{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gold contango\n",
    "\n",
    "We examine futures prices for gold, in particular, the contango situation. \n",
    "The futures price may be either higher or lower than the spot price. \n",
    "When the spot price is higher than the futures price, the market is said to \n",
    "be in **backwardation**. If the spot price is lower than the futures price, \n",
    "the market is in **contango**.\n",
    "\n",
    "The futures or forward curve would typically be upward sloping, \n",
    "since contracts for further dates would typically trade at even higher prices. \n",
    "A contango is normal for a non-perishable commodity that has \n",
    "a *cost of carry*. Such costs include warehousing fees and \n",
    "interest forgone on money tied up, \n",
    "less income from leasing out the commodity if possible (e.g. gold). \n",
    "\n",
    "Our study examines a segment of the futures curve, specifically the \n",
    "nearby contract versus another dated six months thereafter, \n",
    "for gold traded on the COMEX exchange. We use the expected \n",
    "LIBOR interest rate for the identical segment to adjust the \n",
    "cost of carry. We then compare this supply/demand indicator against spot prices. \n",
    "\n",
    "The *London Bullion Market Association* ceased publishing daily data \n",
    "on their *Gold Forward Offered Rate* (**GOFO**), as of 30 January 2015 -- \n",
    "so we develop an observable proxy called *tango*. \n",
    "\n",
    "During 2015 we detected strong *negative* correlation between price change and tango, \n",
    "however, in 2016 that strong correlation became *positive* -- \n",
    "thus we conclude the relationship is spurious. \n",
    "The observed correlations are mere artifacts \n",
    "which do not imply any significant economic relationships.\n",
    "\n",
    "Tango as an indicator is **not** insightful for price changes \n",
    "whenever it is at the extremes of its expected range. \n",
    "This can be verified by comparing various commits over time \n",
    "of this notebook in the repository.\n",
    "\n",
    "Short URL: https://git.io/xau-contango"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Dependencies:*\n",
    "\n",
    "- fecon235 repository https://github.com/rsvp/fecon235\n",
    "- Python: matplotlib, pandas\n",
    "     \n",
    "*CHANGE LOG*\n",
    "\n",
    "    2016-12-04  Solve #2 by v5 and PREAMBLE-p6.16.0428 upgrades. \n",
    "                   Switch from fecon to fecon235 for main import module. \n",
    "                   Minor edits given more data and change in futures basis.\n",
    "                   Previous conclusion is negated. Correlation is artificial.\n",
    "    2015-10-11  Code review.\n",
    "    2015-09-11  First version."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from fecon235.fecon235 import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  Python 2.7.11\n",
      " ::  IPython 4.2.0\n",
      " ::  jupyter_core 4.1.0\n",
      " ::  notebook 4.1.0\n",
      " ::  matplotlib 1.5.1\n",
      " ::  numpy 1.10.4\n",
      " ::  pandas 0.18.0\n",
      " ::  pandas_datareader 0.2.1\n",
      " ::  Repository: fecon235 v5.16.1107 develop\n",
      " ::  Timestamp: 2016-12-04, 17:25:44 UTC\n",
      " ::  $pwd: /media/yaya/virt15h/virt/dbx/Dropbox/ipy/fecon235/nb\n"
     ]
    }
   ],
   "source": [
    "#  PREAMBLE-p6.16.0428 :: Settings and system details\n",
    "from __future__ import absolute_import, print_function\n",
    "system.specs()\n",
    "pwd = system.getpwd()   # present working directory as variable.\n",
    "print(\" ::  $pwd:\", pwd)\n",
    "#  If a module is modified, automatically reload it:\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "#       Use 0 to disable this feature.\n",
    "\n",
    "#  Notebook DISPLAY options:\n",
    "#      Represent pandas DataFrames as text; not HTML representation:\n",
    "import pandas as pd\n",
    "pd.set_option( 'display.notebook_repr_html', False )\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",
    "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.core import page\n",
    "get_ipython().set_hook('show_in_pager', page.as_hook(page.display_page), 0)\n",
    "#  Or equivalently in config file: \"InteractiveShell.display_page = True\", \n",
    "#  which will display results in secondary notebook pager frame in a cell.\n",
    "\n",
    "#  Generate PLOTS inside notebook, \"inline\" generates static png:\n",
    "%matplotlib inline   \n",
    "#          \"notebook\" argument allows interactive zoom and resize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#  SET UP the particular (f4) futures contracts of interest:\n",
    "s_libor = 'f4libor16z'\n",
    "s_xau1  = 'f4xau16z'\n",
    "s_xau2  = 'f4xau17m'\n",
    "\n",
    "#  f4libor* refers to the CME Eurodollar futures.\n",
    "\n",
    "#  The second nearby contract for gold (xau)\n",
    "#  should be 6 months after the first using the \n",
    "#  June (m) and December (z) cycle\n",
    "\n",
    "#  RE-RUN this entire study by merely changing the string symbols."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#  Retrieve data:\n",
