{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Drawdowns: Magnitudes and Frequencies\n",
    "\n",
    "This will be an analysis of the market drawdowns from an empirical perspective, using daily data for the past 24 years.\n",
    "\n",
    "I will be focusing on the daily returns of the S&P500 index from January 1993 onwards.\n",
    "\n",
    "The focus on drawdowns is because its is a far more visceral measure of risk than the standard deviation, it's the negative outcome that the investor fundamentally cares about.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"SP500.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taking a peek, we find the following "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1993-01-29</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>43.7500</td>\n",
       "      <td>43.9375</td>\n",
       "      <td>27.607176</td>\n",
       "      <td>1003200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1993-02-01</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>44.2500</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>44.2500</td>\n",
       "      <td>27.803539</td>\n",
       "      <td>480500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1993-02-02</td>\n",
       "      <td>44.2187</td>\n",
       "      <td>44.3750</td>\n",
       "      <td>44.1250</td>\n",
       "      <td>44.3437</td>\n",
       "      <td>27.862408</td>\n",
       "      <td>201300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1993-02-03</td>\n",
       "      <td>44.4062</td>\n",
       "      <td>44.8437</td>\n",
       "      <td>44.3750</td>\n",
       "      <td>44.8125</td>\n",
       "      <td>28.156963</td>\n",
       "      <td>529400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1993-02-04</td>\n",
       "      <td>44.9687</td>\n",
       "      <td>45.0937</td>\n",
       "      <td>44.4687</td>\n",
       "      <td>45.0000</td>\n",
       "      <td>28.274775</td>\n",
       "      <td>531500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Date     Open     High      Low    Close  Adj Close   Volume\n",
       "0  1993-01-29  43.9687  43.9687  43.7500  43.9375  27.607176  1003200\n",
       "1  1993-02-01  43.9687  44.2500  43.9687  44.2500  27.803539   480500\n",
       "2  1993-02-02  44.2187  44.3750  44.1250  44.3437  27.862408   201300\n",
       "3  1993-02-03  44.4062  44.8437  44.3750  44.8125  28.156963   529400\n",
       "4  1993-02-04  44.9687  45.0937  44.4687  45.0000  28.274775   531500"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get log returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/ipykernel/__main__.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  from ipykernel import kernelapp as app\n"
     ]
    }
   ],
   "source": [
    "df[\"log_returns\"] = np.log(df[\"Adj Close\"]).diff()\n",
    "df[\"log_returns\"][0] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>log_returns</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1993-01-29</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>43.7500</td>\n",
       "      <td>43.9375</td>\n",
       "      <td>27.607176</td>\n",
       "      <td>1003200</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1993-02-01</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>44.2500</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>44.2500</td>\n",
       "      <td>27.803539</td>\n",
       "      <td>480500</td>\n",
       "      <td>0.007088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1993-02-02</td>\n",
       "      <td>44.2187</td>\n",
       "      <td>44.3750</td>\n",
       "      <td>44.1250</td>\n",
       "      <td>44.3437</td>\n",
       "      <td>27.862408</td>\n",
       "      <td>201300</td>\n",
       "      <td>0.002115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1993-02-03</td>\n",
       "      <td>44.4062</td>\n",
       "      <td>44.8437</td>\n",
       "      <td>44.3750</td>\n",
       "      <td>44.8125</td>\n",
       "      <td>28.156963</td>\n",
       "      <td>529400</td>\n",
       "      <td>0.010516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1993-02-04</td>\n",
       "      <td>44.9687</td>\n",
       "      <td>45.0937</td>\n",
       "      <td>44.4687</td>\n",
       "      <td>45.0000</td>\n",
       "      <td>28.274775</td>\n",
       "      <td>531500</td>\n",
