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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Oil: Brent vs. West Texas Intermediate (WTI), and their weighted price"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We examine the history of oil prices, and their spreads. Real prices give additional insight, along with some of the statistical characteristics used in financial economics.\n",
      "\n",
      "[Unless otherwise noted, the price per barrel is in U.S. dollars. Near the conclusion, we use USD index units.]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Dependencies:*\n",
      "\n",
      "    - Linux, bash [not crucial, cross-platform prefered]\n",
      "    - Python: matplotlib, pandas [recommend Anaconda distribution]\n",
      "    - Modules: yi_1tools, yi_plot, yi_timeseries, yi_fred\n",
      "     \n",
      "*CHANGE LOG*\n",
      "\n",
      "    2015-05-26  Code review and revision.\n",
      "    2014-10-09  First version for oil, using 2014-09-28 Template."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  NOTEBOOK settings and system details:   [00-tpl v14.12.21]\n",
      "\n",
      "#  Assume that the backend is LINUX (our particular distro is Ubuntu, running bash shell):\n",
      "print '\\n ::  TIMESTAMP of last notebook execution:'\n",
      "!date\n",
      "print '\\n ::  IPython version:'\n",
      "!ipython --version\n",
      "\n",
      "#  Automatically reload modified modules:\n",
      "%load_ext autoreload\n",
      "%autoreload 2\n",
      "#           0 disables autoreload.\n",
      "#  Generate plots inside notebook:\n",
      "%matplotlib inline\n",
      "\n",
      "#  DISPLAY options\n",
      "from IPython.display import Image \n",
      "#  e.g. Image(filename='holt-winters-equations.png', embed=True) # url= also works\n",
      "from IPython.display import YouTubeVideo\n",
      "#  e.g. YouTubeVideo('1j_HxD4iLn8', start='43', width=600, height=400)\n",
      "from IPython.display import HTML # useful for snippets\n",
      "#  e.g. HTML('<iframe src=http://en.mobile.wikipedia.org/?useformat=mobile width=700 height=350></iframe>')\n",
      "\n",
      "import pandas as pd\n",
      "print '\\n ::  pandas version:'\n",
      "print pd.__version__\n",
      "#      pandas DataFrames are represented as text by default; enable HTML representation:\n",
      "#      [Deprecated: pd.core.format.set_printoptions( notebook_repr_html=True ) ]\n",
      "pd.set_option( 'display.notebook_repr_html', False )\n",
      "\n",
      "#  MATH display, use %%latex, rather than the following:\n",
      "#                from IPython.display import Math\n",
      "#                from IPython.display import Latex\n",
      "\n",
      "print '\\n ::  Working directory (set as $workd):'\n",
      "workd, = !pwd\n",
      "print workd + '\\n'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  TIMESTAMP of last notebook execution:\n",
        "Tue May 26 10:26:40 PDT 2015\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  IPython version:\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2.3.0\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  pandas version:\n",
        "0.15.0\n",
        "\n",
        " ::  Working directory (set as $workd):\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "/home/yaya/Dropbox/ipy/fecon235/nb\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from yi_1tools import *\n",
