHJuKW72Vswc2pMTKQX839T+FJRWsnR7LCNf38o/\nbw1l3aFkejjb0MfTnnuu6sO4IHdsLM0ZpvOFH0nMpb+3Ywe/k/Yn+kIBA30dDRvgiq6LKTaB/wM8\nI6Wsaa6hEOJBIUSkECIyMzPTBLdWKFrGieR8AtztcLO34t+3D6Gniy3Bvk6GFcEz357gYEIu868K\nYPX9Y5gS4m2QPA70sMfZ1pLNJ9Mb3TTuSmQUlOHnatfRw1BcBkxhAMKBtUKIBOA24AMhxKyGGkop\nl0spw6WU4Z6enia4tUJPeVU1f8RkUVhW2dFD6VQs+z2Wd389w4mUfG4c0qPe+Ycm9GXD41cbXk8O\n8a7XRghBmJ8zv53OYM7yrp8Ull1Ugbt998l56M5csgtIStlH/7MQYhWwQUr5/aX2q2g5ucUVzPjv\nblLySrnnqgBemTmoXe+3Ylcc4QFuDO3VucMEvz6YxFu6iB8vR2tuGebXYLvBPZ15aEIgucUVBDZS\n6rC3ux27zmkVsqSUXTY+vryqmsLyKiUB0U1o1gAIIdYAEYCHECIZeBmwBJBSLmvX0SlaxJ7YLENk\ny85zme06Qe2JyeIfP58C4OSr12Fv3XmTyT/bl2D4+T+zh+JsZ9lo2+euD26yryenDODXk+lkFJaz\nOyaLsYHuWJh3vTQavQy0m72SgOgOtCQK6A4ppa+U0lJK6Sel/ERKuayhyV9KeY+Ucl37DFXRGL+c\nSMPVzpKXbwwhLrOY+KzidrlPZXUNT359zPB64js7yCupaOKKjiMmo4iolAIejejLNw+P5aogj0vq\nz9Xeih8eGwfA3Z8c4N9bzppimJ0OvQicu1oBdAu63iNMN6O6RrLzXCbTBvvQS7dxV9ROG5VfRyaR\nVlDGJ/PDeX/OUDIKy9lxpnNu5q87lIyZgHuuCmBkgJtJ+vR1tuWtW0IB2HwyzSR9djayDCJwygB0\nB5QB6MRU10hyiyuoqGo8wCo6tYDCsirGBLpjban9OcubaH8pHE/Kx93eimuDvZke6ou5mSC2E8bG\nV1TVsOqPeCYHe+PlZGPSvueM8mdKiDfmXXQPQL8CUC6g7oEyAJ2YuSv2MezvW5i+eBcFDUT3SCl5\nY+MprMzNGNvXHWsLTbmxvLLtBiA1r5TfTqeTnFvCz8cvGLTwpZREpeYT6Kltklqam9HTxZZd57La\nfK/2Yslv5yirrGFGA1E/psDHycZQMKWrcSA+B3src3q4mNZwKjonnXcHT0FUSgEWZoKYjCLCXvmV\nQA97Pp4fTl9PB0BTbNwbl82LM0LwcrQhLb8MqFvQuzVEpxYwe/leCstqXUg//HkcQ3q5cD67hJOp\nBTw/faDh3NX9PPhyfyJlldXYWF66bHBNjeRIUi7Bvk6GGPzWEpNRyOLfYrC1NGd0H9O4fi7Gw8Ga\nvJJKKqpqsLLoOs9Qh87n8s2hJO4Y5W94mFB0bbrOp7eLUVJRRVF5FXNH+3PjkB709bQnLqu4js99\nb2w2ADeG+QLUrgCqakjIKm5VJauq6hoWrDqIhZkwZL4CHE/Oo6q6hq8ikwAYG1i7mTrQR8uKNTYY\nl8L8/x3g1g/3suS3mDb38cH2WOyszNnz7CS8Tez+0eNmr0UT5Zd2rZyLZb/H4uFgzbPXD2y+saJL\noAxAJyWjQHMxDOrpzH/vGMa2JyPwcLDm1IUCknNL+P1sJku2x+DjZGPwc1vrnkajUwuIeGcHr22I\nbvn9CstJKyjjqesGsP7RcXy2YBQAhxPzeHfLWT7cEcu1A70I9q2VQnC21SbChtxTLSW7qJzF286x\nNTrd4E766mASZZXaKiY1r5QVu+JabMwiz+cycaAXbu2YyORgo61O2muzvaM4kpjLhP6eONo0Hi6r\n6FooF1AnZPvpDL47ohUrGWaUbBXs68i6Q8lsPHGBkgptgjR2c+g3gfUbs//bk8D8sQEENJLcZIxe\nEM3bUTMm1/T3ZGqIN4cTc/FytGZEb1dWzA+vk1/gpJsoCi7hSfiryCTe1YVUOtlY8NCEvry9+QxP\nfnOMq4M82HYqna2nMhjSy4W0/DKWbo8ho7CcVfeOJMyvfiJaVlG54T20Fw7W2vsuMtHKpzNQVV1D\nVlEFPV1tO3ooisuIMgCdjGNJedy76iAAk4O96WckPjZtsA+Hz2s+8gn9PTmQkMMburBEqHUBpRrJ\nHX95IJHnpzed5CSl5OEvDgHg6Vgb/REe4Mqv0emczy7hjlH+9ZLLnHQrAH3kSGuRUvLLCS2c8v05\nQwnt6UxuiWZMfj5+gZ+PXzC03RKdzo4zGeQUV5BTXMH205n1DEBJRRUlFdXtHsPuqFsBFJZ3HRdQ\nns6It+fKSdH5UAagg/k6Mom9sdm8fvNg7KwsOJlaAMCGx68m2NepTtu5o3szd3TvRvvSu4BOpxUC\n4O1kTXJuSYNtYzIK+fZwCveOC+CZdce5oNtA7uftYGgzob8Xb2zUpBT6etZfRQz0ccTeypz7P4vk\nvqv78EhE31YVEd91LosTKfk8ML