       "      <td>0.004175</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Date     Open     High      Low    Close  Adj Close   Volume  \\\n",
       "0  1993-01-29  43.9687  43.9687  43.7500  43.9375  27.607176  1003200   \n",
       "1  1993-02-01  43.9687  44.2500  43.9687  44.2500  27.803539   480500   \n",
       "2  1993-02-02  44.2187  44.3750  44.1250  44.3437  27.862408   201300   \n",
       "3  1993-02-03  44.4062  44.8437  44.3750  44.8125  28.156963   529400   \n",
       "4  1993-02-04  44.9687  45.0937  44.4687  45.0000  28.274775   531500   \n",
       "\n",
       "   log_returns  \n",
       "0     0.000000  \n",
       "1     0.007088  \n",
       "2     0.002115  \n",
       "3     0.010516  \n",
       "4     0.004175  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can define drawdown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def drawdown(returns):\n",
    "    out = []\n",
    "    cum_returns = [0]\n",
    "    for i in range(len(returns)):\n",
    "        cum_returns.append(cum_returns[-1] + returns[i])\n",
    "        out.append(max(cum_returns)-cum_returns[-1])\n",
    "    return out\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def max_drawdown(drawdowns):\n",
    "    out = []\n",
    "    for i in range(len(drawdowns)+1):\n",
    "        out.append(max(drawdowns[:i+1]))\n",
    "    return out[:-1]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets try it out with some fake data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0, 0.0, 0.1, 0.1]\n",
      "[0.0, 0.0, 0.1, 0.098]\n"
     ]
    }
   ],
   "source": [
    "print(max_drawdown(drawdown([0.05, 0.001, -0.10, 0.002])))\n",
    "print(drawdown([0.05, 0.001, -0.10, 0.002]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get now get drawdown magnitudes from our returns data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df[\"drawdown\"] = drawdown(df[\"log_returns\"])\n",
    "df[\"maxdrawdown\"] = max_drawdown(df[\"drawdown\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>log_returns</th>\n",
       "      <th>drawdown</th>\n",
       "      <th>maxdrawdown</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1993-01-29</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>43.7500</td>\n",
       "      <td>43.9375</td>\n",
       "      <td>27.607176</td>\n",
       "      <td>1003200</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1993-02-01</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>44.2500</td>\n",
       "      <td>43.9687</td>\n",
       "      <td>44.2500</td>\n",
       "      <td>27.803539</td>\n",
       "      <td>480500</td>\n",
       "      <td>0.007088</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1993-02-02</td>\n",
       "      <td>44.2187</td>\n",
       "      <td>44.3750</td>\n",
       "      <td>44.1250</td>\n",
       "      <td>44.3437</td>\n",
       "      <td>27.862408</td>\n",
       "      <td>201300</td>\n",
       "      <td>0.002115</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1993-02-03</td>\n",
       "      <td>44.4062</td>\n",
       "      <td>44.8437</td>\n",
       "      <td>44.3750</td>\n",
       "      <td>44.8125</td>\n",
       "      <td>28.156963</td>\n",
       "      <td>529400</td>\n",
       "      <td>0.010516</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1993-02-04</td>\n",
       "      <td>44.9687</td>\n",
       "      <td>45.0937</td>\n",
       "      <td>44.4687</td>\n",
       "      <td>45.0000</td>\n",
       "      <td>28.274775</td>\n",
       "      <td>531500</td>\n",
       "      <td>0.004175</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Date     Open     High      Low    Close  Adj Close   Volume  \\\n",
       "0  1993-01-29  43.9687  43.9687  43.7500  43.9375  27.607176  1003200   \n",
       "1  1993-02-01  43.9687  44.2500  43.9687  44.2500  27.803539   480500   \n",
       "2  1993-02-02  44.2187  44.3750  44.1250  44.3437  27.862408   201300   \n",
       "3  1993-02-03  44.4062  44.8437  44.3750  44.8125  28.156963   529400   \n",
       "4  1993-02-04  44.9687  45.0937  44.4687  45.0000  28.274775   531500   \n",
       "\n",
       "   log_returns  drawdown  maxdrawdown  \n",
       "0     0.000000       0.0          0.0  \n",
       "1     0.007088       0.0          0.0  \n",
       "2     0.002115       0.0          0.0  \n",
       "3     0.010516       0.0          0.0  \n",