    "libor = todf( 100 - get(s_libor) )\n",
    "#             ^convert quotes to conventional % format\n",
    "xau1 = get(s_xau1)\n",
    "xau2 = get(s_xau2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                 Y\n",
       "Date              \n",
       "2016-11-23  0.9950\n",
       "2016-11-25  0.9975\n",
       "2016-11-28  0.9925\n",
       "2016-11-29  0.9825\n",
       "2016-11-30  0.9900\n",
       "2016-12-01  0.9875\n",
       "2016-12-02  0.9875"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tail(libor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                 Y\n",
       "Date              \n",
       "2016-11-23  1189.3\n",
       "2016-11-25  1178.4\n",
       "2016-11-28  1190.8\n",
       "2016-11-29  1187.9\n",
       "2016-11-30  1170.8\n",
       "2016-12-01  1166.9\n",
       "2016-12-02  1175.1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tail(xau1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                 Y\n",
       "Date              \n",
       "2016-11-23  1198.3\n",
       "2016-11-25  1187.0\n",
       "2016-11-28  1200.0\n",
       "2016-11-29  1197.0\n",
       "2016-11-30  1179.9\n",
       "2016-12-01  1175.3\n",
       "2016-12-02  1183.8"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tail(xau2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usually contango is described in price unit terms, however, we prefer the scale-free annualized percentage format. This places the measure on par with the way interest rates are usually quoted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#  Compute the contango in terms of annualized percentage:\n",
    "contango = todf( ((xau2 / xau1) - 1) * 200 )\n",
    "\n",
    "#  Multiply by 200 instead of 100 since \n",
    "#  the gold contracts are stipulated to be six months apart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                   Y\n",
       "Date                \n",
       "2016-11-23  1.513495\n",
       "2016-11-25  1.459606\n",
       "2016-11-28  1.545180\n",
       "2016-11-29  1.532115\n",
       "2016-11-30  1.554493\n",
       "2016-12-01  1.439712\n",
       "2016-12-02  1.480725"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tail( contango )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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lShAW9WvoEQed1ahx5cpUIWL/d9hfeu2oo4qfal+ozosussypHTvCySfDAw+k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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaaf7d56c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot( contango )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The largest variable component to the cost-of-carry is **interest**. We filter that out by subtracting the LIBOR rate obtained from the futures on Eurodollars. We shall call the result: **tango**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tango = todf( contango - libor )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                   Y\n",
       "Date                \n",
       "2016-11-23  0.518495\n",
       "2016-11-25  0.462106\n",
       "2016-11-28  0.552680\n",
       "2016-11-29  0.549615\n",
       "2016-11-30  0.564493\n",
       "2016-12-01  0.452212\n",
       "2016-12-02  0.493225"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tail( tango )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NFpHd81FvIagP/s9iEAedcdAI0ddZW30rVpiLpDZD93MhV519+8L99xdWSzoK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa9a817cc>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  MAIN chart <- pay attention here !!\n",
    "plot( tango )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                Y\n",
       "count  512.000000\n",
       "mean    -0.131907\n",
       "std      0.422571\n",
       "min     -0.679746\n",
       "25%     -0.427747\n",
       "50%     -0.321510\n",
       "75%      0.197633\n",
       "max      0.869532"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tango.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usually *tango* has approximate mean of zero, with somewhat \n",
    "wide latitude: 2015-10-09 at 18 bp standard deviation (annualized), \n",
    "2016-12-02 at 42 bp standard deviation (annualized).\n",
    "\n",
    "Since warehousing costs for gold are fairly constant across time, \n",
    "changes in tango mainly reflect supply and demand. \n",
    "A major component of tango is the **leasing rate**. \n",
    "\n",
    "The *London Bullion Market Association* had published daily data \n",
    "on the *Gold Forward Offered Rate*, or **GOFO**.  These are rates \n",
    "at which LBMA members are prepared to lend gold on a swap against \n",
    "U.S. dollars. Historically there has been negative leasing rates, \n",
    "meaning that the lessors were willing to actually pay you to borrow gold from \n",
    "them [but mostly likely it is a  central bank is paying some \n",
    "bullion bank to take their gold]. \n",
    "Unfortunately, the GOFO dataset has been **discontinued** as of 30 January 2015."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://www.mcoscillator.com/data/charts/weekly/GOFO_1mo_1995-2014.gif\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  For historians:\n",