4PNw3tCdQWI5872p/dMVmcz9bGv3xnHAAv3xjC6v2JnEipX6FL\n/x68HNs3hNFBl/3clVYAuboMYNduVPdYoQxAh7LzbCZ/XXccgPVHUvBxsqGftwNmQptcWyvHa2tp\njq+zjWEi7O/tyMYTaZRXVdeJ6kjIKmbyu1rBkw93xALwl8n9eOiavtgaFQHvb2QM+jUgg2xvbcGE\nAZ5sPJHGJ7vjOZ1WwOr7xzQ4ttjMIsyEoI/OHXUyNZ95Kw8AcLORRo+7gzUHX5iMh4MVUmob2vvj\ns1l7IImh/i7MGxvAieR8dsfUDz9ddygZ0LR92hO966srbQKnFWifmdYYcMWVj9oE7iDySip47rsT\nAAzQTa5pBWXsOpeFt5NNm3RmzMwEW/9vguF1qG4iPBify983RJNTXMHnexOIeGcHAPa6yd7W0pwn\nru1XZ/IHTQXz2oFeAIwMaLg84LPTat1LUSkF9c5virrAu7+eYfZH+5j4zg5DpunxZK3q1Ip54YT0\nqLvS8XS0RgiBmZnA1sqciAFeLLt7BA9P6Iu5mSDUz5mMwnLSdZMWwJm0Qj7eGcfEAZ6G32d74eWk\nTZL6sNuKqhpiMjpfQlxrOJigFczRR3YpugdqBdBBPPXNcVLySvn6obGE+Tmz82wm2cWaUfB3a7sW\nu721BSvmheNgY0EPZ1s+2BHLst9j2R2TxaaoNFLySjE3E3wwdzgT+nvy+JojPBrRt1HxuP/eOYys\nwopG4/L93e2If3M6T35zjB+OplJcXmUQiCurrObhLw7Xaf/xzjiemx7MtlPpuNpZMklnYFqD3rCd\nSM7HO0Tb8P3b9ydwsrXk37cPxaydC5nYWJrj4WDF4cRcHvwskpziCiLP53LqtWn1jGhn4nx2MU9+\nfYz3Zg+ll9Fn7I2Np1i+M44xgW64qj2AboUyAB1AXGYR289kcMeoXozSRfFMHeRDTY2ksrqG8N6X\nlsCk17SvrpGYmwmDu0SvGPrKjSFcN8gHgI/nhTfZl52VBf7uTX9MhBDcMsyP7w6nsDsmy9D3H7Ha\nfYf0cuFceiE+TjYs3xXHHaP8OZqUx9QQnzZN1iE9nDATcCw5j8kh3mQVlXMwIZe/Thtw2TYxe7jY\nsv0iHaSsovI6E2tnQEpJjdRWSE+sPcK5jCL+s/Uc/759CKCtRJfvjOP6wT68/achHTxaxeVGGYAO\n4P1t57C1NGfRlP51jpuZCeaNDTDZfczNBN6O1qTml9U5Hm4icbS6fbri6WjNd4eTuW6Qjy6xLBKA\nL+4bhZ2VBafTCrhh8W6DC8rfvW2TpZ2VBcP8XdkUlcZDE/pyNFHbEDaV6FtL6OFsa3Bj6ekMBuBi\nKfBnvj3OnphsCssqKdBtWusNM9TuY1wb7G3Y3FZ0H9Rf/DJzNr2QzSfTuHlYT7zaOV4dtCfV1Pwy\nAj3s6e/tyKHEXIOUhCmxsTRnaC8XgxT1j8dSARgX5G5ILAq5KKrpUibLG0J9eW1DNINf3swdo3ph\nbiYY3KN9N3+N6eGixcs7Wlvw8fxw5izf1+ZwWFNRXF7Fn5btZai/CxkF5TjZWBjySQBW3z+a/fE5\n/Pe3cwYZC30Wt5r8uydqE/gyoc9kfWPjKeysLHji2v7NXGEanrl+ILaW5lzT35PFdwxj59MT202/\nJtDTnvisYvJKKvhyfyL9vR34fMFow3khBO8YuRmG+7e9otitw2sjh9YcSGLiAM/L6n/Xi6V5Olnj\np0ueyi7uWIG448n5RF8o4Mv9iWw9lW6Y/L+4bzSnXpvGuCAPervZISWcuqBt2OtrHOtzGxTdC/VX\nvwwcTsxl/icHWDJ3OH/EZjNvTG98nC+P2uLIADeiX7sOoN3LGE4N8eaj3+PYF5fN+ZwSJg3wqufj\nnxHmi4WZwMbS/JIKjzvbWbJl0TVMeU8LZ71/fOAljb216FcAZkLgrpNOzurgFYC+mtfF+LvZGYzj\n5GBvrMzN2HA8lSG9XAxyFp25spui/VB/9XYmvaCMNfsTKSyvYr4u7j3sMtfSvVz1a4M8tRDC2Mxi\nsorKDZOkMTaW5swa1tMk9+vjYc8do3rh72bfbsqfjaEPl7x3XAC2VubYW5l3uAsoR7cCWfPAGJZu\njzFs/ns718b2O9tZMqK3q0F3SW8AlAuoe6L+6u1ITEYR1/1nJ9U1kkAPezKLyrG2MGdycOtDH68E\nnO0scbO34uNdcUiJoXZAe2Fhbsabt4S16z0aI9DTgejXrjOEx3o72XAgIbte0t3lJFu3AggPcOWL\n+0ezJTqdvbHZ9cZzdT8P3t58hozCMsMmsJOtmgq6I+qv3o58dziZ6hrJsrtGMEUXrmhhJtqsdX8l\n8MiEvry+USsaH95I8lhXwfjv+H9T+/PYl0f4eGccj03qZzheVlnN4cRcg55SexKVkk9vdzssdUmE\nU0K8maILCTbmmn6evL35DKNe34Z+ceimJCCuDE5tMGl3XXcmaieKyqu49YM/qKyu4bFJQdxitBl5\nPDmPfl6O2FqZU1ZZzQ9HU5nQ35Npg7W4+PbSp+9MLLi6j8EAeHYjWYEZYT1465fTxGYWG46VVFQR\n8tJmw+vK6hqThvkaU1Vdw/64HGYM8W227SCjzGspNRXWtmSeKzqAPf8xaXfqr94Kdp3L5OlvjnEm\nvZC4rGKe/e4EucUVFJZV8ujqQ8xcsocX1p9ASsl9nx4kJa+UeWMbF2/rihjrF3W3ScXdwdogdQFw\nJLGuYN16o5BMU3MytYDC8irG9vVotq2ZmWCaLlkPMOQHKK4A8pNN2l33+g+9RB778gi/RGnyxZ/f\nN4qKqhr+90cCm6LS2KiTNd4fn0NKXil7YrJ5ckp/rg2uvwRXdE087K3ILqpASsl7W87yiE5i+6sH\nxzA7vBexGUVkFJY100vb2BunVYcbG+jeovZL5w5n33PX4uVozeOTgtplTAoTs/MdKLzQfLtWoFxA\nLSSvpIL80kocrS34v6n9Gd/Pk97udizedg4AFztLRgW4cSqtwPDkN7ENOjddgRXzwruUUmZLcXew\nIio1ny3R6byv+1xs/b9rCPJy5FxGEV9FJjHq9W3s+utEk2cM74/LJsjLoU49h6YwNxP4ONuw97lr\naWfpJIWpiNlq8i7VCqCFHIjPAWDlvSO5d1wfAN64OZTx/bQl90PX9KWPpz1JOaV8vCsOG0szBnRT\nZcXJId7cOsKv+YZdDHcHa4MwHGhy2kFe2mdg6iBvQ32Hr3X1lU3J+ZySOvLdLcXcTFy2MGHFJZKX\nBGFzTNplswZACLFSCJEhhIhq5PxcIcRxIcQJIcQfQogupyj1wGeRPPj5IawtzAjzq5UbGBfkwWcL\nRvHlA6N5YHwfgwzxqQsFvHzjIEM0xmWjOPvy3k9RB3d7KyqrJVui0wnycmD9o+MM57wcbdi48GoG\n+jiy82xmE720Hiklidkl+Dqrco6dnv0fwYfjIPVI666rKIbCVHANMOlwWuICWgUsAT5r5Hw8MEFK\nmSuEuB5YDoxupO0VR0lFFb+dzmBsoDt3j+1dL6ZaCMFVuo23m4f15Kq+HrjaW17eWHApYf3DcHwt\nzF4NwTMu370VBvTFVOKzipk/tne97FohBCE9nNgfl2PS+/54LJWqGtltV5xXFCe+gfQoOLcVegxr\n+XVpJ0DWQI+hJh1OswZASrlTCBHQxPk/jF7uA7rE2l9KybyVBwwZkw9c04dJA5ve0BVCtI/EQ14i\nVFeCe9+Gzx9coU3+AJufg35TwKL7hGB2Foz1dAI8Gk6C83SwJrOwvJ5qZ2uIyywiq6jCICW+9VQG\nno7WdfSRFJ2Q7x6CZK3eN5XFTbe9mNSj2nffy2wAWsl9wC+NnRRCPAg8CODv375JMZfK4cQ8w+QP\nMNz/Mic1SQmf3ggph6DSqK7vo/vAy6jIe9IB+PVvEDQFQv8E6x+EzDPg2zEZst0ZW8vaVV+Ae8MG\nwNfZhorqGtILytv8sHD9+7sor6rh5mE9WTS5P8m5mv+/tSVEFZcBKaEgBcyttIe0wAiI2wEVDdfq\nbpQLx8DBG5yaz/NoDSZzUgshJqIZgGcaayOlXC6lDJdShnt6eprq1iZHSsnbm0/jYG3BL0+MZ9uT\nE3Bpr0zJw5/DV3dD6UVFzhN2aV9WuonEc6D2/ejq2jZJB+B/14O9F9y0FOx1IYCVrfxwKUyCjZEa\naWO1DobqHiQOJ2obxRuOp/Lb6fQW36OmRlJeVQNoeQX3f3aQI4l5yv/fmShMg5IcbfKP2QbvDYJ3\ndNnhk18Bp56tXwFknATvQaYeqWlWAEKIMGAFcL2U8oreiayukTzyxSH2xeUwbZCPIXKjXfj9bdj+\nD+3nUz/BwBtg7J9h8/Pajr+dO/zlBOSeB6+B8PnNcOBjOPQZWFhBcSYg4OGdYOsKOXFaXxWt/HAp\nTIKdkQHQS0RfTIivE9YWZkQm5DI91JfHvtQ2AxPeuqFF94jN1GoPzxnZi8jzuZxN114PucwCg4pG\niPoO1t2r/TzuCcBoVdZrDPgMAUu71q0Aaqq1Vf3I+006VDCBARBC+APfAXdLKc9e+pA6jpiMIsoq\nq/k1Op1ZQ3vw12kD2+9mBz7WJv8+18CwuyFyJZzeoH0BBE6Eqx4HS1tt8geY9DctiqAgVVsdAHj0\n0yZ/ACvdU2dlafuNW9Eoxi6gxoIArCzMGNLLhUPnc8gsbH39AH2I6YPXBPK0rSVRqQWE93ZVcs6d\nBf3kDxD9I7j4g+8QmLkEPPqDmZn2f9qah7ScOKgqA68Qkw+32U+NEGINEAF4CCGSgZcBSwAp5TLg\nJcAd+EC3qVUlpWy60GwnZMPxVMPTGMCjE4MalDMGoKoCaipr3TOtJe0EbHwKnPzgjrVaP2G3w463\nYMebWpt539e/rucIuGW59nNugmZERj1Ye95SNx7lAuoQWlqQZkRvVz7cEcvdn+w3HPvqYCKTg71x\nb0Y/6dD5XNzsrejjYY8Qggn9O68rtdtRqcvydg+CXqMhdru2eTv4lrp7cha2cG4z7Po3jH+y+X71\nG8etiRpqIS2JArqjmfP3A6Zfm1wm8koqmL/yAMeM6rv6ONkQ2FAUR8IeyDyluW5KsrSkjJuWQHPR\nHAl7YM0dMH6RZvl3vq0dv/6tukbkqoVw5AsYOrf5gbsGwHWv1z2mXwEoF1CHYLwCaAq9W/F0WqHh\n2DPfnuCuMfn8Y1Zoo9flFFdwODGX4f4uKnmrM6LX6Rn/FGSd1eL2of7EPXweJO2DuN9bZgAS94GN\nc+0+oAnp9uvGxdtiOJasyeh+8/BYYtKL6OVm17CQ2erbap+uPQfC0S8gPwluW6n56/9YDANn1IZr\nSgm734Ntr2qvt76ifQ+MgLGPQdDkuv1b2cETx7VlYluw1LuASiDzrGYkLJTM7+VCLw+9sBltnRmh\nvjz19TEqqmsI9LQn0MOBrafSG63oBbA1Op37P4vUrg/rYbpBK0xHfqL23aUXmFvWHu83pW67YXPh\n5HrtIbIlpB6GnuFtnxeaoNtKQZRWVPPtoWS+2H+eSQO92PFUBF6ONlwV5NGwTkt+Su3kP/hWeESX\n/hD/O7zdF151gS0vwfqHaq/RT/6uATDlNW1TyKU3zHhP+1A09BR3KX9kKwcwt4Zzv8LSkfDJZG0D\nSXFZMDcTJLx1A4umNF3v2cxMcNcYTSV2cA9nVswPZ0gvF0OBdtCihO5Yvo+kHO0z9/m+84ZzA1XC\nV8dRXQnVVZB0EPYuhV9f1FzCULsCcPbTBXQ8Bg/vAacGDLati5YNfHZz/XN6yrUNfvKSwK2Pad+H\njm65AsgoLGPcW79RWS1xsLbgqakDml5Sb34Bzm7Sfn4sUtt4BVjwK5zZWFeju1y3rN/3oebj6zMB\n7v6+dmKf8prp35AecwttdXFO96G6cEzbXB71QPvdU1GPlrhnLC20Nn09Nf0eNztLMnVS0lJK/rY+\niugLBbz6UzRv3DyYXedq5SP6eysD0K5ICcmRWtat8ZM8wIrJcOFo3WM+YRD2J0iLAmGuhXmaW9Z3\n0RpTlKF9//J2eEXnft78AgSMhwHT4OiX8ONCmP0FlOU1bERMQLczAFJKvth7nspqyd9uCGbu6N6N\nb97F/qaFYO5doiVhBN9YO/kD+I/WvsyttKf5wgtwZhNknYNNz4L/WJi5uF2Wbo0SPKPWADh4a7kC\npjQAlaXw2U3a7+Kqx03XbzdD/7Svzx52s7fmjG5P4LfTGURfKAAgLquIAwk51EiYHupDekE5AY3k\nGChMxM53tAg9xx5w51e1G7g5cXUnfzsPqCiCAx9p0XxHPtc2fC82Gg3h0qv254Q9UFOlzTN7l4Bb\nX11It4Q1s7U2nsENdnOpdCsDUFRexeCXtclxSC8X7h8f2HjjC8e0uHs98zeAZyNL+0kvaN9/ex2K\nMzS9D4BZH5pcvKlZBtwAPK4ZJXMrOPE1THurNkmsKaoq4Nga2PoyXPO0lpNgTHE2rL0TkvZrX5Wl\n2obX5TRwXYSr+rrz5f5ERgZocg7uDlbklGiuhB+PpeLhYM0NoT58cyiZjAJtZfD6rFBc7dWeTrtS\ncEEL0rBx1pK1PhqvRddVlWr7fAAP7QTvUE2b59iX8OPj8G/d3HDN0y27z7R/wrB58MOfYdX02uM9\nhtUKxfW/Hs7qhBX6TTXN+7uIbvWf++GOGEB7WF96ZxMhVTnxsGcxCDO45q9w4+LGJ39j/Mdo33//\nJzj4XP7JH7SJfv4GuG8L9J2kHUs9XLdNaZ42meuXoekn4Zt74B+e8NNCKM3VktHeDtJ0iPQcXKFN\n/Df8WzM021+vNXaKVjEjrAdHXpxCqE5d1tXOirLKGkoqqjiTVkhoTycCPR0oqahmf3w2luYCZ9sW\nPFkq2k7c7/DBaEDCvB91Wbt+miGQNVripYOP9jRuZqa5XIfdra30AWzdwHNAy+5l7aB5D25aou3b\nDb0L/u+U5i7WM3Ox1uf0d7R7tQPdZgXw5i+nWLUnAYAf/3w1fq6NLKMLUuG/I0BWQ+jttU/3LSHo\nWm1z+MxGbYLsqFC9PuO175NfgcOfaquZ/CQtuezUT7Dlxdq2/ldBopGe36wPNffO6tu148e+ggm6\np5rceM0XOfJ+GLEAXnPVtIfCbu+493oFY/w07677ObuogpS8UsYEujM91Jd//BzN5pPp9HSxxUxp\n/bQvm1/Q3Dp3fg0eQdoewIh74TV3bT64Y62Wi2McWScE3PuL9iDUljh9/zHwTHzDOUUOXvB0bLv+\nb3UpAyClBOpvwm2KSuOj3+MY0duVf/9pSKNKjUgJx7/S/tizlkHIzNYPwntQu2h2tAk7N00n6Le/\nN94m8Q9t0+reX7QoIr2raMEvsHhYrc9TSsg8Dc4636WZGXgMgKwz2sa3TTtKZpiKxP1w6keIeFYz\nipmnNUPWCVxYemOQUVhGYVkVbvZWeDpaM22wLz8dS2WYfxeRerhwHJIPtE3WoDhLc48ETTbdpFic\nBd8/Cr1GQvoJiHhem3ooRkgAABvuSURBVPz1CAGPHdRcQvaN1FsWQnsIaisXT/5/OQFmuqm