       "4     0.004175       0.0          0.0  "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets have a look at our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wnzeQND8iprbzNTvNNdfDNdfDNdfDNVfXytmMdwJTJE2WtAEwHZjTnrLMzMyq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\n/X/UmY+NLG4aswAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106bde510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(3)\n",
    "ax[0].hist(df[\"log_returns\"], bins=\"auto\", normed=True)\n",
    "ax[0].set_title(\"Returns\")\n",
    "ax[1].hist(df[\"drawdown\"], bins=\"auto\", normed=True)\n",
    "ax[1].set_title(\"Drawdown\")\n",
    "ax[2].hist(df[\"maxdrawdown\"], bins=\"auto\", normed=True)\n",
    "ax[2].set_title(\"Maximum Drawdown\")\n",
    "plt.tight_layout(pad=0.4, w_pad=0.5, h_pad=1.0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def print_moments(data):\n",
    "    print(\"Mean: {}\".format(data.mean()))\n",
    "    print(\"Variance: {}\".format(data.var()))\n",
    "    print(\"Skewness: {}\".format(data.skew()))\n",
    "    print(\"Kurtosis: {}\".format(data.kurt()))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 0.000361076100698\n",
      "Variance: 0.000134123754915\n",
      "Skewness: -0.123399178971\n",
      "Kurtosis: 10.4799642916\n"
     ]
    }
   ],
   "source": [
    "print_moments(df[\"log_returns\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 0.121357328453\n",
      "Variance: 0.0237807139796\n",
      "Skewness: 1.52946108724\n",
      "Kurtosis: 1.67269313296\n"
     ]
    }
   ],
   "source": [
    "print_moments(df[\"drawdown\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 0.517234819046\n",
      "Variance: 0.0858882738314\n",
      "Skewness: -0.499654421501\n",
      "Kurtosis: -1.46690984604\n"
     ]
    }
   ],
   "source": [
    "print_moments(df[\"maxdrawdown\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now plotting as timeseries, several variables of interest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x106eeae50>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Sa0Huvsjd69y9rqamJkKRpFSlz27SwLVIvEQJEvXAaDMbZWa9gFnA0swMZnZ0xuRFwIYI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\nW4sBh7+I2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107966750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(x='Date', y='maxdrawdown')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x107c65f50>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GJobQpmENsicN55nR3Xj7T73KLlCOt/7Ui+/vPDeodfy5+qyMsGynsvn3lT1j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\naNi4Cd+ibwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106aca790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(x='Date', y='log_returns')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that large drawdown spikes happen in 2001 and 2008, corresponding to the tech and the housing bubble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x107c5cbd0>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jl8ZOtACI+bp0p8RIMk/dBsA9M+hilwUwxmwzxjhZ658EBvodyBjzuDGm2BhT3KlTpySa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107c619d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(x='Date', y='drawdown')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Return multiple over the period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.575486948294436"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.pow(1 + df[\"log_returns\"].mean(), len(df[\"log_returns\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.5793930896807407"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Adj Close\"].iloc[-1]/df[\"Adj Close\"].iloc[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Omniscient Return over the period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00775197969782\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "9.70966352989536e+20"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "df[\"abs\"] = df[\"log_returns\"].map(math.fabs)\n",
    "print(df[\"abs\"].mean())\n",
    "math.pow(1+ df[\"abs\"].mean(), len(df[\"abs\"]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A buy and hold position, yields a 9.5X multiple over the 25 year period.\n",
    "\n",
    "While an omniscient market timer who is long before every up day\n",
    "and short before ever down day yields a \n",
    "9.7*10^20  multiple over the 25 year period.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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