      "from yi_plot import *\n",
      "from yi_timeseries import *\n",
      "from yi_fred import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Brent vs. WTI"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Retreive daily data:\n",
      "brent = getfred( d4brent )\n",
      "wti   = getfred( d4wti )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  BoW: Brent over WTI spread:\n",
      "bow = todf( brent - wti )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotfred( bow )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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       "text": [
        "<matplotlib.figure.Figure at 0xacfe56ac>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### The difference between Brent and WTI is not superficial. BoW can represent over 20% of the underlying oil price!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Let's look at BoW trend since 1999:\n",
      "plotfred( trend( bow ) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  regresstime slope = 0.00140233726321\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xb737f88c>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Since the slope uses daily data, we annualize it:\n",
      "0.0014023 * 256"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "0.3589888"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Over the long haul, we can **anticipate BoW to increase $0.36 annually per barrel**, though there will be very large deviations around the expected \\$6 spread. Note that the composition of Brent oil benchmark no longer really represents Brent as an location."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Oil: weighted average price"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Set wtbrent, the primary weight for OIL:\n",
      "wtbrent = 0.50\n",
      "#         0.50 represents the mean\n",
      "#  ==================================\n",
      "wtwti   = 1 - wtbrent\n",
      "oil = todf( (wtbrent * brent) + (wtwti * wti) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotfred( oil )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FDPXqDAVSjPQ0DKMl0Ls3fPll7vWbY8ivu86NV3/oIZgxw7k7/Lb8UTP+ggxH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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xacfc864c>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**The Great Recession plunge from \\$140 to \\$40 is extraordinary.** "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[At equal weights, we have created two convenience series called d4oil and m4oil.]"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stats( oil )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Y\n",
        "count  7304.000000\n",
        "mean     44.469187\n",
        "std      32.819087\n",
        "min       9.960000\n",
        "25%      18.948750\n",
        "50%      27.170000\n",
        "75%      68.925000\n",
        "max     144.630000\n",
        "\n",
        " ::  Index on min:\n",
        "Y   1998-12-10\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Index on max:\n",
        "Y   2008-07-03\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Head:\n",
        "                 Y\n",
        "T                 \n",
        "1987-05-20  19.190\n",
        "1987-05-21  19.200\n",
        "1987-05-22  19.115\n",