5nT+b\nXcIApOSV4uVozdubz7DuUDKHX6yNuz10PoeHdbVZn5zSv/7kn3JYC9X0CdVkFqortKfisNvB7DJq\n+rcXvUbVykvoufNr6H+d5sPf+iqMmA+uDRSv73MNHP8aTn6vhbylHtH2E/RcvQi+f1iLZ+7sBiDz\nrJbHUV4AUd/W1latLIOrHmv8Ot1DRXuvcNx0BuCRLw7XeT052IufjqUapJ+veL66C/LOQ5+IuhNt\ncyTs1tyUxZkw91voN7nZS5qlugoOrdKCJvSBE44NSL43JsPeXrhcPqXkTm8AMgvLqaqpwdfZFikl\n1TWyTpLWD0dTeGLtURysLSgq1yIrisqrcLC2QErJ0+uO4+FgxdoHxxjK8xmortSkF+J2aF+eA8He\nU1PW7AqTP8CsD2B3P+gxXJOPiP4eeusqVVnaatnIjTF0rvYP8s18zRc54RkYaRRRpN8UK84GtyY2\n1DsDu/6tRVpM/FutAB/A/mUw5hHt750ere376LWXTn6v7Yl4hcCCTe06PDfDCqC8zuuZQ3rgYmfF\n+KBGnj6vNPRZ6mc2gsfCll1TmA6fzdJi5wF+fAxueBcGTm/6usbIjtX2+b5/WCeoaITtZZZ972A6\ntQGQUnLrh3+QklfK/uev5dHVhzkQn8OoADe+fngs57OLef67E/WuSy8ow8HTgczCcuIyi3lpRkj9\nyX/7G9pmLcDohyFkFvQc3vUKqdg4a3sBesa18J8OwG+kFgpXmKrtC0x8vu55vTZ55Cfwx/tw7Sut\ne6prb2pqtIn/wEfaP/rYx7TUe5/B2u+lKEMzbp/OhNmfa9EYpbmakZv+tuY6K8uHxL3aZng7Ppm5\nO9SN7gntqW0Odym9nyOrtd8vaHk1g2/Rkqb0nFinuVkCI+pel35C09760yrNNbLyOtj4tPaw5jmg\n6dVneaFmPIoztZWvrNFi+fVyzM69NN2eqHXaa2UAOg/rj6SQqMuE/MvaoxyIz2G4vwsHEnLYGp3O\nF/vPYyYEe56dRA9nG/bH5zBn+T72xWUT6GHPF/u1CBbjOr4AxO/SJn9HX21CGHFPy2J3uxtCQNAk\nTZ9o8K31z3sP1gzDsTXa64xT8Pihtt+vqlzbpO5zjbYBdqmc2Vj7tB/xnBaiZ2YGA67XjtXUaG6s\n3e9poXz6yengx9oX1J4/twVG3nfpY2oEJxtL3r4tjAAPe5JyShrORr+SyYmDHx7VVo09hkPMFk0n\n//5t2p5ZVTl8q/v9/i2z7kZrxintu1eItq911UJNduWTyZr0ypzV9e+n5+xmSNEkNIj9TSvOUlkM\nfqNg6B0QvkCTZtYbAJsustfSQjqtAYjJKOSpb44x3N+Fw4l57I7JwsPBmmemDWT28n389dvj5JVU\n8EhEX3rqVDuH+7vi7WTNC+ujWL0vkZjMIib092REbyOrvvNt+O0fmqV//HCtgJqiYab+Q4tX9m+g\nzLMQmrusJAfO74HsGE16oi3us5oa+GSqtukcGAF3fqM9vbUkf6EhKstg57+0CeeejbVuHWPMzLTV\nUU0V/PFf7dh9W2DP+9oTY2WJZjSivtOCA8IXtOtewJ/CtQ12fW5Al+DIF1pilZ3uPc37UVtlL9mi\nvT7+tbYvo3+IAFgxCR7eXfs645QWzKDvI/hGOPSpdt3ZzZrxaGjlXpav7XHZe2mBHbvfhZJsLWzT\n2KVnPAcYJ2h1Azo+/KERlvwWg/X/t3fn0VVV9wLHv78kjAEDhEkJEEBmUNAITqhokUkFhVYcVx3q\nVH3Woj6tLuvTaq2tfdoFFVER9SnWOhQVLOCIVkQCyqjIpBBEAjLKEEiy3x+/E+/NfJOc3On8Pmvd\ndXPPPfecnezcs8+efjstlScvz+Hu0ToL7oLjOjCoSyuGdG/Njn2HKHZwdp/2P32mYVoKky8+DoBV\nW/bQ/ojG3DGyV2hUUN5ivfiDhmSwi3/1mrSs+OJfonEGXDFbq+egkQtrI/dpvfhnDdL+mD+0gT93\n1fhK+V/V/Hjz7tGRPuc+VvHFP9xZ92oTYN/ztdlrwgtw1Vy9CDVM107yTQtDd6ImcvN+r8OHN3s1\nwza9dDb9hBc1hMKSZ0MX/y6n613+98tDa1rs36GxrToOCh2z4yC441v4xXPaNLRgUvnzOqe1ut0b\nYfC1euHft02bgCqqzZawJqDY23PwMDOXfseVp3Qhs1kjrh7SlTEDOpCZ3hARYdJFxzFuyiekN0r7\nqa0UgG8/IWf9+3zz0F0UFbvya6Quma7Po/6iIVmNf44ephNavpoF2adE/rm8xfDa1dpE0LA5jPwT\nPDk09P5/HtPHlXOrLojCHdipTTg5V+rdYnVS0+AXz1b+fu8x8O592pTQzv9FOZLWwd2aFyfdqPNQ\nmrULTWjqNVoXOP9f7+855u8aJXP5K9oUtGODLqDyyhU6cfHU35Y+tgj0GKGj9z58WPttwvsCNi2E\nVTN1IueQidrcu/J1DcQY3u9Q4qp3NI0BE3cFwN6Dh7nu+cU4B2f1DrUDt2kequJlNG3Av28eQmGx\n08kxhYdgxzpdHxdgyERSG5RZcHv+n2HpS3pBsOBo/mvUTGOmbF0R+Wecg9kTtTN24KW6vsJRA2HY\n/brAfdNMrQmATjjre77GTekxXOMQVVTtP7AL/m+c3ukdc6E/v1tmN20bzltkNw6R2rdd+01ckfbp\n9Bhefp+MDqGfs0/1tnlNMHu+01rD+g90Jn7W8eU/n9YQRj0C086G1W/r0O2iwzqSa5p3vpJmu4GX\n6KMyHU/QR8DEXQHw1rItfLLuB24f0ZOTumZqqf3lW3D+FB0BUFwEqWmkpaaQlgpsX6vju3duCB1k\nz+bQ2N3lr2j77pYvNDTCqEdi8nsFQkbH8pESNy/RZpT8L3XI5YQXtS1333YdnbF1ufYjDLw09Jnw\nkUp3bNSLwMuXa2cs6ESi1Abemqtl/Ot6nWw08mEd3eEHEcjK0SX+jr0YOp/kz3GT2cwbQ3FsMqsY\nGTbyYZ1FWzIPpbnXpPvCOG2OOfLYqgvdrBP0/275P3V+x7YvYfD1ofebt6/8syZ++gAOFxWzdNMu\nXs7dRNc26Vx/ejeksEAnf6x4RXvwnz0X7s+Ep4fr3eOWZfD0MO0MGvEnrWqCXmi2LNOJXa9epW1/\ng6+DCTMqnuhh/JHpRTEsaSs/uBumjYDJg3S45cYF8No12uG7aqZe/Ef+WS+qlWmcAX3GwPAHdcTH\nnXm6OMayCmIQFRbA2ne1hjf4Wn87bDufrGF5nxmhtQyjigr1UWrb4dDEqr4X6BoYlRl8LVz9Tuh1\n+AU7oyOcP7XqfExJ0RAsa+fpOXdthDl3ak2ynsMoJIO4qQH8Zc5qnpi/HoC7R/dGfsyHJ04L7fDq\n1Xqhb99fl1Pb8KHOTpUU7bDL7Kb/iCtfh8+m6qPE5W/E1/j0ZHXsRdrUtuEjaNtb51oUFehKZYf3\nQ/fh+iWdcqoGymvRSS/WkXxJT/p1KDrpMRfC27dpZ2F7bwnFLctg7l16vqPP8v93G3wdfLtALzQL\nJsGZd/t/jkRTsFdvxtIz4bKZobAFW1doE9z4aVV3uFYkrRFc+qp2EEc6FPiYC2HJ89osmJerkTt/\n8XzloRvMT+KmBrDMW5M3q2UTxh2XpV+yfflw/hPaPFCwBzqeqMMDG6TDzJt0dMCJ14Wae1LTdARH\ns3YapnjAJXDLSrv4R0urrhot8au3tNlu4RT9It+xUYfcjn9a98tfCatnQbezaneH1n+8/g+UDN0s\n2AvPjNIFOYY/qMf1W8N0uPQV6Ddez7sreB2G5bx7v+blhvnw8mXabg+6WhboiK7aOPpnNZsH0vlk\nuH0dDPsfuGIW/Oq90v0LplJxUwP4YV8Bw/u2Y8olA5EN8/UOvu8FcOwEfZx0k7YTNmgCox6GWRMh\ns7tOCgl31EC49evY/BJBJ6Lt8nPu1Bpau/46rj61QaiQPvPu0FDcnrWcyt+0FeRcoTcJW5bpsMBD\ne+Hq9yruLPTTz+7VAu6Dh2Ds5Po9V7z77nNdweqbj/RvUlgAQ+/UyXeZ3SsebVNfAjZ80y9xUwAc\n2PMDwzJykTn/1DvHBulw2q2hHcLHcg+8VC8ekpJ8oRsS3QlXaQEA0O98KDsa67TbdCLONx/Xralm\nyESN3751uXb85VxV/xd/0IlCPUboxLeg+/F7rZWXhAtZO08fR2RpM461v8e9mBcAn2/cyQOzvuS2\nwqmct3EBbEQv7mMfDwV/qkjTJJotmUzCC+ROJ1e8T/apoWF/tdW0FVz7oYb0aNo6usMzW/fQsNKF\nh0qHLAiS4mIdvtu8nTa75C3WIG2FB+Hs+yuOLmviTswKgMMH9zHjsf9mY/4ubkxbzRmpn1OY2ZO0\nY8ZrM4Ld2Se+DvV8R56SWj5AXTRkZIVWiApqW/OGD/Rif9RA7ftp1VUnYr11C3QfVu3HTXyotgAQ\nkWnAOUC+c65fBe8L8BgwCtgP/NI5t6TsfmUd3pnHRTunQFgMtrSxk0pP+TaJ6bqPtWM2We+OS8Jg\n7/8huAXA0pd0clzP0aFtPYbDb1fFLk2mxiKpAUwHJgHPVfL+SKC79xgMPO49V6mp28/mNqPo0OM4\nOPEG7Si0Zp3kUDI0M1mFFwBBVFSoQdh6jirfx2MSSrUFgHNuvohkV7HLGOA5p+sxfioiLUTkSOfc\nlmrPPuKP0K1cpcKY+PbTQjjbY5uOWPnuc50UV1F4B5NQ/JgH0AEIHxSd520rR0SuEZFcEcktJoUj\ns3v7cHpjoqxFJx2B9sOaWKck+pzTsAugsZ9MQotqJ7BzbiowFaBfn54uJTVJll00wdKgsca32bpS\n1x1I9maQPVtg+mhtpi0sCMXdqirEg0kIfhQAm4HwVRSyvG1Vaty0eXW7GBO/2vXVsCMPtIMLX4AD\nO5I3Uuij/TXuflnJsm52gPlRALwB3CgiL6Gdv7sjav83JpG19QoAgH94YYZ7nZN8AxkO7Qtd/MdO\n0ThcAy6FZkmyTnHARTIMdAZwBtBaRPKA3+MN3nTOTQFmo0NA