    "Image(url='https://www.mcoscillator.com/data/charts/weekly/GOFO_1mo_1995-2014.gif', embed=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relationship to cash prices\n",
    "\n",
    "We now look at the current London PM gold fix series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xau = get( d4xau )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#  This matches the futures sample size:\n",
    "xau0 = tail( xau, 512 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tmhXAIFUdBfwIeERECjYzZtj8XqmIik5wWvMl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\nIAiCPuc/ebwwma5fMDcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa95d1b2c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot( xau0 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  Is there near-term correlation between price and tango?\n",
    "#  stat2( xau0[Y], tango[Y] )\n",
    "#  2015-09-11  correlation: 0.09, so NO."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#  Running annual percentage change in spot price:\n",
    "xau0pc = tail( pcent(xau, 256), 512 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QWY/l4INVX3/d3nfooLpiRd1jBgywNhJpzYSrrlI99FDV/ffP/LNh2xnXJucj3fEA4Czg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\nB2Pp1888wldeSX905JlnWhbIj39soyw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RCcUdjmLgasU4arF9O/z2t3DnnbZ+881wzTVm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\nFnZJmoyFXZImY2GXpMkcAYCMnZXIWGlsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa955ff2c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot ( xau0pc )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  FIRST variable:\n",
      "count    512.000000\n",
      "mean      -0.329825\n",
      "std       11.062097\n",
      "min      -17.529926\n",
      "25%       -9.403597\n",
      "50%       -3.585356\n",
      "75%        7.529238\n",
      "max       24.316317\n",
      "Name: Y, dtype: float64\n",
      "\n",
      " ::  SECOND variable:\n",
      "count    512.000000\n",
      "mean      -0.131907\n",
      "std        0.422571\n",
      "min       -0.679746\n",
      "25%       -0.427747\n",
      "50%       -0.321510\n",
      "75%        0.197633\n",
      "max        0.869532\n",
      "Name: Y, dtype: float64\n",
      "\n",
      " ::  CORRELATION\n",
      "0.807198796038\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      Y   R-squared:                       0.652\n",
      "Model:                            OLS   Adj. R-squared:                  0.651\n",
      "Method:                 Least Squares   F-statistic:                     920.0\n",
      "Date:                Sun, 04 Dec 2016   Prob (F-statistic):          1.02e-114\n",
      "Time:                        09:46:52   Log-Likelihood:                -1628.5\n",
      "No. Observations:                 494   AIC:                             3261.\n",
      "Df Residuals:                     492   BIC:                             3269.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      2.2679      0.306      7.404      0.000         1.666     2.870\n",
      "X             21.0366      0.694     30.332      0.000        19.674    22.399\n",
      "==============================================================================\n",
      "Omnibus:                        4.414   Durbin-Watson:                   0.060\n",
      "Prob(Omnibus):                  0.110   Jarque-Bera (JB):                3.210\n",
      "Skew:                          -0.024   Prob(JB):                        0.201\n",
      "Kurtosis:                       2.608   Cond. No.                         2.39\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "#  Is there near-term correlation between price change and tango?\n",
    "stat2( xau0pc[Y], tango[Y] )\n",
    "#  2015-09-11  correlation: -0.85, so YES.\n",
    "#  2015-10-09  correlation: -0.83\n",
    "#  2016-12-02  correlation: +0.81, but change in sign!"
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    "## Closing comments 2015-10-11\n",
    "\n",
    "So roughly speaking, **increasing tango is correlated to decling prices.** \n",
    "Thus increasing selling pressure in the near-term versus the \n",
    "distant-term (which in effect widens tango) is correlated to \n",
    "future declines in cash prices. \n",
    "Equivalently, **decreasing tango is correlated to increasing prices.**\n",
    "\n",
    "Since tango is currently near its mean value, \n",
    "it seems equally likely to decrease or increase \n",
    "(though its short-term trend is upwards), so the \n",
    "future direction of gold prices seems inconclusive.\n",
    "\n",
    "## Closing comments 2016-12-02\n",
    "\n",
    "The new data over the last 13 months has reversed the sign \n",
    "of the correlation. In other words, the relationship previously \n",
    "noted in closing is spurious. \n",
    "(Please see the previous commit of this entire notebook \n",
    "for specific details.)\n",
    "\n",
    "Tango as an indicator is [**not**] insightful for price changes \n",
    "whenever it is at the extremes of its expected range."
   ]
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