        "1987-05-25  19.140\n",
        "1987-05-26  18.990\n",
        "1987-05-27  18.990\n",
        "1987-05-28  18.940"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  Tail:\n",
        "                 Y\n",
        "T                 \n",
        "2015-05-08  61.615\n",
        "2015-05-11  61.025\n",
        "2015-05-12  62.905\n",
        "2015-05-13  63.415\n",
        "2015-05-14  62.735\n",
        "2015-05-15  62.210\n",
        "2015-05-18  62.295\n",
        "\n",
        " ::  Correlation matrix:\n",
        "   Y\n",
        "Y  1"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Oil on 1998-12-10 at $9.96 is our record LOW"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tmin = '1998-12-10'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "georet( oil[tmin:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[10.97, 16.3, 32.66, 256]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "May 2015: The geometric return since tmin is around 11% with volatility of 33% -- both very high relative to traditional assets."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**The technical support for the 1998 uptrend on the chart is currently $45.40 (on 2015-01-29).** "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Oil trend since 1998-12-10"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "oiltrend = trend( oil[tmin:] )\n",
      "plotfred( oiltrend )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  regresstime slope = 0.0221070094873\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tFQAz254wbfvf7r445/a+Hs9VT6LOmHwSPxA4gvAhE8Bc4GHCh0wf\np5UN4s9XK/bfM8SfMQP54n8tunumvoCzCSeeHwW8CxyVc99raefLSsYky/bAgcCGdW7vm3a2jOSL\n/vcce8bY8+Vkifu1mHaAAnboJGCD5Psq4BXg3Jh+8RnJGPUbKPZ8Gfo9R50x9nxJjuhfi7FMdW4O\nc/clAO4+y8JJ6Uea2VeJ5GodZCPjqcA33X2JmVUR8lW5+7B0Y30h9nyQjd9z7BljzwcZeC1m8cPO\neRbOBwxA8iI4jPDhSOrXzktkIeMabyBgX+C7ZnYjcbyBYs8H2fg9x54x9nyQgddiFgt5f2CNqwF5\nuObfAGCfVBJ9WRYyxv4Gij0fZOP3HHvG2PNBBl6LmRy1IsUzs62A5V7nEnlmZsC33f25dJJ9kSPq\nfNJ6ZOG1qEIuIpJxWWytiIhIDhVyEZGMUyEXEck4FXIRkYz7f05wHWZlyFGxAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad359e4c>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Next the detrended series using percentage deviation since tmin:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotfred( detrendpc(oil[tmin:]) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  regresstime slope = 0.0221070094873\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2tI07P++8wgY96n7p1i17Wffu3odeL2bODDMUlvKVFDWCc+eGMdCWxYvTa8vF\n8uXQo0f6/ViDvmJFY8eix19I8XBhVfj3v4vf3/Ll5qvZEv/a9hga3qDHH9I5czIAbLJJYYNuKz+h\no0Hv1Kl6Pa+75HPLRT01Ro14rmtQyIe+enX2ZzqEpf5KogqvvWaOFS+hl3MObYhjS0ttXH7Vus7x\nEnW8hD55Muy+e+HKX6tv2TLzTO+wg5lfjWtZLi49z6kMuohsKiKTROR1EXlNRM4O5vcTkYkiMl1E\nHhKR1srIDdl2W/MAxw36/Pmm8qVXr9wGff/9O86Ltxjt1MnHzdaLqBEvxfUQd7ksXRp2zrzfftUx\nAg88YIzMmjUdS6Hl0LOneUl061b7qJxKEm0LAB3rqHbZxQw//LC4/b3zjjHqNjvqhRem09espC2h\ntwPnqup2wJ7AGSKyDXABMFFVhwGPBNMVQxXeeAOmT+9o0N97r21taSBq0OM+PUvPnubmi5cgWlqq\nV0J3yeeWi3pqjJZM44bBUsiHvmCBMeibbWamhw4t3niUQr6XRJpz2LVrbVq2Vus6n3FG9rS9jt26\nwaabhvMLuTWtvrffNtdy0CAz/+mnTQtUF3DpeU5l0FX1Q1WdEowvBt4ABgGHAjcHq90MHJ68h/K4\n6CIznD8/ucbblpSskV69OvsTsE+fcFl7u5meNy97H76EXj+iD/mwYR2vTS6WLAnHd98dzjoLtt7a\nFAD+8hf43vcqqxNMgaAaNHoJPf5c2pDO+Esq7hbLxbx5pvVtlKRuJNd1KuZDF5EhwM7Ac8AAVZ0b\nLJoLDKjUcQDuv98MFy5MuiEyWaVtW0q3N1j//vCb38Df/25aFNrolug2229f3RK6Sz63XNRTY9Sg\nL19umtLHSdL35z9nT7/7bmhwc5X00xINi4yT5hzWqoReret8/PFw1FFhw6rf/jZcFr2+0ZdwElbf\nRx+ZyDNwz5C79DxXpKWoiPQG/gZ8V1UXSSSAWFVVRBLr60ePHs2QIUMAaG1tZcSIEWs/X+xJSpo2\ntf8ZHn8cdtihLdhbZu1+O3cO1+/SpY32dnjkkQz9+8OHHxqXzMyZGVatMssBPv7YrP/ww2188Ysw\ncmSGF16AvfYqrKcZp6cEffHV4/jmgTfT0EZLS3H6Fi+Go45q469/DbcfMqQt2I+ZXr3aXP80+j77\nDG6+OcMOO8Af/xjuP5PJXn/KlClln4/Vq839ffzx5W1f7LSl0vufOtVcD3v+n3rKHq+N+fOhpSXD\nqFHw2mtIIo8YAAAgAElEQVRtjBqVvf20afDqqxk23BDuvBN23hl+//sMp5xitjeHCPdXzfPjwnQm\nk2H8+PEAa+1lTlQ11Q/oAvwLOCcybxowMBjfCJiWsJ2Wy4gRqqB6ySWqv/61ao8eZtr+pkwJ1wXV\nDz9UfeMN1eHDw/lPPKE6bJhq//5m+sQTzbovvWSm999f9eGHy5boScGkSdnXc+zY5PXmzlVdujSc\nPuYY1f/7v+xtr7/eLOvd20wvWZJen923qupBB2VPV4rttlN99dXK7rOW/P73qiedlD0vel1A9Uc/\nUh0zpuO2oNqnTzi+775m+MMfmnmrVlXnnDcKge1MtMdpo1wEuBGYqqpXRxbdC5wQjJ8A3B3fNg0D\nB8KWW5rPsGXLQt/at79thvEKzttuMy6XqL9TxPgo4w2KbOhZjx7F+/c8leXpp7Onk/KKz5xpsiie\ndlo475NPTPRTFBsGOHSoGVbSjaFafoOZQnStkculWqxe3fHc7LRTtvusW7eO/9FORyubH3vMDE8/\n3Qztfm0EkyckrQ/9C8BxwH4iMjn4HQiMBb4sItOB/YPpivHZZ7DHHiYaYvly4/NWhSOPBMh0CB9b\nvLijQW9pMd3V/ec/Zto24ugahC9W06DHP3ddpJ4a//Wvwus8/ngGyO7A5KGHOhoIG9FkDcmCBem0\nRQ3N0qXmHrn//uRGMmnOYa0qRat1ndes6WjQp0wxeeItSQY9Wtfx1a+Cda307p0dnfbYY6arSRdw\n6XlOG+XypKq2qOoIVd05+D2oqp+o6gGqOkxVR6lqRTNRr1hhLq6NXrEt9GzjoPiNNHy4qXyJG/Ts\n/2KG9q3fvbsvodeLb3yj8Do2tNFWdtsK7EGDwm7gICyh29woJ5xAKmyaZnvsRx4xrVp33TXdfuN0\n7tzYLZVXr+74jMWxBv3cc8NQxqhBf+CBcHzZsmyDvtlmPgotiYZsKbpihTHOtjWgdZMYg96WVUI/\n6igzTHK5RBkxwgz79TPDHj2qlz/CVny4TD01LlliOkew2EYoUXbcsW3tugC/+IUZbr+9KeFbt028\nOb7NpFkupsLVYDvMGDgwed0051CkNk3/q3Wdk1wuUQYODFtjX301zJ6dnSI3ojBxfy1VjEIrFZee\n54Y26Nblkm3Qsy98r165XS5Rvvvd7M+/Ll18tsV6sWRJdirapJKq/XqyDcvs53f37uaa21wwcZ96\nWjfG5z4XjluDvuWW6faZREtLY+dySXK5RGlpMV8h8VbBxXydQeF2IosWuWPwa0nDGvRevUwulilT\nwlKYMezZcejWF1nIoItkN//v3Nn3KVovfvxjU8I+6ywzvWRJR+P23HMZIEzOtv76xrDaL6/hw407\nJNoRQv/+cOih6bR16wY//7np2vDTT/N3tJDmHIrUxqVQretcyOXS0mKMcvQZS06Lm8m5fT6D3bcv\n/OhHxSgtjo8+yn09XHqeG9ag9+xpcrY8+WTHEnrU5WI/63K5XHL1zB6/2Ty15Zln4Kc/hVNOMc2+\n48bhBz/Inl65Mrs/2ZaWjjl7LrssO2NfOSxZYgoTPXoYgx5P6lYpauVyqRaFXC4iHRPgRXsXs5x1\nFhx8sGkIGKVPH5NR0wY1RDn7bDN8/fXSdScxZ475Mov2duYqDWfQVTtWcFqDboZtWTfSypXGP7d4\ncfY2toIl100XL6GLmLC4SuCSzy0X9dD45JPhi3bcOFPKihvukDYAbDuLFSs6JliL061b+nqRJUtM\nRWuPHiZiJp5hMUvhOupDnzvXdBNXjMvlT38K5x18cMf1dt65jQceyO5RDMLK7ssuy57/2GNw7bVm\nvFJfODfdZIZvvZW83KXnuaEMuqq5EeLG2bpcNtjADKM30o03wtixxhjb5RAmbcqVIS/J5VJsThFP\neXzxi+H4EUeYYdL1iT6odnzlysKl5e7d08d2L14cltBfeMEYr2rQqCX07bYzFZ6//GV+l8sGG+Q3\n+Pa/F+q1auuts6enTw/H8+XZUTUFvWKw9SaN0M9rQxn0gw4Kx+0bGsJSkil1d4xDB/jVr7If+Fwh\njpYkg15ql2i5cMnnlos0GlesMDH+abBfUNGGX/bz3LxYM8yebY4lYrL7vfZa/n1WooQ+ezZsvLGJ\nlrnhBpMELBdpfei1MOiVvBeXL4epU8PpXM/W22+bZGnR5V/5Sjh+5pnh+LRpufX96EdhxbQlGtW0\n0Ua5tV53XXbWx3xYg56rMODS89xQBj3a4CT6eR397H3kkWw/6Q03hONRg26Nc1LiJ6iuQW92uneH\nzTfPvXzePFP/ESWehta+lKMG3T6Aa9aY8NKePbMNdKEEXGlL6M88YxoQbbxxmHRq2LDy95ePRiyh\n//zn2dNxv7dl6FDzixa8os/suHHFHa+1teM1P/74cLxrV/PyiKMa+tmLSal8xx1mOGFCcbrqScMY\n9PjnTvRmiL6V99+/LWu9aAxz0id5rs+oqEGvtCF3yeeWi2pqvOEGU2H5zW+G8954I3ndqEG3FWCr\nV0OPHm0dStznnJP/uGlL6J//vBlGO3DO91m/rvnQL700e7pQBXT02kbDSaPP27e+1ZZz+169OpbQ\nLdttZxqBbbllx/MYPVY+N+qhhxotf/lL7nXAree5YQz6M89kT0c/1/LdONGSfFKlmW1IFCephD5/\nfn6NnuKwD5gt+UDuNKo2ntwydarJ39KpU8fm8YWiknr2LJyuNRfRBz96v1UrH/qcOdXpkKOWXHNN\n/uXR6LS77jLj//u/4XLVsMu5JN5+G4IkhGvZYw8T8nryyWEjspkzk3Xttlv+F/x99+XX7yINYdBV\n4bDDwum9986ucIn60+P+rKgRTyqh52poUs1KUZd8brmopsakc15sI5C77oJ//ANWrDDtDaJfaoUM\net++5XdDF61A69wZTj3VjOfLJ5LmHL7+Opx4YtmbF00ujSKl5b1JOveF0iHY53HMmHDevvtmr5Pv\nHCbdMwsWmELAs8+GDdLiL3GbUqBHj1yx77kjZJK+mlx6nhvCoH/8cfZ0p07Zn2XFltCjrfzAdIhg\nQ5zivPsuXHVVaSVAD8yYUXidpBdjvhCz6ENkx210SbQVaaGXQp8+pRn0Hj3guefMuK2LsZ0r2CyP\nO+5Y/P4agZkzw/qPePeO+bDuk9/9zgxzhfhFsQb9/PPDeaW0E7D9itp0ASImymWLLcxL3xK95qNG\nweOPm3DHV17pmNnTEq9rsdf9rrvcboHaEAY97sOOtxKLJu2J+7OiBj1eUXf00WEOlzgPP2yGUYNR\nKYPuks8tF+VqLMZHbR/6KMU+JLZEZTseiVLo+pRq0JcvN5EzCxeGPe7Yr8Fc902URrzOX/1q6RFK\n0Reu6YQiu54hF9ZtGv3ajj7LSfqiWJdNvOKzW7ew71HIfjHZ67fzzqaS/fXXjTv3xRez9zFtWnYB\n8NhjzfCoozq6eYq5ziJhT2vVpCEMerzislu3sHb7+uvzx7tGDXo893k+7EskWnL0JfTC5PqELYQ1\n6Lffnhx++Oqrpu3A2CARc1L+lEIRJ9agRw3QkiX5I19OPjnbDRBvSFStFLcbb5ztZqwV0etXzEtW\nteMXtGrHr+EkogU1+8VTSsv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adBVWiGq4D+LnfoMNwuPECyv5+usEk67Wlb4AXnwxvXus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\n1fYjEL220S8yT2MyZgz813+l20dqgy4i3xORNSL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       "text": [
        "<matplotlib.figure.Figure at 0xad272f6c>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Oil prices can easily go +/- 40% off their statistical trend (about 1.2 std). \n",
      "\n",
      "From the +100% deviation on 2008-07-03, we see that our record HIGH of $144.63 was an one-time explosive blow-off. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  So discount 40% off the trend, \n",
      "#  to illustrate statistical downside:\n",
      "tailvalue( oiltrend ) * 0.60"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "65.95000820390936"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Real oil prices"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  We change the sampling frequency to match inflation data:\n",
      "oilmth = monthly( oil )\n",
      "defl = getfred( m4defl )\n",
      "oildefl = todf( oilmth * defl )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotfred( oildefl )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CDTfU1HWJBfWhQ2376NGw776p9Rc7228PbdpYJzRkrj/blvpXwBagpYhsA1oC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\n4ziNiP8H0jAaa42jxuwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad1bad4c>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here the supportive 1998 uptrend is broken by the recent crash in prices. The level support from the 1990's is around \\$20 in real terms."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Oil price ex-USD"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we are interested in how oil prices appear outside the United States. A basket of trade-weighted currencies against USD helps our foreign exchange viewpoint."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  rtb is the real trade-weighted USD index,\n",
      "#      computed monthly by the Federal Reserve.\n",
      "rtb = getfred( m4usdrtb )\n",
      "oilrtb = todf( oil / rtb )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  cf. \"oil\" in dollars\n",
      "plotfred( oilrtb )\n",
      "#         ^in index units"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+aMF7yBBbGi5+dGOyIB7G9yC+YdM9ccdxmoyJE2H48NzOaUzDZlUV9OhhPvgn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\nO+Fk2zZr73jwQRv5+sYbNsfJ+efbfNs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       "text": [