16LDQK+or8QaEzcqWhhmd17yFQAf\nP6rP457WGEwDLopteoyvIhkFVGWOe6N/fu1bioxJBF1O16Bl/cZB6566ju2ezcnVMVpcrGshHzWw\n5lE9TUKIeSgIYxJSo2Ya7wZg7/f6vDsvdumpD4/200Jt6O8srk+Siptw0MYkrPS2ulpdSTjkZFCw\nVy/+AL3Pi21aTL2xAsCYukpJ0fhAmxfrOPlksPNbfR77ODRsGtu0mHpjBYAxfjjhal0DYfXsWKfE\nHyVj/dvaZM1kZgWAMX4YfD2kt9GV0JLBDq8AaNkltukw9coKAGP8kJoGrbrB7iRZKnLrSl1noao1\nOUzCswLAGL+06AS7vo11KuquuEhX9up2ZqxTYuqZFQDG+KVFJ9i9WVcK++ZjvZDu/EZj6exMoIJh\n8xINdW3RPpOezQMwxi8tOoErgnn3wMLHofmRsDcsKsoNC0uvbR2v1r8PiNUAAsBqAMb4pVlbfV7h\nTRBr4A2fbOy1o3/wYPTTVBvfL4dWXZIvrIUpx2oAxvilYTN93pevAdPGTg69949LYcN8bRaK9yia\n29dAmwSoqZg6sxqAMX5p1Cz0c9m1rfteAAd2wvNj4dD+6KarJpyDXRuhZXasU2KiwAoAY/zSMGyN\ni7IFQJ+xMPQurQWUrKgVj/bvgMP7tD/DJD0rAIzxS3gNoHXP0u+lpMCQibqS2JLnopuumigZxmoF\nQCBYAWCMXxqGFQApFXy1UlIhewjsWBe9NNXUro36bAVAIFgBYIxfGqbDoGvhqncq36dNL+0L2BWn\nM4bzvwTE+gACwgoAY/wiAqMeho4nVL5Pt6H6vGZudNJUEwV7YcUr0L4fNLI1u4PACgBjoql1D2jR\nOT4LgA//BDvWw/AEma9g6swKAGOiSQR6jIA183TB9XiStxg6DoYup8U6JSZKrAAwJtp6jdaQER/8\n0d/jOgczLoI3bw515oYr2AsLJsPB3RV/fvvXWkMxgWEFgDHR1vV0jRO0fQ18/gKsmunPcfNX6YI0\ni6fDo/1h1kRdr7iwAPZt1xhFc34Hr11b/rP7d8D+7VYABIyFgjAmFjocD3mL4Ot/6+t7K7krr4lt\nX+nzqb+Fj/8Ki57SR1lr5uoFPzzWz/av9bl197qnwyQMqwEYEwsts+HHraHXebl1P+YP6/X5tFvh\n5mWh7VknwNHDoOdomPAiuGL46JHSn926Up/b9ql7OkzCsBqAMbGQ3lqfO50Emz6DOXfBuY/VPlz0\nttU6w7h9f52P0DAdbl6qzUzdh5Xed+Al8NlUOPEGaN4eZt4I697TFcAysur2e5mEElENQERGiMhq\nEVkrIndU8H4nEXlfRD4XkWUiMsr/pBqTRHqdC51PgXFPw4nXw+ZcvSjX1hs3aQyfUWF39i2zy1/8\nAU67HYoLYcEk2J0HS1+EH7+HU2/RUUomMKqtAYhIKjAZGAbkAYtE5A3n3Kqw3e4GXnbOPS4ifYDZ\nQHY9pNeY5ND6aLhitv48/AENElfb9YQ3LYJNC7Xtv9Pg6vdv2VmbhT79u65YBjB+GvQbV7vzm4QV\nSQ1gELDWObfeOXcIeAkYU2YfBxzh/ZwBfOdfEo0JgBad9G48Eqvfhjd/A2/dohO3Fj0FaU3g5Jsi\nP9/Ih71jeYVQ5tE1S69JCpH0AXQAwm9N8oCytxn3AnNF5CYgHfiZL6kzJigysmD9hzqWv6pmmOIi\n+NcNcGCHvl7xqo7r731ezVbwOmqA3vW/cqW+tuBvgeTXKKCLgOnOuSxgFPC8iJQ7tohcIyK5IpK7\nbds2n05tTBLIyIJDe0tP0jqwEwp+LL3f2nf04v/zZ+Gyf+m6vZ1OhgEX1/ycPUbqc9u+0KRl7dNu\nElYkNYDNQMew11netnBXASMAnHMLRKQx0BrID9/JOTcVmAqQk5PjaplmY5JPhvcV250HP6zTuDxr\n5kD34XDJy6H9Fj0NzdrrbOLUBqHgcrXRsCncukZrHSaQIikAFgHdRaQLeuGfAJS93dgInAVMF5He\nQGPAbvGNiVRJAbBmDqx7H775SF+vfx+Ki2HZSzDrVh3pc9rtevH3Q8lC9iaQqi0AnHOFInIjMAdI\nBaY551aKyH1ArnPuDWAi8KSI3IJ2CP/SObutMCZiJePv371PnwdfBx1y4LWr4fVrYXlYLaD3OdFP\nn0lKEU0Ec87NRod2hm+7J+znVcAp/ibNmABp1lYnZn32JBQfhvbHQP/x8OXM0MV/2H2wcaG22Rvj\nA5sJbEw8EIERf9ShnAuf0DZ+ETjzHlg/H7JPgVNuttss4yuJVUtNTk6Oy831If6JMcmu6DCkpNks\nXQOAiCx2zuX4cSyrARgT7/zq8DWmDIsGaowxAWUFgDHGBJQVAMYYE1BWABhjTEBZAWCMMQFlBYAx\nxgSUFQDGGBNQMZsIJiJ7gdXV7JYB7I6jfRL5fH4eqzWw3YfzJfvfPF7PF0n+JfN3z89jxeK7l+mc\nax7BOavnnIvJAw0kV90+U+Npn0Q+n89przbvIjlWsv/N4/h8gf7uJXLagdxIv3+RPOK9CejNONsn\nkc/n97H8OF+y/83j9XyRSObvnp/HitfvXkRi2QSU63yKZ2Giy/IusVn+JS4RyQXwK/9iGQtoagzP\nberG8i6xWf4lLl/zLmY1AGOMMbEV730AcU9Efqzm/Q9ExKrbccryL7FZ/tWNFQDGGBNQVgD4QETO\nEJG3wl5PEpFfxjBJvqju7ipZWP4ltmTMv2jlnRUAxhgTUFYAmCqJSDMReVdElojIchEZ423PFpEv\nReRJEVkpInNFpEms02tKs/xLXNHIOysA/FFI6b9l41glpB4cBM53zh0HDAUeEflpcdruwGTnXF9g\nFzAuRmmsK8s/y794VO95ZwWAP74F+ohIIxFpAZwV6wT5SIAHRWQZ8A7QAWjnvbfBOfeF9/NiIDv6\nyfOF5Z/lXzyq97yzReHrQETSgALn3CYReRlYAWwAPo9tynx1CdAGON45d1hEviF0h1UQtl8RkFBN\nCJZ/ln9xrt7zzgqAuukLrANwzt0O3F52B+fcGVFOk98ygHzvH3Ao0DnWCfKR5V9iS/b8q/e8swKg\nlkTkOuC/gN/EOi31oeTuCngBeFNElqORCL+KacJ8YvmX2JI5/6KZdxYKwlRIRI4FnnTODYp1WkzN\nWf4lrmjmnXUCm3K8u6sZwN2xToupOcu/xBXtvLMagDHGBJTVAAwAIjJNRPJFZEXYtmNFZIE3CeVN\nETnC295QRJ7xti8VkTPCPnO8t32tiPwtbNyyqSc+5t0DIrIpKCEk4oUf+SciTUVkloh85U0OeyiS\nc1sBYEpMB0aU2fYUcIdzrj/wOnCbt/1XAN72YegElZL/pce997t7j7LHNP6bjj959yZgfQbRNx1/\n8u8vzrlewEDgFBEZWd2JrQAwADjn5gM7ymzuAcz3fp5HaLZhH+A973P56EzEHBE5EjjCOfep07bF\n54Cx9Z32oPMj77zXnzrnttR7gk0pfuSfc26/c+59b/shYAmQVd25rQAwVVkJjPF+/jnQ0ft5KXCe\niKSJSBfgeO+9DkBe2OfzvG0m+mqadya+1Dr/vNnQ5wLvVncSKwBMVa4EbhCRxUBz4JC3fRp6cc8F\nHgU+QWcjmvhheZfYapV/3hyCGcDfnHPrqzuJTQQzlXLOfQWcDSAiPYDR3vZC4JaS/UTkE+BrYCel\nq51ZwOZopdeE1CLvTBypQ/5NBdY45x6N5DxWAzCVEpG23nMKOi55ive6qYikez8PAwqdc6u89uM9\nInKiN/rncmBmbFIfbDXNu5gl1FSoNvknIn9Aw0dEPDvaagAGABGZAZwBtBaRPOD3QDMR+bW3y2vA\nM97PbYE5IlKM3uFfFnaoG9BRDU2At72HqUd+5Z2IPAxcDDT1jvOUc+7eqPwSAeZH/olIFnAXGi5i\niTf6epJz7qkqz20TwYwxJpisCcgYYwLKCgBjjAkoKwCMMSagrAAwxpiAsgLAGGMCygoAExgiUiQi\nX3jREpeKyMSwQFqVfSZbRC6OVhqNiSYrAEyQHHDODXDO9UUjKY5Ex1xXJRsdG29M0rF5ACYwRORH\n51yzsNddgUVAa3TB7eeBdO/tG51zn4jIp0BvYAPwLPA34CF04k4jYLJz7omo/RLG+MgKABMYZQsA\nb9suoCewFyh2zh0Uke7ADOdcjrfgxq3OuXO8/a8B2jrn/iAijYD/AD93zm2I6i9jjA8sFIQxqgEw\nSUQGoNEVe1Sy39nAMSIy3nudgS58YwWASThWAJjA8pqAioB8tC9gK3As2jd2sLKPATc55+ZEJZHG\n1CPrBDaBJCJt0AiLk7zVyzKALc65YjTAVqq36140HnuJOcD1ItLAO06PkuiMxiQaqwGYIGkiIl+g\nzT2FaKfvX733/g68KiKXA/8G9nnblwFFIrIUjXL6GDoyaIkX8nobtuylSVDWCWyMMQFlTUDGGBNQ\nVgAYY0xAWQFgjDEBZQWAMcYElBUAxhgTUFYAGGNMQFkBYIwxAWUFgDHGBNT/A9MvwmaiTHqdAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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": {
    "collapsed": true
   },
   "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,
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    {
     "name": "stdout",
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     "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 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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