        "<matplotlib.figure.Figure at 0xad26d2cc>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "No big suprises here. Oil from world-ex-USD perspective looks very similar to the dollar-only perspective."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "BoW spread as a function of Oil"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Do the regression:\n",
      "stat2( bow['Y'], oil['Y'] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  FIRST variable:\n",
        "count    7304.00000\n",
        "mean        0.71444\n",
        "std         5.75087\n",
        "min       -22.18000\n",
        "25%        -1.88000\n",
        "50%        -1.25000\n",
        "75%        -0.02750\n",
        "max        29.59000\n",
        "Name: Y, dtype: float64"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  SECOND variable:\n",
        "count    7304.000000\n",
        "mean       44.469187\n",
        "std        32.819087\n",
        "min         9.960000\n",
        "25%        18.948750\n",
        "50%        27.170000\n",
        "75%        68.925000\n",
        "max       144.630000\n",
        "Name: Y, dtype: float64"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  CORRELATION\n",
        "0.627241758244\n",
        "\n",
        "-------------------------Summary of Regression Analysis-------------------------\n",
        "\n",
        "Formula: Y ~ <x> + <intercept>\n",
        "\n",
        "Number of Observations:         7304\n",
        "Number of Degrees of Freedom:   2\n",
        "\n",
        "R-squared:         0.3934\n",
        "Adj R-squared:     0.3933\n",
        "\n",
        "Rmse:              4.4792\n",
        "\n",
        "F-stat (1, 7302):  4736.2260, p-value:     0.0000\n",
        "\n",
        "Degrees of Freedom: model 1, resid 7302\n",
        "\n",
        "-----------------------Summary of Estimated Coefficients------------------------\n",
        "      Variable       Coef    Std Err     t-stat    p-value    CI 2.5%   CI 97.5%\n",
        "--------------------------------------------------------------------------------\n",
        "             x     0.1099     0.0016      68.82     0.0000     0.1068     0.1130\n",
        "     intercept    -4.1732     0.0883     -47.28     0.0000    -4.3462    -4.0002\n",
        "---------------------------------End of Summary---------------------------------\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Does the price of oil influence the BoW spread? Not much, the correlation is about 63%. And linear regression does not show anything reliable. Maybe: *take 10% of the oil price and subtract $4 to roughly guess at BoW.*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#  Concluding remarks\n",
      "\n",
      "The bottom of the barrel is in the region of \\$45.40 to \\$66 with respect to our weighted oil series. The lower range derives from the technical uptrend dating back to 1998, which is also the year of our record low. The upper range is an estimate derived from statistical trend deviation.\n",
      "\n",
      "A definitive break of the \\$45.40 mark would look downward at the $20 support in real dollars.\n",
      "\n",
      "Before taking a position in oil, carefully evaluate the premium of Brent over WTI.\n",
      "\n",
      "### Caveats\n",
      "\n",
      "- A complete analysis would include the impact of shale oil.\n",
      "\n",
      "- If ISIS becomes dominate over oil fields, expect some minor supply at half the market price."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}